Finite Group Databasebeta

← #35197290

Subgroups — #35197290

Order 20224.

7474 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777238C216yesmaximal, complemented
2#23777235C216yesmaximal, complemented
3#23777232C216yesmaximal, complemented
4#23777228C216yesmaximal, complemented
5#23777094C216yesmaximal, complemented
6#23777092C216yesmaximal, complemented
7#23777086C216yesmaximal, complemented
8#23777083C216yesmaximal, complemented
9#23776812C211yesmaximal, characteristic, complemented
10#23776809C213yesmaximal, complemented
11#23776806C213yesmaximal, complemented
12#543×D79C211yesmaximal, characteristic, complemented
13#534×D79C213yesmaximal, complemented
14C2×#19099035C213yesmaximal, complemented
15C79×#3459C211yesmaximal, characteristic, complemented
16C22×D4×D79C2213yes—
17#19099266C2216yescomplemented
18#19099264C22112yescomplemented
19#19099263C2216yescomplemented
20#19099260C2216yescomplemented
21#19099258C22112yescomplemented
22#19099257C2216yescomplemented
23#19099254C2216yescomplemented
24#19099252C2216yescomplemented
25#19099251C2216yescomplemented
26#19099249C22112yescomplemented
27#19099247C2216yescomplemented
28#19099245C22112yescomplemented
29#19099243C22112yescomplemented
30#19099242C22112yescomplemented
31#19099241C22112yescomplemented
32#19099240C22112yescomplemented
33#19099238C22112yescomplemented
34#19099238C22112yescomplemented
35#19099237C22112yescomplemented
36#19099236C22112yescomplemented
37#19099225C2212yescomplemented
38#19099223C2216yescomplemented
39#19099221C2216yescomplemented
40#19099220C2212yescomplemented
41#19099210C2216yescomplemented
42#19099208C2216yescomplemented
43#19099206C2216yescomplemented
44#19099205C22112yescomplemented
45#19099202C22112yescomplemented
46#19099201C2216yescomplemented
47#19099189C2213yescomplemented
48#19099188C2216yescomplemented
49#19099188C2216yescomplemented
50#19099162C2216yescomplemented
51#19099160C2216yescomplemented
52#19099158C2216yescomplemented
53#19099157C22112yescomplemented
54#19099155C22112yescomplemented
55#19099153C2216yescomplemented
56#19099151C2216yescomplemented
57#19099150C2216yescomplemented
58#19099148C22112yescomplemented
59#19099146C22112yescomplemented
60#19099125C2213yescomplemented
61#19099124C22112yescomplemented
62#19099123C22112yescomplemented
63#19099122C2216yescomplemented
64#19099121C2216yes—
65#19099121C2216yes—
66#19099099C2216yescomplemented
67#19099097C2216yescomplemented
68#19099094C2216yescomplemented
69#19099093C22112yescomplemented
70#19099090C22112yescomplemented
71#19099076C2216yescomplemented
72#19099074C2216yescomplemented
73#19099073C2216yescomplemented
74#19099072C22112yescomplemented
75#19099069C22112yescomplemented
76#123×D79C22112yescomplemented
77C22⋊Q8×D79C2216yescomplemented
78C22⋊Q8×D79C2216yescomplemented
79#121×D79C2216yescomplemented
80#121×D79C2216yescomplemented
81#120×D79C22112yescomplemented
82#19099035C22112yescomplemented
83#19099035C22112yescomplemented
84#19099035C22112yescomplemented
85#19099035C22112yescomplemented
86C2×C4×D316C2213yescomplemented
87C2×D4×Dic79C2213yescomplemented
88C2×#14579123C2213yescomplemented
89C2×C4×C22⋊D79C2213yescomplemented
90C2×C4×C22⋊D79C2213yescomplemented
91C2×(C22⋊D79)⋊C4C2213yescomplemented
92C2×(C22⋊D79)⋊C4C2213yescomplemented
93C2×#14579119C2213yescomplemented
94C2×#14579118C2213yescomplemented
95C22×(C2×D79)⋊C4C2211yescharacteristic
96C22×(C2×D79)⋊C4C2213yescomplemented
97C2×C22⋊C4×D79C2213yes—
98C2×C22⋊C4×D79C2213yescomplemented
99#543×C79C2211yescharacteristic, complemented
100#539×C79C2216yescomplemented
101#538×C79C2216yescomplemented
102#534×C79C2213yescomplemented
103#529×C79C2216yescomplemented
104#525×C79C2216yescomplemented
105C2×C4×D4×C79C2213yescomplemented
106C24×D79C2313yes—
107C24×D79C2311yescharacteristic
108C2×#11929625C2312yescomplemented
109C2×#11929624C2316yescomplemented
110C2×#11929623C2316yescomplemented
111C2×Q8×D79C2312yescomplemented
112C2×Q8×D79C2312yescomplemented
113C22×D316C2313yes—
114C22×C22⋊D79C2313yes—
115C22×C22⋊D79C2313yes—
116C2×D4×D79—224no—
117C2×D4×D79C23112yes—
118C2×D4×D79C23112yes—
119C2×D4×D79C2316yescomplemented
120C2×D4×D79C2316yescomplemented
121C23×Dic79C2311yescharacteristic
122C23×Dic79C2313yescomplemented
123C22×C4×D79C2313yes—
124C22×C4×D79C2313yes—
125C22×C4×D79C2313yes—
126C22×C4×D79C2313yescomplemented
127C22×C4×D79C2313yescomplemented
128#14579156C23112yescomplemented
129#14579156C23112yescomplemented
130#14579156C23112yescomplemented
131#14579155C23112yescomplemented
132#14579154C23112yescomplemented
133#14579154C23112yescomplemented
134#14579154C23112yescomplemented
135#14579153C2316yescomplemented
136#14579152C2316yescomplemented
137#14579152C2316yescomplemented
138#14579151C23112yescomplemented
139#14579151C23112yescomplemented
140#14579150C2316yescomplemented
141#14579149C2316yescomplemented
142#14579148C2316yescomplemented
143#14579147C23112yescomplemented
144#14579147C23112yescomplemented
145#14579146C23112yes—
146#14579146C23112yes—
147#14579146C23112yescomplemented
148#14579146C23112yescomplemented
149#14579145C23112yescomplemented
150#14579145C23112yescomplemented
151#14579144C23112yescomplemented
152#14579144C23112yescomplemented
153#14579143C23112yes—
154#14579143C23112yes—
155#14579143C23112yescomplemented
156#14579143C23112yescomplemented
157#14579142C23112yescomplemented
158#14579142C23112yescomplemented
159#14579141C2316yescomplemented
160#14579141C2316yescomplemented
161#14579141C2316yescomplemented
162#14579140C2316yescomplemented
163#14579140C2316yescomplemented
164#14579140C2316yescomplemented
165#14579139C23112yescomplemented
166#14579139C23112yescomplemented
167#14579139C23112yescomplemented
168#14579138C23112yescomplemented
169#14579138C23112yescomplemented
170#14579138C23112yescomplemented
171#14579137C2316yescomplemented
172#14579137C2316yescomplemented
173#14579137C2316yescomplemented
174#14579136C2316yescomplemented
175#14579136C2316yescomplemented
176#14579136C2316yescomplemented
177#14579135C2316yes—
178#14579135C2316yes—
179#14579135C2316yescomplemented
180#14579134C23112yescomplemented
181#14579134C23112yescomplemented
182#14579134C23112yescomplemented
183#14579133C23112yes—
184#14579133C23112yes—
185#14579133C23112yescomplemented
186#14579132C2316yescomplemented
187#14579132C2316yescomplemented
188#14579132C2316yescomplemented
189#14579131C23112yes—
190#14579131C23112yes—
191#14579131C23112yescomplemented
192#14579130C23112yescomplemented
193#14579129C23112yes—
194#14579129C23112yes—
195#14579129C23112yescomplemented
196Q8×Dic79C2312yescomplemented
197C4×Dic158C2316yescomplemented
198#14579126C2316yescomplemented
199C4×D316C2316yes—
200C4×D316C2316yes—
201C4×D316C2316yescomplemented
202C4×D316C2316yescomplemented
203C4×D316C2316yescomplemented
204D4×Dic79C23112yescomplemented
205D4×Dic79C23112yescomplemented
206D4×Dic79C2316yescomplemented
207#14579123C23112yes—
208#14579123C2316yescomplemented
209#14579123C23112yescomplemented
210C4×C22⋊D79C2316yes—
211C4×C22⋊D79C2316yes—
212C4×C22⋊D79C23112yescomplemented
213C4×C22⋊D79C23112yescomplemented
214C4×C22⋊D79C23112yescomplemented
215C4×C22⋊D79C2316yescomplemented
216C4×C22⋊D79C2316yescomplemented
217(C22⋊D79)⋊C4C23112yes—
218(C22⋊D79)⋊C4C23112yescomplemented
219(C22⋊D79)⋊C4C23112yescomplemented
220(C22⋊D79)⋊C4C23112yescomplemented
221(C22⋊D79)⋊C4C23112yescomplemented
222#14579120C2316yescomplemented
223#14579119C23112yescomplemented
224#14579119C2316yescomplemented
225#14579119C23112yescomplemented
226#14579119C2316yescomplemented
227#14579118C23112yescomplemented
228#14579118C23112yescomplemented
229#14579118C23112yescomplemented
230#14579117C23112yescomplemented
231C2×C4⋊Dic79C2313yescomplemented
232C2×Dic79⋊C4C2313yescomplemented
233C2×Dic79⋊C4C2313yescomplemented
234C4⋊C4×D79C2316yescomplemented
235C4⋊C4×D79C2316yescomplemented
236C4⋊C4×D79C2316yescomplemented
237C4⋊C4×D79C2316yescomplemented
238C2×C22⋊Dic79C2313yes—
239C2×C22⋊Dic79C2313yescomplemented
240C2×(C2×D79)⋊C4C2313yes—
241C2×(C2×D79)⋊C4C2313yes—
242C2×(C2×D79)⋊C4C2313yes—
243C2×(C2×D79)⋊C4C2313yes—
244C2×(C2×D79)⋊C4C2313yes—
245C2×(C2×D79)⋊C4C2313yes—
246C2×(C2×D79)⋊C4C2313yescomplemented
247C2×(C2×D79)⋊C4C2313yescomplemented
248C2×(C2×D79)⋊C4C23112yescomplemented
249C2×(C2×D79)⋊C4C23112yescomplemented
250C22⋊C4×D79C23112yes—
251C22⋊C4×D79C23112yes—
252C22⋊C4×D79C23112yescomplemented
253C22⋊C4×D79C23112yescomplemented
254C22⋊C4×D79C23112yescomplemented
255C22⋊C4×D79C23112yescomplemented
256C2×C4×Dic79C2313yescomplemented
257C2×C4×Dic79C2313yescomplemented
258C2×C4×Dic79C2313yescomplemented
259C2×#41×C79C2312yescomplemented
260C22×D4×C79C2313yes—
261C23×C4×C79C2311yescharacteristic
262C23×C4×C79C2313yescomplemented
263#126×C79C23112yescomplemented
264#125×C79C2316yescomplemented
265#124×C79C2316yescomplemented
266#123×C79C23112yescomplemented
267#123×C79C23112yescomplemented
268C22⋊Q8×C79C2316yescomplemented
269C22⋊Q8×C79C2316yescomplemented
270C22⋊Q8×C79C2316yescomplemented
271#121×C79C2316yes—
272#121×C79C2316yes—
273#121×C79C2316yescomplemented
274#120×C79C23112yescomplemented
275C4×Q8×C79C2312yescomplemented
276C4×D4×C79C23112yescomplemented
277C4×D4×C79C2316yescomplemented
278C4×D4×C79C23112yescomplemented
279#117×C79C2316yescomplemented
280C2×C4⋊C4×C79C2313yescomplemented
281C2×C22⋊C4×C79C2313yes—
282C2×C22⋊C4×C79C2313yescomplemented
283C2×C42×C79C2313yescomplemented
284C23×D79—212no—
285C23×D79—81no—
286C23×D79—81no—
287C23×D79—83no—
288C23×D79—83no—
289C23×D79#4118yescomplemented
290C23×D79C24112yes—
291C23×D79C2413yes—
292C23×D79C2413yes—
293C23×D79C2413yes—
294#11929625—82no—
295#11929624—86no—
296#11929623—86no—
297C2×Dic158C2416yes—
298C2×Dic158C2416yes—
299Q8×D79—82no—
300Q8×D79—82no—
301C2×D316—212no—
302C2×D316C2416yes—
303C2×D316C2416yes—
304C2×D316C2416yes—
305C2×D316C2416yes—
306C2×C22⋊D79—212no—
307C2×C22⋊D79—212no—
308C2×C22⋊D79C2416yes—
309C2×C22⋊D79C24112yes—
310C2×C22⋊D79C2416yes—
311C2×C22⋊D79C24112yes—
312C2×C22⋊D79C24112yes—
313D4×D79—248no—
314D4×D79—248no—
315D4×D79—86no—
316D4×D79—86no—
317C22×Dic79—81no—
318C22×Dic79—83no—
319C22×Dic79C2413yes—
320C22×Dic79C24112yes—
321C22×Dic79C2413yes—
322C22×Dic79C2413yes—
323C22×Dic79C2413yes—
324C22×Dic79C2413yes—
325C2×C4×D79—212no—
326C2×C4×D79—83no—
327C2×C4×D79—83no—
328C2×C4×D79—83no—
329C2×C4×D79—83no—
330C2×C4×D79C24112yes—
331C2×C4×D79C2416yes—
332C2×C4×D79C2416yes—
333C2×C4×D79C2416yes—
334C2×C4×D79C24112yes—
335C2×C4×D79C2416yes—
336C2×C4×D79C2416yes—
337C2×C4×D79C2416yes—
338C4⋊Dic79C2416yes—
339C4⋊Dic79C2416yes—
340C4⋊Dic79C2416yes—
341C4⋊Dic79C2416yes—
342C4⋊Dic79C2416yes—
343C4⋊Dic79C2416yes—
344Dic79⋊C4C24112yes—
345Dic79⋊C4C24112yes—
346Dic79⋊C4C24112yes—
347Dic79⋊C4C24112yes—
348Dic79⋊C4C24112yes—
349Dic79⋊C4C2416yes—
350Dic79⋊C4C2416yes—
351C22⋊Dic79C24112yes—
352C22⋊Dic79C2416yes—
353C22⋊Dic79C2416yes—
354C22⋊Dic79C24112yes—
355C22⋊Dic79C24112yes—
356(C2×D79)⋊C4C24112yes—
357(C2×D79)⋊C4C24112yes—
358(C2×D79)⋊C4C2413yes—
359(C2×D79)⋊C4C2416yes—
360(C2×D79)⋊C4C24112yes—
361(C2×D79)⋊C4C24112yes—
362(C2×D79)⋊C4C24112yes—
363(C2×D79)⋊C4C24112yes—
364(C2×D79)⋊C4C2413yes—
365(C2×D79)⋊C4C2413yes—
366(C2×D79)⋊C4C2411yescharacteristic
367(C2×D79)⋊C4C24112yes—
368(C2×D79)⋊C4C2416yes—
369(C2×D79)⋊C4C2416yes—
370C4×Dic79C2416yes—
371C4×Dic79C24112yes—
372C4×Dic79C24112yes—
373C4×Dic79C2416yes—
374C24×C79C2413yes—
375C24×C79C2411yescharacteristic
376#41×C79—82no—
377C2×Q8×C79C2412yes—
378C2×Q8×C79C2412yes—
379C2×D4×C79—212no—
380C2×D4×C79C24112yes—
381C2×D4×C79C2416yes—
382C2×D4×C79C2416yes—
383C22×C4×C79—81no—
384C22×C4×C79—83no—
385C22×C4×C79C2413yes—
386C22×C4×C79C2416yes—
387C22×C4×C79C2413yes—
388C22×C4×C79C2413yes—
389C22×C4×C79C2413yes—
390C22×C4×C79C2413yes—
391C22×C4×C79C2416yes—
392C4⋊C4×C79C24112yes—
393C4⋊C4×C79C2416yes—
394C4⋊C4×C79C2416yes—
395C4⋊C4×C79C2416yes—
396C4⋊C4×C79C2416yes—
397C22⋊C4×C79C24112yes—
398C22⋊C4×C79C24112yes—
399C22⋊C4×C79C24112yes—
400C22⋊C4×C79C24112yes—
401C42×C79C2416yes—
402C42×C79C2416yes—
403C23×C79—26no—
404C23×C79—41no—
405C23×C79—43no—
406C23×C79—41no—
407C23×C79—43no—
408C23×C79C2×#4114yes—
409C23×C79C2516yes—
410C23×C79C2513yes—
411C22×D79—26no—
412C22×D79—224no—
413C22×D79—43no—
414C22×D79—43no—
415C22×D79—43no—
416C22×D79—43no—
417C22×D79—43no—
418C22×D79—43no—
419C22×D79—412no—
420C22×D79—412no—
421C22×D79—88no—
422C22×D79—824no—
423C22×D79C2×#41112yes—
424C22×D79C2×#41112yes—
425C22×D79C2516yes—
426C22×D79C2513yes—
427C22×D79C2511yescharacteristic
428Q8×C79—42no—
429Q8×C79—42no—
430D4×C79—224no—
431D4×C79—46no—
432D4×C79—46no—
433C2×C4×C79—26no—
434C2×C4×C79—43no—
435C2×C4×C79—43no—
436C2×C4×C79—43no—
437C2×C4×C79—46no—
438C2×C4×C79—43no—
439C2×C4×C79—46no—
440C2×C4×C79C2513yes—
441C2×C4×C79C2516yes—
442C2×C4×C79C2516yes—
443C2×C4×C79C2511yescharacteristic
444C2×C4×C79C2516yes—
445C22⋊D79—224no—
446C22⋊D79—212no—
447C22⋊D79—212no—
448C22⋊D79—412no—
449C22⋊D79—412no—
450C2×Dic79—26no—
451C2×Dic79—43no—
452C2×Dic79—43no—
453C2×Dic79—43no—
454C2×Dic79—43no—
455C2×Dic79—412no—
456C2×Dic79C2513yes—
457C2×Dic79C2511yescharacteristic
458C2×Dic79C2516yes—
459C2×Dic79C2516yes—
460C2×Dic79C2516yes—
461D316—212no—
462D316—212no—
463D316—46no—
464D316—46no—
465C4×D79—224no—
466C4×D79—46no—
467C4×D79—46no—
468C4×D79—46no—
469C4×D79—46no—
470C4×D79—46no—
471C4×D79—412no—
472C4×D79—46no—
473Dic158—46no—
474Dic158—46no—
475C22×C79—23no—
476C22×C79—23no—
477C22×C79—26no—
478C22×C79—26no—
479C22×C79—26no—
480C22×C79—44no—
481C22×C79—412no—
482C22×C79C22×#4116yes—
483C22×C79C2611yescharacteristic
484C2×D79—23no—
485C2×D79—23no—
486C2×D79—21no—
487C2×D79—21no—
488C2×D79—26no—
489C2×D79—26no—
490C2×D79—26no—
491C2×D79—412no—
492C2×D79—412no—
493C2×D79—412no—
494C2×D79—824no—
495C2×D79C22×#4112yes—
496C2×D79C22×#4116yes—
497C4×C79—26no—
498C4×C79—21no—
499C4×C79—23no—
500C4×C79—26no—
501C4×C79—26no—
502Dic79—26no—
503Dic79—26no—
504Dic79—26no—
505Dic79—21no—
506Dic79—23no—
507#62844—791nomaximal, Sylow
508C2×C79—26no—
509C2×C79—46no—
510C2×C79C23×#4111yescharacteristic
511C2×C79H(7,𝔽2)11yescharacteristic
512C2×C79H(7,𝔽2)11yescharacteristic
513D79—26no—
514D79—22no—
515D79—46no—
516#3505—796no—
517#3505—796no—
518#3505—796no—
519#3505—796no—
520#3491—796no—
521#3491—796no—
522#3490—796no—
523#3490—796no—
524#3459—791no—
525#3459—793no—
526#3459—793no—
527#3459D7911yescharacteristic, complemented
528C2×#543—791no—
529C2×#534—793no—
530C2×#518—793no—
531C79#6284411yescharacteristic, complemented, Sylow
532C23×D4—793no—
533#553—7912no—
534#553—796no—
535#553—7912no—
536#553—796no—
537#553—796no—
538#553—796no—
539#552—7912no—
540#552—7912no—
541#552—796no—
542#552—796no—
543#552—796no—
544#552—796no—
545#551—7912no—
546#551—7912no—
547#551—7912no—
548#551—7912no—
549#551—7912no—
550#551—7912no—
551#551—7912no—
552#551—7912no—
553#548—792no—
554#548—796no—
555#548—796no—
556#548—792no—
557#546—796no—
558#546—796no—
559#546—7912no—
560#546—7912no—
561#546—796no—
562#546—796no—
563#543—796no—
564#543—796no—
565#543—793no—
566#543C2×D7911yescharacteristic, complemented
567#539—7912no—
568#539—796no—
569#539—796no—
570#539—7912no—
571#539—796no—
572#539C2×D7916yescomplemented
573#538—796no—
574#538—796no—
575#538—7912no—
576#538—7912no—
577#538—796no—
578#538C2×D7916yescomplemented
579#534—796no—
580#534—7912no—
581#534—796no—
582#534—796no—
583#534—7912no—
584#534—793no—
585#534C2×D7913yescomplemented
586#529—7912no—
587#529—796no—
588#529—796no—
589#529—7912no—
590#529—796no—
591#529C2×D7916yescomplemented
592#525—796no—
593#525—796no—
594#525—796no—
595#525—7912no—
596#525—7912no—
597#525C2×D7916yescomplemented
598C2×#123—7912no—
599C2×C22⋊Q8—796no—
600C2×C22⋊Q8—796no—
601C2×#121—796no—
602C2×#121—796no—
603C2×#120—7912no—
604#518—7912no—
605#518—7912no—
606#518—7912no—
607#518—7912no—
608C2×C4×D4—793no—
609C2×C4×D4—793no—
610C2×C4×D4—793no—
611C2×C4×D4—793no—
612C2×C4×D4—793no—
613C2×C4×D4—793no—
614C2×C4×D4—793no—
615C2×C4×D4C2×D7913yescomplemented
616C2×#117—793no—
617C2×#117—793no—
618C22×C22⋊C4—791no—
619C22×C22⋊C4—793no—
620C22×C22⋊C4—793no—
621C22×C22⋊C4—793no—
622C25—791no—
623C25—793no—
624C2×#41—792no—
625C2×#41—796no—
626C2×#41—796no—
627C2×#41C22×D7912yescomplemented
628C22×Q8—792no—
629C22×Q8—792no—
630C22×D4—793no—
631C22×D4—793no—
632C22×D4—796no—
633C22×D4—796no—
634C22×D4—7912no—
635C22×D4—7912no—
636C22×D4—793no—
637C22×D4—15824no—
638C22×D4C22×D7913yes—
639C23×C4—791no—
640C23×C4—793no—
641C23×C4—793no—
642C23×C4—793no—
643C23×C4—793no—
644C23×C4—793no—
645C23×C4—793no—
646C23×C4C22×D7911yescharacteristic
647C23×C4C22×D7913yescomplemented
648#126—7912no—
649#126—7912no—
650#126—7912no—
651#126—7912no—
652#126—7912no—
653#126—7912no—
654#126—7912no—
655#126C22×D79112yescomplemented
656#125—7912no—
657#125—7912no—
658#125—796no—
659#125—796no—
660#125—796no—
661#125C22×D7916yescomplemented
662#124—796no—
663#124—796no—
664#124—7912no—
665#124—7912no—
666#124—796no—
667#124C22×D7916yescomplemented
668#123—7912no—
669#123—7912no—
670#123—7912no—
671#123—7912no—
672#123—7912no—
673#123—7912no—
674#123—7912no—
675#123—7912no—
676#123—7912no—
677#123—7912no—
678#123—7912no—
679#123—7912no—
680#123—7912no—
681#123—7912no—
682#123C22×D79112yescomplemented
683#123C22×D79112yescomplemented
684C22⋊Q8—796no—
685C22⋊Q8—796no—
686C22⋊Q8—796no—
687C22⋊Q8—796no—
688C22⋊Q8—796no—
689C22⋊Q8—796no—
690C22⋊Q8—7912no—
691C22⋊Q8—7912no—
692C22⋊Q8—796no—
693C22⋊Q8—796no—
694C22⋊Q8—7912no—
695C22⋊Q8—796no—
696C22⋊Q8—7912no—
697C22⋊Q8—7912no—
698C22⋊Q8—7912no—
699C22⋊Q8C22×D7916yescomplemented
700C22⋊Q8C22×D7916yescomplemented
701C22⋊Q8C22×D7916yescomplemented
702#121—7912no—
703#121—7912no—
704#121—796no—
705#121—796no—
706#121—796no—
707#121—7912no—
708#121—796no—
709#121—796no—
710#121—796no—
711#121—796no—
712#121—796no—
713#121—796no—
714#121—7912no—
715#121—7912no—
716#121—7912no—
717#121C22×D7916yes—
718#121C22×D7916yes—
719#121C22×D7916yescomplemented
720#120—7912no—
721#120—7912no—
722#120—7912no—
723#120—7912no—
724#120—7912no—
725#120—7912no—
726#120—7912no—
727#120C22×D79112yescomplemented
728C4×Q8—792no—
729C4×Q8—796no—
730C4×Q8—796no—
731C4×Q8C22×D7912yescomplemented
732C4×D4—7912no—
733C4×D4—7912no—
734C4×D4—796no—
735C4×D4—7912no—
736C4×D4—7912no—
737C4×D4—796no—
738C4×D4—796no—
739C4×D4—796no—
740C4×D4—796no—
741C4×D4—7912no—
742C4×D4—7912no—
743C4×D4—7912no—
744C4×D4—796no—
745C4×D4—7912no—
746C4×D4—7912no—
747C4×D4—7912no—
748C4×D4—7912no—
749C4×D4—7912no—
750C4×D4—796no—
751C4×D4—796no—
752C4×D4—796no—
753C4×D4—796no—
754C4×D4—796no—
755C4×D4C22×D79112yescomplemented
756C4×D4C22×D79112yescomplemented
757C4×D4C22×D7916yescomplemented
758#117—796no—
759#117—7912no—
760#117—7912no—
761#117—796no—
762#117—796no—
763#117—7912no—
764#117—7912no—
765#117—7912no—
766#117—7912no—
767#117C22×D7916yescomplemented
768C2×C4⋊C4—793no—
769C2×C4⋊C4—793no—
770C2×C4⋊C4—793no—
771C2×C4⋊C4—796no—
772C2×C4⋊C4—796no—
773C2×C4⋊C4—796no—
774C2×C4⋊C4—796no—
775C2×C4⋊C4C22×D7913yescomplemented
776C2×C22⋊C4—793no—
777C2×C22⋊C4—793no—
778C2×C22⋊C4—793no—
779C2×C22⋊C4—793no—
780C2×C22⋊C4—793no—
781C2×C22⋊C4—793no—
782C2×C22⋊C4—793no—
783C2×C22⋊C4—793no—
784C2×C22⋊C4—793no—
785C2×C22⋊C4—793no—
786C2×C22⋊C4—7912no—
787C2×C22⋊C4—7912no—
788C2×C22⋊C4—7912no—
789C2×C22⋊C4—7912no—
790C2×C22⋊C4—7912no—
791C2×C22⋊C4—7912no—
792C2×C22⋊C4—7912no—
793C2×C22⋊C4—7912no—
794C2×C22⋊C4C22×D7913yes—
795C2×C22⋊C4C22×D7913yescomplemented
796C2×C42—793no—
797C2×C42—793no—
798C2×C42—793no—
799C2×C42C22×D7913yescomplemented
800C24—793no—
801C24—793no—
802C24—7912no—
803C24—793no—
804C24—798no—
805C24—6321no—
806C24—6323no—
807C24—6321no—
808C24—6323no—
809C24—15812no—
810C24C23×D7913yes—
811C24C23×D7911yescharacteristic
812#41—82no—
813#41—6326no—
814#41—6326no—
815#41—6322no—
816C2×Q8—796no—
817C2×Q8—796no—
818C2×Q8—6322no—
819C2×Q8—6322no—
820C2×Q8C23×D7912yes—
821C2×Q8C23×D7912yes—
822C2×D4—212no—
823C2×D4—7912no—
824C2×D4—7912no—
825C2×D4—796no—
826C2×D4—7912no—
827C2×D4—796no—
828C2×D4—796no—
829C2×D4—796no—
830C2×D4—796no—
831C2×D4—796no—
832C2×D4—6326no—
833C2×D4—6326no—
834C2×D4—15812no—
835C2×D4—15848no—
836C2×D4—15848no—
837C2×D4—15812no—
838C2×D4—15812no—
839C2×D4C23×D79112yes—
840C2×D4C23×D7916yes—
841C2×D4C23×D7916yes—
842C22×C4—81no—
843C22×C4—83no—
844C22×C4—793no—
845C22×C4—793no—
846C22×C4—793no—
847C22×C4—793no—
848C22×C4—7912no—
849C22×C4—796no—
850C22×C4—796no—
851C22×C4—796no—
852C22×C4—796no—
853C22×C4—796no—
854C22×C4—796no—
855C22×C4—7912no—
856C22×C4—793no—
857C22×C4—7912no—
858C22×C4—6323no—
859C22×C4—6323no—
860C22×C4—6323no—
861C22×C4—6323no—
862C22×C4—6321no—
863C22×C4—6323no—
864C22×C4—15812no—
865C22×C4C23×D7913yes—
866C22×C4C23×D7913yes—
867C22×C4C23×D7913yes—
868C22×C4C23×D7913yes—
869C22×C4C23×D7913yes—
870C22×C4C23×D7916yes—
871C22×C4C23×D7916yes—
872C4⋊C4—7912no—
873C4⋊C4—796no—
874C4⋊C4—796no—
875C4⋊C4—7912no—
876C4⋊C4—7912no—
877C4⋊C4—7912no—
878C4⋊C4—7912no—
879C4⋊C4—796no—
880C4⋊C4—796no—
881C4⋊C4—796no—
882C4⋊C4—796no—
883C4⋊C4—796no—
884C4⋊C4—796no—
885C4⋊C4C23×D7916yes—
886C4⋊C4C23×D7916yes—
887C4⋊C4C23×D7916yes—
888C4⋊C4C23×D7916yes—
889C4⋊C4C23×D79112yes—
890C22⋊C4—7912no—
891C22⋊C4—796no—
892C22⋊C4—796no—
893C22⋊C4—7912no—
894C22⋊C4—7912no—
895C22⋊C4—793no—
896C22⋊C4—796no—
897C22⋊C4—793no—
898C22⋊C4—7912no—
899C22⋊C4—7912no—
900C22⋊C4—793no—
901C22⋊C4—791no—
902C22⋊C4—7912no—
903C22⋊C4—796no—
904C22⋊C4—796no—
905C22⋊C4—7912no—
906C22⋊C4—7912no—
907C22⋊C4—7912no—
908C22⋊C4—7912no—
909C22⋊C4C23×D79112yes—
910C22⋊C4C23×D79112yes—
911C22⋊C4C23×D79112yes—
912C22⋊C4C23×D79112yes—
913C42—796no—
914C42—796no—
915C42—7912no—
916C42—7912no—
917C42C23×D7916yes—
918C42C23×D7916yes—
919C23—26no—
920C23—41no—
921C23—43no—
922C23—41no—
923C23—43no—
924C23—3163no—
925C23—3163no—
926C23—3163no—
927C23—3163no—
928C23—3163no—
929C23—3163no—
930C23—31612no—
931C23—31612no—
932C23—7912no—
933C23—7912no—
934C23—793no—
935C23—791no—
936C23—796no—
937C23—6328no—
938C23—63224no—
939C23—15824no—
940C23—1586no—
941C23#41×D7914yes—
942C23C24×D7916yes—
943C23C24×D7913yes—
944Q8—42no—
945Q8—42no—
946Q8—3166no—
947Q8—3166no—
948D4—224no—
949D4—46no—
950D4—46no—
951D4—3166no—
952D4—3166no—
953D4—31612no—
954D4—31612no—
955D4—15812no—
956D4—15812no—
957D4—15812no—
958D4—15812no—
959D4—15824no—
960C2×C4—26no—
961C2×C4—43no—
962C2×C4—43no—
963C2×C4—43no—
964C2×C4—46no—
965C2×C4—46no—
966C2×C4—43no—
967C2×C4—3166no—
968C2×C4—3166no—
969C2×C4—3166no—
970C2×C4—3166no—
971C2×C4—31612no—
972C2×C4—3166no—
973C2×C4—3166no—
974C2×C4—3163no—
975C2×C4—3163no—
976C2×C4—3163no—
977C2×C4—3163no—
978C2×C4—31612no—
979C2×C4—791no—
980C2×C4—793no—
981C2×C4—796no—
982C2×C4—796no—
983C2×C4—796no—
984C2×C4—15824no—
985C2×C4—1586no—
986C2×C4C24×D7913yes—
987C2×C4C24×D7916yes—
988C2×C4C24×D7916yes—
989C2×C4C24×D7911yescharacteristic
990C2×C4C24×D7916yes—
991C22—23no—
992C22—23no—
993C22—26no—
994C22—26no—
995C22—26no—
996C22—44no—
997C22—412no—
998C22—31612no—
999C22—31612no—
1000C22—31612no—
1001C22—796no—
1002C22—792no—
1003C22—63224no—
1004C22—1586no—
1005C22—1586no—
1006C22—1586no—
1007C22—1581no—
1008C22—1583no—
1009C22—1581no—
1010C22—1583no—
1011C22C2×#41×D7916yes—
1012C22C25×D7911yescharacteristic
1013C4—26no—
1014C4—21no—
1015C4—23no—
1016C4—26no—
1017C4—26no—
1018C4—1586no—
1019C4—1586no—
1020C4—1581no—
1021C4—1583no—
1022C4—1586no—
1023C2—26no—
1024C2—46no—
1025C2—3166no—
1026C2—1586no—
1027C2—1582no—
1028C2C22×#41×D7911yescharacteristic
1029C2#2377821011yescharacteristic
1030C2#2377821111yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3459C2
hypercenter#3459D79
hypocenterC79#62844
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3459

Complements

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

NH ≅ G/Ntype
1. #23777238C2semidirect
2. #23777235C2semidirect
3. #23777232C2semidirect
4. #23777228C2semidirect
5. #23777094C2semidirect
6. #23777092C2semidirect
7. #23777086C2semidirect
8. #23777083C2semidirect
9. #23776812C2semidirect
10. #23776809C2semidirect
11. #23776806C2semidirect
12. #543×D79C2semidirect
13. #534×D79C2semidirect
14. C2×#19099035C2semidirect
15. C79×#3459C2semidirect
17. #19099266C22semidirect
18. #19099264C22semidirect
19. #19099263C22semidirect
20. #19099260C22semidirect
21. #19099258C22semidirect
22. #19099257C22semidirect
23. #19099254C22semidirect
24. #19099252C22semidirect
25. #19099251C22semidirect
26. #19099249C22semidirect
27. #19099247C22semidirect
28. #19099245C22semidirect
29. #19099243C22semidirect
30. #19099242C22semidirect
31. #19099241C22semidirect
32. #19099240C22semidirect
33. #19099238C22semidirect
34. #19099238C22semidirect
35. #19099237C22semidirect
36. #19099236C22semidirect
37. #19099225C22semidirect
38. #19099223C22semidirect
39. #19099221C22semidirect
40. #19099220C22semidirect
41. #19099210C22semidirect
42. #19099208C22semidirect
43. #19099206C22semidirect
44. #19099205C22semidirect
45. #19099202C22semidirect
46. #19099201C22semidirect
47. #19099189C22semidirect
48. #19099188C22semidirect
49. #19099188C22semidirect
50. #19099162C22semidirect
51. #19099160C22semidirect
52. #19099158C22semidirect
53. #19099157C22semidirect
54. #19099155C22semidirect
55. #19099153C22semidirect
56. #19099151C22semidirect
57. #19099150C22semidirect
58. #19099148C22semidirect
59. #19099146C22semidirect
60. #19099125C22semidirect
61. #19099124C22semidirect
62. #19099123C22semidirect
63. #19099122C22semidirect
66. #19099099C22semidirect
67. #19099097C22semidirect
68. #19099094C22semidirect
69. #19099093C22semidirect
70. #19099090C22semidirect
71. #19099076C22semidirect
72. #19099074C22semidirect
73. #19099073C22semidirect
74. #19099072C22semidirect
75. #19099069C22semidirect
76. #123×D79C22semidirect
77. C22⋊Q8×D79C22semidirect
78. C22⋊Q8×D79C22semidirect
79. #121×D79C22semidirect
80. #121×D79C22semidirect
81. #120×D79C22semidirect
82. #19099035C22semidirect
83. #19099035C22semidirect
84. #19099035C22semidirect
85. #19099035C22semidirect
86. C2×C4×D316C22semidirect
87. C2×D4×Dic79C22semidirect
88. C2×#14579123C22semidirect
89. C2×C4×C22⋊D79C22semidirect
90. C2×C4×C22⋊D79C22semidirect
91. C2×(C22⋊D79)⋊C4C22semidirect
92. C2×(C22⋊D79)⋊C4C22semidirect
93. C2×#14579119C22semidirect
94. C2×#14579118C22semidirect
96. C22×(C2×D79)⋊C4C22semidirect
98. C2×C22⋊C4×D79C22semidirect
99. #543×C79C22semidirect
100. #539×C79C22semidirect
101. #538×C79C22semidirect
102. #534×C79C22semidirect
103. #529×C79C22semidirect
104. #525×C79C22semidirect
105. C2×C4×D4×C79C22semidirect
108. C2×#11929625C23semidirect
109. C2×#11929624C23semidirect
110. C2×#11929623C23semidirect
111. C2×Q8×D79C23semidirect
112. C2×Q8×D79C23semidirect
119. C2×D4×D79C23semidirect
120. C2×D4×D79C23semidirect
122. C23×Dic79C23semidirect
126. C22×C4×D79C23semidirect
127. C22×C4×D79C23semidirect
128. #14579156C23semidirect
129. #14579156C23semidirect
130. #14579156C23semidirect
131. #14579155C23semidirect
132. #14579154C23semidirect
133. #14579154C23semidirect
134. #14579154C23semidirect
135. #14579153C23semidirect
136. #14579152C23semidirect
137. #14579152C23semidirect
138. #14579151C23semidirect
139. #14579151C23semidirect
140. #14579150C23semidirect
141. #14579149C23semidirect
142. #14579148C23semidirect
143. #14579147C23semidirect
144. #14579147C23semidirect
147. #14579146C23semidirect
148. #14579146C23semidirect
149. #14579145C23semidirect
150. #14579145C23semidirect
151. #14579144C23semidirect
152. #14579144C23semidirect
155. #14579143C23semidirect
156. #14579143C23semidirect
157. #14579142C23semidirect
158. #14579142C23semidirect
159. #14579141C23semidirect
160. #14579141C23semidirect
161. #14579141C23semidirect
162. #14579140C23semidirect
163. #14579140C23semidirect
164. #14579140C23semidirect
165. #14579139C23semidirect
166. #14579139C23semidirect
167. #14579139C23semidirect
168. #14579138C23semidirect
169. #14579138C23semidirect
170. #14579138C23semidirect
171. #14579137C23semidirect
172. #14579137C23semidirect
173. #14579137C23semidirect
174. #14579136C23semidirect
175. #14579136C23semidirect
176. #14579136C23semidirect
179. #14579135C23semidirect
180. #14579134C23semidirect
181. #14579134C23semidirect
182. #14579134C23semidirect
185. #14579133C23semidirect
186. #14579132C23semidirect
187. #14579132C23semidirect
188. #14579132C23semidirect
191. #14579131C23semidirect
192. #14579130C23semidirect
195. #14579129C23semidirect
196. Q8×Dic79C23semidirect
197. C4×Dic158C23semidirect
198. #14579126C23semidirect
201. C4×D316C23semidirect
202. C4×D316C23semidirect
203. C4×D316C23semidirect
204. D4×Dic79C23semidirect
205. D4×Dic79C23semidirect
206. D4×Dic79C23semidirect
208. #14579123C23semidirect
209. #14579123C23semidirect
212. C4×C22⋊D79C23semidirect
213. C4×C22⋊D79C23semidirect
214. C4×C22⋊D79C23semidirect
215. C4×C22⋊D79C23semidirect
216. C4×C22⋊D79C23semidirect
218. (C22⋊D79)⋊C4C23semidirect
219. (C22⋊D79)⋊C4C23semidirect
220. (C22⋊D79)⋊C4C23semidirect
221. (C22⋊D79)⋊C4C23semidirect
222. #14579120C23semidirect
223. #14579119C23semidirect
224. #14579119C23semidirect
225. #14579119C23semidirect
226. #14579119C23semidirect
227. #14579118C23semidirect
228. #14579118C23semidirect
229. #14579118C23semidirect
230. #14579117C23semidirect
231. C2×C4⋊Dic79C23semidirect
232. C2×Dic79⋊C4C23semidirect
233. C2×Dic79⋊C4C23semidirect
234. C4⋊C4×D79C23semidirect
235. C4⋊C4×D79C23semidirect
236. C4⋊C4×D79C23semidirect
237. C4⋊C4×D79C23semidirect
239. C2×C22⋊Dic79C23semidirect
246. C2×(C2×D79)⋊C4C23semidirect
247. C2×(C2×D79)⋊C4C23semidirect
248. C2×(C2×D79)⋊C4C23semidirect
249. C2×(C2×D79)⋊C4C23semidirect
252. C22⋊C4×D79C23semidirect
253. C22⋊C4×D79C23semidirect
254. C22⋊C4×D79C23semidirect
255. C22⋊C4×D79C23semidirect
256. C2×C4×Dic79C23semidirect
257. C2×C4×Dic79C23semidirect
258. C2×C4×Dic79C23semidirect
259. C2×#41×C79C23semidirect
262. C23×C4×C79C23semidirect
263. #126×C79C23semidirect
264. #125×C79C23semidirect
265. #124×C79C23semidirect
266. #123×C79C23semidirect
267. #123×C79C23semidirect
268. C22⋊Q8×C79C23semidirect
269. C22⋊Q8×C79C23semidirect
270. C22⋊Q8×C79C23semidirect
273. #121×C79C23semidirect
274. #120×C79C23semidirect
275. C4×Q8×C79C23semidirect
276. C4×D4×C79C23semidirect
277. C4×D4×C79C23semidirect
278. C4×D4×C79C23semidirect
279. #117×C79C23semidirect
280. C2×C4⋊C4×C79C23semidirect
282. C2×C22⋊C4×C79C23semidirect
283. C2×C42×C79C23semidirect
289. C23×D79#41semidirect
527. #3459D79semidirect
531. C79#62844semidirect
566. #543C2×D79semidirect
572. #539C2×D79semidirect
578. #538C2×D79semidirect
585. #534C2×D79semidirect
591. #529C2×D79semidirect
597. #525C2×D79semidirect
615. C2×C4×D4C2×D79semidirect
627. C2×#41C22×D79semidirect
647. C23×C4C22×D79semidirect
655. #126C22×D79semidirect
661. #125C22×D79semidirect
667. #124C22×D79semidirect
682. #123C22×D79semidirect
683. #123C22×D79semidirect
699. C22⋊Q8C22×D79semidirect
700. C22⋊Q8C22×D79semidirect
701. C22⋊Q8C22×D79semidirect
719. #121C22×D79semidirect
727. #120C22×D79semidirect
731. C4×Q8C22×D79semidirect
755. C4×D4C22×D79semidirect
756. C4×D4C22×D79semidirect
757. C4×D4C22×D79semidirect
767. #117C22×D79semidirect
775. C2×C4⋊C4C22×D79semidirect
795. C2×C22⋊C4C22×D79semidirect
799. C2×C42C22×D79semidirect

Maximal subgroups

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

subgroupindex
#237772382
#237772352
#237772322
#237772282
#237770942
#237770922
#237770862
#237770832
#237768122
#237768092
#237768062
#543×D792
#534×D792
C2×#190990352
C79×#34592
#6284479