Finite Group Databasebeta

← #35197366

Subgroups — #35197366

Order 20224.

7066 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777502C214yesmaximal, complemented
2#23777498C214yesmaximal, complemented
3#23777480C214yesmaximal, complemented
4#23777476C214yesmaximal, complemented
5#23777401C214yesmaximal, complemented
6#23777397C214yesmaximal, complemented
7#23777386C214yesmaximal, complemented
8#23777382C214yesmaximal, complemented
9#23777251C216yesmaximal, complemented
10#23777206C211yesmaximal, characteristic, complemented
11#23777167C211yesmaximal, characteristic, complemented
12#23777106C216yesmaximal, complemented
13#23777058C211yesmaximal, characteristic, complemented
14#23776813C216yesmaximal, complemented
15#23776788C216yesmaximal, complemented
162−1+4×Dic79C211yesmaximal, characteristic, complemented
17#23776609C211yesmaximal, characteristic, complemented
18C2×#19099046C211yesmaximal, characteristic, complemented
19C79×#3487C211yesmaximal, characteristic, complemented
20C2×#14579209C2211yescharacteristic
21#19099299C22112yescomplemented
22#19099295C22112yescomplemented
23Q8×Dic158C2214yescomplemented
24#19099292C2214yescomplemented
25#19099289C2214yescomplemented
26#19099289C2214yescomplemented
27#19099282C22112yescomplemented
28#19099277C22112yescomplemented
29#19099271C22112yescomplemented
30#19099270C22112yescomplemented
31#19099265C22112yescomplemented
32#19099265C22112yescomplemented
33#19099260C22112yescomplemented
34#19099259C22112yescomplemented
35#19099255C22112yescomplemented
36#19099253C22112yescomplemented
37#19099233C22112yescomplemented
38#19099232C2214yes—
39#19099232C2214yes—
40#19099232C2214yescomplemented
41Q8×C22⋊D79C2214yescomplemented
42#19099224C2214yescomplemented
43#19099220C2214yes—
44#19099220C2214yes—
45#19099220C2214yescomplemented
46#19099217C22112yescomplemented
47#19099213C22112yescomplemented
48#19099213C22112yescomplemented
49#19099191C2216yes—
50#19099186C2216yescomplemented
51#19099186C2216yescomplemented
52#19099182C22112yescomplemented
53#19099180C2216yescomplemented
54#19099180C2216yescomplemented
55#19099180C22112yescomplemented
56#19099173C2216yescomplemented
57#19099173C2216yescomplemented
58#19099167C22112yescomplemented
59#19099166C2216yescomplemented
60#19099166C2216yescomplemented
61#19099166C22112yescomplemented
62#19099157C2214yes—
63#19099157C22112yes—
64#19099148C22112yes—
65#19099148C22112yes—
66#19099141C2216yes—
67#19099130C2216yes—
68#19099116C2216yes—
69#19099111C22112yescomplemented
70#19099109C2216yes—
71#19099108C22112yescomplemented
72#19099095C22112yescomplemented
73#19099095C22112yescomplemented
74#19099094C22112yescomplemented
75#19099093C22112yescomplemented
76#19099093C22112yescomplemented
77#19099092C22112yescomplemented
78#19099074C2216yes—
79#19099069C22124yes—
80#19099046C2216yes—
81#19099046C2214yes—
82#19099046C2214yes—
83#19099046C2214yes—
84#19099046C2214yes—
85#19099046C2214yescomplemented
86#19099045C2214yescomplemented
87#19099043C2216yes—
88#19099041C2211yescharacteristic
89#19099041C2214yescomplemented
90#19099039C2214yescomplemented
91#41×Dic79C2216yes—
92#41×Dic79C2214yescomplemented
93C4×#11929625C2214yescomplemented
94#19099031C2216yes—
95C2×Q8×Dic79C2211yescharacteristic
96C2×Q8×Dic79C2211yescharacteristic
97C2×Q8×Dic79C2214yescomplemented
98C4×Q8×D79C2214yescomplemented
99C2×D4×Dic79C2213yes—
100C2×D4×Dic79C2213yes—
101C2×#14579120C2213yes—
102C22×C4⋊Dic79C2213yes—
103C2×2−1+4×C79C2211yescharacteristic
104C22×#41×C79C2211yescharacteristic
105#550×C79C2214yes—
106#550×C79C2214yes—
107#548×C79C2214yes—
108#548×C79C2214yes—
109#535×C79C2216yes—
110#525×C79C2216yes—
111#519×C79C2211yescharacteristic
112#14579209—28no—
113C2×#11929625C2314yes—
114C2×#11929624C2316yes—
115C2×#11929623C23124yes—
116C2×Q8×D79C2314yes—
117C23×Dic79C2316yes—
118#14579161C23112yes—
119#14579160C2316yes—
120#14579160C2316yes—
121#14579160C23112yes—
122#14579159C2316yes—
123#14579157C2316yes—
124#14579157C23112yes—
125#14579156C2314yes—
126#14579156C23112yes—
127#14579154C23112yes—
128#14579154C23112yes—
129#14579154C23112yes—
130#14579154C23112yes—
131#14579154C2314yes—
132#14579154C23112yes—
133#14579153C23112yes—
134#14579152C2314yes—
135#14579152C23112yes—
136#14579152C2316yes—
137#14579152C2316yes—
138#14579152C23112yes—
139#14579151C2314yes—
140#14579151C23112yes—
141#14579150C2316yes—
142#14579148C23112yes—
143#14579148C23112yes—
144#14579148C2316yes—
145#14579148C23112yes—
146#14579147C23112yes—
147#14579147C23112yes—
148#14579145C2314yes—
149#14579145C23112yes—
150#14579145C23124yes—
151#14579144C2314yes—
152#14579143C23112yes—
153#14579143C23112yes—
154#14579143C2314yes—
155#14579143C23112yes—
156#14579142C23112yes—
157#14579142C23112yes—
158#14579142C23124yes—
159#14579141C2314yes—
160#14579141C23112yes—
161#14579140C23112yes—
162#14579140C2316yes—
163#14579140C2316yes—
164#14579138C2314yes—
165#14579138C23112yes—
166#14579138C2314yes—
167#14579138C23112yes—
168#14579138C23124yes—
169#14579137C23112yes—
170#14579135C23112yes—
171#14579135C2316yes—
172#14579135C2316yes—
173#14579133C23112yes—
174#14579133C2314yes—
175#14579133C23112yes—
176#14579133C23112yes—
177#14579133C23124yes—
178#14579132C23112yes—
179#14579132C23112yes—
180#14579132C23112yes—
181#14579132C23112yes—
182#14579132C23112yes—
183#14579130C23112yes—
184Q8×Dic79C2316yes—
185Q8×Dic79C2316yes—
186Q8×Dic79C2314yes—
187Q8×Dic79C2314yes—
188Q8×Dic79C2314yes—
189Q8×Dic79C2314yes—
190Q8×Dic79C23112yes—
191Q8×Dic79C2314yes—
192Q8×Dic79C2314yes—
193C4×Dic158C23112yes—
194C4×Dic158C23112yes—
195C4×Dic158C23112yes—
196#14579126C2316yes—
197#14579126C2316yes—
198C4×D316C23112yes—
199D4×Dic79C2314yes—
200D4×Dic79C23112yes—
201D4×Dic79C2316yes—
202D4×Dic79C23112yes—
203D4×Dic79C2316yes—
204D4×Dic79C23112yes—
205D4×Dic79C23112yes—
206D4×Dic79C23112yes—
207D4×Dic79C23112yes—
208D4×Dic79C23124yes—
209#14579123C2316yes—
210#14579123C2316yes—
211C4×C22⋊D79C23112yes—
212C4×C22⋊D79C23112yes—
213C4×C22⋊D79C23112yes—
214C4×C22⋊D79C23112yes—
215(C22⋊D79)⋊C4C2314yes—
216(C22⋊D79)⋊C4C23112yes—
217(C22⋊D79)⋊C4C23124yes—
218#14579120C2316yes—
219#14579120C2316yes—
220#14579120C23112yes—
221#14579120C2316yes—
222#14579120C2316yes—
223#14579120C2316yes—
224#14579120C23112yes—
225#14579119C23112yes—
226#14579118C23112yes—
227#14579117C23124yes—
228C2×C4⋊Dic79C2313yes—
229C2×C4⋊Dic79C2313yes—
230C2×C4⋊Dic79C2311yescharacteristic
231C2×C4⋊Dic79C23112yes—
232C2×C4⋊Dic79C23112yes—
233C2×C4⋊Dic79C23112yes—
234C2×C4⋊Dic79C2313yes—
235C4⋊C4×D79C23112yes—
236C2×C22⋊Dic79C2313yes—
237C2×C22⋊Dic79C2313yes—
238C2×C4×Dic79C2313yes—
239C2×C4×Dic79C2313yes—
240C2×C4×Dic79C23112yes—
241C42×D79C23112yes—
2422−1+4×C79—28no—
243C2×#41×C79—28no—
244C2×#41×C79C2316yes—
245C2×#41×C79C2314yes—
246C2×#41×C79C2314yes—
247C2×#41×C79C2314yes—
248C22×Q8×C79C2314yes—
249C22×Q8×C79C2311yescharacteristic
250C22×D4×C79C2313yes—
251C23×C4×C79C2313yes—
252#127×C79C23112yes—
253#124×C79C23112yes—
254#123×C79C2314yes—
255C22⋊Q8×C79C2316yes—
256C22⋊Q8×C79C2316yes—
257#121×C79C2316yes—
258#121×C79C2316yes—
259#121×C79C23112yes—
260#121×C79C23112yes—
261#120×C79C23112yes—
262C4×Q8×C79C2314yes—
263C4×Q8×C79C2314yes—
264C4×D4×C79C23112yes—
265C4×D4×C79C23112yes—
266#117×C79C2316yes—
267#11929625—216no—
268#11929624—224no—
269#11929623—824no—
270C2×Dic158C2416yes—
271C2×Dic158C24112yes—
272C2×Dic158C2414yes—
273Q8×D79—216no—
274C2×D316C2416yes—
275C2×C22⋊D79C2414yes—
276C2×C22⋊D79C24112yes—
277C2×C22⋊D79C24112yes—
278C2×C22⋊D79C24112yes—
279C2×C22⋊D79C2414yes—
280C22×Dic79—86no—
281C22×Dic79C24112yes—
282C22×Dic79C24124yes—
283C22×Dic79C2411yescharacteristic
284C22×Dic79C2411yescharacteristic
285C22×Dic79C2414yes—
286C22×Dic79C2413yes—
287C22×Dic79C2413yes—
288C2×C4×D79C24112yes—
289C2×C4×D79C24112yes—
290C2×C4×D79C2414yes—
291C4⋊Dic79C24112yes—
292C4⋊Dic79C2416yes—
293C4⋊Dic79C2416yes—
294C4⋊Dic79C24112yes—
295C4⋊Dic79C2416yes—
296C4⋊Dic79C24112yes—
297C4⋊Dic79C2411yescharacteristic
298C4⋊Dic79C2411yescharacteristic
299C4⋊Dic79C2411yescharacteristic
300C4⋊Dic79C2411yescharacteristic
301C4⋊Dic79C2416yes—
302C4⋊Dic79C2414yes—
303C4⋊Dic79C24112yes—
304C4⋊Dic79C2414yes—
305Dic79⋊C4C24112yes—
306Dic79⋊C4C24112yes—
307Dic79⋊C4C24112yes—
308Dic79⋊C4C2414yes—
309Dic79⋊C4C24112yes—
310Dic79⋊C4C2414yes—
311Dic79⋊C4C2414yes—
312Dic79⋊C4C2414yes—
313Dic79⋊C4C2414yes—
314Dic79⋊C4C2414yes—
315C22⋊Dic79C2416yes—
316C22⋊Dic79C2416yes—
317C22⋊Dic79C2416yes—
318C22⋊Dic79C2416yes—
319C22⋊Dic79C24112yes—
320C22⋊Dic79C2414yes—
321C22⋊Dic79C2414yes—
322C22⋊Dic79C24112yes—
323C22⋊Dic79C2414yes—
324C22⋊Dic79C24112yes—
325C22⋊Dic79C24112yes—
326(C2×D79)⋊C4C2414yes—
327(C2×D79)⋊C4C24112yes—
328(C2×D79)⋊C4C24112yes—
329(C2×D79)⋊C4C2414yes—
330(C2×D79)⋊C4C2414yes—
331(C2×D79)⋊C4C2414yes—
332C4×Dic79C2414yes—
333C4×Dic79C2416yes—
334C4×Dic79C24112yes—
335C4×Dic79C2416yes—
336C4×Dic79C2414yes—
337C4×Dic79C24112yes—
338C4×Dic79C2416yes—
339C4×Dic79C2416yes—
340C4×Dic79C24112yes—
341C24×C79C2413yes—
342#41×C79—216no—
343#41×C79—216no—
344#41×C79—216no—
345#41×C79—224no—
346C2×Q8×C79—216no—
347C2×Q8×C79#4118yescomplemented
348C2×Q8×C79C2416yes—
349C2×Q8×C79C2414yes—
350C2×D4×C79—212no—
351C2×D4×C79C2414yes—
352C2×D4×C79C24112yes—
353C2×D4×C79C2416yes—
354C2×D4×C79C24112yes—
355C2×D4×C79C24112yes—
356C22×C4×C79—212no—
357C22×C4×C79C24112yes—
358C22×C4×C79C2416yes—
359C22×C4×C79C2416yes—
360C22×C4×C79C2411yescharacteristic
361C22×C4×C79C2413yes—
362C4⋊C4×C79C2416yes—
363C4⋊C4×C79C2416yes—
364C4⋊C4×C79C2414yes—
365C4⋊C4×C79C2414yes—
366C22⋊C4×C79C2414yes—
367C22⋊C4×C79C2414yes—
368C22⋊C4×C79C2414yes—
369C22⋊C4×C79C24112yes—
370C22⋊C4×C79C24112yes—
371C42×C79C24112yes—
372C23×C79—26no—
373C23×C79—43no—
374C23×C79—43no—
375C23×C79C2516yes—
376C23×C79C2514yes—
377C23×C79C2511yescharacteristic
378C22×D79C2514yes—
379Q8×C79—212no—
380Q8×C79C2×#41116yes—
381D4×C79—28no—
382D4×C79—224no—
383D4×C79—212no—
384D4×C79—412no—
385D4×C79—412no—
386C2×C4×C79—22no—
387C2×C4×C79—212no—
388C2×C4×C79—212no—
389C2×C4×C79—224no—
390C2×C4×C79C2×#41112yes—
391C2×C4×C79C2514yes—
392C2×C4×C79C2514yes—
393C2×C4×C79C2514yes—
394C2×C4×C79C2511yescharacteristic
395C2×C4×C79C2511yescharacteristic
396C2×C4×C79C2516yes—
397C22⋊D79—28no—
398C22⋊D79—44no—
399C22⋊D79—412no—
400C22⋊D79—412no—
401C22⋊D79—412no—
402C2×Dic79—43no—
403C2×Dic79—43no—
404C2×Dic79—424no—
405C2×Dic79—41no—
406C2×Dic79—44no—
407C2×Dic79—41no—
408C2×Dic79—412no—
409C2×Dic79C2511yescharacteristic
410C2×Dic79C2511yescharacteristic
411C2×Dic79C2511yescharacteristic
412C2×Dic79C2516yes—
413C2×Dic79C2514yes—
414C2×Dic79C2511yescharacteristic
415C2×Dic79C2514yes—
416C2×Dic79C2514yes—
417C2×Dic79C2516yes—
418D316—212no—
419C4×D79—224no—
420C4×D79—44no—
421C4×D79—412no—
422Dic158—212no—
423Dic158—44no—
424Dic158—412no—
425C22×C79—21no—
426C22×C79—21no—
427C22×C79—24no—
428C22×C79—26no—
429C22×C79—24no—
430C22×C79—26no—
431C22×C79—26no—
432C22×C79—24no—
433C22×C79—412no—
434C22×C79C22×#4112yes—
435C22×C79C2611yescharacteristic
436C2×D79—24no—
437C2×D79—24no—
438C2×D79—24no—
439C4×C79—21no—
440C4×C79—21no—
441C4×C79—24no—
442C4×C79—24no—
443C4×C79—24no—
444C4×C79C22×#41112yes—
445Dic79—24no—
446Dic79—24no—
447Dic79—26no—
448Dic79—26no—
449Dic79—21no—
450Dic79—24no—
451Dic79—21no—
452Dic79—21no—
453Dic79—21no—
454#62851—791nomaximal, Sylow
455C2×C79—22no—
456C2×C79—44no—
457C2×C79—46no—
458C2×C79C23×#4111yescharacteristic
459C2×C79H(7,𝔽2)11yescharacteristic
460C2×C792−1+611yescharacteristic
461D79—44no—
462#3524—794no—
463#3524—794no—
464#3522—794no—
465#3522—794no—
466#3517—794no—
467#3517—794no—
468#3516—794no—
469#3516—794no—
470#3506—796no—
471#3502—791no—
472#3497—791no—
473#3492—796no—
474#3487—791no—
475#3487D7911yescharacteristic, complemented
476#3460—796no—
477#3455—796no—
478C4×2−1+4—791no—
479C4×2−1+4—791no—
480C2×#520—791no—
481C79#6285111yescharacteristic, complemented, Sylow
482C2×2−1+4—791no—
483C2×2−1+4C2×D7911yescharacteristic
484C22×#41C2×D7911yescharacteristic
485#559—7912no—
486#559—7912no—
487Q82—794no—
488#557—794no—
489#557—794no—
490#557—794no—
491#556—7912no—
492#555—7912no—
493#554—7912no—
494#554—7912no—
495#553—7912no—
496#553—7912no—
497#553—7912no—
498#553—7912no—
499#552—7912no—
500#552—7912no—
501#550—794no—
502#550—794no—
503#550—794no—
504#550—7912no—
505#550C2×D7914yes—
506#550C2×D7914yes—
507D4×Q8—794no—
508#548—794no—
509#548—794no—
510#548—794no—
511#548—794no—
512#548C2×D7914yes—
513#548C2×D7914yes—
514#547—7912no—
515#547—7912no—
516#547—7912no—
517#544—796no—
518#542—7912no—
519#542—796no—
520#542—796no—
521#542—796no—
522#542—796no—
523#542—7912no—
524#541—796no—
525#541—796no—
526#540—7912no—
527#540—796no—
528#540—796no—
529#540—7912no—
530#539—794no—
531#539—7912no—
532#538—7912no—
533#538—7912no—
534#537—796no—
535#535—796no—
536#535C2×D7916yes—
537#533—796no—
538#532—796no—
539#532—7912no—
540#532—7912no—
541#529—7912no—
542#529—7912no—
543#529—7912no—
544#529—7912no—
545#529—7912no—
546#529—7912no—
547#525—796no—
548#525—7924no—
549#525C2×D7916yes—
550#520—794no—
551#520—794no—
552#520—794no—
553#520—794no—
554#520—796no—
555#520—794no—
556#520—794no—
557#520—796no—
558#519—791no—
559#519—794no—
560#519—794no—
561#519C2×D7911yescharacteristic
562C4×#41—796no—
563C4×#41—794no—
564C4×#41—794no—
565C4×#41—796no—
566C2×C4×Q8—791no—
567C2×C4×Q8—791no—
568C2×C4×Q8—794no—
569C2×C4×Q8—794no—
570C2×C4×D4—793no—
571C2×C4×D4—793no—
572C2×#117—793no—
573C22×C4⋊C4—793no—
5742−1+4—28no—
5752−1+4—1588no—
576C2×#41—28no—
577C2×#41—794no—
578C2×#41—7924no—
579C2×#41—796no—
580C2×#41C22×D7916yes—
581C2×#41C22×D7914yes—
582C2×#41C22×D7914yes—
583C2×#41C22×D7914yes—
584C22×Q8—794no—
585C22×Q8C22×D7914yes—
586C22×Q8C22×D7911yescharacteristic
587C22×D4C22×D7913yes—
588C23×C4—796no—
589C23×C4C22×D7913yes—
590C4⋊Q8—796no—
591C4⋊Q8—7912no—
592C4⋊Q8—796no—
593C4⋊Q8—796no—
594C4⋊Q8—7912no—
595#127—7912no—
596#127—796no—
597#127C22×D79112yes—
598#126—794no—
599#126—7912no—
600#126—7912no—
601#126—7912no—
602#126—794no—
603#126—7912no—
604#126—7912no—
605#126—7912no—
606#125—794no—
607#125—794no—
608#125—7912no—
609#125—7912no—
610#125—7912no—
611#125—796no—
612#125—796no—
613#125—7912no—
614#124—796no—
615#124—7912no—
616#124—7912no—
617#124—7912no—
618#124—796no—
619#124—7912no—
620#124—7912no—
621#124C22×D79112yes—
622#123—7924no—
623#123—7912no—
624#123—7912no—
625#123—794no—
626#123—7924no—
627#123—7912no—
628#123—794no—
629#123—794no—
630#123—7912no—
631#123—7912no—
632#123—7912no—
633#123C22×D7914yes—
634C22⋊Q8—7912no—
635C22⋊Q8—796no—
636C22⋊Q8—796no—
637C22⋊Q8—7912no—
638C22⋊Q8—794no—
639C22⋊Q8—7912no—
640C22⋊Q8—7912no—
641C22⋊Q8—7924no—
642C22⋊Q8—794no—
643C22⋊Q8—7912no—
644C22⋊Q8—794no—
645C22⋊Q8C22×D7916yes—
646C22⋊Q8C22×D7916yes—
647#121—7912no—
648#121—7924no—
649#121—7912no—
650#121—7912no—
651#121—7912no—
652#121—7912no—
653#121—7912no—
654#121—794no—
655#121—7912no—
656#121—7912no—
657#121—796no—
658#121—796no—
659#121—7912no—
660#121C22×D7916yes—
661#121C22×D7916yes—
662#121C22×D79112yes—
663#121C22×D79112yes—
664#120—7912no—
665#120C22×D79112yes—
666C4×Q8—794no—
667C4×Q8—794no—
668C4×Q8—796no—
669C4×Q8—794no—
670C4×Q8—7912no—
671C4×Q8—794no—
672C4×Q8—794no—
673C4×Q8—796no—
674C4×Q8—794no—
675C4×Q8—796no—
676C4×Q8—796no—
677C4×Q8—7912no—
678C4×Q8—7912no—
679C4×Q8—7912no—
680C4×Q8C22×D7914yes—
681C4×Q8C22×D7914yes—
682C4×D4—7912no—
683C4×D4—7912no—
684C4×D4—7912no—
685C4×D4—7912no—
686C4×D4—794no—
687C4×D4—796no—
688C4×D4—7912no—
689C4×D4—796no—
690C4×D4—7912no—
691C4×D4—7924no—
692C4×D4—7912no—
693C4×D4—7912no—
694C4×D4—7912no—
695C4×D4—7912no—
696C4×D4—796no—
697C4×D4—796no—
698C4×D4—794no—
699C4×D4—7912no—
700C4×D4—7924no—
701C4×D4—7912no—
702C4×D4C22×D79112yes—
703C4×D4C22×D79112yes—
704#117—796no—
705#117—796no—
706#117—796no—
707#117—796no—
708#117—796no—
709#117—7912no—
710#117—7912no—
711#117—7912no—
712#117—7924no—
713#117—7912no—
714#117C22×D7916yes—
715C2×C4⋊C4—793no—
716C2×C4⋊C4—793no—
717C2×C4⋊C4—793no—
718C2×C4⋊C4—7912no—
719C2×C4⋊C4—7912no—
720C2×C4⋊C4—791no—
721C2×C4⋊C4—7912no—
722C2×C4⋊C4—7912no—
723C2×C22⋊C4—793no—
724C2×C22⋊C4—793no—
725C2×C42—793no—
726C2×C42—793no—
727C2×C42—7912no—
728C2×C42—7912no—
729C24C23×D7913yes—
730#41—216no—
731#41—216no—
732#41—216no—
733#41—224no—
734#41—63224no—
735#41—15816no—
736#41—15824no—
737C2×Q8—216no—
738C2×Q8—794no—
739C2×Q8—7912no—
740C2×Q8—796no—
741C2×Q8—15816no—
742C2×Q8#1192962318yescomplemented
743C2×Q8C23×D7916yes—
744C2×Q8C23×D7914yes—
745C2×D4—212no—
746C2×D4—7912no—
747C2×D4—794no—
748C2×D4—7912no—
749C2×D4—7912no—
750C2×D4—794no—
751C2×D4—796no—
752C2×D4C23×D7914yes—
753C2×D4C23×D79112yes—
754C2×D4C23×D7916yes—
755C2×D4C23×D79112yes—
756C2×D4C23×D79112yes—
757C22×C4—212no—
758C22×C4—791no—
759C22×C4—791no—
760C22×C4—794no—
761C22×C4—793no—
762C22×C4—793no—
763C22×C4—7912no—
764C22×C4—7924no—
765C22×C4—794no—
766C22×C4—7912no—
767C22×C4—7912no—
768C22×C4—6326no—
769C22×C4C23×D79112yes—
770C22×C4C23×D7911yescharacteristic
771C22×C4C23×D7916yes—
772C22×C4C23×D7916yes—
773C22×C4C23×D7913yes—
774C4⋊C4—7912no—
775C4⋊C4—794no—
776C4⋊C4—7912no—
777C4⋊C4—7912no—
778C4⋊C4—794no—
779C4⋊C4—794no—
780C4⋊C4—794no—
781C4⋊C4—7912no—
782C4⋊C4—794no—
783C4⋊C4—794no—
784C4⋊C4—7912no—
785C4⋊C4—796no—
786C4⋊C4—796no—
787C4⋊C4—7912no—
788C4⋊C4—796no—
789C4⋊C4—7912no—
790C4⋊C4—791no—
791C4⋊C4—791no—
792C4⋊C4—791no—
793C4⋊C4—791no—
794C4⋊C4—796no—
795C4⋊C4—794no—
796C4⋊C4—7912no—
797C4⋊C4—794no—
798C4⋊C4C23×D7916yes—
799C4⋊C4C23×D7916yes—
800C4⋊C4C23×D7914yes—
801C4⋊C4C23×D7914yes—
802C22⋊C4—796no—
803C22⋊C4—796no—
804C22⋊C4—796no—
805C22⋊C4—796no—
806C22⋊C4—794no—
807C22⋊C4—7912no—
808C22⋊C4—794no—
809C22⋊C4—7912no—
810C22⋊C4—7912no—
811C22⋊C4—7912no—
812C22⋊C4—794no—
813C22⋊C4—7912no—
814C22⋊C4—794no—
815C22⋊C4—794no—
816C22⋊C4—7912no—
817C22⋊C4—794no—
818C22⋊C4—794no—
819C22⋊C4C23×D79112yes—
820C22⋊C4C23×D7914yes—
821C22⋊C4C23×D79112yes—
822C22⋊C4C23×D7914yes—
823C22⋊C4C23×D7914yes—
824C42—796no—
825C42—796no—
826C42—794no—
827C42—794no—
828C42—7912no—
829C42—7912no—
830C42—796no—
831C42—796no—
832C42—7912no—
833C42C23×D79112yes—
834C23—26no—
835C23—43no—
836C23—43no—
837C23—794no—
838C23C24×D7916yes—
839C23C24×D7914yes—
840C23C24×D7911yescharacteristic
841Q8—212no—
842Q8—31612no—
843Q8—3164no—
844Q8—15812no—
845Q8C2×#11929623116yes—
846D4—28no—
847D4—224no—
848D4—212no—
849D4—412no—
850D4—412no—
851D4—3164no—
852D4—31612no—
853D4—31612no—
854D4—31612no—
855D4—1588no—
856D4—15812no—
857C2×C4—22no—
858C2×C4—212no—
859C2×C4—212no—
860C2×C4—224no—
861C2×C4—31612no—
862C2×C4—3164no—
863C2×C4—3163no—
864C2×C4—3163no—
865C2×C4—31624no—
866C2×C4—31612no—
867C2×C4—3161no—
868C2×C4—3164no—
869C2×C4—3161no—
870C2×C4—791no—
871C2×C4—791no—
872C2×C4—791no—
873C2×C4—794no—
874C2×C4—791no—
875C2×C4—796no—
876C2×C4—794no—
877C2×C4—794no—
878C2×C4—796no—
879C2×C4—15824no—
880C2×C4C2×#11929623112yes—
881C2×C4C24×D7914yes—
882C2×C4C24×D7914yes—
883C2×C4C24×D7914yes—
884C2×C4C24×D7911yescharacteristic
885C2×C4C24×D7911yescharacteristic
886C2×C4C24×D7916yes—
887C22—21no—
888C22—21no—
889C22—24no—
890C22—26no—
891C22—26no—
892C22—24no—
893C22—24no—
894C22—26no—
895C22—412no—
896C22—1584no—
897C22—1584no—
898C22—1584no—
899C22C22×#1192962312yes—
900C22C25×D7911yescharacteristic
901C4—21no—
902C4—21no—
903C4—24no—
904C4—24no—
905C4—24no—
906C4—1584no—
907C4—1586no—
908C4—1586no—
909C4—1584no—
910C4—1581no—
911C4—1581no—
912C4—1581no—
913C4—1584no—
914C4—1581no—
915C4C22×#11929623112yes—
916C2—22no—
917C2—46no—
918C2—44no—
919C2—3164no—
920C2C23×#1192962311yescharacteristic
921C2#2377821111yescharacteristic
922C2#2377821311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3487C2
hypercenter#3487D79
hypocenterC79#62851
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3487

Complements

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

NH ≅ G/Ntype
1. #23777502C2semidirect
2. #23777498C2semidirect
3. #23777480C2semidirect
4. #23777476C2semidirect
5. #23777401C2semidirect
6. #23777397C2semidirect
7. #23777386C2semidirect
8. #23777382C2semidirect
9. #23777251C2semidirect
10. #23777206C2semidirect
11. #23777167C2semidirect
12. #23777106C2semidirect
13. #23777058C2semidirect
14. #23776813C2semidirect
15. #23776788C2semidirect
16. 2−1+4×Dic79C2semidirect
17. #23776609C2semidirect
18. C2×#19099046C2semidirect
19. C79×#3487C2semidirect
21. #19099299C22semidirect
22. #19099295C22semidirect
23. Q8×Dic158C22semidirect
24. #19099292C22semidirect
25. #19099289C22semidirect
26. #19099289C22semidirect
27. #19099282C22semidirect
28. #19099277C22semidirect
29. #19099271C22semidirect
30. #19099270C22semidirect
31. #19099265C22semidirect
32. #19099265C22semidirect
33. #19099260C22semidirect
34. #19099259C22semidirect
35. #19099255C22semidirect
36. #19099253C22semidirect
37. #19099233C22semidirect
40. #19099232C22semidirect
41. Q8×C22⋊D79C22semidirect
42. #19099224C22semidirect
45. #19099220C22semidirect
46. #19099217C22semidirect
47. #19099213C22semidirect
48. #19099213C22semidirect
50. #19099186C22semidirect
51. #19099186C22semidirect
52. #19099182C22semidirect
53. #19099180C22semidirect
54. #19099180C22semidirect
55. #19099180C22semidirect
56. #19099173C22semidirect
57. #19099173C22semidirect
58. #19099167C22semidirect
59. #19099166C22semidirect
60. #19099166C22semidirect
61. #19099166C22semidirect
69. #19099111C22semidirect
71. #19099108C22semidirect
72. #19099095C22semidirect
73. #19099095C22semidirect
74. #19099094C22semidirect
75. #19099093C22semidirect
76. #19099093C22semidirect
77. #19099092C22semidirect
85. #19099046C22semidirect
86. #19099045C22semidirect
89. #19099041C22semidirect
90. #19099039C22semidirect
92. #41×Dic79C22semidirect
93. C4×#11929625C22semidirect
97. C2×Q8×Dic79C22semidirect
98. C4×Q8×D79C22semidirect
347. C2×Q8×C79#41semidirect
475. #3487D79semidirect
481. C79#62851semidirect
742. C2×Q8#11929623semidirect

Maximal subgroups

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

subgroupindex
#237775022
#237774982
#237774802
#237774762
#237774012
#237773972
#237773862
#237773822
#237772512
#237772062
#237771672
#237771062
#237770582
#237768132
#237767882
2−1+4×Dic792
#237766092
C2×#190990462
C79×#34872
#6285179