Finite Group Databasebeta

← #3499×D79 #35196677

Subgroups — #3499×D79 #35196677

Order 20224.

11126 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D79C212yesmaximal, complemented
2#23777185C211yesmaximal, characteristic, complemented
3#23777184C214yesmaximal, complemented
4#23777183C213yesmaximal, complemented
5#23777182C216yesmaximal, complemented
6#23777181C212yesmaximal, complemented
7#23777180C213yesmaximal, complemented
8#23777179C2112yesmaximal, complemented
9D4×Q8×D79C214yesmaximal, complemented
10#547×D79C2112yesmaximal, complemented
11#536×D79C216yesmaximal, complemented
12#532×D79C213yesmaximal, complemented
13C2×C4⋊Q8×D79C213yesmaximal, complemented
14C4×#41×D79C211yesmaximal, characteristic, complemented
15C79×#3499C211yesmaximal, characteristic, complemented
16C2×#14579209C2216yescomplemented
17C2×#14579209C2214yescomplemented
18C2×#14579208C22112yescomplemented
19C2×#14579208C2216yescomplemented
20C2×#14579208C2212yescomplemented
212−1+4×D79—232no—
22C2×#41×D79C22112yes—
23C2×#41×D79C2216yes—
24C2×#41×D79C2211yescharacteristic
25C22×Q8×D79C2214yes—
26C22×Q8×D79C2216yes—
27Q8×D316C2214yescomplemented
28D4×Dic158C22112yescomplemented
29#19099228C22112yescomplemented
30Q8×C22⋊D79C2218yescomplemented
31#19099226C22124yescomplemented
32#19099218C22112yescomplemented
33#19099217C22112yescomplemented
34#19099216C22112yescomplemented
35#19099215C22124yescomplemented
36#19099214C22124yescomplemented
37#19099213C22124yescomplemented
38#19099212C22124yescomplemented
39#19099211C22148yescomplemented
40#19099139C2216yescomplemented
41#19099138C22112yescomplemented
42#19099137C2216yescomplemented
43#19099136C22124yescomplemented
44#19099135C22124yescomplemented
45#19099134C2216yescomplemented
46#19099133C22112yescomplemented
47#19099114C2213yescomplemented
48#19099113C2213yescomplemented
49#19099112C2216yescomplemented
50#19099111C2213yescomplemented
51#19099110C22112yescomplemented
52#19099109C2216yescomplemented
53#19099108C22112yescomplemented
54C2×#14579161C2213yescomplemented
55C2×#14579160C22112yescomplemented
56C2×#14579159C2216yescomplemented
57C4⋊Q8×D79C22112yes—
58C4⋊Q8×D79C2213yes—
59C4⋊Q8×D79C2216yes—
60C4⋊Q8×D79C22112yescomplemented
61C4⋊Q8×D79C2216yescomplemented
62C4⋊Q8×D79C2216yescomplemented
63#127×D79C2211yescharacteristic
64#124×D79C2216yes—
65#123×D79C22124yes—
66C22⋊Q8×D79C22124yes—
67#121×D79C22112yes—
68#41×Dic79C2211yescharacteristic, complemented
69C4×#11929625C2212yescomplemented
70C4×#11929624C2213yescomplemented
71#19099031C2213yescomplemented
72C4×#11929623C2216yescomplemented
73C4×Q8×D79C2212yes—
74C4×D4×D79C2216yes—
75C4×D4×D79C22112yes—
76#117×D79C2213yes—
77C2×C4⋊C4×D79C22112yes—
78C2×C42×D79C2213yes—
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—232no—
87#14579209—248no—
88#14579208—216no—
89#14579208—248no—
90#14579208—296no—
91C2×#11929625C2316yes—
92C2×#11929625C23112yes—
93C2×#11929625C2311yescharacteristic
94C2×#11929624C23112yes—
95C2×#11929624C2316yes—
96C2×#11929624C23124yes—
97C2×#11929624C23112yes—
98C2×#11929624C2313yes—
99C2×#11929623C23124yes—
100C2×#11929623C23112yes—
101C2×#11929623C23112yes—
102C2×#11929623C2316yes—
103C2×#11929623C2313yes—
104#41×D79—296no—
105#41×D79—248no—
106#41×D79D4116yescomplemented
107C22×Dic158C2316yes—
108C22×Dic158C23112yes—
109C22×Dic158C23112yes—
110C2×Q8×D79—232no—
111C2×Q8×D79—248no—
112C2×Q8×D79C23112yes—
113C2×Q8×D79C23112yes—
114C2×Q8×D79C23112yes—
115C2×Q8×D79C2314yes—
116C2×Q8×D79C23112yes—
117C2×Q8×D79C2316yes—
118C2×Q8×D79C2311yescharacteristic
119C2×D4×D79C2314yes—
120C2×D4×D79C23112yes—
121C2×D4×D79C2312yes—
122C2×D4×D79C2313yes—
123C22×C4×D79C2316yes—
124C22×C4×D79C23112yes—
125C22×C4×D79C23112yes—
126C22×C4×D79C2313yes—
127#14579161C2316yes—
128#14579161C23112yes—
129#14579161C2313yes—
130#14579160C23124yes—
131#14579160C23124yes—
132#14579160C23124yes—
133#14579160C23112yes—
134#14579159C23112yes—
135#14579159C23124yes—
136#14579159C2316yes—
137#14579158C2311yescharacteristic
138#14579157C2314yes—
139#14579157C2312yes—
140#14579150C2316yes—
141#14579149C2316yes—
142#14579148C2316yes—
143#14579147C23124yes—
144#14579146C23148yes—
145#14579145C23124yes—
146#14579144C23124yes—
147#14579143C23148yes—
148#14579142C23124yes—
149#14579141C23124yes—
150#14579140C23124yes—
151#14579139C23148yes—
152#14579138C23148yes—
153#14579137C23124yes—
154#14579136C23112yes—
155#14579135C23112yes—
156#14579134C23124yes—
157#14579133C23124yes—
158#14579132C23112yes—
159Q8×Dic79C2312yes—
160C4×Dic158C2316yes—
161#14579126C2316yes—
162C4×D316C2316yes—
163C4×D316C23112yes—
164D4×Dic79C2316yes—
165D4×Dic79C23112yes—
166#14579123C23112yes—
167#14579123C2316yes—
168C4×C22⋊D79C23124yes—
169C4×C22⋊D79C23112yes—
170(C22⋊D79)⋊C4C23112yes—
171(C22⋊D79)⋊C4C23124yes—
172#14579120C2313yes—
173#14579119C2316yes—
174#14579118C2316yes—
175#14579117C2316yes—
176C2×C4⋊Dic79C23112yes—
177C2×Dic79⋊C4C23124yes—
178C4⋊C4×D79C23124yes—
179C4⋊C4×D79C23124yes—
180C4⋊C4×D79C23112yes—
181C4⋊C4×D79C23124yes—
182C4⋊C4×D79C2316yes—
183C22⋊C4×D79C2316yes—
184C22⋊C4×D79C23124yes—
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×D79C2414yes—
214C23×D79C2413yes—
215#11929625—248no—
216#11929625—224no—
217#11929625C2×D418yescomplemented
218#11929624—248no—
219#11929624—248no—
220#11929624—224no—
221#11929624—296no—
222#11929624C2×D4124yescomplemented
223#11929623—248no—
224#11929623—224no—
225#11929623—248no—
226#11929623—296no—
227#11929623C2×D4124yescomplemented
228C2×Dic158—248no—
229C2×Dic158—248no—
230C2×Dic158—224no—
231C2×Dic158C24124yes—
232C2×Dic158C24112yes—
233C2×Dic158C24112yes—
234C2×Dic158C2416yes—
235C2×Dic158C2413yes—
236Q8×D79—248no—
237Q8×D79—224no—
238Q8×D79—248no—
239Q8×D79—248no—
240Q8×D79—248no—
241Q8×D79—216no—
242Q8×D79C2×D418yes—
243C2×D316C24112yes—
244C2×D316C2412yes—
245C2×D316C2414yes—
246C2×D316C2413yes—
247C2×C22⋊D79C24112yes—
248C2×C22⋊D79C24112yes—
249C2×C22⋊D79C2414yes—
250C2×C22⋊D79C2418yes—
251C2×C22⋊D79C2416yes—
252D4×D79—28no—
253D4×D79—216no—
254D4×D79—248no—
255D4×D79C2×D4124yes—
256C22×Dic79C24112yes—
257C22×Dic79C24112yes—
258C22×Dic79C2416yes—
259C22×Dic79C2413yes—
260C2×C4×D79—248no—
261C2×C4×D79—224no—
262C2×C4×D79—248no—
263C2×C4×D79C2×D4124yes—
264C2×C4×D79C24112yes—
265C2×C4×D79C24124yes—
266C2×C4×D79C24112yes—
267C2×C4×D79C24112yes—
268C2×C4×D79C2416yes—
269C2×C4×D79C2416yes—
270C2×C4×D79C2416yes—
271C2×C4×D79C2411yescharacteristic
272C2×C4×D79C2413yes—
273C2×C4×D79C2413yes—
274C2×C4×D79C2413yes—
275C2×C4×D79C2412yes—
276C4⋊Dic79C24112yes—
277C4⋊Dic79C24124yes—
278C4⋊Dic79C2416yes—
279Dic79⋊C4C24124yes—
280Dic79⋊C4C24148yes—
281Dic79⋊C4C24112yes—
282C22⋊Dic79C2416yes—
283C22⋊Dic79C24124yes—
284(C2×D79)⋊C4C24112yes—
285(C2×D79)⋊C4C24124yes—
286(C2×D79)⋊C4C24124yes—
287C4×Dic79C2411yescharacteristic
288C4×Dic79C2412yes—
289C4×Dic79C2416yes—
290C4×Dic79C2413yes—
291C4×Dic79C2416yes—
292C4×Dic79C2416yes—
293C4×Dic79C2416yes—
294#41×C79—248no—
295#41×C79—224no—
296#41×C79C2×D418yescomplemented
297C2×Q8×C79—216no—
298C2×Q8×C79—224no—
299C2×Q8×C79C24112yes—
300C2×Q8×C79C2416yes—
301C2×Q8×C79C2411yescharacteristic
302C2×D4×C79C24112yes—
303C2×D4×C79C2412yes—
304C2×D4×C79C2414yes—
305C2×D4×C79C2413yes—
306C22×C4×C79C24112yes—
307C22×C4×C79C24112yes—
308C22×C4×C79C2416yes—
309C22×C4×C79C2413yes—
310C4⋊C4×C79C24112yes—
311C4⋊C4×C79C24124yes—
312C4⋊C4×C79C2416yes—
313C22⋊C4×C79C2416yes—
314C22⋊C4×C79C24124yes—
315C42×C79C2411yescharacteristic
316C42×C79C2413yes—
317C42×C79C2416yes—
318C23×C79C2514yes—
319C23×C79C2513yes—
320C22×D79—212no—
321C22×D79—28no—
322C22×D79—216no—
323C22×D79C22×D4112yes—
324C22×D79C2514yes—
325C22×D79C2513yes—
326C22×D79C2511yescharacteristic
327Q8×C79—224no—
328Q8×C79—212no—
329Q8×C79C22×D414yes—
330D4×C79—224no—
331D4×C79—24no—
332D4×C79—28no—
333D4×C79C22×D4112yes—
334C2×C4×C79—224no—
335C2×C4×C79—224no—
336C2×C4×C79—212no—
337C2×C4×C79C22×D4112yes—
338C2×C4×C79C2516yes—
339C2×C4×C79C25112yes—
340C2×C4×C79C2511yescharacteristic
341C2×C4×C79C2513yes—
342C2×C4×C79C2512yes—
343C22⋊D79—224no—
344C22⋊D79—224no—
345C22⋊D79—28no—
346C22⋊D79—216no—
347C22⋊D79C22×D4124yes—
348C2×Dic79—224no—
349C2×Dic79—224no—
350C2×Dic79—212no—
351C2×Dic79C22×D4112yes—
352C2×Dic79C2516yes—
353C2×Dic79C25112yes—
354C2×Dic79C2511yescharacteristic
355C2×Dic79C2513yes—
356C2×Dic79C2512yes—
357D316—224no—
358D316—24no—
359D316—28no—
360D316C22×D4112yes—
361C4×D79—224no—
362C4×D79—248no—
363C4×D79—212no—
364C4×D79—224no—
365C4×D79—212no—
366C4×D79—224no—
367C4×D79—212no—
368C4×D79C22×D4112yes—
369C4×D79C22×D414yes—
370C4×D79C22×D4112yes—
371C4×D79C22×D4112yes—
372C4×D792−1+418yescomplemented
373Dic158—224no—
374Dic158—212no—
375Dic158—224no—
376Dic158—248no—
377Dic158C22×D4112yes—
378C22×C79—26no—
379C22×C79—24no—
380C22×C79—28no—
381C22×C79C23×D416yes—
382C22×C79C2611yescharacteristic
383C2×D79—26no—
384C2×D79—224no—
385C2×D79—24no—
386C2×D79—28no—
387C2×D79—416no—
388C2×D79C23×D416yes—
389C2×D79C23×D412yes—
390C2×D79C2×2−1+414yes—
391C4×C79—212no—
392C4×C79—26no—
393C4×C79C23×D416yes—
394C4×C79C23×D412yes—
395C4×C79C2×2−1+414yescomplemented
396Dic79—212no—
397Dic79—26no—
398Dic79C23×D412yes—
399Dic79C23×D416yes—
400Dic79C2×2−1+414yescomplemented
401C2×#3499—791nomaximal, Sylow
402C2×C79—26no—
403C2×C79—44no—
404C2×C79C24×D411yescharacteristic
405C2×C79C22×2−1+412yes—
406D79—26no—
407D79—44no—
408D79#349914yesdirect product factor
409C22×2−1+4—792no—
410#3499—792no—
411#3499—794no—
412#3499—7912no—
413#3499—796no—
414#3499—793no—
415#3499—793no—
416#3499—791no—
417#3499D7911yescharacteristic, direct product factor
418C2×D4×Q8—794no—
419C2×#547—7912no—
420C2×#536—796no—
421C2×#532—793no—
422C22×C4⋊Q8—793no—
423C2×C4×#41—791no—
424C79C2×#349911yescharacteristic, complemented, Sylow
425C2×2−1+4—796no—
426C2×2−1+4—7912no—
427C2×2−1+4—792no—
428C2×2−1+4—794no—
429C2×2−1+4—796no—
430C2×2−1+4—15832no—
431C2×2−1+4C2×D7912yescomplemented
432C22×#41—791no—
433C22×#41—796no—
434C22×#41—7912no—
435C23×Q8—796no—
436C23×Q8—794no—
437D4×Q8—798no—
438D4×Q8—7912no—
439D4×Q8—7924no—
440D4×Q8—794no—
441D4×Q8—7912no—
442D4×Q8C2×D7914yescomplemented
443#547—7924no—
444#547—7912no—
445#547—7948no—
446#547—7924no—
447#547—7924no—
448#547—7912no—
449#547—7912no—
450#547—7924no—
451#547C2×D79112yescomplemented
452#536—796no—
453#536—796no—
454#536—7912no—
455#536—7912no—
456#536—7924no—
457#536—7924no—
458#536—796no—
459#536C2×D7916yescomplemented
460#532—796no—
461#532—793no—
462#532—793no—
463#532—796no—
464#532—7912no—
465#532—7912no—
466#532—793no—
467#532C2×D7913yescomplemented
468C2×C4⋊Q8—796no—
469C2×C4⋊Q8—793no—
470C2×C4⋊Q8—796no—
471C2×C4⋊Q8—7912no—
472C2×C4⋊Q8—796no—
473C2×C4⋊Q8—796no—
474C2×C4⋊Q8—7912no—
475C2×C4⋊Q8—7912no—
476C2×C4⋊Q8—793no—
477C2×C4⋊Q8C2×D7913yescomplemented
478C2×#127—791no—
479C2×#124—796no—
480C2×#123—7924no—
481C2×C22⋊Q8—7924no—
482C2×#121—7912no—
483C4×#41—791no—
484C4×#41—792no—
485C4×#41—796no—
486C4×#41—793no—
487C4×#41—793no—
488C4×#41C2×D7911yescharacteristic, complemented
489C2×C4×Q8—792no—
490C2×C4×D4—796no—
491C2×C4×D4—7912no—
492C2×#117—793no—
493C22×C4⋊C4—7912no—
494C22×C42—793no—
4952−1+4—216no—
4962−1+4—15832no—
4972−1+4—15848no—
4982−1+4—15896no—
4992−1+4—15848no—
5002−1+4—15816no—
501C2×#41—7916no—
502C2×#41—791no—
503C2×#41—796no—
504C2×#41—7912no—
505C2×#41—793no—
506C2×#41—7912no—
507C2×#41—796no—
508C2×#41—7912no—
509C2×#41—7924no—
510C2×#41—793no—
511C2×#41—7912no—
512C2×#41—796no—
513C2×#41—7912no—
514C2×#41—7924no—
515C2×#41—15848no—
516C2×#41—15896no—
517C2×#41C22×D7916yes—
518C2×#41C22×D79112yes—
519C2×#41C22×D7911yescharacteristic
520C22×Q8—791no—
521C22×Q8—7912no—
522C22×Q8—796no—
523C22×Q8—7912no—
524C22×Q8—7912no—
525C22×Q8—7912no—
526C22×Q8—794no—
527C22×Q8—7912no—
528C22×Q8—796no—
529C22×Q8—7912no—
530C22×Q8—15848no—
531C22×Q8—15832no—
532C22×Q8C22×D7916yes—
533C22×Q8C22×D7914yes—
534C22×D4—793no—
535C22×D4—794no—
536C22×D4—7912no—
537C22×D4—792no—
538C23×C4—793no—
539C23×C4—796no—
540C23×C4—7912no—
541C23×C4—7912no—
542C4⋊Q8—796no—
543C4⋊Q8—7912no—
544C4⋊Q8—7924no—
545C4⋊Q8—7912no—
546C4⋊Q8—7924no—
547C4⋊Q8—7924no—
548C4⋊Q8—7924no—
549C4⋊Q8—793no—
550C4⋊Q8—796no—
551C4⋊Q8—7912no—
552C4⋊Q8C22×D7913yes—
553C4⋊Q8C22×D7916yes—
554C4⋊Q8C22×D79112yes—
555#127—792no—
556#127—794no—
557#127—791no—
558#127C22×D7911yescharacteristic
559#124—796no—
560#124—796no—
561#124—7924no—
562#124—796no—
563#124C22×D7916yes—
564#123—7924no—
565#123—7924no—
566#123—7948no—
567#123—7948no—
568#123—7924no—
569#123C22×D79124yes—
570C22⋊Q8—7924no—
571C22⋊Q8—7924no—
572C22⋊Q8—7948no—
573C22⋊Q8—7924no—
574C22⋊Q8—7948no—
575C22⋊Q8C22×D79124yes—
576#121—7912no—
577#121—7924no—
578#121—7912no—
579#121—7912no—
580#121—7924no—
581#121C22×D79112yes—
582C4×Q8—792no—
583C4×Q8—796no—
584C4×Q8—796no—
585C4×Q8C22×D7912yes—
586C4×D4—796no—
587C4×D4—7912no—
588C4×D4—7912no—
589C4×D4—7924no—
590C4×D4—796no—
591C4×D4—7912no—
592C4×D4—7912no—
593C4×D4—7924no—
594C4×D4—796no—
595C4×D4—7912no—
596C4×D4C22×D7916yes—
597C4×D4C22×D79112yes—
598#117—793no—
599#117—796no—
600#117—796no—
601#117—796no—
602#117C22×D7913yes—
603C2×C4⋊C4—7924no—
604C2×C4⋊C4—7912no—
605C2×C4⋊C4—7912no—
606C2×C4⋊C4—7924no—
607C2×C4⋊C4—7924no—
608C2×C4⋊C4—7924no—
609C2×C4⋊C4—796no—
610C2×C4⋊C4C22×D79112yes—
611C2×C22⋊C4—796no—
612C2×C22⋊C4—7924no—
613C2×C42—796no—
614C2×C42—793no—
615C2×C42—793no—
616C2×C42—796no—
617C2×C42—796no—
618C2×C42—793no—
619C2×C42—793no—
620C2×C42—791no—
621C2×C42C22×D7913yes—
622C24—793no—
623C24—794no—
624#41—248no—
625#41—224no—
626#41—798no—
627#41—7924no—
628#41—7924no—
629#41—15848no—
630#41—15896no—
631#41—15848no—
632#41—15848no—
633#41—15824no—
634#41—15824no—
635#41—15896no—
636#41—15848no—
637#41—15848no—
638#41—15824no—
639#41D4×D7918yescomplemented
640C2×Q8—216no—
641C2×Q8—224no—
642C2×Q8—798no—
643C2×Q8—793no—
644C2×Q8—7924no—
645C2×Q8—7912no—
646C2×Q8—7912no—
647C2×Q8—796no—
648C2×Q8—15848no—
649C2×Q8—15848no—
650C2×Q8—15824no—
651C2×Q8—15848no—
652C2×Q8—15848no—
653C2×Q8—15848no—
654C2×Q8—15848no—
655C2×Q8—15816no—
656C2×Q8—15824no—
657C2×Q8C23×D79112yes—
658C2×Q8C23×D7916yes—
659C2×Q8C23×D7911yescharacteristic
660C2×D4—796no—
661C2×D4—7924no—
662C2×D4—798no—
663C2×D4—7912no—
664C2×D4—7912no—
665C2×D4—794no—
666C2×D4—793no—
667C2×D4—794no—
668C2×D4—7912no—
669C2×D4—792no—
670C2×D4—15816no—
671C2×D4—1588no—
672C2×D4—15848no—
673C2×D4C23×D7914yes—
674C2×D4C23×D79112yes—
675C2×D4C23×D7912yes—
676C2×D4C23×D7913yes—
677C22×C4—793no—
678C22×C4—792no—
679C22×C4—791no—
680C22×C4—793no—
681C22×C4—793no—
682C22×C4—793no—
683C22×C4—7924no—
684C22×C4—796no—
685C22×C4—7912no—
686C22×C4—7912no—
687C22×C4—796no—
688C22×C4—796no—
689C22×C4—796no—
690C22×C4—7912no—
691C22×C4—7924no—
692C22×C4—7912no—
693C22×C4—7912no—
694C22×C4—15824no—
695C22×C4—15848no—
696C22×C4—15848no—
697C22×C4C23×D7916yes—
698C22×C4C23×D79112yes—
699C22×C4C23×D79112yes—
700C22×C4C23×D7913yes—
701C4⋊C4—7924no—
702C4⋊C4—7948no—
703C4⋊C4—7912no—
704C4⋊C4—7912no—
705C4⋊C4—7924no—
706C4⋊C4—796no—
707C4⋊C4C23×D79112yes—
708C4⋊C4C23×D79124yes—
709C4⋊C4C23×D7916yes—
710C22⋊C4—796no—
711C22⋊C4—7924no—
712C22⋊C4—7912no—
713C22⋊C4—7924no—
714C22⋊C4—7924no—
715C22⋊C4C23×D7916yes—
716C22⋊C4C23×D79124yes—
717C42—791no—
718C42—792no—
719C42—796no—
720C42—793no—
721C42—796no—
722C42—796no—
723C42—796no—
724C42C23×D7911yescharacteristic
725C42C23×D7913yes—
726C42C23×D7916yes—
727C23—791no—
728C23—793no—
729C23—7912no—
730C23—794no—
731C23—1588no—
732C23—15816no—
733C23—15812no—
734C23C24×D7914yes—
735C23C24×D7913yes—
736Q8—224no—
737Q8—212no—
738Q8—7912no—
739Q8—15824no—
740Q8—15848no—
741Q8—15824no—
742Q8—15812no—
743Q8C2×D4×D7914yes—
744D4—224no—
745D4—28no—
746D4—24no—
747D4—7924no—
748D4—7912no—
749D4—15824no—
750D4—15816no—
751D4—1588no—
752D4—15824no—
753D4—15824no—
754D4—1588no—
755D4—1584no—
756D4C2×D4×D79112yes—
757C2×C4—224no—
758C2×C4—212no—
759C2×C4—224no—
760C2×C4—792no—
761C2×C4—791no—
762C2×C4—793no—
763C2×C4—7912no—
764C2×C4—798no—
765C2×C4—794no—
766C2×C4—7912no—
767C2×C4—7912no—
768C2×C4—7912no—
769C2×C4—796no—
770C2×C4—7912no—
771C2×C4—15824no—
772C2×C4—15812no—
773C2×C4—15824no—
774C2×C4—15848no—
775C2×C4—15812no—
776C2×C4—15824no—
777C2×C4—15812no—
778C2×C4—15824no—
779C2×C4—15812no—
780C2×C4—15824no—
781C2×C4C2×D4×D79112yes—
782C2×C4C24×D7916yes—
783C2×C4C24×D79112yes—
784C2×C4C24×D7912yes—
785C2×C4C24×D7911yescharacteristic
786C2×C4C24×D7913yes—
787C22—26no—
788C22—24no—
789C22—28no—
790C22—31616no—
791C22—792no—
792C22—794no—
793C22—796no—
794C22—15824no—
795C22—1584no—
796C22—1588no—
797C22—1586no—
798C22C22×D4×D7916yes—
799C22C25×D7911yescharacteristic
800C4—212no—
801C4—26no—
802C4—792no—
803C4—796no—
804C4—794no—
805C4—15812no—
806C4—1586no—
807C4C22×D4×D7916yes—
808C4C22×D4×D7912yes—
809C42−1+4×D7914yescomplemented
810C2—26no—
811C2—44no—
812C2—3164no—
813C2—794no—
814C2—1586no—
815C2C23×D4×D7911yescharacteristic
816C2C2×2−1+4×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3499C2
hypercenter#3499D79
hypocenterC79C2×#3499
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D79C2semidirect
2. #23777185C2semidirect
3. #23777184C2semidirect
4. #23777183C2semidirect
5. #23777182C2semidirect
6. #23777181C2semidirect
7. #23777180C2semidirect
8. #23777179C2semidirect
9. D4×Q8×D79C2semidirect
10. #547×D79C2semidirect
11. #536×D79C2semidirect
12. #532×D79C2semidirect
13. C2×C4⋊Q8×D79C2semidirect
14. C4×#41×D79C2semidirect
15. C79×#3499C2semidirect
16. C2×#14579209C22semidirect
17. C2×#14579209C22semidirect
18. C2×#14579208C22semidirect
19. C2×#14579208C22semidirect
20. C2×#14579208C22semidirect
27. Q8×D316C22semidirect
28. D4×Dic158C22semidirect
29. #19099228C22semidirect
30. Q8×C22⋊D79C22semidirect
31. #19099226C22semidirect
32. #19099218C22semidirect
33. #19099217C22semidirect
34. #19099216C22semidirect
35. #19099215C22semidirect
36. #19099214C22semidirect
37. #19099213C22semidirect
38. #19099212C22semidirect
39. #19099211C22semidirect
40. #19099139C22semidirect
41. #19099138C22semidirect
42. #19099137C22semidirect
43. #19099136C22semidirect
44. #19099135C22semidirect
45. #19099134C22semidirect
46. #19099133C22semidirect
47. #19099114C22semidirect
48. #19099113C22semidirect
49. #19099112C22semidirect
50. #19099111C22semidirect
51. #19099110C22semidirect
52. #19099109C22semidirect
53. #19099108C22semidirect
54. C2×#14579161C22semidirect
55. C2×#14579160C22semidirect
56. C2×#14579159C22semidirect
60. C4⋊Q8×D79C22semidirect
61. C4⋊Q8×D79C22semidirect
62. C4⋊Q8×D79C22semidirect
68. #41×Dic79C22semidirect
69. C4×#11929625C22semidirect
70. C4×#11929624C22semidirect
71. #19099031C22semidirect
72. C4×#11929623C22semidirect
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
106. #41×D79D4semidirect
217. #11929625C2×D4semidirect
222. #11929624C2×D4semidirect
227. #11929623C2×D4semidirect
296. #41×C79C2×D4semidirect
372. C4×D792−1+4semidirect
395. C4×C79C2×2−1+4semidirect
400. Dic79C2×2−1+4semidirect
408. D79#3499direct (N × H)
417. #3499D79direct (N × H)
424. C79C2×#3499semidirect
431. C2×2−1+4C2×D79semidirect
442. D4×Q8C2×D79semidirect
451. #547C2×D79semidirect
459. #536C2×D79semidirect
467. #532C2×D79semidirect
477. C2×C4⋊Q8C2×D79semidirect
488. C4×#41C2×D79semidirect
639. #41D4×D79semidirect
809. C42−1+4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D792
#237771852
#237771842
#237771832
#237771822
#237771812
#237771802
#237771792
D4×Q8×D792
#547×D792
#536×D792
#532×D792
C2×C4⋊Q8×D792
C4×#41×D792
C79×#34992
C2×#349979