Finite Group Databasebeta

← #35197304

Subgroups — #35197304

Order 20224.

7390 conjugacy classes of subgroups.

The subgroup lattice has 1590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777457C214yesmaximal, complemented
2#23777453C214yesmaximal, complemented
3#23777423C214yesmaximal, complemented
4#23777419C214yesmaximal, complemented
5#23777352C214yesmaximal, complemented
6#23777348C214yesmaximal, complemented
7#23777329C214yesmaximal, complemented
8#23777325C214yesmaximal, complemented
9#23777251C212yesmaximal, complemented
10#23777237C214yesmaximal, complemented
11#23777198C211yesmaximal, characteristic, complemented
12#23777159C211yesmaximal, characteristic, complemented
13#23777117C212yesmaximal, complemented
14#23777087C214yesmaximal, complemented
15#23777035C211yesmaximal, characteristic, complemented
16#23776813C212yesmaximal, complemented
17#23776806C214yesmaximal, complemented
18#23776788C212yesmaximal, complemented
19C2×#19099148C214yesmaximal, complemented
20H(5,𝔽2)×Dic79C211yesmaximal, characteristic, complemented
21#23776604C211yesmaximal, characteristic, complemented
22C2×#19099038C211yesmaximal, characteristic, complemented
23C79×#3484C211yesmaximal, characteristic, complemented
24C2×#14579206C2211yescharacteristic
25#19099299C2214yescomplemented
26#19099295C2214yescomplemented
27#19099284C2214yescomplemented
28#19099283C2214yescomplemented
29#19099282C2214yescomplemented
30#19099278C2214yescomplemented
31#19099277C2214yescomplemented
32#19099277C2214yescomplemented
33#19099272C2214yescomplemented
34#19099272C2214yescomplemented
35#19099270C2214yescomplemented
36#19099265C2214yescomplemented
37#19099265C2218yescomplemented
38#19099260C2214yescomplemented
39#19099260C2214yescomplemented
40#19099259C2214yescomplemented
41#19099256C2218yescomplemented
42#19099256C2218yescomplemented
43#19099253C2214yescomplemented
44#19099250C2218yescomplemented
45#19099247C2214yescomplemented
46#19099244C2218yescomplemented
47#19099244C2218yescomplemented
48#19099244C2218yescomplemented
49#19099239C2218yescomplemented
50#19099239C2218yescomplemented
51#19099236C2218yescomplemented
52#19099233C2214yescomplemented
53D4×Dic158C2214yescomplemented
54#19099219C2218yescomplemented
55#19099213C2214yescomplemented
56#19099212C2214yescomplemented
57#19099207C2214yescomplemented
58#19099207C2214yescomplemented
59#19099207C2214yescomplemented
60#19099207C2218yescomplemented
61#19099207C2218yescomplemented
62#19099201C2214yescomplemented
63#19099200C2218yescomplemented
64#19099200C2218yescomplemented
65#19099200C2218yescomplemented
66D4×C22⋊D79C2214yescomplemented
67D4×C22⋊D79C2214yescomplemented
68D4×C22⋊D79C2214yescomplemented
69#19099191C2212yescomplemented
70#19099189C2214yescomplemented
71#19099186C2212yescomplemented
72#19099186C2212yescomplemented
73#19099182C2214yescomplemented
74#19099180C2212yescomplemented
75#19099180C2212yescomplemented
76#19099180C2214yescomplemented
77#19099173C2212yescomplemented
78#19099173C2212yescomplemented
79#19099167C2214yescomplemented
80#19099166C2212yescomplemented
81#19099166C2212yescomplemented
82#19099166C2214yescomplemented
83#19099158C2218yescomplemented
84#19099157C2214yescomplemented
85#19099157C2214yescomplemented
86#19099157C2218yescomplemented
87#19099150C2218yescomplemented
88#19099148C2214yescomplemented
89#19099148C2214yescomplemented
90#19099148C2218yescomplemented
91#19099148C2218yescomplemented
92#19099148C2218yescomplemented
93#19099148C2218yescomplemented
94#19099148C2218yescomplemented
95#19099148C2218yescomplemented
96#19099148C2218yescomplemented
97#19099148C2218yescomplemented
98#19099141C2212yescomplemented
99#19099130C2212yescomplemented
100#19099122C2214yescomplemented
101#19099122C2214yescomplemented
102#19099116C2212yescomplemented
103#19099111C2214yescomplemented
104#19099109C2212yescomplemented
105#19099108C2214yescomplemented
106#19099095C2214yescomplemented
107#19099095C2214yescomplemented
108#19099094C2218yescomplemented
109#19099094C2214yescomplemented
110#19099093C2214yescomplemented
111#19099093C2214yescomplemented
112#19099092C2214yescomplemented
113#19099090C2218yescomplemented
114#19099090C2218yescomplemented
115C2×#14579154C2214yescomplemented
116C2×#14579154C2214yescomplemented
117C2×#14579148C2214yescomplemented
118C2×#14579147C2214yescomplemented
119#19099074C2212yescomplemented
120#19099073C2218yescomplemented
121#19099069C2218yescomplemented
122#19099069C2218yescomplemented
123#19099069C2218yescomplemented
124C2×#14579143C2214yescomplemented
125C2×#14579142C2214yescomplemented
126C2×#14579138C2214yescomplemented
127C2×#14579133C2214yescomplemented
128C2×#14579133C2214yescomplemented
129C2×#14579132C2214yescomplemented
130C2×#14579130C2214yescomplemented
131#19099046C2212yescomplemented
132#19099046C2214yescomplemented
133#19099043C2212yescomplemented
134#19099042C2214yescomplemented
135#19099038C2211yescharacteristic
136#19099038C2214yescomplemented
137#19099038C2214yescomplemented
138#19099038C2214yescomplemented
139#19099038C2214yescomplemented
140#19099038C2214yescomplemented
141#19099038C2214yescomplemented
142#19099036C2214yescomplemented
143#19099035C2214yescomplemented
144#41×Dic79C2212yescomplemented
145#41×Dic79C2214yescomplemented
146#19099031C2212yescomplemented
147C4×#11929623C2214yescomplemented
148C2×D4×Dic79C2211yescharacteristic
149C2×D4×Dic79C2211yescharacteristic
150C2×D4×Dic79C2212yescomplemented
151C2×D4×Dic79C2211yescharacteristic, complemented
152C2×D4×Dic79C2212yescomplemented
153C2×D4×Dic79C2211yescharacteristic, complemented
154C2×D4×Dic79C2214yescomplemented
155C2×D4×Dic79C2214yescomplemented
156C2×(C22⋊D79)⋊C4C2214yescomplemented
157C4×D4×D79C2214yescomplemented
158C2×#14579120C2211yescharacteristic, complemented
159C2×#14579120C2211yescharacteristic, complemented
160C22×C22⋊Dic79C2212yescomplemented
161C22×C22⋊Dic79C2212yescomplemented
162C2×H(5,𝔽2)×C79C2211yescharacteristic
163C23×D4×C79C2211yescharacteristic
164#546×C79C2214yescomplemented
165#546×C79C2214yescomplemented
166D42×C79C2214yescomplemented
167D42×C79C2214yescomplemented
168#535×C79C2212yescomplemented
169#534×C79C2214yescomplemented
170#525×C79C2212yescomplemented
171C2×#120×C79C2214yescomplemented
172#518×C79C2211yescharacteristic
173#14579206—28no—
174C2×#11929624C2312yes—
175C2×#11929623C2314yes—
176C2×#11929623C2318yescomplemented
177C2×#11929623C2318yescomplemented
178C22×Dic158C2314yescomplemented
179C22×C22⋊D79C2314yes—
180C22×C22⋊D79C2314yes—
181C22×C22⋊D79C2314yes—
182C22×C22⋊D79C2314yescomplemented
183C2×D4×D79C2314yes—
184C23×Dic79C2312yes—
185C23×Dic79C2312yes—
186C23×Dic79C2312yes—
187C23×Dic79C2312yes—
188C23×Dic79C2314yescomplemented
189C22×C4×D79C2314yescomplemented
190#14579161C2314yescomplemented
191#14579160C2312yescomplemented
192#14579160C2312yescomplemented
193#14579160C2314yescomplemented
194#14579159C2312yescomplemented
195#14579157C2314yes—
196#14579157C2312yescomplemented
197#14579156C2314yescomplemented
198#14579156C2318yescomplemented
199#14579156C2314yescomplemented
200#14579154C2314yes—
201#14579154C2314yes—
202#14579154C2318yes—
203#14579154C2318yes—
204#14579154C2314yes—
205#14579154C2314yes—
206#14579154C2318yescomplemented
207#14579154C2314yescomplemented
208#14579154C2318yescomplemented
209#14579154C2318yescomplemented
210#14579154C2318yescomplemented
211#14579154C2318yescomplemented
212#14579154C2314yescomplemented
213#14579153C2314yescomplemented
214#14579152C2314yescomplemented
215#14579152C2314yescomplemented
216#14579152C2312yescomplemented
217#14579152C2312yescomplemented
218#14579152C2314yescomplemented
219#14579151C2314yescomplemented
220#14579151C2318yescomplemented
221#14579151C2314yescomplemented
222#14579150C2312yescomplemented
223#14579148C2314yes—
224#14579148C2318yes—
225#14579148C2314yes—
226#14579148C2314yes—
227#14579148C2318yescomplemented
228#14579148C2318yescomplemented
229#14579148C2312yescomplemented
230#14579147C2314yes—
231#14579147C2318yes—
232#14579147C2314yes—
233#14579147C2318yescomplemented
234#14579147C2318yescomplemented
235#14579147C2318yescomplemented
236#14579145C2314yescomplemented
237#14579145C2318yescomplemented
238#14579145C2314yescomplemented
239#14579145C2318yescomplemented
240#14579144C2314yes—
241#14579144C2318yescomplemented
242#14579143C2314yes—
243#14579143C2318yes—
244#14579143C2314yes—
245#14579143C2318yescomplemented
246#14579143C2314yescomplemented
247#14579143C2318yescomplemented
248#14579143C2314yescomplemented
249#14579142C2314yes—
250#14579142C2318yes—
251#14579142C2314yes—
252#14579142C2318yes—
253#14579142C2318yescomplemented
254#14579142C2318yescomplemented
255#14579142C2318yescomplemented
256#14579142C2318yescomplemented
257#14579142C2318yescomplemented
258#14579141C2314yescomplemented
259#14579141C2314yescomplemented
260#14579140C2312yes—
261#14579140C2312yes—
262#14579140C2314yescomplemented
263#14579140C2318yescomplemented
264#14579140C2318yescomplemented
265#14579138C2314yes—
266#14579138C2318yes—
267#14579138C2314yes—
268#14579138C2318yescomplemented
269#14579138C2318yescomplemented
270#14579138C2318yescomplemented
271#14579138C2314yescomplemented
272#14579138C2318yescomplemented
273#14579138C2314yescomplemented
274#14579138C2318yescomplemented
275#14579138C2318yescomplemented
276#14579137C2314yescomplemented
277#14579135C2312yes—
278#14579135C2312yes—
279#14579135C2314yescomplemented
280#14579133C2318yes—
281#14579133C2314yes—
282#14579133C2314yes—
283#14579133C2318yes—
284#14579133C2314yes—
285#14579133C2314yes—
286#14579133C2318yes—
287#14579133C2318yes—
288#14579133C2318yescomplemented
289#14579133C2318yescomplemented
290#14579133C2318yescomplemented
291#14579133C2318yescomplemented
292#14579133C2318yescomplemented
293#14579133C2318yescomplemented
294#14579132C2314yes—
295#14579132C2318yes—
296#14579132C2314yes—
297#14579132C2314yes—
298#14579132C2314yes—
299#14579132C2314yescomplemented
300#14579132C2318yescomplemented
301#14579132C2318yescomplemented
302#14579130C2314yes—
303#14579130C2318yes—
304#14579130C2318yes—
305#14579130C2318yes—
306#14579130C2318yescomplemented
307#14579129C2318yes—
308#14579129C2318yescomplemented
309Q8×Dic79C2312yescomplemented
310Q8×Dic79C2312yescomplemented
311Q8×Dic79C2314yescomplemented
312C4×Dic158C2314yescomplemented
313C4×Dic158C2314yescomplemented
314C4×Dic158C2314yescomplemented
315#14579126C2312yescomplemented
316#14579126C2312yescomplemented
317#14579126C2318yescomplemented
318C4×D316C2314yescomplemented
319D4×Dic79C2314yes—
320D4×Dic79C2318yes—
321D4×Dic79C2318yes—
322D4×Dic79C2314yes—
323D4×Dic79C2318yes—
324D4×Dic79C2314yes—
325D4×Dic79C2314yes—
326D4×Dic79C2314yes—
327D4×Dic79C2314yes—
328D4×Dic79C2314yes—
329D4×Dic79C2318yes—
330D4×Dic79C2314yes—
331D4×Dic79C2314yes—
332D4×Dic79C2318yes—
333D4×Dic79C2314yes—
334D4×Dic79C2314yes—
335D4×Dic79C2314yes—
336D4×Dic79C2318yescomplemented
337D4×Dic79C2318yescomplemented
338D4×Dic79C2312yescomplemented
339D4×Dic79C2312yescomplemented
340D4×Dic79C2318yescomplemented
341D4×Dic79C2318yescomplemented
342D4×Dic79C2318yescomplemented
343D4×Dic79C2318yescomplemented
344D4×Dic79C2314yescomplemented
345#14579123C2312yescomplemented
346#14579123C2312yescomplemented
347C4×C22⋊D79C2314yes—
348C4×C22⋊D79C2314yes—
349C4×C22⋊D79C2314yescomplemented
350C4×C22⋊D79C2314yescomplemented
351C4×C22⋊D79C2318yescomplemented
352C4×C22⋊D79C2318yescomplemented
353(C22⋊D79)⋊C4C2314yes—
354(C22⋊D79)⋊C4C2318yes—
355(C22⋊D79)⋊C4C2314yes—
356(C22⋊D79)⋊C4C2318yescomplemented
357(C22⋊D79)⋊C4C2318yescomplemented
358(C22⋊D79)⋊C4C2318yescomplemented
359(C22⋊D79)⋊C4C2318yescomplemented
360(C22⋊D79)⋊C4C2318yescomplemented
361#14579120C2312yes—
362#14579120C2312yes—
363#14579120C2312yes—
364#14579120C2312yes—
365#14579120C2312yes—
366#14579120C2314yes—
367#14579120C2314yes—
368#14579120C2314yescomplemented
369#14579120C2318yescomplemented
370#14579120C2314yescomplemented
371#14579119C2318yescomplemented
372#14579119C2314yescomplemented
373#14579118C2314yescomplemented
374#14579117C2318yescomplemented
375#14579117C2318yescomplemented
376#14579117C2318yescomplemented
377#14579117C2318yescomplemented
378C2×C4⋊Dic79C2311yescharacteristic
379C2×C4⋊Dic79C2311yescharacteristic
380C2×C4⋊Dic79C2311yescharacteristic
381C2×C4⋊Dic79C2311yescharacteristic
382C2×C4⋊Dic79C2314yescomplemented
383C2×C4⋊Dic79C2314yescomplemented
384C2×C4⋊Dic79C2314yescomplemented
385C2×Dic79⋊C4C2314yescomplemented
386C2×Dic79⋊C4C2314yescomplemented
387C2×Dic79⋊C4C2314yescomplemented
388C2×Dic79⋊C4C2314yescomplemented
389C4⋊C4×D79C2314yescomplemented
390C2×C22⋊Dic79C2311yescharacteristic
391C2×C22⋊Dic79C2311yescharacteristic
392C2×C22⋊Dic79C2312yes—
393C2×C22⋊Dic79C2312yes—
394C2×C22⋊Dic79C2312yes—
395C2×C22⋊Dic79C2314yes—
396C2×C22⋊Dic79C2314yes—
397C2×C22⋊Dic79C2314yes—
398C2×C22⋊Dic79C2314yes—
399C2×C22⋊Dic79C2312yes—
400C2×C22⋊Dic79C2314yes—
401C2×C22⋊Dic79C2318yes—
402C2×C22⋊Dic79C2318yes—
403C2×C22⋊Dic79C2314yes—
404C2×C22⋊Dic79C2314yes—
405C2×C22⋊Dic79C2312yes—
406C2×C22⋊Dic79C2314yescomplemented
407C2×C22⋊Dic79C2318yescomplemented
408C2×C22⋊Dic79C2314yescomplemented
409C2×(C2×D79)⋊C4C2314yescomplemented
410C2×(C2×D79)⋊C4C2314yescomplemented
411C22⋊C4×D79C2318yescomplemented
412C2×C4×Dic79C2311yescharacteristic
413C2×C4×Dic79C2311yescharacteristic
414C2×C4×Dic79C2312yes—
415C2×C4×Dic79C2314yescomplemented
416C2×C4×Dic79C2314yescomplemented
417C2×C4×Dic79C2314yescomplemented
418C42×D79C2314yescomplemented
419C25×C79C2312yes—
420H(5,𝔽2)×C79—28no—
421C2×#41×C79C2312yes—
422C2×#41×C79C2314yes—
423C22×D4×C79—28no—
424C22×D4×C79C2314yes—
425C22×D4×C79C2314yes—
426C22×D4×C79C2314yes—
427C22×D4×C79C2314yes—
428C22×D4×C79C2312yes—
429C22×D4×C79C2311yescharacteristic
430C22×D4×C79C2314yes—
431C22×D4×C79C2314yes—
432C22×D4×C79C2311yescharacteristic
433C23×C4×C79C2311yescharacteristic
434#127×C79C2314yes—
435#124×C79C2314yes—
436#123×C79C2314yes—
437#123×C79C2318yes—
438C22⋊Q8×C79C2312yes—
439C22⋊Q8×C79C2312yes—
440#121×C79C2318yes—
441#121×C79C2318yes—
442#121×C79C2312yes—
443#121×C79C2312yes—
444#121×C79C2314yes—
445#121×C79C2314yes—
446#120×C79C2314yes—
447#120×C79C2318yes—
448#120×C79C2318yes—
449#120×C79C2318yes—
450#120×C79C2318yes—
451C4×D4×C79C2314yes—
452C4×D4×C79C2314yes—
453C4×D4×C79C2314yes—
454C4×D4×C79C2314yes—
455#117×C79C2312yes—
456C2×C22⋊C4×C79C2314yes—
457C2×C22⋊C4×C79C2314yes—
458C2×C22⋊C4×C79C2314yes—
459C23×D79C2414yes—
460#11929624—28no—
461#11929623—216no—
462#11929623—88no—
463#11929623—88no—
464C2×Dic158—84no—
465C2×Dic158C2412yes—
466C2×Dic158C2414yes—
467C2×Dic158C2418yes—
468C2×Dic158C2414yes—
469C2×D316C2412yes—
470C2×C22⋊D79—216no—
471C2×C22⋊D79—84no—
472C2×C22⋊D79—84no—
473C2×C22⋊D79—84no—
474C2×C22⋊D79C2418yes—
475C2×C22⋊D79C2414yes—
476C2×C22⋊D79C2414yes—
477C2×C22⋊D79C2418yes—
478C2×C22⋊D79C2418yes—
479C2×C22⋊D79C2418yes—
480C2×C22⋊D79C2414yes—
481C2×C22⋊D79C2414yes—
482C2×C22⋊D79C2414yes—
483D4×D79—216no—
484C22×Dic79—82no—
485C22×Dic79—82no—
486C22×Dic79—82no—
487C22×Dic79—82no—
488C22×Dic79—84no—
489C22×Dic79C2414yes—
490C22×Dic79C2414yes—
491C22×Dic79C2414yes—
492C22×Dic79C2414yes—
493C22×Dic79C2418yes—
494C22×Dic79C2418yes—
495C22×Dic79C2418yes—
496C22×Dic79C2411yescharacteristic
497C22×Dic79C2411yescharacteristic
498C22×Dic79C2412yes—
499C22×Dic79C2411yescharacteristic
500C22×Dic79C2411yescharacteristic
501C22×Dic79C2412yes—
502C22×Dic79C2414yes—
503C22×Dic79C2414yes—
504C22×Dic79C2414yes—
505C22×Dic79C2414yes—
506C22×Dic79C2414yes—
507C2×C4×D79—84no—
508C2×C4×D79C2414yes—
509C2×C4×D79C2414yes—
510C2×C4×D79C2418yes—
511C2×C4×D79C2414yes—
512C4⋊Dic79C2414yes—
513C4⋊Dic79C2414yes—
514C4⋊Dic79C2412yes—
515C4⋊Dic79C2412yes—
516C4⋊Dic79C2412yes—
517C4⋊Dic79C2412yes—
518C4⋊Dic79C2412yes—
519C4⋊Dic79C2418yes—
520C4⋊Dic79C2414yes—
521C4⋊Dic79C2414yes—
522C4⋊Dic79C2418yes—
523C4⋊Dic79C2412yes—
524C4⋊Dic79C2414yes—
525C4⋊Dic79C2414yes—
526Dic79⋊C4C2418yes—
527Dic79⋊C4C2414yes—
528Dic79⋊C4C2414yes—
529Dic79⋊C4C2414yes—
530Dic79⋊C4C2414yes—
531Dic79⋊C4C2418yes—
532Dic79⋊C4C2418yes—
533Dic79⋊C4C2418yes—
534Dic79⋊C4C2414yes—
535Dic79⋊C4C2414yes—
536Dic79⋊C4C2414yes—
537Dic79⋊C4C2414yes—
538Dic79⋊C4C2414yes—
539Dic79⋊C4C2414yes—
540C22⋊Dic79C2418yes—
541C22⋊Dic79C2411yescharacteristic
542C22⋊Dic79C2414yes—
543C22⋊Dic79C2412yes—
544C22⋊Dic79C2411yescharacteristic
545C22⋊Dic79C2414yes—
546C22⋊Dic79C2412yes—
547C22⋊Dic79C2411yescharacteristic
548C22⋊Dic79C2411yescharacteristic
549C22⋊Dic79C2418yes—
550C22⋊Dic79C2414yes—
551C22⋊Dic79C2414yes—
552C22⋊Dic79C2414yes—
553C22⋊Dic79C2414yes—
554C22⋊Dic79C2414yes—
555C22⋊Dic79C2414yes—
556C22⋊Dic79C2414yes—
557C22⋊Dic79C2418yes—
558C22⋊Dic79C2418yes—
559C22⋊Dic79C2418yes—
560C22⋊Dic79C2414yes—
561C22⋊Dic79C2418yes—
562C22⋊Dic79C2414yes—
563C22⋊Dic79C2414yes—
564C22⋊Dic79C2418yes—
565C22⋊Dic79C2414yes—
566(C2×D79)⋊C4C2414yes—
567(C2×D79)⋊C4C2418yes—
568(C2×D79)⋊C4C2414yes—
569(C2×D79)⋊C4C2414yes—
570(C2×D79)⋊C4C2418yes—
571(C2×D79)⋊C4C2414yes—
572(C2×D79)⋊C4C2414yes—
573(C2×D79)⋊C4C2414yes—
574C4×Dic79C2412yes—
575C4×Dic79C2414yes—
576C4×Dic79C2414yes—
577C4×Dic79C2412yes—
578C4×Dic79C2418yes—
579C4×Dic79C2412yes—
580C4×Dic79C2412yes—
581C4×Dic79C2414yes—
582C4×Dic79C2418yes—
583C4×Dic79C2414yes—
584C4×Dic79C2418yes—
585C4×Dic79C2414yes—
586C24×C79—28no—
587C24×C79—82no—
588C24×C79—82no—
589C24×C79C2414yes—
590C24×C79C2414yes—
591C24×C79C2411yescharacteristic
592C24×C79C2412yes—
593C24×C79C2414yes—
594C24×C79C2412yes—
595#41×C79—216no—
596#41×C79—28no—
597C2×Q8×C79C2412yes—
598C2×D4×C79—28no—
599C2×D4×C79—216no—
600C2×D4×C79—216no—
601C2×D4×C79—216no—
602C2×D4×C79—216no—
603C2×D4×C79—24no—
604C2×D4×C79—84no—
605C2×D4×C79—84no—
606C2×D4×C79#4118yescomplemented
607C2×D4×C79C2414yes—
608C2×D4×C79C2418yes—
609C2×D4×C79C2418yes—
610C2×D4×C79C2414yes—
611C2×D4×C79C2412yes—
612C2×D4×C79C2418yes—
613C2×D4×C79C2418yes—
614C2×D4×C79C2414yes—
615C2×D4×C79C2414yes—
616C2×D4×C79C2414yes—
617C22×C4×C79—24no—
618C22×C4×C79C2414yes—
619C22×C4×C79C2414yes—
620C22×C4×C79C2412yes—
621C22×C4×C79C2412yes—
622C22×C4×C79C2411yescharacteristic
623C22×C4×C79C2414yes—
624C22×C4×C79C2414yes—
625C22×C4×C79C2411yescharacteristic
626C4⋊C4×C79C2412yes—
627C4⋊C4×C79C2412yes—
628C4⋊C4×C79C2414yes—
629C4⋊C4×C79C2414yes—
630C22⋊C4×C79C2414yes—
631C22⋊C4×C79C2414yes—
632C22⋊C4×C79C2414yes—
633C22⋊C4×C79C2418yes—
634C22⋊C4×C79C2418yes—
635C22⋊C4×C79C2418yes—
636C22⋊C4×C79C2414yes—
637C22⋊C4×C79C2414yes—
638C42×C79C2414yes—
639C23×C79—22no—
640C23×C79—24no—
641C23×C79—28no—
642C23×C79—28no—
643C23×C79—28no—
644C23×C79—42no—
645C23×C79—42no—
646C23×C79—42no—
647C23×C79—42no—
648C23×C79—41no—
649C23×C79—41no—
650C23×C79—44no—
651C23×C79—44no—
652C23×C79—44no—
653C23×C79—44no—
654C23×C79—44no—
655C23×C79—44no—
656C23×C79—816no—
657C23×C79C2×#4118yes—
658C23×C79C2511yescharacteristic
659C23×C79C2511yescharacteristic
660C23×C79C2514yes—
661C23×C79C2514yes—
662C23×C79C2514yes—
663C23×C79C2511yescharacteristic
664C22×D79—28no—
665C22×D79—44no—
666C22×D79—44no—
667C22×D79C2514yes—
668Q8×C79—24no—
669D4×C79—216no—
670D4×C79—28no—
671D4×C79—216no—
672D4×C79—28no—
673D4×C79—24no—
674D4×C79—48no—
675D4×C79—48no—
676D4×C79—44no—
677D4×C79—44no—
678D4×C79C2×#41116yes—
679C2×C4×C79—22no—
680C2×C4×C79—28no—
681C2×C4×C79—24no—
682C2×C4×C79—24no—
683C2×C4×C79—28no—
684C2×C4×C79—44no—
685C2×C4×C79—44no—
686C2×C4×C79C2×#4114yes—
687C2×C4×C79C2514yes—
688C2×C4×C79C2512yes—
689C2×C4×C79C2514yes—
690C2×C4×C79C2514yes—
691C2×C4×C79C2512yes—
692C22⋊D79—216no—
693C22⋊D79—28no—
694C22⋊D79—44no—
695C22⋊D79—44no—
696C22⋊D79—44no—
697C22⋊D79—48no—
698C22⋊D79—48no—
699C22⋊D79—48no—
700C22⋊D79—44no—
701C2×Dic79—28no—
702C2×Dic79—44no—
703C2×Dic79—41no—
704C2×Dic79—44no—
705C2×Dic79—42no—
706C2×Dic79—41no—
707C2×Dic79—41no—
708C2×Dic79—42no—
709C2×Dic79—41no—
710C2×Dic79—44no—
711C2×Dic79—44no—
712C2×Dic79—44no—
713C2×Dic79—44no—
714C2×Dic79—48no—
715C2×Dic79—48no—
716C2×Dic79—48no—
717C2×Dic79—44no—
718C2×Dic79—44no—
719C2×Dic79C2511yescharacteristic
720C2×Dic79C2512yes—
721C2×Dic79C2514yes—
722C2×Dic79C2511yescharacteristic
723C2×Dic79C2514yes—
724C2×Dic79C2514yes—
725C2×Dic79C2511yescharacteristic
726C2×Dic79C2514yes—
727C2×Dic79C2512yes—
728C2×Dic79C2514yes—
729C2×Dic79C2511yescharacteristic
730D316—24no—
731C4×D79—28no—
732C4×D79—44no—
733C4×D79—48no—
734C4×D79—44no—
735Dic158—24no—
736Dic158—44no—
737Dic158—48no—
738Dic158—44no—
739C22×C79—24no—
740C22×C79—24no—
741C22×C79—21no—
742C22×C79—21no—
743C22×C79—21no—
744C22×C79—21no—
745C22×C79—24no—
746C22×C79—24no—
747C22×C79—21no—
748C22×C79—21no—
749C22×C79—24no—
750C22×C79—24no—
751C22×C79—24no—
752C22×C79—24no—
753C22×C79—21no—
754C22×C79—21no—
755C22×C79—48no—
756C22×C79—48no—
757C22×C79—44no—
758C22×C79—88no—
759C22×C79—88no—
760C22×C79—88no—
761C22×C79C22×#4112yes—
762C22×C79C22×#4118yes—
763C22×C79C2611yescharacteristic
764C2×D79—24no—
765C2×D79—24no—
766C2×D79—24no—
767C2×D79—88no—
768C4×C79—22no—
769C4×C79—24no—
770C4×C79—24no—
771C4×C79—24no—
772C4×C79C22×#4114yes—
773Dic79—24no—
774Dic79—21no—
775Dic79—24no—
776Dic79—24no—
777Dic79—24no—
778Dic79—22no—
779Dic79—21no—
780Dic79—21no—
781Dic79—24no—
782Dic79—22no—
783Dic79—21no—
784#62846—791nomaximal, Sylow
785C2×C79—28no—
786C2×C79—22no—
787C2×C79—44no—
788C2×C79—41no—
789C2×C79—41no—
790C2×C79—44no—
791C2×C79C23×#4111yescharacteristic
792C2×C79H(7,𝔽2)11yescharacteristic
793C2×C79H(7,𝔽2)11yescharacteristic
794D79—44no—
795#3521—794no—
796#3521—794no—
797#3519—794no—
798#3519—794no—
799#3514—794no—
800#3514—794no—
801#3513—794no—
802#3513—794no—
803#3506—792no—
804#3505—794no—
805#3501—791no—
806#3496—791no—
807#3493—792no—
808#3490—794no—
809#3484—791no—
810#3484D7911yescharacteristic, complemented
811#3460—792no—
812#3459—794no—
813#3455—792no—
814C2×#538—794no—
815C4×H(5,𝔽2)—791no—
816C4×H(5,𝔽2)—791no—
817C2×#518—791no—
818C79#6284611yescharacteristic, complemented, Sylow
819C2×H(5,𝔽2)—791no—
820C2×H(5,𝔽2)C2×D7911yescharacteristic
821C23×D4C2×D7911yescharacteristic
822#559—794no—
823#559—794no—
824#556—794no—
825#556—794no—
826#556—794no—
827#555—794no—
828#555—794no—
829#555—794no—
830#554—794no—
831#554—794no—
832#554—794no—
833#553—798no—
834#553—798no—
835#553—794no—
836#553—794no—
837#553—798no—
838#553—794no—
839#553—794no—
840#552—798no—
841#552—794no—
842#552—794no—
843#551—798no—
844#551—798no—
845#551—798no—
846#551—798no—
847#551—798no—
848#551—798no—
849#550—794no—
850D4×Q8—794no—
851#548—798no—
852#547—794no—
853#547—794no—
854#546—794no—
855#546—794no—
856#546—794no—
857#546—798no—
858#546—798no—
859#546—794no—
860#546—798no—
861#546—798no—
862#546—798no—
863#546C2×D7914yescomplemented
864#546C2×D7914yescomplemented
865D42—794no—
866D42—794no—
867D42—794no—
868D42C2×D7914yescomplemented
869D42C2×D7914yescomplemented
870#544—792no—
871#543—794no—
872#542—794no—
873#542—792no—
874#542—792no—
875#542—792no—
876#542—792no—
877#542—794no—
878#541—792no—
879#541—792no—
880#540—794no—
881#540—792no—
882#540—792no—
883#540—794no—
884#539—794no—
885#539—794no—
886#539—798no—
887#539—798no—
888#538—798no—
889#538—794no—
890#538—798no—
891#538—798no—
892#538—798no—
893#538—798no—
894#538—798no—
895#538—798no—
896#538—798no—
897#538—794no—
898#538—798no—
899#537—792no—
900#535—792no—
901#535C2×D7912yescomplemented
902#534—794no—
903#534—794no—
904#534C2×D7914yescomplemented
905#533—792no—
906#532—792no—
907#532—794no—
908#532—794no—
909#529—794no—
910#529—798no—
911#529—798no—
912#529—798no—
913#529—794no—
914#529—794no—
915#529—794no—
916#529—794no—
917#529—794no—
918C2×#126—794no—
919C2×#126—794no—
920C2×#124—794no—
921C2×#124—794no—
922#525—792no—
923#525—798no—
924#525—798no—
925#525—798no—
926#525—798no—
927#525C2×D7912yescomplemented
928C2×#123—794no—
929C2×#123—794no—
930C2×C22⋊Q8—794no—
931C2×#121—794no—
932C2×#121—794no—
933C2×#121—794no—
934C2×#120—794no—
935C2×#120C2×D7914yescomplemented
936#520—792no—
937#520—794no—
938#520—794no—
939#520—792no—
940#518—794no—
941#518—794no—
942#518—794no—
943#518—794no—
944#518—791no—
945#518—794no—
946#518—794no—
947#518—794no—
948#518—794no—
949#518C2×D7911yescharacteristic
950C4×#41—792no—
951C4×#41—794no—
952C4×#41—794no—
953C4×#41—792no—
954C2×C4×D4—791no—
955C2×C4×D4—792no—
956C2×C4×D4—791no—
957C2×C4×D4—791no—
958C2×C4×D4—792no—
959C2×C4×D4—791no—
960C2×C4×D4—794no—
961C2×C4×D4—794no—
962C2×C4×D4—794no—
963C2×C4×D4—794no—
964C2×#117—791no—
965C2×#117—791no—
966C22×C22⋊C4—792no—
967C22×C22⋊C4—792no—
968C25C22×D7912yes—
969H(5,𝔽2)—28no—
970H(5,𝔽2)—1588no—
971C2×#41—798no—
972C2×#41—798no—
973C2×#41—794no—
974C2×#41—792no—
975C2×#41C22×D7912yes—
976C2×#41C22×D7914yes—
977C22×Q8—794no—
978C22×D4—28no—
979C22×D4—794no—
980C22×D4—794no—
981C22×D4—794no—
982C22×D4—794no—
983C22×D4—794no—
984C22×D4C22×D7912yes—
985C22×D4C22×D7911yescharacteristic
986C22×D4C22×D7914yes—
987C22×D4C22×D7914yes—
988C22×D4C22×D7914yes—
989C22×D4C22×D7914yes—
990C22×D4C22×D7914yes—
991C22×D4C22×D7914yes—
992C22×D4C22×D7911yescharacteristic
993C23×C4—792no—
994C23×C4—792no—
995C23×C4—792no—
996C23×C4—792no—
997C23×C4—794no—
998C23×C4—794no—
999C23×C4C22×D7911yescharacteristic
1000C4⋊Q8—792no—
1001C4⋊Q8—794no—
1002C4⋊Q8—792no—
1003C4⋊Q8—792no—
1004C4⋊Q8—794no—
1005#127—794no—
1006#127—792no—
1007#127C22×D7914yes—
1008#126—794no—
1009#126—798no—
1010#126—794no—
1011#126—794no—
1012#126—794no—
1013#126—798no—
1014#126—798no—
1015#126—798no—
1016#126—798no—
1017#126—798no—
1018#126—798no—
1019#126—794no—
1020#126—798no—
1021#126—794no—
1022#126—794no—
1023#126—794no—
1024#125—794no—
1025#125—794no—
1026#125—798no—
1027#125—794no—
1028#125—794no—
1029#125—794no—
1030#125—792no—
1031#125—792no—
1032#125—794no—
1033#124—792no—
1034#124—794no—
1035#124—798no—
1036#124—798no—
1037#124—798no—
1038#124—794no—
1039#124—794no—
1040#124—792no—
1041#124—794no—
1042#124—798no—
1043#124—798no—
1044#124—798no—
1045#124—798no—
1046#124—794no—
1047#124C22×D7914yes—
1048#123—794no—
1049#123—798no—
1050#123—798no—
1051#123—798no—
1052#123—798no—
1053#123—798no—
1054#123—798no—
1055#123—798no—
1056#123—794no—
1057#123—794no—
1058#123—798no—
1059#123—794no—
1060#123—798no—
1061#123—798no—
1062#123—798no—
1063#123—794no—
1064#123—794no—
1065#123—798no—
1066#123—798no—
1067#123—794no—
1068#123—794no—
1069#123—794no—
1070#123C22×D7914yes—
1071#123C22×D7918yes—
1072C22⋊Q8—794no—
1073C22⋊Q8—798no—
1074C22⋊Q8—792no—
1075C22⋊Q8—792no—
1076C22⋊Q8—794no—
1077C22⋊Q8—798no—
1078C22⋊Q8—794no—
1079C22⋊Q8—794no—
1080C22⋊Q8—794no—
1081C22⋊Q8—798no—
1082C22⋊Q8—798no—
1083C22⋊Q8—798no—
1084C22⋊Q8—794no—
1085C22⋊Q8—794no—
1086C22⋊Q8—798no—
1087C22⋊Q8—798no—
1088C22⋊Q8—798no—
1089C22⋊Q8—798no—
1090C22⋊Q8—794no—
1091C22⋊Q8C22×D7912yes—
1092C22⋊Q8C22×D7912yes—
1093#121—794no—
1094#121—794no—
1095#121—794no—
1096#121—798no—
1097#121—798no—
1098#121—798no—
1099#121—798no—
1100#121—798no—
1101#121—798no—
1102#121—798no—
1103#121—798no—
1104#121—798no—
1105#121—794no—
1106#121—798no—
1107#121—798no—
1108#121—798no—
1109#121—798no—
1110#121—794no—
1111#121—794no—
1112#121—794no—
1113#121—794no—
1114#121—794no—
1115#121—792no—
1116#121—792no—
1117#121—794no—
1118#121C22×D7918yes—
1119#121C22×D7912yes—
1120#121C22×D7912yes—
1121#121C22×D7918yes—
1122#121C22×D7914yes—
1123#121C22×D7914yes—
1124#120—794no—
1125#120—798no—
1126#120—798no—
1127#120—798no—
1128#120—798no—
1129#120—798no—
1130#120—798no—
1131#120C22×D7914yes—
1132#120C22×D7918yes—
1133#120C22×D7918yes—
1134#120C22×D7918yes—
1135#120C22×D7918yes—
1136C4×Q8—792no—
1137C4×Q8—792no—
1138C4×Q8—794no—
1139C4×Q8—792no—
1140C4×Q8—792no—
1141C4×Q8—798no—
1142C4×Q8—794no—
1143C4×Q8—794no—
1144C4×Q8—794no—
1145C4×D4—794no—
1146C4×D4—794no—
1147C4×D4—794no—
1148C4×D4—798no—
1149C4×D4—792no—
1150C4×D4—798no—
1151C4×D4—798no—
1152C4×D4—794no—
1153C4×D4—794no—
1154C4×D4—794no—
1155C4×D4—794no—
1156C4×D4—798no—
1157C4×D4—794no—
1158C4×D4—798no—
1159C4×D4—794no—
1160C4×D4—798no—
1161C4×D4—798no—
1162C4×D4—794no—
1163C4×D4—798no—
1164C4×D4—794no—
1165C4×D4—794no—
1166C4×D4—792no—
1167C4×D4—794no—
1168C4×D4—798no—
1169C4×D4—798no—
1170C4×D4—798no—
1171C4×D4—798no—
1172C4×D4—798no—
1173C4×D4—794no—
1174C4×D4—794no—
1175C4×D4—794no—
1176C4×D4—794no—
1177C4×D4—792no—
1178C4×D4—792no—
1179C4×D4—794no—
1180C4×D4—798no—
1181C4×D4—798no—
1182C4×D4—798no—
1183C4×D4—794no—
1184C4×D4—798no—
1185C4×D4—798no—
1186C4×D4—798no—
1187C4×D4—794no—
1188C4×D4C22×D7914yes—
1189C4×D4C22×D7914yes—
1190C4×D4C22×D7914yes—
1191C4×D4C22×D7914yes—
1192#117—792no—
1193#117—792no—
1194#117—792no—
1195#117—792no—
1196#117—794no—
1197#117—794no—
1198#117—792no—
1199#117—794no—
1200#117—798no—
1201#117—794no—
1202#117—794no—
1203#117—798no—
1204#117—798no—
1205#117—798no—
1206#117—798no—
1207#117—798no—
1208#117—794no—
1209#117C22×D7912yes—
1210C2×C4⋊C4—791no—
1211C2×C4⋊C4—791no—
1212C2×C4⋊C4—791no—
1213C2×C4⋊C4—791no—
1214C2×C4⋊C4—794no—
1215C2×C4⋊C4—794no—
1216C2×C4⋊C4—794no—
1217C2×C4⋊C4—794no—
1218C2×C4⋊C4—794no—
1219C2×C4⋊C4—794no—
1220C2×C4⋊C4—794no—
1221C2×C4⋊C4—794no—
1222C2×C22⋊C4—791no—
1223C2×C22⋊C4—792no—
1224C2×C22⋊C4—791no—
1225C2×C22⋊C4—792no—
1226C2×C22⋊C4—792no—
1227C2×C22⋊C4—792no—
1228C2×C22⋊C4—792no—
1229C2×C22⋊C4—794no—
1230C2×C22⋊C4—794no—
1231C2×C22⋊C4—794no—
1232C2×C22⋊C4—794no—
1233C2×C22⋊C4—798no—
1234C2×C22⋊C4—798no—
1235C2×C22⋊C4—794no—
1236C2×C22⋊C4—794no—
1237C2×C22⋊C4—798no—
1238C2×C22⋊C4—794no—
1239C2×C22⋊C4—794no—
1240C2×C22⋊C4—794no—
1241C2×C22⋊C4—794no—
1242C2×C22⋊C4—794no—
1243C2×C22⋊C4—798no—
1244C2×C22⋊C4C22×D7914yes—
1245C2×C22⋊C4C22×D7914yes—
1246C2×C22⋊C4C22×D7914yes—
1247C2×C42—791no—
1248C2×C42—792no—
1249C2×C42—791no—
1250C2×C42—794no—
1251C2×C42—794no—
1252C2×C42—794no—
1253C2×C42—794no—
1254C24—28no—
1255C24—82no—
1256C24—82no—
1257C24—794no—
1258C24C23×D7914yes—
1259C24C23×D7914yes—
1260C24C23×D7911yescharacteristic
1261C24C23×D7914yes—
1262C24C23×D7912yes—
1263C24C23×D7912yes—
1264#41—216no—
1265#41—28no—
1266#41—6328no—
1267#41—6328no—
1268#41—15816no—
1269#41—1588no—
1270C2×Q8—794no—
1271C2×Q8—794no—
1272C2×Q8—798no—
1273C2×Q8—792no—
1274C2×Q8—6324no—
1275C2×Q8C23×D7912yes—
1276C2×D4—28no—
1277C2×D4—216no—
1278C2×D4—216no—
1279C2×D4—216no—
1280C2×D4—216no—
1281C2×D4—24no—
1282C2×D4—84no—
1283C2×D4—84no—
1284C2×D4—794no—
1285C2×D4—794no—
1286C2×D4—798no—
1287C2×D4—794no—
1288C2×D4—798no—
1289C2×D4—798no—
1290C2×D4—794no—
1291C2×D4—798no—
1292C2×D4—794no—
1293C2×D4—792no—
1294C2×D4—6324no—
1295C2×D4—6324no—
1296C2×D4—6324no—
1297C2×D4—15816no—
1298C2×D4—15816no—
1299C2×D4#1192962318yescomplemented
1300C2×D4C23×D7918yes—
1301C2×D4C23×D7918yes—
1302C2×D4C23×D7914yes—
1303C2×D4C23×D7914yes—
1304C2×D4C23×D7912yes—
1305C2×D4C23×D7918yes—
1306C2×D4C23×D7918yes—
1307C2×D4C23×D7914yes—
1308C2×D4C23×D7914yes—
1309C2×D4C23×D7914yes—
1310C22×C4—24no—
1311C22×C4—794no—
1312C22×C4—794no—
1313C22×C4—791no—
1314C22×C4—791no—
1315C22×C4—792no—
1316C22×C4—794no—
1317C22×C4—791no—
1318C22×C4—792no—
1319C22×C4—791no—
1320C22×C4—794no—
1321C22×C4—794no—
1322C22×C4—794no—
1323C22×C4—794no—
1324C22×C4—794no—
1325C22×C4—798no—
1326C22×C4—798no—
1327C22×C4—798no—
1328C22×C4—794no—
1329C22×C4—794no—
1330C22×C4—798no—
1331C22×C4—794no—
1332C22×C4—794no—
1333C22×C4—6324no—
1334C22×C4—6322no—
1335C22×C4—6324no—
1336C22×C4—6322no—
1337C22×C4—6322no—
1338C22×C4—6322no—
1339C22×C4C23×D7911yescharacteristic
1340C22×C4C23×D7914yes—
1341C22×C4C23×D7914yes—
1342C22×C4C23×D7912yes—
1343C22×C4C23×D7912yes—
1344C22×C4C23×D7914yes—
1345C22×C4C23×D7914yes—
1346C22×C4C23×D7911yescharacteristic
1347C4⋊C4—798no—
1348C4⋊C4—794no—
1349C4⋊C4—794no—
1350C4⋊C4—794no—
1351C4⋊C4—794no—
1352C4⋊C4—798no—
1353C4⋊C4—798no—
1354C4⋊C4—798no—
1355C4⋊C4—794no—
1356C4⋊C4—794no—
1357C4⋊C4—794no—
1358C4⋊C4—794no—
1359C4⋊C4—794no—
1360C4⋊C4—794no—
1361C4⋊C4—794no—
1362C4⋊C4—792no—
1363C4⋊C4—798no—
1364C4⋊C4—794no—
1365C4⋊C4—794no—
1366C4⋊C4—794no—
1367C4⋊C4—792no—
1368C4⋊C4—792no—
1369C4⋊C4—792no—
1370C4⋊C4—792no—
1371C4⋊C4—798no—
1372C4⋊C4—792no—
1373C4⋊C4—794no—
1374C4⋊C4—794no—
1375C4⋊C4C23×D7912yes—
1376C4⋊C4C23×D7912yes—
1377C4⋊C4C23×D7914yes—
1378C4⋊C4C23×D7914yes—
1379C22⋊C4—798no—
1380C22⋊C4—791no—
1381C22⋊C4—791no—
1382C22⋊C4—794no—
1383C22⋊C4—792no—
1384C22⋊C4—794no—
1385C22⋊C4—792no—
1386C22⋊C4—791no—
1387C22⋊C4—791no—
1388C22⋊C4—798no—
1389C22⋊C4—794no—
1390C22⋊C4—794no—
1391C22⋊C4—794no—
1392C22⋊C4—794no—
1393C22⋊C4—798no—
1394C22⋊C4—794no—
1395C22⋊C4—794no—
1396C22⋊C4—794no—
1397C22⋊C4—798no—
1398C22⋊C4—794no—
1399C22⋊C4—794no—
1400C22⋊C4—794no—
1401C22⋊C4—798no—
1402C22⋊C4—798no—
1403C22⋊C4—798no—
1404C22⋊C4—794no—
1405C22⋊C4—794no—
1406C22⋊C4—798no—
1407C22⋊C4—794no—
1408C22⋊C4—794no—
1409C22⋊C4—798no—
1410C22⋊C4—794no—
1411C22⋊C4—794no—
1412C22⋊C4—794no—
1413C22⋊C4C23×D7918yes—
1414C22⋊C4C23×D7914yes—
1415C22⋊C4C23×D7914yes—
1416C22⋊C4C23×D7914yes—
1417C22⋊C4C23×D7918yes—
1418C22⋊C4C23×D7918yes—
1419C22⋊C4C23×D7914yes—
1420C22⋊C4C23×D7914yes—
1421C42—792no—
1422C42—792no—
1423C42—794no—
1424C42—794no—
1425C42—794no—
1426C42—798no—
1427C42—794no—
1428C42—798no—
1429C42—798no—
1430C42—792no—
1431C42—792no—
1432C42—794no—
1433C42C23×D7914yes—
1434C23—22no—
1435C23—24no—
1436C23—28no—
1437C23—28no—
1438C23—28no—
1439C23—42no—
1440C23—42no—
1441C23—42no—
1442C23—42no—
1443C23—41no—
1444C23—41no—
1445C23—44no—
1446C23—44no—
1447C23—44no—
1448C23—44no—
1449C23—44no—
1450C23—44no—
1451C23—816no—
1452C23—3164no—
1453C23—3164no—
1454C23—794no—
1455C23—1588no—
1456C23C2×#1192962318yes—
1457C23C24×D7911yescharacteristic
1458C23C24×D7911yescharacteristic
1459C23C24×D7914yes—
1460C23C24×D7914yes—
1461C23C24×D7914yes—
1462C23C24×D7911yescharacteristic
1463Q8—24no—
1464Q8—3164no—
1465Q8—3168no—
1466Q8—3164no—
1467Q8—1584no—
1468D4—216no—
1469D4—216no—
1470D4—28no—
1471D4—28no—
1472D4—24no—
1473D4—44no—
1474D4—44no—
1475D4—48no—
1476D4—48no—
1477D4—3164no—
1478D4—3164no—
1479D4—3164no—
1480D4—3168no—
1481D4—3168no—
1482D4—3168no—
1483D4—3164no—
1484D4—15816no—
1485D4—1588no—
1486D4—1584no—
1487D4C2×#11929623116yes—
1488C2×C4—22no—
1489C2×C4—28no—
1490C2×C4—24no—
1491C2×C4—24no—
1492C2×C4—28no—
1493C2×C4—44no—
1494C2×C4—44no—
1495C2×C4—3164no—
1496C2×C4—3168no—
1497C2×C4—3164no—
1498C2×C4—3164no—
1499C2×C4—3164no—
1500C2×C4—3161no—
1501C2×C4—3162no—
1502C2×C4—3161no—
1503C2×C4—3164no—
1504C2×C4—3161no—
1505C2×C4—3162no—
1506C2×C4—3161no—
1507C2×C4—3164no—
1508C2×C4—3164no—
1509C2×C4—3164no—
1510C2×C4—3168no—
1511C2×C4—3168no—
1512C2×C4—3168no—
1513C2×C4—3164no—
1514C2×C4—3164no—
1515C2×C4—791no—
1516C2×C4—791no—
1517C2×C4—792no—
1518C2×C4—794no—
1519C2×C4—794no—
1520C2×C4—794no—
1521C2×C4—791no—
1522C2×C4—794no—
1523C2×C4—792no—
1524C2×C4—794no—
1525C2×C4—791no—
1526C2×C4—1588no—
1527C2×C4—1588no—
1528C2×C4C2×#1192962314yes—
1529C2×C4C24×D7914yes—
1530C2×C4C24×D7912yes—
1531C2×C4C24×D7914yes—
1532C2×C4C24×D7914yes—
1533C2×C4C24×D7912yes—
1534C22—24no—
1535C22—24no—
1536C22—21no—
1537C22—21no—
1538C22—21no—
1539C22—21no—
1540C22—24no—
1541C22—24no—
1542C22—24no—
1543C22—24no—
1544C22—24no—
1545C22—24no—
1546C22—21no—
1547C22—21no—
1548C22—21no—
1549C22—21no—
1550C22—48no—
1551C22—44no—
1552C22—48no—
1553C22—88no—
1554C22—88no—
1555C22—88no—
1556C22—6328no—
1557C22—1584no—
1558C22—1584no—
1559C22—1584no—
1560C22C22×#1192962318yes—
1561C22C22×#1192962312yes—
1562C22C25×D7911yescharacteristic
1563C4—22no—
1564C4—24no—
1565C4—24no—
1566C4—24no—
1567C4—1584no—
1568C4—1581no—
1569C4—1584no—
1570C4—1582no—
1571C4—1581no—
1572C4—1581no—
1573C4—1584no—
1574C4—1584no—
1575C4—1582no—
1576C4—1581no—
1577C4—1584no—
1578C4C22×#1192962314yes—
1579C2—22no—
1580C2—28no—
1581C2—41no—
1582C2—41no—
1583C2—44no—
1584C2—44no—
1585C2—3164no—
1586C2C23×#1192962311yescharacteristic
1587C2#2377821011yescharacteristic
1588C2#2377821011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3484C2
hypercenter#3484D79
hypocenterC79#62846
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3484

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777457C2semidirect
2. #23777453C2semidirect
3. #23777423C2semidirect
4. #23777419C2semidirect
5. #23777352C2semidirect
6. #23777348C2semidirect
7. #23777329C2semidirect
8. #23777325C2semidirect
9. #23777251C2semidirect
10. #23777237C2semidirect
11. #23777198C2semidirect
12. #23777159C2semidirect
13. #23777117C2semidirect
14. #23777087C2semidirect
15. #23777035C2semidirect
16. #23776813C2semidirect
17. #23776806C2semidirect
18. #23776788C2semidirect
19. C2×#19099148C2semidirect
20. H(5,𝔽2)×Dic79C2semidirect
21. #23776604C2semidirect
22. C2×#19099038C2semidirect
23. C79×#3484C2semidirect
25. #19099299C22semidirect
26. #19099295C22semidirect
27. #19099284C22semidirect
28. #19099283C22semidirect
29. #19099282C22semidirect
30. #19099278C22semidirect
31. #19099277C22semidirect
32. #19099277C22semidirect
33. #19099272C22semidirect
34. #19099272C22semidirect
35. #19099270C22semidirect
36. #19099265C22semidirect
37. #19099265C22semidirect
38. #19099260C22semidirect
39. #19099260C22semidirect
40. #19099259C22semidirect
41. #19099256C22semidirect
42. #19099256C22semidirect
43. #19099253C22semidirect
44. #19099250C22semidirect
45. #19099247C22semidirect
46. #19099244C22semidirect
47. #19099244C22semidirect
48. #19099244C22semidirect
49. #19099239C22semidirect
50. #19099239C22semidirect
51. #19099236C22semidirect
52. #19099233C22semidirect
53. D4×Dic158C22semidirect
54. #19099219C22semidirect
55. #19099213C22semidirect
56. #19099212C22semidirect
57. #19099207C22semidirect
58. #19099207C22semidirect
59. #19099207C22semidirect
60. #19099207C22semidirect
61. #19099207C22semidirect
62. #19099201C22semidirect
63. #19099200C22semidirect
64. #19099200C22semidirect
65. #19099200C22semidirect
66. D4×C22⋊D79C22semidirect
67. D4×C22⋊D79C22semidirect
68. D4×C22⋊D79C22semidirect
69. #19099191C22semidirect
70. #19099189C22semidirect
71. #19099186C22semidirect
72. #19099186C22semidirect
73. #19099182C22semidirect
74. #19099180C22semidirect
75. #19099180C22semidirect
76. #19099180C22semidirect
77. #19099173C22semidirect
78. #19099173C22semidirect
79. #19099167C22semidirect
80. #19099166C22semidirect
81. #19099166C22semidirect
82. #19099166C22semidirect
83. #19099158C22semidirect
84. #19099157C22semidirect
85. #19099157C22semidirect
86. #19099157C22semidirect
87. #19099150C22semidirect
88. #19099148C22semidirect
89. #19099148C22semidirect
90. #19099148C22semidirect
91. #19099148C22semidirect
92. #19099148C22semidirect
93. #19099148C22semidirect
94. #19099148C22semidirect
95. #19099148C22semidirect
96. #19099148C22semidirect
97. #19099148C22semidirect
98. #19099141C22semidirect
99. #19099130C22semidirect
100. #19099122C22semidirect
101. #19099122C22semidirect
102. #19099116C22semidirect
103. #19099111C22semidirect
104. #19099109C22semidirect
105. #19099108C22semidirect
106. #19099095C22semidirect
107. #19099095C22semidirect
108. #19099094C22semidirect
109. #19099094C22semidirect
110. #19099093C22semidirect
111. #19099093C22semidirect
112. #19099092C22semidirect
113. #19099090C22semidirect
114. #19099090C22semidirect
115. C2×#14579154C22semidirect
116. C2×#14579154C22semidirect
117. C2×#14579148C22semidirect
118. C2×#14579147C22semidirect
119. #19099074C22semidirect
120. #19099073C22semidirect
121. #19099069C22semidirect
122. #19099069C22semidirect
123. #19099069C22semidirect
124. C2×#14579143C22semidirect
125. C2×#14579142C22semidirect
126. C2×#14579138C22semidirect
127. C2×#14579133C22semidirect
128. C2×#14579133C22semidirect
129. C2×#14579132C22semidirect
130. C2×#14579130C22semidirect
131. #19099046C22semidirect
132. #19099046C22semidirect
133. #19099043C22semidirect
134. #19099042C22semidirect
136. #19099038C22semidirect
137. #19099038C22semidirect
138. #19099038C22semidirect
139. #19099038C22semidirect
140. #19099038C22semidirect
141. #19099038C22semidirect
142. #19099036C22semidirect
143. #19099035C22semidirect
144. #41×Dic79C22semidirect
145. #41×Dic79C22semidirect
146. #19099031C22semidirect
147. C4×#11929623C22semidirect
150. C2×D4×Dic79C22semidirect
151. C2×D4×Dic79C22semidirect
152. C2×D4×Dic79C22semidirect
153. C2×D4×Dic79C22semidirect
154. C2×D4×Dic79C22semidirect
155. C2×D4×Dic79C22semidirect
156. C2×(C22⋊D79)⋊C4C22semidirect
157. C4×D4×D79C22semidirect
158. C2×#14579120C22semidirect
159. C2×#14579120C22semidirect
160. C22×C22⋊Dic79C22semidirect
161. C22×C22⋊Dic79C22semidirect
164. #546×C79C22semidirect
165. #546×C79C22semidirect
166. D42×C79C22semidirect
167. D42×C79C22semidirect
168. #535×C79C22semidirect
169. #534×C79C22semidirect
170. #525×C79C22semidirect
171. C2×#120×C79C22semidirect
176. C2×#11929623C23semidirect
177. C2×#11929623C23semidirect
178. C22×Dic158C23semidirect
182. C22×C22⋊D79C23semidirect
188. C23×Dic79C23semidirect
189. C22×C4×D79C23semidirect
190. #14579161C23semidirect
191. #14579160C23semidirect
192. #14579160C23semidirect
193. #14579160C23semidirect
194. #14579159C23semidirect
196. #14579157C23semidirect
197. #14579156C23semidirect
198. #14579156C23semidirect
199. #14579156C23semidirect
206. #14579154C23semidirect
207. #14579154C23semidirect
208. #14579154C23semidirect
209. #14579154C23semidirect
210. #14579154C23semidirect
211. #14579154C23semidirect
212. #14579154C23semidirect
213. #14579153C23semidirect
214. #14579152C23semidirect
215. #14579152C23semidirect
216. #14579152C23semidirect
217. #14579152C23semidirect
218. #14579152C23semidirect
219. #14579151C23semidirect
220. #14579151C23semidirect
221. #14579151C23semidirect
222. #14579150C23semidirect
227. #14579148C23semidirect
228. #14579148C23semidirect
229. #14579148C23semidirect
233. #14579147C23semidirect
234. #14579147C23semidirect
235. #14579147C23semidirect
236. #14579145C23semidirect
237. #14579145C23semidirect
238. #14579145C23semidirect
239. #14579145C23semidirect
241. #14579144C23semidirect
245. #14579143C23semidirect
246. #14579143C23semidirect
247. #14579143C23semidirect
248. #14579143C23semidirect
253. #14579142C23semidirect
254. #14579142C23semidirect
255. #14579142C23semidirect
256. #14579142C23semidirect
257. #14579142C23semidirect
258. #14579141C23semidirect
259. #14579141C23semidirect
262. #14579140C23semidirect
263. #14579140C23semidirect
264. #14579140C23semidirect
268. #14579138C23semidirect
269. #14579138C23semidirect
270. #14579138C23semidirect
271. #14579138C23semidirect
272. #14579138C23semidirect
273. #14579138C23semidirect
274. #14579138C23semidirect
275. #14579138C23semidirect
276. #14579137C23semidirect
279. #14579135C23semidirect
288. #14579133C23semidirect
289. #14579133C23semidirect
290. #14579133C23semidirect
291. #14579133C23semidirect
292. #14579133C23semidirect
293. #14579133C23semidirect
299. #14579132C23semidirect
300. #14579132C23semidirect
301. #14579132C23semidirect
306. #14579130C23semidirect
308. #14579129C23semidirect
309. Q8×Dic79C23semidirect
310. Q8×Dic79C23semidirect
311. Q8×Dic79C23semidirect
312. C4×Dic158C23semidirect
313. C4×Dic158C23semidirect
314. C4×Dic158C23semidirect
315. #14579126C23semidirect
316. #14579126C23semidirect
317. #14579126C23semidirect
318. C4×D316C23semidirect
336. D4×Dic79C23semidirect
337. D4×Dic79C23semidirect
338. D4×Dic79C23semidirect
339. D4×Dic79C23semidirect
340. D4×Dic79C23semidirect
341. D4×Dic79C23semidirect
342. D4×Dic79C23semidirect
343. D4×Dic79C23semidirect
344. D4×Dic79C23semidirect
345. #14579123C23semidirect
346. #14579123C23semidirect
349. C4×C22⋊D79C23semidirect
350. C4×C22⋊D79C23semidirect
351. C4×C22⋊D79C23semidirect
352. C4×C22⋊D79C23semidirect
356. (C22⋊D79)⋊C4C23semidirect
357. (C22⋊D79)⋊C4C23semidirect
358. (C22⋊D79)⋊C4C23semidirect
359. (C22⋊D79)⋊C4C23semidirect
360. (C22⋊D79)⋊C4C23semidirect
368. #14579120C23semidirect
369. #14579120C23semidirect
370. #14579120C23semidirect
371. #14579119C23semidirect
372. #14579119C23semidirect
373. #14579118C23semidirect
374. #14579117C23semidirect
375. #14579117C23semidirect
376. #14579117C23semidirect
377. #14579117C23semidirect
382. C2×C4⋊Dic79C23semidirect
383. C2×C4⋊Dic79C23semidirect
384. C2×C4⋊Dic79C23semidirect
385. C2×Dic79⋊C4C23semidirect
386. C2×Dic79⋊C4C23semidirect
387. C2×Dic79⋊C4C23semidirect
388. C2×Dic79⋊C4C23semidirect
389. C4⋊C4×D79C23semidirect
406. C2×C22⋊Dic79C23semidirect
407. C2×C22⋊Dic79C23semidirect
408. C2×C22⋊Dic79C23semidirect
409. C2×(C2×D79)⋊C4C23semidirect
410. C2×(C2×D79)⋊C4C23semidirect
411. C22⋊C4×D79C23semidirect
415. C2×C4×Dic79C23semidirect
416. C2×C4×Dic79C23semidirect
417. C2×C4×Dic79C23semidirect
418. C42×D79C23semidirect
606. C2×D4×C79#41semidirect
810. #3484D79semidirect
818. C79#62846semidirect
863. #546C2×D79semidirect
864. #546C2×D79semidirect
868. D42C2×D79semidirect
869. D42C2×D79semidirect
901. #535C2×D79semidirect
904. #534C2×D79semidirect
927. #525C2×D79semidirect
935. C2×#120C2×D79semidirect
1299. C2×D4#11929623semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237774572
#237774532
#237774232
#237774192
#237773522
#237773482
#237773292
#237773252
#237772512
#237772372
#237771982
#237771592
#237771172
#237770872
#237770352
#237768132
#237768062
#237767882
C2×#190991482
H(5,𝔽2)×Dic792
#237766042
C2×#190990382
C79×#34842
#6284679