Finite Group Databasebeta

← #35197387

Subgroups — #35197387

Order 20224.

11222 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099400C212yesmaximal, complemented
2#23777171C211yesmaximal, characteristic, complemented
3#23777167C212yesmaximal, complemented
4#23777163C216yesmaximal, complemented
5#23777162C216yesmaximal, complemented
6#23777079C218yesmaximal, complemented
7#23777077C218yesmaximal, complemented
8#23777068C218yesmaximal, complemented
9#23777066C218yesmaximal, complemented
10#23776727C216yesmaximal, complemented
11#537×D79C216yesmaximal, complemented
12C2×#19099045C211yesmaximal, characteristic, complemented
13C79×#3497C211yesmaximal, characteristic, complemented
14#19099400—232no—
15C2×#14579209C2218yescomplemented
16C2×#14579209C2212yescomplemented
17C2×#14579207C2218yescomplemented
18C2×#14579207C22112yescomplemented
19C22×#11929625C2211yescharacteristic
20C22×#11929625C2218yescomplemented
21C2×#41×D79C2218yescomplemented
22C2×#41×D79C22112yescomplemented
23#19099235C2214yescomplemented
24#19099232C2218yescomplemented
25Q8×D316C2214yescomplemented
26Q8×C22⋊D79C2218yescomplemented
27#19099225C2218yescomplemented
28#19099224C2218yescomplemented
29#19099220C2218yescomplemented
30#19099218C22112yescomplemented
31#19099216C22112yescomplemented
32#19099215C22124yescomplemented
33#19099210C22124yescomplemented
34#19099209C22124yescomplemented
35#19099206C22124yescomplemented
36#19099204C22124yescomplemented
37D4×D316C22112yescomplemented
38#19099198C22112yescomplemented
39#19099197C22124yescomplemented
40#19099144C2216yescomplemented
41#19099143C22124yescomplemented
42#19099142C22124yescomplemented
43#19099141C22112yescomplemented
44#19099140C22112yescomplemented
45#19099140C2214yescomplemented
46#19099138C22112yescomplemented
47#19099133C22112yescomplemented
48#19099131C22112yescomplemented
49#19099126C22112yescomplemented
50#19099121C22112yescomplemented
51#19099121C22112yescomplemented
52#19099113C2216yescomplemented
53#19099109C22112yescomplemented
54#19099072C22124yescomplemented
55#19099072C22124yescomplemented
56C22⋊Q8×D79C22124yescomplemented
57#121×D79C22124yescomplemented
58#121×D79C22124yescomplemented
59#19099045C2218yescomplemented
60#19099045C2218yescomplemented
61C2×Q8×Dic79C2211yescharacteristic, complemented
62C2×C4×D316C2213yescomplemented
63C2×#14579123C2213yescomplemented
64C2×#14579118C2213yescomplemented
65C2×C4⋊C4×D79C2213yescomplemented
66C2×2−1+4×C79C2212yescomplemented
67#550×C79C2214yescomplemented
68D4×Q8×C79C2214yescomplemented
69#548×C79C2218yescomplemented
70#537×C79C2216yescomplemented
71#532×C79C2216yescomplemented
72C2×C4×Q8×C79C2211yescharacteristic, complemented
73#14579209—216no—
74#14579209—264no—
75#14579207—264no—
76#14579207—296no—
77C2×#11929625—264no—
78C2×#11929625D4116yescomplemented
79C2×#11929625C23112yes—
80C2×#11929625C23124yes—
81C2×#11929625C2318yes—
82C2×#11929625C2318yes—
83C2×#11929624C23112yes—
84C2×#11929624C23124yes—
85C2×#11929624C23124yes—
86C2×#11929623C2318yes—
87C2×#11929623C23112yes—
88#41×D79—264no—
89#41×D79—296no—
90C2×Q8×D79C23112yes—
91C2×Q8×D79C2318yes—
92C22×D316C23124yes—
93C22×D316C2313yes—
94C2×D4×D79C23124yes—
95C2×D4×D79C23124yes—
96C2×D4×D79C23112yes—
97C2×D4×D79C23124yes—
98C22×C4×D79C23124yes—
99C22×C4×D79C2316yes—
100C22×C4×D79C2313yes—
101#14579161C2316yes—
102#14579159C23112yes—
103#14579158C2316yes—
104#14579157C23112yes—
105#14579150C23112yes—
106#14579149C23112yes—
107#14579148C23112yes—
108#14579146C23124yes—
109#14579146C23124yes—
110#14579143C23124yes—
111#14579143C23124yes—
112#14579141C23124yes—
113#14579140C23124yes—
114#14579139C2318yes—
115#14579139C23124yes—
116#14579138C23124yes—
117#14579138C2318yes—
118#14579137C23124yes—
119#14579136C23124yes—
120#14579136C23124yes—
121#14579135C23112yes—
122#14579135C2314yes—
123#14579135C23124yes—
124#14579134C23124yes—
125#14579134C2318yes—
126#14579134C23148yes—
127#14579133C23124yes—
128#14579133C23124yes—
129#14579133C2318yes—
130#14579133C2318yes—
131#14579132C23124yes—
132#14579132C23124yes—
133#14579131C23124yes—
134#14579131C23124yes—
135#14579129C23124yes—
136#14579129C23124yes—
137Q8×Dic79C2318yes—
138C4×D316C23112yes—
139C4×D316C23112yes—
140C4×D316C23112yes—
141C4×D316C23112yes—
142#14579123C23124yes—
143C4×C22⋊D79C23124yes—
144C4×C22⋊D79C23124yes—
145#14579118C23112yes—
146#14579118C23112yes—
147C2×C4⋊Dic79C2313yes—
148C2×Dic79⋊C4C2313yes—
149C2×Dic79⋊C4C2311yescharacteristic
150C4⋊C4×D79C23124yes—
151C4⋊C4×D79C23124yes—
152C2×(C2×D79)⋊C4C2313yes—
153C2×(C2×D79)⋊C4C2313yes—
154C22⋊C4×D79C23148yes—
155C2×C4×Dic79C2313yes—
1562−1+4×C79—216no—
157C2×#41×C79C23112yes—
158C2×#41×C79C2318yes—
159C22×Q8×C79C2318yes—
160C22×Q8×C79C2311yescharacteristic
161C4⋊Q8×C79C2316yes—
162#127×C79C2316yes—
163#124×C79C23112yes—
164C22⋊Q8×C79C23124yes—
165#121×C79C2314yes—
166#121×C79C23112yes—
167#121×C79C23124yes—
168C4×Q8×C79C2314yes—
169C4×Q8×C79C2314yes—
170C4×D4×C79C23112yes—
171C4×D4×C79C23112yes—
172C2×C4⋊C4×C79C2313yes—
173C2×C42×C79C2313yes—
174C23×D79C24124yes—
175C23×D79C2413yes—
176#11929625—296no—
177#11929625—248no—
178#11929625—232no—
179#11929625C2×D4164yescomplemented
180#11929624—296no—
181#11929624—296no—
182#11929624—248no—
183#11929623—232no—
184#11929623—248no—
185C2×Dic158C2418yes—
186C2×Dic158C24112yes—
187Q8×D79—248no—
188Q8×D79—232no—
189C2×D316—296no—
190C2×D316C2×D4124yescomplemented
191C2×D316C24124yes—
192C2×D316C24112yes—
193C2×D316C2414yes—
194C2×D316C24112yes—
195C2×D316C24112yes—
196C2×C22⋊D79C24124yes—
197C2×C22⋊D79C2418yes—
198C2×C22⋊D79C2418yes—
199C2×C22⋊D79C2418yes—
200C2×C22⋊D79C24124yes—
201D4×D79—296no—
202D4×D79—248no—
203D4×D79—296no—
204D4×D79—824no—
205C22×Dic79C2418yes—
206C22×Dic79C2411yescharacteristic
207C22×Dic79C2413yes—
208C22×Dic79C2411yescharacteristic
209C2×C4×D79—296no—
210C2×C4×D79—86no—
211C2×C4×D79C2×D4124yescomplemented
212C2×C4×D79C24124yes—
213C2×C4×D79C24124yes—
214C2×C4×D79C2418yes—
215C2×C4×D79C24124yes—
216C2×C4×D79C24112yes—
217C4⋊Dic79C24112yes—
218C4⋊Dic79C24112yes—
219C4⋊Dic79C2414yes—
220Dic79⋊C4C24112yes—
221Dic79⋊C4C24124yes—
222Dic79⋊C4C2412yes—
223Dic79⋊C4C2412yes—
224Dic79⋊C4C2418yes—
225C22⋊Dic79C24124yes—
226C22⋊Dic79C2418yes—
227(C2×D79)⋊C4C24124yes—
228(C2×D79)⋊C4C24124yes—
229(C2×D79)⋊C4C24112yes—
230(C2×D79)⋊C4C2416yes—
231(C2×D79)⋊C4C2416yes—
232(C2×D79)⋊C4C2418yes—
233(C2×D79)⋊C4C2418yes—
234C4×Dic79C24112yes—
235#41×C79—232no—
236#41×C79—248no—
237C2×Q8×C79—232no—
238C2×Q8×C79C2×D418yescomplemented
239C2×Q8×C79C24112yes—
240C2×Q8×C79C2414yes—
241C2×D4×C79C2418yes—
242C2×D4×C79C24112yes—
243C2×D4×C79C2414yes—
244C2×D4×C79C24112yes—
245C22×C4×C79C24124yes—
246C22×C4×C79C2411yescharacteristic
247C22×C4×C79C2413yes—
248C22×C4×C79C2413yes—
249C4⋊C4×C79C24112yes—
250C4⋊C4×C79C2414yes—
251C4⋊C4×C79C24112yes—
252C22⋊C4×C79C2418yes—
253C22⋊C4×C79C24124yes—
254C42×C79C2416yes—
255C42×C79C2416yes—
256C23×C79C2518yes—
257C23×C79C2511yescharacteristic
258C22×D79—248no—
259C22×D79—43no—
260C22×D79—43no—
261C22×D79—424no—
262C22×D79—424no—
263C22×D79C22×D4112yes—
264C22×D79C2518yes—
265C22×D79C2516yes—
266Q8×C79—224no—
267Q8×C79C22×D4116yes—
268D4×C79—216no—
269D4×C79—224no—
270D4×C79—412no—
271D4×C79—44no—
272C2×C4×C79—248no—
273C2×C4×C79—43no—
274C2×C4×C79—41no—
275C2×C4×C79C22×D4112yes—
276C2×C4×C79C2511yescharacteristic
277C2×C4×C79C2511yescharacteristic
278C2×C4×C79C2516yes—
279C2×C4×C79C2518yes—
280C2×C4×C79C2516yes—
281C22⋊D79—216no—
282C22⋊D79—248no—
283C22⋊D79—216no—
284C22⋊D79—424no—
285C22⋊D79—48no—
286C2×Dic79—216no—
287C2×Dic79—43no—
288C2×Dic79—41no—
289C2×Dic79C22×D414yes—
290C2×Dic79C2512yes—
291C2×Dic79C2516yes—
292C2×Dic79C2518yes—
293C2×Dic79C2512yes—
294D316—248no—
295D316—224no—
296D316—412no—
297D316—44no—
298D316C22×D4148yes—
299C4×D79—248no—
300C4×D79—248no—
301C4×D79—216no—
302C4×D79—424no—
303C4×D79C22×D4148yes—
304Dic158—224no—
305Dic158—216no—
306C22×C79—21no—
307C22×C79—21no—
308C22×C79—28no—
309C22×C79—28no—
310C22×C79—28no—
311C22×C79C23×D412yes—
312C22×C79C2611yescharacteristic
313C2×D79—26no—
314C2×D79—26no—
315C2×D79—28no—
316C2×D79—28no—
317C2×D79—28no—
318C2×D79—412no—
319C2×D79—848no—
320C2×D79C23×D4112yes—
321C4×C79—28no—
322C4×C79—26no—
323C4×C79—21no—
324C4×C79—21no—
325C4×C79C23×D4112yes—
326Dic79—28no—
327Dic79—26no—
328Dic79—22no—
329Dic79C23×D414yes—
330#62853—791nomaximal, Sylow
331C2×C79—22no—
332C2×C79—48no—
333C2×C79C24×D411yescharacteristic
334C2×C79H(7,𝔽2)11yescharacteristic
335C2×C792−1+611yescharacteristic
336D79—212no—
337D79—48no—
338C2×#585—792no—
339#3497—792no—
340#3497—791no—
341#3497D7911yescharacteristic, complemented
342#3496—796no—
343#3496—796no—
344#3489—798no—
345#3489—798no—
346#3488—798no—
347#3488—798no—
348#3449—796no—
349C2×#537—796no—
350C2×#520—791no—
351C79#6285311yescharacteristic, complemented, Sylow
352#585—15832no—
353C2×2−1+4—798no—
354C2×2−1+4—792no—
355C2×2−1+4C2×D7912yescomplemented
356C2×H(5,𝔽2)—798no—
357C2×H(5,𝔽2)—7912no—
358C22×#41—7912no—
359C22×#41—798no—
360C22×#41—791no—
361C22×#41—798no—
362#550—798no—
363#550—794no—
364#550C2×D7914yescomplemented
365D4×Q8—798no—
366D4×Q8—794no—
367D4×Q8C2×D7914yescomplemented
368#548—798no—
369#548—798no—
370#548—798no—
371#548C2×D7918yescomplemented
372#547—7912no—
373#547—7924no—
374#547—7912no—
375#546—7924no—
376#546—7924no—
377#546—7924no—
378#546—7924no—
379D42—7912no—
380D42—7924no—
381D42—7912no—
382#537—7912no—
383#537—7924no—
384#537—7912no—
385#537—794no—
386#537—7924no—
387#537—796no—
388#537C2×D7916yescomplemented
389#536—7912no—
390#536—7912no—
391#535—7912no—
392#535—7912no—
393#534—7912no—
394#534—7912no—
395#532—7912no—
396#532—796no—
397#532C2×D7916yescomplemented
398#525—7924no—
399#525—7924no—
400C2×C22⋊Q8—7924no—
401C2×#121—7924no—
402C2×#121—7924no—
403#520—798no—
404#520—798no—
405C2×C4×Q8—791no—
406C2×C4×Q8C2×D7911yescharacteristic, complemented
407C2×C4×D4—793no—
408C2×C4×D4—793no—
409C2×#117—793no—
410C22×C4⋊C4—793no—
4112−1+4—216no—
4122−1+4—15864no—
4132−1+4—15816no—
414H(5,𝔽2)—15896no—
415H(5,𝔽2)—15864no—
416C2×#41—7916no—
417C2×#41—798no—
418C2×#41—7912no—
419C2×#41—7924no—
420C2×#41—798no—
421C2×#41—7912no—
422C2×#41—798no—
423C2×#41—7924no—
424C2×#41—7912no—
425C2×#41—7924no—
426C2×#41—15896no—
427C2×#41—15864no—
428C2×#41—15864no—
429C2×#41C22×D79112yes—
430C2×#41C22×D7918yes—
431C22×Q8—7912no—
432C22×Q8—798no—
433C22×Q8C22×D7918yes—
434C22×Q8C22×D7911yescharacteristic
435C22×D4—7924no—
436C22×D4—7924no—
437C22×D4—7912no—
438C22×D4—7924no—
439C22×D4—793no—
440C22×D4—7924no—
441C23×C4—793no—
442C23×C4—796no—
443C23×C4—7924no—
444C4⋊Q8—7912no—
445C4⋊Q8—796no—
446C4⋊Q8C22×D7916yes—
447#127—7912no—
448#127—796no—
449#127C22×D7916yes—
450#124—7912no—
451#124—7912no—
452#124—7912no—
453#124C22×D79112yes—
454#123—7924no—
455#123—7924no—
456#123—7924no—
457#123—7924no—
458C22⋊Q8—7924no—
459C22⋊Q8—7924no—
460C22⋊Q8—7924no—
461C22⋊Q8—7924no—
462C22⋊Q8—798no—
463C22⋊Q8—7924no—
464C22⋊Q8—798no—
465C22⋊Q8C22×D79124yes—
466#121—7924no—
467#121—7924no—
468#121—7924no—
469#121—7924no—
470#121—798no—
471#121—798no—
472#121—7912no—
473#121—7924no—
474#121—794no—
475#121—7924no—
476#121—7924no—
477#121—7924no—
478#121—7948no—
479#121—798no—
480#121C22×D79112yes—
481#121C22×D79124yes—
482#121C22×D7914yes—
483#120—7924no—
484#120—7924no—
485#120—7924no—
486#120—7924no—
487C4×Q8—798no—
488C4×Q8C22×D7914yes—
489C4×Q8C22×D7914yes—
490C4×D4—7924no—
491C4×D4—7924no—
492C4×D4—7924no—
493C4×D4—7912no—
494C4×D4—7912no—
495C4×D4—7912no—
496C4×D4—7912no—
497C4×D4C22×D79112yes—
498C4×D4C22×D79112yes—
499#117—7912no—
500#117—7912no—
501C2×C4⋊C4—793no—
502C2×C4⋊C4—793no—
503C2×C4⋊C4—791no—
504C2×C4⋊C4—7924no—
505C2×C4⋊C4—7924no—
506C2×C4⋊C4C22×D7913yes—
507C2×C22⋊C4—793no—
508C2×C22⋊C4—793no—
509C2×C22⋊C4—7948no—
510C2×C42—793no—
511C2×C42C22×D7913yes—
512C24—793no—
513C24—7924no—
514#41—232no—
515#41—248no—
516#41—7964no—
517#41—15896no—
518#41—15896no—
519#41—15832no—
520#41—15848no—
521#41—15848no—
522#41—15896no—
523#41—15832no—
524#41—15848no—
525C2×Q8—232no—
526C2×Q8—798no—
527C2×Q8—7912no—
528C2×Q8—15848no—
529C2×Q8—15832no—
530C2×Q8D4×D7918yescomplemented
531C2×Q8C23×D79112yes—
532C2×Q8C23×D7914yes—
533C2×D4—798no—
534C2×D4—7924no—
535C2×D4—7924no—
536C2×D4—798no—
537C2×D4—798no—
538C2×D4—794no—
539C2×D4—7912no—
540C2×D4—7912no—
541C2×D4—7924no—
542C2×D4—7912no—
543C2×D4—7924no—
544C2×D4—63224no—
545C2×D4—15896no—
546C2×D4—15848no—
547C2×D4—15896no—
548C2×D4—15896no—
549C2×D4C23×D7918yes—
550C2×D4C23×D79112yes—
551C2×D4C23×D7914yes—
552C2×D4C23×D79112yes—
553C22×C4—791no—
554C22×C4—793no—
555C22×C4—7924no—
556C22×C4—791no—
557C22×C4—7912no—
558C22×C4—7924no—
559C22×C4—798no—
560C22×C4—7924no—
561C22×C4—7924no—
562C22×C4—798no—
563C22×C4—6326no—
564C22×C4—15896no—
565C22×C4C23×D79124yes—
566C22×C4C23×D7911yescharacteristic
567C22×C4C23×D7913yes—
568C22×C4C23×D7913yes—
569C4⋊C4—7912no—
570C4⋊C4—7924no—
571C4⋊C4—792no—
572C4⋊C4—792no—
573C4⋊C4—798no—
574C4⋊C4—7912no—
575C4⋊C4—7912no—
576C4⋊C4—794no—
577C4⋊C4C23×D79112yes—
578C4⋊C4C23×D79112yes—
579C4⋊C4C23×D7914yes—
580C22⋊C4—7924no—
581C22⋊C4—798no—
582C22⋊C4—7924no—
583C22⋊C4—7924no—
584C22⋊C4—7912no—
585C22⋊C4—796no—
586C22⋊C4—796no—
587C22⋊C4—798no—
588C22⋊C4—798no—
589C22⋊C4C23×D79124yes—
590C22⋊C4C23×D7918yes—
591C42—7912no—
592C42C23×D7916yes—
593C42C23×D7916yes—
594C23—3163no—
595C23—3163no—
596C23—31624no—
597C23—31624no—
598C23—7912no—
599C23—796no—
600C23—798no—
601C23—15848no—
602C23C24×D7918yes—
603C23C24×D7911yescharacteristic
604Q8—224no—
605Q8—15816no—
606Q8—15824no—
607Q8C2×D4×D79116yes—
608D4—216no—
609D4—224no—
610D4—412no—
611D4—44no—
612D4—31612no—
613D4—3164no—
614D4—3168no—
615D4—31624no—
616D4—7948no—
617D4—15848no—
618D4—15816no—
619D4—15848no—
620D4—15816no—
621D4—15824no—
622C2×C4—248no—
623C2×C4—43no—
624C2×C4—41no—
625C2×C4—31624no—
626C2×C4—3163no—
627C2×C4—3161no—
628C2×C4—792no—
629C2×C4—794no—
630C2×C4—7948no—
631C2×C4—792no—
632C2×C4—796no—
633C2×C4—798no—
634C2×C4—15816no—
635C2×C4—15848no—
636C2×C4—15816no—
637C2×C4—15848no—
638C2×C4C2×D4×D79112yes—
639C2×C4C24×D7911yescharacteristic
640C2×C4C24×D7911yescharacteristic
641C2×C4C24×D7916yes—
642C2×C4C24×D7918yes—
643C2×C4C24×D7916yes—
644C22—21no—
645C22—21no—
646C22—28no—
647C22—28no—
648C22—28no—
649C22—31612no—
650C22—7912no—
651C22—63248no—
652C22—1588no—
653C22—1588no—
654C22—1588no—
655C22—1586no—
656C22—1586no—
657C22C22×D4×D7912yes—
658C22C25×D7911yescharacteristic
659C4—28no—
660C4—26no—
661C4—21no—
662C4—21no—
663C4—794no—
664C4—1588no—
665C4—1586no—
666C4—1582no—
667C4C22×D4×D79112yes—
668C2—22no—
669C2—48no—
670C2—3168no—
671C2—15812no—
672C2C23×D4×D7911yescharacteristic
673C2#2377821111yescharacteristic
674C2#2377821211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3497C2
hypercenter#3497D79
hypocenterC79#62853
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×#19099400C2semidirect
2. #23777171C2semidirect
3. #23777167C2semidirect
4. #23777163C2semidirect
5. #23777162C2semidirect
6. #23777079C2semidirect
7. #23777077C2semidirect
8. #23777068C2semidirect
9. #23777066C2semidirect
10. #23776727C2semidirect
11. #537×D79C2semidirect
12. C2×#19099045C2semidirect
13. C79×#3497C2semidirect
15. C2×#14579209C22semidirect
16. C2×#14579209C22semidirect
17. C2×#14579207C22semidirect
18. C2×#14579207C22semidirect
20. C22×#11929625C22semidirect
21. C2×#41×D79C22semidirect
22. C2×#41×D79C22semidirect
23. #19099235C22semidirect
24. #19099232C22semidirect
25. Q8×D316C22semidirect
26. Q8×C22⋊D79C22semidirect
27. #19099225C22semidirect
28. #19099224C22semidirect
29. #19099220C22semidirect
30. #19099218C22semidirect
31. #19099216C22semidirect
32. #19099215C22semidirect
33. #19099210C22semidirect
34. #19099209C22semidirect
35. #19099206C22semidirect
36. #19099204C22semidirect
37. D4×D316C22semidirect
38. #19099198C22semidirect
39. #19099197C22semidirect
40. #19099144C22semidirect
41. #19099143C22semidirect
42. #19099142C22semidirect
43. #19099141C22semidirect
44. #19099140C22semidirect
45. #19099140C22semidirect
46. #19099138C22semidirect
47. #19099133C22semidirect
48. #19099131C22semidirect
49. #19099126C22semidirect
50. #19099121C22semidirect
51. #19099121C22semidirect
52. #19099113C22semidirect
53. #19099109C22semidirect
54. #19099072C22semidirect
55. #19099072C22semidirect
56. C22⋊Q8×D79C22semidirect
57. #121×D79C22semidirect
58. #121×D79C22semidirect
59. #19099045C22semidirect
60. #19099045C22semidirect
61. C2×Q8×Dic79C22semidirect
62. C2×C4×D316C22semidirect
63. C2×#14579123C22semidirect
64. C2×#14579118C22semidirect
65. C2×C4⋊C4×D79C22semidirect
66. C2×2−1+4×C79C22semidirect
67. #550×C79C22semidirect
68. D4×Q8×C79C22semidirect
69. #548×C79C22semidirect
70. #537×C79C22semidirect
71. #532×C79C22semidirect
72. C2×C4×Q8×C79C22semidirect
78. C2×#11929625D4semidirect
179. #11929625C2×D4semidirect
190. C2×D316C2×D4semidirect
211. C2×C4×D79C2×D4semidirect
238. C2×Q8×C79C2×D4semidirect
341. #3497D79semidirect
351. C79#62853semidirect
355. C2×2−1+4C2×D79semidirect
364. #550C2×D79semidirect
367. D4×Q8C2×D79semidirect
371. #548C2×D79semidirect
388. #537C2×D79semidirect
397. #532C2×D79semidirect
406. C2×C4×Q8C2×D79semidirect
530. C2×Q8D4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190994002
#237771712
#237771672
#237771632
#237771622
#237770792
#237770772
#237770682
#237770662
#237767272
#537×D792
C2×#190990452
C79×#34972
#6285379