Finite Group Databasebeta

← #3522×D79 #35196470

Subgroups — #3522×D79 #35196470

Order 20224.

7758 conjugacy classes of subgroups.

The subgroup lattice has 1378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777486C211yesmaximal, characteristic, complemented
2#23777485C211yesmaximal, characteristic, complemented
3#23777484C213yesmaximal, complemented
4#23777483C213yesmaximal, complemented
5#23777482C213yesmaximal, complemented
6#23777481C216yesmaximal, complemented
7#23777480C211yesmaximal, characteristic, complemented
8#23777479C212yesmaximal, complemented
9#23777478C216yesmaximal, complemented
10#23777477C213yesmaximal, complemented
11#23777476C212yesmaximal, complemented
12#559×D79C213yesmaximal, complemented
13Q82×D79C211yesmaximal, characteristic, complemented
14#554×D79C213yesmaximal, complemented
15#550×D79C211yesmaximal, characteristic, complemented
16#548×D79C212yesmaximal, complemented
17#547×D79C216yesmaximal, complemented
18#542×D79C216yesmaximal, complemented
19#532×D79C213yesmaximal, complemented
20#529×D79C213yesmaximal, complemented
21#520×D79C212yesmaximal, complemented
22C2×C4×Q8×D79C211yesmaximal, characteristic, complemented
23C79×#3522C211yesmaximal, characteristic, complemented
24C2×#41×D79C2212yes—
25C2×#41×D79C2216yes—
26C22×Q8×D79C2211yescharacteristic
27#19099299C2213yescomplemented
28#19099298C2213yescomplemented
29#19099298C2213yescomplemented
30#19099297C22112yescomplemented
31#19099296C2216yescomplemented
32#19099296C2216yescomplemented
33#19099295C2216yescomplemented
34#19099295C2216yescomplemented
35Q8×Dic158C2212yescomplemented
36Q8×Dic158C2211yescharacteristic, complemented
37Q8×Dic158C2213yescomplemented
38#19099293C2213yescomplemented
39#19099293C2216yescomplemented
40#19099274C2213yescomplemented
41#19099273C2213yescomplemented
42#19099272C2216yescomplemented
43#19099271C2216yescomplemented
44#19099270C2213yescomplemented
45#19099269C2216yescomplemented
46#19099268C2216yescomplemented
47#19099267C22112yescomplemented
48#19099235C2211yescharacteristic, complemented
49#19099234C2213yescomplemented
50#19099233C2213yescomplemented
51#19099232C2212yescomplemented
52#19099231C2216yescomplemented
53#19099225C2212yescomplemented
54#19099224C2212yescomplemented
55#19099223C2216yescomplemented
56#19099222C2216yescomplemented
57#19099221C2216yescomplemented
58#19099220C2212yescomplemented
59#19099219C2216yescomplemented
60#19099218C2216yescomplemented
61#19099217C2216yescomplemented
62#19099216C2216yescomplemented
63#19099215C22112yescomplemented
64#19099214C2216yescomplemented
65#19099214C2216yescomplemented
66#19099213C2216yescomplemented
67#19099213C2216yescomplemented
68#19099212C22112yescomplemented
69#19099211C22112yescomplemented
70#19099211C22112yescomplemented
71#19099187C2216yescomplemented
72#19099186C2216yescomplemented
73#19099185C2216yescomplemented
74#19099184C2216yescomplemented
75#19099183C22112yescomplemented
76#19099182C2216yescomplemented
77#19099181C22112yescomplemented
78#19099180C2216yescomplemented
79#19099179C22112yescomplemented
80#19099178C2216yescomplemented
81#19099177C22112yescomplemented
82#19099114C2213yescomplemented
83#19099113C2213yescomplemented
84#19099112C2216yescomplemented
85#19099111C2213yescomplemented
86#19099110C2216yescomplemented
87#19099110C2216yescomplemented
88#19099109C2216yescomplemented
89#19099108C2216yescomplemented
90#19099108C2216yescomplemented
91C4⋊Q8×D79C2216yes—
92C4⋊Q8×D79C2213yes—
93#127×D79C2213yes—
94#19099100C2213yescomplemented
95#19099099C2213yescomplemented
96#19099098C2213yescomplemented
97#19099097C2213yescomplemented
98#19099096C2216yescomplemented
99#19099095C2213yescomplemented
100#19099094C2213yescomplemented
101#19099093C2216yescomplemented
102#19099092C2213yescomplemented
103#19099091C2216yescomplemented
104#19099090C2216yescomplemented
105#126×D79C2216yes—
106#125×D79C2213yes—
107#124×D79C2216yes—
108#124×D79C2216yes—
109#124×D79C2213yes—
110#123×D79C22112yes—
111#123×D79C2216yes—
112C22⋊Q8×D79C22112yes—
113C22⋊Q8×D79C2216yes—
114C22⋊Q8×D79C2211yescharacteristic
115#121×D79C2216yes—
116#121×D79C2216yes—
117#121×D79C2213yes—
118#19099046C2212yescomplemented
119#19099045C2212yescomplemented
120#19099045C2212yescomplemented
121#19099044C2216yescomplemented
122#19099043C2216yescomplemented
123#19099042C2216yescomplemented
124#19099042C2216yescomplemented
125C2×Q8×Dic79C2211yescharacteristic, complemented
126C2×C4×Dic158C2213yescomplemented
127C2×#14579126C2213yescomplemented
128C4×Q8×D79C2213yes—
129C4×Q8×D79C2211yescharacteristic
130C4×Q8×D79C2211yescharacteristic
131C4×Q8×D79C2213yes—
132C4×Q8×D79C2212yes—
133C4×Q8×D79C2213yes—
134C4×Q8×D79C2211yescharacteristic, complemented
135C4×Q8×D79C2211yescharacteristic, complemented
136C4×Q8×D79C2213yescomplemented
137C4×Q8×D79C2213yescomplemented
138C4×D4×D79C2216yes—
139C4×D4×D79C2216yes—
140C4×D4×D79C2216yes—
141C4×D4×D79C2213yes—
142C4×D4×D79C2216yes—
143#117×D79C2216yes—
144C2×C4⋊C4×D79C2213yes—
145C2×C4⋊C4×D79C2216yes—
146C2×C42×D79C2213yes—
147#559×C79C2213yescomplemented
148Q82×C79C2211yescharacteristic, complemented
149#554×C79C2213yescomplemented
150#550×C79C2211yescharacteristic, complemented
151#548×C79C2212yescomplemented
152#547×C79C2216yescomplemented
153#542×C79C2216yescomplemented
154#532×C79C2213yescomplemented
155#529×C79C2213yescomplemented
156#520×C79C2212yescomplemented
157C2×C4×Q8×C79C2211yescharacteristic, complemented
158C2×#11929625C2312yes—
159C2×#11929625C2316yes—
160C2×#11929624C2316yes—
161C2×#11929624C2316yes—
162C2×#11929624C23112yes—
163C2×#11929623C2316yes—
164C2×#11929623C2316yes—
165C2×#11929623C23112yes—
166#41×D79—216no—
167#41×D79—424no—
168C22×Dic158C2313yes—
169C2×Q8×D79—28no—
170C2×Q8×D79C2311yescharacteristic
171C2×Q8×D79C2313yes—
172C2×Q8×D79C2311yescharacteristic
173C2×Q8×D79C2313yes—
174C2×Q8×D79C2316yes—
175C2×Q8×D79C2311yescharacteristic
176C2×D4×D79C2313yes—
177C2×D4×D79C2316yes—
178C2×D4×D79C2316yes—
179C2×D4×D79C2316yes—
180C22×C4×D79C2311yescharacteristic
181C22×C4×D79C2313yes—
182C22×C4×D79C2313yes—
183C22×C4×D79C2316yes—
184C22×C4×D79C23112yes—
185#14579161C2316yes—
186#14579161C2313yes—
187#14579160C2316yes—
188#14579160C23112yes—
189#14579160C2316yes—
190#14579160C2316yes—
191#14579160C2316yes—
192#14579159C23112yes—
193#14579159C2316yes—
194#14579158C2313yes—
195#14579157C2316yes—
196#14579157C2316yes—
197#14579157C2316yes—
198#14579156C2316yes—
199#14579156C2316yes—
200#14579156C2316yes—
201#14579155C2316yes—
202#14579154C2316yes—
203#14579154C2316yes—
204#14579154C2316yes—
205#14579153C2313yes—
206#14579152C2313yes—
207#14579152C2313yes—
208#14579151C2316yes—
209#14579151C2316yes—
210#14579150C2316yes—
211#14579150C2316yes—
212#14579150C2313yes—
213#14579149C2316yes—
214#14579149C2316yes—
215#14579149C2313yes—
216#14579148C2316yes—
217#14579148C2316yes—
218#14579148C2313yes—
219#14579147C23112yes—
220#14579147C23112yes—
221#14579147C23112yes—
222#14579147C23112yes—
223#14579147C2316yes—
224#14579147C2316yes—
225#14579146C23112yes—
226#14579146C23112yes—
227#14579146C2316yes—
228#14579146C2316yes—
229#14579145C23112yes—
230#14579145C2316yes—
231#14579144C23112yes—
232#14579144C2316yes—
233#14579143C23112yes—
234#14579143C23112yes—
235#14579143C2316yes—
236#14579143C2316yes—
237#14579142C23112yes—
238#14579142C2316yes—
239#14579141C2316yes—
240#14579141C23112yes—
241#14579141C2311yescharacteristic
242#14579140C23112yes—
243#14579140C2316yes—
244#14579140C2311yescharacteristic
245#14579139C23112yes—
246#14579139C23112yes—
247#14579139C23112yes—
248#14579139C2312yes—
249#14579138C23112yes—
250#14579138C23112yes—
251#14579138C23112yes—
252#14579138C2312yes—
253#14579137C23112yes—
254#14579137C2316yes—
255#14579137C2311yescharacteristic
256#14579136C2316yes—
257#14579136C2316yes—
258#14579136C2313yes—
259#14579135C2316yes—
260#14579135C2316yes—
261#14579135C2313yes—
262#14579134C23112yes—
263#14579134C23112yes—
264#14579134C2316yes—
265#14579133C23112yes—
266#14579133C23112yes—
267#14579133C2316yes—
268#14579132C2316yes—
269#14579132C2316yes—
270#14579132C2313yes—
271Q8×Dic79C2313yes—
272Q8×Dic79C2312yes—
273Q8×Dic79C2311yescharacteristic
274Q8×Dic79C2313yes—
275Q8×Dic79C2311yescharacteristic
276Q8×Dic79C2313yes—
277C4×Dic158C2316yes—
278C4×Dic158C2313yes—
279C4×Dic158C2316yes—
280C4×Dic158C2313yes—
281C4×Dic158C2316yes—
282C4×Dic158C2313yes—
283C4×Dic158C2313yes—
284C4×Dic158C2316yes—
285C4×Dic158C2313yes—
286#14579126C2313yes—
287#14579126C2316yes—
288#14579126C2316yes—
289#14579126C2313yes—
290#14579126C2316yes—
291#14579126C2313yes—
292#14579126C2313yes—
293#14579126C2313yes—
294#14579126C2316yes—
295C4×D316C2316yes—
296C4×D316C2316yes—
297C4×D316C2316yes—
298C4×D316C2313yes—
299C4×D316C2316yes—
300D4×Dic79C2316yes—
301D4×Dic79C2316yes—
302D4×Dic79C2316yes—
303D4×Dic79C2313yes—
304D4×Dic79C2316yes—
305#14579123C2316yes—
306#14579123C2316yes—
307#14579123C2316yes—
308#14579123C2313yes—
309#14579123C2316yes—
310C4×C22⋊D79C23112yes—
311C4×C22⋊D79C23112yes—
312C4×C22⋊D79C2316yes—
313C4×C22⋊D79C2316yes—
314C4×C22⋊D79C2316yes—
315C4×C22⋊D79C23112yes—
316(C22⋊D79)⋊C4C23112yes—
317(C22⋊D79)⋊C4C2316yes—
318(C22⋊D79)⋊C4C2316yes—
319(C22⋊D79)⋊C4C23112yes—
320(C22⋊D79)⋊C4C2316yes—
321(C22⋊D79)⋊C4C23112yes—
322#14579120C2316yes—
323#14579119C2316yes—
324#14579119C2316yes—
325#14579118C2316yes—
326#14579118C2316yes—
327#14579117C2316yes—
328#14579117C2316yes—
329C2×C4⋊Dic79C2313yes—
330C2×C4⋊Dic79C2316yes—
331C2×Dic79⋊C4C2316yes—
332C2×Dic79⋊C4C23112yes—
333C4⋊C4×D79C2316yes—
334C4⋊C4×D79C23112yes—
335C4⋊C4×D79C2313yes—
336C4⋊C4×D79C2316yes—
337C4⋊C4×D79C2313yes—
338C4⋊C4×D79C2316yes—
339C4⋊C4×D79C2313yes—
340C4⋊C4×D79C2316yes—
341C4⋊C4×D79C2316yes—
342C4⋊C4×D79C2313yes—
343C4⋊C4×D79C2316yes—
344C4⋊C4×D79C2312yes—
345C4⋊C4×D79C2311yescharacteristic
346C4⋊C4×D79C2313yes—
347C4⋊C4×D79C2316yes—
348C4⋊C4×D79C2316yes—
349C22⋊C4×D79C2316yes—
350C22⋊C4×D79C2316yes—
351C22⋊C4×D79C2312yes—
352C22⋊C4×D79C2316yes—
353C22⋊C4×D79C23112yes—
354C22⋊C4×D79C2316yes—
355C2×C4×Dic79C2313yes—
356C2×C4×Dic79C2313yes—
357C2×C4×Dic79C2313yes—
358C42×D79C2313yes—
359C42×D79C2313yes—
360C42×D79C2313yes—
361C42×D79C2313yes—
362C42×D79C2313yes—
363C42×D79C2313yes—
364C42×D79C2313yes—
365C42×D79C2313yes—
366C42×D79C2316yes—
367C2×#41×C79C2312yes—
368C2×#41×C79C2316yes—
369C22×Q8×C79C2311yescharacteristic
370C4⋊Q8×C79C2316yes—
371C4⋊Q8×C79C2313yes—
372#127×C79C2313yes—
373#126×C79C2316yes—
374#125×C79C2313yes—
375#124×C79C2316yes—
376#124×C79C2316yes—
377#124×C79C2313yes—
378#123×C79C23112yes—
379#123×C79C2316yes—
380C22⋊Q8×C79C23112yes—
381C22⋊Q8×C79C2316yes—
382C22⋊Q8×C79C2311yescharacteristic
383#121×C79C2316yes—
384#121×C79C2316yes—
385#121×C79C2313yes—
386C4×Q8×C79C2313yes—
387C4×Q8×C79C2312yes—
388C4×Q8×C79C2311yescharacteristic
389C4×Q8×C79C2311yescharacteristic
390C4×Q8×C79C2313yes—
391C4×Q8×C79C2313yes—
392C4×D4×C79C2316yes—
393C4×D4×C79C2316yes—
394C4×D4×C79C2316yes—
395C4×D4×C79C2313yes—
396C4×D4×C79C2316yes—
397#117×C79C2316yes—
398C2×C4⋊C4×C79C2313yes—
399C2×C4⋊C4×C79C2316yes—
400C2×C42×C79C2313yes—
401C23×D79C2416yes—
402C23×D79C2411yescharacteristic
403#11929625—28no—
404#11929625—412no—
405#11929624—224no—
406#11929624—412no—
407#11929624—424no—
408#11929623—224no—
409#11929623—412no—
410#11929623—424no—
411C2×Dic158—212no—
412C2×Dic158C2416yes—
413C2×Dic158C2413yes—
414C2×Dic158C2412yes—
415C2×Dic158C2411yescharacteristic
416C2×Dic158C2416yes—
417C2×Dic158C24112yes—
418C2×Dic158C2413yes—
419Q8×D79—212no—
420Q8×D79—24no—
421Q8×D79—212no—
422Q8×D79—24no—
423Q8×D79—412no—
424Q8×D79#4118yescomplemented
425C2×D316C2416yes—
426C2×D316C2416yes—
427C2×D316C2413yes—
428C2×D316C2416yes—
429C2×C22⋊D79C2416yes—
430C2×C22⋊D79C2416yes—
431C2×C22⋊D79C24112yes—
432C2×C22⋊D79C2416yes—
433C2×C22⋊D79C24112yes—
434D4×D79—224no—
435D4×D79—212no—
436D4×D79—224no—
437D4×D79—412no—
438C22×Dic79C2413yes—
439C22×Dic79C2413yes—
440C22×Dic79C2416yes—
441C22×Dic79C2411yescharacteristic
442C22×Dic79C24112yes—
443C2×C4×D79—212no—
444C2×C4×D79—224no—
445C2×C4×D79—24no—
446C2×C4×D79—212no—
447C2×C4×D79—424no—
448C2×C4×D79C2413yes—
449C2×C4×D79C2413yes—
450C2×C4×D79C2413yes—
451C2×C4×D79C2413yes—
452C2×C4×D79C2416yes—
453C2×C4×D79C2412yes—
454C2×C4×D79C2413yes—
455C2×C4×D79C2416yes—
456C2×C4×D79C2413yes—
457C2×C4×D79C2416yes—
458C2×C4×D79C2411yescharacteristic
459C2×C4×D79C2411yescharacteristic
460C2×C4×D79C2411yescharacteristic
461C2×C4×D79C2413yes—
462C2×C4×D79C2412yes—
463C2×C4×D79C24112yes—
464C2×C4×D79C24112yes—
465C2×C4×D79C2413yes—
466C2×C4×D79C2411yescharacteristic
467C4⋊Dic79C2413yes—
468C4⋊Dic79C2416yes—
469C4⋊Dic79C2416yes—
470C4⋊Dic79C2413yes—
471C4⋊Dic79C2416yes—
472C4⋊Dic79C2412yes—
473C4⋊Dic79C2411yescharacteristic
474C4⋊Dic79C2413yes—
475C4⋊Dic79C2416yes—
476C4⋊Dic79C2416yes—
477Dic79⋊C4C2416yes—
478Dic79⋊C4C2416yes—
479Dic79⋊C4C2416yes—
480Dic79⋊C4C24112yes—
481Dic79⋊C4C2416yes—
482Dic79⋊C4C2416yes—
483Dic79⋊C4C2416yes—
484Dic79⋊C4C2412yes—
485Dic79⋊C4C2412yes—
486Dic79⋊C4C2412yes—
487Dic79⋊C4C2416yes—
488Dic79⋊C4C2416yes—
489Dic79⋊C4C2416yes—
490Dic79⋊C4C2416yes—
491Dic79⋊C4C2416yes—
492C22⋊Dic79C2416yes—
493C22⋊Dic79C2416yes—
494C22⋊Dic79C2412yes—
495C22⋊Dic79C2416yes—
496C22⋊Dic79C24112yes—
497C22⋊Dic79C2416yes—
498(C2×D79)⋊C4C2416yes—
499(C2×D79)⋊C4C2416yes—
500(C2×D79)⋊C4C2416yes—
501(C2×D79)⋊C4C2416yes—
502(C2×D79)⋊C4C2412yes—
503(C2×D79)⋊C4C2416yes—
504(C2×D79)⋊C4C24112yes—
505(C2×D79)⋊C4C2416yes—
506(C2×D79)⋊C4C2412yes—
507(C2×D79)⋊C4C24112yes—
508(C2×D79)⋊C4C2416yes—
509(C2×D79)⋊C4C2416yes—
510C4×Dic79C2413yes—
511C4×Dic79C2413yes—
512C4×Dic79C2413yes—
513C4×Dic79C2413yes—
514C4×Dic79C2413yes—
515C4×Dic79C2413yes—
516C4×Dic79C2413yes—
517C4×Dic79C2413yes—
518C4×Dic79C2413yes—
519C4×Dic79C2413yes—
520C4×Dic79C2413yes—
521C4×Dic79C2413yes—
522C4×Dic79C2416yes—
523C4×Dic79C2416yes—
524C4×Dic79C2416yes—
525#41×C79—28no—
526#41×C79—412no—
527C2×Q8×C79—24no—
528C2×Q8×C79C2413yes—
529C2×Q8×C79C2411yescharacteristic
530C2×Q8×C79C2416yes—
531C2×Q8×C79C2411yescharacteristic
532C2×D4×C79C2416yes—
533C2×D4×C79C2416yes—
534C2×D4×C79C2413yes—
535C2×D4×C79C2416yes—
536C22×C4×C79C2413yes—
537C22×C4×C79C2413yes—
538C22×C4×C79C2416yes—
539C22×C4×C79C2411yescharacteristic
540C22×C4×C79C24112yes—
541C4⋊C4×C79C2413yes—
542C4⋊C4×C79C2416yes—
543C4⋊C4×C79C2416yes—
544C4⋊C4×C79C2413yes—
545C4⋊C4×C79C2416yes—
546C4⋊C4×C79C2412yes—
547C4⋊C4×C79C2411yescharacteristic
548C4⋊C4×C79C2413yes—
549C4⋊C4×C79C2416yes—
550C4⋊C4×C79C2416yes—
551C22⋊C4×C79C2416yes—
552C22⋊C4×C79C2416yes—
553C22⋊C4×C79C2412yes—
554C22⋊C4×C79C2416yes—
555C22⋊C4×C79C24112yes—
556C22⋊C4×C79C2416yes—
557C42×C79C2413yes—
558C42×C79C2413yes—
559C42×C79C2413yes—
560C42×C79C2413yes—
561C42×C79C2416yes—
562C23×C79C2516yes—
563C23×C79C2511yescharacteristic
564C22×D79—22no—
565C22×D79—22no—
566C22×D79—212no—
567C22×D79—212no—
568C22×D79—212no—
569C22×D79H(5,𝔽2)14yes—
570C22×D79C2516yes—
571C22×D79C2511yescharacteristic
572C22×D79C2511yescharacteristic
573Q8×C79—26no—
574Q8×C79—22no—
575Q8×C79—46no—
576Q8×C79C2×#4114yescomplemented
577D4×C79—212no—
578D4×C79—212no—
579D4×C79—26no—
580D4×C79—46no—
581C2×C4×C79—26no—
582C2×C4×C79—26no—
583C2×C4×C79—212no—
584C2×C4×C79—22no—
585C2×C4×C79—412no—
586C2×C4×C79C2511yescharacteristic
587C2×C4×C79C2512yes—
588C2×C4×C79C2513yes—
589C2×C4×C79C2513yes—
590C2×C4×C79C2513yes—
591C2×C4×C79C2516yes—
592C2×C4×C79C2512yes—
593C2×C4×C79C2513yes—
594C2×C4×C79C2511yescharacteristic
595C22⋊D79—212no—
596C22⋊D79—212no—
597C22⋊D79—224no—
598C22⋊D79—212no—
599C22⋊D79—412no—
600C2×Dic79—26no—
601C2×Dic79—26no—
602C2×Dic79—212no—
603C2×Dic79—22no—
604C2×Dic79—412no—
605C2×Dic79C2511yescharacteristic
606C2×Dic79C2512yes—
607C2×Dic79C2513yes—
608C2×Dic79C2513yes—
609C2×Dic79C2513yes—
610C2×Dic79C2516yes—
611C2×Dic79C2512yes—
612C2×Dic79C2513yes—
613C2×Dic79C2511yescharacteristic
614D316—212no—
615D316—212no—
616D316—26no—
617D316—46no—
618C4×D79—24no—
619C4×D79—26no—
620C4×D79—26no—
621C4×D79—26no—
622C4×D79—26no—
623C4×D79—26no—
624C4×D79—212no—
625C4×D79—22no—
626C4×D79—24no—
627C4×D79—26no—
628C4×D79—212no—
629C4×D79—22no—
630C4×D79—26no—
631C4×D79—212no—
632C4×D79—22no—
633C4×D79—412no—
634C4×D79—412no—
635C4×D79C2×#41112yes—
636C4×D792−1+414yes—
637Dic158—26no—
638Dic158—22no—
639Dic158—212no—
640Dic158—24no—
641Dic158—46no—
642Dic158—412no—
643Dic158C2×#41112yescomplemented
644C22×C79—21no—
645C22×C79—21no—
646C22×C79—26no—
647C22×C79—26no—
648C22×C79—26no—
649C22×C79C2×H(5,𝔽2)12yes—
650C22×C79C2611yescharacteristic
651C2×D79—21no—
652C2×D79—21no—
653C2×D79—28no—
654C2×D79—26no—
655C2×D79—26no—
656C2×D79—26no—
657C2×D79—424no—
658C2×D79C22×#4112yes—
659C2×D79C2×H(5,𝔽2)12yes—
660C2×D79C2×H(5,𝔽2)12yes—
661C2×D79C2×2−1+412yes—
662C4×C79—22no—
663C4×C79—23no—
664C4×C79—23no—
665C4×C79—23no—
666C4×C79—26no—
667C4×C79—21no—
668C4×C79—22no—
669C4×C79C22×#4116yes—
670C4×C79C2×2−1+412yes—
671Dic79—23no—
672Dic79—22no—
673Dic79—26no—
674Dic79—23no—
675Dic79—23no—
676Dic79—22no—
677Dic79—21no—
678Dic79C22×#4116yes—
679Dic79C2×2−1+412yes—
680C2×#3522—791nomaximal, Sylow
681C2×C79—22no—
682C2×C79—46no—
683C2×C79C23×#4111yescharacteristic
684C2×C79C22×H(5,𝔽2)11yescharacteristic
685C2×C79C22×2−1+411yescharacteristic
686D79—22no—
687D79—46no—
688D79#352214yesdirect product factor
689#3522—793no—
690#3522—791no—
691#3522—793no—
692#3522—791no—
693#3522—792no—
694#3522—796no—
695#3522—796no—
696#3522—793no—
697#3522—793no—
698#3522—792no—
699#3522—791no—
700#3522D7911yescharacteristic, direct product factor
701C2×#559—793no—
702C2×Q82—791no—
703C2×#554—793no—
704C2×#550—791no—
705C2×#548—792no—
706C2×#547—796no—
707C2×#542—796no—
708C2×#532—793no—
709C2×#529—793no—
710C2×#520—792no—
711C22×C4×Q8—791no—
712C79C2×#352211yescharacteristic, complemented, Sylow
713C22×#41—796no—
714C22×#41—792no—
715C23×Q8—791no—
716#559—793no—
717#559—796no—
718#559—796no—
719#559—7912no—
720#559—793no—
721#559—793no—
722#559—796no—
723#559—796no—
724#559C2×D7913yescomplemented
725Q82—796no—
726Q82—793no—
727Q82—792no—
728Q82—791no—
729Q82—793no—
730Q82C2×D7911yescharacteristic, complemented
731#554—793no—
732#554—796no—
733#554—7912no—
734#554—796no—
735#554—793no—
736#554—793no—
737#554—796no—
738#554—796no—
739#554C2×D7913yescomplemented
740#550—792no—
741#550—793no—
742#550—796no—
743#550—791no—
744#550—793no—
745#550C2×D7911yescharacteristic, complemented
746#548—792no—
747#548—792no—
748#548—796no—
749#548—796no—
750#548—796no—
751#548—792no—
752#548—796no—
753#548C2×D7912yescomplemented
754#547—7912no—
755#547—796no—
756#547—7912no—
757#547—7912no—
758#547—7912no—
759#547—796no—
760#547—796no—
761#547—796no—
762#547—796no—
763#547—796no—
764#547—796no—
765#547C2×D7916yescomplemented
766#542—796no—
767#542—7912no—
768#542—7912no—
769#542—796no—
770#542—7912no—
771#542—7912no—
772#542—796no—
773#542—796no—
774#542—796no—
775#542—796no—
776#542—796no—
777#542C2×D7916yescomplemented
778#532—796no—
779#532—793no—
780#532—793no—
781#532—796no—
782#532—796no—
783#532—796no—
784#532—796no—
785#532—796no—
786#532—793no—
787#532C2×D7913yescomplemented
788C2×C4⋊Q8—793no—
789C2×C4⋊Q8—796no—
790C2×#127—793no—
791#529—796no—
792#529—793no—
793#529—793no—
794#529—796no—
795#529—793no—
796#529—793no—
797#529—793no—
798#529—796no—
799#529—793no—
800#529—796no—
801#529—793no—
802#529C2×D7913yescomplemented
803C2×#126—796no—
804C2×#125—793no—
805C2×#124—793no—
806C2×#124—796no—
807C2×#124—796no—
808C2×#123—796no—
809C2×#123—7912no—
810C2×C22⋊Q8—791no—
811C2×C22⋊Q8—7912no—
812C2×C22⋊Q8—796no—
813C2×#121—793no—
814C2×#121—796no—
815C2×#121—796no—
816#520—792no—
817#520—792no—
818#520—792no—
819#520—796no—
820#520—796no—
821#520—796no—
822#520—796no—
823#520C2×D7912yescomplemented
824C2×C4×Q8—791no—
825C2×C4×Q8—791no—
826C2×C4×Q8—793no—
827C2×C4×Q8—791no—
828C2×C4×Q8—793no—
829C2×C4×Q8—791no—
830C2×C4×Q8—793no—
831C2×C4×Q8—791no—
832C2×C4×Q8—793no—
833C2×C4×Q8—792no—
834C2×C4×Q8—793no—
835C2×C4×Q8—793no—
836C2×C4×Q8—793no—
837C2×C4×Q8C2×D7911yescharacteristic, complemented
838C2×C4×D4—796no—
839C2×C4×D4—796no—
840C2×C4×D4—796no—
841C2×C4×D4—793no—
842C2×C4×D4—796no—
843C2×#117—796no—
844C22×C4⋊C4—793no—
845C22×C4⋊C4—796no—
846C22×C42—793no—
847C2×#41—31624no—
848C2×#41—796no—
849C2×#41—792no—
850C2×#41—796no—
851C2×#41—7912no—
852C2×#41—796no—
853C2×#41—796no—
854C2×#41—7912no—
855C2×#41—796no—
856C2×#41—15816no—
857C2×#41C22×D7912yes—
858C2×#41C22×D7916yes—
859C22×Q8—796no—
860C22×Q8—791no—
861C22×Q8—791no—
862C22×Q8—793no—
863C22×Q8—793no—
864C22×Q8—791no—
865C22×Q8—793no—
866C22×Q8—1588no—
867C22×Q8C22×D7911yescharacteristic
868C22×D4—796no—
869C22×D4—793no—
870C22×D4—796no—
871C22×D4—796no—
872C23×C4—7912no—
873C23×C4—793no—
874C23×C4—796no—
875C23×C4—793no—
876C23×C4—791no—
877C4⋊Q8—796no—
878C4⋊Q8—7912no—
879C4⋊Q8—796no—
880C4⋊Q8—796no—
881C4⋊Q8—7912no—
882C4⋊Q8—796no—
883C4⋊Q8—796no—
884C4⋊Q8—793no—
885C4⋊Q8—796no—
886C4⋊Q8C22×D7913yes—
887C4⋊Q8C22×D7916yes—
888#127—796no—
889#127—796no—
890#127—796no—
891#127—793no—
892#127C22×D7913yes—
893#126—796no—
894#126—796no—
895#126—796no—
896#126—796no—
897#126—796no—
898#126—796no—
899#126—796no—
900#126C22×D7916yes—
901#125—796no—
902#125—796no—
903#125—793no—
904#125—793no—
905#125—793no—
906#125C22×D7913yes—
907#124—793no—
908#124—796no—
909#124—796no—
910#124—793no—
911#124—796no—
912#124—796no—
913#124—796no—
914#124—796no—
915#124—7912no—
916#124—7912no—
917#124—7912no—
918#124—7912no—
919#124—793no—
920#124—796no—
921#124—796no—
922#124C22×D7913yes—
923#124C22×D7916yes—
924#124C22×D7916yes—
925#123—796no—
926#123—7912no—
927#123—796no—
928#123—7912no—
929#123—796no—
930#123—796no—
931#123—7912no—
932#123—7912no—
933#123—796no—
934#123—796no—
935#123—796no—
936#123—7912no—
937#123—7912no—
938#123—7912no—
939#123C22×D7916yes—
940#123C22×D79112yes—
941C22⋊Q8—791no—
942C22⋊Q8—7912no—
943C22⋊Q8—796no—
944C22⋊Q8—791no—
945C22⋊Q8—7912no—
946C22⋊Q8—796no—
947C22⋊Q8—792no—
948C22⋊Q8—791no—
949C22⋊Q8—7912no—
950C22⋊Q8—7912no—
951C22⋊Q8—7912no—
952C22⋊Q8—7912no—
953C22⋊Q8—796no—
954C22⋊Q8—792no—
955C22⋊Q8—7912no—
956C22⋊Q8—7912no—
957C22⋊Q8—7912no—
958C22⋊Q8C22×D7911yescharacteristic
959C22⋊Q8C22×D79112yes—
960C22⋊Q8C22×D7916yes—
961#121—793no—
962#121—796no—
963#121—796no—
964#121—7912no—
965#121—796no—
966#121—7912no—
967#121—793no—
968#121—796no—
969#121—796no—
970#121—793no—
971#121—796no—
972#121—796no—
973#121—796no—
974#121—7912no—
975#121—7912no—
976#121C22×D7913yes—
977#121C22×D7916yes—
978#121C22×D7916yes—
979C4×Q8—791no—
980C4×Q8—793no—
981C4×Q8—791no—
982C4×Q8—793no—
983C4×Q8—792no—
984C4×Q8—793no—
985C4×Q8—793no—
986C4×Q8—796no—
987C4×Q8—793no—
988C4×Q8—793no—
989C4×Q8—796no—
990C4×Q8—793no—
991C4×Q8—796no—
992C4×Q8—796no—
993C4×Q8—793no—
994C4×Q8—793no—
995C4×Q8—796no—
996C4×Q8—793no—
997C4×Q8—793no—
998C4×Q8—793no—
999C4×Q8—796no—
1000C4×Q8—796no—
1001C4×Q8—796no—
1002C4×Q8—793no—
1003C4×Q8C22×D7911yescharacteristic
1004C4×Q8C22×D7913yes—
1005C4×Q8C22×D7911yescharacteristic
1006C4×Q8C22×D7913yes—
1007C4×Q8C22×D7912yes—
1008C4×Q8C22×D7913yes—
1009C4×D4—796no—
1010C4×D4—796no—
1011C4×D4—796no—
1012C4×D4—793no—
1013C4×D4—796no—
1014C4×D4—7912no—
1015C4×D4—7912no—
1016C4×D4—796no—
1017C4×D4—796no—
1018C4×D4—796no—
1019C4×D4—7912no—
1020C4×D4—796no—
1021C4×D4—796no—
1022C4×D4—796no—
1023C4×D4—793no—
1024C4×D4—796no—
1025C4×D4—7912no—
1026C4×D4—7912no—
1027C4×D4—796no—
1028C4×D4—796no—
1029C4×D4—796no—
1030C4×D4—7912no—
1031C4×D4—796no—
1032C4×D4—796no—
1033C4×D4—796no—
1034C4×D4—793no—
1035C4×D4—796no—
1036C4×D4C22×D7916yes—
1037C4×D4C22×D7916yes—
1038C4×D4C22×D7916yes—
1039C4×D4C22×D7913yes—
1040C4×D4C22×D7916yes—
1041#117—796no—
1042#117—796no—
1043#117—796no—
1044#117—796no—
1045#117—796no—
1046#117—796no—
1047#117—796no—
1048#117C22×D7916yes—
1049C2×C4⋊C4—796no—
1050C2×C4⋊C4—793no—
1051C2×C4⋊C4—7912no—
1052C2×C4⋊C4—796no—
1053C2×C4⋊C4—793no—
1054C2×C4⋊C4—796no—
1055C2×C4⋊C4—796no—
1056C2×C4⋊C4—793no—
1057C2×C4⋊C4—796no—
1058C2×C4⋊C4—796no—
1059C2×C4⋊C4—793no—
1060C2×C4⋊C4—793no—
1061C2×C4⋊C4—7912no—
1062C2×C4⋊C4—796no—
1063C2×C4⋊C4—796no—
1064C2×C4⋊C4—792no—
1065C2×C4⋊C4—791no—
1066C2×C4⋊C4—793no—
1067C2×C4⋊C4—796no—
1068C2×C4⋊C4—796no—
1069C2×C4⋊C4C22×D7913yes—
1070C2×C4⋊C4C22×D7916yes—
1071C2×C22⋊C4—796no—
1072C2×C22⋊C4—796no—
1073C2×C22⋊C4—792no—
1074C2×C22⋊C4—796no—
1075C2×C22⋊C4—7912no—
1076C2×C22⋊C4—796no—
1077C2×C42—793no—
1078C2×C42—793no—
1079C2×C42—793no—
1080C2×C42—793no—
1081C2×C42—796no—
1082C2×C42—793no—
1083C2×C42—793no—
1084C2×C42—793no—
1085C2×C42—793no—
1086C2×C42—793no—
1087C2×C42—793no—
1088C2×C42—793no—
1089C2×C42C22×D7913yes—
1090C24—791no—
1091C24—796no—
1092#41—28no—
1093#41—412no—
1094#41—31612no—
1095#41—31624no—
1096#41—31624no—
1097#41—31612no—
1098#41—31612no—
1099#41—15824no—
1100#41—15824no—
1101#41—1588no—
1102C2×Q8—24no—
1103C2×Q8—31612no—
1104C2×Q8—798no—
1105C2×Q8—7912no—
1106C2×Q8—796no—
1107C2×Q8—793no—
1108C2×Q8—792no—
1109C2×Q8—791no—
1110C2×Q8—796no—
1111C2×Q8—793no—
1112C2×Q8—15812no—
1113C2×Q8—1584no—
1114C2×Q8—15812no—
1115C2×Q8—15812no—
1116C2×Q8—1584no—
1117C2×Q8C23×D7911yescharacteristic
1118C2×Q8C23×D7913yes—
1119C2×Q8C23×D7916yes—
1120C2×Q8C23×D7911yescharacteristic
1121C2×D4—31612no—
1122C2×D4—7912no—
1123C2×D4—796no—
1124C2×D4—7912no—
1125C2×D4—796no—
1126C2×D4—796no—
1127C2×D4—796no—
1128C2×D4—793no—
1129C2×D4—796no—
1130C2×D4—796no—
1131C2×D4—15812no—
1132C2×D4—15824no—
1133C2×D4—15824no—
1134C2×D4C23×D7913yes—
1135C2×D4C23×D7916yes—
1136C2×D4C23×D7916yes—
1137C2×D4C23×D7916yes—
1138C22×C4—31624no—
1139C22×C4—7912no—
1140C22×C4—7912no—
1141C22×C4—7912no—
1142C22×C4—791no—
1143C22×C4—793no—
1144C22×C4—791no—
1145C22×C4—793no—
1146C22×C4—793no—
1147C22×C4—796no—
1148C22×C4—791no—
1149C22×C4—791no—
1150C22×C4—791no—
1151C22×C4—792no—
1152C22×C4—793no—
1153C22×C4—793no—
1154C22×C4—793no—
1155C22×C4—793no—
1156C22×C4—793no—
1157C22×C4—793no—
1158C22×C4—793no—
1159C22×C4—796no—
1160C22×C4—792no—
1161C22×C4—796no—
1162C22×C4—796no—
1163C22×C4—1584no—
1164C22×C4—15812no—
1165C22×C4—15824no—
1166C22×C4—15812no—
1167C22×C4C23×D7911yescharacteristic
1168C22×C4C23×D7913yes—
1169C22×C4C23×D7913yes—
1170C22×C4C23×D7916yes—
1171C22×C4C23×D79112yes—
1172C4⋊C4—796no—
1173C4⋊C4—796no—
1174C4⋊C4—796no—
1175C4⋊C4—7912no—
1176C4⋊C4—796no—
1177C4⋊C4—796no—
1178C4⋊C4—796no—
1179C4⋊C4—792no—
1180C4⋊C4—792no—
1181C4⋊C4—792no—
1182C4⋊C4—796no—
1183C4⋊C4—796no—
1184C4⋊C4—796no—
1185C4⋊C4—796no—
1186C4⋊C4—796no—
1187C4⋊C4—793no—
1188C4⋊C4—796no—
1189C4⋊C4—796no—
1190C4⋊C4—793no—
1191C4⋊C4—796no—
1192C4⋊C4—792no—
1193C4⋊C4—791no—
1194C4⋊C4—793no—
1195C4⋊C4—796no—
1196C4⋊C4—796no—
1197C4⋊C4C23×D7913yes—
1198C4⋊C4C23×D7916yes—
1199C4⋊C4C23×D7916yes—
1200C4⋊C4C23×D7913yes—
1201C4⋊C4C23×D7916yes—
1202C4⋊C4C23×D7912yes—
1203C4⋊C4C23×D7911yescharacteristic
1204C4⋊C4C23×D7913yes—
1205C4⋊C4C23×D7916yes—
1206C4⋊C4C23×D7916yes—
1207C22⋊C4—796no—
1208C22⋊C4—796no—
1209C22⋊C4—792no—
1210C22⋊C4—796no—
1211C22⋊C4—7912no—
1212C22⋊C4—796no—
1213C22⋊C4—796no—
1214C22⋊C4—796no—
1215C22⋊C4—796no—
1216C22⋊C4—796no—
1217C22⋊C4—792no—
1218C22⋊C4—792no—
1219C22⋊C4—796no—
1220C22⋊C4—796no—
1221C22⋊C4—7912no—
1222C22⋊C4—7912no—
1223C22⋊C4—796no—
1224C22⋊C4—796no—
1225C22⋊C4C23×D7916yes—
1226C22⋊C4C23×D7916yes—
1227C22⋊C4C23×D7912yes—
1228C22⋊C4C23×D7916yes—
1229C22⋊C4C23×D79112yes—
1230C22⋊C4C23×D7916yes—
1231C42—793no—
1232C42—793no—
1233C42—793no—
1234C42—793no—
1235C42—793no—
1236C42—793no—
1237C42—793no—
1238C42—793no—
1239C42—793no—
1240C42—793no—
1241C42—793no—
1242C42—793no—
1243C42—796no—
1244C42—796no—
1245C42—796no—
1246C42C23×D7913yes—
1247C42C23×D7913yes—
1248C42C23×D7913yes—
1249C42C23×D7913yes—
1250C42C23×D7916yes—
1251C23—791no—
1252C23—794no—
1253C23—791no—
1254C23—796no—
1255C23—15812no—
1256C23—15812no—
1257C23—15812no—
1258C23—1582no—
1259C23—1582no—
1260C23C24×D7916yes—
1261C23C24×D7911yescharacteristic
1262Q8—22no—
1263Q8—26no—
1264Q8—46no—
1265Q8—3166no—
1266Q8—31612no—
1267Q8—7912no—
1268Q8—15812no—
1269Q8—1584no—
1270Q8—1582no—
1271Q8—1586no—
1272Q8#41×D7914yescomplemented
1273D4—212no—
1274D4—26no—
1275D4—212no—
1276D4—46no—
1277D4—3166no—
1278D4—31612no—
1279D4—15812no—
1280D4—15812no—
1281D4—15824no—
1282D4—15812no—
1283D4—15812no—
1284D4—1586no—
1285D4—15812no—
1286C2×C4—26no—
1287C2×C4—22no—
1288C2×C4—26no—
1289C2×C4—212no—
1290C2×C4—412no—
1291C2×C4—31612no—
1292C2×C4—31612no—
1293C2×C4—31612no—
1294C2×C4—791no—
1295C2×C4—793no—
1296C2×C4—794no—
1297C2×C4—7912no—
1298C2×C4—791no—
1299C2×C4—792no—
1300C2×C4—793no—
1301C2×C4—793no—
1302C2×C4—793no—
1303C2×C4—796no—
1304C2×C4—792no—
1305C2×C4—1586no—
1306C2×C4—15812no—
1307C2×C4—1582no—
1308C2×C4—1586no—
1309C2×C4—15812no—
1310C2×C4—1584no—
1311C2×C4—1586no—
1312C2×C4—1586no—
1313C2×C4—1586no—
1314C2×C4—1586no—
1315C2×C4—1582no—
1316C2×C4—1584no—
1317C2×C4—1586no—
1318C2×C4—15812no—
1319C2×C4—1582no—
1320C2×C4—1586no—
1321C2×C4—1582no—
1322C2×C4—1586no—
1323C2×C4—15812no—
1324C2×C4C24×D7911yescharacteristic
1325C2×C4C24×D7912yes—
1326C2×C4C24×D7913yes—
1327C2×C4C24×D7913yes—
1328C2×C4C24×D7913yes—
1329C2×C4C24×D7916yes—
1330C2×C4C24×D7912yes—
1331C2×C4C24×D7911yescharacteristic
1332C2×C4C24×D7913yes—
1333C22—21no—
1334C22—21no—
1335C22—26no—
1336C22—26no—
1337C22—26no—
1338C22—31624no—
1339C22—792no—
1340C22—792no—
1341C22—792no—
1342C22—792no—
1343C22—1588no—
1344C22—1586no—
1345C22—1586no—
1346C22—1586no—
1347C22—1581no—
1348C22—1581no—
1349C22H(5,𝔽2)×D7912yes—
1350C22C25×D7911yescharacteristic
1351C4—22no—
1352C4—23no—
1353C4—23no—
1354C4—23no—
1355C4—26no—
1356C4—21no—
1357C4—22no—
1358C4—796no—
1359C4—792no—
1360C4—1582no—
1361C4—1583no—
1362C4—1583no—
1363C4—1586no—
1364C4—1583no—
1365C4—1581no—
1366C4—1582no—
1367C4C2×#41×D7916yes—
1368C42−1+4×D7912yes—
1369C2—22no—
1370C2—46no—
1371C2—3166no—
1372C2—794no—
1373C2—1582no—
1374C2C22×#41×D7911yescharacteristic
1375C2C2×H(5,𝔽2)×D7911yescharacteristic
1376C2C2×2−1+4×D7911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3522C2
hypercenter#3522D79
hypocenterC79C2×#3522
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3522

Complements

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

NH ≅ G/Ntype
1. #23777486C2semidirect
2. #23777485C2semidirect
3. #23777484C2semidirect
4. #23777483C2semidirect
5. #23777482C2semidirect
6. #23777481C2semidirect
7. #23777480C2semidirect
8. #23777479C2semidirect
9. #23777478C2semidirect
10. #23777477C2semidirect
11. #23777476C2semidirect
12. #559×D79C2semidirect
13. Q82×D79C2semidirect
14. #554×D79C2semidirect
15. #550×D79C2semidirect
16. #548×D79C2semidirect
17. #547×D79C2semidirect
18. #542×D79C2semidirect
19. #532×D79C2semidirect
20. #529×D79C2semidirect
21. #520×D79C2semidirect
22. C2×C4×Q8×D79C2semidirect
23. C79×#3522C2semidirect
27. #19099299C22semidirect
28. #19099298C22semidirect
29. #19099298C22semidirect
30. #19099297C22semidirect
31. #19099296C22semidirect
32. #19099296C22semidirect
33. #19099295C22semidirect
34. #19099295C22semidirect
35. Q8×Dic158C22semidirect
36. Q8×Dic158C22semidirect
37. Q8×Dic158C22semidirect
38. #19099293C22semidirect
39. #19099293C22semidirect
40. #19099274C22semidirect
41. #19099273C22semidirect
42. #19099272C22semidirect
43. #19099271C22semidirect
44. #19099270C22semidirect
45. #19099269C22semidirect
46. #19099268C22semidirect
47. #19099267C22semidirect
48. #19099235C22semidirect
49. #19099234C22semidirect
50. #19099233C22semidirect
51. #19099232C22semidirect
52. #19099231C22semidirect
53. #19099225C22semidirect
54. #19099224C22semidirect
55. #19099223C22semidirect
56. #19099222C22semidirect
57. #19099221C22semidirect
58. #19099220C22semidirect
59. #19099219C22semidirect
60. #19099218C22semidirect
61. #19099217C22semidirect
62. #19099216C22semidirect
63. #19099215C22semidirect
64. #19099214C22semidirect
65. #19099214C22semidirect
66. #19099213C22semidirect
67. #19099213C22semidirect
68. #19099212C22semidirect
69. #19099211C22semidirect
70. #19099211C22semidirect
71. #19099187C22semidirect
72. #19099186C22semidirect
73. #19099185C22semidirect
74. #19099184C22semidirect
75. #19099183C22semidirect
76. #19099182C22semidirect
77. #19099181C22semidirect
78. #19099180C22semidirect
79. #19099179C22semidirect
80. #19099178C22semidirect
81. #19099177C22semidirect
82. #19099114C22semidirect
83. #19099113C22semidirect
84. #19099112C22semidirect
85. #19099111C22semidirect
86. #19099110C22semidirect
87. #19099110C22semidirect
88. #19099109C22semidirect
89. #19099108C22semidirect
90. #19099108C22semidirect
94. #19099100C22semidirect
95. #19099099C22semidirect
96. #19099098C22semidirect
97. #19099097C22semidirect
98. #19099096C22semidirect
99. #19099095C22semidirect
100. #19099094C22semidirect
101. #19099093C22semidirect
102. #19099092C22semidirect
103. #19099091C22semidirect
104. #19099090C22semidirect
118. #19099046C22semidirect
119. #19099045C22semidirect
120. #19099045C22semidirect
121. #19099044C22semidirect
122. #19099043C22semidirect
123. #19099042C22semidirect
124. #19099042C22semidirect
125. C2×Q8×Dic79C22semidirect
126. C2×C4×Dic158C22semidirect
127. C2×#14579126C22semidirect
134. C4×Q8×D79C22semidirect
135. C4×Q8×D79C22semidirect
136. C4×Q8×D79C22semidirect
137. C4×Q8×D79C22semidirect
147. #559×C79C22semidirect
148. Q82×C79C22semidirect
149. #554×C79C22semidirect
150. #550×C79C22semidirect
151. #548×C79C22semidirect
152. #547×C79C22semidirect
153. #542×C79C22semidirect
154. #532×C79C22semidirect
155. #529×C79C22semidirect
156. #520×C79C22semidirect
157. C2×C4×Q8×C79C22semidirect
424. Q8×D79#41semidirect
576. Q8×C79C2×#41semidirect
643. Dic158C2×#41semidirect
688. D79#3522direct (N × H)
700. #3522D79direct (N × H)
712. C79C2×#3522semidirect
724. #559C2×D79semidirect
730. Q82C2×D79semidirect
739. #554C2×D79semidirect
745. #550C2×D79semidirect
753. #548C2×D79semidirect
765. #547C2×D79semidirect
777. #542C2×D79semidirect
787. #532C2×D79semidirect
802. #529C2×D79semidirect
823. #520C2×D79semidirect
837. C2×C4×Q8C2×D79semidirect
1272. Q8#41×D79semidirect

Maximal subgroups

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

subgroupindex
#237774862
#237774852
#237774842
#237774832
#237774822
#237774812
#237774802
#237774792
#237774782
#237774772
#237774762
#559×D792
Q82×D792
#554×D792
#550×D792
#548×D792
#547×D792
#542×D792
#532×D792
#529×D792
#520×D792
C2×C4×Q8×D792
C79×#35222
C2×#352279