Finite Group Databasebeta

← #35197327

Subgroups — #35197327

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#23777468C214yesmaximal, complemented
2#23777456C214yesmaximal, complemented
3#23777449C214yesmaximal, complemented
4#23777439C214yesmaximal, complemented
5#23777378C214yesmaximal, complemented
6#23777368C214yesmaximal, complemented
7#23777340C214yesmaximal, complemented
8#23777328C214yesmaximal, complemented
9#23777258C212yesmaximal, complemented
10#23777230C214yesmaximal, complemented
11#23777198C211yesmaximal, characteristic, complemented
12#23777159C211yesmaximal, characteristic, complemented
13#23777103C212yesmaximal, complemented
14#23777093C214yesmaximal, complemented
15#23777045C211yesmaximal, characteristic, complemented
16#23777040C211yesmaximal, characteristic, complemented
17#23776827C212yesmaximal, complemented
18#23776809C214yesmaximal, complemented
19#23776785C212yesmaximal, complemented
20C2×#19099155C214yesmaximal, complemented
21C4×#14579206C211yesmaximal, characteristic, complemented
22C2×#19099042C211yesmaximal, characteristic, complemented
23C4×H(5,𝔽2)×C79C211yesmaximal, characteristic, complemented
24C2×#14579206C2211yescharacteristic
25C22×#11929623C2211yescharacteristic
26#19099296C2214yescomplemented
27#19099291C2214yescomplemented
28#19099285C2214yescomplemented
29#19099283C2214yescomplemented
30#19099281C2214yescomplemented
31#19099273C2214yescomplemented
32#19099272C2214yescomplemented
33#19099272C2214yescomplemented
34#19099270C2214yescomplemented
35#19099268C2214yescomplemented
36#19099268C2214yescomplemented
37#19099263C2214yescomplemented
38#19099262C2218yescomplemented
39#19099262C2218yescomplemented
40#19099259C2218yescomplemented
41#19099257C2214yescomplemented
42#19099254C2214yescomplemented
43#19099253C2218yescomplemented
44#19099253C2218yescomplemented
45#19099252C2214yescomplemented
46#19099252C2214yescomplemented
47#19099248C2214yescomplemented
48#19099246C2218yescomplemented
49#19099246C2218yescomplemented
50#19099246C2218yescomplemented
51#19099242C2218yescomplemented
52#19099242C2218yescomplemented
53#19099239C2218yescomplemented
54#19099239C2218yescomplemented
55#19099239C2218yescomplemented
56#19099237C2218yescomplemented
57D4×Dic158C2214yescomplemented
58#19099222C2218yescomplemented
59#19099218C2214yescomplemented
60#19099217C2214yescomplemented
61#19099217C2214yescomplemented
62#19099214C2214yescomplemented
63#19099212C2214yescomplemented
64#19099212C2214yescomplemented
65#19099212C2214yescomplemented
66#19099208C2214yescomplemented
67#19099208C2214yescomplemented
68#19099207C2214yescomplemented
69#19099207C2214yescomplemented
70#19099207C2214yescomplemented
71#19099203C2218yescomplemented
72#19099201C2214yescomplemented
73D4×C22⋊D79C2214yescomplemented
74#19099191C2212yescomplemented
75#19099189C2214yescomplemented
76#19099185C2212yescomplemented
77#19099185C2212yescomplemented
78#19099184C2214yescomplemented
79#19099178C2212yescomplemented
80#19099178C2212yescomplemented
81#19099178C2214yescomplemented
82#19099175C2214yescomplemented
83#19099171C2212yescomplemented
84#19099171C2212yescomplemented
85#19099171C2214yescomplemented
86#19099164C2212yescomplemented
87#19099164C2212yescomplemented
88#19099160C2218yescomplemented
89#19099155C2214yescomplemented
90#19099155C2214yescomplemented
91#19099155C2218yescomplemented
92#19099155C2218yescomplemented
93#19099155C2218yescomplemented
94#19099155C2218yescomplemented
95#19099155C2218yescomplemented
96#19099155C2218yescomplemented
97#19099155C2218yescomplemented
98#19099155C2218yescomplemented
99#19099151C2218yescomplemented
100#19099146C2214yescomplemented
101#19099146C2214yescomplemented
102#19099146C2218yescomplemented
103#19099141C2212yes—
104#19099139C2212yescomplemented
105#19099134C2212yescomplemented
106#19099125C2214yescomplemented
107#19099122C2214yes—
108#19099122C2214yescomplemented
109#19099120C2214yescomplemented
110#19099117C2214yescomplemented
111#19099116C2212yescomplemented
112#19099109C2212yes—
113#19099097C2214yescomplemented
114#19099097C2214yescomplemented
115#19099097C2218yescomplemented
116#19099097C2214yescomplemented
117#19099095C2214yescomplemented
118#19099093C2218yescomplemented
119#19099093C2218yescomplemented
120#19099093C2218yescomplemented
121#19099091C2214yescomplemented
122#19099091C2214yescomplemented
123C2×#14579155C2214yescomplemented
124C2×#14579154C2214yescomplemented
125C2×#14579153C2214yescomplemented
126C2×#14579151C2214yescomplemented
127#19099075C2212yescomplemented
128#19099074C2218yescomplemented
129#19099072C2218yescomplemented
130#19099072C2218yescomplemented
131#19099070C2212yescomplemented
132C2×#14579145C2214yescomplemented
133C2×#14579144C2214yescomplemented
134C2×#14579143C2214yescomplemented
135C2×#14579142C2214yescomplemented
136C2×#14579140C2214yescomplemented
137C2×#14579139C2214yescomplemented
138C2×#14579138C2214yescomplemented
139C2×#14579133C2214yes—
140#19099044C2212yescomplemented
141#19099042C2214yescomplemented
142#19099042C2214yescomplemented
143#19099042C2214yescomplemented
144#19099042C2214yescomplemented
145#19099042C2214yescomplemented
146#19099038C2211yescharacteristic
147#19099036C2214yescomplemented
148#19099035C2214yescomplemented
149C4×#11929624C2212yescomplemented
150C4×#11929623C2214yescomplemented
151C2×C4×Dic158C2211yescharacteristic, complemented
152C2×#14579126C2211yescharacteristic, complemented
153C2×D4×Dic79C2211yescharacteristic
154C2×C4×C22⋊D79C2212yescomplemented
155C2×C4×C22⋊D79C2214yescomplemented
156C2×(C22⋊D79)⋊C4C2212yescomplemented
157C4×D4×D79C2214yescomplemented
158C2×#14579118C2211yescharacteristic, complemented
159C2×#14579117C2212yescomplemented
160C22×Dic79⋊C4C2212yescomplemented
161C2×C4⋊C4×D79C2211yescharacteristic, complemented
162C2×H(5,𝔽2)×C79C2211yescharacteristic
163#520×C79C2212yescomplemented
164#520×C79C2214yescomplemented
165#518×C79C2211yescharacteristic
166#518×C79C2214yescomplemented
167#518×C79C2214yescomplemented
168C4×#41×C79C2212yescomplemented
169C4×#41×C79C2214yescomplemented
170C2×C4×D4×C79C2211yescharacteristic
171C2×C4×D4×C79C2214yescomplemented
172C2×C4×D4×C79C2214yescomplemented
173#14579206—28no—
174C2×#11929624C2312yes—
175C2×#11929624C2318yes—
176C2×#11929623—28no—
177C2×#11929623C2314yes—
178C2×#11929623C2314yes—
179C2×#11929623C2314yes—
180C22×Dic158C2311yescharacteristic
181C22×Dic158C2314yes—
182C22×C22⋊D79C2314yes—
183C22×C22⋊D79C2312yes—
184C22×C22⋊D79C2314yes—
185C2×D4×D79C2314yes—
186C23×Dic79C2312yes—
187C23×Dic79C2312yes—
188C22×C4×D79C2311yescharacteristic
189C22×C4×D79C2312yes—
190C22×C4×D79C2314yes—
191#14579161C2314yes—
192#14579161C2314yes—
193#14579160C2312yes—
194#14579160C2312yes—
195#14579160C2314yes—
196#14579159C2312yes—
197#14579159C2314yes—
198#14579157C2312yes—
199#14579156C2314yes—
200#14579156C2318yes—
201#14579156C2314yes—
202#14579156C2318yes—
203#14579155C2318yes—
204#14579155C2314yes—
205#14579155C2314yes—
206#14579155C2314yes—
207#14579155C2318yes—
208#14579155C2318yes—
209#14579155C2314yes—
210#14579154C2318yes—
211#14579154C2318yes—
212#14579154C2314yes—
213#14579154C2318yes—
214#14579154C2318yes—
215#14579154C2314yes—
216#14579154C2318yes—
217#14579153C2314yes—
218#14579153C2318yes—
219#14579153C2318yes—
220#14579153C2318yes—
221#14579153C2314yes—
222#14579153C2314yes—
223#14579152C2312yes—
224#14579152C2312yes—
225#14579152C2314yes—
226#14579151C2314yes—
227#14579151C2318yes—
228#14579151C2318yes—
229#14579151C2318yes—
230#14579151C2318yes—
231#14579151C2314yes—
232#14579151C2318yes—
233#14579150C2312yes—
234#14579149C2314yes—
235#14579149C2314yes—
236#14579149C2314yes—
237#14579148C2312yes—
238#14579148C2314yes—
239#14579147C2314yes—
240#14579147C2318yes—
241#14579147C2314yes—
242#14579147C2318yes—
243#14579146C2314yes—
244#14579146C2318yes—
245#14579146C2314yes—
246#14579145C2318yes—
247#14579145C2314yes—
248#14579145C2318yes—
249#14579145C2318yes—
250#14579145C2318yes—
251#14579144C2318yes—
252#14579144C2314yes—
253#14579144C2314yes—
254#14579144C2314yes—
255#14579144C2318yes—
256#14579144C2318yes—
257#14579144C2314yes—
258#14579144C2318yes—
259#14579144C2318yes—
260#14579143C2318yes—
261#14579143C2318yes—
262#14579143C2314yes—
263#14579143C2318yes—
264#14579143C2318yes—
265#14579143C2314yes—
266#14579142C2314yes—
267#14579142C2318yes—
268#14579142C2318yes—
269#14579142C2318yes—
270#14579142C2318yes—
271#14579141C2314yes—
272#14579141C2314yes—
273#14579141C2312yes—
274#14579141C2312yes—
275#14579140C2314yes—
276#14579140C2318yes—
277#14579140C2314yes—
278#14579140C2318yes—
279#14579140C2318yes—
280#14579140C2318yes—
281#14579140C2314yes—
282#14579140C2318yes—
283#14579140C2314yes—
284#14579140C2314yes—
285#14579139C2314yes—
286#14579139C2318yes—
287#14579139C2318yes—
288#14579139C2318yes—
289#14579139C2318yes—
290#14579139C2314yes—
291#14579138C2314yes—
292#14579138C2314yes—
293#14579138C2318yes—
294#14579138C2318yes—
295#14579138C2318yes—
296#14579138C2318yes—
297#14579138C2318yes—
298#14579137C2314yes—
299#14579137C2312yes—
300#14579137C2312yes—
301#14579136C2312yes—
302#14579136C2312yes—
303#14579135C2314yes—
304#14579135C2314yes—
305#14579135C2314yes—
306#14579135C2318yes—
307#14579135C2318yes—
308#14579134C2314yes—
309#14579134C2318yes—
310#14579134C2314yes—
311#14579133C2318yes—
312#14579133C2314yes—
313#14579133C2314yes—
314#14579133C2318yes—
315#14579133C2318yes—
316#14579133C2318yes—
317#14579133C2318yes—
318#14579132C2314yes—
319#14579132C2312yes—
320#14579132C2312yes—
321#14579131C2314yes—
322#14579131C2318yes—
323#14579130C2318yes—
324#14579130C2318yes—
325#14579129C2314yes—
326#14579129C2318yes—
327C4×Dic158C2312yes—
328C4×Dic158C2314yes—
329C4×Dic158C2312yes—
330C4×Dic158C2314yes—
331C4×Dic158C2318yes—
332C4×Dic158C2314yes—
333C4×Dic158C2318yes—
334C4×Dic158C2314yes—
335#14579126C2314yes—
336#14579126C2314yes—
337#14579126C2314yes—
338C4×D316C2312yes—
339C4×D316C2312yes—
340C4×D316C2314yes—
341C4×D316C2314yes—
342C4×D316C2318yes—
343D4×Dic79C2314yes—
344D4×Dic79C2314yes—
345D4×Dic79C2314yes—
346D4×Dic79C2314yes—
347#14579123C2314yes—
348C4×C22⋊D79C2314yes—
349C4×C22⋊D79C2318yes—
350C4×C22⋊D79C2314yes—
351C4×C22⋊D79C2318yes—
352C4×C22⋊D79C2318yes—
353C4×C22⋊D79C2318yes—
354C4×C22⋊D79C2318yes—
355C4×C22⋊D79C2314yes—
356C4×C22⋊D79C2314yes—
357C4×C22⋊D79C2318yes—
358C4×C22⋊D79C2314yes—
359C4×C22⋊D79C2314yes—
360C4×C22⋊D79C2318yes—
361C4×C22⋊D79C2318yes—
362(C22⋊D79)⋊C4C2318yes—
363(C22⋊D79)⋊C4C2318yes—
364(C22⋊D79)⋊C4C2318yes—
365(C22⋊D79)⋊C4C2318yes—
366#14579120C2312yes—
367#14579120C2318yes—
368#14579120C2318yes—
369#14579119C2314yes—
370#14579118C2312yes—
371#14579118C2312yes—
372#14579118C2314yes—
373#14579118C2312yes—
374#14579118C2312yes—
375#14579118C2318yes—
376#14579118C2318yes—
377#14579118C2318yes—
378#14579117C2318yes—
379#14579117C2318yes—
380#14579117C2318yes—
381C2×C4⋊Dic79C2311yescharacteristic
382C2×C4⋊Dic79C2314yes—
383C2×C4⋊Dic79C2314yes—
384C2×C4⋊Dic79C2314yes—
385C2×Dic79⋊C4C2312yes—
386C2×Dic79⋊C4C2311yescharacteristic
387C2×Dic79⋊C4C2312yes—
388C2×Dic79⋊C4C2312yes—
389C2×Dic79⋊C4C2311yescharacteristic
390C2×Dic79⋊C4C2314yes—
391C2×Dic79⋊C4C2314yes—
392C2×Dic79⋊C4C2314yes—
393C2×Dic79⋊C4C2314yes—
394C2×Dic79⋊C4C2314yes—
395C2×Dic79⋊C4C2314yes—
396C2×Dic79⋊C4C2314yes—
397C2×Dic79⋊C4C2314yes—
398C2×Dic79⋊C4C2314yes—
399C2×Dic79⋊C4C2314yes—
400C4⋊C4×D79C2314yes—
401C4⋊C4×D79C2314yes—
402C4⋊C4×D79C2314yes—
403C2×C22⋊Dic79C2312yes—
404C2×C22⋊Dic79C2314yes—
405C2×C22⋊Dic79C2314yes—
406C2×C22⋊Dic79C2314yes—
407C2×C22⋊Dic79C2314yes—
408C2×(C2×D79)⋊C4C2311yescharacteristic
409C2×(C2×D79)⋊C4C2311yescharacteristic
410C2×(C2×D79)⋊C4C2314yes—
411C2×(C2×D79)⋊C4C2314yes—
412C2×(C2×D79)⋊C4C2314yes—
413C2×(C2×D79)⋊C4C2314yes—
414C22⋊C4×D79C2318yes—
415C2×C4×Dic79C2312yes—
416C2×C4×Dic79C2312yes—
417C2×C4×Dic79C2311yescharacteristic
418C2×C4×Dic79C2314yes—
419C42×D79C2314yes—
420H(5,𝔽2)×C79—28no—
421C2×#41×C79C2312yes—
422C2×#41×C79C2314yes—
423C22×D4×C79C2314yes—
424C22×D4×C79C2314yes—
425C22×D4×C79C2311yescharacteristic
426C23×C4×C79C2312yes—
427C23×C4×C79C2314yes—
428C4×Q8×C79C2312yes—
429C4×Q8×C79C2312yes—
430C4×Q8×C79C2314yes—
431C4×D4×C79C2314yes—
432C4×D4×C79C2318yes—
433C4×D4×C79C2314yes—
434C4×D4×C79C2318yes—
435C4×D4×C79C2318yes—
436C4×D4×C79C2312yes—
437C4×D4×C79C2312yes—
438C4×D4×C79C2314yes—
439C4×D4×C79C2314yes—
440C4×D4×C79C2314yes—
441C4×D4×C79C2318yes—
442C4×D4×C79C2314yes—
443C4×D4×C79C2314yes—
444C4×D4×C79C2318yes—
445#117×C79C2312yes—
446#117×C79C2314yes—
447#117×C79C2318yes—
448#117×C79C2314yes—
449C2×C4⋊C4×C79C2314yes—
450C2×C4⋊C4×C79C2314yes—
451C2×C4⋊C4×C79C2311yescharacteristic
452C2×C22⋊C4×C79C2314yes—
453C2×C22⋊C4×C79C2314yes—
454C2×C22⋊C4×C79C2318yes—
455C2×C22⋊C4×C79C2312yes—
456C2×C42×C79C2311yescharacteristic
457C2×C42×C79C2314yes—
458C2×C42×C79C2314yes—
459C23×D79C2414yes—
460C23×D79C2411yescharacteristic
461#11929624—28no—
462#11929624—88no—
463#11929623—216no—
464#11929623—216no—
465#11929623—216no—
466C2×Dic158—24no—
467C2×Dic158—84no—
468C2×Dic158C2414yes—
469C2×Dic158C2412yes—
470C2×Dic158C2414yes—
471C2×Dic158C2418yes—
472C2×Dic158C2414yes—
473C2×D316C2412yes—
474C2×D316C2414yes—
475C2×D316C2414yes—
476C2×C22⋊D79—28no—
477C2×C22⋊D79—216no—
478C2×C22⋊D79—84no—
479C2×C22⋊D79C2418yes—
480C2×C22⋊D79C2418yes—
481C2×C22⋊D79C2414yes—
482C2×C22⋊D79C2414yes—
483C2×C22⋊D79C2418yes—
484C2×C22⋊D79C2414yes—
485C2×C22⋊D79C2414yes—
486C2×C22⋊D79C2414yes—
487D4×D79—216no—
488C22×Dic79—28no—
489C22×Dic79—82no—
490C22×Dic79C2412yes—
491C22×Dic79C2414yes—
492C22×Dic79C2414yes—
493C22×Dic79C2414yes—
494C22×Dic79C2411yescharacteristic
495C22×Dic79C2414yes—
496C22×Dic79C2414yes—
497C22×Dic79C2411yescharacteristic
498C22×Dic79C2414yes—
499C22×Dic79C2411yescharacteristic
500C22×Dic79C2412yes—
501C22×Dic79C2414yes—
502C2×C4×D79—24no—
503C2×C4×D79—82no—
504C2×C4×D79—84no—
505C2×C4×D79C2412yes—
506C2×C4×D79C2412yes—
507C2×C4×D79C2414yes—
508C2×C4×D79C2418yes—
509C2×C4×D79C2418yes—
510C2×C4×D79C2414yes—
511C2×C4×D79C2414yes—
512C4⋊Dic79C2414yes—
513C4⋊Dic79C2412yes—
514C4⋊Dic79C2414yes—
515C4⋊Dic79C2414yes—
516C4⋊Dic79C2414yes—
517C4⋊Dic79C2418yes—
518C4⋊Dic79C2418yes—
519C4⋊Dic79C2418yes—
520C4⋊Dic79C2412yes—
521C4⋊Dic79C2414yes—
522Dic79⋊C4C2414yes—
523Dic79⋊C4C2414yes—
524Dic79⋊C4C2418yes—
525Dic79⋊C4C2411yescharacteristic
526Dic79⋊C4C2411yescharacteristic
527Dic79⋊C4C2411yescharacteristic
528Dic79⋊C4C2411yescharacteristic
529Dic79⋊C4C2414yes—
530Dic79⋊C4C2414yes—
531Dic79⋊C4C2414yes—
532Dic79⋊C4C2414yes—
533Dic79⋊C4C2414yes—
534Dic79⋊C4C2414yes—
535Dic79⋊C4C2414yes—
536Dic79⋊C4C2414yes—
537Dic79⋊C4C2414yes—
538Dic79⋊C4C2414yes—
539Dic79⋊C4C2412yes—
540Dic79⋊C4C2412yes—
541Dic79⋊C4C2418yes—
542Dic79⋊C4C2418yes—
543Dic79⋊C4C2418yes—
544Dic79⋊C4C2418yes—
545Dic79⋊C4C2418yes—
546Dic79⋊C4C2414yes—
547Dic79⋊C4C2414yes—
548Dic79⋊C4C2414yes—
549Dic79⋊C4C2414yes—
550C22⋊Dic79C2418yes—
551C22⋊Dic79C2414yes—
552C22⋊Dic79C2414yes—
553C22⋊Dic79C2414yes—
554C22⋊Dic79C2414yes—
555C22⋊Dic79C2418yes—
556C22⋊Dic79C2418yes—
557C22⋊Dic79C2418yes—
558C22⋊Dic79C2418yes—
559C22⋊Dic79C2414yes—
560(C2×D79)⋊C4C2414yes—
561(C2×D79)⋊C4C2418yes—
562(C2×D79)⋊C4C2414yes—
563(C2×D79)⋊C4C2414yes—
564(C2×D79)⋊C4C2414yes—
565(C2×D79)⋊C4C2414yes—
566(C2×D79)⋊C4C2412yes—
567(C2×D79)⋊C4C2412yes—
568(C2×D79)⋊C4C2412yes—
569(C2×D79)⋊C4C2412yes—
570(C2×D79)⋊C4C2418yes—
571(C2×D79)⋊C4C2418yes—
572(C2×D79)⋊C4C2418yes—
573(C2×D79)⋊C4C2414yes—
574(C2×D79)⋊C4C2414yes—
575(C2×D79)⋊C4C2414yes—
576(C2×D79)⋊C4C2414yes—
577(C2×D79)⋊C4C2414yes—
578C4×Dic79C2414yes—
579C4×Dic79C2414yes—
580C4×Dic79C2414yes—
581C4×Dic79C2418yes—
582C4×Dic79C2418yes—
583C4×Dic79C2418yes—
584C4×Dic79C2412yes—
585C4×Dic79C2412yes—
586C24×C79C2414yes—
587C24×C79C2412yes—
588#41×C79—216no—
589#41×C79—28no—
590C2×Q8×C79C2412yes—
591C2×D4×C79—216no—
592C2×D4×C79—216no—
593C2×D4×C79#4118yescomplemented
594C2×D4×C79C2414yes—
595C2×D4×C79C2418yes—
596C2×D4×C79C2412yes—
597C2×D4×C79C2414yes—
598C22×C4×C79—82no—
599C22×C4×C79—84no—
600C22×C4×C79C2414yes—
601C22×C4×C79C2414yes—
602C22×C4×C79C2414yes—
603C22×C4×C79C2418yes—
604C22×C4×C79C2411yescharacteristic
605C22×C4×C79C2414yes—
606C22×C4×C79C2414yes—
607C22×C4×C79C2411yescharacteristic
608C22×C4×C79C2414yes—
609C22×C4×C79C2414yes—
610C22×C4×C79C2414yes—
611C22×C4×C79C2412yes—
612C22×C4×C79C2411yescharacteristic
613C4⋊C4×C79C2414yes—
614C4⋊C4×C79C2412yes—
615C4⋊C4×C79C2414yes—
616C4⋊C4×C79C2418yes—
617C4⋊C4×C79C2412yes—
618C4⋊C4×C79C2414yes—
619C22⋊C4×C79C2418yes—
620C22⋊C4×C79C2414yes—
621C22⋊C4×C79C2418yes—
622C22⋊C4×C79C2414yes—
623C22⋊C4×C79C2418yes—
624C22⋊C4×C79C2414yes—
625C42×C79C2412yes—
626C42×C79C2414yes—
627C42×C79C2412yes—
628C42×C79C2418yes—
629C42×C79C2414yes—
630C42×C79C2414yes—
631C23×C79—28no—
632C23×C79—42no—
633C23×C79—42no—
634C23×C79—44no—
635C23×C79—44no—
636C23×C79C2×#4118yes—
637C23×C79C2514yes—
638C23×C79C2514yes—
639C23×C79C2511yescharacteristic
640C22×D79—22no—
641C22×D79—28no—
642C22×D79—41no—
643C22×D79—41no—
644C22×D79—44no—
645C22×D79—44no—
646C22×D79C2514yes—
647C22×D79C2512yes—
648Q8×C79—24no—
649D4×C79—216no—
650D4×C79—28no—
651D4×C79—24no—
652D4×C79C2×#41116yes—
653C2×C4×C79—28no—
654C2×C4×C79—28no—
655C2×C4×C79—44no—
656C2×C4×C79—42no—
657C2×C4×C79—44no—
658C2×C4×C79—48no—
659C2×C4×C79—44no—
660C2×C4×C79—41no—
661C2×C4×C79—44no—
662C2×C4×C79—44no—
663C2×C4×C79—44no—
664C2×C4×C79—41no—
665C2×C4×C79C2×#4114yes—
666C2×C4×C79C2512yes—
667C2×C4×C79C2511yescharacteristic
668C2×C4×C79C2514yes—
669C2×C4×C79C2511yescharacteristic
670C2×C4×C79C2514yes—
671C2×C4×C79C2514yes—
672C2×C4×C79C2514yes—
673C2×C4×C79C2512yes—
674C22⋊D79—216no—
675C22⋊D79—28no—
676C22⋊D79—216no—
677C22⋊D79—44no—
678C22⋊D79—48no—
679C22⋊D79—44no—
680C22⋊D79—44no—
681C22⋊D79—44no—
682C2×Dic79—22no—
683C2×Dic79—24no—
684C2×Dic79—28no—
685C2×Dic79—28no—
686C2×Dic79—28no—
687C2×Dic79—42no—
688C2×Dic79—44no—
689C2×Dic79—41no—
690C2×Dic79—44no—
691C2×Dic79—44no—
692C2×Dic79—41no—
693C2×Dic79—44no—
694C2×Dic79C2512yes—
695C2×Dic79C2514yes—
696C2×Dic79C2514yes—
697C2×Dic79C2514yes—
698C2×Dic79C2511yescharacteristic
699C2×Dic79C2514yes—
700C2×Dic79C2514yes—
701C2×Dic79C2511yescharacteristic
702C2×Dic79C2511yescharacteristic
703C2×Dic79C2511yescharacteristic
704D316—24no—
705D316—44no—
706D316—44no—
707C4×D79—24no—
708C4×D79—24no—
709C4×D79—28no—
710C4×D79—44no—
711C4×D79—48no—
712C4×D79—48no—
713C4×D79—44no—
714Dic158—28no—
715Dic158—24no—
716Dic158—44no—
717Dic158—48no—
718Dic158—44no—
719C22×C79—21no—
720C22×C79—24no—
721C22×C79—21no—
722C22×C79—24no—
723C22×C79—24no—
724C22×C79—24no—
725C22×C79—24no—
726C22×C79—48no—
727C22×C79—88no—
728C22×C79C22×#4118yes—
729C22×C79C22×#4112yes—
730C22×C79C2611yescharacteristic
731C2×D79—22no—
732C2×D79—24no—
733C2×D79—24no—
734C2×D79—22no—
735C2×D79—22no—
736C2×D79—24no—
737C2×D79—44no—
738C2×D79—88no—
739C4×C79—24no—
740C4×C79—21no—
741C4×C79—24no—
742C4×C79—21no—
743C4×C79—24no—
744C4×C79—24no—
745C4×C79—22no—
746C4×C79C22×#4114yes—
747Dic79—24no—
748Dic79—24no—
749Dic79—21no—
750Dic79—21no—
751Dic79—21no—
752Dic79—24no—
753Dic79—24no—
754Dic79—21no—
755Dic79—22no—
756Dic79—24no—
757#62847—791nomaximal, Sylow
758C2×C79—22no—
759C2×C79—28no—
760C2×C79—44no—
761C2×C79C23×#4111yescharacteristic
762C2×C79H(7,𝔽2)11yescharacteristic
763C2×C792−1+611yescharacteristic
764D79—42no—
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#3485—791no—
782#3461—792no—
783#3459—794no—
784#3455—792no—
785C2×#539—794no—
786C4×H(5,𝔽2)—791no—
787C4×H(5,𝔽2)D7911yescharacteristic, complemented
788C2×#520—791no—
789C79#6284711yescharacteristic, complemented, Sylow
790C2×H(5,𝔽2)—791no—
791C2×H(5,𝔽2)C2×D7911yescharacteristic
792C22×#41—791no—
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—798no—
807#553—794no—
808#553—794no—
809#552—794no—
810#552—798no—
811#552—798no—
812#552—798no—
813#552—798no—
814#552—798no—
815#552—794no—
816#552—794no—
817#552—794no—
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#547—794no—
832#547—794no—
833#546—794no—
834#546—794no—
835#546—794no—
836#546—794no—
837#546—794no—
838#546—794no—
839#546—798no—
840D42—794no—
841#544—792no—
842#543—794no—
843#542—792no—
844#542—792no—
845#542—792no—
846#542—792no—
847#542—794no—
848#542—794no—
849#541—792no—
850#541—792no—
851#541—794no—
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—794no—
867#538—794no—
868#538—798no—
869#538—798no—
870#537—792no—
871#536—792no—
872#536—792no—
873#534—794no—
874#534—794no—
875#534—794no—
876#533—794no—
877#533—792no—
878#533—794no—
879#532—792no—
880#529—798no—
881#529—798no—
882#529—798no—
883#529—794no—
884#529—794no—
885#529—794no—
886#529—794no—
887#529—794no—
888#529—798no—
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#525—792no—
899C2×#123—794no—
900C2×#123—794no—
901C2×#123—794no—
902C2×#123—794no—
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—794no—
912#520—792no—
913#520C2×D7912yescomplemented
914#520C2×D7914yescomplemented
915#518—791no—
916#518—794no—
917#518—794no—
918#518C2×D7911yescharacteristic
919#518C2×D7914yescomplemented
920#518C2×D7914yescomplemented
921C4×#41—794no—
922C4×#41—792no—
923C4×#41C2×D7912yescomplemented
924C4×#41C2×D7914yescomplemented
925C2×C4×Q8—791no—
926C2×C4×Q8—791no—
927C2×C4×D4—791no—
928C2×C4×D4—792no—
929C2×C4×D4—794no—
930C2×C4×D4—794no—
931C2×C4×D4—792no—
932C2×C4×D4C2×D7911yescharacteristic
933C2×C4×D4C2×D7914yescomplemented
934C2×C4×D4C2×D7914yescomplemented
935C2×#117—792no—
936C2×#117—791no—
937C22×C4⋊C4—792no—
938C22×C4⋊C4—791no—
939H(5,𝔽2)—28no—
940H(5,𝔽2)—1588no—
941C2×#41—794no—
942C2×#41—794no—
943C2×#41—794no—
944C2×#41—798no—
945C2×#41—792no—
946C2×#41—1588no—
947C2×#41C22×D7912yes—
948C2×#41C22×D7914yes—
949C22×Q8—794no—
950C22×Q8—791no—
951C22×D4—794no—
952C22×D4—792no—
953C22×D4—794no—
954C22×D4—794no—
955C22×D4C22×D7914yes—
956C22×D4C22×D7914yes—
957C22×D4C22×D7911yescharacteristic
958C23×C4—792no—
959C23×C4—792no—
960C23×C4—792no—
961C23×C4—794no—
962C23×C4—791no—
963C23×C4C22×D7912yes—
964C23×C4C22×D7914yes—
965C4⋊Q8—792no—
966C4⋊Q8—794no—
967C4⋊Q8—792no—
968C4⋊Q8—792no—
969C4⋊Q8—794no—
970C4⋊Q8—794no—
971C4⋊Q8—794no—
972#127—792no—
973#126—794no—
974#126—798no—
975#126—794no—
976#126—798no—
977#126—794no—
978#126—798no—
979#126—798no—
980#126—798no—
981#126—798no—
982#126—794no—
983#126—798no—
984#126—794no—
985#126—798no—
986#126—798no—
987#126—798no—
988#126—794no—
989#126—794no—
990#126—794no—
991#125—794no—
992#125—798no—
993#125—798no—
994#125—798no—
995#125—798no—
996#125—794no—
997#125—798no—
998#125—794no—
999#125—792no—
1000#125—792no—
1001#125—794no—
1002#125—798no—
1003#125—798no—
1004#125—798no—
1005#125—794no—
1006#125—794no—
1007#124—792no—
1008#124—794no—
1009#124—792no—
1010#124—794no—
1011#124—798no—
1012#124—794no—
1013#124—798no—
1014#124—794no—
1015#124—794no—
1016#124—794no—
1017#123—794no—
1018#123—798no—
1019#123—798no—
1020#123—798no—
1021#123—798no—
1022#123—794no—
1023#123—798no—
1024#123—798no—
1025#123—798no—
1026#123—794no—
1027#123—798no—
1028#123—798no—
1029#123—794no—
1030#123—794no—
1031#123—794no—
1032#123—798no—
1033#123—794no—
1034#123—794no—
1035#123—794no—
1036#123—798no—
1037#123—798no—
1038#123—798no—
1039#123—798no—
1040#123—798no—
1041#123—798no—
1042#123—798no—
1043#123—798no—
1044#123—794no—
1045C22⋊Q8—792no—
1046C22⋊Q8—792no—
1047C22⋊Q8—794no—
1048C22⋊Q8—794no—
1049C22⋊Q8—798no—
1050C22⋊Q8—798no—
1051C22⋊Q8—798no—
1052C22⋊Q8—798no—
1053C22⋊Q8—794no—
1054C22⋊Q8—798no—
1055C22⋊Q8—794no—
1056C22⋊Q8—794no—
1057C22⋊Q8—794no—
1058C22⋊Q8—794no—
1059C22⋊Q8—798no—
1060C22⋊Q8—798no—
1061C22⋊Q8—798no—
1062C22⋊Q8—798no—
1063C22⋊Q8—792no—
1064C22⋊Q8—792no—
1065C22⋊Q8—794no—
1066C22⋊Q8—794no—
1067C22⋊Q8—794no—
1068C22⋊Q8—794no—
1069C22⋊Q8—798no—
1070C22⋊Q8—798no—
1071C22⋊Q8—798no—
1072C22⋊Q8—798no—
1073C22⋊Q8—794no—
1074C22⋊Q8—798no—
1075#121—794no—
1076#121—798no—
1077#121—798no—
1078#121—798no—
1079#121—798no—
1080#121—792no—
1081#121—792no—
1082#121—794no—
1083#121—798no—
1084#121—794no—
1085#121—794no—
1086#121—798no—
1087#121—798no—
1088#121—794no—
1089#121—794no—
1090#121—792no—
1091#121—792no—
1092#121—794no—
1093#121—798no—
1094#121—794no—
1095#120—798no—
1096#120—798no—
1097#120—794no—
1098#120—798no—
1099#120—794no—
1100#120—798no—
1101C4×Q8—794no—
1102C4×Q8—794no—
1103C4×Q8—794no—
1104C4×Q8—794no—
1105C4×Q8—794no—
1106C4×Q8—792no—
1107C4×Q8—792no—
1108C4×Q8—798no—
1109C4×Q8—794no—
1110C4×Q8—794no—
1111C4×Q8—798no—
1112C4×Q8C22×D7912yes—
1113C4×Q8C22×D7912yes—
1114C4×Q8C22×D7914yes—
1115C4×D4—794no—
1116C4×D4—794no—
1117C4×D4—794no—
1118C4×D4—794no—
1119C4×D4—798no—
1120C4×D4—794no—
1121C4×D4—798no—
1122C4×D4—798no—
1123C4×D4—798no—
1124C4×D4—798no—
1125C4×D4—794no—
1126C4×D4—798no—
1127C4×D4—798no—
1128C4×D4—794no—
1129C4×D4—794no—
1130C4×D4—798no—
1131C4×D4—794no—
1132C4×D4—794no—
1133C4×D4—794no—
1134C4×D4—798no—
1135C4×D4—798no—
1136C4×D4—798no—
1137C4×D4—798no—
1138C4×D4—792no—
1139C4×D4—792no—
1140C4×D4—798no—
1141C4×D4—794no—
1142C4×D4—794no—
1143C4×D4C22×D7914yes—
1144C4×D4C22×D7914yes—
1145C4×D4C22×D7914yes—
1146C4×D4C22×D7918yes—
1147C4×D4C22×D7912yes—
1148C4×D4C22×D7914yes—
1149C4×D4C22×D7918yes—
1150C4×D4C22×D7918yes—
1151C4×D4C22×D7914yes—
1152C4×D4C22×D7918yes—
1153C4×D4C22×D7914yes—
1154C4×D4C22×D7914yes—
1155C4×D4C22×D7912yes—
1156C4×D4C22×D7918yes—
1157#117—792no—
1158#117—798no—
1159#117—798no—
1160#117—794no—
1161#117—798no—
1162#117—798no—
1163#117—798no—
1164#117—792no—
1165#117—792no—
1166#117—792no—
1167#117—792no—
1168#117—794no—
1169#117—798no—
1170#117—798no—
1171#117—798no—
1172#117C22×D7912yes—
1173#117C22×D7914yes—
1174#117C22×D7918yes—
1175#117C22×D7914yes—
1176C2×C4⋊C4—791no—
1177C2×C4⋊C4—792no—
1178C2×C4⋊C4—791no—
1179C2×C4⋊C4—792no—
1180C2×C4⋊C4—792no—
1181C2×C4⋊C4—794no—
1182C2×C4⋊C4—794no—
1183C2×C4⋊C4—794no—
1184C2×C4⋊C4—794no—
1185C2×C4⋊C4—791no—
1186C2×C4⋊C4—794no—
1187C2×C4⋊C4—794no—
1188C2×C4⋊C4—794no—
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⋊C4C22×D7911yescharacteristic
1199C2×C4⋊C4C22×D7914yes—
1200C2×C4⋊C4C22×D7914yes—
1201C2×C22⋊C4—792no—
1202C2×C22⋊C4—794no—
1203C2×C22⋊C4—794no—
1204C2×C22⋊C4—794no—
1205C2×C22⋊C4—794no—
1206C2×C22⋊C4—791no—
1207C2×C22⋊C4—791no—
1208C2×C22⋊C4—794no—
1209C2×C22⋊C4—794no—
1210C2×C22⋊C4—794no—
1211C2×C22⋊C4—794no—
1212C2×C22⋊C4—798no—
1213C2×C22⋊C4C22×D7912yes—
1214C2×C22⋊C4C22×D7914yes—
1215C2×C22⋊C4C22×D7914yes—
1216C2×C22⋊C4C22×D7918yes—
1217C2×C42—792no—
1218C2×C42—792no—
1219C2×C42—791no—
1220C2×C42—794no—
1221C2×C42—794no—
1222C2×C42C22×D7911yescharacteristic
1223C2×C42C22×D7914yes—
1224C2×C42C22×D7914yes—
1225C24—794no—
1226C24—791no—
1227C24C23×D7914yes—
1228C24C23×D7912yes—
1229#41—216no—
1230#41—28no—
1231#41—6328no—
1232#41—15816no—
1233#41—15816no—
1234#41—15816no—
1235#41—1588no—
1236C2×Q8—794no—
1237C2×Q8—794no—
1238C2×Q8—798no—
1239C2×Q8—794no—
1240C2×Q8—792no—
1241C2×Q8—6324no—
1242C2×Q8—1584no—
1243C2×Q8C23×D7912yes—
1244C2×D4—216no—
1245C2×D4—216no—
1246C2×D4—794no—
1247C2×D4—794no—
1248C2×D4—794no—
1249C2×D4—798no—
1250C2×D4—794no—
1251C2×D4—798no—
1252C2×D4—798no—
1253C2×D4—794no—
1254C2×D4—794no—
1255C2×D4—794no—
1256C2×D4—792no—
1257C2×D4—6324no—
1258C2×D4—1588no—
1259C2×D4—15816no—
1260C2×D4—15816no—
1261C2×D4#1192962418yescomplemented
1262C2×D4C23×D7914yes—
1263C2×D4C23×D7918yes—
1264C2×D4C23×D7912yes—
1265C2×D4C23×D7914yes—
1266C22×C4—82no—
1267C22×C4—84no—
1268C22×C4—791no—
1269C22×C4—794no—
1270C22×C4—791no—
1271C22×C4—792no—
1272C22×C4—794no—
1273C22×C4—794no—
1274C22×C4—794no—
1275C22×C4—794no—
1276C22×C4—794no—
1277C22×C4—798no—
1278C22×C4—798no—
1279C22×C4—792no—
1280C22×C4—794no—
1281C22×C4—794no—
1282C22×C4—794no—
1283C22×C4—791no—
1284C22×C4—794no—
1285C22×C4—792no—
1286C22×C4—792no—
1287C22×C4—6324no—
1288C22×C4—6322no—
1289C22×C4—6322no—
1290C22×C4—1588no—
1291C22×C4—1584no—
1292C22×C4C23×D7914yes—
1293C22×C4C23×D7914yes—
1294C22×C4C23×D7911yescharacteristic
1295C22×C4C23×D7912yes—
1296C22×C4C23×D7914yes—
1297C22×C4C23×D7914yes—
1298C22×C4C23×D7911yescharacteristic
1299C22×C4C23×D7914yes—
1300C22×C4C23×D7914yes—
1301C22×C4C23×D7914yes—
1302C22×C4C23×D7914yes—
1303C22×C4C23×D7918yes—
1304C22×C4C23×D7911yescharacteristic
1305C4⋊C4—791no—
1306C4⋊C4—791no—
1307C4⋊C4—794no—
1308C4⋊C4—794no—
1309C4⋊C4—791no—
1310C4⋊C4—791no—
1311C4⋊C4—794no—
1312C4⋊C4—794no—
1313C4⋊C4—794no—
1314C4⋊C4—794no—
1315C4⋊C4—798no—
1316C4⋊C4—794no—
1317C4⋊C4—794no—
1318C4⋊C4—794no—
1319C4⋊C4—794no—
1320C4⋊C4—794no—
1321C4⋊C4—794no—
1322C4⋊C4—792no—
1323C4⋊C4—792no—
1324C4⋊C4—798no—
1325C4⋊C4—798no—
1326C4⋊C4—798no—
1327C4⋊C4—798no—
1328C4⋊C4—798no—
1329C4⋊C4—794no—
1330C4⋊C4—794no—
1331C4⋊C4—794no—
1332C4⋊C4—794no—
1333C4⋊C4—794no—
1334C4⋊C4—792no—
1335C4⋊C4—794no—
1336C4⋊C4—794no—
1337C4⋊C4—794no—
1338C4⋊C4—798no—
1339C4⋊C4—798no—
1340C4⋊C4—798no—
1341C4⋊C4—792no—
1342C4⋊C4—794no—
1343C4⋊C4C23×D7914yes—
1344C4⋊C4C23×D7912yes—
1345C4⋊C4C23×D7914yes—
1346C4⋊C4C23×D7918yes—
1347C4⋊C4C23×D7912yes—
1348C4⋊C4C23×D7914yes—
1349C22⋊C4—798no—
1350C22⋊C4—794no—
1351C22⋊C4—794no—
1352C22⋊C4—794no—
1353C22⋊C4—794no—
1354C22⋊C4—798no—
1355C22⋊C4—798no—
1356C22⋊C4—798no—
1357C22⋊C4—798no—
1358C22⋊C4—794no—
1359C22⋊C4—798no—
1360C22⋊C4—794no—
1361C22⋊C4—794no—
1362C22⋊C4—794no—
1363C22⋊C4—794no—
1364C22⋊C4—794no—
1365C22⋊C4—792no—
1366C22⋊C4—792no—
1367C22⋊C4—792no—
1368C22⋊C4—792no—
1369C22⋊C4—798no—
1370C22⋊C4—798no—
1371C22⋊C4—798no—
1372C22⋊C4—794no—
1373C22⋊C4—794no—
1374C22⋊C4—794no—
1375C22⋊C4—794no—
1376C22⋊C4—794no—
1377C22⋊C4C23×D7918yes—
1378C22⋊C4C23×D7914yes—
1379C22⋊C4C23×D7918yes—
1380C22⋊C4C23×D7914yes—
1381C22⋊C4C23×D7918yes—
1382C22⋊C4C23×D7914yes—
1383C42—794no—
1384C42—798no—
1385C42—798no—
1386C42—798no—
1387C42—794no—
1388C42—794no—
1389C42—792no—
1390C42—792no—
1391C42C23×D7912yes—
1392C42C23×D7912yes—
1393C42C23×D7914yes—
1394C42C23×D7918yes—
1395C42C23×D7914yes—
1396C42C23×D7914yes—
1397C23—28no—
1398C23—42no—
1399C23—42no—
1400C23—44no—
1401C23—44no—
1402C23—3161no—
1403C23—3161no—
1404C23—3164no—
1405C23—3164no—
1406C23—794no—
1407C23—792no—
1408C23—1582no—
1409C23—1588no—
1410C23C2×#1192962418yes—
1411C23C24×D7914yes—
1412C23C24×D7914yes—
1413C23C24×D7911yescharacteristic
1414Q8—24no—
1415Q8—3164no—
1416Q8—3168no—
1417Q8—3164no—
1418Q8—1588no—
1419Q8—1584no—
1420D4—216no—
1421D4—28no—
1422D4—24no—
1423D4—3164no—
1424D4—3164no—
1425D4—3164no—
1426D4—3164no—
1427D4—3164no—
1428D4—3168no—
1429D4—3164no—
1430D4—15816no—
1431D4—1588no—
1432D4—15816no—
1433D4—1584no—
1434D4C2×#11929624116yes—
1435C2×C4—28no—
1436C2×C4—28no—
1437C2×C4—41no—
1438C2×C4—44no—
1439C2×C4—44no—
1440C2×C4—44no—
1441C2×C4—42no—
1442C2×C4—44no—
1443C2×C4—48no—
1444C2×C4—41no—
1445C2×C4—44no—
1446C2×C4—44no—
1447C2×C4—3164no—
1448C2×C4—3168no—
1449C2×C4—3168no—
1450C2×C4—3164no—
1451C2×C4—3161no—
1452C2×C4—3162no—
1453C2×C4—3164no—
1454C2×C4—3164no—
1455C2×C4—3164no—
1456C2×C4—3164no—
1457C2×C4—3161no—
1458C2×C4—792no—
1459C2×C4—794no—
1460C2×C4—794no—
1461C2×C4—794no—
1462C2×C4—791no—
1463C2×C4—794no—
1464C2×C4—794no—
1465C2×C4—791no—
1466C2×C4—791no—
1467C2×C4—791no—
1468C2×C4—1582no—
1469C2×C4—1584no—
1470C2×C4—1588no—
1471C2×C4—1588no—
1472C2×C4—1588no—
1473C2×C4—1584no—
1474C2×C4—1584no—
1475C2×C4—1588no—
1476C2×C4C2×#1192962414yes—
1477C2×C4C24×D7912yes—
1478C2×C4C24×D7911yescharacteristic
1479C2×C4C24×D7914yes—
1480C2×C4C24×D7911yescharacteristic
1481C2×C4C24×D7914yes—
1482C2×C4C24×D7914yes—
1483C2×C4C24×D7914yes—
1484C2×C4C24×D7912yes—
1485C22—21no—
1486C22—24no—
1487C22—21no—
1488C22—24no—
1489C22—24no—
1490C22—24no—
1491C22—24no—
1492C22—48no—
1493C22—88no—
1494C22—3164no—
1495C22—6328no—
1496C22—1582no—
1497C22—1584no—
1498C22—1582no—
1499C22—1584no—
1500C22—1584no—
1501C22—1582no—
1502C22C22×#1192962418yes—
1503C22C22×#1192962412yes—
1504C22C25×D7911yescharacteristic
1505C4—24no—
1506C4—21no—
1507C4—21no—
1508C4—24no—
1509C4—24no—
1510C4—22no—
1511C4—24no—
1512C4—1581no—
1513C4—1581no—
1514C4—1584no—
1515C4—1584no—
1516C4—1581no—
1517C4—1584no—
1518C4—1584no—
1519C4—1581no—
1520C4—1584no—
1521C4—1582no—
1522C4C22×#1192962414yes—
1523C2—22no—
1524C2—28no—
1525C2—44no—
1526C2—3162no—
1527C2—3164no—
1528C2C23×#1192962411yescharacteristic
1529C2#2377821011yescharacteristic
1530C2#2377821311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC4×H(5,𝔽2)×C79C2
hypercenterC4×H(5,𝔽2)D79
hypocenterC79#62847
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #23777468C2semidirect
2. #23777456C2semidirect
3. #23777449C2semidirect
4. #23777439C2semidirect
5. #23777378C2semidirect
6. #23777368C2semidirect
7. #23777340C2semidirect
8. #23777328C2semidirect
9. #23777258C2semidirect
10. #23777230C2semidirect
11. #23777198C2semidirect
12. #23777159C2semidirect
13. #23777103C2semidirect
14. #23777093C2semidirect
15. #23777045C2semidirect
16. #23777040C2semidirect
17. #23776827C2semidirect
18. #23776809C2semidirect
19. #23776785C2semidirect
20. C2×#19099155C2semidirect
21. C4×#14579206C2semidirect
22. C2×#19099042C2semidirect
23. C4×H(5,𝔽2)×C79C2semidirect
26. #19099296C22semidirect
27. #19099291C22semidirect
28. #19099285C22semidirect
29. #19099283C22semidirect
30. #19099281C22semidirect
31. #19099273C22semidirect
32. #19099272C22semidirect
33. #19099272C22semidirect
34. #19099270C22semidirect
35. #19099268C22semidirect
36. #19099268C22semidirect
37. #19099263C22semidirect
38. #19099262C22semidirect
39. #19099262C22semidirect
40. #19099259C22semidirect
41. #19099257C22semidirect
42. #19099254C22semidirect
43. #19099253C22semidirect
44. #19099253C22semidirect
45. #19099252C22semidirect
46. #19099252C22semidirect
47. #19099248C22semidirect
48. #19099246C22semidirect
49. #19099246C22semidirect
50. #19099246C22semidirect
51. #19099242C22semidirect
52. #19099242C22semidirect
53. #19099239C22semidirect
54. #19099239C22semidirect
55. #19099239C22semidirect
56. #19099237C22semidirect
57. D4×Dic158C22semidirect
58. #19099222C22semidirect
59. #19099218C22semidirect
60. #19099217C22semidirect
61. #19099217C22semidirect
62. #19099214C22semidirect
63. #19099212C22semidirect
64. #19099212C22semidirect
65. #19099212C22semidirect
66. #19099208C22semidirect
67. #19099208C22semidirect
68. #19099207C22semidirect
69. #19099207C22semidirect
70. #19099207C22semidirect
71. #19099203C22semidirect
72. #19099201C22semidirect
73. D4×C22⋊D79C22semidirect
74. #19099191C22semidirect
75. #19099189C22semidirect
76. #19099185C22semidirect
77. #19099185C22semidirect
78. #19099184C22semidirect
79. #19099178C22semidirect
80. #19099178C22semidirect
81. #19099178C22semidirect
82. #19099175C22semidirect
83. #19099171C22semidirect
84. #19099171C22semidirect
85. #19099171C22semidirect
86. #19099164C22semidirect
87. #19099164C22semidirect
88. #19099160C22semidirect
89. #19099155C22semidirect
90. #19099155C22semidirect
91. #19099155C22semidirect
92. #19099155C22semidirect
93. #19099155C22semidirect
94. #19099155C22semidirect
95. #19099155C22semidirect
96. #19099155C22semidirect
97. #19099155C22semidirect
98. #19099155C22semidirect
99. #19099151C22semidirect
100. #19099146C22semidirect
101. #19099146C22semidirect
102. #19099146C22semidirect
104. #19099139C22semidirect
105. #19099134C22semidirect
106. #19099125C22semidirect
108. #19099122C22semidirect
109. #19099120C22semidirect
110. #19099117C22semidirect
111. #19099116C22semidirect
113. #19099097C22semidirect
114. #19099097C22semidirect
115. #19099097C22semidirect
116. #19099097C22semidirect
117. #19099095C22semidirect
118. #19099093C22semidirect
119. #19099093C22semidirect
120. #19099093C22semidirect
121. #19099091C22semidirect
122. #19099091C22semidirect
123. C2×#14579155C22semidirect
124. C2×#14579154C22semidirect
125. C2×#14579153C22semidirect
126. C2×#14579151C22semidirect
127. #19099075C22semidirect
128. #19099074C22semidirect
129. #19099072C22semidirect
130. #19099072C22semidirect
131. #19099070C22semidirect
132. C2×#14579145C22semidirect
133. C2×#14579144C22semidirect
134. C2×#14579143C22semidirect
135. C2×#14579142C22semidirect
136. C2×#14579140C22semidirect
137. C2×#14579139C22semidirect
138. C2×#14579138C22semidirect
140. #19099044C22semidirect
141. #19099042C22semidirect
142. #19099042C22semidirect
143. #19099042C22semidirect
144. #19099042C22semidirect
145. #19099042C22semidirect
147. #19099036C22semidirect
148. #19099035C22semidirect
149. C4×#11929624C22semidirect
150. C4×#11929623C22semidirect
151. C2×C4×Dic158C22semidirect
152. C2×#14579126C22semidirect
154. C2×C4×C22⋊D79C22semidirect
155. C2×C4×C22⋊D79C22semidirect
156. C2×(C22⋊D79)⋊C4C22semidirect
157. C4×D4×D79C22semidirect
158. C2×#14579118C22semidirect
159. C2×#14579117C22semidirect
160. C22×Dic79⋊C4C22semidirect
161. C2×C4⋊C4×D79C22semidirect
163. #520×C79C22semidirect
164. #520×C79C22semidirect
166. #518×C79C22semidirect
167. #518×C79C22semidirect
168. C4×#41×C79C22semidirect
169. C4×#41×C79C22semidirect
171. C2×C4×D4×C79C22semidirect
172. C2×C4×D4×C79C22semidirect
593. C2×D4×C79#41semidirect
787. C4×H(5,𝔽2)D79semidirect
789. C79#62847semidirect
913. #520C2×D79semidirect
914. #520C2×D79semidirect
919. #518C2×D79semidirect
920. #518C2×D79semidirect
923. C4×#41C2×D79semidirect
924. C4×#41C2×D79semidirect
933. C2×C4×D4C2×D79semidirect
934. C2×C4×D4C2×D79semidirect
1261. C2×D4#11929624semidirect

Maximal subgroups

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

subgroupindex
#237774682
#237774562
#237774492
#237774392
#237773782
#237773682
#237773402
#237773282
#237772582
#237772302
#237771982
#237771592
#237771032
#237770932
#237770452
#237770402
#237768272
#237768092
#237767852
C2×#190991552
C4×#145792062
C2×#190990422
C4×H(5,𝔽2)×C792
#6284779