Finite Group Databasebeta

← #35197417

Subgroups — #35197417

Order 20224.

7086 conjugacy classes of subgroups.

The subgroup lattice has 1582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777318C214yesmaximal, complemented
2#23777314C214yesmaximal, complemented
3#23777304C214yesmaximal, complemented
4#23777300C214yesmaximal, complemented
5#23777238C214yesmaximal, complemented
6#23777235C214yesmaximal, complemented
7#23777145C214yesmaximal, complemented
8#23777141C214yesmaximal, complemented
9#23777134C214yesmaximal, complemented
10#23777131C214yesmaximal, complemented
11#23777120C211yesmaximal, characteristic, complemented
12#23777113C212yesmaximal, complemented
13#23777110C211yesmaximal, characteristic, complemented
14#23777107C211yesmaximal, characteristic, complemented
15#23777106C212yesmaximal, complemented
16#23776829C214yesmaximal, complemented
17#23776819C214yesmaximal, complemented
18#544×D79C211yesmaximal, characteristic, complemented
19#23776730C212yesmaximal, complemented
20#537×D79C211yesmaximal, characteristic, complemented
21#23776600C212yesmaximal, complemented
22C2×#19099043C211yesmaximal, characteristic, complemented
23C79×#3493C211yesmaximal, characteristic, complemented
24C22×#11929624C2211yescharacteristic
25C2×#41×D79C2212yes—
26#19099286C2214yescomplemented
27#19099281C2214yescomplemented
28#19099281C2214yescomplemented
29#19099278C2214yescomplemented
30#19099276C2214yescomplemented
31#19099276C2214yescomplemented
32#19099274C2214yescomplemented
33#19099271C2214yescomplemented
34#19099271C2214yescomplemented
35#19099270C2214yescomplemented
36#19099266C2214yescomplemented
37#19099266C2214yescomplemented
38#19099265C2214yescomplemented
39#19099264C2218yescomplemented
40#19099264C2218yescomplemented
41#19099263C2214yescomplemented
42#19099263C2214yescomplemented
43#19099261C2214yescomplemented
44#19099260C2218yescomplemented
45#19099260C2214yescomplemented
46#19099259C2214yescomplemented
47#19099258C2218yescomplemented
48#19099257C2218yescomplemented
49#19099257C2214yescomplemented
50#19099255C2214yescomplemented
51#19099254C2214yescomplemented
52#19099254C2214yescomplemented
53#19099253C2214yescomplemented
54#19099252C2214yescomplemented
55#19099251C2214yescomplemented
56#19099251C2214yescomplemented
57#19099249C2218yescomplemented
58#19099248C2214yescomplemented
59#19099247C2214yescomplemented
60#19099243C2218yescomplemented
61#19099238C2218yescomplemented
62#19099237C2218yescomplemented
63#19099236C2218yescomplemented
64#19099225C2214yescomplemented
65#19099221C2214yescomplemented
66#19099221C2218yescomplemented
67#19099217C2214yescomplemented
68#19099216C2214yescomplemented
69#19099213C2214yescomplemented
70#19099213C2214yescomplemented
71#19099208C2214yescomplemented
72#19099206C2214yescomplemented
73#19099202C2218yescomplemented
74#19099194C2211yescharacteristic, complemented
75#19099193C2214yescomplemented
76#19099192C2214yescomplemented
77#19099191C2212yescomplemented
78#19099190C2214yescomplemented
79#19099179C2218yescomplemented
80#19099179C2218yescomplemented
81#19099177C2218yescomplemented
82#19099177C2218yescomplemented
83#19099172C2218yescomplemented
84#19099170C2218yescomplemented
85#19099165C2218yescomplemented
86#19099163C2218yescomplemented
87#19099162C2214yescomplemented
88#19099158C2214yescomplemented
89#19099157C2218yescomplemented
90#19099151C2214yescomplemented
91#19099146C2218yescomplemented
92#19099144C2211yescharacteristic
93#19099143C2212yescomplemented
94#19099143C2214yescomplemented
95#19099143C2212yescomplemented
96#19099142C2212yescomplemented
97#19099142C2214yescomplemented
98#19099142C2212yescomplemented
99#19099141C2212yes—
100#19099140C2214yes—
101#19099136C2212yes—
102#19099136C2212yes—
103#19099135C2214yescomplemented
104#19099129C2212yes—
105#19099129C2212yes—
106#19099128C2214yescomplemented
107#19099124C2214yes—
108#19099123C2214yes—
109#19099117C2218yescomplemented
110#19099116C2218yescomplemented
111#19099112C2218yescomplemented
112#19099110C2214yescomplemented
113#19099110C2214yescomplemented
114#19099108C2218yescomplemented
115C4⋊Q8×D79C2214yescomplemented
116#19099097C2214yescomplemented
117#19099096C2218yescomplemented
118#19099093C2218yescomplemented
119#19099093C2218yescomplemented
120#19099091C2218yescomplemented
121#19099090C2218yescomplemented
122#125×D79C2214yescomplemented
123#19099076C2214yescomplemented
124#19099075C2212yescomplemented
125#19099074C2212yescomplemented
126#19099073C2214yescomplemented
127#19099072C2214yes—
128#19099072C2214yes—
129#19099070C2212yescomplemented
130#19099069C2218yescomplemented
131C22⋊Q8×D79C2214yes—
132C22⋊Q8×D79C2214yescomplemented
133#121×D79C2214yes—
134#121×D79C2214yescomplemented
135#19099046C2212yescomplemented
136#19099044C2214yescomplemented
137#19099044C2212yescomplemented
138#19099043C2214yes—
139#19099043C2214yes—
140#19099043C2214yescomplemented
141#19099043C2214yescomplemented
142#19099043C2214yescomplemented
143#19099043C2212yescomplemented
144#19099039C2214yescomplemented
145#19099035C2218yes—
146#19099035C2214yescomplemented
147C4×#11929625C2214yescomplemented
148C4×#11929623C2214yescomplemented
149C4×#11929623C2218yescomplemented
150C2×C4×Dic158C2212yescomplemented
151C2×C4×D316C2212yes—
152C2×(C22⋊D79)⋊C4C2212yes—
153C2×(C22⋊D79)⋊C4C2212yescomplemented
154C2×#14579119C2211yescharacteristic
155C2×#14579119C2211yescharacteristic, complemented
156C2×#14579119C2214yescomplemented
157#117×D79C2212yes—
158#117×D79C2214yescomplemented
159C22×C4⋊Dic79C2211yescharacteristic, complemented
160C2×C4⋊C4×D79C2211yescharacteristic
161C2×C4⋊C4×D79C2211yescharacteristic, complemented
162#556×C79C2214yescomplemented
163#555×C79C2214yescomplemented
164#553×C79C2214yescomplemented
165#552×C79C2214yescomplemented
166#544×C79C2211yescharacteristic, complemented
167#538×C79C2214yescomplemented
168#537×C79C2211yescharacteristic
169#529×C79C2214yescomplemented
170#525×C79C2212yescomplemented
171#520×C79C2212yescomplemented
172C2×#117×C79C2211yescharacteristic, complemented
173C2×#11929625C2312yes—
174C2×#11929625C2314yes—
175C2×#11929624—28no—
176C2×#11929624C2312yes—
177C2×#11929624C2312yes—
178C2×#11929624C2312yes—
179C2×#11929624C2312yes—
180C2×#11929624C2312yes—
181C2×#11929624C2314yes—
182C2×#11929623C2314yes—
183C2×#11929623C2312yes—
184C2×#11929623C2318yes—
185C2×#11929623C2314yes—
186#41×D79—216no—
187C22×Dic158C2311yescharacteristic
188C2×Q8×D79C2312yes—
189C2×Q8×D79C2314yes—
190C22×D316C2311yescharacteristic
191C22×C22⋊D79C2311yescharacteristic
192C22×C22⋊D79C2311yescharacteristic
193C2×D4×D79C2314yes—
194C2×D4×D79C2312yes—
195C2×D4×D79C2314yes—
196C23×Dic79C2312yes—
197C22×C4×D79C2311yescharacteristic
198C22×C4×D79C2314yes—
199C22×C4×D79C2312yes—
200C22×C4×D79C2312yes—
201C22×C4×D79C2311yescharacteristic
202#14579161C2314yes—
203#14579160C2314yes—
204#14579160C2314yes—
205#14579160C2318yes—
206#14579160C2314yes—
207#14579160C2314yes—
208#14579159C2318yes—
209#14579157C2314yes—
210#14579157C2314yes—
211#14579156C2318yes—
212#14579156C2318yes—
213#14579156C2318yes—
214#14579156C2318yes—
215#14579155C2318yes—
216#14579155C2318yes—
217#14579154C2318yes—
218#14579154C2318yes—
219#14579154C2318yes—
220#14579154C2318yes—
221#14579153C2314yes—
222#14579153C2314yes—
223#14579152C2318yes—
224#14579152C2318yes—
225#14579152C2314yes—
226#14579152C2314yes—
227#14579151C2318yes—
228#14579151C2318yes—
229#14579151C2318yes—
230#14579151C2318yes—
231#14579151C2318yes—
232#14579149C2318yes—
233#14579149C2314yes—
234#14579147C2314yes—
235#14579147C2314yes—
236#14579147C2318yes—
237#14579147C2318yes—
238#14579147C2314yes—
239#14579147C2318yes—
240#14579147C2314yes—
241#14579146C2314yes—
242#14579146C2314yes—
243#14579146C2318yes—
244#14579146C2318yes—
245#14579146C2318yes—
246#14579145C2318yes—
247#14579145C2314yes—
248#14579145C2318yes—
249#14579144C2318yes—
250#14579144C2314yes—
251#14579143C2314yes—
252#14579143C2314yes—
253#14579143C2318yes—
254#14579143C2318yes—
255#14579143C2318yes—
256#14579142C2314yes—
257#14579142C2318yes—
258#14579142C2318yes—
259#14579141C2312yes—
260#14579141C2312yes—
261#14579141C2314yes—
262#14579141C2318yes—
263#14579141C2314yes—
264#14579141C2314yes—
265#14579140C2312yes—
266#14579140C2312yes—
267#14579140C2314yes—
268#14579140C2314yes—
269#14579139C2318yes—
270#14579139C2314yes—
271#14579139C2314yes—
272#14579139C2318yes—
273#14579138C2318yes—
274#14579138C2314yes—
275#14579138C2314yes—
276#14579138C2318yes—
277#14579138C2318yes—
278#14579138C2318yes—
279#14579138C2318yes—
280#14579137C2312yes—
281#14579137C2312yes—
282#14579137C2314yes—
283#14579137C2318yes—
284#14579137C2314yes—
285#14579137C2314yes—
286#14579136C2314yes—
287#14579136C2314yes—
288#14579136C2312yes—
289#14579136C2314yes—
290#14579136C2314yes—
291#14579136C2312yes—
292#14579136C2314yes—
293#14579135C2314yes—
294#14579135C2314yes—
295#14579135C2312yes—
296#14579135C2312yes—
297#14579135C2318yes—
298#14579134C2318yes—
299#14579134C2318yes—
300#14579134C2314yes—
301#14579134C2314yes—
302#14579134C2314yes—
303#14579134C2314yes—
304#14579134C2314yes—
305#14579134C2314yes—
306#14579134C2318yes—
307#14579134C2318yes—
308#14579133C2318yes—
309#14579133C2318yes—
310#14579133C2314yes—
311#14579133C2314yes—
312#14579133C2318yes—
313#14579132C2314yes—
314#14579132C2314yes—
315#14579132C2312yes—
316#14579132C2314yes—
317#14579132C2314yes—
318#14579132C2312yes—
319#14579132C2314yes—
320#14579131C2314yes—
321#14579131C2314yes—
322#14579131C2314yes—
323#14579130C2314yes—
324#14579129C2314yes—
325#14579129C2314yes—
326#14579129C2314yes—
327Q8×Dic79C2314yes—
328C4×Dic158C2318yes—
329C4×Dic158C2318yes—
330C4×Dic158C2318yes—
331C4×Dic158C2318yes—
332C4×Dic158C2314yes—
333C4×Dic158C2314yes—
334#14579126C2318yes—
335#14579126C2314yes—
336C4×D316C2314yes—
337C4×D316C2314yes—
338C4×D316C2314yes—
339C4×D316C2314yes—
340C4×D316C2314yes—
341C4×D316C2318yes—
342C4×D316C2314yes—
343C4×D316C2314yes—
344C4×D316C2314yes—
345D4×Dic79C2318yes—
346D4×Dic79C2314yes—
347D4×Dic79C2318yes—
348#14579123C2318yes—
349#14579123C2314yes—
350#14579123C2318yes—
351C4×C22⋊D79C2318yes—
352C4×C22⋊D79C2318yes—
353C4×C22⋊D79C2318yes—
354C4×C22⋊D79C2314yes—
355C4×C22⋊D79C2314yes—
356C4×C22⋊D79C2314yes—
357C4×C22⋊D79C2314yes—
358C4×C22⋊D79C2318yes—
359(C22⋊D79)⋊C4C2318yes—
360(C22⋊D79)⋊C4C2318yes—
361(C22⋊D79)⋊C4C2318yes—
362(C22⋊D79)⋊C4C2318yes—
363(C22⋊D79)⋊C4C2318yes—
364(C22⋊D79)⋊C4C2318yes—
365(C22⋊D79)⋊C4C2318yes—
366(C22⋊D79)⋊C4C2318yes—
367(C22⋊D79)⋊C4C2318yes—
368#14579120C2312yes—
369#14579120C2318yes—
370#14579120C2314yes—
371#14579119C2312yes—
372#14579119C2312yes—
373#14579119C2318yes—
374#14579119C2318yes—
375#14579119C2314yes—
376#14579119C2314yes—
377#14579119C2314yes—
378#14579119C2314yes—
379#14579119C2314yes—
380#14579119C2314yes—
381#14579119C2314yes—
382#14579119C2314yes—
383#14579118C2314yes—
384#14579118C2318yes—
385#14579118C2318yes—
386#14579118C2318yes—
387#14579117C2318yes—
388#14579117C2314yes—
389#14579117C2318yes—
390C2×C4⋊Dic79C2311yescharacteristic
391C2×C4⋊Dic79C2312yes—
392C2×C4⋊Dic79C2314yes—
393C2×C4⋊Dic79C2314yes—
394C2×C4⋊Dic79C2314yes—
395C2×C4⋊Dic79C2311yescharacteristic
396C2×Dic79⋊C4C2312yes—
397C2×Dic79⋊C4C2312yes—
398C4⋊C4×D79C2314yes—
399C4⋊C4×D79C2312yes—
400C4⋊C4×D79C2312yes—
401C4⋊C4×D79C2314yes—
402C4⋊C4×D79C2314yes—
403C4⋊C4×D79C2314yes—
404C4⋊C4×D79C2314yes—
405C4⋊C4×D79C2314yes—
406C4⋊C4×D79C2314yes—
407C4⋊C4×D79C2318yes—
408C4⋊C4×D79C2314yes—
409C2×(C2×D79)⋊C4C2312yes—
410C2×(C2×D79)⋊C4C2318yes—
411C2×(C2×D79)⋊C4C2312yes—
412C22⋊C4×D79C2318yes—
413C22⋊C4×D79C2318yes—
414C22⋊C4×D79C2314yes—
415C2×C4×Dic79C2312yes—
416C2×C4×Dic79C2312yes—
417C2×C4×Dic79C2318yes—
418C42×D79C2314yes—
419C42×D79C2318yes—
420C2×#41×C79C2312yes—
421C23×C4×C79C2311yescharacteristic
422C4⋊Q8×C79C2314yes—
423#126×C79C2318yes—
424#126×C79C2318yes—
425#125×C79C2314yes—
426#125×C79C2314yes—
427#124×C79C2314yes—
428#124×C79C2318yes—
429#123×C79C2314yes—
430#123×C79C2318yes—
431C22⋊Q8×C79C2312yes—
432C22⋊Q8×C79C2312yes—
433C22⋊Q8×C79C2314yes—
434C22⋊Q8×C79C2314yes—
435#121×C79C2314yes—
436#121×C79C2312yes—
437#121×C79C2314yes—
438#121×C79C2312yes—
439#121×C79C2318yes—
440#120×C79C2314yes—
441C4×Q8×C79C2314yes—
442C4×Q8×C79C2314yes—
443C4×D4×C79C2318yes—
444C4×D4×C79C2314yes—
445C4×D4×C79C2314yes—
446C4×D4×C79C2314yes—
447C4×D4×C79C2314yes—
448#117×C79C2312yes—
449#117×C79C2314yes—
450#117×C79C2314yes—
451#117×C79C2318yes—
452#117×C79C2314yes—
453C2×C4⋊C4×C79C2311yescharacteristic
454C2×C4⋊C4×C79C2311yescharacteristic
455C2×C4⋊C4×C79C2314yes—
456C2×C22⋊C4×C79C2312yes—
457C2×C42×C79C2312yes—
458C23×D79C2414yes—
459C23×D79C2411yescharacteristic
460C23×D79C2411yescharacteristic
461#11929625—28no—
462#11929625—84no—
463#11929624—216no—
464#11929624—28no—
465#11929624—28no—
466#11929624—28no—
467#11929624—28no—
468#11929624—28no—
469#11929623—216no—
470#11929623—28no—
471#11929623—88no—
472#11929623—84no—
473C2×Dic158—24no—
474C2×Dic158C2414yes—
475C2×Dic158C2412yes—
476C2×Dic158C2412yes—
477C2×Dic158C2412yes—
478C2×Dic158C2418yes—
479C2×Dic158C2414yes—
480Q8×D79—28no—
481Q8×D79—84no—
482C2×D316—24no—
483C2×D316C2411yescharacteristic
484C2×D316C2411yescharacteristic
485C2×D316C2411yescharacteristic
486C2×D316C2411yescharacteristic
487C2×D316C2414yes—
488C2×D316C2412yes—
489C2×D316C2414yes—
490C2×D316C2414yes—
491C2×D316C2414yes—
492C2×C22⋊D79—24no—
493C2×C22⋊D79—24no—
494C2×C22⋊D79C2414yes—
495C2×C22⋊D79C2414yes—
496C2×C22⋊D79C2414yes—
497C2×C22⋊D79C2412yes—
498C2×C22⋊D79C2412yes—
499C2×C22⋊D79C2412yes—
500C2×C22⋊D79C2412yes—
501C2×C22⋊D79C2414yes—
502C2×C22⋊D79C2414yes—
503C2×C22⋊D79C2418yes—
504C2×C22⋊D79C2414yes—
505C2×C22⋊D79C2414yes—
506D4×D79—28no—
507D4×D79—216no—
508D4×D79—84no—
509C22×Dic79—82no—
510C22×Dic79C2411yescharacteristic
511C22×Dic79C2414yes—
512C22×Dic79C2418yes—
513C22×Dic79C2418yes—
514C22×Dic79C2412yes—
515C22×Dic79C2412yes—
516C22×Dic79C2411yescharacteristic
517C2×C4×D79—216no—
518C2×C4×D79—24no—
519C2×C4×D79—82no—
520C2×C4×D79—82no—
521C2×C4×D79#4118yescomplemented
522C2×C4×D79C2414yes—
523C2×C4×D79C2414yes—
524C2×C4×D79C2412yes—
525C2×C4×D79C2412yes—
526C2×C4×D79C2414yes—
527C2×C4×D79C2414yes—
528C2×C4×D79C2414yes—
529C2×C4×D79C2418yes—
530C2×C4×D79C2414yes—
531C2×C4×D79C2414yes—
532C2×C4×D79C2414yes—
533C2×C4×D79C2418yes—
534C2×C4×D79C2414yes—
535C2×C4×D79C2412yes—
536C2×C4×D79C2412yes—
537C4⋊Dic79C2414yes—
538C4⋊Dic79C2412yes—
539C4⋊Dic79C2414yes—
540C4⋊Dic79C2412yes—
541C4⋊Dic79C2414yes—
542C4⋊Dic79C2414yes—
543C4⋊Dic79C2418yes—
544C4⋊Dic79C2414yes—
545C4⋊Dic79C2414yes—
546C4⋊Dic79C2418yes—
547C4⋊Dic79C2414yes—
548C4⋊Dic79C2414yes—
549Dic79⋊C4C2418yes—
550Dic79⋊C4C2418yes—
551Dic79⋊C4C2414yes—
552Dic79⋊C4C2418yes—
553Dic79⋊C4C2414yes—
554Dic79⋊C4C2418yes—
555Dic79⋊C4C2418yes—
556Dic79⋊C4C2418yes—
557Dic79⋊C4C2418yes—
558Dic79⋊C4C2418yes—
559Dic79⋊C4C2414yes—
560Dic79⋊C4C2414yes—
561Dic79⋊C4C2414yes—
562Dic79⋊C4C2414yes—
563C22⋊Dic79C2414yes—
564C22⋊Dic79C2418yes—
565C22⋊Dic79C2418yes—
566C22⋊Dic79C2414yes—
567C22⋊Dic79C2414yes—
568C22⋊Dic79C2414yes—
569C22⋊Dic79C2414yes—
570(C2×D79)⋊C4C2414yes—
571(C2×D79)⋊C4C2414yes—
572(C2×D79)⋊C4C2414yes—
573(C2×D79)⋊C4C2418yes—
574(C2×D79)⋊C4C2418yes—
575(C2×D79)⋊C4C2414yes—
576(C2×D79)⋊C4C2414yes—
577(C2×D79)⋊C4C2414yes—
578(C2×D79)⋊C4C2418yes—
579(C2×D79)⋊C4C2418yes—
580(C2×D79)⋊C4C2414yes—
581(C2×D79)⋊C4C2414yes—
582(C2×D79)⋊C4C2414yes—
583(C2×D79)⋊C4C2414yes—
584(C2×D79)⋊C4C2414yes—
585(C2×D79)⋊C4C2414yes—
586(C2×D79)⋊C4C2414yes—
587(C2×D79)⋊C4C2414yes—
588C4×Dic79C2414yes—
589C4×Dic79C2418yes—
590C4×Dic79C2414yes—
591C4×Dic79C2418yes—
592C4×Dic79C2414yes—
593C4×Dic79C2418yes—
594C4×Dic79C2418yes—
595C4×Dic79C2418yes—
596C24×C79C2411yescharacteristic
597#41×C79—28no—
598C2×Q8×C79C2412yes—
599C2×Q8×C79C2414yes—
600C2×D4×C79C2414yes—
601C2×D4×C79C2412yes—
602C2×D4×C79C2414yes—
603C2×D4×C79C2414yes—
604C2×D4×C79C2414yes—
605C22×C4×C79—24no—
606C22×C4×C79C2411yescharacteristic
607C22×C4×C79C2412yes—
608C22×C4×C79C2412yes—
609C22×C4×C79C2414yes—
610C22×C4×C79C2412yes—
611C22×C4×C79C2412yes—
612C22×C4×C79C2418yes—
613C22×C4×C79C2411yescharacteristic
614C4⋊C4×C79C2414yes—
615C4⋊C4×C79C2412yes—
616C4⋊C4×C79C2414yes—
617C4⋊C4×C79C2418yes—
618C4⋊C4×C79C2412yes—
619C4⋊C4×C79C2414yes—
620C4⋊C4×C79C2418yes—
621C4⋊C4×C79C2414yes—
622C4⋊C4×C79C2414yes—
623C4⋊C4×C79C2414yes—
624C22⋊C4×C79C2418yes—
625C22⋊C4×C79C2414yes—
626C22⋊C4×C79C2414yes—
627C22⋊C4×C79C2418yes—
628C22⋊C4×C79C2418yes—
629C22⋊C4×C79C2414yes—
630C22⋊C4×C79C2414yes—
631C22⋊C4×C79C2414yes—
632C42×C79C2414yes—
633C42×C79C2414yes—
634C42×C79C2418yes—
635C42×C79C2414yes—
636C23×C79—22no—
637C23×C79—41no—
638C23×C79—41no—
639C23×C79C2514yes—
640C23×C79C2512yes—
641C23×C79C2511yescharacteristic
642C22×D79—22no—
643C22×D79—28no—
644C22×D79—41no—
645C22×D79—41no—
646C22×D79—41no—
647C22×D79—41no—
648C22×D79—44no—
649C22×D79—44no—
650C22×D79C2×#4114yes—
651C22×D79C2511yescharacteristic
652C22×D79C2514yes—
653C22×D79C2511yescharacteristic
654C22×D79C2511yescharacteristic
655C22×D79C2511yescharacteristic
656Q8×C79—24no—
657Q8×C79—44no—
658D4×C79—28no—
659D4×C79—24no—
660D4×C79—44no—
661D4×C79—44no—
662D4×C79—44no—
663C2×C4×C79—22no—
664C2×C4×C79—28no—
665C2×C4×C79—24no—
666C2×C4×C79—24no—
667C2×C4×C79—42no—
668C2×C4×C79—42no—
669C2×C4×C79—48no—
670C2×C4×C79C2×#4114yes—
671C2×C4×C79C2514yes—
672C2×C4×C79C2514yes—
673C2×C4×C79C2514yes—
674C2×C4×C79C2514yes—
675C2×C4×C79C2511yescharacteristic
676C2×C4×C79C2511yescharacteristic
677C2×C4×C79C2514yes—
678C2×C4×C79C2512yes—
679C22⋊D79—28no—
680C22⋊D79—28no—
681C22⋊D79—24no—
682C22⋊D79—24no—
683C22⋊D79—28no—
684C22⋊D79—24no—
685C22⋊D79—24no—
686C22⋊D79—48no—
687C22⋊D79—44no—
688C22⋊D79—44no—
689C22⋊D79—44no—
690C22⋊D79—44no—
691C2×Dic79—22no—
692C2×Dic79—28no—
693C2×Dic79—42no—
694C2×Dic79—42no—
695C2×Dic79—48no—
696C2×Dic79—48no—
697C2×Dic79C2×#4114yes—
698C2×Dic79C2514yes—
699C2×Dic79C2514yes—
700C2×Dic79C2514yes—
701C2×Dic79C2512yes—
702C2×Dic79C2514yes—
703C2×Dic79C2514yes—
704C2×Dic79C2512yes—
705D316—28no—
706D316—22no—
707D316—22no—
708D316—22no—
709D316—22no—
710D316—24no—
711D316—44no—
712D316—44no—
713D316—44no—
714C4×D79—28no—
715C4×D79—28no—
716C4×D79—24no—
717C4×D79—24no—
718C4×D79—28no—
719C4×D79—44no—
720C4×D79—44no—
721C4×D79—44no—
722C4×D79—44no—
723C4×D79—48no—
724C4×D79—44no—
725C4×D79—44no—
726C4×D79—48no—
727C4×D79C2×#4118yes—
728C4×D79C2×#4118yes—
729Dic158—24no—
730Dic158—28no—
731Dic158—24no—
732Dic158—24no—
733Dic158—44no—
734Dic158—48no—
735C22×C79—21no—
736C22×C79—21no—
737C22×C79—22no—
738C22×C79—24no—
739C22×C79—24no—
740C22×C79—22no—
741C22×C79—22no—
742C22×C79—24no—
743C22×C79—44no—
744C22×C79C22×#4112yes—
745C22×C79C2611yescharacteristic
746C2×D79—21no—
747C2×D79—21no—
748C2×D79—21no—
749C2×D79—21no—
750C2×D79—21no—
751C2×D79—21no—
752C2×D79—24no—
753C2×D79—21no—
754C2×D79—24no—
755C2×D79—21no—
756C2×D79—21no—
757C2×D79—24no—
758C2×D79—21no—
759C2×D79—44no—
760C2×D79—44no—
761C2×D79—88no—
762C2×D79C22×#4112yes—
763C2×D79C22×#4112yes—
764C4×C79—21no—
765C4×C79—21no—
766C4×C79—24no—
767C4×C79—24no—
768C4×C79—24no—
769C4×C79—24no—
770C4×C79—24no—
771C4×C79C22×#4114yes—
772Dic79—24no—
773Dic79—22no—
774Dic79—24no—
775Dic79—24no—
776Dic79—24no—
777Dic79—24no—
778Dic79C22×#4114yes—
779#62856—791nomaximal, Sylow
780C2×C79—22no—
781C2×C79—44no—
782C2×C79—42no—
783C2×C79C23×#4111yescharacteristic
784C2×C79H(7,𝔽2)11yescharacteristic
785C2×C792−1+611yescharacteristic
786D79—22no—
787D79—22no—
788D79—41no—
789D79—41no—
790D79—44no—
791#3512—794no—
792#3512—794no—
793#3511—794no—
794#3511—794no—
795#3505—794no—
796#3505—794no—
797#3495—794no—
798#3495—794no—
799#3494—794no—
800#3494—794no—
801#3493—792no—
802#3493—791no—
803#3493D7911yescharacteristic, complemented
804#3492—791no—
805#3492—791no—
806#3492—792no—
807#3461—794no—
808#3460—794no—
809C2×#544—791no—
810#3449—792no—
811C2×#537—791no—
812#3428—792no—
813C2×#520—791no—
814C79#6285611yescharacteristic, complemented, Sylow
815C22×#41—792no—
816C22×#41—791no—
817#556—794no—
818#556—794no—
819#556—794no—
820#556C2×D7914yescomplemented
821#555—794no—
822#555—794no—
823#555—794no—
824#555C2×D7914yescomplemented
825#554—794no—
826#554—794no—
827#554—794no—
828#554—794no—
829#553—798no—
830#553—798no—
831#553—794no—
832#553—794no—
833#553—798no—
834#553—794no—
835#553—798no—
836#553—794no—
837#553—794no—
838#553—794no—
839#553—794no—
840#553—794no—
841#553—798no—
842#553—794no—
843#553C2×D7914yescomplemented
844#552—798no—
845#552—794no—
846#552—794no—
847#552—794no—
848#552—794no—
849#552—794no—
850#552—794no—
851#552—794no—
852#552—794no—
853#552—794no—
854#552C2×D7914yescomplemented
855#551—798no—
856#551—798no—
857#551—798no—
858#551—798no—
859#548—798no—
860#548—794no—
861#548—794no—
862#547—794no—
863#547—794no—
864#547—794no—
865#547—794no—
866#546—794no—
867#546—798no—
868#546—794no—
869#544—794no—
870#544—794no—
871#544—794no—
872#544—792no—
873#544—791no—
874#544C2×D7911yescharacteristic, complemented
875#542—798no—
876#542—798no—
877#542—798no—
878#542—798no—
879#541—798no—
880#541—798no—
881#540—798no—
882#540—798no—
883#539—798no—
884#539—794no—
885#539—794no—
886#538—798no—
887#538—794no—
888#538C2×D7914yescomplemented
889#537—792no—
890#537—794no—
891#537—792no—
892#537—792no—
893#537—794no—
894#537—794no—
895#537—792no—
896#537—792no—
897#537—791no—
898#537C2×D7911yescharacteristic
899#536—794no—
900#536—792no—
901#536—792no—
902#535—792no—
903#535—792no—
904#535—794no—
905#534—794no—
906#534—794no—
907#533—798no—
908#533—798no—
909#532—798no—
910#532—798no—
911#532—794no—
912#532—794no—
913C2×C4⋊Q8—794no—
914#529—798no—
915#529—798no—
916#529—798no—
917#529—798no—
918#529—798no—
919#529—794no—
920#529C2×D7914yescomplemented
921C2×#125—794no—
922#525—792no—
923#525—792no—
924#525—794no—
925#525—794no—
926#525—798no—
927#525—794no—
928#525—794no—
929#525—792no—
930#525C2×D7912yescomplemented
931C2×C22⋊Q8—794no—
932C2×C22⋊Q8—794no—
933C2×#121—794no—
934C2×#121—794no—
935#520—792no—
936#520—794no—
937#520—794no—
938#520—794no—
939#520—794no—
940#520—792no—
941#520—794no—
942#520—792no—
943#520—794no—
944#520C2×D7912yescomplemented
945#519—794no—
946#518—798no—
947#518—794no—
948C4×#41—794no—
949C4×#41—798no—
950C4×#41—794no—
951C2×C4×Q8—792no—
952C2×C4×D4—792no—
953C2×C4×D4—792no—
954C2×C4×D4—792no—
955C2×#117—792no—
956C2×#117—794no—
957C2×#117—791no—
958C2×#117—791no—
959C2×#117—794no—
960C2×#117C2×D7911yescharacteristic, complemented
961C22×C4⋊C4—791no—
962C22×C4⋊C4—791no—
963C22×C4⋊C4—791no—
964C2×#41—794no—
965C2×#41—792no—
966C2×#41—794no—
967C2×#41—798no—
968C2×#41—794no—
969C2×#41—792no—
970C2×#41—792no—
971C2×#41—792no—
972C2×#41—792no—
973C2×#41—792no—
974C2×#41—792no—
975C2×#41—794no—
976C2×#41—1588no—
977C2×#41—15816no—
978C2×#41C22×D7912yes—
979C22×Q8—794no—
980C22×Q8—792no—
981C22×Q8—791no—
982C22×D4—791no—
983C22×D4—791no—
984C22×D4—794no—
985C22×D4—794no—
986C22×D4—792no—
987C22×D4—791no—
988C23×C4—791no—
989C23×C4—792no—
990C23×C4—792no—
991C23×C4—792no—
992C23×C4—791no—
993C23×C4—794no—
994C23×C4C22×D7911yescharacteristic
995C4⋊Q8—798no—
996C4⋊Q8—798no—
997C4⋊Q8—794no—
998C4⋊Q8—794no—
999C4⋊Q8—794no—
1000C4⋊Q8—794no—
1001C4⋊Q8—794no—
1002C4⋊Q8C22×D7914yes—
1003#127—794no—
1004#127—794no—
1005#126—798no—
1006#126—798no—
1007#126—798no—
1008#126—798no—
1009#126—798no—
1010#126—798no—
1011#126—798no—
1012#126—798no—
1013#126—798no—
1014#126—798no—
1015#126C22×D7918yes—
1016#126C22×D7918yes—
1017#125—798no—
1018#125—798no—
1019#125—794no—
1020#125—794no—
1021#125—798no—
1022#125—798no—
1023#125—798no—
1024#125—798no—
1025#125—798no—
1026#125—794no—
1027#125—794no—
1028#125C22×D7914yes—
1029#125C22×D7914yes—
1030#124—794no—
1031#124—794no—
1032#124—794no—
1033#124—794no—
1034#124—798no—
1035#124—798no—
1036#124—798no—
1037#124—794no—
1038#124—798no—
1039#124C22×D7914yes—
1040#124C22×D7918yes—
1041#123—794no—
1042#123—798no—
1043#123—798no—
1044#123—794no—
1045#123—798no—
1046#123—794no—
1047#123—794no—
1048#123—798no—
1049#123—798no—
1050#123—798no—
1051#123—794no—
1052#123—794no—
1053#123—794no—
1054#123—798no—
1055#123—798no—
1056#123—798no—
1057#123—798no—
1058#123—798no—
1059#123C22×D7914yes—
1060#123C22×D7918yes—
1061C22⋊Q8—794no—
1062C22⋊Q8—794no—
1063C22⋊Q8—792no—
1064C22⋊Q8—792no—
1065C22⋊Q8—794no—
1066C22⋊Q8—798no—
1067C22⋊Q8—794no—
1068C22⋊Q8—794no—
1069C22⋊Q8—792no—
1070C22⋊Q8—792no—
1071C22⋊Q8—798no—
1072C22⋊Q8—794no—
1073C22⋊Q8—798no—
1074C22⋊Q8—794no—
1075C22⋊Q8—794no—
1076C22⋊Q8—794no—
1077C22⋊Q8—792no—
1078C22⋊Q8—792no—
1079C22⋊Q8—794no—
1080C22⋊Q8—798no—
1081C22⋊Q8—798no—
1082C22⋊Q8—798no—
1083C22⋊Q8—794no—
1084C22⋊Q8—794no—
1085C22⋊Q8—798no—
1086C22⋊Q8—798no—
1087C22⋊Q8—798no—
1088C22⋊Q8C22×D7914yes—
1089C22⋊Q8C22×D7914yes—
1090C22⋊Q8C22×D7912yes—
1091C22⋊Q8C22×D7912yes—
1092#121—798no—
1093#121—798no—
1094#121—794no—
1095#121—794no—
1096#121—794no—
1097#121—794no—
1098#121—792no—
1099#121—792no—
1100#121—794no—
1101#121—798no—
1102#121—794no—
1103#121—794no—
1104#121—794no—
1105#121—794no—
1106#121—792no—
1107#121—792no—
1108#121—798no—
1109#121—794no—
1110#121—794no—
1111#121—792no—
1112#121—792no—
1113#121—794no—
1114#121—794no—
1115#121—794no—
1116#121—798no—
1117#121—798no—
1118#121—794no—
1119#121—794no—
1120#121—794no—
1121#121—794no—
1122#121—794no—
1123#121—794no—
1124#121—798no—
1125#121—798no—
1126#121C22×D7914yes—
1127#121C22×D7914yes—
1128#121C22×D7912yes—
1129#121C22×D7912yes—
1130#121C22×D7918yes—
1131#120—794no—
1132#120—794no—
1133#120—794no—
1134#120—794no—
1135#120—794no—
1136#120—794no—
1137#120—794no—
1138#120C22×D7914yes—
1139C4×Q8—794no—
1140C4×Q8—798no—
1141C4×Q8—794no—
1142C4×Q8—798no—
1143C4×Q8—798no—
1144C4×Q8—798no—
1145C4×Q8—794no—
1146C4×Q8—798no—
1147C4×Q8—794no—
1148C4×Q8C22×D7914yes—
1149C4×Q8C22×D7914yes—
1150C4×D4—798no—
1151C4×D4—794no—
1152C4×D4—798no—
1153C4×D4—798no—
1154C4×D4—798no—
1155C4×D4—798no—
1156C4×D4—794no—
1157C4×D4—794no—
1158C4×D4—794no—
1159C4×D4—794no—
1160C4×D4—798no—
1161C4×D4—798no—
1162C4×D4—794no—
1163C4×D4—798no—
1164C4×D4—798no—
1165C4×D4—798no—
1166C4×D4—798no—
1167C4×D4—798no—
1168C4×D4—798no—
1169C4×D4—798no—
1170C4×D4—798no—
1171C4×D4—798no—
1172C4×D4—798no—
1173C4×D4—794no—
1174C4×D4—794no—
1175C4×D4—794no—
1176C4×D4—794no—
1177C4×D4—794no—
1178C4×D4—798no—
1179C4×D4—794no—
1180C4×D4—794no—
1181C4×D4—794no—
1182C4×D4C22×D7918yes—
1183C4×D4C22×D7914yes—
1184C4×D4C22×D7914yes—
1185C4×D4C22×D7914yes—
1186C4×D4C22×D7914yes—
1187#117—792no—
1188#117—794no—
1189#117—798no—
1190#117—794no—
1191#117—792no—
1192#117—792no—
1193#117—794no—
1194#117—798no—
1195#117—798no—
1196#117—794no—
1197#117—794no—
1198#117—794no—
1199#117—794no—
1200#117—794no—
1201#117—794no—
1202#117—794no—
1203#117—798no—
1204#117—798no—
1205#117—794no—
1206#117—798no—
1207#117—798no—
1208#117—798no—
1209#117C22×D7912yes—
1210#117C22×D7914yes—
1211#117C22×D7914yes—
1212#117C22×D7914yes—
1213#117C22×D7918yes—
1214C2×C4⋊C4—791no—
1215C2×C4⋊C4—791no—
1216C2×C4⋊C4—792no—
1217C2×C4⋊C4—792no—
1218C2×C4⋊C4—792no—
1219C2×C4⋊C4—794no—
1220C2×C4⋊C4—794no—
1221C2×C4⋊C4—794no—
1222C2×C4⋊C4—794no—
1223C2×C4⋊C4—794no—
1224C2×C4⋊C4—794no—
1225C2×C4⋊C4—794no—
1226C2×C4⋊C4—792no—
1227C2×C4⋊C4—792no—
1228C2×C4⋊C4—794no—
1229C2×C4⋊C4—794no—
1230C2×C4⋊C4—794no—
1231C2×C4⋊C4—794no—
1232C2×C4⋊C4—798no—
1233C2×C4⋊C4C22×D7911yescharacteristic
1234C2×C4⋊C4C22×D7911yescharacteristic
1235C2×C4⋊C4C22×D7914yes—
1236C2×C22⋊C4—792no—
1237C2×C22⋊C4—792no—
1238C2×C22⋊C4—798no—
1239C2×C22⋊C4—794no—
1240C2×C22⋊C4—798no—
1241C2×C22⋊C4—798no—
1242C2×C22⋊C4C22×D7912yes—
1243C2×C42—792no—
1244C2×C42—792no—
1245C2×C42—798no—
1246C2×C42—794no—
1247C2×C42—798no—
1248C2×C42C22×D7912yes—
1249C24—791no—
1250C24—794no—
1251C24—791no—
1252C24C23×D7911yescharacteristic
1253#41—28no—
1254#41—6324no—
1255#41—6328no—
1256#41—6324no—
1257#41—1588no—
1258#41—1588no—
1259#41—1588no—
1260#41—1588no—
1261#41—15816no—
1262#41—15816no—
1263#41—1588no—
1264#41—1588no—
1265#41—1588no—
1266C2×Q8—794no—
1267C2×Q8—798no—
1268C2×Q8—792no—
1269C2×Q8—794no—
1270C2×Q8—792no—
1271C2×Q8—792no—
1272C2×Q8—6324no—
1273C2×Q8—1584no—
1274C2×Q8—1588no—
1275C2×Q8C23×D7912yes—
1276C2×Q8C23×D7914yes—
1277C2×D4—794no—
1278C2×D4—794no—
1279C2×D4—794no—
1280C2×D4—794no—
1281C2×D4—798no—
1282C2×D4—792no—
1283C2×D4—794no—
1284C2×D4—794no—
1285C2×D4—792no—
1286C2×D4—794no—
1287C2×D4—792no—
1288C2×D4—792no—
1289C2×D4—794no—
1290C2×D4—794no—
1291C2×D4—794no—
1292C2×D4—791no—
1293C2×D4—791no—
1294C2×D4—794no—
1295C2×D4—791no—
1296C2×D4—791no—
1297C2×D4—792no—
1298C2×D4—6324no—
1299C2×D4—1584no—
1300C2×D4—1588no—
1301C2×D4—1584no—
1302C2×D4—15816no—
1303C2×D4—1584no—
1304C2×D4C23×D7914yes—
1305C2×D4C23×D7912yes—
1306C2×D4C23×D7914yes—
1307C2×D4C23×D7914yes—
1308C2×D4C23×D7914yes—
1309C22×C4—24no—
1310C22×C4—792no—
1311C22×C4—792no—
1312C22×C4—798no—
1313C22×C4—798no—
1314C22×C4—794no—
1315C22×C4—794no—
1316C22×C4—798no—
1317C22×C4—798no—
1318C22×C4—794no—
1319C22×C4—794no—
1320C22×C4—794no—
1321C22×C4—794no—
1322C22×C4—791no—
1323C22×C4—798no—
1324C22×C4—792no—
1325C22×C4—792no—
1326C22×C4—791no—
1327C22×C4—794no—
1328C22×C4—794no—
1329C22×C4—794no—
1330C22×C4—792no—
1331C22×C4—792no—
1332C22×C4—794no—
1333C22×C4—6322no—
1334C22×C4—6322no—
1335C22×C4—6322no—
1336C22×C4—15816no—
1337C22×C4—1584no—
1338C22×C4C23×D7911yescharacteristic
1339C22×C4C23×D7912yes—
1340C22×C4C23×D7912yes—
1341C22×C4C23×D7914yes—
1342C22×C4C23×D7912yes—
1343C22×C4C23×D7918yes—
1344C22×C4C23×D7912yes—
1345C22×C4C23×D7911yescharacteristic
1346C4⋊C4—798no—
1347C4⋊C4—798no—
1348C4⋊C4—794no—
1349C4⋊C4—794no—
1350C4⋊C4—798no—
1351C4⋊C4—798no—
1352C4⋊C4—798no—
1353C4⋊C4—798no—
1354C4⋊C4—798no—
1355C4⋊C4—798no—
1356C4⋊C4—794no—
1357C4⋊C4—794no—
1358C4⋊C4—794no—
1359C4⋊C4—794no—
1360C4⋊C4—794no—
1361C4⋊C4—794no—
1362C4⋊C4—792no—
1363C4⋊C4—792no—
1364C4⋊C4—794no—
1365C4⋊C4—794no—
1366C4⋊C4—798no—
1367C4⋊C4—794no—
1368C4⋊C4—798no—
1369C4⋊C4—794no—
1370C4⋊C4—794no—
1371C4⋊C4—794no—
1372C4⋊C4C23×D7914yes—
1373C4⋊C4C23×D7912yes—
1374C4⋊C4C23×D7914yes—
1375C4⋊C4C23×D7912yes—
1376C4⋊C4C23×D7914yes—
1377C4⋊C4C23×D7914yes—
1378C4⋊C4C23×D7918yes—
1379C4⋊C4C23×D7918yes—
1380C4⋊C4C23×D7914yes—
1381C4⋊C4C23×D7914yes—
1382C22⋊C4—794no—
1383C22⋊C4—798no—
1384C22⋊C4—798no—
1385C22⋊C4—794no—
1386C22⋊C4—794no—
1387C22⋊C4—794no—
1388C22⋊C4—794no—
1389C22⋊C4—794no—
1390C22⋊C4—794no—
1391C22⋊C4—794no—
1392C22⋊C4—794no—
1393C22⋊C4—798no—
1394C22⋊C4—794no—
1395C22⋊C4—794no—
1396C22⋊C4—798no—
1397C22⋊C4—798no—
1398C22⋊C4—798no—
1399C22⋊C4—794no—
1400C22⋊C4—794no—
1401C22⋊C4—794no—
1402C22⋊C4—794no—
1403C22⋊C4—794no—
1404C22⋊C4—794no—
1405C22⋊C4—794no—
1406C22⋊C4—794no—
1407C22⋊C4C23×D7914yes—
1408C22⋊C4C23×D7918yes—
1409C22⋊C4C23×D7918yes—
1410C22⋊C4C23×D7918yes—
1411C22⋊C4C23×D7914yes—
1412C22⋊C4C23×D7914yes—
1413C22⋊C4C23×D7914yes—
1414C22⋊C4C23×D7914yes—
1415C42—798no—
1416C42—794no—
1417C42—794no—
1418C42—798no—
1419C42—798no—
1420C42—798no—
1421C42—798no—
1422C42—794no—
1423C42C23×D7918yes—
1424C42C23×D7914yes—
1425C42C23×D7914yes—
1426C42C23×D7914yes—
1427C23—22no—
1428C23—41no—
1429C23—41no—
1430C23—3161no—
1431C23—3161no—
1432C23—3161no—
1433C23—3161no—
1434C23—3164no—
1435C23—3164no—
1436C23—794no—
1437C23—791no—
1438C23—791no—
1439C23—791no—
1440C23—791no—
1441C23—794no—
1442C23—1588no—
1443C23—1582no—
1444C23C24×D7914yes—
1445C23C24×D7912yes—
1446C23C24×D7911yescharacteristic
1447Q8—24no—
1448Q8—44no—
1449Q8—3164no—
1450Q8—3168no—
1451Q8—1584no—
1452Q8—1584no—
1453Q8—1588no—
1454Q8—1584no—
1455D4—28no—
1456D4—24no—
1457D4—44no—
1458D4—44no—
1459D4—44no—
1460D4—3164no—
1461D4—3164no—
1462D4—3164no—
1463D4—3164no—
1464D4—3164no—
1465D4—3168no—
1466D4—3164no—
1467D4—3164no—
1468D4—1582no—
1469D4—1582no—
1470D4—1582no—
1471D4—1582no—
1472D4—1588no—
1473D4—1584no—
1474D4—1584no—
1475D4—1588no—
1476D4—1584no—
1477D4—1584no—
1478D4—1588no—
1479D4—1588no—
1480D4—1584no—
1481C2×C4—22no—
1482C2×C4—24no—
1483C2×C4—24no—
1484C2×C4—28no—
1485C2×C4—42no—
1486C2×C4—42no—
1487C2×C4—48no—
1488C2×C4—3164no—
1489C2×C4—3164no—
1490C2×C4—3164no—
1491C2×C4—3164no—
1492C2×C4—3164no—
1493C2×C4—3168no—
1494C2×C4—3168no—
1495C2×C4—3164no—
1496C2×C4—3162no—
1497C2×C4—3162no—
1498C2×C4—3168no—
1499C2×C4—3168no—
1500C2×C4—792no—
1501C2×C4—794no—
1502C2×C4—798no—
1503C2×C4—798no—
1504C2×C4—794no—
1505C2×C4—794no—
1506C2×C4—794no—
1507C2×C4—792no—
1508C2×C4—794no—
1509C2×C4—794no—
1510C2×C4—1588no—
1511C2×C4—1588no—
1512C2×C4—1588no—
1513C2×C4—1582no—
1514C2×C4—1588no—
1515C2×C4—1584no—
1516C2×C4—1584no—
1517C2×C4#41×D7914yes—
1518C2×C4C24×D7914yes—
1519C2×C4C24×D7914yes—
1520C2×C4C24×D7914yes—
1521C2×C4C24×D7914yes—
1522C2×C4C24×D7911yescharacteristic
1523C2×C4C24×D7911yescharacteristic
1524C2×C4C24×D7914yes—
1525C2×C4C24×D7912yes—
1526C22—21no—
1527C22—21no—
1528C22—22no—
1529C22—24no—
1530C22—22no—
1531C22—24no—
1532C22—24no—
1533C22—22no—
1534C22—44no—
1535C22—3164no—
1536C22—3164no—
1537C22—792no—
1538C22—792no—
1539C22—6328no—
1540C22—1581no—
1541C22—1581no—
1542C22—1584no—
1543C22—1581no—
1544C22—1581no—
1545C22—1584no—
1546C22—1584no—
1547C22—1581no—
1548C22—1581no—
1549C22—1581no—
1550C22—1581no—
1551C22—1581no—
1552C22—1581no—
1553C22C2×#41×D7912yes—
1554C22C25×D7911yescharacteristic
1555C4—21no—
1556C4—21no—
1557C4—24no—
1558C4—24no—
1559C4—24no—
1560C4—24no—
1561C4—24no—
1562C4—794no—
1563C4—1584no—
1564C4—1582no—
1565C4—1584no—
1566C4—1584no—
1567C4—1584no—
1568C4—1584no—
1569C4C2×#41×D7914yes—
1570C2—22no—
1571C2—42no—
1572C2—44no—
1573C2—3161no—
1574C2—3161no—
1575C2—3164no—
1576C2—1582no—
1577C2—1582no—
1578C2C22×#41×D7911yescharacteristic
1579C2#2377821111yescharacteristic
1580C2#2377821311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3493C2
hypercenter#3493D79
hypocenterC79#62856
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3493

Complements

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

NH ≅ G/Ntype
1. #23777318C2semidirect
2. #23777314C2semidirect
3. #23777304C2semidirect
4. #23777300C2semidirect
5. #23777238C2semidirect
6. #23777235C2semidirect
7. #23777145C2semidirect
8. #23777141C2semidirect
9. #23777134C2semidirect
10. #23777131C2semidirect
11. #23777120C2semidirect
12. #23777113C2semidirect
13. #23777110C2semidirect
14. #23777107C2semidirect
15. #23777106C2semidirect
16. #23776829C2semidirect
17. #23776819C2semidirect
18. #544×D79C2semidirect
19. #23776730C2semidirect
20. #537×D79C2semidirect
21. #23776600C2semidirect
22. C2×#19099043C2semidirect
23. C79×#3493C2semidirect
26. #19099286C22semidirect
27. #19099281C22semidirect
28. #19099281C22semidirect
29. #19099278C22semidirect
30. #19099276C22semidirect
31. #19099276C22semidirect
32. #19099274C22semidirect
33. #19099271C22semidirect
34. #19099271C22semidirect
35. #19099270C22semidirect
36. #19099266C22semidirect
37. #19099266C22semidirect
38. #19099265C22semidirect
39. #19099264C22semidirect
40. #19099264C22semidirect
41. #19099263C22semidirect
42. #19099263C22semidirect
43. #19099261C22semidirect
44. #19099260C22semidirect
45. #19099260C22semidirect
46. #19099259C22semidirect
47. #19099258C22semidirect
48. #19099257C22semidirect
49. #19099257C22semidirect
50. #19099255C22semidirect
51. #19099254C22semidirect
52. #19099254C22semidirect
53. #19099253C22semidirect
54. #19099252C22semidirect
55. #19099251C22semidirect
56. #19099251C22semidirect
57. #19099249C22semidirect
58. #19099248C22semidirect
59. #19099247C22semidirect
60. #19099243C22semidirect
61. #19099238C22semidirect
62. #19099237C22semidirect
63. #19099236C22semidirect
64. #19099225C22semidirect
65. #19099221C22semidirect
66. #19099221C22semidirect
67. #19099217C22semidirect
68. #19099216C22semidirect
69. #19099213C22semidirect
70. #19099213C22semidirect
71. #19099208C22semidirect
72. #19099206C22semidirect
73. #19099202C22semidirect
74. #19099194C22semidirect
75. #19099193C22semidirect
76. #19099192C22semidirect
77. #19099191C22semidirect
78. #19099190C22semidirect
79. #19099179C22semidirect
80. #19099179C22semidirect
81. #19099177C22semidirect
82. #19099177C22semidirect
83. #19099172C22semidirect
84. #19099170C22semidirect
85. #19099165C22semidirect
86. #19099163C22semidirect
87. #19099162C22semidirect
88. #19099158C22semidirect
89. #19099157C22semidirect
90. #19099151C22semidirect
91. #19099146C22semidirect
93. #19099143C22semidirect
94. #19099143C22semidirect
95. #19099143C22semidirect
96. #19099142C22semidirect
97. #19099142C22semidirect
98. #19099142C22semidirect
103. #19099135C22semidirect
106. #19099128C22semidirect
109. #19099117C22semidirect
110. #19099116C22semidirect
111. #19099112C22semidirect
112. #19099110C22semidirect
113. #19099110C22semidirect
114. #19099108C22semidirect
115. C4⋊Q8×D79C22semidirect
116. #19099097C22semidirect
117. #19099096C22semidirect
118. #19099093C22semidirect
119. #19099093C22semidirect
120. #19099091C22semidirect
121. #19099090C22semidirect
122. #125×D79C22semidirect
123. #19099076C22semidirect
124. #19099075C22semidirect
125. #19099074C22semidirect
126. #19099073C22semidirect
129. #19099070C22semidirect
130. #19099069C22semidirect
132. C22⋊Q8×D79C22semidirect
134. #121×D79C22semidirect
135. #19099046C22semidirect
136. #19099044C22semidirect
137. #19099044C22semidirect
140. #19099043C22semidirect
141. #19099043C22semidirect
142. #19099043C22semidirect
143. #19099043C22semidirect
144. #19099039C22semidirect
146. #19099035C22semidirect
147. C4×#11929625C22semidirect
148. C4×#11929623C22semidirect
149. C4×#11929623C22semidirect
150. C2×C4×Dic158C22semidirect
153. C2×(C22⋊D79)⋊C4C22semidirect
155. C2×#14579119C22semidirect
156. C2×#14579119C22semidirect
158. #117×D79C22semidirect
159. C22×C4⋊Dic79C22semidirect
161. C2×C4⋊C4×D79C22semidirect
162. #556×C79C22semidirect
163. #555×C79C22semidirect
164. #553×C79C22semidirect
165. #552×C79C22semidirect
166. #544×C79C22semidirect
167. #538×C79C22semidirect
169. #529×C79C22semidirect
170. #525×C79C22semidirect
171. #520×C79C22semidirect
172. C2×#117×C79C22semidirect
521. C2×C4×D79#41semidirect
803. #3493D79semidirect
814. C79#62856semidirect
820. #556C2×D79semidirect
824. #555C2×D79semidirect
843. #553C2×D79semidirect
854. #552C2×D79semidirect
874. #544C2×D79semidirect
888. #538C2×D79semidirect
920. #529C2×D79semidirect
930. #525C2×D79semidirect
944. #520C2×D79semidirect
960. C2×#117C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237773182
#237773142
#237773042
#237773002
#237772382
#237772352
#237771452
#237771412
#237771342
#237771312
#237771202
#237771132
#237771102
#237771072
#237771062
#237768292
#237768192
#544×D792
#237767302
#537×D792
#237766002
C2×#190990432
C79×#34932
#6285679