Finite Group Databasebeta

← #35197329

Subgroups — #35197329

Order 20224.

7106 conjugacy classes of subgroups.

The subgroup lattice has 1532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777469C214yesmaximal, complemented
2#23777457C214yesmaximal, complemented
3#23777440C214yesmaximal, complemented
4#23777436C214yesmaximal, complemented
5#23777369C214yesmaximal, complemented
6#23777365C214yesmaximal, complemented
7#23777341C214yesmaximal, complemented
8#23777329C214yesmaximal, complemented
9#23777264C212yesmaximal, complemented
10#23777237C214yesmaximal, complemented
11#23777198C211yesmaximal, characteristic, complemented
12#23777159C211yesmaximal, characteristic, complemented
13#23777106C212yesmaximal, complemented
14#23777096C214yesmaximal, complemented
15#23777044C211yesmaximal, characteristic, complemented
16#23776824C212yesmaximal, complemented
17#23776806C214yesmaximal, complemented
18#23776788C212yesmaximal, complemented
19C2×#19099157C214yesmaximal, complemented
20H(5,𝔽2)×Dic79C211yesmaximal, characteristic, complemented
21#23776604C211yesmaximal, characteristic, complemented
22C2×#19099046C211yesmaximal, characteristic, complemented
23C79×#3485C211yesmaximal, characteristic, complemented
24C2×#14579206C2211yescharacteristic
25#19099295C2214yescomplemented
26#19099288C2214yescomplemented
27#19099287C2214yescomplemented
28#19099284C2214yescomplemented
29#19099282C2214yescomplemented
30#19099272C2214yescomplemented
31#19099272C2214yescomplemented
32#19099271C2214yescomplemented
33#19099271C2214yescomplemented
34#19099270C2214yescomplemented
35#19099270C2214yescomplemented
36#19099265C2214yescomplemented
37#19099265C2218yescomplemented
38#19099259C2214yescomplemented
39#19099256C2218yescomplemented
40#19099256C2218yescomplemented
41#19099255C2214yescomplemented
42#19099255C2214yescomplemented
43#19099253C2214yescomplemented
44#19099250C2218yescomplemented
45#19099250C2218yescomplemented
46#19099250C2218yescomplemented
47#19099248C2218yescomplemented
48#19099248C2218yescomplemented
49#19099247C2214yescomplemented
50#19099244C2218yescomplemented
51#19099239C2218yescomplemented
52#19099239C2218yescomplemented
53#19099236C2218yescomplemented
54#19099236C2218yescomplemented
55#19099236C2218yescomplemented
56D4×Dic158C2214yescomplemented
57#19099219C2218yescomplemented
58#19099217C2214yescomplemented
59#19099213C2214yescomplemented
60#19099212C2214yescomplemented
61#19099212C2214yescomplemented
62#19099212C2214yescomplemented
63#19099207C2214yescomplemented
64#19099201C2214yescomplemented
65#19099201C2214yescomplemented
66#19099201C2214yescomplemented
67#19099200C2218yescomplemented
68D4×C22⋊D79C2214yescomplemented
69#19099191C2212yescomplemented
70#19099189C2214yescomplemented
71#19099186C2212yescomplemented
72#19099186C2212yescomplemented
73#19099186C2214yescomplemented
74#19099182C2214yescomplemented
75#19099180C2212yescomplemented
76#19099180C2212yescomplemented
77#19099174C2214yescomplemented
78#19099173C2212yescomplemented
79#19099173C2212yescomplemented
80#19099173C2214yescomplemented
81#19099166C2212yescomplemented
82#19099166C2212yescomplemented
83#19099158C2218yescomplemented
84#19099157C2214yescomplemented
85#19099157C2214yescomplemented
86#19099157C2218yescomplemented
87#19099157C2218yescomplemented
88#19099157C2218yescomplemented
89#19099157C2218yescomplemented
90#19099157C2218yescomplemented
91#19099157C2218yescomplemented
92#19099157C2218yescomplemented
93#19099157C2218yescomplemented
94#19099150C2218yescomplemented
95#19099148C2214yescomplemented
96#19099148C2214yescomplemented
97#19099148C2218yescomplemented
98#19099141C2212yes—
99#19099137C2212yescomplemented
100#19099122C2214yes—
101#19099122C2214yescomplemented
102#19099118C2214yescomplemented
103#19099116C2212yescomplemented
104#19099115C2214yescomplemented
105#19099109C2212yes—
106#19099099C2214yescomplemented
107#19099095C2214yescomplemented
108#19099095C2214yescomplemented
109#19099094C2218yescomplemented
110#19099093C2214yescomplemented
111#19099093C2214yescomplemented
112#19099092C2214yescomplemented
113#19099090C2218yescomplemented
114#19099090C2218yescomplemented
115#19099090C2218yescomplemented
116C2×#14579156C2214yescomplemented
117C2×#14579154C2214yescomplemented
118C2×#14579152C2214yescomplemented
119C2×#14579151C2214yescomplemented
120#19099074C2212yescomplemented
121#19099073C2218yescomplemented
122#19099069C2218yescomplemented
123#19099069C2218yescomplemented
124C2×#14579145C2214yescomplemented
125C2×#14579144C2214yescomplemented
126C2×#14579143C2214yescomplemented
127C2×#14579141C2214yescomplemented
128C2×#14579138C2214yescomplemented
129C2×#14579138C2214yescomplemented
130C2×#14579133C2214yes—
131#19099046C2214yescomplemented
132#19099046C2214yescomplemented
133#19099046C2212yescomplemented
134#19099046C2214yescomplemented
135#19099046C2214yescomplemented
136#19099046C2214yescomplemented
137#19099043C2212yescomplemented
138#19099042C2214yescomplemented
139#19099038C2211yescharacteristic
140#19099038C2214yescomplemented
141#19099038C2214yescomplemented
142#19099036C2214yescomplemented
143#19099035C2214yescomplemented
144#41×Dic79C2212yescomplemented
145#41×Dic79C2214yescomplemented
146#19099031C2212yescomplemented
147C4×#11929623C2214yescomplemented
148C2×Q8×Dic79C2211yescharacteristic, complemented
149C2×Q8×Dic79C2211yescharacteristic, complemented
150C2×D4×Dic79C2211yescharacteristic
151C2×D4×Dic79C2211yescharacteristic
152C2×D4×Dic79C2212yescomplemented
153C2×D4×Dic79C2214yescomplemented
154C2×D4×Dic79C2214yescomplemented
155C2×D4×Dic79C2212yescomplemented
156C2×(C22⋊D79)⋊C4C2214yescomplemented
157C4×D4×D79C2214yescomplemented
158C2×#14579120C2211yescharacteristic, complemented
159C2×#14579120C2212yescomplemented
160C22×C4⋊Dic79C2211yescharacteristic, complemented
161C22×C4⋊Dic79C2212yescomplemented
162C2×H(5,𝔽2)×C79C2211yescharacteristic
163C22×#41×C79C2211yescharacteristic
164#547×C79C2214yescomplemented
165#547×C79C2214yescomplemented
166#546×C79C2214yescomplemented
167#546×C79C2214yescomplemented
168#536×C79C2212yescomplemented
169#534×C79C2214yescomplemented
170#525×C79C2212yescomplemented
171C2×#123×C79C2214yescomplemented
172#518×C79C2211yescharacteristic
173#14579206—28no—
174C2×#11929624C2312yes—
175C2×#11929623C2314yes—
176C2×#11929623C2318yes—
177C22×Dic158C2314yes—
178C22×C22⋊D79C2314yes—
179C22×C22⋊D79C2314yes—
180C2×D4×D79C2314yes—
181C23×Dic79C2312yes—
182C23×Dic79C2312yes—
183C23×Dic79C2312yes—
184C23×Dic79C2314yes—
185C22×C4×D79C2314yes—
186#14579161C2314yes—
187#14579160C2312yes—
188#14579160C2312yes—
189#14579160C2314yes—
190#14579159C2314yes—
191#14579159C2312yes—
192#14579157C2312yes—
193#14579156C2318yes—
194#14579156C2318yes—
195#14579156C2314yes—
196#14579156C2318yes—
197#14579156C2318yes—
198#14579156C2314yes—
199#14579156C2318yes—
200#14579154C2318yes—
201#14579154C2314yes—
202#14579154C2314yes—
203#14579154C2318yes—
204#14579154C2314yes—
205#14579154C2314yes—
206#14579154C2314yes—
207#14579154C2318yes—
208#14579154C2318yes—
209#14579154C2314yes—
210#14579154C2318yes—
211#14579153C2314yes—
212#14579152C2314yes—
213#14579152C2318yes—
214#14579152C2318yes—
215#14579152C2318yes—
216#14579152C2314yes—
217#14579152C2312yes—
218#14579152C2312yes—
219#14579152C2314yes—
220#14579151C2314yes—
221#14579151C2318yes—
222#14579151C2318yes—
223#14579151C2318yes—
224#14579151C2318yes—
225#14579151C2314yes—
226#14579151C2318yes—
227#14579150C2314yes—
228#14579150C2312yes—
229#14579148C2314yes—
230#14579148C2314yes—
231#14579148C2312yes—
232#14579147C2314yes—
233#14579147C2318yes—
234#14579147C2314yes—
235#14579147C2318yes—
236#14579145C2318yes—
237#14579145C2318yes—
238#14579145C2314yes—
239#14579145C2318yes—
240#14579145C2318yes—
241#14579145C2314yes—
242#14579144C2318yes—
243#14579144C2314yes—
244#14579144C2318yes—
245#14579144C2318yes—
246#14579144C2318yes—
247#14579143C2318yes—
248#14579143C2314yes—
249#14579143C2314yes—
250#14579143C2314yes—
251#14579143C2318yes—
252#14579143C2318yes—
253#14579143C2314yes—
254#14579142C2314yes—
255#14579142C2318yes—
256#14579142C2314yes—
257#14579142C2318yes—
258#14579142C2318yes—
259#14579141C2314yes—
260#14579141C2318yes—
261#14579141C2318yes—
262#14579141C2318yes—
263#14579141C2314yes—
264#14579140C2314yes—
265#14579140C2318yes—
266#14579140C2318yes—
267#14579140C2312yes—
268#14579140C2312yes—
269#14579138C2314yes—
270#14579138C2314yes—
271#14579138C2318yes—
272#14579138C2314yes—
273#14579138C2318yes—
274#14579138C2318yes—
275#14579138C2318yes—
276#14579138C2318yes—
277#14579138C2318yes—
278#14579138C2318yes—
279#14579138C2318yes—
280#14579138C2314yes—
281#14579138C2318yes—
282#14579137C2314yes—
283#14579137C2314yes—
284#14579137C2314yes—
285#14579135C2314yes—
286#14579135C2312yes—
287#14579135C2312yes—
288#14579133C2318yes—
289#14579133C2314yes—
290#14579133C2318yes—
291#14579133C2314yes—
292#14579133C2314yes—
293#14579133C2314yes—
294#14579133C2318yes—
295#14579133C2318yes—
296#14579133C2318yes—
297#14579133C2318yes—
298#14579132C2314yes—
299#14579132C2314yes—
300#14579132C2314yes—
301#14579130C2314yes—
302#14579130C2318yes—
303#14579129C2318yes—
304#14579129C2318yes—
305Q8×Dic79C2312yes—
306Q8×Dic79C2314yes—
307Q8×Dic79C2312yes—
308Q8×Dic79C2314yes—
309Q8×Dic79C2314yes—
310Q8×Dic79C2314yes—
311Q8×Dic79C2314yes—
312C4×Dic158C2314yes—
313C4×Dic158C2314yes—
314C4×Dic158C2314yes—
315#14579126C2312yes—
316#14579126C2312yes—
317#14579126C2318yes—
318#14579126C2318yes—
319C4×D316C2314yes—
320D4×Dic79C2314yes—
321D4×Dic79C2318yes—
322D4×Dic79C2314yes—
323D4×Dic79C2318yes—
324D4×Dic79C2318yes—
325D4×Dic79C2318yes—
326D4×Dic79C2318yes—
327D4×Dic79C2312yes—
328D4×Dic79C2312yes—
329D4×Dic79C2314yes—
330D4×Dic79C2318yes—
331D4×Dic79C2314yes—
332D4×Dic79C2314yes—
333D4×Dic79C2314yes—
334D4×Dic79C2314yes—
335D4×Dic79C2318yes—
336D4×Dic79C2318yes—
337D4×Dic79C2318yes—
338D4×Dic79C2318yes—
339D4×Dic79C2314yes—
340D4×Dic79C2314yes—
341#14579123C2312yes—
342#14579123C2312yes—
343C4×C22⋊D79C2314yes—
344C4×C22⋊D79C2314yes—
345C4×C22⋊D79C2314yes—
346C4×C22⋊D79C2314yes—
347C4×C22⋊D79C2318yes—
348C4×C22⋊D79C2318yes—
349(C22⋊D79)⋊C4C2318yes—
350(C22⋊D79)⋊C4C2314yes—
351(C22⋊D79)⋊C4C2314yes—
352(C22⋊D79)⋊C4C2318yes—
353(C22⋊D79)⋊C4C2318yes—
354(C22⋊D79)⋊C4C2318yes—
355(C22⋊D79)⋊C4C2318yes—
356(C22⋊D79)⋊C4C2318yes—
357#14579120C2312yes—
358#14579120C2312yes—
359#14579120C2312yes—
360#14579120C2314yes—
361#14579120C2312yes—
362#14579120C2312yes—
363#14579120C2318yes—
364#14579120C2318yes—
365#14579120C2318yes—
366#14579120C2314yes—
367#14579119C2318yes—
368#14579119C2318yes—
369#14579119C2314yes—
370#14579118C2314yes—
371#14579117C2318yes—
372#14579117C2318yes—
373#14579117C2318yes—
374#14579117C2318yes—
375C2×C4⋊Dic79C2311yescharacteristic
376C2×C4⋊Dic79C2311yescharacteristic
377C2×C4⋊Dic79C2312yes—
378C2×C4⋊Dic79C2312yes—
379C2×C4⋊Dic79C2312yes—
380C2×C4⋊Dic79C2311yescharacteristic
381C2×C4⋊Dic79C2314yes—
382C2×C4⋊Dic79C2314yes—
383C2×C4⋊Dic79C2314yes—
384C2×C4⋊Dic79C2314yes—
385C2×C4⋊Dic79C2314yes—
386C2×C4⋊Dic79C2314yes—
387C2×C4⋊Dic79C2314yes—
388C2×C4⋊Dic79C2314yes—
389C2×C4⋊Dic79C2314yes—
390C2×C4⋊Dic79C2311yescharacteristic
391C2×Dic79⋊C4C2314yes—
392C2×Dic79⋊C4C2314yes—
393C2×Dic79⋊C4C2314yes—
394C2×Dic79⋊C4C2314yes—
395C2×Dic79⋊C4C2314yes—
396C2×Dic79⋊C4C2314yes—
397C4⋊C4×D79C2314yes—
398C2×C22⋊Dic79C2311yescharacteristic
399C2×C22⋊Dic79C2311yescharacteristic
400C2×C22⋊Dic79C2314yes—
401C2×C22⋊Dic79C2312yes—
402C2×C22⋊Dic79C2314yes—
403C2×C22⋊Dic79C2318yes—
404C2×C22⋊Dic79C2314yes—
405C2×C22⋊Dic79C2312yes—
406C2×(C2×D79)⋊C4C2314yes—
407C2×(C2×D79)⋊C4C2314yes—
408C2×(C2×D79)⋊C4C2314yes—
409C2×(C2×D79)⋊C4C2314yes—
410C22⋊C4×D79C2318yes—
411C2×C4×Dic79C2311yescharacteristic
412C2×C4×Dic79C2311yescharacteristic
413C2×C4×Dic79C2312yes—
414C2×C4×Dic79C2312yes—
415C2×C4×Dic79C2314yes—
416C2×C4×Dic79C2314yes—
417C2×C4×Dic79C2314yes—
418C42×D79C2314yes—
419H(5,𝔽2)×C79—28no—
420C2×#41×C79—28no—
421C2×#41×C79C2312yes—
422C2×#41×C79C2314yes—
423C2×#41×C79C2314yes—
424C2×#41×C79C2314yes—
425C22×Q8×C79C2311yescharacteristic
426C22×D4×C79C2314yes—
427C22×D4×C79C2314yes—
428C22×D4×C79C2312yes—
429C22×D4×C79C2311yescharacteristic
430C23×C4×C79C2312yes—
431C23×C4×C79C2311yescharacteristic
432C4⋊Q8×C79C2314yes—
433#124×C79C2314yes—
434#123×C79C2314yes—
435#123×C79C2318yes—
436#123×C79C2318yes—
437#123×C79C2318yes—
438#123×C79C2318yes—
439C22⋊Q8×C79C2312yes—
440C22⋊Q8×C79C2312yes—
441C22⋊Q8×C79C2314yes—
442C22⋊Q8×C79C2314yes—
443#121×C79C2318yes—
444#121×C79C2318yes—
445#121×C79C2312yes—
446#121×C79C2312yes—
447#120×C79C2314yes—
448#120×C79C2318yes—
449C4×D4×C79C2314yes—
450C4×D4×C79C2314yes—
451C4×D4×C79C2314yes—
452C4×D4×C79C2314yes—
453#117×C79C2312yes—
454C2×C4⋊C4×C79C2314yes—
455C2×C4⋊C4×C79C2314yes—
456C2×C22⋊C4×C79C2314yes—
457C2×C22⋊C4×C79C2314yes—
458C2×C22⋊C4×C79C2314yes—
459C23×D79C2414yes—
460#11929624—28no—
461#11929623—216no—
462#11929623—88no—
463C2×Dic158—84no—
464C2×Dic158C2412yes—
465C2×Dic158C2414yes—
466C2×Dic158C2418yes—
467C2×Dic158C2414yes—
468C2×D316C2412yes—
469C2×C22⋊D79—216no—
470C2×C22⋊D79—84no—
471C2×C22⋊D79C2418yes—
472C2×C22⋊D79C2414yes—
473C2×C22⋊D79C2414yes—
474C2×C22⋊D79C2418yes—
475C2×C22⋊D79C2414yes—
476C2×C22⋊D79C2414yes—
477C2×C22⋊D79C2414yes—
478D4×D79—216no—
479C22×Dic79—82no—
480C22×Dic79—82no—
481C22×Dic79—82no—
482C22×Dic79—84no—
483C22×Dic79C2414yes—
484C22×Dic79C2414yes—
485C22×Dic79C2414yes—
486C22×Dic79C2418yes—
487C22×Dic79C2418yes—
488C22×Dic79C2411yescharacteristic
489C22×Dic79C2411yescharacteristic
490C22×Dic79C2414yes—
491C22×Dic79C2414yes—
492C22×Dic79C2414yes—
493C22×Dic79C2411yescharacteristic
494C22×Dic79C2412yes—
495C22×Dic79C2414yes—
496C22×Dic79C2411yescharacteristic
497C22×Dic79C2412yes—
498C22×Dic79C2414yes—
499C22×Dic79C2414yes—
500C2×C4×D79—84no—
501C2×C4×D79C2414yes—
502C2×C4×D79C2418yes—
503C2×C4×D79C2414yes—
504C2×C4×D79C2414yes—
505C4⋊Dic79C2414yes—
506C4⋊Dic79C2411yescharacteristic
507C4⋊Dic79C2414yes—
508C4⋊Dic79C2411yescharacteristic
509C4⋊Dic79C2414yes—
510C4⋊Dic79C2411yescharacteristic
511C4⋊Dic79C2411yescharacteristic
512C4⋊Dic79C2414yes—
513C4⋊Dic79C2414yes—
514C4⋊Dic79C2414yes—
515C4⋊Dic79C2414yes—
516C4⋊Dic79C2414yes—
517C4⋊Dic79C2412yes—
518C4⋊Dic79C2418yes—
519C4⋊Dic79C2414yes—
520C4⋊Dic79C2414yes—
521C4⋊Dic79C2418yes—
522C4⋊Dic79C2412yes—
523C4⋊Dic79C2412yes—
524C4⋊Dic79C2414yes—
525C4⋊Dic79C2412yes—
526C4⋊Dic79C2414yes—
527Dic79⋊C4C2418yes—
528Dic79⋊C4C2414yes—
529Dic79⋊C4C2414yes—
530Dic79⋊C4C2414yes—
531Dic79⋊C4C2414yes—
532Dic79⋊C4C2414yes—
533Dic79⋊C4C2414yes—
534Dic79⋊C4C2418yes—
535Dic79⋊C4C2418yes—
536Dic79⋊C4C2418yes—
537Dic79⋊C4C2418yes—
538Dic79⋊C4C2418yes—
539Dic79⋊C4C2414yes—
540Dic79⋊C4C2414yes—
541Dic79⋊C4C2414yes—
542Dic79⋊C4C2414yes—
543C22⋊Dic79C2418yes—
544C22⋊Dic79C2418yes—
545C22⋊Dic79C2414yes—
546C22⋊Dic79C2414yes—
547C22⋊Dic79C2414yes—
548C22⋊Dic79C2418yes—
549C22⋊Dic79C2414yes—
550C22⋊Dic79C2418yes—
551C22⋊Dic79C2418yes—
552C22⋊Dic79C2412yes—
553C22⋊Dic79C2412yes—
554C22⋊Dic79C2412yes—
555C22⋊Dic79C2412yes—
556C22⋊Dic79C2414yes—
557C22⋊Dic79C2414yes—
558C22⋊Dic79C2414yes—
559(C2×D79)⋊C4C2414yes—
560(C2×D79)⋊C4C2418yes—
561(C2×D79)⋊C4C2414yes—
562(C2×D79)⋊C4C2414yes—
563(C2×D79)⋊C4C2414yes—
564(C2×D79)⋊C4C2414yes—
565(C2×D79)⋊C4C2418yes—
566(C2×D79)⋊C4C2418yes—
567(C2×D79)⋊C4C2418yes—
568(C2×D79)⋊C4C2414yes—
569C4×Dic79C2412yes—
570C4×Dic79C2414yes—
571C4×Dic79C2414yes—
572C4×Dic79C2412yes—
573C4×Dic79C2414yes—
574C4×Dic79C2418yes—
575C4×Dic79C2418yes—
576C4×Dic79C2418yes—
577C4×Dic79C2418yes—
578C4×Dic79C2414yes—
579C4×Dic79C2414yes—
580C4×Dic79C2412yes—
581C4×Dic79C2412yes—
582C24×C79C2414yes—
583C24×C79C2411yescharacteristic
584C24×C79C2412yes—
585#41×C79—216no—
586#41×C79—216no—
587#41×C79—216no—
588#41×C79—28no—
589C2×Q8×C79—24no—
590C2×Q8×C79C2414yes—
591C2×Q8×C79C2412yes—
592C2×D4×C79—28no—
593C2×D4×C79—216no—
594C2×D4×C79—216no—
595C2×D4×C79#4118yescomplemented
596C2×D4×C79C2418yes—
597C2×D4×C79C2414yes—
598C2×D4×C79C2418yes—
599C2×D4×C79C2412yes—
600C2×D4×C79C2414yes—
601C2×D4×C79C2414yes—
602C2×D4×C79C2414yes—
603C22×C4×C79—28no—
604C22×C4×C79—24no—
605C22×C4×C79C2414yes—
606C22×C4×C79C2414yes—
607C22×C4×C79C2414yes—
608C22×C4×C79C2412yes—
609C22×C4×C79C2412yes—
610C22×C4×C79C2414yes—
611C22×C4×C79C2411yescharacteristic
612C22×C4×C79C2412yes—
613C22×C4×C79C2414yes—
614C22×C4×C79C2414yes—
615C22×C4×C79C2411yescharacteristic
616C4⋊C4×C79C2414yes—
617C4⋊C4×C79C2414yes—
618C4⋊C4×C79C2418yes—
619C4⋊C4×C79C2418yes—
620C4⋊C4×C79C2412yes—
621C4⋊C4×C79C2412yes—
622C22⋊C4×C79C2414yes—
623C22⋊C4×C79C2414yes—
624C22⋊C4×C79C2414yes—
625C22⋊C4×C79C2418yes—
626C22⋊C4×C79C2418yes—
627C22⋊C4×C79C2418yes—
628C22⋊C4×C79C2414yes—
629C22⋊C4×C79C2414yes—
630C42×C79C2414yes—
631C23×C79—22no—
632C23×C79—28no—
633C23×C79—42no—
634C23×C79—41no—
635C23×C79—42no—
636C23×C79—41no—
637C23×C79—44no—
638C23×C79—44no—
639C23×C79C2×#4118yes—
640C23×C79C2514yes—
641C23×C79C2512yes—
642C23×C79C2514yes—
643C23×C79C2511yescharacteristic
644C22×D79—28no—
645C22×D79—44no—
646C22×D79—44no—
647C22×D79C2514yes—
648Q8×C79—28no—
649Q8×C79—24no—
650D4×C79—28no—
651D4×C79—216no—
652D4×C79—216no—
653D4×C79—24no—
654D4×C79—44no—
655D4×C79—44no—
656D4×C79C2×#41116yes—
657C2×C4×C79—22no—
658C2×C4×C79—24no—
659C2×C4×C79—28no—
660C2×C4×C79—28no—
661C2×C4×C79—28no—
662C2×C4×C79—24no—
663C2×C4×C79—24no—
664C2×C4×C79—28no—
665C2×C4×C79—44no—
666C2×C4×C79—44no—
667C2×C4×C79C2×#4114yes—
668C2×C4×C79C2514yes—
669C2×C4×C79C2514yes—
670C2×C4×C79C2514yes—
671C2×C4×C79C2514yes—
672C2×C4×C79C2511yescharacteristic
673C2×C4×C79C2511yescharacteristic
674C2×C4×C79C2512yes—
675C22⋊D79—216no—
676C22⋊D79—28no—
677C22⋊D79—44no—
678C22⋊D79—48no—
679C22⋊D79—44no—
680C22⋊D79—44no—
681C22⋊D79—44no—
682C2×Dic79—28no—
683C2×Dic79—44no—
684C2×Dic79—41no—
685C2×Dic79—42no—
686C2×Dic79—44no—
687C2×Dic79—41no—
688C2×Dic79—42no—
689C2×Dic79—44no—
690C2×Dic79—44no—
691C2×Dic79—44no—
692C2×Dic79—44no—
693C2×Dic79—48no—
694C2×Dic79—48no—
695C2×Dic79—41no—
696C2×Dic79—44no—
697C2×Dic79—44no—
698C2×Dic79—41no—
699C2×Dic79C2512yes—
700C2×Dic79C2511yescharacteristic
701C2×Dic79C2512yes—
702C2×Dic79C2514yes—
703C2×Dic79C2511yescharacteristic
704C2×Dic79C2514yes—
705C2×Dic79C2514yes—
706C2×Dic79C2511yescharacteristic
707C2×Dic79C2514yes—
708C2×Dic79C2514yes—
709C2×Dic79C2511yescharacteristic
710D316—24no—
711C4×D79—28no—
712C4×D79—44no—
713C4×D79—48no—
714C4×D79—44no—
715Dic158—24no—
716Dic158—44no—
717Dic158—48no—
718Dic158—44no—
719C22×C79—24no—
720C22×C79—21no—
721C22×C79—24no—
722C22×C79—21no—
723C22×C79—22no—
724C22×C79—24no—
725C22×C79—24no—
726C22×C79—22no—
727C22×C79—22no—
728C22×C79—24no—
729C22×C79—48no—
730C22×C79—44no—
731C22×C79—88no—
732C22×C79C22×#4112yes—
733C22×C79C22×#4118yes—
734C22×C79C2611yescharacteristic
735C2×D79—24no—
736C2×D79—24no—
737C2×D79—24no—
738C2×D79—88no—
739C4×C79—21no—
740C4×C79—21no—
741C4×C79—24no—
742C4×C79—24no—
743C4×C79—24no—
744C4×C79—24no—
745C4×C79C22×#4114yes—
746Dic79—24no—
747Dic79—21no—
748Dic79—24no—
749Dic79—24no—
750Dic79—21no—
751Dic79—21no—
752Dic79—24no—
753Dic79—21no—
754Dic79—22no—
755Dic79—24no—
756Dic79—22no—
757#62847—791nomaximal, Sylow
758C2×C79—28no—
759C2×C79—22no—
760C2×C79—42no—
761C2×C79—44no—
762C2×C79C23×#4111yescharacteristic
763C2×C79H(7,𝔽2)11yescharacteristic
764C2×C792−1+611yescharacteristic
765D79—44no—
766#3521—794no—
767#3521—794no—
768#3520—794no—
769#3520—794no—
770#3515—794no—
771#3515—794no—
772#3513—794no—
773#3513—794no—
774#3507—792no—
775#3505—794no—
776#3501—791no—
777#3496—791no—
778#3492—792no—
779#3491—794no—
780#3485—791no—
781#3485D7911yescharacteristic, complemented
782#3461—792no—
783#3459—794no—
784#3455—792no—
785C2×#539—794no—
786C4×H(5,𝔽2)—791no—
787C4×H(5,𝔽2)—791no—
788C2×#520—791no—
789C79#6284711yescharacteristic, complemented, Sylow
790C2×H(5,𝔽2)—791no—
791C2×H(5,𝔽2)C2×D7911yescharacteristic
792C22×#41C2×D7911yescharacteristic
793#559—794no—
794#557—794no—
795#556—794no—
796#556—794no—
797#556—794no—
798#554—794no—
799#554—794no—
800#554—794no—
801#554—794no—
802#554—794no—
803#554—794no—
804#553—798no—
805#553—798no—
806#553—794no—
807#553—798no—
808#553—794no—
809#552—798no—
810#552—798no—
811#552—798no—
812#552—794no—
813#552—794no—
814#552—794no—
815#552—794no—
816#552—798no—
817#552—798no—
818#551—798no—
819#551—798no—
820#551—798no—
821#551—798no—
822#551—798no—
823#551—798no—
824D4×Q8—794no—
825#548—798no—
826#547—794no—
827#547—794no—
828#547—794no—
829#547—794no—
830#547—794no—
831#547C2×D7914yescomplemented
832#547C2×D7914yescomplemented
833#546—794no—
834#546—794no—
835#546—794no—
836#546—794no—
837#546—798no—
838#546C2×D7914yescomplemented
839#546C2×D7914yescomplemented
840D42—794no—
841#544—792no—
842#543—794no—
843#542—794no—
844#542—792no—
845#542—792no—
846#542—794no—
847#542—792no—
848#542—792no—
849#541—794no—
850#541—792no—
851#541—792no—
852#541—794no—
853#540—792no—
854#540—792no—
855#539—794no—
856#539—798no—
857#539—798no—
858#539—798no—
859#539—798no—
860#539—798no—
861#539—798no—
862#539—798no—
863#539—794no—
864#539—798no—
865#539—798no—
866#538—798no—
867#538—794no—
868#538—794no—
869#538—798no—
870#537—792no—
871#536—792no—
872#536C2×D7912yescomplemented
873#534—794no—
874#534—794no—
875#534C2×D7914yescomplemented
876#533—794no—
877#533—794no—
878#533—792no—
879#532—792no—
880#529—794no—
881#529—798no—
882#529—798no—
883#529—798no—
884#529—794no—
885#529—798no—
886#529—794no—
887#529—794no—
888#529—794no—
889#529—794no—
890C2×#126—794no—
891C2×#126—794no—
892C2×#125—794no—
893C2×#125—794no—
894#525—792no—
895#525—798no—
896#525—798no—
897#525—798no—
898#525C2×D7912yescomplemented
899C2×#123—794no—
900C2×#123—794no—
901C2×#123—794no—
902C2×#123C2×D7914yescomplemented
903C2×C22⋊Q8—794no—
904C2×C22⋊Q8—794no—
905C2×C22⋊Q8—794no—
906C2×#121—794no—
907#520—794no—
908#520—794no—
909#520—794no—
910#520—794no—
911#520—792no—
912#520—794no—
913#520—794no—
914#520—792no—
915#518—791no—
916#518—794no—
917#518—794no—
918#518—794no—
919#518—794no—
920#518C2×D7911yescharacteristic
921C4×#41—792no—
922C4×#41—794no—
923C4×#41—794no—
924C4×#41—792no—
925C2×C4×Q8—791no—
926C2×C4×Q8—791no—
927C2×C4×D4—791no—
928C2×C4×D4—792no—
929C2×C4×D4—791no—
930C2×C4×D4—792no—
931C2×C4×D4—794no—
932C2×C4×D4—794no—
933C2×C4×D4—794no—
934C2×C4×D4—794no—
935C2×#117—791no—
936C2×#117—792no—
937C22×C4⋊C4—792no—
938C22×C4⋊C4—791no—
939H(5,𝔽2)—28no—
940H(5,𝔽2)—1588no—
941C2×#41—28no—
942C2×#41—798no—
943C2×#41—794no—
944C2×#41—792no—
945C2×#41C22×D7912yes—
946C2×#41C22×D7914yes—
947C2×#41C22×D7914yes—
948C2×#41C22×D7914yes—
949C22×Q8—794no—
950C22×Q8C22×D7911yescharacteristic
951C22×D4—794no—
952C22×D4—794no—
953C22×D4—794no—
954C22×D4C22×D7912yes—
955C22×D4C22×D7914yes—
956C22×D4C22×D7914yes—
957C22×D4C22×D7911yescharacteristic
958C23×C4—792no—
959C23×C4—792no—
960C23×C4—792no—
961C23×C4—794no—
962C23×C4—794no—
963C23×C4C22×D7912yes—
964C23×C4C22×D7911yescharacteristic
965C4⋊Q8—792no—
966C4⋊Q8—794no—
967C4⋊Q8—792no—
968C4⋊Q8—792no—
969C4⋊Q8—794no—
970C4⋊Q8—794no—
971C4⋊Q8C22×D7914yes—
972#127—792no—
973#126—794no—
974#126—798no—
975#126—798no—
976#126—798no—
977#126—798no—
978#126—794no—
979#126—798no—
980#126—794no—
981#126—798no—
982#126—798no—
983#126—798no—
984#126—794no—
985#126—794no—
986#126—798no—
987#126—794no—
988#126—794no—
989#126—794no—
990#126—798no—
991#125—794no—
992#125—794no—
993#125—798no—
994#125—798no—
995#125—798no—
996#125—798no—
997#125—798no—
998#125—798no—
999#125—798no—
1000#125—794no—
1001#125—794no—
1002#125—798no—
1003#125—794no—
1004#125—792no—
1005#125—792no—
1006#125—794no—
1007#124—794no—
1008#124—792no—
1009#124—794no—
1010#124—794no—
1011#124—792no—
1012#124—794no—
1013#124—798no—
1014#124—794no—
1015#124—798no—
1016#124C22×D7914yes—
1017#123—794no—
1018#123—798no—
1019#123—798no—
1020#123—798no—
1021#123—794no—
1022#123—794no—
1023#123—798no—
1024#123—798no—
1025#123—798no—
1026#123—798no—
1027#123—794no—
1028#123—794no—
1029#123—798no—
1030#123—798no—
1031#123—798no—
1032#123—798no—
1033#123—798no—
1034#123—798no—
1035#123—794no—
1036#123—798no—
1037#123—794no—
1038#123—794no—
1039#123—794no—
1040#123C22×D7914yes—
1041#123C22×D7918yes—
1042#123C22×D7918yes—
1043#123C22×D7918yes—
1044#123C22×D7918yes—
1045C22⋊Q8—794no—
1046C22⋊Q8—794no—
1047C22⋊Q8—794no—
1048C22⋊Q8—798no—
1049C22⋊Q8—792no—
1050C22⋊Q8—792no—
1051C22⋊Q8—798no—
1052C22⋊Q8—794no—
1053C22⋊Q8—794no—
1054C22⋊Q8—798no—
1055C22⋊Q8—798no—
1056C22⋊Q8—798no—
1057C22⋊Q8—794no—
1058C22⋊Q8—794no—
1059C22⋊Q8—794no—
1060C22⋊Q8—798no—
1061C22⋊Q8—798no—
1062C22⋊Q8—798no—
1063C22⋊Q8—798no—
1064C22⋊Q8—798no—
1065C22⋊Q8—798no—
1066C22⋊Q8—798no—
1067C22⋊Q8—798no—
1068C22⋊Q8—794no—
1069C22⋊Q8—798no—
1070C22⋊Q8—794no—
1071C22⋊Q8C22×D7912yes—
1072C22⋊Q8C22×D7912yes—
1073C22⋊Q8C22×D7914yes—
1074C22⋊Q8C22×D7914yes—
1075#121—794no—
1076#121—798no—
1077#121—798no—
1078#121—798no—
1079#121—794no—
1080#121—794no—
1081#121—798no—
1082#121—798no—
1083#121—794no—
1084#121—798no—
1085#121—794no—
1086#121—794no—
1087#121—794no—
1088#121—792no—
1089#121—792no—
1090#121—794no—
1091#121C22×D7918yes—
1092#121C22×D7912yes—
1093#121C22×D7912yes—
1094#121C22×D7918yes—
1095#120—794no—
1096#120—798no—
1097#120—798no—
1098#120—798no—
1099#120C22×D7914yes—
1100#120C22×D7918yes—
1101C4×Q8—794no—
1102C4×Q8—794no—
1103C4×Q8—794no—
1104C4×Q8—794no—
1105C4×Q8—792no—
1106C4×Q8—792no—
1107C4×Q8—794no—
1108C4×Q8—792no—
1109C4×Q8—792no—
1110C4×Q8—798no—
1111C4×Q8—798no—
1112C4×Q8—794no—
1113C4×Q8—794no—
1114C4×Q8—794no—
1115C4×D4—794no—
1116C4×D4—794no—
1117C4×D4—798no—
1118C4×D4—794no—
1119C4×D4—792no—
1120C4×D4—798no—
1121C4×D4—798no—
1122C4×D4—794no—
1123C4×D4—794no—
1124C4×D4—798no—
1125C4×D4—798no—
1126C4×D4—798no—
1127C4×D4—794no—
1128C4×D4—794no—
1129C4×D4—798no—
1130C4×D4—798no—
1131C4×D4—794no—
1132C4×D4—792no—
1133C4×D4—794no—
1134C4×D4—798no—
1135C4×D4—798no—
1136C4×D4—798no—
1137C4×D4—798no—
1138C4×D4—794no—
1139C4×D4—794no—
1140C4×D4—794no—
1141C4×D4—794no—
1142C4×D4—792no—
1143C4×D4—792no—
1144C4×D4—798no—
1145C4×D4—794no—
1146C4×D4—798no—
1147C4×D4—798no—
1148C4×D4—794no—
1149C4×D4—798no—
1150C4×D4—798no—
1151C4×D4—798no—
1152C4×D4—794no—
1153C4×D4C22×D7914yes—
1154C4×D4C22×D7914yes—
1155C4×D4C22×D7914yes—
1156C4×D4C22×D7914yes—
1157#117—792no—
1158#117—792no—
1159#117—792no—
1160#117—792no—
1161#117—798no—
1162#117—798no—
1163#117—792no—
1164#117—794no—
1165#117—798no—
1166#117—794no—
1167#117—794no—
1168#117—798no—
1169#117—798no—
1170#117—798no—
1171#117—798no—
1172#117—798no—
1173#117—798no—
1174#117—794no—
1175#117C22×D7912yes—
1176C2×C4⋊C4—791no—
1177C2×C4⋊C4—792no—
1178C2×C4⋊C4—791no—
1179C2×C4⋊C4—791no—
1180C2×C4⋊C4—792no—
1181C2×C4⋊C4—792no—
1182C2×C4⋊C4—794no—
1183C2×C4⋊C4—794no—
1184C2×C4⋊C4—794no—
1185C2×C4⋊C4—794no—
1186C2×C4⋊C4—794no—
1187C2×C4⋊C4—794no—
1188C2×C4⋊C4—791no—
1189C2×C4⋊C4—794no—
1190C2×C4⋊C4—794no—
1191C2×C4⋊C4—794no—
1192C2×C4⋊C4—794no—
1193C2×C4⋊C4—794no—
1194C2×C4⋊C4—794no—
1195C2×C4⋊C4—794no—
1196C2×C4⋊C4—794no—
1197C2×C4⋊C4—794no—
1198C2×C4⋊C4—794no—
1199C2×C4⋊C4C22×D7914yes—
1200C2×C4⋊C4C22×D7914yes—
1201C2×C22⋊C4—792no—
1202C2×C22⋊C4—792no—
1203C2×C22⋊C4—791no—
1204C2×C22⋊C4—791no—
1205C2×C22⋊C4—794no—
1206C2×C22⋊C4—794no—
1207C2×C22⋊C4—798no—
1208C2×C22⋊C4—794no—
1209C2×C22⋊C4—794no—
1210C2×C22⋊C4—794no—
1211C2×C22⋊C4—794no—
1212C2×C22⋊C4—794no—
1213C2×C22⋊C4—798no—
1214C2×C22⋊C4C22×D7914yes—
1215C2×C22⋊C4C22×D7914yes—
1216C2×C22⋊C4C22×D7914yes—
1217C2×C42—791no—
1218C2×C42—792no—
1219C2×C42—792no—
1220C2×C42—791no—
1221C2×C42—794no—
1222C2×C42—794no—
1223C2×C42—794no—
1224C2×C42—794no—
1225C24—794no—
1226C24C23×D7914yes—
1227C24C23×D7911yescharacteristic
1228C24C23×D7912yes—
1229#41—216no—
1230#41—216no—
1231#41—216no—
1232#41—28no—
1233#41—6328no—
1234#41—15816no—
1235#41—1588no—
1236C2×Q8—24no—
1237C2×Q8—794no—
1238C2×Q8—794no—
1239C2×Q8—798no—
1240C2×Q8—792no—
1241C2×Q8—6324no—
1242C2×Q8C23×D7914yes—
1243C2×Q8C23×D7912yes—
1244C2×D4—28no—
1245C2×D4—216no—
1246C2×D4—216no—
1247C2×D4—794no—
1248C2×D4—794no—
1249C2×D4—794no—
1250C2×D4—798no—
1251C2×D4—794no—
1252C2×D4—798no—
1253C2×D4—794no—
1254C2×D4—792no—
1255C2×D4—6324no—
1256C2×D4—15816no—
1257C2×D4—15816no—
1258C2×D4#1192962318yescomplemented
1259C2×D4C23×D7918yes—
1260C2×D4C23×D7918yes—
1261C2×D4C23×D7914yes—
1262C2×D4C23×D7912yes—
1263C2×D4C23×D7914yes—
1264C2×D4C23×D7914yes—
1265C2×D4C23×D7914yes—
1266C22×C4—28no—
1267C22×C4—24no—
1268C22×C4—791no—
1269C22×C4—791no—
1270C22×C4—794no—
1271C22×C4—794no—
1272C22×C4—794no—
1273C22×C4—794no—
1274C22×C4—791no—
1275C22×C4—792no—
1276C22×C4—791no—
1277C22×C4—792no—
1278C22×C4—794no—
1279C22×C4—794no—
1280C22×C4—794no—
1281C22×C4—798no—
1282C22×C4—794no—
1283C22×C4—798no—
1284C22×C4—794no—
1285C22×C4—794no—
1286C22×C4—798no—
1287C22×C4—794no—
1288C22×C4—794no—
1289C22×C4—6324no—
1290C22×C4—6322no—
1291C22×C4—6324no—
1292C22×C4—6322no—
1293C22×C4—6322no—
1294C22×C4C23×D7912yes—
1295C22×C4C23×D7914yes—
1296C22×C4C23×D7914yes—
1297C22×C4C23×D7914yes—
1298C22×C4C23×D7914yes—
1299C22×C4C23×D7911yescharacteristic
1300C22×C4C23×D7912yes—
1301C22×C4C23×D7912yes—
1302C22×C4C23×D7914yes—
1303C22×C4C23×D7914yes—
1304C22×C4C23×D7911yescharacteristic
1305C4⋊C4—798no—
1306C4⋊C4—794no—
1307C4⋊C4—794no—
1308C4⋊C4—794no—
1309C4⋊C4—794no—
1310C4⋊C4—794no—
1311C4⋊C4—794no—
1312C4⋊C4—798no—
1313C4⋊C4—798no—
1314C4⋊C4—798no—
1315C4⋊C4—798no—
1316C4⋊C4—798no—
1317C4⋊C4—794no—
1318C4⋊C4—794no—
1319C4⋊C4—794no—
1320C4⋊C4—794no—
1321C4⋊C4—794no—
1322C4⋊C4—791no—
1323C4⋊C4—791no—
1324C4⋊C4—794no—
1325C4⋊C4—794no—
1326C4⋊C4—791no—
1327C4⋊C4—791no—
1328C4⋊C4—794no—
1329C4⋊C4—794no—
1330C4⋊C4—794no—
1331C4⋊C4—794no—
1332C4⋊C4—794no—
1333C4⋊C4—792no—
1334C4⋊C4—798no—
1335C4⋊C4—794no—
1336C4⋊C4—794no—
1337C4⋊C4—792no—
1338C4⋊C4—792no—
1339C4⋊C4—798no—
1340C4⋊C4—792no—
1341C4⋊C4—794no—
1342C4⋊C4—794no—
1343C4⋊C4C23×D7912yes—
1344C4⋊C4C23×D7914yes—
1345C4⋊C4C23×D7914yes—
1346C4⋊C4C23×D7918yes—
1347C4⋊C4C23×D7918yes—
1348C4⋊C4C23×D7912yes—
1349C22⋊C4—798no—
1350C22⋊C4—798no—
1351C22⋊C4—794no—
1352C22⋊C4—794no—
1353C22⋊C4—798no—
1354C22⋊C4—794no—
1355C22⋊C4—794no—
1356C22⋊C4—798no—
1357C22⋊C4—792no—
1358C22⋊C4—792no—
1359C22⋊C4—792no—
1360C22⋊C4—792no—
1361C22⋊C4—798no—
1362C22⋊C4—794no—
1363C22⋊C4—794no—
1364C22⋊C4—794no—
1365C22⋊C4—798no—
1366C22⋊C4—794no—
1367C22⋊C4—794no—
1368C22⋊C4—794no—
1369C22⋊C4—794no—
1370C22⋊C4—794no—
1371C22⋊C4—798no—
1372C22⋊C4—798no—
1373C22⋊C4—798no—
1374C22⋊C4—794no—
1375C22⋊C4C23×D7918yes—
1376C22⋊C4C23×D7914yes—
1377C22⋊C4C23×D7914yes—
1378C22⋊C4C23×D7914yes—
1379C22⋊C4C23×D7918yes—
1380C22⋊C4C23×D7918yes—
1381C22⋊C4C23×D7914yes—
1382C22⋊C4C23×D7914yes—
1383C42—792no—
1384C42—792no—
1385C42—794no—
1386C42—794no—
1387C42—798no—
1388C42—798no—
1389C42—794no—
1390C42—794no—
1391C42—798no—
1392C42—798no—
1393C42—794no—
1394C42—792no—
1395C42—792no—
1396C42C23×D7914yes—
1397C23—22no—
1398C23—28no—
1399C23—42no—
1400C23—41no—
1401C23—42no—
1402C23—41no—
1403C23—44no—
1404C23—44no—
1405C23—3164no—
1406C23—3164no—
1407C23—794no—
1408C23—1588no—
1409C23C2×#1192962318yes—
1410C23C24×D7914yes—
1411C23C24×D7912yes—
1412C23C24×D7914yes—
1413C23C24×D7911yescharacteristic
1414Q8—28no—
1415Q8—24no—
1416Q8—3164no—
1417Q8—3168no—
1418Q8—3164no—
1419Q8—1584no—
1420D4—216no—
1421D4—28no—
1422D4—216no—
1423D4—24no—
1424D4—44no—
1425D4—44no—
1426D4—3164no—
1427D4—3164no—
1428D4—3164no—
1429D4—3168no—
1430D4—3164no—
1431D4—15816no—
1432D4—1588no—
1433D4—1584no—
1434D4C2×#11929623116yes—
1435C2×C4—22no—
1436C2×C4—24no—
1437C2×C4—28no—
1438C2×C4—28no—
1439C2×C4—28no—
1440C2×C4—24no—
1441C2×C4—24no—
1442C2×C4—28no—
1443C2×C4—44no—
1444C2×C4—44no—
1445C2×C4—3164no—
1446C2×C4—3168no—
1447C2×C4—3164no—
1448C2×C4—3164no—
1449C2×C4—3164no—
1450C2×C4—3161no—
1451C2×C4—3162no—
1452C2×C4—3164no—
1453C2×C4—3161no—
1454C2×C4—3162no—
1455C2×C4—3164no—
1456C2×C4—3164no—
1457C2×C4—3164no—
1458C2×C4—3168no—
1459C2×C4—3168no—
1460C2×C4—3161no—
1461C2×C4—3164no—
1462C2×C4—3164no—
1463C2×C4—3161no—
1464C2×C4—792no—
1465C2×C4—792no—
1466C2×C4—791no—
1467C2×C4—791no—
1468C2×C4—794no—
1469C2×C4—794no—
1470C2×C4—794no—
1471C2×C4—791no—
1472C2×C4—794no—
1473C2×C4—794no—
1474C2×C4—791no—
1475C2×C4—1588no—
1476C2×C4—1588no—
1477C2×C4C2×#1192962314yes—
1478C2×C4C24×D7914yes—
1479C2×C4C24×D7914yes—
1480C2×C4C24×D7914yes—
1481C2×C4C24×D7914yes—
1482C2×C4C24×D7911yescharacteristic
1483C2×C4C24×D7911yescharacteristic
1484C2×C4C24×D7912yes—
1485C22—24no—
1486C22—21no—
1487C22—24no—
1488C22—21no—
1489C22—22no—
1490C22—24no—
1491C22—22no—
1492C22—24no—
1493C22—24no—
1494C22—22no—
1495C22—48no—
1496C22—44no—
1497C22—88no—
1498C22—6328no—
1499C22—1584no—
1500C22—1584no—
1501C22—1584no—
1502C22C22×#1192962318yes—
1503C22C22×#1192962312yes—
1504C22C25×D7911yescharacteristic
1505C4—21no—
1506C4—21no—
1507C4—24no—
1508C4—24no—
1509C4—24no—
1510C4—24no—
1511C4—1584no—
1512C4—1581no—
1513C4—1584no—
1514C4—1581no—
1515C4—1581no—
1516C4—1584no—
1517C4—1584no—
1518C4—1581no—
1519C4—1582no—
1520C4—1584no—
1521C4—1582no—
1522C4C22×#1192962314yes—
1523C2—22no—
1524C2—28no—
1525C2—42no—
1526C2—44no—
1527C2—3164no—
1528C2C23×#1192962311yescharacteristic
1529C2#2377821111yescharacteristic
1530C2#2377821311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3485C2
hypercenter#3485D79
hypocenterC79#62847
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3485

Complements

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

NH ≅ G/Ntype
1. #23777469C2semidirect
2. #23777457C2semidirect
3. #23777440C2semidirect
4. #23777436C2semidirect
5. #23777369C2semidirect
6. #23777365C2semidirect
7. #23777341C2semidirect
8. #23777329C2semidirect
9. #23777264C2semidirect
10. #23777237C2semidirect
11. #23777198C2semidirect
12. #23777159C2semidirect
13. #23777106C2semidirect
14. #23777096C2semidirect
15. #23777044C2semidirect
16. #23776824C2semidirect
17. #23776806C2semidirect
18. #23776788C2semidirect
19. C2×#19099157C2semidirect
20. H(5,𝔽2)×Dic79C2semidirect
21. #23776604C2semidirect
22. C2×#19099046C2semidirect
23. C79×#3485C2semidirect
25. #19099295C22semidirect
26. #19099288C22semidirect
27. #19099287C22semidirect
28. #19099284C22semidirect
29. #19099282C22semidirect
30. #19099272C22semidirect
31. #19099272C22semidirect
32. #19099271C22semidirect
33. #19099271C22semidirect
34. #19099270C22semidirect
35. #19099270C22semidirect
36. #19099265C22semidirect
37. #19099265C22semidirect
38. #19099259C22semidirect
39. #19099256C22semidirect
40. #19099256C22semidirect
41. #19099255C22semidirect
42. #19099255C22semidirect
43. #19099253C22semidirect
44. #19099250C22semidirect
45. #19099250C22semidirect
46. #19099250C22semidirect
47. #19099248C22semidirect
48. #19099248C22semidirect
49. #19099247C22semidirect
50. #19099244C22semidirect
51. #19099239C22semidirect
52. #19099239C22semidirect
53. #19099236C22semidirect
54. #19099236C22semidirect
55. #19099236C22semidirect
56. D4×Dic158C22semidirect
57. #19099219C22semidirect
58. #19099217C22semidirect
59. #19099213C22semidirect
60. #19099212C22semidirect
61. #19099212C22semidirect
62. #19099212C22semidirect
63. #19099207C22semidirect
64. #19099201C22semidirect
65. #19099201C22semidirect
66. #19099201C22semidirect
67. #19099200C22semidirect
68. D4×C22⋊D79C22semidirect
69. #19099191C22semidirect
70. #19099189C22semidirect
71. #19099186C22semidirect
72. #19099186C22semidirect
73. #19099186C22semidirect
74. #19099182C22semidirect
75. #19099180C22semidirect
76. #19099180C22semidirect
77. #19099174C22semidirect
78. #19099173C22semidirect
79. #19099173C22semidirect
80. #19099173C22semidirect
81. #19099166C22semidirect
82. #19099166C22semidirect
83. #19099158C22semidirect
84. #19099157C22semidirect
85. #19099157C22semidirect
86. #19099157C22semidirect
87. #19099157C22semidirect
88. #19099157C22semidirect
89. #19099157C22semidirect
90. #19099157C22semidirect
91. #19099157C22semidirect
92. #19099157C22semidirect
93. #19099157C22semidirect
94. #19099150C22semidirect
95. #19099148C22semidirect
96. #19099148C22semidirect
97. #19099148C22semidirect
99. #19099137C22semidirect
101. #19099122C22semidirect
102. #19099118C22semidirect
103. #19099116C22semidirect
104. #19099115C22semidirect
106. #19099099C22semidirect
107. #19099095C22semidirect
108. #19099095C22semidirect
109. #19099094C22semidirect
110. #19099093C22semidirect
111. #19099093C22semidirect
112. #19099092C22semidirect
113. #19099090C22semidirect
114. #19099090C22semidirect
115. #19099090C22semidirect
116. C2×#14579156C22semidirect
117. C2×#14579154C22semidirect
118. C2×#14579152C22semidirect
119. C2×#14579151C22semidirect
120. #19099074C22semidirect
121. #19099073C22semidirect
122. #19099069C22semidirect
123. #19099069C22semidirect
124. C2×#14579145C22semidirect
125. C2×#14579144C22semidirect
126. C2×#14579143C22semidirect
127. C2×#14579141C22semidirect
128. C2×#14579138C22semidirect
129. C2×#14579138C22semidirect
131. #19099046C22semidirect
132. #19099046C22semidirect
133. #19099046C22semidirect
134. #19099046C22semidirect
135. #19099046C22semidirect
136. #19099046C22semidirect
137. #19099043C22semidirect
138. #19099042C22semidirect
140. #19099038C22semidirect
141. #19099038C22semidirect
142. #19099036C22semidirect
143. #19099035C22semidirect
144. #41×Dic79C22semidirect
145. #41×Dic79C22semidirect
146. #19099031C22semidirect
147. C4×#11929623C22semidirect
148. C2×Q8×Dic79C22semidirect
149. C2×Q8×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×C4⋊Dic79C22semidirect
161. C22×C4⋊Dic79C22semidirect
164. #547×C79C22semidirect
165. #547×C79C22semidirect
166. #546×C79C22semidirect
167. #546×C79C22semidirect
168. #536×C79C22semidirect
169. #534×C79C22semidirect
170. #525×C79C22semidirect
171. C2×#123×C79C22semidirect
595. C2×D4×C79#41semidirect
781. #3485D79semidirect
789. C79#62847semidirect
831. #547C2×D79semidirect
832. #547C2×D79semidirect
838. #546C2×D79semidirect
839. #546C2×D79semidirect
872. #536C2×D79semidirect
875. #534C2×D79semidirect
898. #525C2×D79semidirect
902. C2×#123C2×D79semidirect
1258. C2×D4#11929623semidirect

Maximal subgroups

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

subgroupindex
#237774692
#237774572
#237774402
#237774362
#237773692
#237773652
#237773412
#237773292
#237772642
#237772372
#237771982
#237771592
#237771062
#237770962
#237770442
#237768242
#237768062
#237767882
C2×#190991572
H(5,𝔽2)×Dic792
#237766042
C2×#190990462
C79×#34852
#6284779