Finite Group Databasebeta

← #35196994

Subgroups — #35196994

Order 20224.

6530 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23778007C214yesmaximal, complemented
2#23778005C214yesmaximal, complemented
3#23777930C214yesmaximal, complemented
4#23777924C214yesmaximal, complemented
5#23777848C218yesmaximal, complemented
6#23777380C214yesmaximal, complemented
7#23777375C214yesmaximal, complemented
8#23777371C214yesmaximal, complemented
9#23777366C214yesmaximal, complemented
10#23777321C212yesmaximal, complemented
11#23777320C211yesmaximal, characteristic, complemented
12#23777226C211yesmaximal, characteristic, complemented
13#23777224C211yesmaximal, characteristic, complemented
14#23777222C212yesmaximal, complemented
15#23777107C212yesmaximal, complemented
16#23777104C218yesmaximal, complemented
17#23777103C212yesmaximal, complemented
18#23776695C211yesmaximal, characteristic, complemented
19#23776693C211yesmaximal, characteristic, complemented
20C2×#125×D79C211yesmaximal, characteristic, complemented
21C79×#3512C211yesmaximal, characteristic, complemented
22C79⋊#564C2218yescomplemented
23#19099316C2218yescomplemented
24#19099315C2218yescomplemented
25#19099308C2218yescomplemented
26#19099292C2214yescomplemented
27#19099290C2214yescomplemented
28#19099289C2214yescomplemented
29#19099289C2214yescomplemented
30#19099273C2214yes—
31#19099272C2218yes—
32#19099272C2218yes—
33#19099272C2214yescomplemented
34#19099272C2214yescomplemented
35#19099271C2214yes—
36#19099271C2214yes—
37#19099270C2218yes—
38#19099270C2214yescomplemented
39#19099269C2214yescomplemented
40#19099268C2218yes—
41#19099268C2214yes—
42#19099265C2218yes—
43#19099265C2214yescomplemented
44#19099263C2214yes—
45#19099260C2214yes—
46#19099260C2214yes—
47#19099260C2214yescomplemented
48#19099259C2214yescomplemented
49#19099257C2214yes—
50#19099256C2218yes—
51#19099256C2218yes—
52#19099255C2214yescomplemented
53#19099254C2214yes—
54#19099253C2214yescomplemented
55#19099253C2218yescomplemented
56#19099252C2214yes—
57#19099252C2218yes—
58#19099251C2218yes—
59#19099250C2218yescomplemented
60#19099249C2218yes—
61#19099249C2218yes—
62#19099249C2218yescomplemented
63#19099247C2214yes—
64#19099247C2214yes—
65#19099247C2214yescomplemented
66#19099246C2218yescomplemented
67#19099218C2214yes—
68#19099218C2218yes—
69#19099214C2214yes—
70#19099213C2218yes—
71#19099213C2214yes—
72#19099213C2214yes—
73#19099211C2218yes—
74#19099211C2218yes—
75#19099194C2212yes—
76#19099194C2214yescomplemented
77#19099193C2218yes—
78#19099193C2214yescomplemented
79#19099191C2212yes—
80#19099191C2214yescomplemented
81#19099191C2214yescomplemented
82#19099175C2218yescomplemented
83#19099174C2212yescomplemented
84#19099173C2214yescomplemented
85#19099172C2218yescomplemented
86#19099170C2218yescomplemented
87#19099170C2218yescomplemented
88#19099167C2212yescomplemented
89#19099166C2214yescomplemented
90#19099158C2218yes—
91#19099158C2218yescomplemented
92#19099157C2218yescomplemented
93#19099156C2218yes—
94#19099156C2218yes—
95#19099156C2218yescomplemented
96#19099155C2218yes—
97#19099155C2218yescomplemented
98#19099154C2218yes—
99#19099154C2218yes—
100#19099142C2218yes—
101#19099141C2212yes—
102#19099120C2211yescharacteristic
103#19099120C2212yescomplemented
104#19099119C2212yescomplemented
105#19099118C2212yes—
106#19099117C2212yes—
107#19099116C2211yescharacteristic
108#19099116C2214yescomplemented
109#19099111C2212yes—
110#19099110C2212yes—
111#19099109C2211yescharacteristic
112#19099100C2212yes—
113#19099099C2214yescomplemented
114#19099095C2212yes—
115#19099095C2214yes—
116#19099094C2214yes—
117#19099094C2214yescomplemented
118#19099093C2214yes—
119#19099092C2212yes—
120#19099092C2212yes—
121#19099092C2214yescomplemented
122#19099091C2214yes—
123C2×#14579153C2211yescharacteristic
124C2×#14579153C2212yescomplemented
125C2×#14579152C2212yes—
126C2×#14579152C2214yescomplemented
127C2×#14579151C2214yes—
128#125×D79C2214yes—
129#125×D79C2214yes—
130#125×D79C2214yes—
131#125×D79C2214yes—
132#125×D79C2212yescomplemented
133#19099075C2211yescharacteristic
134#19099073C2218yes—
135#19099073C2214yes—
136#19099072C2218yes—
137#19099072C2214yes—
138#19099070C2212yes—
139#19099070C2211yescharacteristic
140#19099046C2212yes—
141#19099046C2212yes—
142#19099044C2212yes—
143#19099043C2218yes—
144#19099042C2218yes—
145#41×Dic79C2212yes—
146C4×#11929624C2211yescharacteristic
147C4×#11929624C2214yes—
148C4×#11929623C2214yes—
149C2×C4⋊C4×D79C2212yes—
150C2×C4⋊C4×D79C2214yes—
151C2×C42×D79C2211yescharacteristic
152#553×C79C2218yes—
153#553×C79C2214yescomplemented
154#552×C79C2214yescomplemented
155#541×C79C2212yescomplemented
156#540×C79C2212yescomplemented
157#537×C79C2212yes—
158#532×C79C2211yescharacteristic
159#529×C79C2214yescomplemented
160C2×#125×C79C2211yescharacteristic
161#520×C79C2212yes—
162C4×#41×C79C2211yescharacteristic
163C2×#11929624C2311yescharacteristic
164C2×#11929624C2318yes—
165C2×#11929624C2314yes—
166C2×#11929623C2318yes—
167C2×#11929623C2314yes—
168C22×C4×D79C2311yescharacteristic
169C22×C4×D79C2312yes—
170C22×C4×D79C2314yes—
171#14579161C2318yes—
172#14579161C2314yes—
173#14579161C2312yes—
174#14579160C2318yes—
175#14579160C2318yes—
176#14579160C2318yes—
177#14579160C2314yes—
178#14579160C2312yes—
179#14579160C2314yes—
180#14579160C2314yes—
181#14579159C2311yescharacteristic
182#14579157C2311yescharacteristic
183#14579156C2318yes—
184#14579156C2318yes—
185#14579156C2314yes—
186#14579155C2318yes—
187#14579154C2318yes—
188#14579154C2314yes—
189#14579154C2318yes—
190#14579154C2318yes—
191#14579154C2318yes—
192#14579154C2318yes—
193#14579154C2314yes—
194#14579154C2318yes—
195#14579154C2318yes—
196#14579154C2314yes—
197#14579153C2318yes—
198#14579153C2318yes—
199#14579153C2318yes—
200#14579153C2312yes—
201#14579153C2314yes—
202#14579153C2314yes—
203#14579153C2312yes—
204#14579153C2311yescharacteristic
205#14579153C2311yescharacteristic
206#14579152C2318yes—
207#14579152C2318yes—
208#14579152C2318yes—
209#14579152C2318yes—
210#14579152C2314yes—
211#14579152C2318yes—
212#14579152C2314yes—
213#14579152C2314yes—
214#14579152C2314yes—
215#14579152C2314yes—
216#14579152C2314yes—
217#14579152C2314yes—
218#14579152C2314yes—
219#14579152C2312yes—
220#14579151C2318yes—
221#14579151C2318yes—
222#14579151C2318yes—
223#14579151C2318yes—
224#14579151C2318yes—
225#14579151C2318yes—
226#14579151C2318yes—
227#14579151C2318yes—
228#14579151C2318yes—
229#14579151C2318yes—
230#14579151C2318yes—
231#14579151C2314yes—
232#14579150C2311yescharacteristic
233#14579148C2314yes—
234#14579148C2311yescharacteristic
235#14579147C2314yes—
236#14579146C2318yes—
237#14579146C2314yes—
238#14579145C2318yes—
239#14579145C2318yes—
240#14579145C2312yes—
241#14579144C2318yes—
242#14579143C2318yes—
243#14579143C2318yes—
244#14579143C2318yes—
245#14579143C2318yes—
246#14579143C2318yes—
247#14579143C2318yes—
248#14579143C2314yes—
249#14579143C2314yes—
250#14579143C2314yes—
251#14579142C2314yes—
252#14579142C2318yes—
253#14579142C2318yes—
254#14579142C2318yes—
255#14579142C2318yes—
256#14579142C2312yes—
257#14579141C2318yes—
258#14579141C2314yes—
259#14579141C2318yes—
260#14579141C2312yes—
261#14579140C2314yes—
262#14579140C2318yes—
263#14579140C2318yes—
264#14579140C2318yes—
265#14579140C2318yes—
266#14579140C2318yes—
267#14579140C2314yes—
268#14579139C2318yes—
269#14579139C2318yes—
270#14579139C2318yes—
271#14579139C2314yes—
272#14579139C2318yes—
273#14579138C2318yes—
274#14579138C2318yes—
275#14579138C2318yes—
276#14579138C2318yes—
277#14579138C2318yes—
278#14579138C2318yes—
279#14579138C2318yes—
280#14579138C2318yes—
281#14579138C2318yes—
282#14579138C2314yes—
283#14579137C2314yes—
284#14579137C2312yes—
285#14579137C2312yes—
286#14579137C2312yes—
287#14579136C2312yes—
288#14579135C2314yes—
289#14579134C2314yes—
290#14579134C2318yes—
291#14579133C2318yes—
292#14579133C2318yes—
293#14579133C2318yes—
294#14579133C2314yes—
295#14579132C2314yes—
296#14579132C2314yes—
297#14579132C2318yes—
298#14579132C2318yes—
299#14579132C2312yes—
300#14579132C2312yes—
301#14579132C2312yes—
302#14579131C2312yes—
303#14579129C2314yes—
304#14579129C2312yes—
305Q8×Dic79C2314yes—
306Q8×Dic79C2314yes—
307Q8×Dic79C2312yes—
308Q8×Dic79C2312yes—
309C4×Dic158C2314yes—
310C4×Dic158C2318yes—
311C4×Dic158C2318yes—
312C4×Dic158C2318yes—
313C4×Dic158C2312yes—
314C4×Dic158C2314yes—
315C4×Dic158C2314yes—
316#14579126C2314yes—
317#14579126C2318yes—
318#14579126C2314yes—
319C4×D316C2314yes—
320C4×D316C2318yes—
321C4×D316C2314yes—
322C4×D316C2312yes—
323D4×Dic79C2314yes—
324D4×Dic79C2318yes—
325D4×Dic79C2318yes—
326D4×Dic79C2318yes—
327D4×Dic79C2314yes—
328D4×Dic79C2314yes—
329D4×Dic79C2314yes—
330D4×Dic79C2312yes—
331D4×Dic79C2314yes—
332D4×Dic79C2312yes—
333#14579123C2314yes—
334C4×C22⋊D79C2318yes—
335C4×C22⋊D79C2314yes—
336C4×C22⋊D79C2314yes—
337C4×C22⋊D79C2318yes—
338C4×C22⋊D79C2314yes—
339C4×C22⋊D79C2314yes—
340C4×C22⋊D79C2314yes—
341C4×C22⋊D79C2314yes—
342C4×C22⋊D79C2314yes—
343(C22⋊D79)⋊C4C2314yes—
344(C22⋊D79)⋊C4C2318yes—
345(C22⋊D79)⋊C4C2314yes—
346(C22⋊D79)⋊C4C2318yes—
347(C22⋊D79)⋊C4C2318yes—
348(C22⋊D79)⋊C4C2318yes—
349#14579120C2314yes—
350#14579120C2312yes—
351#14579120C2314yes—
352#14579120C2311yescharacteristic
353#14579120C2314yes—
354#14579120C2314yes—
355#14579119C2318yes—
356#14579119C2318yes—
357#14579119C2314yes—
358#14579119C2314yes—
359#14579118C2312yes—
360#14579118C2318yes—
361#14579118C2314yes—
362#14579118C2314yes—
363#14579117C2318yes—
364#14579117C2318yes—
365#14579117C2314yes—
366#14579117C2314yes—
367C2×C4⋊Dic79C2312yes—
368C2×C4⋊Dic79C2318yes—
369C2×C4⋊Dic79C2314yes—
370C2×C4⋊Dic79C2314yes—
371C2×C4⋊Dic79C2314yes—
372C2×Dic79⋊C4C2314yes—
373C2×Dic79⋊C4C2318yes—
374C2×Dic79⋊C4C2318yes—
375C2×Dic79⋊C4C2314yes—
376C2×Dic79⋊C4C2314yes—
377C4⋊C4×D79C2318yes—
378C4⋊C4×D79C2318yes—
379C4⋊C4×D79C2318yes—
380C4⋊C4×D79C2314yes—
381C4⋊C4×D79C2318yes—
382C4⋊C4×D79C2318yes—
383C4⋊C4×D79C2314yes—
384C4⋊C4×D79C2314yes—
385C4⋊C4×D79C2314yes—
386C4⋊C4×D79C2314yes—
387C2×C4×Dic79C2311yescharacteristic
388C2×C4×Dic79C2312yes—
389C2×C4×Dic79C2314yes—
390C42×D79C2312yes—
391C42×D79C2312yes—
392C42×D79C2312yes—
393C42×D79C2312yes—
394C42×D79C2312yes—
395C2×#41×C79C2312yes—
396C2×#41×C79C2311yescharacteristic
397C4⋊Q8×C79C2311yescharacteristic
398#127×C79C2311yescharacteristic
399#126×C79C2318yes—
400#126×C79C2318yes—
401#125×C79C2318yes—
402#125×C79C2312yes—
403#125×C79C2312yes—
404#125×C79C2314yes—
405#124×C79C2312yes—
406#123×C79C2318yes—
407#123×C79C2318yes—
408C22⋊Q8×C79C2314yes—
409C22⋊Q8×C79C2314yes—
410#121×C79C2318yes—
411#121×C79C2318yes—
412#121×C79C2314yes—
413#121×C79C2314yes—
414#121×C79C2314yes—
415C4×Q8×C79C2312yes—
416C4×Q8×C79C2314yes—
417C4×D4×C79C2318yes—
418C4×D4×C79C2318yes—
419C4×D4×C79C2314yes—
420C4×D4×C79C2314yes—
421C4×D4×C79C2312yes—
422C4×D4×C79C2314yes—
423#117×C79C2318yes—
424#117×C79C2311yescharacteristic
425#117×C79C2312yes—
426#117×C79C2314yes—
427C2×C4⋊C4×C79C2312yes—
428C2×C4⋊C4×C79C2314yes—
429C2×C4⋊C4×C79C2314yes—
430C2×C42×C79C2311yescharacteristic
431C2×C42×C79C2312yes—
432C23×D79C2411yescharacteristic
433#11929624—24no—
434#11929624—48no—
435#11929624—416no—
436#11929623—416no—
437#11929623—48no—
438C2×Dic158C2411yescharacteristic
439C2×Dic158C2418yes—
440C2×Dic158C2414yes—
441C2×Dic158C2418yes—
442C2×Dic158C2414yes—
443C2×D316C2414yes—
444C2×D316C2411yescharacteristic
445C2×C22⋊D79C2414yes—
446C2×C22⋊D79C2414yes—
447C2×C22⋊D79C2414yes—
448C2×C22⋊D79C2412yes—
449C2×C22⋊D79C2418yes—
450C2×C22⋊D79C2414yes—
451C22×Dic79C2411yescharacteristic
452C22×Dic79C2414yes—
453C22×Dic79C2414yes—
454C22×Dic79C2418yes—
455C22×Dic79C2418yes—
456C22×Dic79C2412yes—
457C22×Dic79C2414yes—
458C2×C4×D79—24no—
459C2×C4×D79—44no—
460C2×C4×D79—48no—
461C2×C4×D79C2412yes—
462C2×C4×D79C2418yes—
463C2×C4×D79C2412yes—
464C2×C4×D79C2412yes—
465C2×C4×D79C2412yes—
466C2×C4×D79C2412yes—
467C2×C4×D79C2414yes—
468C2×C4×D79C2418yes—
469C2×C4×D79C2412yes—
470C2×C4×D79C2412yes—
471C2×C4×D79C2418yes—
472C4⋊Dic79C2418yes—
473C4⋊Dic79C2414yes—
474C4⋊Dic79C2414yes—
475C4⋊Dic79C2418yes—
476C4⋊Dic79C2412yes—
477C4⋊Dic79C2418yes—
478C4⋊Dic79C2412yes—
479C4⋊Dic79C2412yes—
480C4⋊Dic79C2414yes—
481C4⋊Dic79C2418yes—
482C4⋊Dic79C2418yes—
483C4⋊Dic79C2418yes—
484C4⋊Dic79C2414yes—
485C4⋊Dic79C2414yes—
486C4⋊Dic79C2414yes—
487C4⋊Dic79C2414yes—
488Dic79⋊C4C2418yes—
489Dic79⋊C4C2418yes—
490Dic79⋊C4C2418yes—
491Dic79⋊C4C2418yes—
492Dic79⋊C4C2418yes—
493Dic79⋊C4C2418yes—
494Dic79⋊C4C2414yes—
495Dic79⋊C4C2418yes—
496Dic79⋊C4C2418yes—
497Dic79⋊C4C2414yes—
498Dic79⋊C4C2414yes—
499Dic79⋊C4C2418yes—
500Dic79⋊C4C2418yes—
501Dic79⋊C4C2418yes—
502Dic79⋊C4C2418yes—
503Dic79⋊C4C2414yes—
504Dic79⋊C4C2414yes—
505Dic79⋊C4C2414yes—
506Dic79⋊C4C2414yes—
507Dic79⋊C4C2414yes—
508Dic79⋊C4C2414yes—
509C22⋊Dic79C2414yes—
510C22⋊Dic79C2418yes—
511C22⋊Dic79C2414yes—
512C22⋊Dic79C2414yes—
513C22⋊Dic79C2414yes—
514C22⋊Dic79C2412yes—
515C22⋊Dic79C2414yes—
516C22⋊Dic79C2414yes—
517C22⋊Dic79C2418yes—
518C22⋊Dic79C2414yes—
519C22⋊Dic79C2418yes—
520(C2×D79)⋊C4C2414yes—
521(C2×D79)⋊C4C2414yes—
522(C2×D79)⋊C4C2414yes—
523(C2×D79)⋊C4C2414yes—
524(C2×D79)⋊C4C2414yes—
525(C2×D79)⋊C4C2414yes—
526(C2×D79)⋊C4C2414yes—
527(C2×D79)⋊C4C2418yes—
528(C2×D79)⋊C4C2418yes—
529C4×Dic79C2411yescharacteristic
530C4×Dic79C2412yes—
531C4×Dic79C2411yescharacteristic
532C4×Dic79C2412yes—
533C4×Dic79C2412yes—
534C4×Dic79C2412yes—
535C4×Dic79C2412yes—
536C4×Dic79C2414yes—
537C4×Dic79C2412yes—
538C4×Dic79C2414yes—
539C4×Dic79C2414yes—
540C4×Dic79C2414yes—
541C4×Dic79C2418yes—
542C4×Dic79C2418yes—
543C4×Dic79C2418yes—
544#41×C79—28no—
545#41×C79—24no—
546C2×Q8×C79C2411yescharacteristic
547C2×Q8×C79C2412yes—
548C2×D4×C79C2414yes—
549C2×D4×C79C2412yes—
550C2×D4×C79C2411yescharacteristic
551C2×D4×C79C2412yes—
552C2×D4×C79C2418yes—
553C2×D4×C79C2414yes—
554C22×C4×C79C2412yes—
555C22×C4×C79C2414yes—
556C22×C4×C79C2414yes—
557C22×C4×C79C2418yes—
558C22×C4×C79C2412yes—
559C22×C4×C79C2414yes—
560C22×C4×C79C2411yescharacteristic
561C4⋊C4×C79C2412yes—
562C4⋊C4×C79C2414yes—
563C4⋊C4×C79C2418yes—
564C4⋊C4×C79C2414yes—
565C4⋊C4×C79C2418yes—
566C4⋊C4×C79C2418yes—
567C4⋊C4×C79C2414yes—
568C4⋊C4×C79C2418yes—
569C4⋊C4×C79C2414yes—
570C22⋊C4×C79C2414yes—
571C22⋊C4×C79C2412yes—
572C22⋊C4×C79C2414yes—
573C22⋊C4×C79C2418yes—
574C22⋊C4×C79C2418yes—
575C22⋊C4×C79C2414yes—
576C22⋊C4×C79C2418yes—
577C42×C79C2411yescharacteristic
578C42×C79C2412yes—
579C42×C79C2414yes—
580C42×C79C2411yescharacteristic
581C42×C79C2412yes—
582C42×C79C2418yes—
583C23×C79C2514yes—
584C23×C79C2512yes—
585C23×C79C2511yescharacteristic
586C22×D79—22no—
587C22×D79—24no—
588C22×D79C2512yes—
589C22×D79C2512yes—
590Q8×C79—22no—
591Q8×C79—24no—
592D4×C79—28no—
593D4×C79—24no—
594D4×C79—22no—
595D4×C79—24no—
596D4×C79—48no—
597D4×C79—44no—
598C2×C4×C79—28no—
599C2×C4×C79—24no—
600C2×C4×C79—42no—
601C2×C4×C79—44no—
602C2×C4×C79—44no—
603C2×C4×C79—48no—
604C2×C4×C792−1+414yes—
605C2×C4×C79C2514yes—
606C2×C4×C79C2512yes—
607C2×C4×C79C2512yes—
608C2×C4×C79C2512yes—
609C2×C4×C79C2518yes—
610C2×C4×C79C2514yes—
611C2×C4×C79C2511yescharacteristic
612C2×C4×C79C2511yescharacteristic
613C22⋊D79—24no—
614C22⋊D79—28no—
615C22⋊D79—28no—
616C22⋊D79—28no—
617C22⋊D79—44no—
618C22⋊D79—48no—
619C2×Dic79—22no—
620C2×Dic79—42no—
621C2×Dic79—44no—
622C2×Dic79—44no—
623C2×Dic79—48no—
624C2×Dic79—48no—
625C2×Dic79—44no—
626C2×Dic79C2512yes—
627C2×Dic79C2512yes—
628C2×Dic79C2514yes—
629C2×Dic79C2512yes—
630C2×Dic79C2514yes—
631C2×Dic79C2514yes—
632C2×Dic79C2512yes—
633C2×Dic79C2518yes—
634D316—28no—
635D316—22no—
636C4×D79—24no—
637C4×D79—216no—
638C4×D79—24no—
639C4×D79—24no—
640C4×D79—24no—
641C4×D79—24no—
642C4×D79—42no—
643C4×D79—48no—
644C4×D79—42no—
645C4×D79—48no—
646C4×D79—44no—
647Dic158—22no—
648Dic158—44no—
649Dic158—48no—
650Dic158—48no—
651Dic158—44no—
652C22×C79—22no—
653C22×C79—24no—
654C22×C79—22no—
655C22×C79—24no—
656C22×C79—24no—
657C22×C79—24no—
658C22×C79C2×2−1+412yes—
659C22×C79C2611yescharacteristic
660C2×D79—28no—
661C2×D79—22no—
662C2×D79—22no—
663C2×D79—22no—
664C2×D79—24no—
665C2×D79#58514yes—
666C4×C79—24no—
667C4×C79—22no—
668C4×C79—24no—
669C4×C79—22no—
670C4×C79—28no—
671C4×C79—22no—
672C4×C79C2×2−1+412yes—
673C4×C79C2×2−1+412yes—
674Dic79—22no—
675Dic79—22no—
676Dic79—24no—
677Dic79—24no—
678Dic79—24no—
679Dic79—22no—
680Dic79—28no—
681Dic79—22no—
682#62825—791nomaximal, Sylow
683C2×C79—22no—
684C2×C79—44no—
685C2×C79—42no—
686C2×C79C22×2−1+411yescharacteristic
687C2×C79C2×#58512yes—
688D79—24no—
689D79—42no—
690#3563—794no—
691#3563—794no—
692#3559—794no—
693#3559—794no—
694#3553—798no—
695#3515—794no—
696#3515—794no—
697#3515—794no—
698#3515—794no—
699#3512—792no—
700#3512—791no—
701#3512D7911yescharacteristic, complemented
702#3504—791no—
703#3504—792no—
704#3504—791no—
705#3492—798no—
706#3492—792no—
707#3492—792no—
708#3444—791no—
709#3444—791no—
710C22×#125—791no—
711C79#6282511yescharacteristic, complemented, Sylow
712#564—798no—
713#563—798no—
714#563—798no—
715#562—798no—
716#557—794no—
717#557—794no—
718#557—794no—
719#557—794no—
720#554—794no—
721#554—794no—
722#554—794no—
723#554—794no—
724#554—798no—
725#554—794no—
726#554—798no—
727#554—798no—
728#554—794no—
729#554—794no—
730#554—798no—
731#554—794no—
732#553—798no—
733#553—798no—
734#553—794no—
735#553—794no—
736#553—794no—
737#553—798no—
738#553—794no—
739#553—794no—
740#553—794no—
741#553—794no—
742#553C2×D7918yes—
743#553C2×D7914yescomplemented
744#552—798no—
745#552—798no—
746#552—798no—
747#552—798no—
748#552—798no—
749#552—794no—
750#552—794no—
751#552—794no—
752#552—794no—
753#552—794no—
754#552—794no—
755#552—798no—
756#552—798no—
757#552—798no—
758#552—794no—
759#552C2×D7914yescomplemented
760#547—798no—
761#547—798no—
762#547—798no—
763#547—794no—
764#547—794no—
765#547—798no—
766#547—794no—
767#547—794no—
768#544—798no—
769#544—794no—
770#544—792no—
771#544—794no—
772#544—794no—
773#544—792no—
774#544—794no—
775#541—792no—
776#541—798no—
777#541—798no—
778#541—798no—
779#541—794no—
780#541—798no—
781#541C2×D7912yescomplemented
782#540—792no—
783#540—794no—
784#540C2×D7912yescomplemented
785#539—798no—
786#539—798no—
787#539—798no—
788#539—798no—
789#539—798no—
790#539—798no—
791#539—798no—
792#539—798no—
793#539—798no—
794#539—798no—
795#537—792no—
796#537—798no—
797#537C2×D7912yes—
798#533—792no—
799#533—792no—
800#533—792no—
801#533—791no—
802#533—794no—
803#533—791no—
804#533—792no—
805#532—791no—
806#532—792no—
807#532—792no—
808#532C2×D7911yescharacteristic
809#529—792no—
810#529—792no—
811#529—794no—
812#529—794no—
813#529—794no—
814#529—794no—
815#529—792no—
816#529—792no—
817#529—794no—
818#529—794no—
819#529—794no—
820#529C2×D7914yescomplemented
821C2×#125—794no—
822C2×#125—794no—
823C2×#125—794no—
824C2×#125—794no—
825C2×#125—792no—
826C2×#125—792no—
827C2×#125—794no—
828C2×#125—794no—
829C2×#125—791no—
830C2×#125—792no—
831C2×#125C2×D7911yescharacteristic
832#525—792no—
833#525—791no—
834#525—794no—
835#525—798no—
836#525—794no—
837#525—798no—
838#525—791no—
839#520—792no—
840#520—792no—
841#520—798no—
842#520—798no—
843#520—792no—
844#520C2×D7912yes—
845C4×#41—792no—
846C4×#41—794no—
847C4×#41—791no—
848C4×#41—794no—
849C4×#41C2×D7911yescharacteristic
850C22×C4⋊C4—792no—
851C22×C4⋊C4—794no—
852C22×C42—791no—
853C2×#41—794no—
854C2×#41—798no—
855C2×#41—794no—
856C2×#41—798no—
857C2×#41—791no—
858C2×#41C22×D7912yes—
859C2×#41C22×D7911yescharacteristic
860C23×C4—794no—
861C23×C4—792no—
862C23×C4—791no—
863C4⋊Q8—791no—
864C4⋊Q8—792no—
865C4⋊Q8—794no—
866C4⋊Q8—794no—
867C4⋊Q8—794no—
868C4⋊Q8—798no—
869C4⋊Q8—798no—
870C4⋊Q8—798no—
871C4⋊Q8—792no—
872C4⋊Q8—794no—
873C4⋊Q8—798no—
874C4⋊Q8C22×D7911yescharacteristic
875#127—791no—
876#127C22×D7911yescharacteristic
877#126—794no—
878#126—798no—
879#126—798no—
880#126—794no—
881#126—794no—
882#126—794no—
883#126—798no—
884#126—798no—
885#126—798no—
886#126—798no—
887#126—798no—
888#126—798no—
889#126—798no—
890#126—798no—
891#126C22×D7918yes—
892#126C22×D7918yes—
893#125—794no—
894#125—798no—
895#125—798no—
896#125—794no—
897#125—798no—
898#125—794no—
899#125—794no—
900#125—798no—
901#125—792no—
902#125—798no—
903#125—798no—
904#125—798no—
905#125—794no—
906#125—794no—
907#125—794no—
908#125—794no—
909#125—794no—
910#125—798no—
911#125—798no—
912#125—798no—
913#125—798no—
914#125—798no—
915#125—798no—
916#125—798no—
917#125—798no—
918#125—798no—
919#125—792no—
920#125—792no—
921#125—794no—
922#125—791no—
923#125—791no—
924#125—798no—
925#125—794no—
926#125—798no—
927#125—798no—
928#125C22×D7912yes—
929#125C22×D7912yes—
930#125C22×D7914yes—
931#125C22×D7918yes—
932#124—791no—
933#124—791no—
934#124—794no—
935#124—794no—
936#124C22×D7912yes—
937#123—794no—
938#123—792no—
939#123—798no—
940#123—798no—
941#123—798no—
942#123—798no—
943#123—798no—
944#123—794no—
945#123—798no—
946#123—792no—
947#123—794no—
948#123—794no—
949#123—794no—
950#123—798no—
951#123—798no—
952#123—798no—
953#123—798no—
954#123—798no—
955#123—798no—
956#123—798no—
957#123—798no—
958#123C22×D7918yes—
959#123C22×D7918yes—
960C22⋊Q8—792no—
961C22⋊Q8—792no—
962C22⋊Q8—792no—
963C22⋊Q8—794no—
964C22⋊Q8—794no—
965C22⋊Q8—798no—
966C22⋊Q8—794no—
967C22⋊Q8—798no—
968C22⋊Q8—798no—
969C22⋊Q8—798no—
970C22⋊Q8—798no—
971C22⋊Q8—794no—
972C22⋊Q8—794no—
973C22⋊Q8—792no—
974C22⋊Q8—798no—
975C22⋊Q8—798no—
976C22⋊Q8—798no—
977C22⋊Q8—798no—
978C22⋊Q8—798no—
979C22⋊Q8—798no—
980C22⋊Q8—794no—
981C22⋊Q8—798no—
982C22⋊Q8—798no—
983C22⋊Q8—798no—
984C22⋊Q8—798no—
985C22⋊Q8—798no—
986C22⋊Q8—798no—
987C22⋊Q8—798no—
988C22⋊Q8—798no—
989C22⋊Q8—798no—
990C22⋊Q8C22×D7914yes—
991C22⋊Q8C22×D7914yes—
992#121—794no—
993#121—792no—
994#121—792no—
995#121—792no—
996#121—794no—
997#121—798no—
998#121—798no—
999#121—794no—
1000#121—798no—
1001#121—798no—
1002#121—798no—
1003#121—794no—
1004#121—792no—
1005#121—794no—
1006#121—798no—
1007#121C22×D7914yes—
1008#121C22×D7918yes—
1009#121C22×D7914yes—
1010#121C22×D7914yes—
1011#121C22×D7918yes—
1012#120—794no—
1013#120—792no—
1014#120—792no—
1015C4×Q8—792no—
1016C4×Q8—792no—
1017C4×Q8—794no—
1018C4×Q8—794no—
1019C4×Q8—794no—
1020C4×Q8—794no—
1021C4×Q8—798no—
1022C4×Q8—794no—
1023C4×Q8—792no—
1024C4×Q8—794no—
1025C4×Q8—794no—
1026C4×Q8—798no—
1027C4×Q8—798no—
1028C4×Q8—798no—
1029C4×Q8C22×D7912yes—
1030C4×Q8C22×D7914yes—
1031C4×D4—794no—
1032C4×D4—794no—
1033C4×D4—794no—
1034C4×D4—792no—
1035C4×D4—792no—
1036C4×D4—798no—
1037C4×D4—798no—
1038C4×D4—798no—
1039C4×D4—794no—
1040C4×D4—794no—
1041C4×D4—794no—
1042C4×D4—794no—
1043C4×D4—794no—
1044C4×D4—794no—
1045C4×D4—794no—
1046C4×D4—794no—
1047C4×D4—794no—
1048C4×D4—798no—
1049C4×D4—798no—
1050C4×D4—794no—
1051C4×D4—794no—
1052C4×D4—794no—
1053C4×D4—798no—
1054C4×D4—798no—
1055C4×D4—798no—
1056C4×D4—798no—
1057C4×D4—794no—
1058C4×D4—794no—
1059C4×D4—792no—
1060C4×D4—798no—
1061C4×D4C22×D7914yes—
1062C4×D4C22×D7914yes—
1063C4×D4C22×D7912yes—
1064C4×D4C22×D7918yes—
1065C4×D4C22×D7918yes—
1066C4×D4C22×D7914yes—
1067#117—792no—
1068#117—791no—
1069#117—794no—
1070#117—794no—
1071#117—794no—
1072#117—794no—
1073#117—794no—
1074#117—798no—
1075#117—798no—
1076#117—794no—
1077#117—794no—
1078#117—794no—
1079#117—798no—
1080#117—798no—
1081#117—794no—
1082#117—792no—
1083#117—794no—
1084#117—798no—
1085#117C22×D7911yescharacteristic
1086#117C22×D7912yes—
1087#117C22×D7918yes—
1088#117C22×D7914yes—
1089C2×C4⋊C4—792no—
1090C2×C4⋊C4—794no—
1091C2×C4⋊C4—794no—
1092C2×C4⋊C4—794no—
1093C2×C4⋊C4—794no—
1094C2×C4⋊C4—798no—
1095C2×C4⋊C4—798no—
1096C2×C4⋊C4—798no—
1097C2×C4⋊C4—794no—
1098C2×C4⋊C4—794no—
1099C2×C4⋊C4—798no—
1100C2×C4⋊C4—798no—
1101C2×C4⋊C4—798no—
1102C2×C4⋊C4—798no—
1103C2×C4⋊C4—794no—
1104C2×C4⋊C4—794no—
1105C2×C4⋊C4—794no—
1106C2×C4⋊C4—794no—
1107C2×C4⋊C4—798no—
1108C2×C4⋊C4—794no—
1109C2×C4⋊C4C22×D7912yes—
1110C2×C4⋊C4C22×D7914yes—
1111C2×C4⋊C4C22×D7914yes—
1112C2×C42—794no—
1113C2×C42—791no—
1114C2×C42—792no—
1115C2×C42—792no—
1116C2×C42—792no—
1117C2×C42—792no—
1118C2×C42—792no—
1119C2×C42—792no—
1120C2×C42C22×D7912yes—
1121C2×C42C22×D7911yescharacteristic
1122C24—791no—
1123#41—28no—
1124#41—24no—
1125#41—3168no—
1126#41—31616no—
1127#41—3168no—
1128#41—31616no—
1129#41—1584no—
1130C2×Q8—798no—
1131C2×Q8—798no—
1132C2×Q8—794no—
1133C2×Q8—794no—
1134C2×Q8—791no—
1135C2×Q8C23×D7912yes—
1136C2×Q8C23×D7911yescharacteristic
1137C2×D4—798no—
1138C2×D4—794no—
1139C2×D4—792no—
1140C2×D4—794no—
1141C2×D4—794no—
1142C2×D4—794no—
1143C2×D4—791no—
1144C2×D4—794no—
1145C2×D4C23×D7914yes—
1146C2×D4C23×D7912yes—
1147C2×D4C23×D7912yes—
1148C2×D4C23×D7911yescharacteristic
1149C2×D4C23×D7918yes—
1150C2×D4C23×D7914yes—
1151C22×C4—3168no—
1152C22×C4—3164no—
1153C22×C4—792no—
1154C22×C4—794no—
1155C22×C4—794no—
1156C22×C4—794no—
1157C22×C4—798no—
1158C22×C4—798no—
1159C22×C4—792no—
1160C22×C4—792no—
1161C22×C4—794no—
1162C22×C4—798no—
1163C22×C4—798no—
1164C22×C4—791no—
1165C22×C4—792no—
1166C22×C4—792no—
1167C22×C4—792no—
1168C22×C4—792no—
1169C22×C4—792no—
1170C22×C4—798no—
1171C22×C4—1584no—
1172C22×C4C23×D7914yes—
1173C22×C4C23×D7912yes—
1174C22×C4C23×D7912yes—
1175C22×C4C23×D7914yes—
1176C22×C4C23×D7914yes—
1177C22×C4C23×D7918yes—
1178C22×C4C23×D7911yescharacteristic
1179C4⋊C4—798no—
1180C4⋊C4—798no—
1181C4⋊C4—798no—
1182C4⋊C4—798no—
1183C4⋊C4—798no—
1184C4⋊C4—798no—
1185C4⋊C4—794no—
1186C4⋊C4—794no—
1187C4⋊C4—794no—
1188C4⋊C4—798no—
1189C4⋊C4—798no—
1190C4⋊C4—798no—
1191C4⋊C4—798no—
1192C4⋊C4—798no—
1193C4⋊C4—798no—
1194C4⋊C4—794no—
1195C4⋊C4—794no—
1196C4⋊C4—794no—
1197C4⋊C4—794no—
1198C4⋊C4—794no—
1199C4⋊C4—794no—
1200C4⋊C4—794no—
1201C4⋊C4—794no—
1202C4⋊C4—798no—
1203C4⋊C4—798no—
1204C4⋊C4—792no—
1205C4⋊C4—792no—
1206C4⋊C4—792no—
1207C4⋊C4—794no—
1208C4⋊C4—798no—
1209C4⋊C4—798no—
1210C4⋊C4—798no—
1211C4⋊C4—798no—
1212C4⋊C4—794no—
1213C4⋊C4—794no—
1214C4⋊C4—794no—
1215C4⋊C4—794no—
1216C4⋊C4C23×D7914yes—
1217C4⋊C4C23×D7918yes—
1218C4⋊C4C23×D7914yes—
1219C4⋊C4C23×D7918yes—
1220C4⋊C4C23×D7912yes—
1221C4⋊C4C23×D7918yes—
1222C4⋊C4C23×D7918yes—
1223C4⋊C4C23×D7914yes—
1224C4⋊C4C23×D7914yes—
1225C22⋊C4—794no—
1226C22⋊C4—794no—
1227C22⋊C4—792no—
1228C22⋊C4—794no—
1229C22⋊C4—794no—
1230C22⋊C4—798no—
1231C22⋊C4—798no—
1232C22⋊C4—798no—
1233C22⋊C4—794no—
1234C22⋊C4—794no—
1235C22⋊C4—794no—
1236C22⋊C4—794no—
1237C22⋊C4—794no—
1238C22⋊C4—794no—
1239C22⋊C4—794no—
1240C22⋊C4—794no—
1241C22⋊C4—794no—
1242C22⋊C4—798no—
1243C22⋊C4—798no—
1244C22⋊C4—794no—
1245C22⋊C4C23×D7914yes—
1246C22⋊C4C23×D7914yes—
1247C22⋊C4C23×D7918yes—
1248C22⋊C4C23×D7918yes—
1249C22⋊C4C23×D7912yes—
1250C22⋊C4C23×D7914yes—
1251C22⋊C4C23×D7918yes—
1252C42—791no—
1253C42—792no—
1254C42—791no—
1255C42—792no—
1256C42—792no—
1257C42—792no—
1258C42—792no—
1259C42—794no—
1260C42—794no—
1261C42—794no—
1262C42—794no—
1263C42—792no—
1264C42—798no—
1265C42—798no—
1266C42—798no—
1267C42C23×D7911yescharacteristic
1268C42C23×D7911yescharacteristic
1269C42C23×D7912yes—
1270C42C23×D7914yes—
1271C42C23×D7912yes—
1272C42C23×D7918yes—
1273C23—792no—
1274C23—792no—
1275C23—1584no—
1276C23—1582no—
1277C23C24×D7914yes—
1278C23C24×D7912yes—
1279C23C24×D7911yescharacteristic
1280Q8—22no—
1281Q8—24no—
1282Q8—3168no—
1283Q8—3164no—
1284Q8—3168no—
1285Q8—3164no—
1286Q8—1582no—
1287D4—28no—
1288D4—24no—
1289D4—22no—
1290D4—24no—
1291D4—48no—
1292D4—44no—
1293D4—3168no—
1294D4—3164no—
1295D4—1588no—
1296D4—1588no—
1297D4—1588no—
1298D4—1588no—
1299D4—1584no—
1300D4—1582no—
1301C2×C4—28no—
1302C2×C4—24no—
1303C2×C4—42no—
1304C2×C4—44no—
1305C2×C4—44no—
1306C2×C4—48no—
1307C2×C4—3162no—
1308C2×C4—3168no—
1309C2×C4—3162no—
1310C2×C4—3164no—
1311C2×C4—3168no—
1312C2×C4—3162no—
1313C2×C4—3164no—
1314C2×C4—3164no—
1315C2×C4—3164no—
1316C2×C4—3168no—
1317C2×C4—3168no—
1318C2×C4—792no—
1319C2×C4—792no—
1320C2×C4—792no—
1321C2×C4—794no—
1322C2×C4—794no—
1323C2×C4—794no—
1324C2×C4—792no—
1325C2×C4—798no—
1326C2×C4—1584no—
1327C2×C4—15816no—
1328C2×C4—1584no—
1329C2×C4—1582no—
1330C2×C4—1584no—
1331C2×C4—1584no—
1332C2×C4—1584no—
1333C2×C4#1457920814yes—
1334C2×C4C24×D7912yes—
1335C2×C4C24×D7914yes—
1336C2×C4C24×D7912yes—
1337C2×C4C24×D7912yes—
1338C2×C4C24×D7918yes—
1339C2×C4C24×D7914yes—
1340C2×C4C24×D7911yescharacteristic
1341C2×C4C24×D7911yescharacteristic
1342C22—22no—
1343C22—24no—
1344C22—22no—
1345C22—24no—
1346C22—24no—
1347C22—24no—
1348C22—794no—
1349C22—1588no—
1350C22—1582no—
1351C22—1584no—
1352C22—1582no—
1353C22—1582no—
1354C22C2×#1457920812yes—
1355C22C25×D7911yescharacteristic
1356C4—24no—
1357C4—22no—
1358C4—22no—
1359C4—24no—
1360C4—28no—
1361C4—22no—
1362C4—1582no—
1363C4—1582no—
1364C4—1582no—
1365C4—1588no—
1366C4—1584no—
1367C4—1584no—
1368C4—1584no—
1369C4—1582no—
1370C4C2×#1457920812yes—
1371C4C2×#1457920812yes—
1372C2—22no—
1373C2—44no—
1374C2—42no—
1375C2—3162no—
1376C2—1584no—
1377C2C22×#1457920811yescharacteristic
1378C2#585×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3512C2
hypercenter#3512D79
hypocenterC79#62825
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3512

Complements

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

NH ≅ G/Ntype
1. #23778007C2semidirect
2. #23778005C2semidirect
3. #23777930C2semidirect
4. #23777924C2semidirect
5. #23777848C2semidirect
6. #23777380C2semidirect
7. #23777375C2semidirect
8. #23777371C2semidirect
9. #23777366C2semidirect
10. #23777321C2semidirect
11. #23777320C2semidirect
12. #23777226C2semidirect
13. #23777224C2semidirect
14. #23777222C2semidirect
15. #23777107C2semidirect
16. #23777104C2semidirect
17. #23777103C2semidirect
18. #23776695C2semidirect
19. #23776693C2semidirect
20. C2×#125×D79C2semidirect
21. C79×#3512C2semidirect
22. C79⋊#564C22semidirect
23. #19099316C22semidirect
24. #19099315C22semidirect
25. #19099308C22semidirect
26. #19099292C22semidirect
27. #19099290C22semidirect
28. #19099289C22semidirect
29. #19099289C22semidirect
33. #19099272C22semidirect
34. #19099272C22semidirect
38. #19099270C22semidirect
39. #19099269C22semidirect
43. #19099265C22semidirect
47. #19099260C22semidirect
48. #19099259C22semidirect
52. #19099255C22semidirect
54. #19099253C22semidirect
55. #19099253C22semidirect
59. #19099250C22semidirect
62. #19099249C22semidirect
65. #19099247C22semidirect
66. #19099246C22semidirect
76. #19099194C22semidirect
78. #19099193C22semidirect
80. #19099191C22semidirect
81. #19099191C22semidirect
82. #19099175C22semidirect
83. #19099174C22semidirect
84. #19099173C22semidirect
85. #19099172C22semidirect
86. #19099170C22semidirect
87. #19099170C22semidirect
88. #19099167C22semidirect
89. #19099166C22semidirect
91. #19099158C22semidirect
92. #19099157C22semidirect
95. #19099156C22semidirect
97. #19099155C22semidirect
103. #19099120C22semidirect
104. #19099119C22semidirect
108. #19099116C22semidirect
113. #19099099C22semidirect
117. #19099094C22semidirect
121. #19099092C22semidirect
124. C2×#14579153C22semidirect
126. C2×#14579152C22semidirect
132. #125×D79C22semidirect
153. #553×C79C22semidirect
154. #552×C79C22semidirect
155. #541×C79C22semidirect
156. #540×C79C22semidirect
159. #529×C79C22semidirect
701. #3512D79semidirect
711. C79#62825semidirect
743. #553C2×D79semidirect
759. #552C2×D79semidirect
781. #541C2×D79semidirect
784. #540C2×D79semidirect
820. #529C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237780072
#237780052
#237779302
#237779242
#237778482
#237773802
#237773752
#237773712
#237773662
#237773212
#237773202
#237772262
#237772242
#237772222
#237771072
#237771042
#237771032
#237766952
#237766932
C2×#125×D792
C79×#35122
#6282579