Finite Group Databasebeta

← #35196815

Subgroups — #35196815

Order 20224.

11346 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099400C212yesmaximal, complemented
2#23777194C212yesmaximal, complemented
3#23777189C216yesmaximal, complemented
4#23777183C213yesmaximal, complemented
5#23777178C211yesmaximal, characteristic, complemented
6#23777173C213yesmaximal, complemented
7#23777170C214yesmaximal, complemented
8#23777158C2112yesmaximal, complemented
9D4×#11929625C214yesmaximal, complemented
10#23776887C2112yesmaximal, complemented
11#23776732C216yesmaximal, complemented
12C2×#19099114C213yesmaximal, complemented
13#532×D79C213yesmaximal, complemented
14C4×#41×D79C211yesmaximal, characteristic, complemented
15C79×#3499C211yesmaximal, characteristic, complemented
16#19099400—232no—
17C2×#14579209C2214yescomplemented
18C2×#14579209C2216yescomplemented
19C2×#14579207C22112yescomplemented
20C2×#14579207C2216yescomplemented
21C2×#14579207C2212yescomplemented
22C22×#11929625C2214yescomplemented
23C22×#11929625C2216yescomplemented
24C2×#41×D79C2211yescharacteristic
25C2×#41×D79C22112yescomplemented
26C2×#41×D79C2216yescomplemented
27#19099235C2214yescomplemented
28#19099234C22112yescomplemented
29#19099228C22112yescomplemented
30#19099224C2218yescomplemented
31#19099223C22124yescomplemented
32#19099216C22112yescomplemented
33#19099214C22124yescomplemented
34#19099205C22148yescomplemented
35#19099204C22124yescomplemented
36#19099201C22124yescomplemented
37D4×D316C22112yescomplemented
38D4×D316C22112yescomplemented
39#19099197C22124yescomplemented
40#19099143C22124yescomplemented
41#19099138C22112yescomplemented
42#19099137C2216yescomplemented
43#19099132C2216yescomplemented
44#19099131C22112yescomplemented
45#19099127C2216yescomplemented
46#19099124C22124yescomplemented
47#19099114C22112yescomplemented
48#19099114C22112yescomplemented
49#19099114C2216yescomplemented
50#19099114C2213yescomplemented
51#19099114C2216yescomplemented
52#19099114C2216yescomplemented
53#19099113C2213yescomplemented
54#19099112C2216yescomplemented
55#19099111C2211yescharacteristic, complemented
56#19099110C22112yescomplemented
57#19099109C2216yescomplemented
58#19099108C22112yescomplemented
59C4⋊Q8×D79C2213yescomplemented
60C2×#14579158C2213yescomplemented
61#127×D79C2213yescomplemented
62C2×#14579150C2216yescomplemented
63#124×D79C2216yescomplemented
64#19099076C22124yescomplemented
65#19099071C22124yescomplemented
66C2×#14579136C22112yescomplemented
67#121×D79C22112yescomplemented
68#41×Dic79C2211yescharacteristic, complemented
69C4×#11929625C2212yescomplemented
70C4×#11929624C2213yescomplemented
71#19099031C2213yescomplemented
72C4×#11929623C2216yescomplemented
73C4×Q8×D79C2212yescomplemented
74C2×#14579123C22112yescomplemented
75C4×D4×D79C2216yescomplemented
76C4×D4×D79C22112yescomplemented
77#117×D79C2213yescomplemented
78C2×C42×D79C2213yescomplemented
79C2×2−1+4×C79C2212yescomplemented
80D4×Q8×C79C2214yescomplemented
81#547×C79C22112yescomplemented
82#536×C79C2216yescomplemented
83#532×C79C2213yescomplemented
84C2×C4⋊Q8×C79C2213yescomplemented
85C4×#41×C79C2211yescharacteristic, complemented
86#14579209—248no—
87#14579209—232no—
88#14579207—216no—
89#14579207—248no—
90#14579207—296no—
91C2×#11929625—232no—
92C2×#11929625—248no—
93C2×#11929625C23112yes—
94C2×#11929625C23112yes—
95C2×#11929625C23112yes—
96C2×#11929625C2314yes—
97C2×#11929625C23112yes—
98C2×#11929625C2316yes—
99C2×#11929625C2311yescharacteristic
100C2×#11929624C2316yes—
101C2×#11929624C23112yes—
102C2×#11929624C23124yes—
103C2×#11929624C23112yes—
104C2×#11929624C2313yes—
105C2×#11929623C23112yes—
106C2×#11929623C2312yes—
107C2×#11929623C2313yes—
108#41×D79—296no—
109#41×D79—248no—
110#41×D79D4116yescomplemented
111C2×Q8×D79C2316yes—
112C2×Q8×D79C23112yes—
113C2×Q8×D79C2311yescharacteristic
114C22×D316C23112yes—
115C22×D316C23112yes—
116C22×D316C2316yes—
117C22×D316C23112yes—
118C2×D4×D79C23124yes—
119C2×D4×D79C23112yes—
120C2×D4×D79C23112yes—
121C2×D4×D79C2316yes—
122C2×D4×D79C23112yes—
123C2×D4×D79C2313yes—
124C22×C4×D79C23112yes—
125C22×C4×D79C23112yes—
126C22×C4×D79C2316yes—
127C22×C4×D79C2313yes—
128#14579161C2311yescharacteristic
129#14579160C23112yes—
130#14579159C2316yes—
131#14579158C23112yes—
132#14579158C2313yes—
133#14579158C2316yes—
134#14579157C23112yes—
135#14579157C2316yes—
136#14579150C23112yes—
137#14579150C23124yes—
138#14579150C2316yes—
139#14579149C2316yes—
140#14579148C2312yes—
141#14579147C23124yes—
142#14579146C23148yes—
143#14579144C23124yes—
144#14579139C23148yes—
145#14579137C23124yes—
146#14579136C23124yes—
147#14579136C23124yes—
148#14579136C23124yes—
149#14579136C23124yes—
150#14579136C23112yes—
151#14579135C23124yes—
152#14579135C23112yes—
153#14579134C23124yes—
154#14579134C23148yes—
155#14579133C23124yes—
156#14579132C2314yes—
157#14579131C23148yes—
158#14579131C23124yes—
159#14579129C23124yes—
160Q8×Dic79C2312yes—
161C4×Dic158C2316yes—
162#14579126C2316yes—
163C4×D316C2316yes—
164C4×D316C23112yes—
165D4×Dic79C2316yes—
166D4×Dic79C2314yes—
167#14579123C23124yes—
168#14579123C2316yes—
169#14579123C23124yes—
170#14579123C23112yes—
171#14579123C23124yes—
172C4×C22⋊D79C23112yes—
173C4×C22⋊D79C23124yes—
174(C22⋊D79)⋊C4C23112yes—
175(C22⋊D79)⋊C4C23124yes—
176#14579120C2313yes—
177#14579119C2316yes—
178#14579118C2316yes—
179#14579117C2316yes—
180C4⋊C4×D79C2316yes—
181C4⋊C4×D79C23112yes—
182C2×(C2×D79)⋊C4C23124yes—
183C22⋊C4×D79C23124yes—
184C22⋊C4×D79C2316yes—
185C2×C4×Dic79C2316yes—
186C2×C4×Dic79C2313yes—
187C42×D79C2311yescharacteristic
188C42×D79C2313yes—
189C42×D79C2316yes—
190C42×D79C2316yes—
191C42×D79C2313yes—
192C42×D79C2313yes—
1932−1+4×C79—216no—
194C2×#41×C79C23112yes—
195C2×#41×C79C2316yes—
196C2×#41×C79C2311yescharacteristic
197C22×Q8×C79C2316yes—
198C22×Q8×C79C2314yes—
199C4⋊Q8×C79C2316yes—
200C4⋊Q8×C79C23112yes—
201C4⋊Q8×C79C2313yes—
202#127×C79C2311yescharacteristic
203#124×C79C2316yes—
204#123×C79C23124yes—
205C22⋊Q8×C79C23124yes—
206#121×C79C23112yes—
207C4×Q8×C79C2312yes—
208C4×D4×C79C2316yes—
209C4×D4×C79C23112yes—
210#117×C79C2313yes—
211C2×C4⋊C4×C79C23112yes—
212C2×C42×C79C2313yes—
213C23×D79C24112yes—
214C23×D79C24112yes—
215C23×D79C2413yes—
216#11929625—248no—
217#11929625—248no—
218#11929625—224no—
219#11929625—248no—
220#11929625—248no—
221#11929625—216no—
222#11929625C2×D418yescomplemented
223#11929624—248no—
224#11929624—248no—
225#11929624—224no—
226#11929624—296no—
227#11929624C2×D4124yescomplemented
228#11929623—248no—
229#11929623—28no—
230#11929623C2×D4124yescomplemented
231C2×Dic158C24112yes—
232C2×Dic158C2412yes—
233C2×Dic158C2413yes—
234Q8×D79—224no—
235Q8×D79—248no—
236Q8×D79C2×D418yescomplemented
237C2×D316—248no—
238C2×D316—248no—
239C2×D316—224no—
240C2×D316—424no—
241C2×D316C24124yes—
242C2×D316C24112yes—
243C2×D316C24112yes—
244C2×D316C2416yes—
245C2×D316C24112yes—
246C2×D316C24124yes—
247C2×D316C2413yes—
248C2×C22⋊D79C24112yes—
249C2×C22⋊D79C2414yes—
250C2×C22⋊D79C24112yes—
251C2×C22⋊D79C24124yes—
252C2×C22⋊D79C2416yes—
253D4×D79—224no—
254D4×D79—248no—
255D4×D79—248no—
256D4×D79—296no—
257D4×D79—424no—
258D4×D79C2×D4124yescomplemented
259C22×Dic79C2414yes—
260C22×Dic79C2416yes—
261C22×Dic79C2413yes—
262C2×C4×D79—248no—
263C2×C4×D79—248no—
264C2×C4×D79—412no—
265C2×C4×D79C2×D4124yescomplemented
266C2×C4×D79C24112yes—
267C2×C4×D79C24112yes—
268C2×C4×D79C24124yes—
269C2×C4×D79C24112yes—
270C2×C4×D79C2412yes—
271C2×C4×D79C2416yes—
272C2×C4×D79C2416yes—
273C2×C4×D79C2416yes—
274C2×C4×D79C2413yes—
275C2×C4×D79C2413yes—
276C2×C4×D79C2411yescharacteristic
277C2×C4×D79C2413yes—
278C4⋊Dic79C2414yes—
279C4⋊Dic79C2416yes—
280Dic79⋊C4C24112yes—
281Dic79⋊C4C24124yes—
282C22⋊Dic79C2418yes—
283C22⋊Dic79C2416yes—
284(C2×D79)⋊C4C24124yes—
285(C2×D79)⋊C4C24112yes—
286(C2×D79)⋊C4C24124yes—
287(C2×D79)⋊C4C24148yes—
288C4×Dic79C2412yes—
289C4×Dic79C2411yescharacteristic
290C4×Dic79C2416yes—
291C4×Dic79C2413yes—
292C4×Dic79C2416yes—
293C4×Dic79C2416yes—
294C4×Dic79C2416yes—
295#41×C79—248no—
296#41×C79—224no—
297#41×C79C2×D418yescomplemented
298C2×Q8×C79—216no—
299C2×Q8×C79—224no—
300C2×Q8×C79C24112yes—
301C2×Q8×C79C2416yes—
302C2×Q8×C79C2411yescharacteristic
303C2×D4×C79C24112yes—
304C2×D4×C79C2412yes—
305C2×D4×C79C2414yes—
306C2×D4×C79C2413yes—
307C22×C4×C79C24112yes—
308C22×C4×C79C24112yes—
309C22×C4×C79C2416yes—
310C22×C4×C79C2413yes—
311C4⋊C4×C79C24112yes—
312C4⋊C4×C79C24124yes—
313C4⋊C4×C79C2416yes—
314C22⋊C4×C79C2416yes—
315C22⋊C4×C79C24124yes—
316C42×C79C2411yescharacteristic
317C42×C79C2413yes—
318C42×C79C2416yes—
319C23×C79C2514yes—
320C23×C79C2513yes—
321C22×D79—224no—
322C22×D79—224no—
323C22×D79—46no—
324C22×D79—424no—
325C22×D79—424no—
326C22×D79C22×D4112yes—
327C22×D79C25112yes—
328C22×D79C2513yes—
329C22×D79C2511yescharacteristic
330Q8×C79—224no—
331Q8×C79—212no—
332Q8×C79C22×D414yes—
333D4×C79—224no—
334D4×C79—24no—
335D4×C79—28no—
336D4×C79C22×D4112yes—
337C2×C4×C79—224no—
338C2×C4×C79—224no—
339C2×C4×C79—212no—
340C2×C4×C79C22×D4112yes—
341C2×C4×C79C2516yes—
342C2×C4×C79C25112yes—
343C2×C4×C79C2511yescharacteristic
344C2×C4×C79C2513yes—
345C2×C4×C79C2512yes—
346C22⋊D79—224no—
347C22⋊D79—28no—
348C22⋊D79—224no—
349C22⋊D79—424no—
350C22⋊D79C22×D4124yes—
351C2×Dic79—28no—
352C2×Dic79—46no—
353C2×Dic79C22×D4112yes—
354C2×Dic79C2512yes—
355C2×Dic79C2516yes—
356C2×Dic79C2514yes—
357C2×Dic79C2511yescharacteristic
358C2×Dic79C2513yes—
359D316—224no—
360D316—248no—
361D316—224no—
362D316—212no—
363D316—224no—
364D316—424no—
365D316C22×D4112yes—
366C4×D79—224no—
367C4×D79—224no—
368C4×D79—24no—
369C4×D79—212no—
370C4×D79—224no—
371C4×D79—248no—
372C4×D79—46no—
373C4×D79—46no—
374C4×D79C22×D4112yes—
375C4×D79C22×D414yes—
376C4×D79C22×D4112yes—
377C4×D79C22×D4112yes—
378Dic158—24no—
379Dic158—224no—
380Dic158C22×D4112yes—
381C22×C79—26no—
382C22×C79—24no—
383C22×C79—28no—
384C22×C79C23×D416yes—
385C22×C79C2611yescharacteristic
386C2×D79—26no—
387C2×D79—22no—
388C2×D79—212no—
389C2×D79—224no—
390C2×D79—412no—
391C2×D79—824no—
392C2×D79—824no—
393C2×D79C23×D412yes—
394C2×D79C23×D416yes—
395C4×C79—212no—
396C4×C79—26no—
397C4×C79C23×D416yes—
398C4×C79C23×D412yes—
399C4×C79#58514yescomplemented
400Dic79—24no—
401Dic79—26no—
402Dic79—22no—
403Dic79C23×D416yes—
404Dic79C23×D412yes—
405#62812—791nomaximal, Sylow
406C2×C79—26no—
407C2×C79—44no—
408C2×C79C24×D411yescharacteristic
409C2×C79C2×#58512yes—
410D79—22no—
411D79—26no—
412D79—412no—
413C2×#585—792no—
414#3500—792no—
415#3500—796no—
416#3499—793no—
417#3499D7911yescharacteristic, complemented
418#3498—793no—
419#3498—791no—
420#3497—794no—
421#3496—7912no—
422D4×#41—794no—
423D4×#41—7912no—
424#3449—796no—
425C2×#532—793no—
426C2×#532—793no—
427C2×C4×#41—791no—
428C79#6281211yescharacteristic, complemented, Sylow
429#585—15832no—
430C2×2−1+4—794no—
431C2×2−1+4—796no—
432C2×2−1+4C2×D7912yescomplemented
433C2×H(5,𝔽2)—7912no—
434C2×H(5,𝔽2)—796no—
435C2×H(5,𝔽2)—792no—
436C22×#41—791no—
437C22×#41—796no—
438C22×#41—7912no—
439C22×#41—796no—
440C22×#41—794no—
441#550—794no—
442#550—7912no—
443D4×Q8—7912no—
444D4×Q8C2×D7914yescomplemented
445#548—798no—
446#548—7924no—
447#547—7912no—
448#547—7924no—
449#547C2×D79112yescomplemented
450#546—7924no—
451#546—7948no—
452#546—7924no—
453D42—7924no—
454D42—7912no—
455D42—7912no—
456#537—7924no—
457#536—796no—
458#536—7912no—
459#536C2×D7916yescomplemented
460#535—796no—
461#535—7912no—
462#535—796no—
463#534—7924no—
464#532—796no—
465#532—793no—
466#532—796no—
467#532—7912no—
468#532—7912no—
469#532—796no—
470#532—796no—
471#532—791no—
472#532—796no—
473#532—7912no—
474#532—7912no—
475#532—793no—
476#532C2×D7913yescomplemented
477C2×C4⋊Q8—793no—
478C2×C4⋊Q8C2×D7913yescomplemented
479C2×#127—793no—
480C2×#127—793no—
481C2×#124—796no—
482C2×#124—796no—
483#525—7924no—
484#525—7924no—
485C2×#121—7912no—
486C2×#121—7912no—
487C4×#41—791no—
488C4×#41—792no—
489C4×#41—796no—
490C4×#41—793no—
491C4×#41—793no—
492C4×#41C2×D7911yescharacteristic, complemented
493C2×C4×Q8—792no—
494C2×C4×D4—796no—
495C2×C4×D4—7912no—
496C2×C4×D4—7912no—
497C2×#117—793no—
498C22×C42—793no—
4992−1+4—216no—
5002−1+4—15832no—
5012−1+4—15848no—
502H(5,𝔽2)—15896no—
503H(5,𝔽2)—15848no—
504H(5,𝔽2)—15816no—
505C2×#41—7916no—
506C2×#41—791no—
507C2×#41—7912no—
508C2×#41—796no—
509C2×#41—7912no—
510C2×#41—7912no—
511C2×#41—7912no—
512C2×#41—794no—
513C2×#41—793no—
514C2×#41—7912no—
515C2×#41—792no—
516C2×#41—793no—
517C2×#41—796no—
518C2×#41—7912no—
519C2×#41—7924no—
520C2×#41—7912no—
521C2×#41—15848no—
522C2×#41—15848no—
523C2×#41—15832no—
524C2×#41—15896no—
525C2×#41C22×D7916yes—
526C2×#41C22×D79112yes—
527C2×#41C22×D7911yescharacteristic
528C22×Q8—791no—
529C22×Q8—796no—
530C22×Q8—7912no—
531C22×Q8C22×D7916yes—
532C22×Q8C22×D7914yes—
533C22×D4—7912no—
534C22×D4—793no—
535C22×D4—7912no—
536C22×D4—796no—
537C22×D4—7924no—
538C22×D4—7912no—
539C22×D4—7912no—
540C22×D4—7912no—
541C22×D4—796no—
542C22×D4—7912no—
543C23×C4—796no—
544C23×C4—793no—
545C23×C4—7912no—
546C23×C4—7912no—
547C4⋊Q8—796no—
548C4⋊Q8—7912no—
549C4⋊Q8—791no—
550C4⋊Q8C22×D7913yes—
551C4⋊Q8C22×D7916yes—
552C4⋊Q8C22×D79112yes—
553#127—796no—
554#127—7912no—
555#127—793no—
556#127—796no—
557#127—7912no—
558#127C22×D7911yescharacteristic
559#124—796no—
560#124—7912no—
561#124—7924no—
562#124—792no—
563#124—7924no—
564#124—796no—
565#124C22×D7916yes—
566#123—7924no—
567#123—7948no—
568#123C22×D79124yes—
569C22⋊Q8—7924no—
570C22⋊Q8—7948no—
571C22⋊Q8C22×D79124yes—
572#121—794no—
573#121—7924no—
574#121—7912no—
575#121—7924no—
576#121—7912no—
577#121—7924no—
578#121—7924no—
579#121—7924no—
580#121—7924no—
581#121—7924no—
582#121—7948no—
583#121C22×D79112yes—
584#120—7924no—
585#120—7948no—
586#120—7924no—
587C4×Q8—792no—
588C4×Q8—796no—
589C4×Q8—796no—
590C4×Q8C22×D7912yes—
591C4×D4—794no—
592C4×D4—796no—
593C4×D4—7912no—
594C4×D4—7924no—
595C4×D4—7912no—
596C4×D4—796no—
597C4×D4—7924no—
598C4×D4—7924no—
599C4×D4—7924no—
600C4×D4—7912no—
601C4×D4—7924no—
602C4×D4—796no—
603C4×D4—7912no—
604C4×D4C22×D7916yes—
605C4×D4C22×D79112yes—
606#117—793no—
607#117—796no—
608#117—796no—
609#117—796no—
610#117C22×D7913yes—
611C2×C4⋊C4—796no—
612C2×C4⋊C4—7912no—
613C2×C4⋊C4C22×D79112yes—
614C2×C22⋊C4—7924no—
615C2×C22⋊C4—796no—
616C2×C22⋊C4—7924no—
617C2×C42—796no—
618C2×C42—793no—
619C2×C42—793no—
620C2×C42—796no—
621C2×C42—796no—
622C2×C42—793no—
623C2×C42—793no—
624C2×C42—791no—
625C2×C42C22×D7913yes—
626C24—793no—
627C24—7912no—
628C24—7912no—
629#41—248no—
630#41—224no—
631#41—798no—
632#41—7924no—
633#41—7924no—
634#41—15848no—
635#41—15896no—
636#41—15848no—
637#41—15848no—
638#41—1588no—
639#41—15824no—
640#41—15848no—
641#41—15848no—
642#41—15848no—
643#41—15848no—
644#41—15816no—
645#41—15824no—
646#41D4×D7918yescomplemented
647C2×Q8—216no—
648C2×Q8—224no—
649C2×Q8—798no—
650C2×Q8—793no—
651C2×Q8—7912no—
652C2×Q8—792no—
653C2×Q8—15824no—
654C2×Q8—15848no—
655C2×Q8C23×D79112yes—
656C2×Q8C23×D7916yes—
657C2×Q8C23×D7911yescharacteristic
658C2×D4—31624no—
659C2×D4—31624no—
660C2×D4—7924no—
661C2×D4—796no—
662C2×D4—7924no—
663C2×D4—7912no—
664C2×D4—794no—
665C2×D4—7912no—
666C2×D4—7924no—
667C2×D4—793no—
668C2×D4—7912no—
669C2×D4—7924no—
670C2×D4—7912no—
671C2×D4—7912no—
672C2×D4—796no—
673C2×D4—15848no—
674C2×D4—15848no—
675C2×D4—15824no—
676C2×D4—15896no—
677C2×D4—15848no—
678C2×D4—15848no—
679C2×D4—15824no—
680C2×D4C23×D7914yes—
681C2×D4C23×D79112yes—
682C2×D4C23×D7912yes—
683C2×D4C23×D7913yes—
684C22×C4—31612no—
685C22×C4—796no—
686C22×C4—796no—
687C22×C4—796no—
688C22×C4—793no—
689C22×C4—791no—
690C22×C4—793no—
691C22×C4—793no—
692C22×C4—793no—
693C22×C4—7924no—
694C22×C4—794no—
695C22×C4—792no—
696C22×C4—796no—
697C22×C4—7912no—
698C22×C4—7912no—
699C22×C4—7924no—
700C22×C4—7912no—
701C22×C4—15848no—
702C22×C4—15848no—
703C22×C4C23×D7916yes—
704C22×C4C23×D79112yes—
705C22×C4C23×D79112yes—
706C22×C4C23×D7913yes—
707C4⋊C4—7912no—
708C4⋊C4—7924no—
709C4⋊C4—794no—
710C4⋊C4—796no—
711C4⋊C4C23×D79112yes—
712C4⋊C4C23×D7916yes—
713C4⋊C4C23×D79124yes—
714C22⋊C4—798no—
715C22⋊C4—796no—
716C22⋊C4—7924no—
717C22⋊C4—7912no—
718C22⋊C4—7948no—
719C22⋊C4—7924no—
720C22⋊C4C23×D7916yes—
721C22⋊C4C23×D79124yes—
722C42—792no—
723C42—791no—
724C42—796no—
725C42—793no—
726C42—796no—
727C42—796no—
728C42—796no—
729C42C23×D7911yescharacteristic
730C42C23×D7913yes—
731C42C23×D7916yes—
732C23—3166no—
733C23—31624no—
734C23—31624no—
735C23—7912no—
736C23—793no—
737C23—791no—
738C23—7912no—
739C23—15824no—
740C23—15824no—
741C23C24×D7914yes—
742C23C24×D7913yes—
743Q8—224no—
744Q8—212no—
745Q8—7912no—
746Q8—15824no—
747Q8—1584no—
748Q8C2×D4×D7914yes—
749D4—224no—
750D4—28no—
751D4—24no—
752D4—31624no—
753D4—31624no—
754D4—7924no—
755D4—7912no—
756D4—15824no—
757D4—15848no—
758D4—15824no—
759D4—1588no—
760D4—15824no—
761D4—15824no—
762D4—15824no—
763D4—15812no—
764D4C2×D4×D79112yes—
765C2×C4—224no—
766C2×C4—212no—
767C2×C4—224no—
768C2×C4—3166no—
769C2×C4—3166no—
770C2×C4—3166no—
771C2×C4—791no—
772C2×C4—793no—
773C2×C4—7912no—
774C2×C4—794no—
775C2×C4—7912no—
776C2×C4—7912no—
777C2×C4—7912no—
778C2×C4—792no—
779C2×C4—796no—
780C2×C4—794no—
781C2×C4—15824no—
782C2×C4—15848no—
783C2×C4—15824no—
784C2×C4—1588no—
785C2×C4—1584no—
786C2×C4—15812no—
787C2×C4—15824no—
788C2×C4C2×D4×D79112yes—
789C2×C4C24×D7916yes—
790C2×C4C24×D79112yes—
791C2×C4C24×D7912yes—
792C2×C4C24×D7911yescharacteristic
793C2×C4C24×D7913yes—
794C22—26no—
795C22—24no—
796C22—28no—
797C22—31612no—
798C22—792no—
799C22—796no—
800C22—63224no—
801C22—63224no—
802C22—15812no—
803C22—15824no—
804C22—1582no—
805C22—1586no—
806C22C22×D4×D7916yes—
807C22C25×D7911yescharacteristic
808C4—212no—
809C4—26no—
810C4—792no—
811C4—796no—
812C4—1584no—
813C4—1582no—
814C4—1586no—
815C4C22×D4×D7916yes—
816C4C22×D4×D7912yes—
817C4#1909940014yescomplemented
818C2—26no—
819C2—44no—
820C2—31612no—
821C2—1582no—
822C2—1586no—
823C2C23×D4×D7911yescharacteristic
824C2C2×#1909940012yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3499C2
hypercenter#3499D79
hypocenterC79#62812
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×#19099400C2semidirect
2. #23777194C2semidirect
3. #23777189C2semidirect
4. #23777183C2semidirect
5. #23777178C2semidirect
6. #23777173C2semidirect
7. #23777170C2semidirect
8. #23777158C2semidirect
9. D4×#11929625C2semidirect
10. #23776887C2semidirect
11. #23776732C2semidirect
12. C2×#19099114C2semidirect
13. #532×D79C2semidirect
14. C4×#41×D79C2semidirect
15. C79×#3499C2semidirect
17. C2×#14579209C22semidirect
18. C2×#14579209C22semidirect
19. C2×#14579207C22semidirect
20. C2×#14579207C22semidirect
21. C2×#14579207C22semidirect
22. C22×#11929625C22semidirect
23. C22×#11929625C22semidirect
25. C2×#41×D79C22semidirect
26. C2×#41×D79C22semidirect
27. #19099235C22semidirect
28. #19099234C22semidirect
29. #19099228C22semidirect
30. #19099224C22semidirect
31. #19099223C22semidirect
32. #19099216C22semidirect
33. #19099214C22semidirect
34. #19099205C22semidirect
35. #19099204C22semidirect
36. #19099201C22semidirect
37. D4×D316C22semidirect
38. D4×D316C22semidirect
39. #19099197C22semidirect
40. #19099143C22semidirect
41. #19099138C22semidirect
42. #19099137C22semidirect
43. #19099132C22semidirect
44. #19099131C22semidirect
45. #19099127C22semidirect
46. #19099124C22semidirect
47. #19099114C22semidirect
48. #19099114C22semidirect
49. #19099114C22semidirect
50. #19099114C22semidirect
51. #19099114C22semidirect
52. #19099114C22semidirect
53. #19099113C22semidirect
54. #19099112C22semidirect
55. #19099111C22semidirect
56. #19099110C22semidirect
57. #19099109C22semidirect
58. #19099108C22semidirect
59. C4⋊Q8×D79C22semidirect
60. C2×#14579158C22semidirect
61. #127×D79C22semidirect
62. C2×#14579150C22semidirect
63. #124×D79C22semidirect
64. #19099076C22semidirect
65. #19099071C22semidirect
66. C2×#14579136C22semidirect
67. #121×D79C22semidirect
68. #41×Dic79C22semidirect
69. C4×#11929625C22semidirect
70. C4×#11929624C22semidirect
71. #19099031C22semidirect
72. C4×#11929623C22semidirect
73. C4×Q8×D79C22semidirect
74. C2×#14579123C22semidirect
75. C4×D4×D79C22semidirect
76. C4×D4×D79C22semidirect
77. #117×D79C22semidirect
78. C2×C42×D79C22semidirect
79. C2×2−1+4×C79C22semidirect
80. D4×Q8×C79C22semidirect
81. #547×C79C22semidirect
82. #536×C79C22semidirect
83. #532×C79C22semidirect
84. C2×C4⋊Q8×C79C22semidirect
85. C4×#41×C79C22semidirect
110. #41×D79D4semidirect
222. #11929625C2×D4semidirect
227. #11929624C2×D4semidirect
230. #11929623C2×D4semidirect
236. Q8×D79C2×D4semidirect
258. D4×D79C2×D4semidirect
265. C2×C4×D79C2×D4semidirect
297. #41×C79C2×D4semidirect
399. C4×C79#585semidirect
417. #3499D79semidirect
428. C79#62812semidirect
432. C2×2−1+4C2×D79semidirect
444. D4×Q8C2×D79semidirect
449. #547C2×D79semidirect
459. #536C2×D79semidirect
476. #532C2×D79semidirect
478. C2×C4⋊Q8C2×D79semidirect
492. C4×#41C2×D79semidirect
646. #41D4×D79semidirect
817. C4#19099400semidirect

Maximal subgroups

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

subgroupindex
C2×#190994002
#237771942
#237771892
#237771832
#237771782
#237771732
#237771702
#237771582
D4×#119296252
#237768872
#237767322
C2×#190991142
#532×D792
C4×#41×D792
C79×#34992
#6281279