Finite Group Databasebeta

← #3523×D79 #35196482

Subgroups — #3523×D79 #35196482

Order 20224.

7022 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777497C211yesmaximal, characteristic, complemented
2#23777496C211yesmaximal, characteristic, complemented
3#23777495C213yesmaximal, complemented
4#23777494C213yesmaximal, complemented
5#23777493C213yesmaximal, complemented
6#23777492C216yesmaximal, complemented
7#23777491C211yesmaximal, characteristic, complemented
8#23777490C212yesmaximal, complemented
9#23777489C216yesmaximal, complemented
10#23777488C213yesmaximal, complemented
11#23777487C212yesmaximal, complemented
12#557×D79C213yesmaximal, complemented
13#557×D79C211yesmaximal, characteristic, complemented
14#556×D79C213yesmaximal, complemented
15#552×D79C216yesmaximal, complemented
16D4×Q8×D79C212yesmaximal, complemented
17D4×Q8×D79C211yesmaximal, characteristic, complemented
18#541×D79C216yesmaximal, complemented
19#533×D79C213yesmaximal, complemented
20#529×D79C213yesmaximal
21#519×D79C212yesmaximal, complemented
22C2×C4×Q8×D79C211yesmaximal, characteristic, complemented
23C79×#3523C211yesmaximal, characteristic, complemented
24C22×Q8×D79C2211yescharacteristic
25C22×Q8×D79C2212yes—
26#19099292C2211yescharacteristic, complemented
27#19099292C2213yescomplemented
28#19099291C2216yescomplemented
29#19099291C2213yescomplemented
30#19099291C2213yescomplemented
31#19099290C22112yescomplemented
32#19099290C2216yescomplemented
33#19099290C2216yescomplemented
34#19099289C2212yescomplemented
35#19099289C2216yescomplemented
36#19099288C2216yescomplemented
37#19099288C2213yescomplemented
38#19099288C2213yescomplemented
39#19099287C2213yescomplemented
40#19099286C2213yescomplemented
41#19099285C2216yescomplemented
42#19099284C2216yescomplemented
43#19099283C2213yescomplemented
44#19099282C2216yescomplemented
45#19099281C2216yescomplemented
46#19099280C22112yescomplemented
47#19099255C2216yescomplemented
48#19099254C2216yescomplemented
49#19099253C2216yescomplemented
50#19099252C2216yescomplemented
51#19099251C2216yescomplemented
52#19099250C22112yescomplemented
53#19099249C22112yescomplemented
54#19099248C2216yescomplemented
55#19099247C2216yescomplemented
56#19099246C22112yescomplemented
57#19099245C22112yescomplemented
58Q8×D316C2212yescomplemented
59Q8×D316C2211yescharacteristic, complemented
60D4×Dic158C2216yescomplemented
61D4×Dic158C2213yescomplemented
62#19099228C2213yescomplemented
63#19099228C2216yescomplemented
64Q8×C22⋊D79C2212yescomplemented
65Q8×C22⋊D79C2212yescomplemented
66Q8×C22⋊D79C2212yescomplemented
67#19099226C2216yescomplemented
68#19099226C2216yescomplemented
69#19099226C2216yescomplemented
70#19099176C2216yescomplemented
71#19099175C2216yescomplemented
72#19099174C2216yescomplemented
73#19099173C2216yescomplemented
74#19099173C2216yescomplemented
75#19099172C22112yescomplemented
76#19099172C22112yescomplemented
77#19099171C2216yescomplemented
78#19099171C2216yescomplemented
79#19099170C22112yescomplemented
80#19099170C22112yescomplemented
81#19099120C2213yescomplemented
82#19099119C2216yescomplemented
83#19099118C2213yescomplemented
84#19099118C2213yescomplemented
85#19099117C2216yescomplemented
86#19099117C2216yescomplemented
87#19099116C2216yescomplemented
88#19099115C2216yescomplemented
89#19099115C2216yescomplemented
90C4⋊Q8×D79C2213yes—
91C4⋊Q8×D79C2216yes—
92C4⋊Q8×D79C2213yes—
93#19099100C2213yes—
94#19099099C2213yes—
95#19099098C2213yes—
96#19099097C2213yes—
97#19099096C2216yes—
98#19099095C2213yes—
99#19099094C2213yes—
100#19099093C2216yes—
101#19099092C2213yes—
102#19099091C2216yes—
103#19099090C2216yes—
104#126×D79C22112yes—
105#126×D79C2216yes—
106#125×D79C22112yes—
107#125×D79C2216yes—
108#125×D79C2213yes—
109#125×D79C2216yes—
110#124×D79C2213yes—
111#123×D79C2216yes—
112C22⋊Q8×D79C2216yes—
113C22⋊Q8×D79C2216yes—
114C22⋊Q8×D79C2216yes—
115C22⋊Q8×D79C2213yes—
116#121×D79C2211yescharacteristic
117#19099041C2212yescomplemented
118#19099040C2216yescomplemented
119#19099040C2216yescomplemented
120#19099039C2212yescomplemented
121#19099039C2216yescomplemented
122#19099039C2216yescomplemented
123#19099039C2212yescomplemented
124C2×Q8×Dic79C2211yescharacteristic, complemented
125C2×C4×Dic158C2213yescomplemented
126C2×#14579126C2213yescomplemented
127C4×Q8×D79C2211yescharacteristic
128C4×Q8×D79C2211yescharacteristic
129C4×Q8×D79C2213yes—
130C4×Q8×D79C2213yes—
131C4×Q8×D79C2212yes—
132C4×Q8×D79C2216yes—
133C4×Q8×D79C2216yes—
134C4×Q8×D79C2213yes—
135C4×Q8×D79C2216yes—
136C4×Q8×D79C2211yescharacteristic, complemented
137C4×Q8×D79C2211yescharacteristic, complemented
138C4×Q8×D79C2213yescomplemented
139C4×Q8×D79C2213yescomplemented
140C4×D4×D79C2216yes—
141C4×D4×D79C2213yes—
142#117×D79C2216yes—
143#117×D79C2216yes—
144#117×D79C2216yes—
145C2×C4⋊C4×D79C2213yes—
146C2×C42×D79C2213yes—
147#557×C79C2213yescomplemented
148#557×C79C2211yescharacteristic, complemented
149#556×C79C2213yescomplemented
150#552×C79C2216yescomplemented
151D4×Q8×C79C2212yescomplemented
152D4×Q8×C79C2211yescharacteristic, complemented
153#541×C79C2216yescomplemented
154#533×C79C2213yescomplemented
155#529×C79C2213yes—
156#519×C79C2212yescomplemented
157C2×C4×Q8×C79C2211yescharacteristic, complemented
158C22×Dic158C2313yes—
159C22×Dic158C2316yes—
160C2×Q8×D79—28no—
161C2×Q8×D79—216no—
162C2×Q8×D79C2313yes—
163C2×Q8×D79C2316yes—
164C2×Q8×D79C2311yescharacteristic
165C2×Q8×D79C2312yes—
166C2×Q8×D79C2313yes—
167C2×Q8×D79C2313yes—
168C2×Q8×D79C2316yes—
169C2×Q8×D79C2311yescharacteristic
170C2×D4×D79C2312yes—
171C2×D4×D79C2311yescharacteristic
172C22×C4×D79C2311yescharacteristic
173C22×C4×D79C2313yes—
174C22×C4×D79C2313yes—
175C22×C4×D79C2316yes—
176#14579161C2316yes—
177#14579161C2313yes—
178#14579161C2313yes—
179#14579160C23112yes—
180#14579160C23112yes—
181#14579160C2316yes—
182#14579160C2316yes—
183#14579160C2316yes—
184#14579160C2316yes—
185#14579159C2316yes—
186#14579159C2316yes—
187#14579159C2316yes—
188#14579159C2316yes—
189#14579156C2316yes—
190#14579156C23112yes—
191#14579156C2316yes—
192#14579156C2316yes—
193#14579156C23112yes—
194#14579156C23112yes—
195#14579155C2316yes—
196#14579155C23112yes—
197#14579154C2316yes—
198#14579154C2316yes—
199#14579154C2316yes—
200#14579154C23112yes—
201#14579154C23112yes—
202#14579154C23112yes—
203#14579153C2316yes—
204#14579153C23112yes—
205#14579153C2316yes—
206#14579153C2313yes—
207#14579152C2316yes—
208#14579152C23112yes—
209#14579152C2316yes—
210#14579152C2316yes—
211#14579152C2316yes—
212#14579152C23112yes—
213#14579152C2313yes—
214#14579152C2313yes—
215#14579151C23112yes—
216#14579151C23112yes—
217#14579151C23112yes—
218#14579151C23112yes—
219#14579151C23112yes—
220#14579151C23112yes—
221#14579151C23112yes—
222#14579151C23112yes—
223#14579151C2316yes—
224#14579151C2316yes—
225#14579150C2313yes—
226#14579149C2313yes—
227#14579148C2313yes—
228#14579147C2316yes—
229#14579147C2316yes—
230#14579146C2316yes—
231#14579146C2316yes—
232#14579145C2316yes—
233#14579144C2316yes—
234#14579143C2316yes—
235#14579143C2316yes—
236#14579142C2316yes—
237#14579141C2316yes—
238#14579141C2316yes—
239#14579141C2316yes—
240#14579141C2313yes—
241#14579140C2316yes—
242#14579140C2316yes—
243#14579140C2316yes—
244#14579140C2313yes—
245#14579139C23112yes—
246#14579139C23112yes—
247#14579139C23112yes—
248#14579139C2316yes—
249#14579138C23112yes—
250#14579138C23112yes—
251#14579138C23112yes—
252#14579138C2316yes—
253#14579137C2316yes—
254#14579137C2316yes—
255#14579137C2316yes—
256#14579137C2313yes—
257#14579136C2311yescharacteristic
258#14579135C2311yescharacteristic
259#14579134C2312yes—
260#14579133C2312yes—
261#14579132C2311yescharacteristic
262Q8×Dic79C2313yes—
263Q8×Dic79C2316yes—
264Q8×Dic79C2311yescharacteristic
265Q8×Dic79C2312yes—
266Q8×Dic79C2316yes—
267Q8×Dic79C2313yes—
268Q8×Dic79C2311yescharacteristic
269Q8×Dic79C2316yes—
270Q8×Dic79C2313yes—
271C4×Dic158C2316yes—
272C4×Dic158C23112yes—
273C4×Dic158C2313yes—
274C4×Dic158C2316yes—
275C4×Dic158C2313yes—
276C4×Dic158C2316yes—
277C4×Dic158C23112yes—
278C4×Dic158C2316yes—
279C4×Dic158C23112yes—
280C4×Dic158C2316yes—
281C4×Dic158C2313yes—
282C4×Dic158C2313yes—
283C4×Dic158C2316yes—
284C4×Dic158C2313yes—
285C4×Dic158C2316yes—
286#14579126C2316yes—
287#14579126C23112yes—
288#14579126C2313yes—
289#14579126C2316yes—
290#14579126C2313yes—
291#14579126C2316yes—
292#14579126C23112yes—
293#14579126C2316yes—
294#14579126C2316yes—
295#14579126C23112yes—
296#14579126C2313yes—
297#14579126C2313yes—
298#14579126C2316yes—
299#14579126C2316yes—
300#14579126C2313yes—
301C4×D316C2316yes—
302C4×D316C2313yes—
303D4×Dic79C2316yes—
304D4×Dic79C2313yes—
305#14579123C2316yes—
306#14579123C2313yes—
307C4×C22⋊D79C2316yes—
308C4×C22⋊D79C2316yes—
309C4×C22⋊D79C2316yes—
310(C22⋊D79)⋊C4C2316yes—
311(C22⋊D79)⋊C4C2316yes—
312(C22⋊D79)⋊C4C2316yes—
313#14579120C2316yes—
314#14579120C2316yes—
315#14579120C2316yes—
316#14579119C2316yes—
317#14579119C2316yes—
318#14579119C2316yes—
319#14579119C2316yes—
320#14579119C2316yes—
321#14579119C2316yes—
322#14579118C2316yes—
323#14579118C2316yes—
324#14579118C23112yes—
325#14579118C23112yes—
326#14579117C2316yes—
327#14579117C2316yes—
328#14579117C23112yes—
329#14579117C23112yes—
330C2×C4⋊Dic79C2313yes—
331C2×Dic79⋊C4C2316yes—
332C4⋊C4×D79C2316yes—
333C4⋊C4×D79C2313yes—
334C4⋊C4×D79C2313yes—
335C4⋊C4×D79C2313yes—
336C4⋊C4×D79C2313yes—
337C4⋊C4×D79C2316yes—
338C4⋊C4×D79C2316yes—
339C4⋊C4×D79C2316yes—
340C4⋊C4×D79C2316yes—
341C4⋊C4×D79C2316yes—
342C4⋊C4×D79C2316yes—
343C4⋊C4×D79C2313yes—
344C4⋊C4×D79C2316yes—
345C4⋊C4×D79C2311yescharacteristic
346C4⋊C4×D79C23112yes—
347C4⋊C4×D79C2316yes—
348C22⋊C4×D79C2312yes—
349C22⋊C4×D79C2316yes—
350C22⋊C4×D79C2316yes—
351C22⋊C4×D79C2316yes—
352C22⋊C4×D79C2316yes—
353C2×C4×Dic79C2313yes—
354C2×C4×Dic79C2313yes—
355C2×C4×Dic79C2313yes—
356C42×D79C2313yes—
357C42×D79C2313yes—
358C42×D79C2313yes—
359C42×D79C2313yes—
360C42×D79C2313yes—
361C42×D79C2313yes—
362C42×D79C2313yes—
363C42×D79C2313yes—
364C42×D79C23112yes—
365C42×D79C2316yes—
366C22×Q8×C79C2311yescharacteristic
367C22×Q8×C79C2312yes—
368C4⋊Q8×C79C2316yes—
369C4⋊Q8×C79C2313yes—
370C4⋊Q8×C79C2313yes—
371#126×C79C2316yes—
372#126×C79C23112yes—
373#125×C79C2316yes—
374#125×C79C23112yes—
375#125×C79C2316yes—
376#125×C79C2313yes—
377#124×C79C2313yes—
378#123×C79C2316yes—
379C22⋊Q8×C79C2316yes—
380C22⋊Q8×C79C2316yes—
381C22⋊Q8×C79C2316yes—
382C22⋊Q8×C79C2313yes—
383#121×C79C2311yescharacteristic
384C4×Q8×C79C2313yes—
385C4×Q8×C79C2316yes—
386C4×Q8×C79C2311yescharacteristic
387C4×Q8×C79C2312yes—
388C4×Q8×C79C2311yescharacteristic
389C4×Q8×C79C2313yes—
390C4×Q8×C79C2316yes—
391C4×Q8×C79C2313yes—
392C4×Q8×C79C2316yes—
393C4×D4×C79C2316yes—
394C4×D4×C79C2313yes—
395#117×C79C2316yes—
396#117×C79C2316yes—
397#117×C79C2316yes—
398C2×C4⋊C4×C79C2313yes—
399C2×C42×C79C2313yes—
400C23×D79C2412yes—
401C23×D79C2411yescharacteristic
402C2×Dic158—212no—
403C2×Dic158—224no—
404C2×Dic158C2416yes—
405C2×Dic158C24112yes—
406C2×Dic158C2413yes—
407C2×Dic158C2416yes—
408C2×Dic158C2416yes—
409C2×Dic158C2413yes—
410C2×Dic158C2413yes—
411Q8×D79—212no—
412Q8×D79—224no—
413Q8×D79—212no—
414Q8×D79—212no—
415Q8×D79—224no—
416Q8×D79—24no—
417Q8×D79—28no—
418Q8×D79#4118yes—
419C2×D316C2412yes—
420C2×D316C2411yescharacteristic
421C2×C22⋊D79C2412yes—
422C2×C22⋊D79C2412yes—
423C2×C22⋊D79C2412yes—
424D4×D79—24no—
425D4×D79—28no—
426C22×Dic79C2413yes—
427C22×Dic79C2416yes—
428C22×Dic79C2411yescharacteristic
429C22×Dic79C2413yes—
430C2×C4×D79—212no—
431C2×C4×D79—224no—
432C2×C4×D79—24no—
433C2×C4×D79—212no—
434C2×C4×D79C2413yes—
435C2×C4×D79C2416yes—
436C2×C4×D79C2413yes—
437C2×C4×D79C2413yes—
438C2×C4×D79C2416yes—
439C2×C4×D79C2416yes—
440C2×C4×D79C2416yes—
441C2×C4×D79C2411yescharacteristic
442C2×C4×D79C2413yes—
443C2×C4×D79C2411yescharacteristic
444C2×C4×D79C2411yescharacteristic
445C2×C4×D79C2412yes—
446C2×C4×D79C2413yes—
447C2×C4×D79C2413yes—
448C2×C4×D79C2413yes—
449C2×C4×D79C2413yes—
450C2×C4×D79C2411yescharacteristic
451C4⋊Dic79C2413yes—
452C4⋊Dic79C2413yes—
453C4⋊Dic79C2416yes—
454C4⋊Dic79C2416yes—
455C4⋊Dic79C2416yes—
456C4⋊Dic79C2416yes—
457C4⋊Dic79C2416yes—
458C4⋊Dic79C2416yes—
459C4⋊Dic79C2413yes—
460C4⋊Dic79C2416yes—
461C4⋊Dic79C2411yescharacteristic
462C4⋊Dic79C24112yes—
463C4⋊Dic79C2416yes—
464Dic79⋊C4C2416yes—
465Dic79⋊C4C2416yes—
466Dic79⋊C4C2416yes—
467Dic79⋊C4C2416yes—
468Dic79⋊C4C2416yes—
469Dic79⋊C4C24112yes—
470Dic79⋊C4C2416yes—
471Dic79⋊C4C2416yes—
472Dic79⋊C4C2416yes—
473Dic79⋊C4C24112yes—
474Dic79⋊C4C24112yes—
475Dic79⋊C4C2416yes—
476Dic79⋊C4C2416yes—
477Dic79⋊C4C2416yes—
478Dic79⋊C4C2412yes—
479Dic79⋊C4C24112yes—
480Dic79⋊C4C24112yes—
481Dic79⋊C4C2416yes—
482Dic79⋊C4C2416yes—
483C22⋊Dic79C2412yes—
484C22⋊Dic79C2416yes—
485C22⋊Dic79C2416yes—
486C22⋊Dic79C2416yes—
487C22⋊Dic79C2416yes—
488(C2×D79)⋊C4C2412yes—
489(C2×D79)⋊C4C2412yes—
490(C2×D79)⋊C4C2416yes—
491(C2×D79)⋊C4C2416yes—
492(C2×D79)⋊C4C2416yes—
493(C2×D79)⋊C4C2416yes—
494(C2×D79)⋊C4C2416yes—
495(C2×D79)⋊C4C2416yes—
496(C2×D79)⋊C4C2416yes—
497(C2×D79)⋊C4C2416yes—
498C4×Dic79C2413yes—
499C4×Dic79C2413yes—
500C4×Dic79C2413yes—
501C4×Dic79C2413yes—
502C4×Dic79C2413yes—
503C4×Dic79C2413yes—
504C4×Dic79C2413yes—
505C4×Dic79C2413yes—
506C4×Dic79C2413yes—
507C4×Dic79C2413yes—
508C4×Dic79C2413yes—
509C4×Dic79C2413yes—
510C4×Dic79C24112yes—
511C4×Dic79C24112yes—
512C4×Dic79C24112yes—
513C4×Dic79C2416yes—
514C4×Dic79C2416yes—
515C4×Dic79C2416yes—
516C2×Q8×C79—24no—
517C2×Q8×C79—28no—
518C2×Q8×C79C2413yes—
519C2×Q8×C79C2416yes—
520C2×Q8×C79C2413yes—
521C2×Q8×C79C2411yescharacteristic
522C2×D4×C79C2412yes—
523C2×D4×C79C2411yescharacteristic
524C22×C4×C79C2413yes—
525C22×C4×C79C2416yes—
526C22×C4×C79C2411yescharacteristic
527C22×C4×C79C2413yes—
528C4⋊C4×C79C2413yes—
529C4⋊C4×C79C2413yes—
530C4⋊C4×C79C2416yes—
531C4⋊C4×C79C2416yes—
532C4⋊C4×C79C2416yes—
533C4⋊C4×C79C2416yes—
534C4⋊C4×C79C2416yes—
535C4⋊C4×C79C2416yes—
536C4⋊C4×C79C2413yes—
537C4⋊C4×C79C2416yes—
538C4⋊C4×C79C2411yescharacteristic
539C4⋊C4×C79C24112yes—
540C4⋊C4×C79C2416yes—
541C22⋊C4×C79C2412yes—
542C22⋊C4×C79C2416yes—
543C22⋊C4×C79C2416yes—
544C22⋊C4×C79C2416yes—
545C22⋊C4×C79C2416yes—
546C42×C79C2413yes—
547C42×C79C2413yes—
548C42×C79C2413yes—
549C42×C79C2413yes—
550C42×C79C24112yes—
551C42×C79C2416yes—
552C23×C79C2512yes—
553C23×C79C2511yescharacteristic
554C22×D79—22no—
555C22×D79—22no—
556C22×D79—24no—
557C22×D79—24no—
558C22×D79—24no—
559C22×D792−1+414yes—
560C22×D79C2512yes—
561C22×D79C2511yescharacteristic
562C22×D79C2511yescharacteristic
563Q8×C79—26no—
564Q8×C79—212no—
565Q8×C79—26no—
566Q8×C79C2×#4114yes—
567D4×C79—24no—
568D4×C79—22no—
569C2×C4×C79—26no—
570C2×C4×C79—26no—
571C2×C4×C79—212no—
572C2×C4×C79—22no—
573C2×C4×C79C2511yescharacteristic
574C2×C4×C79C2513yes—
575C2×C4×C79C2516yes—
576C2×C4×C79C2512yes—
577C2×C4×C79C2513yes—
578C2×C4×C79C2513yes—
579C2×C4×C79C2516yes—
580C2×C4×C79C2513yes—
581C2×C4×C79C2511yescharacteristic
582C22⋊D79—24no—
583C22⋊D79—24no—
584C22⋊D79—24no—
585C2×Dic79—26no—
586C2×Dic79—26no—
587C2×Dic79—212no—
588C2×Dic79—22no—
589C2×Dic79C2511yescharacteristic
590C2×Dic79C2513yes—
591C2×Dic79C2516yes—
592C2×Dic79C2512yes—
593C2×Dic79C2513yes—
594C2×Dic79C2513yes—
595C2×Dic79C2516yes—
596C2×Dic79C2513yes—
597C2×Dic79C2511yescharacteristic
598D316—24no—
599D316—22no—
600C4×D79—26no—
601C4×D79—212no—
602C4×D79—26no—
603C4×D79—26no—
604C4×D79—22no—
605C4×D79—26no—
606C4×D79—26no—
607C4×D79—24no—
608C4×D79—212no—
609C4×D79—26no—
610C4×D79—212no—
611C4×D79—22no—
612C4×D79—26no—
613C4×D79—212no—
614C4×D79—22no—
615C4×D79C2×#41112yes—
616C4×D792−1+414yes—
617Dic158—26no—
618Dic158—212no—
619Dic158—26no—
620Dic158—212no—
621Dic158—224no—
622Dic158—212no—
623Dic158C2×#41112yes—
624C22×C79—21no—
625C22×C79—21no—
626C22×C79—22no—
627C22×C79—22no—
628C22×C79—22no—
629C22×C79C2×2−1+412yes—
630C22×C79C2611yescharacteristic
631C2×D79—21no—
632C2×D79—21no—
633C2×D79—28no—
634C2×D79—22no—
635C2×D79—22no—
636C2×D79—22no—
637C2×D79—48no—
638C2×D79C22×#4112yes—
639C2×D79C2×2−1+412yes—
640C2×D79C2×2−1+412yes—
641C2×D79C2×2−1+412yes—
642C4×C79—23no—
643C4×C79—26no—
644C4×C79—23no—
645C4×C79—23no—
646C4×C79—21no—
647C4×C79—22no—
648C4×C79—26no—
649C4×C79C22×#4116yes—
650C4×C79C2×2−1+412yes—
651Dic79—23no—
652Dic79—26no—
653Dic79—22no—
654Dic79—26no—
655Dic79—23no—
656Dic79—23no—
657Dic79—21no—
658Dic79C22×#4116yes—
659Dic79C2×2−1+412yes—
660C2×#3523—791nomaximal, Sylow
661C2×C79—22no—
662C2×C79—42no—
663C2×C79C23×#4111yescharacteristic
664C2×C79C22×2−1+411yescharacteristic
665C2×C79C22×2−1+411yescharacteristic
666D79—22no—
667D79—42no—
668D79#352314yesdirect product factor
669#3523—793no—
670#3523—791no—
671#3523—793no—
672#3523—796no—
673#3523—792no—
674#3523—791no—
675#3523—796no—
676#3523—793no—
677#3523—793no—
678#3523—792no—
679#3523—791no—
680#3523D7911yescharacteristic, direct product factor
681C2×#557—791no—
682C2×#557—793no—
683C2×#556—793no—
684C2×#552—796no—
685C2×D4×Q8—792no—
686C2×D4×Q8—791no—
687C2×#541—796no—
688C2×#533—793no—
689C2×#529—793no—
690C2×#519—792no—
691C22×C4×Q8—791no—
692C79C2×#352311yescharacteristic, complemented, Sylow
693C23×Q8—791no—
694C23×Q8—792no—
695#557—796no—
696#557—793no—
697#557—793no—
698#557—796no—
699#557—7912no—
700#557—796no—
701#557—792no—
702#557—796no—
703#557—796no—
704#557—793no—
705#557—793no—
706#557—791no—
707#557—793no—
708#557C2×D7911yescharacteristic, complemented
709#557C2×D7913yescomplemented
710#556—793no—
711#556—7912no—
712#556—796no—
713#556—796no—
714#556—796no—
715#556—793no—
716#556—793no—
717#556—796no—
718#556C2×D7913yescomplemented
719#552—7912no—
720#552—7912no—
721#552—796no—
722#552—7912no—
723#552—796no—
724#552—796no—
725#552—796no—
726#552—796no—
727#552—7912no—
728#552—796no—
729#552—796no—
730#552C2×D7916yescomplemented
731D4×Q8—792no—
732D4×Q8—792no—
733D4×Q8—792no—
734D4×Q8—796no—
735D4×Q8—793no—
736D4×Q8—796no—
737D4×Q8—796no—
738D4×Q8—796no—
739D4×Q8—792no—
740D4×Q8—791no—
741D4×Q8—796no—
742D4×Q8—793no—
743D4×Q8C2×D7912yescomplemented
744D4×Q8C2×D7911yescharacteristic, complemented
745#541—796no—
746#541—7912no—
747#541—7912no—
748#541—7912no—
749#541—7912no—
750#541—796no—
751#541—796no—
752#541—796no—
753#541—796no—
754#541—796no—
755#541—796no—
756#541C2×D7916yescomplemented
757#533—793no—
758#533—793no—
759#533—796no—
760#533—796no—
761#533—796no—
762#533—796no—
763#533—796no—
764#533—796no—
765#533—793no—
766#533C2×D7913yescomplemented
767C2×C4⋊Q8—793no—
768C2×C4⋊Q8—793no—
769C2×C4⋊Q8—796no—
770#529—796no—
771#529—793no—
772#529—793no—
773#529—796no—
774#529—793no—
775#529—793no—
776#529—793no—
777#529—796no—
778#529—793no—
779#529—796no—
780#529—793no—
781#529C2×D7913yes—
782C2×#126—796no—
783C2×#126—7912no—
784C2×#125—793no—
785C2×#125—796no—
786C2×#125—7912no—
787C2×#125—796no—
788C2×#124—793no—
789C2×#123—796no—
790C2×C22⋊Q8—793no—
791C2×C22⋊Q8—796no—
792C2×C22⋊Q8—796no—
793C2×C22⋊Q8—796no—
794C2×#121—791no—
795#519—792no—
796#519—796no—
797#519—796no—
798#519—792no—
799#519—792no—
800#519—796no—
801#519—796no—
802#519C2×D7912yescomplemented
803C2×C4×Q8—791no—
804C2×C4×Q8—791no—
805C2×C4×Q8—793no—
806C2×C4×Q8—791no—
807C2×C4×Q8—793no—
808C2×C4×Q8—791no—
809C2×C4×Q8—793no—
810C2×C4×Q8—791no—
811C2×C4×Q8—793no—
812C2×C4×Q8—796no—
813C2×C4×Q8—792no—
814C2×C4×Q8—796no—
815C2×C4×Q8—793no—
816C2×C4×Q8—796no—
817C2×C4×Q8—793no—
818C2×C4×Q8—793no—
819C2×C4×Q8C2×D7911yescharacteristic, complemented
820C2×C4×D4—796no—
821C2×C4×D4—793no—
822C2×#117—796no—
823C2×#117—796no—
824C2×#117—796no—
825C22×C4⋊C4—793no—
826C22×C42—793no—
827C22×Q8—791no—
828C22×Q8—793no—
829C22×Q8—793no—
830C22×Q8—796no—
831C22×Q8—793no—
832C22×Q8—791no—
833C22×Q8—796no—
834C22×Q8—792no—
835C22×Q8—793no—
836C22×Q8—796no—
837C22×Q8—1588no—
838C22×Q8—15816no—
839C22×Q8C22×D7911yescharacteristic
840C22×Q8C22×D7912yes—
841C22×D4—792no—
842C22×D4—791no—
843C23×C4—793no—
844C23×C4—793no—
845C23×C4—796no—
846C23×C4—791no—
847C4⋊Q8—796no—
848C4⋊Q8—796no—
849C4⋊Q8—796no—
850C4⋊Q8—796no—
851C4⋊Q8—796no—
852C4⋊Q8—796no—
853C4⋊Q8—796no—
854C4⋊Q8—796no—
855C4⋊Q8—7912no—
856C4⋊Q8—7912no—
857C4⋊Q8—793no—
858C4⋊Q8—793no—
859C4⋊Q8—796no—
860C4⋊Q8C22×D7913yes—
861C4⋊Q8C22×D7913yes—
862C4⋊Q8C22×D7916yes—
863#126—796no—
864#126—796no—
865#126—796no—
866#126—7912no—
867#126—7912no—
868#126—7912no—
869#126—796no—
870#126—796no—
871#126—796no—
872#126—7912no—
873#126—7912no—
874#126—7912no—
875#126—796no—
876#126—7912no—
877#126C22×D7916yes—
878#126C22×D79112yes—
879#125—796no—
880#125—796no—
881#125—793no—
882#125—793no—
883#125—7912no—
884#125—7912no—
885#125—796no—
886#125—796no—
887#125—7912no—
888#125—7912no—
889#125—7912no—
890#125—7912no—
891#125—7912no—
892#125—7912no—
893#125—7912no—
894#125—7912no—
895#125—796no—
896#125—796no—
897#125—793no—
898#125—796no—
899#125—7912no—
900#125—796no—
901#125C22×D7913yes—
902#125C22×D7916yes—
903#125C22×D79112yes—
904#125C22×D7916yes—
905#124—793no—
906#124—793no—
907#124—796no—
908#124—796no—
909#124—793no—
910#124C22×D7913yes—
911#123—796no—
912#123—796no—
913#123—796no—
914#123—796no—
915#123—796no—
916#123—796no—
917#123—796no—
918#123C22×D7916yes—
919C22⋊Q8—793no—
920C22⋊Q8—796no—
921C22⋊Q8—796no—
922C22⋊Q8—796no—
923C22⋊Q8—793no—
924C22⋊Q8—796no—
925C22⋊Q8—796no—
926C22⋊Q8—796no—
927C22⋊Q8—796no—
928C22⋊Q8—793no—
929C22⋊Q8—7912no—
930C22⋊Q8—796no—
931C22⋊Q8—7912no—
932C22⋊Q8—796no—
933C22⋊Q8—7912no—
934C22⋊Q8—796no—
935C22⋊Q8—796no—
936C22⋊Q8—7912no—
937C22⋊Q8—7912no—
938C22⋊Q8—7912no—
939C22⋊Q8C22×D7913yes—
940C22⋊Q8C22×D7916yes—
941C22⋊Q8C22×D7916yes—
942C22⋊Q8C22×D7916yes—
943#121—791no—
944#121—792no—
945#121—791no—
946#121—791no—
947#121—792no—
948#121C22×D7911yescharacteristic
949C4×Q8—791no—
950C4×Q8—793no—
951C4×Q8—791no—
952C4×Q8—793no—
953C4×Q8—796no—
954C4×Q8—792no—
955C4×Q8—796no—
956C4×Q8—793no—
957C4×Q8—796no—
958C4×Q8—793no—
959C4×Q8—796no—
960C4×Q8—793no—
961C4×Q8—793no—
962C4×Q8—796no—
963C4×Q8—793no—
964C4×Q8—7912no—
965C4×Q8—796no—
966C4×Q8—796no—
967C4×Q8—7912no—
968C4×Q8—796no—
969C4×Q8—796no—
970C4×Q8—793no—
971C4×Q8—7912no—
972C4×Q8—796no—
973C4×Q8—793no—
974C4×Q8—796no—
975C4×Q8—793no—
976C4×Q8—793no—
977C4×Q8—796no—
978C4×Q8—793no—
979C4×Q8—7912no—
980C4×Q8—796no—
981C4×Q8—796no—
982C4×Q8—796no—
983C4×Q8—7912no—
984C4×Q8—796no—
985C4×Q8—793no—
986C4×Q8—7912no—
987C4×Q8—796no—
988C4×Q8C22×D7911yescharacteristic
989C4×Q8C22×D7913yes—
990C4×Q8C22×D7911yescharacteristic
991C4×Q8C22×D7913yes—
992C4×Q8C22×D7916yes—
993C4×Q8C22×D7912yes—
994C4×Q8C22×D7916yes—
995C4×Q8C22×D7913yes—
996C4×Q8C22×D7916yes—
997C4×D4—796no—
998C4×D4—793no—
999C4×D4—796no—
1000C4×D4—796no—
1001C4×D4—796no—
1002C4×D4—796no—
1003C4×D4—793no—
1004C4×D4—796no—
1005C4×D4—796no—
1006C4×D4—796no—
1007C4×D4—796no—
1008C4×D4—793no—
1009C4×D4C22×D7916yes—
1010C4×D4C22×D7913yes—
1011#117—796no—
1012#117—796no—
1013#117—796no—
1014#117—796no—
1015#117—796no—
1016#117—796no—
1017#117—796no—
1018#117—796no—
1019#117—796no—
1020#117—796no—
1021#117—796no—
1022#117—7912no—
1023#117—7912no—
1024#117—796no—
1025#117—796no—
1026#117—7912no—
1027#117—7912no—
1028#117C22×D7916yes—
1029#117C22×D7916yes—
1030#117C22×D7916yes—
1031C2×C4⋊C4—796no—
1032C2×C4⋊C4—793no—
1033C2×C4⋊C4—793no—
1034C2×C4⋊C4—793no—
1035C2×C4⋊C4—796no—
1036C2×C4⋊C4—796no—
1037C2×C4⋊C4—793no—
1038C2×C4⋊C4—793no—
1039C2×C4⋊C4—796no—
1040C2×C4⋊C4—796no—
1041C2×C4⋊C4—796no—
1042C2×C4⋊C4—796no—
1043C2×C4⋊C4—796no—
1044C2×C4⋊C4—793no—
1045C2×C4⋊C4—796no—
1046C2×C4⋊C4—791no—
1047C2×C4⋊C4—7912no—
1048C2×C4⋊C4—796no—
1049C2×C4⋊C4C22×D7913yes—
1050C2×C22⋊C4—792no—
1051C2×C22⋊C4—796no—
1052C2×C22⋊C4—796no—
1053C2×C22⋊C4—796no—
1054C2×C22⋊C4—796no—
1055C2×C42—793no—
1056C2×C42—793no—
1057C2×C42—793no—
1058C2×C42—793no—
1059C2×C42—7912no—
1060C2×C42—796no—
1061C2×C42—793no—
1062C2×C42—793no—
1063C2×C42—793no—
1064C2×C42—793no—
1065C2×C42—793no—
1066C2×C42—793no—
1067C2×C42—793no—
1068C2×C42C22×D7913yes—
1069C24—791no—
1070C24—792no—
1071C2×Q8—24no—
1072C2×Q8—28no—
1073C2×Q8—798no—
1074C2×Q8—793no—
1075C2×Q8—796no—
1076C2×Q8—793no—
1077C2×Q8—796no—
1078C2×Q8—7912no—
1079C2×Q8—793no—
1080C2×Q8—796no—
1081C2×Q8—15812no—
1082C2×Q8—15824no—
1083C2×Q8—15812no—
1084C2×Q8—15812no—
1085C2×Q8—15824no—
1086C2×Q8—15812no—
1087C2×Q8—15824no—
1088C2×Q8—1584no—
1089C2×Q8—1588no—
1090C2×Q8C23×D7913yes—
1091C2×Q8C23×D7913yes—
1092C2×Q8C23×D7916yes—
1093C2×Q8C23×D7911yescharacteristic
1094C2×D4—792no—
1095C2×D4—792no—
1096C2×D4—792no—
1097C2×D4—792no—
1098C2×D4—791no—
1099C2×D4—1584no—
1100C2×D4—1588no—
1101C2×D4C23×D7912yes—
1102C2×D4C23×D7911yescharacteristic
1103C22×C4—791no—
1104C22×C4—793no—
1105C22×C4—791no—
1106C22×C4—793no—
1107C22×C4—793no—
1108C22×C4—796no—
1109C22×C4—791no—
1110C22×C4—793no—
1111C22×C4—791no—
1112C22×C4—791no—
1113C22×C4—796no—
1114C22×C4—792no—
1115C22×C4—793no—
1116C22×C4—796no—
1117C22×C4—793no—
1118C22×C4—793no—
1119C22×C4—793no—
1120C22×C4—793no—
1121C22×C4—793no—
1122C22×C4—796no—
1123C22×C4—796no—
1124C22×C4—1584no—
1125C22×C4—15824no—
1126C22×C4—15812no—
1127C22×C4—15812no—
1128C22×C4C23×D7911yescharacteristic
1129C22×C4C23×D7913yes—
1130C22×C4C23×D7913yes—
1131C22×C4C23×D7916yes—
1132C4⋊C4—796no—
1133C4⋊C4—796no—
1134C4⋊C4—796no—
1135C4⋊C4—796no—
1136C4⋊C4—7912no—
1137C4⋊C4—796no—
1138C4⋊C4—796no—
1139C4⋊C4—796no—
1140C4⋊C4—796no—
1141C4⋊C4—7912no—
1142C4⋊C4—7912no—
1143C4⋊C4—796no—
1144C4⋊C4—796no—
1145C4⋊C4—796no—
1146C4⋊C4—792no—
1147C4⋊C4—7912no—
1148C4⋊C4—7912no—
1149C4⋊C4—796no—
1150C4⋊C4—796no—
1151C4⋊C4—793no—
1152C4⋊C4—793no—
1153C4⋊C4—796no—
1154C4⋊C4—796no—
1155C4⋊C4—796no—
1156C4⋊C4—796no—
1157C4⋊C4—796no—
1158C4⋊C4—796no—
1159C4⋊C4—793no—
1160C4⋊C4—796no—
1161C4⋊C4—791no—
1162C4⋊C4—7912no—
1163C4⋊C4—796no—
1164C4⋊C4C23×D7913yes—
1165C4⋊C4C23×D7913yes—
1166C4⋊C4C23×D7916yes—
1167C4⋊C4C23×D7916yes—
1168C4⋊C4C23×D7916yes—
1169C4⋊C4C23×D7916yes—
1170C4⋊C4C23×D7916yes—
1171C4⋊C4C23×D7916yes—
1172C4⋊C4C23×D7913yes—
1173C4⋊C4C23×D7916yes—
1174C4⋊C4C23×D7911yescharacteristic
1175C4⋊C4C23×D79112yes—
1176C4⋊C4C23×D7916yes—
1177C22⋊C4—792no—
1178C22⋊C4—796no—
1179C22⋊C4—796no—
1180C22⋊C4—796no—
1181C22⋊C4—796no—
1182C22⋊C4—792no—
1183C22⋊C4—792no—
1184C22⋊C4—796no—
1185C22⋊C4—796no—
1186C22⋊C4—796no—
1187C22⋊C4—796no—
1188C22⋊C4—796no—
1189C22⋊C4—796no—
1190C22⋊C4—796no—
1191C22⋊C4—796no—
1192C22⋊C4C23×D7912yes—
1193C22⋊C4C23×D7916yes—
1194C22⋊C4C23×D7916yes—
1195C22⋊C4C23×D7916yes—
1196C22⋊C4C23×D7916yes—
1197C42—793no—
1198C42—793no—
1199C42—793no—
1200C42—793no—
1201C42—793no—
1202C42—793no—
1203C42—793no—
1204C42—793no—
1205C42—793no—
1206C42—793no—
1207C42—793no—
1208C42—793no—
1209C42—7912no—
1210C42—7912no—
1211C42—7912no—
1212C42—796no—
1213C42—796no—
1214C42—796no—
1215C42C23×D7913yes—
1216C42C23×D7913yes—
1217C42C23×D7913yes—
1218C42C23×D7913yes—
1219C42C23×D79112yes—
1220C42C23×D7916yes—
1221C23—791no—
1222C23—794no—
1223C23—791no—
1224C23—792no—
1225C23—1584no—
1226C23—1584no—
1227C23—1584no—
1228C23—1582no—
1229C23—1582no—
1230C23C24×D7912yes—
1231C23C24×D7911yescharacteristic
1232Q8—26no—
1233Q8—26no—
1234Q8—212no—
1235Q8—7912no—
1236Q8—15812no—
1237Q8—15824no—
1238Q8—15812no—
1239Q8—1586no—
1240Q8—1586no—
1241Q8—15812no—
1242Q8#41×D7914yes—
1243D4—24no—
1244D4—22no—
1245D4—1584no—
1246D4—1584no—
1247D4—1584no—
1248D4—1584no—
1249D4—1582no—
1250C2×C4—26no—
1251C2×C4—22no—
1252C2×C4—26no—
1253C2×C4—212no—
1254C2×C4—791no—
1255C2×C4—793no—
1256C2×C4—794no—
1257C2×C4—7912no—
1258C2×C4—791no—
1259C2×C4—793no—
1260C2×C4—796no—
1261C2×C4—792no—
1262C2×C4—793no—
1263C2×C4—793no—
1264C2×C4—796no—
1265C2×C4—15812no—
1266C2×C4—1586no—
1267C2×C4—1582no—
1268C2×C4—15812no—
1269C2×C4—1586no—
1270C2×C4—1582no—
1271C2×C4—1586no—
1272C2×C4—1586no—
1273C2×C4—1586no—
1274C2×C4—1586no—
1275C2×C4—1584no—
1276C2×C4—15812no—
1277C2×C4—1586no—
1278C2×C4—15812no—
1279C2×C4—1582no—
1280C2×C4—1586no—
1281C2×C4—1582no—
1282C2×C4—15812no—
1283C2×C4—1586no—
1284C2×C4C24×D7911yescharacteristic
1285C2×C4C24×D7913yes—
1286C2×C4C24×D7916yes—
1287C2×C4C24×D7912yes—
1288C2×C4C24×D7913yes—
1289C2×C4C24×D7913yes—
1290C2×C4C24×D7916yes—
1291C2×C4C24×D7911yescharacteristic
1292C2×C4C24×D7913yes—
1293C22—21no—
1294C22—21no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—3168no—
1299C22—792no—
1300C22—792no—
1301C22—792no—
1302C22—792no—
1303C22—1588no—
1304C22—1582no—
1305C22—1582no—
1306C22—1582no—
1307C22—1581no—
1308C22—1581no—
1309C222−1+4×D7912yes—
1310C22C25×D7911yescharacteristic
1311C4—23no—
1312C4—26no—
1313C4—23no—
1314C4—23no—
1315C4—21no—
1316C4—22no—
1317C4—26no—
1318C4—796no—
1319C4—792no—
1320C4—1583no—
1321C4—1586no—
1322C4—1583no—
1323C4—1583no—
1324C4—1581no—
1325C4—1582no—
1326C4—1586no—
1327C4C2×#41×D7916yes—
1328C42−1+4×D7912yes—
1329C2—22no—
1330C2—42no—
1331C2—3162no—
1332C2—794no—
1333C2—1582no—
1334C2C22×#41×D7911yescharacteristic
1335C2C2×2−1+4×D7911yescharacteristic
1336C2C2×2−1+4×D7911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3523C2
prime radical#121×D79C22
hypercenter#3523D79
hypocenterC79C2×#3523
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3523

Complements

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

NH ≅ G/Ntype
1. #23777497C2semidirect
2. #23777496C2semidirect
3. #23777495C2semidirect
4. #23777494C2semidirect
5. #23777493C2semidirect
6. #23777492C2semidirect
7. #23777491C2semidirect
8. #23777490C2semidirect
9. #23777489C2semidirect
10. #23777488C2semidirect
11. #23777487C2semidirect
12. #557×D79C2semidirect
13. #557×D79C2semidirect
14. #556×D79C2semidirect
15. #552×D79C2semidirect
16. D4×Q8×D79C2semidirect
17. D4×Q8×D79C2semidirect
18. #541×D79C2semidirect
19. #533×D79C2semidirect
21. #519×D79C2semidirect
22. C2×C4×Q8×D79C2semidirect
23. C79×#3523C2semidirect
26. #19099292C22semidirect
27. #19099292C22semidirect
28. #19099291C22semidirect
29. #19099291C22semidirect
30. #19099291C22semidirect
31. #19099290C22semidirect
32. #19099290C22semidirect
33. #19099290C22semidirect
34. #19099289C22semidirect
35. #19099289C22semidirect
36. #19099288C22semidirect
37. #19099288C22semidirect
38. #19099288C22semidirect
39. #19099287C22semidirect
40. #19099286C22semidirect
41. #19099285C22semidirect
42. #19099284C22semidirect
43. #19099283C22semidirect
44. #19099282C22semidirect
45. #19099281C22semidirect
46. #19099280C22semidirect
47. #19099255C22semidirect
48. #19099254C22semidirect
49. #19099253C22semidirect
50. #19099252C22semidirect
51. #19099251C22semidirect
52. #19099250C22semidirect
53. #19099249C22semidirect
54. #19099248C22semidirect
55. #19099247C22semidirect
56. #19099246C22semidirect
57. #19099245C22semidirect
58. Q8×D316C22semidirect
59. Q8×D316C22semidirect
60. D4×Dic158C22semidirect
61. D4×Dic158C22semidirect
62. #19099228C22semidirect
63. #19099228C22semidirect
64. Q8×C22⋊D79C22semidirect
65. Q8×C22⋊D79C22semidirect
66. Q8×C22⋊D79C22semidirect
67. #19099226C22semidirect
68. #19099226C22semidirect
69. #19099226C22semidirect
70. #19099176C22semidirect
71. #19099175C22semidirect
72. #19099174C22semidirect
73. #19099173C22semidirect
74. #19099173C22semidirect
75. #19099172C22semidirect
76. #19099172C22semidirect
77. #19099171C22semidirect
78. #19099171C22semidirect
79. #19099170C22semidirect
80. #19099170C22semidirect
81. #19099120C22semidirect
82. #19099119C22semidirect
83. #19099118C22semidirect
84. #19099118C22semidirect
85. #19099117C22semidirect
86. #19099117C22semidirect
87. #19099116C22semidirect
88. #19099115C22semidirect
89. #19099115C22semidirect
117. #19099041C22semidirect
118. #19099040C22semidirect
119. #19099040C22semidirect
120. #19099039C22semidirect
121. #19099039C22semidirect
122. #19099039C22semidirect
123. #19099039C22semidirect
124. C2×Q8×Dic79C22semidirect
125. C2×C4×Dic158C22semidirect
126. C2×#14579126C22semidirect
136. C4×Q8×D79C22semidirect
137. C4×Q8×D79C22semidirect
138. C4×Q8×D79C22semidirect
139. C4×Q8×D79C22semidirect
147. #557×C79C22semidirect
148. #557×C79C22semidirect
149. #556×C79C22semidirect
150. #552×C79C22semidirect
151. D4×Q8×C79C22semidirect
152. D4×Q8×C79C22semidirect
153. #541×C79C22semidirect
154. #533×C79C22semidirect
156. #519×C79C22semidirect
157. C2×C4×Q8×C79C22semidirect
668. D79#3523direct (N × H)
680. #3523D79direct (N × H)
692. C79C2×#3523semidirect
708. #557C2×D79semidirect
709. #557C2×D79semidirect
718. #556C2×D79semidirect
730. #552C2×D79semidirect
743. D4×Q8C2×D79semidirect
744. D4×Q8C2×D79semidirect
756. #541C2×D79semidirect
766. #533C2×D79semidirect
802. #519C2×D79semidirect
819. C2×C4×Q8C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237774972
#237774962
#237774952
#237774942
#237774932
#237774922
#237774912
#237774902
#237774892
#237774882
#237774872
#557×D792
#556×D792
#552×D792
D4×Q8×D792
#541×D792
#533×D792
#529×D792
#519×D792
C2×C4×Q8×D792
C79×#35232
C2×#352379