Finite Group Databasebeta

← #35196943

Subgroups — #35196943

Order 20224.

7338 conjugacy classes of subgroups.

The subgroup lattice has 1538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777708C214yesmaximal, complemented
2#23777685C214yesmaximal, complemented
3#23777668C214yesmaximal, complemented
4#23777656C214yesmaximal, complemented
5#23777571C214yesmaximal, complemented
6#23777555C214yesmaximal, complemented
7#23777437C214yesmaximal, complemented
8#23777420C214yesmaximal, complemented
9#23777340C218yesmaximal, complemented
10#23777243C214yesmaximal, complemented
11#23777228C214yesmaximal, complemented
12#23777146C212yesmaximal, complemented
13#23777129C212yesmaximal, complemented
14#23777120C212yesmaximal, complemented
15#23777076C212yesmaximal, complemented
16#23777065C212yesmaximal, complemented
17#23777058C211yesmaximal, characteristic, complemented
18#23777044C211yesmaximal, characteristic, complemented
19C2×#19099074C212yesmaximal, complemented
20C2×#525×C79C211yesmaximal, characteristic, complemented
21C2×#14579209C2211yescharacteristic, complemented
22C2×#14579206C2211yescharacteristic, complemented
23C22×#11929624C2212yescomplemented
24#19099316C2214yescomplemented
25#19099310C2218yescomplemented
26#19099306C2214yescomplemented
27#19099303C2214yescomplemented
28#19099302C2214yescomplemented
29#19099302C2218yescomplemented
30#19099297C2214yescomplemented
31#19099296C2218yescomplemented
32#19099284C2214yescomplemented
33#19099281C2214yescomplemented
34#19099281C2214yescomplemented
35#19099277C2214yescomplemented
36#19099276C2214yescomplemented
37#19099276C2214yescomplemented
38#19099272C2218yescomplemented
39#19099271C2214yescomplemented
40#19099265C2214yescomplemented
41#19099263C2218yescomplemented
42#19099262C2218yescomplemented
43#19099262C2218yescomplemented
44#19099260C2214yescomplemented
45#19099258C2218yescomplemented
46#19099257C2214yescomplemented
47#19099257C2214yescomplemented
48#19099255C2214yescomplemented
49#19099252C2214yescomplemented
50#19099252C2214yescomplemented
51#19099248C2218yescomplemented
52#19099247C2214yescomplemented
53#19099244C2214yescomplemented
54#19099242C2218yescomplemented
55#19099242C2218yescomplemented
56#19099241C2214yescomplemented
57#19099239C2218yescomplemented
58#19099239C2218yescomplemented
59#19099232C2214yescomplemented
60#19099232C2214yescomplemented
61#19099231C2214yescomplemented
62#19099226C2214yescomplemented
63#19099223C2214yescomplemented
64#19099220C2214yescomplemented
65#19099220C2214yescomplemented
66#19099219C2214yescomplemented
67#19099215C2214yescomplemented
68#19099214C2218yescomplemented
69#19099213C2214yescomplemented
70#19099212C2214yescomplemented
71#19099212C2214yescomplemented
72#19099210C2214yescomplemented
73#19099208C2218yescomplemented
74#19099207C2218yescomplemented
75#19099204C2214yescomplemented
76#19099203C2218yescomplemented
77#19099203C2218yescomplemented
78#19099201C2214yescomplemented
79#19099201C2214yescomplemented
80#19099200C2218yescomplemented
81#19099197C2214yescomplemented
82D4×C22⋊D79C2218yescomplemented
83#19099195C2214yescomplemented
84#19099194C2212yescomplemented
85#19099186C2214yescomplemented
86#19099181C2218yescomplemented
87#19099180C2214yescomplemented
88#19099178C2218yescomplemented
89#19099173C2214yescomplemented
90#19099166C2214yescomplemented
91#19099165C2218yescomplemented
92#19099164C2218yescomplemented
93#19099156C2218yescomplemented
94#19099155C2218yescomplemented
95#19099155C2218yescomplemented
96#19099151C2218yescomplemented
97#19099149C2218yescomplemented
98#19099148C2218yescomplemented
99#19099148C2218yescomplemented
100#19099146C2218yescomplemented
101#19099146C2218yescomplemented
102#19099144C2212yescomplemented
103#19099143C2214yescomplemented
104#19099142C2214yescomplemented
105#19099137C2212yescomplemented
106#19099136C2214yescomplemented
107#19099130C2214yescomplemented
108#19099130C2212yescomplemented
109#19099129C2214yescomplemented
110#19099128C2218yescomplemented
111#19099123C2218yescomplemented
112#19099122C2214yescomplemented
113#19099115C2214yescomplemented
114#19099108C2214yescomplemented
115#19099099C2214yescomplemented
116#19099097C2218yescomplemented
117#19099094C2214yescomplemented
118#19099076C2214yescomplemented
119#19099074C2212yes—
120#19099074C2212yescomplemented
121#19099074C2212yescomplemented
122#19099074C2214yescomplemented
123#19099074C2212yescomplemented
124#19099074C2214yescomplemented
125#19099074C2212yescomplemented
126#19099074C2214yescomplemented
127#19099074C2212yescomplemented
128#19099074C2214yescomplemented
129#19099074C2212yescomplemented
130#19099074C2212yescomplemented
131#19099074C2214yescomplemented
132#19099073C2214yescomplemented
133C2×#14579144C2214yescomplemented
134C2×#14579144C2214yescomplemented
135C2×#14579140C2212yescomplemented
136C2×#14579140C2212yescomplemented
137C22⋊Q8×D79C2214yescomplemented
138C2×#14579135C2212yescomplemented
139C2×#14579135C2212yescomplemented
140#121×D79C2214yescomplemented
141C2×#14579130C2214yescomplemented
142#19099044C2212yescomplemented
143#19099044C2212yescomplemented
144#19099042C2218yescomplemented
145#19099041C2211yescharacteristic, complemented
146#19099038C2211yescharacteristic, complemented
147#19099035C2218yescomplemented
148C2×C4×C22⋊D79C2214yescomplemented
149C2×C4×C22⋊D79C2214yescomplemented
150C2×#14579120C2212yescomplemented
151C22×#41×C79C2211yescharacteristic, complemented
152C24×C4×C79C2211yescharacteristic, complemented
153#525×C79C2214yescomplemented
154#525×C79C2214yescomplemented
155#525×C79C2214yescomplemented
156#525×C79C2214yescomplemented
157C2×#123×C79C2212yescomplemented
158C2×C22⋊Q8×C79C2212yescomplemented
159C2×#121×C79C2212yescomplemented
160C2×#120×C79C2212yescomplemented
161C2×C4×D4×C79C2214yescomplemented
162C2×#117×C79C2211yescharacteristic, complemented
163#14579209—44no—
164#14579206—44no—
165C2×#11929625C2314yescomplemented
166C2×#11929624—48no—
167C2×#11929624C2312yes—
168C2×#11929624C2312yes—
169C2×#11929624C2314yes—
170C2×#11929624C2314yes—
171C2×#11929624C2314yes—
172C2×#11929624C2312yes—
173C2×#11929624C2312yes—
174C2×#11929623C2318yes—
175C2×#11929623C2314yescomplemented
176C22×Dic158C2312yes—
177C2×Q8×D79C2314yescomplemented
178C22×D316C2312yes—
179C22×C22⋊D79C2314yes—
180C22×C22⋊D79C2314yes—
181C22×C22⋊D79C2314yes—
182C22×C22⋊D79C2314yes—
183C2×D4×D79C2318yes—
184C2×D4×D79C2314yescomplemented
185C22×C4×D79C2314yes—
186#14579160C2318yescomplemented
187#14579160C2314yescomplemented
188#14579160C2314yescomplemented
189#14579159C2314yescomplemented
190#14579157C2318yes—
191#14579157C2314yes—
192#14579157C2314yes—
193#14579157C2314yescomplemented
194#14579156C2318yescomplemented
195#14579156C2318yescomplemented
196#14579155C2318yescomplemented
197#14579155C2318yescomplemented
198#14579154C2318yes—
199#14579154C2318yes—
200#14579154C2318yes—
201#14579154C2318yes—
202#14579154C2318yescomplemented
203#14579154C2318yescomplemented
204#14579153C2318yescomplemented
205#14579152C2318yescomplemented
206#14579152C2314yescomplemented
207#14579152C2314yescomplemented
208#14579151C2318yescomplemented
209#14579151C2318yescomplemented
210#14579150C2314yescomplemented
211#14579149C2318yescomplemented
212#14579148C2314yes—
213#14579148C2318yes—
214#14579148C2314yes—
215#14579148C2314yescomplemented
216#14579147C2318yes—
217#14579147C2318yes—
218#14579147C2318yes—
219#14579147C2318yes—
220#14579147C2318yescomplemented
221#14579147C2318yescomplemented
222#14579146C2318yescomplemented
223#14579146C2318yescomplemented
224#14579145C2318yes—
225#14579145C2318yescomplemented
226#14579144C2318yes—
227#14579144C2314yes—
228#14579144C2314yes—
229#14579144C2314yes—
230#14579144C2314yes—
231#14579144C2314yes—
232#14579144C2314yes—
233#14579144C2314yes—
234#14579144C2314yes—
235#14579144C2318yescomplemented
236#14579144C2318yescomplemented
237#14579143C2318yes—
238#14579143C2318yes—
239#14579143C2318yes—
240#14579143C2318yes—
241#14579143C2318yescomplemented
242#14579143C2318yescomplemented
243#14579142C2314yes—
244#14579142C2318yes—
245#14579142C2318yes—
246#14579142C2314yes—
247#14579141C2314yescomplemented
248#14579141C2314yescomplemented
249#14579141C2318yescomplemented
250#14579140C2312yes—
251#14579140C2312yes—
252#14579140C2318yes—
253#14579140C2314yes—
254#14579140C2314yes—
255#14579140C2312yes—
256#14579140C2312yes—
257#14579140C2312yes—
258#14579140C2312yes—
259#14579140C2314yes—
260#14579140C2314yes—
261#14579140C2312yes—
262#14579140C2312yes—
263#14579140C2318yescomplemented
264#14579139C2318yescomplemented
265#14579139C2318yescomplemented
266#14579138C2318yes—
267#14579138C2318yes—
268#14579138C2318yescomplemented
269#14579138C2318yescomplemented
270#14579137C2314yescomplemented
271#14579137C2314yescomplemented
272#14579136C2314yescomplemented
273#14579136C2318yescomplemented
274#14579136C2314yescomplemented
275#14579135C2312yes—
276#14579135C2318yes—
277#14579135C2314yes—
278#14579135C2314yes—
279#14579135C2312yes—
280#14579135C2312yes—
281#14579135C2312yes—
282#14579135C2314yes—
283#14579135C2312yes—
284#14579135C2312yes—
285#14579135C2314yes—
286#14579135C2312yes—
287#14579135C2312yes—
288#14579135C2318yescomplemented
289#14579134C2318yes—
290#14579134C2318yes—
291#14579134C2318yes—
292#14579134C2318yes—
293#14579134C2318yescomplemented
294#14579134C2318yescomplemented
295#14579133C2318yes—
296#14579133C2318yes—
297#14579133C2318yes—
298#14579133C2318yes—
299#14579133C2318yes—
300#14579133C2318yes—
301#14579132C2318yes—
302#14579132C2318yes—
303#14579132C2318yes—
304#14579132C2318yes—
305#14579132C2314yescomplemented
306#14579132C2314yescomplemented
307#14579131C2318yes—
308#14579131C2318yescomplemented
309#14579130C2314yes—
310#14579130C2314yes—
311#14579130C2314yes—
312#14579130C2314yes—
313#14579130C2314yes—
314#14579130C2318yes—
315#14579130C2314yes—
316#14579130C2314yes—
317#14579130C2314yes—
318#14579129C2318yes—
319#14579129C2318yes—
320#14579129C2314yes—
321#14579129C2314yes—
322Q8×Dic79C2314yescomplemented
323Q8×Dic79C2314yescomplemented
324C4×Dic158C2318yescomplemented
325#14579126C2314yescomplemented
326#14579126C2314yescomplemented
327#14579126C2318yescomplemented
328C4×D316C2318yescomplemented
329D4×Dic79C2318yes—
330D4×Dic79C2318yes—
331D4×Dic79C2314yescomplemented
332D4×Dic79C2314yescomplemented
333#14579123C2318yescomplemented
334#14579123C2314yescomplemented
335#14579123C2314yescomplemented
336C4×C22⋊D79C2314yes—
337C4×C22⋊D79C2314yes—
338C4×C22⋊D79C2318yes—
339C4×C22⋊D79C2318yes—
340C4×C22⋊D79C2314yes—
341C4×C22⋊D79C2314yes—
342C4×C22⋊D79C2314yes—
343C4×C22⋊D79C2314yes—
344C4×C22⋊D79C2314yes—
345C4×C22⋊D79C2314yes—
346C4×C22⋊D79C2314yes—
347C4×C22⋊D79C2314yes—
348C4×C22⋊D79C2314yes—
349C4×C22⋊D79C2314yes—
350C4×C22⋊D79C2314yes—
351C4×C22⋊D79C2314yes—
352C4×C22⋊D79C2314yes—
353C4×C22⋊D79C2314yes—
354C4×C22⋊D79C2318yescomplemented
355C4×C22⋊D79C2318yescomplemented
356(C22⋊D79)⋊C4C2318yes—
357(C22⋊D79)⋊C4C2318yes—
358(C22⋊D79)⋊C4C2318yescomplemented
359(C22⋊D79)⋊C4C2318yescomplemented
360#14579120C2312yes—
361#14579120C2314yes—
362#14579120C2312yes—
363#14579120C2314yes—
364#14579120C2314yes—
365#14579120C2312yes—
366#14579120C2312yes—
367#14579119C2314yescomplemented
368#14579119C2318yescomplemented
369#14579119C2314yescomplemented
370#14579118C2318yescomplemented
371#14579118C2318yescomplemented
372#14579117C2318yes—
373#14579117C2318yescomplemented
374C2×C4⋊Dic79C2312yes—
375C2×C4⋊Dic79C2312yes—
376C2×Dic79⋊C4C2314yes—
377C2×Dic79⋊C4C2314yes—
378C2×Dic79⋊C4C2318yescomplemented
379C4⋊C4×D79C2314yescomplemented
380C4⋊C4×D79C2314yescomplemented
381C4⋊C4×D79C2318yescomplemented
382C2×C22⋊Dic79C2314yes—
383C2×C22⋊Dic79C2314yes—
384C2×C22⋊Dic79C2314yes—
385C2×C22⋊Dic79C2314yes—
386C2×(C2×D79)⋊C4C2314yes—
387C2×(C2×D79)⋊C4C2314yes—
388C2×(C2×D79)⋊C4C2318yescomplemented
389C22⋊C4×D79C2318yes—
390C22⋊C4×D79C2318yescomplemented
391C2×C4×Dic79C2314yes—
392C25×C79C2311yescharacteristic
393C2×#41×C79—44no—
394C2×#41×C79C2314yes—
395C2×#41×C79C2314yes—
396C22×Q8×C79C2311yescharacteristic
397C22×D4×C79C2311yescharacteristic
398C22×D4×C79C2314yes—
399C22×D4×C79C2312yes—
400C23×C4×C79—44no—
401C23×C4×C79C2311yescharacteristic
402C23×C4×C79C2312yes—
403C23×C4×C79C2312yes—
404C23×C4×C79C2312yes—
405C23×C4×C79C2311yescharacteristic
406C23×C4×C79C2312yes—
407C23×C4×C79C2312yes—
408C23×C4×C79C2312yes—
409C23×C4×C79C2312yes—
410#123×C79C2318yes—
411#123×C79C2314yes—
412#123×C79C2314yes—
413C22⋊Q8×C79C2314yes—
414C22⋊Q8×C79C2314yes—
415C22⋊Q8×C79C2314yes—
416C22⋊Q8×C79C2314yes—
417#121×C79C2314yes—
418#121×C79C2314yes—
419#121×C79C2314yes—
420#121×C79C2314yes—
421#120×C79C2318yes—
422#120×C79C2314yes—
423#120×C79C2314yes—
424C4×D4×C79C2318yes—
425C4×D4×C79C2318yes—
426C4×D4×C79C2318yes—
427C4×D4×C79C2318yes—
428#117×C79C2314yes—
429#117×C79C2314yes—
430C2×C4⋊C4×C79C2312yes—
431C2×C4⋊C4×C79C2314yes—
432C2×C22⋊C4×C79C2312yes—
433C2×C22⋊C4×C79C2314yes—
434C2×C22⋊C4×C79C2314yes—
435C2×C42×C79C2312yes—
436C23×D79C2414yes—
437C23×D79C2414yes—
438#11929625—48no—
439#11929624—28no—
440#11929624—28no—
441#11929624—48no—
442#11929624—48no—
443#11929624—44no—
444#11929624—44no—
445#11929624—48no—
446#11929623—416no—
447#11929623—48no—
448C2×Dic158—44no—
449C2×Dic158C2412yes—
450C2×Dic158C2412yes—
451C2×Dic158C2414yes—
452C2×Dic158C2414yes—
453C2×Dic158C2418yes—
454Q8×D79—48no—
455C2×D316—44no—
456C2×D316C2412yes—
457C2×D316C2412yes—
458C2×D316C2414yes—
459C2×D316C2414yes—
460C2×D316C2418yes—
461C2×C22⋊D79—48no—
462C2×C22⋊D79—48no—
463C2×C22⋊D79—48no—
464C2×C22⋊D79—48no—
465C2×C22⋊D79C2414yes—
466C2×C22⋊D79C2414yes—
467C2×C22⋊D79C2414yes—
468C2×C22⋊D79C2414yes—
469C2×C22⋊D79C2418yes—
470C2×C22⋊D79C2418yes—
471C2×C22⋊D79C2414yes—
472C2×C22⋊D79C2414yes—
473C2×C22⋊D79C2418yes—
474C2×C22⋊D79C2414yes—
475C2×C22⋊D79C2414yes—
476C2×C22⋊D79C2414yes—
477C2×C22⋊D79C2414yes—
478C2×C22⋊D79C2414yes—
479C2×C22⋊D79C2414yes—
480D4×D79—416no—
481D4×D79—48no—
482C22×Dic79C2414yes—
483C22×Dic79C2414yes—
484C22×Dic79C2418yes—
485C22×Dic79C2414yes—
486C22×Dic79C2414yes—
487C2×C4×D79—48no—
488C2×C4×D79C2414yes—
489C2×C4×D79C2414yes—
490C2×C4×D79C2418yes—
491C2×C4×D79C2418yes—
492C2×C4×D79C2414yes—
493C2×C4×D79C2414yes—
494C2×C4×D79C2418yes—
495C4⋊Dic79C2412yes—
496C4⋊Dic79C2412yes—
497C4⋊Dic79C2418yes—
498C4⋊Dic79C2412yes—
499C4⋊Dic79C2412yes—
500C4⋊Dic79C2414yes—
501C4⋊Dic79C2414yes—
502C4⋊Dic79C2418yes—
503C4⋊Dic79C2418yes—
504Dic79⋊C4C2414yes—
505Dic79⋊C4C2418yes—
506Dic79⋊C4C2418yes—
507Dic79⋊C4C2418yes—
508Dic79⋊C4C2414yes—
509Dic79⋊C4C2414yes—
510Dic79⋊C4C2414yes—
511Dic79⋊C4C2414yes—
512Dic79⋊C4C2414yes—
513Dic79⋊C4C2414yes—
514Dic79⋊C4C2414yes—
515Dic79⋊C4C2418yes—
516Dic79⋊C4C2418yes—
517Dic79⋊C4C2418yes—
518C22⋊Dic79C2414yes—
519C22⋊Dic79C2418yes—
520C22⋊Dic79C2414yes—
521C22⋊Dic79C2414yes—
522C22⋊Dic79C2414yes—
523C22⋊Dic79C2414yes—
524C22⋊Dic79C2414yes—
525C22⋊Dic79C2414yes—
526C22⋊Dic79C2414yes—
527C22⋊Dic79C2414yes—
528C22⋊Dic79C2414yes—
529C22⋊Dic79C2414yes—
530C22⋊Dic79C2414yes—
531C22⋊Dic79C2414yes—
532C22⋊Dic79C2414yes—
533C22⋊Dic79C2418yes—
534(C2×D79)⋊C4C2418yes—
535(C2×D79)⋊C4C2418yes—
536(C2×D79)⋊C4C2414yes—
537(C2×D79)⋊C4C2414yes—
538(C2×D79)⋊C4C2414yes—
539(C2×D79)⋊C4C2414yes—
540(C2×D79)⋊C4C2414yes—
541(C2×D79)⋊C4C2414yes—
542(C2×D79)⋊C4C2414yes—
543(C2×D79)⋊C4C2414yes—
544(C2×D79)⋊C4C2418yes—
545(C2×D79)⋊C4C2418yes—
546(C2×D79)⋊C4C2418yes—
547(C2×D79)⋊C4C2418yes—
548C4×Dic79C2414yes—
549C4×Dic79C2414yes—
550C4×Dic79C2414yes—
551C4×Dic79C2414yes—
552C4×Dic79C2414yes—
553C4×Dic79C2418yes—
554C4×Dic79C2418yes—
555C4×Dic79C2414yes—
556C24×C79—42no—
557C24×C79—44no—
558C24×C79C2412yes—
559C24×C79C2411yescharacteristic
560C24×C79C2411yescharacteristic
561C24×C79C2412yes—
562C24×C79C2412yes—
563C24×C79C2411yescharacteristic
564#41×C79—48no—
565#41×C79—48no—
566C2×Q8×C79—24no—
567C2×Q8×C79C2414yes—
568C2×D4×C79—24no—
569C2×D4×C79—44no—
570C2×D4×C79—48no—
571C2×D4×C79C2418yes—
572C2×D4×C79C2414yes—
573C2×D4×C79C2418yes—
574C2×D4×C79C2414yes—
575C2×D4×C79C2414yes—
576C22×C4×C79—28no—
577C22×C4×C79—24no—
578C22×C4×C79—44no—
579C22×C4×C79—44no—
580C22×C4×C79—44no—
581C22×C4×C79—44no—
582C22×C4×C79—42no—
583C22×C4×C79—44no—
584C22×C4×C79—44no—
585C22×C4×C79C2412yes—
586C22×C4×C79C2412yes—
587C22×C4×C79C2412yes—
588C22×C4×C79C2412yes—
589C22×C4×C79C2412yes—
590C22×C4×C79C2411yescharacteristic
591C22×C4×C79C2412yes—
592C22×C4×C79C2412yes—
593C22×C4×C79C2412yes—
594C22×C4×C79C2414yes—
595C22×C4×C79C2412yes—
596C22×C4×C79C2412yes—
597C22×C4×C79C2412yes—
598C22×C4×C79C2412yes—
599C22×C4×C79C2418yes—
600C22×C4×C79C2411yescharacteristic
601C22×C4×C79C2412yes—
602C22×C4×C79C2411yescharacteristic
603C22×C4×C79C2411yescharacteristic
604C4⋊C4×C79C2414yes—
605C4⋊C4×C79C2414yes—
606C4⋊C4×C79C2418yes—
607C4⋊C4×C79C2418yes—
608C22⋊C4×C79C2414yes—
609C22⋊C4×C79C2414yes—
610C22⋊C4×C79C2418yes—
611C22⋊C4×C79C2418yes—
612C22⋊C4×C79C2418yes—
613C22⋊C4×C79C2418yes—
614C42×C79C2418yes—
615C23×C79—24no—
616C23×C79—22no—
617C23×C79—24no—
618C23×C79—24no—
619C23×C79—24no—
620C23×C79—24no—
621C23×C79—41no—
622C23×C79—42no—
623C23×C79—41no—
624C23×C79—42no—
625C23×C79—42no—
626C23×C79—42no—
627C23×C79—42no—
628C23×C79—44no—
629C23×C79—416no—
630C23×C79C2512yes—
631C23×C79C2511yescharacteristic
632C23×C79C2511yescharacteristic
633C23×C79C2514yes—
634C23×C79C2511yescharacteristic
635C23×C79C2512yes—
636C22×D79—28no—
637C22×D79—44no—
638C22×D79—44no—
639C22×D79—44no—
640C22×D79—48no—
641C22×D79C2514yes—
642C22×D79C2514yes—
643Q8×C79—28no—
644D4×C79—216no—
645D4×C79—28no—
646D4×C79—48no—
647D4×C79—44no—
648D4×C79—44no—
649C2×C4×C79—24no—
650C2×C4×C79—24no—
651C2×C4×C79—22no—
652C2×C4×C79—24no—
653C2×C4×C79—24no—
654C2×C4×C79—24no—
655C2×C4×C79—24no—
656C2×C4×C79—24no—
657C2×C4×C79—24no—
658C2×C4×C79—42no—
659C2×C4×C79—42no—
660C2×C4×C79—42no—
661C2×C4×C79—42no—
662C2×C4×C79—41no—
663C2×C4×C79—42no—
664C2×C4×C79—41no—
665C2×C4×C79—48no—
666C2×C4×C79—44no—
667C2×C4×C79H(5,𝔽2)14yes—
668C2×C4×C79C2512yes—
669C2×C4×C79C2518yes—
670C2×C4×C79C2514yes—
671C2×C4×C79C2512yes—
672C2×C4×C79C2512yes—
673C2×C4×C79C2512yes—
674C22⋊D79—28no—
675C22⋊D79—28no—
676C22⋊D79—28no—
677C22⋊D79—28no—
678C22⋊D79—48no—
679C22⋊D79—48no—
680C22⋊D79—44no—
681C22⋊D79—44no—
682C22⋊D79—44no—
683C22⋊D79—44no—
684C22⋊D79—44no—
685C22⋊D79—44no—
686C22⋊D79—44no—
687C22⋊D79—44no—
688C22⋊D79—48no—
689C2×Dic79—28no—
690C2×Dic79—44no—
691C2×Dic79—44no—
692C2×Dic79—44no—
693C2×Dic79—48no—
694C2×Dic79C2514yes—
695C2×Dic79C2514yes—
696C2×Dic79C2514yes—
697C2×Dic79C2514yes—
698C2×Dic79C2514yes—
699C2×Dic79C2514yes—
700D316—24no—
701D316—24no—
702D316—48no—
703D316—44no—
704D316—44no—
705C4×D79—28no—
706C4×D79—28no—
707C4×D79—44no—
708C4×D79—44no—
709C4×D79—48no—
710C4×D79—48no—
711C4×D79—48no—
712Dic158—24no—
713Dic158—24no—
714Dic158—44no—
715Dic158—44no—
716Dic158—48no—
717C22×C79—22no—
718C22×C79—22no—
719C22×C79—22no—
720C22×C79—22no—
721C22×C79—24no—
722C22×C79—21no—
723C22×C79—21no—
724C22×C79—22no—
725C22×C79—22no—
726C22×C79—22no—
727C22×C79—28no—
728C22×C79—22no—
729C22×C79—44no—
730C22×C79—48no—
731C22×C79—48no—
732C22×C79—44no—
733C22×C79—44no—
734C22×C79—84no—
735C22×C79C2×H(5,𝔽2)12yes—
736C22×C79#58514yes—
737C22×C79C2611yescharacteristic
738C2×D79—24no—
739C2×D79—24no—
740C2×D79—24no—
741C2×D79—24no—
742C2×D79—24no—
743C2×D79—24no—
744C2×D79—88no—
745C2×D79—164no—
746C4×C79—22no—
747C4×C79—22no—
748C4×C79—22no—
749C4×C79—24no—
750C4×C79—28no—
751C4×C79C2×H(5,𝔽2)14yes—
752Dic79—24no—
753Dic79—24no—
754Dic79—24no—
755Dic79—24no—
756Dic79—24no—
757Dic79—24no—
758#62821—791nomaximal, Sylow
759C2×C79—24no—
760C2×C79—22no—
761C2×C79—44no—
762C2×C79—42no—
763C2×C79—41no—
764C2×C79—41no—
765C2×C79C22×H(5,𝔽2)11yescharacteristic
766C2×C79C2×#58512yes—
767D79—44no—
768D79—44no—
769#3542—794no—
770#3541—794no—
771#3540—794no—
772#3539—794no—
773#3533—794no—
774#3532—794no—
775#3520—794no—
776#3519—794no—
777#3513—798no—
778#3506—794no—
779#3505—794no—
780#3495—792no—
781#3494—792no—
782#3493—792no—
783#3489—792no—
784#3488—792no—
785#3487—791no—
786#3485—791no—
787C2×#525—792no—
788C2×#525D7911yescharacteristic, complemented
789C79#6282111yescharacteristic, complemented, Sylow
790C2×2−1+4—791no—
791C2×H(5,𝔽2)—791no—
792C22×#41—792no—
793C22×#41C2×D7911yescharacteristic, complemented
794C24×C4C2×D7911yescharacteristic, complemented
795#563—794no—
796#562—798no—
797H(3,𝔽4)—794no—
798#560—794no—
799#560—794no—
800#560—798no—
801#559—794no—
802#559—798no—
803#556—794no—
804#556—794no—
805#556—794no—
806#555—794no—
807#555—794no—
808#555—794no—
809#554—794no—
810#554—798no—
811#553—798no—
812#553—794no—
813#553—794no—
814#553—798no—
815#553—798no—
816#553—798no—
817#553—794no—
818#553—794no—
819#552—794no—
820#552—794no—
821#552—794no—
822#552—794no—
823#552—798no—
824#551—794no—
825#551—794no—
826#551—798no—
827#551—798no—
828#551—798no—
829#551—798no—
830#550—794no—
831#550—794no—
832#550—794no—
833D4×Q8—794no—
834#548—794no—
835#548—794no—
836#548—794no—
837#548—794no—
838#547—794no—
839#547—794no—
840#547—794no—
841#547—794no—
842#547—798no—
843#546—794no—
844#546—794no—
845#546—798no—
846#546—794no—
847#546—794no—
848#546—798no—
849#546—798no—
850#546—798no—
851#546—798no—
852D42—798no—
853D42—794no—
854D42—794no—
855#544—792no—
856#542—798no—
857#542—794no—
858#542—794no—
859#542—798no—
860#541—794no—
861#540—798no—
862#540—794no—
863#540—798no—
864#539—798no—
865#539—798no—
866#539—798no—
867#538—798no—
868#538—798no—
869#538—798no—
870#538—798no—
871#538—798no—
872#538—798no—
873#537—794no—
874#537—794no—
875#537—792no—
876#536—792no—
877#536—794no—
878#535—792no—
879#535—794no—
880#535—794no—
881#535—798no—
882#534—794no—
883#534—798no—
884#533—794no—
885#532—794no—
886#529—794no—
887#529—794no—
888#529—798no—
889#525—792no—
890#525—792no—
891#525—792no—
892#525—792no—
893#525—792no—
894#525—792no—
895#525—794no—
896#525—794no—
897#525—792no—
898#525—794no—
899#525—792no—
900#525—794no—
901#525—794no—
902#525—794no—
903#525—794no—
904#525C2×D7914yescomplemented
905#525C2×D7914yescomplemented
906#525C2×D7914yescomplemented
907#525C2×D7914yescomplemented
908C2×#123—794no—
909C2×#123—794no—
910C2×#123C2×D7912yescomplemented
911C2×C22⋊Q8—792no—
912C2×C22⋊Q8—792no—
913C2×C22⋊Q8—794no—
914C2×C22⋊Q8C2×D7912yescomplemented
915C2×#121—792no—
916C2×#121—792no—
917C2×#121—794no—
918C2×#121C2×D7912yescomplemented
919C2×#120—794no—
920C2×#120C2×D7912yescomplemented
921#520—798no—
922#520—792no—
923#520—792no—
924#519—791no—
925#518—791no—
926#518—798no—
927C2×C4×D4—794no—
928C2×C4×D4—794no—
929C2×C4×D4C2×D7914yescomplemented
930C2×#117—792no—
931C2×#117C2×D7911yescharacteristic, complemented
932C25C22×D7911yescharacteristic
9332−1+4—3164no—
934H(5,𝔽2)—3164no—
935C2×#41—44no—
936C2×#41—3168no—
937C2×#41—794no—
938C2×#41—798no—
939C2×#41—794no—
940C2×#41—794no—
941C2×#41—794no—
942C2×#41—792no—
943C2×#41—792no—
944C2×#41—794no—
945C2×#41—792no—
946C2×#41—792no—
947C2×#41C22×D7914yes—
948C2×#41C22×D7914yes—
949C22×Q8—794no—
950C22×Q8—792no—
951C22×Q8C22×D7911yescharacteristic
952C22×D4—794no—
953C22×D4—794no—
954C22×D4—794no—
955C22×D4—794no—
956C22×D4—798no—
957C22×D4—794no—
958C22×D4—792no—
959C22×D4C22×D7911yescharacteristic
960C22×D4C22×D7914yes—
961C22×D4C22×D7912yes—
962C23×C4—44no—
963C23×C4—794no—
964C23×C4C22×D7912yes—
965C23×C4C22×D7911yescharacteristic
966C23×C4C22×D7912yes—
967C23×C4C22×D7912yes—
968C23×C4C22×D7912yes—
969C23×C4C22×D7912yes—
970C23×C4C22×D7912yes—
971C23×C4C22×D7911yescharacteristic
972C23×C4C22×D7912yes—
973C4⋊Q8—794no—
974C4⋊Q8—794no—
975C4⋊Q8—794no—
976C4⋊Q8—798no—
977#127—794no—
978#127—794no—
979#127—798no—
980#127—794no—
981#126—798no—
982#126—798no—
983#126—798no—
984#126—798no—
985#126—798no—
986#126—798no—
987#126—798no—
988#126—798no—
989#126—798no—
990#126—798no—
991#125—794no—
992#125—794no—
993#125—798no—
994#125—798no—
995#125—798no—
996#125—798no—
997#124—794no—
998#124—794no—
999#124—794no—
1000#124—794no—
1001#124—798no—
1002#124—798no—
1003#124—798no—
1004#124—798no—
1005#124—798no—
1006#124—798no—
1007#124—798no—
1008#124—798no—
1009#123—798no—
1010#123—794no—
1011#123—794no—
1012#123—798no—
1013#123—794no—
1014#123—794no—
1015#123—794no—
1016#123—794no—
1017#123—794no—
1018#123—794no—
1019#123—794no—
1020#123—794no—
1021#123—798no—
1022#123—798no—
1023#123—798no—
1024#123—798no—
1025#123—798no—
1026#123—798no—
1027#123—798no—
1028#123—798no—
1029#123—798no—
1030#123—798no—
1031#123—798no—
1032#123—798no—
1033#123—798no—
1034#123C22×D7918yes—
1035#123C22×D7914yes—
1036#123C22×D7914yes—
1037C22⋊Q8—794no—
1038C22⋊Q8—794no—
1039C22⋊Q8—792no—
1040C22⋊Q8—792no—
1041C22⋊Q8—792no—
1042C22⋊Q8—792no—
1043C22⋊Q8—794no—
1044C22⋊Q8—794no—
1045C22⋊Q8—792no—
1046C22⋊Q8—792no—
1047C22⋊Q8—792no—
1048C22⋊Q8—792no—
1049C22⋊Q8—794no—
1050C22⋊Q8—794no—
1051C22⋊Q8—798no—
1052C22⋊Q8—798no—
1053C22⋊Q8—794no—
1054C22⋊Q8—798no—
1055C22⋊Q8—794no—
1056C22⋊Q8—798no—
1057C22⋊Q8—798no—
1058C22⋊Q8—798no—
1059C22⋊Q8—798no—
1060C22⋊Q8—798no—
1061C22⋊Q8—798no—
1062C22⋊Q8C22×D7914yes—
1063C22⋊Q8C22×D7914yes—
1064C22⋊Q8C22×D7914yes—
1065C22⋊Q8C22×D7914yes—
1066#121—794no—
1067#121—798no—
1068#121—794no—
1069#121—798no—
1070#121—798no—
1071#121—798no—
1072#121—798no—
1073#121—798no—
1074#121—798no—
1075#121—798no—
1076#121—798no—
1077#121—798no—
1078#121—792no—
1079#121—792no—
1080#121—792no—
1081#121—792no—
1082#121—794no—
1083#121—794no—
1084#121—794no—
1085#121—792no—
1086#121—792no—
1087#121—792no—
1088#121—792no—
1089#121—794no—
1090#121—798no—
1091#121—798no—
1092#121—794no—
1093#121—794no—
1094#121—798no—
1095#121—798no—
1096#121—798no—
1097#121—798no—
1098#121—798no—
1099#121—798no—
1100#121—798no—
1101#121C22×D7914yes—
1102#121C22×D7914yes—
1103#121C22×D7914yes—
1104#121C22×D7914yes—
1105#120—794no—
1106#120—794no—
1107#120—794no—
1108#120—794no—
1109#120—794no—
1110#120—794no—
1111#120—794no—
1112#120—794no—
1113#120—798no—
1114#120—798no—
1115#120—794no—
1116#120—798no—
1117#120—794no—
1118#120—798no—
1119#120—798no—
1120#120C22×D7918yes—
1121#120C22×D7914yes—
1122#120C22×D7914yes—
1123C4×Q8—794no—
1124C4×Q8—794no—
1125C4×Q8—794no—
1126C4×Q8—794no—
1127C4×Q8—798no—
1128C4×Q8—798no—
1129C4×D4—798no—
1130C4×D4—794no—
1131C4×D4—794no—
1132C4×D4—798no—
1133C4×D4—794no—
1134C4×D4—794no—
1135C4×D4—794no—
1136C4×D4—794no—
1137C4×D4—794no—
1138C4×D4—794no—
1139C4×D4—794no—
1140C4×D4—794no—
1141C4×D4—794no—
1142C4×D4—794no—
1143C4×D4—794no—
1144C4×D4—794no—
1145C4×D4—794no—
1146C4×D4—794no—
1147C4×D4—794no—
1148C4×D4—794no—
1149C4×D4—798no—
1150C4×D4—798no—
1151C4×D4—798no—
1152C4×D4—798no—
1153C4×D4—798no—
1154C4×D4—794no—
1155C4×D4—794no—
1156C4×D4—798no—
1157C4×D4—798no—
1158C4×D4—798no—
1159C4×D4—798no—
1160C4×D4—798no—
1161C4×D4C22×D7918yes—
1162C4×D4C22×D7918yes—
1163C4×D4C22×D7918yes—
1164C4×D4C22×D7918yes—
1165#117—792no—
1166#117—792no—
1167#117—794no—
1168#117—794no—
1169#117—792no—
1170#117—792no—
1171#117—794no—
1172#117—798no—
1173#117—794no—
1174#117—794no—
1175#117—798no—
1176#117—798no—
1177#117—798no—
1178#117—798no—
1179#117C22×D7914yes—
1180#117C22×D7914yes—
1181C2×C4⋊C4—792no—
1182C2×C4⋊C4—792no—
1183C2×C4⋊C4—794no—
1184C2×C4⋊C4—794no—
1185C2×C4⋊C4—798no—
1186C2×C4⋊C4—794no—
1187C2×C4⋊C4—794no—
1188C2×C4⋊C4—798no—
1189C2×C4⋊C4C22×D7912yes—
1190C2×C4⋊C4C22×D7914yes—
1191C2×C22⋊C4—794no—
1192C2×C22⋊C4—794no—
1193C2×C22⋊C4—794no—
1194C2×C22⋊C4—794no—
1195C2×C22⋊C4—794no—
1196C2×C22⋊C4—794no—
1197C2×C22⋊C4—798no—
1198C2×C22⋊C4—798no—
1199C2×C22⋊C4—798no—
1200C2×C22⋊C4C22×D7912yes—
1201C2×C22⋊C4C22×D7914yes—
1202C2×C22⋊C4C22×D7914yes—
1203C2×C42—794no—
1204C2×C42C22×D7912yes—
1205C24—42no—
1206C24—44no—
1207C24—794no—
1208C24—794no—
1209C24C23×D7911yescharacteristic
1210C24C23×D7912yes—
1211C24C23×D7912yes—
1212C24C23×D7912yes—
1213C24C23×D7911yescharacteristic
1214C24C23×D7911yescharacteristic
1215#41—48no—
1216#41—48no—
1217#41—3164no—
1218#41—3164no—
1219#41—3168no—
1220#41—3168no—
1221#41—3168no—
1222#41—3168no—
1223#41—31616no—
1224#41—3168no—
1225#41—1588no—
1226#41—1588no—
1227C2×Q8—24no—
1228C2×Q8—3164no—
1229C2×Q8—3168no—
1230C2×Q8—798no—
1231C2×Q8—794no—
1232C2×Q8—794no—
1233C2×Q8—792no—
1234C2×Q8—792no—
1235C2×Q8C23×D7914yes—
1236C2×D4—24no—
1237C2×D4—44no—
1238C2×D4—48no—
1239C2×D4—3164no—
1240C2×D4—31616no—
1241C2×D4—3168no—
1242C2×D4—3168no—
1243C2×D4—3168no—
1244C2×D4—3168no—
1245C2×D4—3168no—
1246C2×D4—794no—
1247C2×D4—794no—
1248C2×D4—794no—
1249C2×D4—798no—
1250C2×D4—794no—
1251C2×D4—794no—
1252C2×D4—794no—
1253C2×D4—798no—
1254C2×D4—794no—
1255C2×D4—794no—
1256C2×D4—798no—
1257C2×D4—794no—
1258C2×D4—794no—
1259C2×D4—794no—
1260C2×D4—794no—
1261C2×D4—798no—
1262C2×D4—794no—
1263C2×D4—794no—
1264C2×D4—792no—
1265C2×D4—792no—
1266C2×D4C23×D7918yes—
1267C2×D4C23×D7914yes—
1268C2×D4C23×D7918yes—
1269C2×D4C23×D7914yes—
1270C2×D4C23×D7914yes—
1271C22×C4—24no—
1272C22×C4—28no—
1273C22×C4—44no—
1274C22×C4—44no—
1275C22×C4—44no—
1276C22×C4—44no—
1277C22×C4—44no—
1278C22×C4—42no—
1279C22×C4—44no—
1280C22×C4—3168no—
1281C22×C4—794no—
1282C22×C4—794no—
1283C22×C4—798no—
1284C22×C4—794no—
1285C22×C4—794no—
1286C22×C4—798no—
1287C22×C4—798no—
1288C22×C4—798no—
1289C22×C4—794no—
1290C22×C4—794no—
1291C22×C4—794no—
1292C22×C4—794no—
1293C22×C4C23×D7912yes—
1294C22×C4C23×D7911yescharacteristic
1295C22×C4C23×D7912yes—
1296C22×C4C23×D7912yes—
1297C22×C4C23×D7912yes—
1298C22×C4C23×D7912yes—
1299C22×C4C23×D7912yes—
1300C22×C4C23×D7912yes—
1301C22×C4C23×D7912yes—
1302C22×C4C23×D7914yes—
1303C22×C4C23×D7912yes—
1304C22×C4C23×D7912yes—
1305C22×C4C23×D7918yes—
1306C22×C4C23×D7911yescharacteristic
1307C22×C4C23×D7912yes—
1308C22×C4C23×D7912yes—
1309C22×C4C23×D7912yes—
1310C22×C4C23×D7911yescharacteristic
1311C22×C4C23×D7911yescharacteristic
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—798no—
1322C4⋊C4—798no—
1323C4⋊C4—798no—
1324C4⋊C4—798no—
1325C4⋊C4—798no—
1326C4⋊C4—792no—
1327C4⋊C4—792no—
1328C4⋊C4—792no—
1329C4⋊C4—792no—
1330C4⋊C4—794no—
1331C4⋊C4—794no—
1332C4⋊C4—798no—
1333C4⋊C4—798no—
1334C4⋊C4—798no—
1335C4⋊C4C23×D7914yes—
1336C4⋊C4C23×D7914yes—
1337C4⋊C4C23×D7918yes—
1338C4⋊C4C23×D7918yes—
1339C22⋊C4—794no—
1340C22⋊C4—794no—
1341C22⋊C4—794no—
1342C22⋊C4—794no—
1343C22⋊C4—794no—
1344C22⋊C4—794no—
1345C22⋊C4—794no—
1346C22⋊C4—794no—
1347C22⋊C4—794no—
1348C22⋊C4—794no—
1349C22⋊C4—794no—
1350C22⋊C4—794no—
1351C22⋊C4—798no—
1352C22⋊C4—794no—
1353C22⋊C4—794no—
1354C22⋊C4—798no—
1355C22⋊C4—794no—
1356C22⋊C4—794no—
1357C22⋊C4—794no—
1358C22⋊C4—798no—
1359C22⋊C4—798no—
1360C22⋊C4—794no—
1361C22⋊C4—794no—
1362C22⋊C4—794no—
1363C22⋊C4—794no—
1364C22⋊C4—798no—
1365C22⋊C4—794no—
1366C22⋊C4—798no—
1367C22⋊C4—798no—
1368C22⋊C4—798no—
1369C22⋊C4C23×D7918yes—
1370C22⋊C4C23×D7918yes—
1371C22⋊C4C23×D7914yes—
1372C22⋊C4C23×D7914yes—
1373C22⋊C4C23×D7918yes—
1374C22⋊C4C23×D7918yes—
1375C42—794no—
1376C42—794no—
1377C42—794no—
1378C42—794no—
1379C42—798no—
1380C42—794no—
1381C42—798no—
1382C42—794no—
1383C42C23×D7918yes—
1384C23—22no—
1385C23—24no—
1386C23—24no—
1387C23—24no—
1388C23—24no—
1389C23—24no—
1390C23—41no—
1391C23—42no—
1392C23—41no—
1393C23—42no—
1394C23—42no—
1395C23—42no—
1396C23—42no—
1397C23—44no—
1398C23—416no—
1399C23—3164no—
1400C23—3164no—
1401C23—3164no—
1402C23—3168no—
1403C23—794no—
1404C23—794no—
1405C23—1588no—
1406C23C24×D7911yescharacteristic
1407C23C24×D7911yescharacteristic
1408C23C24×D7912yes—
1409C23C24×D7914yes—
1410C23C24×D7911yescharacteristic
1411C23C24×D7912yes—
1412Q8—28no—
1413Q8—3164no—
1414Q8—3164no—
1415Q8—3168no—
1416Q8—1584no—
1417Q8—1584no—
1418D4—216no—
1419D4—28no—
1420D4—48no—
1421D4—44no—
1422D4—44no—
1423D4—3164no—
1424D4—3168no—
1425D4—3164no—
1426D4—3168no—
1427D4—3164no—
1428D4—3164no—
1429D4—3168no—
1430D4—3164no—
1431D4—3164no—
1432D4—3164no—
1433D4—3164no—
1434D4—3164no—
1435D4—3164no—
1436D4—3168no—
1437D4—1588no—
1438D4—1588no—
1439D4—1588no—
1440D4—1588no—
1441D4—1584no—
1442D4—1584no—
1443C2×C4—22no—
1444C2×C4—24no—
1445C2×C4—24no—
1446C2×C4—24no—
1447C2×C4—24no—
1448C2×C4—24no—
1449C2×C4—24no—
1450C2×C4—24no—
1451C2×C4—24no—
1452C2×C4—42no—
1453C2×C4—42no—
1454C2×C4—42no—
1455C2×C4—42no—
1456C2×C4—41no—
1457C2×C4—42no—
1458C2×C4—41no—
1459C2×C4—48no—
1460C2×C4—44no—
1461C2×C4—3164no—
1462C2×C4—3164no—
1463C2×C4—3168no—
1464C2×C4—3168no—
1465C2×C4—3168no—
1466C2×C4—3164no—
1467C2×C4—3164no—
1468C2×C4—3164no—
1469C2×C4—3168no—
1470C2×C4—794no—
1471C2×C4—794no—
1472C2×C4—794no—
1473C2×C4—794no—
1474C2×C4—794no—
1475C2×C4—794no—
1476C2×C4—1588no—
1477C2×C4—1588no—
1478C2×C4—1588no—
1479C2×C4#1457920614yes—
1480C2×C4C24×D7912yes—
1481C2×C4C24×D7918yes—
1482C2×C4C24×D7914yes—
1483C2×C4C24×D7912yes—
1484C2×C4C24×D7912yes—
1485C2×C4C24×D7912yes—
1486C22—22no—
1487C22—22no—
1488C22—22no—
1489C22—21no—
1490C22—21no—
1491C22—22no—
1492C22—24no—
1493C22—28no—
1494C22—22no—
1495C22—22no—
1496C22—22no—
1497C22—22no—
1498C22—48no—
1499C22—44no—
1500C22—44no—
1501C22—48no—
1502C22—44no—
1503C22—84no—
1504C22—6328no—
1505C22—1584no—
1506C22—1584no—
1507C22—1584no—
1508C22—1584no—
1509C22—1584no—
1510C22—1584no—
1511C22—12644no—
1512C22C2×#1457920612yes—
1513C22#1909939914yes—
1514C22C25×D7911yescharacteristic
1515C4—22no—
1516C4—22no—
1517C4—22no—
1518C4—24no—
1519C4—28no—
1520C4—1584no—
1521C4—1584no—
1522C4—1584no—
1523C4—1584no—
1524C4—1584no—
1525C4—1584no—
1526C4C2×#1457920614yes—
1527C2—22no—
1528C2—24no—
1529C2—41no—
1530C2—41no—
1531C2—42no—
1532C2—44no—
1533C2—3164no—
1534C2—3164no—
1535C2C22×#1457920611yescharacteristic
1536C2C2×#1909939912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC2×#525×C79C2
hypercenterC2×#525D79
hypocenterC79#62821
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. #23777708C2semidirect
2. #23777685C2semidirect
3. #23777668C2semidirect
4. #23777656C2semidirect
5. #23777571C2semidirect
6. #23777555C2semidirect
7. #23777437C2semidirect
8. #23777420C2semidirect
9. #23777340C2semidirect
10. #23777243C2semidirect
11. #23777228C2semidirect
12. #23777146C2semidirect
13. #23777129C2semidirect
14. #23777120C2semidirect
15. #23777076C2semidirect
16. #23777065C2semidirect
17. #23777058C2semidirect
18. #23777044C2semidirect
19. C2×#19099074C2semidirect
20. C2×#525×C79C2semidirect
21. C2×#14579209C22semidirect
22. C2×#14579206C22semidirect
23. C22×#11929624C22semidirect
24. #19099316C22semidirect
25. #19099310C22semidirect
26. #19099306C22semidirect
27. #19099303C22semidirect
28. #19099302C22semidirect
29. #19099302C22semidirect
30. #19099297C22semidirect
31. #19099296C22semidirect
32. #19099284C22semidirect
33. #19099281C22semidirect
34. #19099281C22semidirect
35. #19099277C22semidirect
36. #19099276C22semidirect
37. #19099276C22semidirect
38. #19099272C22semidirect
39. #19099271C22semidirect
40. #19099265C22semidirect
41. #19099263C22semidirect
42. #19099262C22semidirect
43. #19099262C22semidirect
44. #19099260C22semidirect
45. #19099258C22semidirect
46. #19099257C22semidirect
47. #19099257C22semidirect
48. #19099255C22semidirect
49. #19099252C22semidirect
50. #19099252C22semidirect
51. #19099248C22semidirect
52. #19099247C22semidirect
53. #19099244C22semidirect
54. #19099242C22semidirect
55. #19099242C22semidirect
56. #19099241C22semidirect
57. #19099239C22semidirect
58. #19099239C22semidirect
59. #19099232C22semidirect
60. #19099232C22semidirect
61. #19099231C22semidirect
62. #19099226C22semidirect
63. #19099223C22semidirect
64. #19099220C22semidirect
65. #19099220C22semidirect
66. #19099219C22semidirect
67. #19099215C22semidirect
68. #19099214C22semidirect
69. #19099213C22semidirect
70. #19099212C22semidirect
71. #19099212C22semidirect
72. #19099210C22semidirect
73. #19099208C22semidirect
74. #19099207C22semidirect
75. #19099204C22semidirect
76. #19099203C22semidirect
77. #19099203C22semidirect
78. #19099201C22semidirect
79. #19099201C22semidirect
80. #19099200C22semidirect
81. #19099197C22semidirect
82. D4×C22⋊D79C22semidirect
83. #19099195C22semidirect
84. #19099194C22semidirect
85. #19099186C22semidirect
86. #19099181C22semidirect
87. #19099180C22semidirect
88. #19099178C22semidirect
89. #19099173C22semidirect
90. #19099166C22semidirect
91. #19099165C22semidirect
92. #19099164C22semidirect
93. #19099156C22semidirect
94. #19099155C22semidirect
95. #19099155C22semidirect
96. #19099151C22semidirect
97. #19099149C22semidirect
98. #19099148C22semidirect
99. #19099148C22semidirect
100. #19099146C22semidirect
101. #19099146C22semidirect
102. #19099144C22semidirect
103. #19099143C22semidirect
104. #19099142C22semidirect
105. #19099137C22semidirect
106. #19099136C22semidirect
107. #19099130C22semidirect
108. #19099130C22semidirect
109. #19099129C22semidirect
110. #19099128C22semidirect
111. #19099123C22semidirect
112. #19099122C22semidirect
113. #19099115C22semidirect
114. #19099108C22semidirect
115. #19099099C22semidirect
116. #19099097C22semidirect
117. #19099094C22semidirect
118. #19099076C22semidirect
120. #19099074C22semidirect
121. #19099074C22semidirect
122. #19099074C22semidirect
123. #19099074C22semidirect
124. #19099074C22semidirect
125. #19099074C22semidirect
126. #19099074C22semidirect
127. #19099074C22semidirect
128. #19099074C22semidirect
129. #19099074C22semidirect
130. #19099074C22semidirect
131. #19099074C22semidirect
132. #19099073C22semidirect
133. C2×#14579144C22semidirect
134. C2×#14579144C22semidirect
135. C2×#14579140C22semidirect
136. C2×#14579140C22semidirect
137. C22⋊Q8×D79C22semidirect
138. C2×#14579135C22semidirect
139. C2×#14579135C22semidirect
140. #121×D79C22semidirect
141. C2×#14579130C22semidirect
142. #19099044C22semidirect
143. #19099044C22semidirect
144. #19099042C22semidirect
145. #19099041C22semidirect
146. #19099038C22semidirect
147. #19099035C22semidirect
148. C2×C4×C22⋊D79C22semidirect
149. C2×C4×C22⋊D79C22semidirect
150. C2×#14579120C22semidirect
151. C22×#41×C79C22semidirect
152. C24×C4×C79C22semidirect
153. #525×C79C22semidirect
154. #525×C79C22semidirect
155. #525×C79C22semidirect
156. #525×C79C22semidirect
157. C2×#123×C79C22semidirect
158. C2×C22⋊Q8×C79C22semidirect
159. C2×#121×C79C22semidirect
160. C2×#120×C79C22semidirect
161. C2×C4×D4×C79C22semidirect
162. C2×#117×C79C22semidirect
165. C2×#11929625C23semidirect
175. C2×#11929623C23semidirect
177. C2×Q8×D79C23semidirect
184. C2×D4×D79C23semidirect
186. #14579160C23semidirect
187. #14579160C23semidirect
188. #14579160C23semidirect
189. #14579159C23semidirect
193. #14579157C23semidirect
194. #14579156C23semidirect
195. #14579156C23semidirect
196. #14579155C23semidirect
197. #14579155C23semidirect
202. #14579154C23semidirect
203. #14579154C23semidirect
204. #14579153C23semidirect
205. #14579152C23semidirect
206. #14579152C23semidirect
207. #14579152C23semidirect
208. #14579151C23semidirect
209. #14579151C23semidirect
210. #14579150C23semidirect
211. #14579149C23semidirect
215. #14579148C23semidirect
220. #14579147C23semidirect
221. #14579147C23semidirect
222. #14579146C23semidirect
223. #14579146C23semidirect
225. #14579145C23semidirect
235. #14579144C23semidirect
236. #14579144C23semidirect
241. #14579143C23semidirect
242. #14579143C23semidirect
247. #14579141C23semidirect
248. #14579141C23semidirect
249. #14579141C23semidirect
263. #14579140C23semidirect
264. #14579139C23semidirect
265. #14579139C23semidirect
268. #14579138C23semidirect
269. #14579138C23semidirect
270. #14579137C23semidirect
271. #14579137C23semidirect
272. #14579136C23semidirect
273. #14579136C23semidirect
274. #14579136C23semidirect
288. #14579135C23semidirect
293. #14579134C23semidirect
294. #14579134C23semidirect
305. #14579132C23semidirect
306. #14579132C23semidirect
308. #14579131C23semidirect
322. Q8×Dic79C23semidirect
323. Q8×Dic79C23semidirect
324. C4×Dic158C23semidirect
325. #14579126C23semidirect
326. #14579126C23semidirect
327. #14579126C23semidirect
328. C4×D316C23semidirect
331. D4×Dic79C23semidirect
332. D4×Dic79C23semidirect
333. #14579123C23semidirect
334. #14579123C23semidirect
335. #14579123C23semidirect
354. C4×C22⋊D79C23semidirect
355. C4×C22⋊D79C23semidirect
358. (C22⋊D79)⋊C4C23semidirect
359. (C22⋊D79)⋊C4C23semidirect
367. #14579119C23semidirect
368. #14579119C23semidirect
369. #14579119C23semidirect
370. #14579118C23semidirect
371. #14579118C23semidirect
373. #14579117C23semidirect
378. C2×Dic79⋊C4C23semidirect
379. C4⋊C4×D79C23semidirect
380. C4⋊C4×D79C23semidirect
381. C4⋊C4×D79C23semidirect
388. C2×(C2×D79)⋊C4C23semidirect
390. C22⋊C4×D79C23semidirect
788. C2×#525D79semidirect
789. C79#62821semidirect
793. C22×#41C2×D79semidirect
794. C24×C4C2×D79semidirect
904. #525C2×D79semidirect
905. #525C2×D79semidirect
906. #525C2×D79semidirect
907. #525C2×D79semidirect
910. C2×#123C2×D79semidirect
914. C2×C22⋊Q8C2×D79semidirect
918. C2×#121C2×D79semidirect
920. C2×#120C2×D79semidirect
929. C2×C4×D4C2×D79semidirect
931. C2×#117C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237777082
#237776852
#237776682
#237776562
#237775712
#237775552
#237774372
#237774202
#237773402
#237772432
#237772282
#237771462
#237771292
#237771202
#237770762
#237770652
#237770582
#237770442
C2×#190990742
C2×#525×C792
#6282179