Finite Group Databasebeta

← #35197347

Subgroups — #35197347

Order 20224.

6846 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#23777510C214yesmaximal, complemented
2#23777502C214yesmaximal, complemented
3#23777491C214yesmaximal, complemented
4#23777487C214yesmaximal, complemented
5#23777412C214yesmaximal, complemented
6#23777408C214yesmaximal, complemented
7#23777394C214yesmaximal, complemented
8#23777386C214yesmaximal, complemented
9#23777264C216yesmaximal, complemented
10#23777206C211yesmaximal, characteristic, complemented
11#23777167C211yesmaximal, characteristic, complemented
12#23777117C216yesmaximal, complemented
13#23777051C211yesmaximal, characteristic, complemented
14#23776824C216yesmaximal, complemented
15#23776788C216yesmaximal, complemented
162−1+4×Dic79C211yesmaximal, characteristic, complemented
17#23776609C211yesmaximal, characteristic, complemented
18C2×#19099041C211yesmaximal, characteristic, complemented
19C79×#3486C211yesmaximal, characteristic, complemented
20C2×#14579209C2211yescharacteristic
21#19099295C22112yescomplemented
22Q8×Dic158C2214yescomplemented
23#19099292C2214yescomplemented
24#19099289C2214yescomplemented
25#19099289C2214yescomplemented
26#19099288C22112yescomplemented
27#19099287C22112yescomplemented
28#19099284C22112yes—
29#19099284C22112yescomplemented
30#19099283C22112yes—
31#19099282C22112yescomplemented
32#19099278C22112yes—
33#19099277C22112yes—
34#19099271C22112yescomplemented
35#19099260C22112yes—
36#19099259C22112yes—
37#19099255C22112yescomplemented
38#19099253C22112yes—
39#19099247C22112yes—
40#19099247C22112yescomplemented
41#19099232C2214yescomplemented
42Q8×C22⋊D79C2214yes—
43Q8×C22⋊D79C2214yes—
44Q8×C22⋊D79C2214yescomplemented
45#19099224C2214yes—
46#19099224C2214yes—
47#19099224C2214yescomplemented
48#19099220C2214yescomplemented
49#19099191C2216yes—
50#19099186C2216yes—
51#19099186C2216yes—
52#19099186C22112yescomplemented
53#19099182C22112yescomplemented
54#19099180C2216yes—
55#19099180C2216yes—
56#19099174C22112yescomplemented
57#19099173C2216yes—
58#19099173C2216yes—
59#19099173C22112yescomplemented
60#19099166C2216yes—
61#19099166C2216yes—
62#19099157C22112yes—
63#19099157C22112yes—
64#19099148C2214yes—
65#19099148C22112yes—
66#19099141C2216yes—
67#19099137C2216yes—
68#19099118C22112yescomplemented
69#19099116C2216yes—
70#19099115C22112yescomplemented
71#19099109C2216yes—
72#19099099C22112yescomplemented
73#19099095C22112yes—
74#19099095C22112yes—
75#19099093C22112yes—
76#19099093C22112yes—
77#19099092C22112yescomplemented
78#19099090C22124yes—
79#19099074C2216yes—
80#19099046C2216yes—
81#19099046C2214yescomplemented
82#19099045C2214yescomplemented
83#19099043C2216yes—
84#19099041C2211yescharacteristic
85#19099041C2214yes—
86#19099041C2214yes—
87#19099041C2214yes—
88#19099041C2214yes—
89#19099041C2214yescomplemented
90#19099039C2214yescomplemented
91#41×Dic79C2216yes—
92#41×Dic79C2214yescomplemented
93C4×#11929625C2214yescomplemented
94#19099031C2216yes—
95C2×Q8×Dic79C2213yes—
96C2×Q8×Dic79C2211yescharacteristic
97C2×Q8×Dic79C2211yescharacteristic
98C2×Q8×Dic79C2213yes—
99C2×Q8×Dic79C2214yescomplemented
100C4×Q8×D79C2214yescomplemented
101C2×#14579120C2213yes—
102C2×#14579120C2213yes—
103C2×2−1+4×C79C2211yescharacteristic
104C23×Q8×C79C2211yescharacteristic
105D4×Q8×C79C2214yes—
106D4×Q8×C79C2214yes—
107#548×C79C2214yes—
108#548×C79C2214yes—
109#536×C79C2216yes—
110#525×C79C2216yes—
111#519×C79C2211yescharacteristic
112#14579209—28no—
113C2×#11929625C2314yes—
114C2×#11929624C2316yes—
115C2×Q8×D79C2314yes—
116#14579161C23112yes—
117#14579160C2316yes—
118#14579160C2316yes—
119#14579160C23112yes—
120#14579159C23112yes—
121#14579159C2316yes—
122#14579157C2316yes—
123#14579156C23112yes—
124#14579156C23112yes—
125#14579156C23124yes—
126#14579154C2314yes—
127#14579154C2314yes—
128#14579154C23112yes—
129#14579154C23112yes—
130#14579154C23112yes—
131#14579154C23112yes—
132#14579154C23124yes—
133#14579153C23112yes—
134#14579152C23112yes—
135#14579152C23112yes—
136#14579152C2316yes—
137#14579152C2316yes—
138#14579152C23112yes—
139#14579151C23112yes—
140#14579151C23112yes—
141#14579151C23124yes—
142#14579150C23112yes—
143#14579150C2316yes—
144#14579148C2314yes—
145#14579148C23112yes—
146#14579148C2316yes—
147#14579147C2314yes—
148#14579147C23112yes—
149#14579147C23124yes—
150#14579145C23112yes—
151#14579145C23112yes—
152#14579144C23112yes—
153#14579143C2314yes—
154#14579143C23112yes—
155#14579143C23112yes—
156#14579143C23112yes—
157#14579142C2314yes—
158#14579142C23112yes—
159#14579141C23112yes—
160#14579141C23112yes—
161#14579140C23112yes—
162#14579140C2316yes—
163#14579140C2316yes—
164#14579138C2314yes—
165#14579138C23112yes—
166#14579138C23112yes—
167#14579138C23112yes—
168#14579137C23112yes—
169#14579137C23112yes—
170#14579137C23112yes—
171#14579135C23112yes—
172#14579135C2316yes—
173#14579135C2316yes—
174#14579133C23112yes—
175#14579133C2314yes—
176#14579133C2314yes—
177#14579133C23112yes—
178#14579132C23112yes—
179#14579132C2314yes—
180#14579132C23112yes—
181#14579130C2314yes—
182Q8×Dic79C2316yes—
183Q8×Dic79C2316yes—
184Q8×Dic79C23112yes—
185Q8×Dic79C23112yes—
186Q8×Dic79C2314yes—
187Q8×Dic79C2314yes—
188Q8×Dic79C2314yes—
189Q8×Dic79C2314yes—
190Q8×Dic79C23112yes—
191Q8×Dic79C23112yes—
192Q8×Dic79C23112yes—
193Q8×Dic79C2314yes—
194Q8×Dic79C2314yes—
195C4×Dic158C23112yes—
196C4×Dic158C23112yes—
197C4×Dic158C23112yes—
198#14579126C2316yes—
199#14579126C2316yes—
200#14579126C23124yes—
201C4×D316C23112yes—
202D4×Dic79C2314yes—
203D4×Dic79C23112yes—
204D4×Dic79C2316yes—
205D4×Dic79C2316yes—
206D4×Dic79C23112yes—
207#14579123C2316yes—
208#14579123C2316yes—
209C4×C22⋊D79C23112yes—
210C4×C22⋊D79C23112yes—
211C4×C22⋊D79C23112yes—
212C4×C22⋊D79C23112yes—
213(C22⋊D79)⋊C4C2314yes—
214(C22⋊D79)⋊C4C23112yes—
215(C22⋊D79)⋊C4C23124yes—
216#14579120C2316yes—
217#14579120C2316yes—
218#14579120C2316yes—
219#14579120C23112yes—
220#14579120C2316yes—
221#14579120C2316yes—
222#14579120C23112yes—
223#14579120C23112yes—
224#14579120C23112yes—
225#14579119C23124yes—
226#14579119C23112yes—
227#14579118C23112yes—
228#14579117C23124yes—
229C2×C4⋊Dic79C2313yes—
230C2×C4⋊Dic79C2313yes—
231C2×C4⋊Dic79C2313yes—
232C2×C4⋊Dic79C23112yes—
233C2×C4⋊Dic79C2313yes—
234C4⋊C4×D79C23112yes—
235C2×C22⋊Dic79C2311yescharacteristic
236C2×C22⋊Dic79C2313yes—
237C2×C4×Dic79C2313yes—
238C2×C4×Dic79C2316yes—
239C2×C4×Dic79C2313yes—
240C2×C4×Dic79C23112yes—
241C42×D79C23112yes—
2422−1+4×C79—28no—
243C2×#41×C79C2316yes—
244C2×#41×C79C2314yes—
245C22×Q8×C79—28no—
246C22×Q8×C79C2313yes—
247C22×Q8×C79C2314yes—
248C22×Q8×C79C2314yes—
249C22×Q8×C79C2314yes—
250C22×Q8×C79C2311yescharacteristic
251C23×C4×C79C2313yes—
252C4⋊Q8×C79C23112yes—
253#124×C79C23112yes—
254#123×C79C23112yes—
255C22⋊Q8×C79C2316yes—
256C22⋊Q8×C79C2316yes—
257C22⋊Q8×C79C23112yes—
258C22⋊Q8×C79C23112yes—
259#121×C79C2316yes—
260#121×C79C2316yes—
261#120×C79C2314yes—
262C4×Q8×C79C2314yes—
263C4×Q8×C79C2314yes—
264C4×D4×C79C23112yes—
265C4×D4×C79C23112yes—
266#117×C79C2316yes—
267#11929625—216no—
268#11929624—224no—
269C2×Dic158C2416yes—
270C2×Dic158C24112yes—
271C2×Dic158C2414yes—
272Q8×D79—216no—
273C2×D316C2416yes—
274C2×C22⋊D79C2414yes—
275C2×C22⋊D79C24112yes—
276C2×C22⋊D79C2414yes—
277C2×C22⋊D79C2414yes—
278C2×C22⋊D79C2414yes—
279C22×Dic79C2411yescharacteristic
280C22×Dic79C2413yes—
281C22×Dic79C2411yescharacteristic
282C22×Dic79C2413yes—
283C22×Dic79C2414yes—
284C22×Dic79C24112yes—
285C2×C4×D79C24112yes—
286C2×C4×D79C2414yes—
287C2×C4×D79C24112yes—
288C4⋊Dic79C24112yes—
289C4⋊Dic79C2416yes—
290C4⋊Dic79C24112yes—
291C4⋊Dic79C24112yes—
292C4⋊Dic79C2416yes—
293C4⋊Dic79C2416yes—
294C4⋊Dic79C2416yes—
295C4⋊Dic79C2416yes—
296C4⋊Dic79C24112yes—
297C4⋊Dic79C2416yes—
298C4⋊Dic79C2414yes—
299C4⋊Dic79C2414yes—
300Dic79⋊C4C24112yes—
301Dic79⋊C4C24112yes—
302Dic79⋊C4C24112yes—
303Dic79⋊C4C2414yes—
304Dic79⋊C4C24112yes—
305Dic79⋊C4C2414yes—
306Dic79⋊C4C24112yes—
307Dic79⋊C4C24112yes—
308Dic79⋊C4C2414yes—
309Dic79⋊C4C2414yes—
310C22⋊Dic79C2411yescharacteristic
311C22⋊Dic79C2416yes—
312C22⋊Dic79C2411yescharacteristic
313C22⋊Dic79C2416yes—
314C22⋊Dic79C2411yescharacteristic
315C22⋊Dic79C2411yescharacteristic
316C22⋊Dic79C24112yes—
317C22⋊Dic79C2414yes—
318C22⋊Dic79C2414yes—
319C22⋊Dic79C24112yes—
320C22⋊Dic79C2414yes—
321C22⋊Dic79C2414yes—
322C22⋊Dic79C2414yes—
323(C2×D79)⋊C4C2414yes—
324(C2×D79)⋊C4C24112yes—
325(C2×D79)⋊C4C24112yes—
326(C2×D79)⋊C4C24112yes—
327(C2×D79)⋊C4C24112yes—
328(C2×D79)⋊C4C2414yes—
329C4×Dic79C2414yes—
330C4×Dic79C2416yes—
331C4×Dic79C24112yes—
332C4×Dic79C2416yes—
333C4×Dic79C2414yes—
334C4×Dic79C24124yes—
335C4×Dic79C24112yes—
336C4×Dic79C24112yes—
337C4×Dic79C2416yes—
338C4×Dic79C2416yes—
339C24×C79C2411yescharacteristic
340#41×C79—216no—
341#41×C79—224no—
342C2×Q8×C79—216no—
343C2×Q8×C79—216no—
344C2×Q8×C79—216no—
345C2×Q8×C79—212no—
346C2×Q8×C79#4118yes—
347C2×Q8×C79C24112yes—
348C2×Q8×C79C2416yes—
349C2×Q8×C79C2414yes—
350C2×D4×C79C2414yes—
351C2×D4×C79C2416yes—
352C2×D4×C79C2414yes—
353C2×D4×C79C2414yes—
354C22×C4×C79—212no—
355C22×C4×C79C2416yes—
356C22×C4×C79C2416yes—
357C22×C4×C79C24112yes—
358C22×C4×C79C2413yes—
359C22×C4×C79C2413yes—
360C4⋊C4×C79C2416yes—
361C4⋊C4×C79C2416yes—
362C4⋊C4×C79C24112yes—
363C4⋊C4×C79C24112yes—
364C22⋊C4×C79C2414yes—
365C22⋊C4×C79C2414yes—
366C22⋊C4×C79C2414yes—
367C22⋊C4×C79C24112yes—
368C22⋊C4×C79C24112yes—
369C42×C79C24112yes—
370C23×C79—22no—
371C23×C79—41no—
372C23×C79—41no—
373C23×C79C2511yescharacteristic
374C23×C79C2511yescharacteristic
375C23×C79C2514yes—
376C23×C79C2511yescharacteristic
377C22×D79C2514yes—
378Q8×C79—224no—
379Q8×C79—212no—
380Q8×C79C2×#41116yes—
381D4×C79—28no—
382D4×C79—212no—
383D4×C79—44no—
384D4×C79—44no—
385C2×C4×C79—26no—
386C2×C4×C79—212no—
387C2×C4×C79—212no—
388C2×C4×C79—224no—
389C2×C4×C79C2×#41112yes—
390C2×C4×C79C2516yes—
391C2×C4×C79C2514yes—
392C2×C4×C79C2514yes—
393C2×C4×C79C2514yes—
394C2×C4×C79C2516yes—
395C22⋊D79—28no—
396C22⋊D79—44no—
397C22⋊D79—412no—
398C22⋊D79—44no—
399C22⋊D79—44no—
400C2×Dic79—41no—
401C2×Dic79—43no—
402C2×Dic79—44no—
403C2×Dic79—412no—
404C2×Dic79—41no—
405C2×Dic79—43no—
406C2×Dic79C2511yescharacteristic
407C2×Dic79C2516yes—
408C2×Dic79C2511yescharacteristic
409C2×Dic79C2511yescharacteristic
410C2×Dic79C2514yes—
411C2×Dic79C2516yes—
412C2×Dic79C2511yescharacteristic
413C2×Dic79C2514yes—
414C2×Dic79C2514yes—
415D316—212no—
416C4×D79—224no—
417C4×D79—44no—
418C4×D79—412no—
419Dic158—212no—
420Dic158—412no—
421Dic158—44no—
422C22×C79—21no—
423C22×C79—21no—
424C22×C79—21no—
425C22×C79—21no—
426C22×C79—24no—
427C22×C79—21no—
428C22×C79—21no—
429C22×C79—24no—
430C22×C79—24no—
431C22×C79—21no—
432C22×C79—21no—
433C22×C79—44no—
434C22×C79C22×#4112yes—
435C22×C79C2611yescharacteristic
436C2×D79—24no—
437C2×D79—24no—
438C2×D79—24no—
439C4×C79—24no—
440C4×C79—26no—
441C4×C79—24no—
442C4×C79—24no—
443C4×C79C22×#41112yes—
444Dic79—24no—
445Dic79—21no—
446Dic79—26no—
447Dic79—24no—
448Dic79—24no—
449Dic79—21no—
450Dic79—21no—
451Dic79—26no—
452Dic79—21no—
453#62850—791nomaximal, Sylow
454C2×C79—22no—
455C2×C79—44no—
456C2×C79—41no—
457C2×C79—41no—
458C2×C79C23×#4111yescharacteristic
459C2×C792−1+611yescharacteristic
460C2×C792−1+611yescharacteristic
461D79—44no—
462#3524—794no—
463#3524—794no—
464#3523—794no—
465#3523—794no—
466#3518—794no—
467#3518—794no—
468#3516—794no—
469#3516—794no—
470#3507—796no—
471#3502—791no—
472#3497—791no—
473#3493—796no—
474#3486—791no—
475#3486D7911yescharacteristic, complemented
476#3461—796no—
477#3455—796no—
478C4×2−1+4—791no—
479C4×2−1+4—791no—
480C2×#519—791no—
481C79#6285011yescharacteristic, complemented, Sylow
482C2×2−1+4—791no—
483C2×2−1+4C2×D7911yescharacteristic
484C23×Q8C2×D7911yescharacteristic
485#559—7912no—
486Q82—794no—
487#557—7912no—
488#557—794no—
489#557—794no—
490#557—794no—
491#556—7912no—
492#556—7912no—
493#556—7912no—
494#556—7912no—
495#556—7912no—
496#555—7912no—
497#555—7912no—
498#554—7912no—
499#553—7912no—
500#553—7912no—
501#552—7912no—
502#552—7912no—
503#552—7912no—
504#552—7912no—
505#550—794no—
506D4×Q8—794no—
507D4×Q8—794no—
508D4×Q8—794no—
509D4×Q8C2×D7914yes—
510D4×Q8C2×D7914yes—
511#548—794no—
512#548—794no—
513#548—794no—
514#548—794no—
515#548C2×D7914yes—
516#548C2×D7914yes—
517#544—796no—
518#542—7912no—
519#542—796no—
520#542—796no—
521#542—7912no—
522#542—796no—
523#542—796no—
524#541—7912no—
525#541—796no—
526#541—796no—
527#541—7912no—
528#540—796no—
529#540—796no—
530#539—7912no—
531#539—7912no—
532#538—794no—
533#538—7912no—
534#537—796no—
535#536—796no—
536#536C2×D7916yes—
537#533—7912no—
538#533—7912no—
539#533—796no—
540#532—796no—
541#529—7912no—
542#529—7924no—
543#529—7912no—
544#529—7912no—
545#529—7912no—
546#529—7912no—
547#529—7912no—
548#525—796no—
549#525C2×D7916yes—
550#520—796no—
551#520—794no—
552#520—794no—
553#520—796no—
554#519—794no—
555#519—794no—
556#519—794no—
557#519—794no—
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—793no—
568C2×C4×Q8—791no—
569C2×C4×Q8—793no—
570C2×C4×Q8—794no—
571C2×C4×Q8—794no—
572C2×#117—793no—
573C2×#117—793no—
5742−1+4—28no—
5752−1+4—1588no—
576C2×#41—794no—
577C2×#41—796no—
578C2×#41C22×D7916yes—
579C2×#41C22×D7914yes—
580C22×Q8—28no—
581C22×Q8—794no—
582C22×Q8C22×D7913yes—
583C22×Q8C22×D7914yes—
584C22×Q8C22×D7914yes—
585C22×Q8C22×D7914yes—
586C22×Q8C22×D7911yescharacteristic
587C23×C4C22×D7913yes—
588C4⋊Q8—796no—
589C4⋊Q8—7912no—
590C4⋊Q8—796no—
591C4⋊Q8—796no—
592C4⋊Q8—7912no—
593C4⋊Q8—7912no—
594C4⋊Q8C22×D79112yes—
595#127—796no—
596#126—7912no—
597#126—7912no—
598#126—7924no—
599#126—794no—
600#126—794no—
601#126—7912no—
602#126—7912no—
603#126—7912no—
604#126—7912no—
605#126—7924no—
606#125—7912no—
607#125—7912no—
608#125—7912no—
609#125—7912no—
610#125—7924no—
611#125—7912no—
612#125—796no—
613#125—796no—
614#125—7912no—
615#124—7912no—
616#124—796no—
617#124—794no—
618#124—7912no—
619#124—796no—
620#124—794no—
621#124—7912no—
622#124—7924no—
623#124C22×D79112yes—
624#123—794no—
625#123—7912no—
626#123—7912no—
627#123—794no—
628#123—7912no—
629#123—7912no—
630#123—7912no—
631#123—7912no—
632#123—7912no—
633#123C22×D79112yes—
634C22⋊Q8—7912no—
635C22⋊Q8—7912no—
636C22⋊Q8—7912no—
637C22⋊Q8—796no—
638C22⋊Q8—796no—
639C22⋊Q8—7912no—
640C22⋊Q8—7912no—
641C22⋊Q8—7912no—
642C22⋊Q8—7912no—
643C22⋊Q8—7912no—
644C22⋊Q8—7912no—
645C22⋊Q8—794no—
646C22⋊Q8C22×D7916yes—
647C22⋊Q8C22×D7916yes—
648C22⋊Q8C22×D79112yes—
649C22⋊Q8C22×D79112yes—
650#121—794no—
651#121—794no—
652#121—7912no—
653#121—7912no—
654#121—7912no—
655#121—7912no—
656#121—794no—
657#121—796no—
658#121—796no—
659#121—7912no—
660#121C22×D7916yes—
661#121C22×D7916yes—
662#120—794no—
663#120C22×D7914yes—
664C4×Q8—794no—
665C4×Q8—794no—
666C4×Q8—796no—
667C4×Q8—7912no—
668C4×Q8—7912no—
669C4×Q8—794no—
670C4×Q8—794no—
671C4×Q8—7912no—
672C4×Q8—7912no—
673C4×Q8—794no—
674C4×Q8—7912no—
675C4×Q8—796no—
676C4×Q8—794no—
677C4×Q8—796no—
678C4×Q8—796no—
679C4×Q8—7924no—
680C4×Q8—7912no—
681C4×Q8—7912no—
682C4×Q8—7912no—
683C4×Q8C22×D7914yes—
684C4×Q8C22×D7914yes—
685C4×D4—794no—
686C4×D4—796no—
687C4×D4—7912no—
688C4×D4—796no—
689C4×D4—7912no—
690C4×D4—7912no—
691C4×D4—7912no—
692C4×D4—7912no—
693C4×D4—7912no—
694C4×D4—796no—
695C4×D4—796no—
696C4×D4—794no—
697C4×D4—7912no—
698C4×D4—7924no—
699C4×D4—7912no—
700C4×D4C22×D79112yes—
701C4×D4C22×D79112yes—
702#117—796no—
703#117—796no—
704#117—796no—
705#117—796no—
706#117—7912no—
707#117—7912no—
708#117—796no—
709#117—7912no—
710#117—7912no—
711#117—7912no—
712#117—7924no—
713#117—7924no—
714#117—7912no—
715#117C22×D7916yes—
716C2×C4⋊C4—793no—
717C2×C4⋊C4—793no—
718C2×C4⋊C4—793no—
719C2×C4⋊C4—793no—
720C2×C4⋊C4—7912no—
721C2×C4⋊C4—7912no—
722C2×C22⋊C4—791no—
723C2×C22⋊C4—793no—
724C2×C42—793no—
725C2×C42—796no—
726C2×C42—793no—
727C2×C42—7912no—
728C2×C42—7912no—
729C24C23×D7911yescharacteristic
730#41—216no—
731#41—224no—
732#41—15816no—
733#41—15824no—
734C2×Q8—216no—
735C2×Q8—216no—
736C2×Q8—216no—
737C2×Q8—212no—
738C2×Q8—794no—
739C2×Q8—7912no—
740C2×Q8—796no—
741C2×Q8—15816no—
742C2×Q8#1192962318yes—
743C2×Q8C23×D79112yes—
744C2×Q8C23×D7916yes—
745C2×Q8C23×D7914yes—
746C2×D4—794no—
747C2×D4—794no—
748C2×D4—7912no—
749C2×D4—794no—
750C2×D4—794no—
751C2×D4—796no—
752C2×D4C23×D7914yes—
753C2×D4C23×D7916yes—
754C2×D4C23×D7914yes—
755C2×D4C23×D7914yes—
756C22×C4—212no—
757C22×C4—791no—
758C22×C4—793no—
759C22×C4—791no—
760C22×C4—793no—
761C22×C4—794no—
762C22×C4—7912no—
763C22×C4—794no—
764C22×C4—7912no—
765C22×C4—7912no—
766C22×C4C23×D7913yes—
767C22×C4C23×D79112yes—
768C22×C4C23×D7916yes—
769C22×C4C23×D7916yes—
770C22×C4C23×D7913yes—
771C4⋊C4—7912no—
772C4⋊C4—794no—
773C4⋊C4—7912no—
774C4⋊C4—7912no—
775C4⋊C4—794no—
776C4⋊C4—7912no—
777C4⋊C4—7912no—
778C4⋊C4—7912no—
779C4⋊C4—794no—
780C4⋊C4—794no—
781C4⋊C4—7912no—
782C4⋊C4—796no—
783C4⋊C4—7912no—
784C4⋊C4—7912no—
785C4⋊C4—796no—
786C4⋊C4—796no—
787C4⋊C4—796no—
788C4⋊C4—796no—
789C4⋊C4—796no—
790C4⋊C4—794no—
791C4⋊C4—7912no—
792C4⋊C4—794no—
793C4⋊C4C23×D7916yes—
794C4⋊C4C23×D7916yes—
795C4⋊C4C23×D79112yes—
796C4⋊C4C23×D79112yes—
797C22⋊C4—791no—
798C22⋊C4—791no—
799C22⋊C4—796no—
800C22⋊C4—796no—
801C22⋊C4—791no—
802C22⋊C4—791no—
803C22⋊C4—794no—
804C22⋊C4—794no—
805C22⋊C4—7912no—
806C22⋊C4—7912no—
807C22⋊C4—794no—
808C22⋊C4—794no—
809C22⋊C4—794no—
810C22⋊C4—794no—
811C22⋊C4—7912no—
812C22⋊C4—7912no—
813C22⋊C4—7912no—
814C22⋊C4—7912no—
815C22⋊C4—794no—
816C22⋊C4C23×D79112yes—
817C22⋊C4C23×D7914yes—
818C22⋊C4C23×D79112yes—
819C22⋊C4C23×D7914yes—
820C22⋊C4C23×D7914yes—
821C42—796no—
822C42—796no—
823C42—794no—
824C42—794no—
825C42—7912no—
826C42—7924no—
827C42—7912no—
828C42—7912no—
829C42—796no—
830C42—796no—
831C42C23×D79112yes—
832C23—22no—
833C23—41no—
834C23—41no—
835C23—794no—
836C23C24×D7911yescharacteristic
837C23C24×D7911yescharacteristic
838C23C24×D7914yes—
839C23C24×D7911yescharacteristic
840Q8—224no—
841Q8—212no—
842Q8—3164no—
843Q8—31612no—
844Q8—15812no—
845Q8C2×#11929623116yes—
846D4—28no—
847D4—212no—
848D4—44no—
849D4—44no—
850D4—3164no—
851D4—3164no—
852D4—31612no—
853D4—3164no—
854D4—1588no—
855D4—15812no—
856C2×C4—26no—
857C2×C4—212no—
858C2×C4—212no—
859C2×C4—224no—
860C2×C4—31612no—
861C2×C4—3164no—
862C2×C4—3161no—
863C2×C4—3163no—
864C2×C4—31612no—
865C2×C4—3164no—
866C2×C4—3161no—
867C2×C4—3163no—
868C2×C4—791no—
869C2×C4—791no—
870C2×C4—796no—
871C2×C4—791no—
872C2×C4—794no—
873C2×C4—796no—
874C2×C4—791no—
875C2×C4—794no—
876C2×C4—794no—
877C2×C4—15824no—
878C2×C4C2×#11929623112yes—
879C2×C4C24×D7916yes—
880C2×C4C24×D7914yes—
881C2×C4C24×D7914yes—
882C2×C4C24×D7914yes—
883C2×C4C24×D7916yes—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—44no—
896C22—1584no—
897C22—1584no—
898C22—1584no—
899C22C22×#1192962312yes—
900C22C25×D7911yescharacteristic
901C4—24no—
902C4—26no—
903C4—24no—
904C4—24no—
905C4—1584no—
906C4—1581no—
907C4—1586no—
908C4—1581no—
909C4—1584no—
910C4—1581no—
911C4—1586no—
912C4—1584no—
913C4—1581no—
914C4C22×#11929623112yes—
915C2—22no—
916C2—41no—
917C2—41no—
918C2—44no—
919C2—3164no—
920C2C23×#1192962311yescharacteristic
921C2#2377821211yescharacteristic
922C2#2377821211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3486C2
hypercenter#3486D79
hypocenterC79#62850
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. #23777510C2semidirect
2. #23777502C2semidirect
3. #23777491C2semidirect
4. #23777487C2semidirect
5. #23777412C2semidirect
6. #23777408C2semidirect
7. #23777394C2semidirect
8. #23777386C2semidirect
9. #23777264C2semidirect
10. #23777206C2semidirect
11. #23777167C2semidirect
12. #23777117C2semidirect
13. #23777051C2semidirect
14. #23776824C2semidirect
15. #23776788C2semidirect
16. 2−1+4×Dic79C2semidirect
17. #23776609C2semidirect
18. C2×#19099041C2semidirect
19. C79×#3486C2semidirect
21. #19099295C22semidirect
22. Q8×Dic158C22semidirect
23. #19099292C22semidirect
24. #19099289C22semidirect
25. #19099289C22semidirect
26. #19099288C22semidirect
27. #19099287C22semidirect
29. #19099284C22semidirect
31. #19099282C22semidirect
34. #19099271C22semidirect
37. #19099255C22semidirect
40. #19099247C22semidirect
41. #19099232C22semidirect
44. Q8×C22⋊D79C22semidirect
47. #19099224C22semidirect
48. #19099220C22semidirect
52. #19099186C22semidirect
53. #19099182C22semidirect
56. #19099174C22semidirect
59. #19099173C22semidirect
68. #19099118C22semidirect
70. #19099115C22semidirect
72. #19099099C22semidirect
77. #19099092C22semidirect
81. #19099046C22semidirect
82. #19099045C22semidirect
89. #19099041C22semidirect
90. #19099039C22semidirect
92. #41×Dic79C22semidirect
93. C4×#11929625C22semidirect
99. C2×Q8×Dic79C22semidirect
100. C4×Q8×D79C22semidirect
475. #3486D79semidirect
481. C79#62850semidirect

Maximal subgroups

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

subgroupindex
#237775102
#237775022
#237774912
#237774872
#237774122
#237774082
#237773942
#237773862
#237772642
#237772062
#237771672
#237771172
#237770512
#237768242
#237767882
2−1+4×Dic792
#237766092
C2×#190990412
C79×#34862
#6285079