Finite Group Databasebeta

← #34310702

Subgroups — #34310702

Order 20224.

1046 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098763C211yesmaximal, characteristic
2C2×#19098661C211yesmaximal, characteristic, complemented
3C2×C4×#11929611C211yesmaximal, characteristic, complemented
4#23766464C211yesmaximal, characteristic
5#23764223C211yesmaximal, characteristic
6#23764166C211yesmaximal, characteristic, complemented
7#23764096C211yesmaximal, characteristic, complemented
8#23764082C211yesmaximal, characteristic, complemented
9#23763755C211yesmaximal, characteristic, complemented
10#23763755C211yesmaximal, characteristic, complemented
11#23763660C211yesmaximal, characteristic, complemented
12#23763646C211yesmaximal, characteristic, complemented
13#23763275C211yesmaximal, characteristic, complemented
14#23763230C211yesmaximal, characteristic, complemented
15C79×#2351C211yesmaximal, characteristic, complemented
16C22×#11929611C2211yescharacteristic
17C22×#11929611C2211yescharacteristic
18C2×#14579158C2211yescharacteristic
19C2×C4×D316C2211yescharacteristic
20C2×C4×D316C2211yescharacteristic
21C2×#14579123—21no—
22#19098763C418yescomplemented
23#19098661—24no—
24C4×#11929611—24no—
25C2×#14579094C2211yescharacteristic
26C2×#14579092C2211yescharacteristic
27C2×C4⋊(C79⋊C8)C2211yescharacteristic
28C2×#14579085C2211yescharacteristic
29C2×#14579085C2211yescharacteristic
30C2×#14579081C2211yescharacteristic
31C2×#14579081C2211yescharacteristic
32C2×#14579081C2211yescharacteristic
33C2×#14579081C2211yescharacteristic
34C2×#14579081C2211yescharacteristic
35C2×#14579081C2211yescharacteristic
36C2×#14579072C2211yescharacteristic
37C2×#14579072C2211yescharacteristic
38C2×C4×C79⋊C8C2211yescharacteristic
39#19098465C2211yescharacteristic
40#19098465C2211yescharacteristic
41#19098464—21no—
42#19098441—21no—
43#19098441—21no—
44C4×C4⋊Dic79C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098318C2211yescharacteristic
50#19098318C2211yescharacteristic
51C2×C4×Q8×C79C2211yescharacteristic
52C2×C4×Q8×C79C2211yescharacteristic
53C2×C4×Q8×C79C2211yescharacteristic
54#389×C79—21no—
55#389×C79—21no—
56#389×C79C2211yescharacteristic
57#389×C79C2211yescharacteristic
58#382×C79—21no—
59#382×C79C2211yescharacteristic
60C4×C4⋊C4×C79—21no—
61C4×C4⋊C4×C79C2211yescharacteristic
62C22×D316—21no—
63C22×D316—21no—
64C22×D316C2311yescharacteristic
65C22×D316C2311yescharacteristic
66C22×C4×D79—21no—
67C22×C4×D79—21no—
68C2×#11929611—22no—
69C2×#11929611—22no—
70C2×#11929611—22no—
71C2×#11929611—22no—
72C2×#11929611C2×C414yescomplemented
73C2×#11929611C2×C414yescomplemented
74C22×C79⋊C8C2311yescharacteristic
75C22×C79⋊C8C2311yescharacteristic
76C22×C79⋊C8C2311yescharacteristic
77C22×C79⋊C8C2311yescharacteristic
78#14579158—22no—
79#14579158C2×C414yes—
80C4×D316—22no—
81C4×D316—22no—
82C4×D316—41no—
83C4×D316—41no—
84#14579123—44no—
85C2×C4⋊Dic79C2311yescharacteristic
86C2×C4⋊Dic79C2311yescharacteristic
87C2×(C2×D79)⋊C4—21no—
88C2×(C2×D79)⋊C4—21no—
89C2×(C2×D79)⋊C4—21no—
90C2×(C2×D79)⋊C4—21no—
91C2×(C2×D79)⋊C4—21no—
92C2×(C2×D79)⋊C4—21no—
93C2×C4×Dic79—21no—
94#14579094—22no—
95#14579092—22no—
96C4⋊(C79⋊C8)C2×C414yescomplemented
97#14579085—22no—
98#14579085D414yescomplemented
99#14579081—22no—
100#14579081—22no—
101#14579081—41no—
102#14579081—41no—
103#14579081C2×C414yescomplemented
104#14579081C2×C414yescomplemented
105#14579072—22no—
106#14579072—22no—
107C4×C79⋊C8—22no—
108C79⋊#95—21no—
109C22×Q8×C79C2311yescharacteristic
110C4×Q8×C79—22no—
111C4×Q8×C79—22no—
112C4×Q8×C79—22no—
113C4×Q8×C79—41no—
114C4×Q8×C79—41no—
115C4×Q8×C79C2×C414yescomplemented
116C2×C4⋊C4×C79—21no—
117C2×C4⋊C4×C79—21no—
118C2×C4⋊C4×C79—21no—
119C2×C4⋊C4×C79—21no—
120C2×C4⋊C4×C79—21no—
121C2×C4⋊C4×C79D411yescharacteristic
122C2×C4⋊C4×C79D411yescharacteristic
123C2×C4⋊C4×C79C2311yescharacteristic
124C2×C4⋊C4×C79C2311yescharacteristic
125C2×C4⋊C4×C79C2311yescharacteristic
126C2×C42×C79—21no—
127C2×C42×C79—21no—
128C2×C42×C79—21no—
129C2×C42×C79C2311yescharacteristic
130C2×C42×C79C2311yescharacteristic
131C2×C42×C79C2311yescharacteristic
132#95×C79—21no—
133#95×C79—21no—
134#95×C79—21no—
135#95×C79—21no—
136#95×C79D411yescharacteristic
137#95×C79D411yescharacteristic
138C23×D79—21no—
139C23×D79—21no—
140C2×D316—24no—
141C2×D316—24no—
142C2×D316—21no—
143C2×D316—21no—
144C2×D316—21no—
145C2×D316—21no—
146C2×D316—21no—
147C2×D316—21no—
148C2×D316—21no—
149C2×D316—21no—
150C2×D316—21no—
151C2×D316—21no—
152C2×D316—42no—
153C2×D316—42no—
154C2×D316—81no—
155C2×D316—81no—
156C2×D316C22×C412yes—
157C2×D316C22×C412yes—
158C22×Dic79—21no—
159C22×Dic79—21no—
160C2×C4×D79—42no—
161C2×C4×D79—42no—
162C2×C4×D79—42no—
163C2×C4×D79—42no—
164C2×C4×D79—81no—
165C2×C4×D79—81no—
166#11929611—28no—
167#11929611—28no—
168C2×C79⋊C8—21no—
169C2×C79⋊C8—21no—
170C2×C79⋊C8—21no—
171C2×C79⋊C8—21no—
172C2×C79⋊C8—21no—
173C2×C79⋊C8—21no—
174C2×C79⋊C8—21no—
175C2×C79⋊C8—21no—
176C2×C79⋊C8—21no—
177C2×C79⋊C8C22×C412yes—
178C2×C79⋊C8C22×C412yes—
179C2×C79⋊C8C2×D412yes—
180C4⋊Dic79—21no—
181C4⋊Dic79—21no—
182C4⋊Dic79—21no—
183C4⋊Dic79C2×D412yes—
184(C2×D79)⋊C4—42no—
185(C2×D79)⋊C4—42no—
186(C2×D79)⋊C4—42no—
187(C2×D79)⋊C4—42no—
188(C2×D79)⋊C4—81no—
189(C2×D79)⋊C4—81no—
190C4×Dic79—42no—
191C2×Q8×C79—21no—
192C2×Q8×C79—21no—
193C2×Q8×C79—21no—
194C2×Q8×C79C22×C412yes—
195C2×Q8×C79C2×D412yes—
196C2×Q8×C79#4112yes—
197C22×C4×C79—21no—
198C22×C4×C79—21no—
199C22×C4×C79—21no—
200C22×C4×C79—21no—
201C22×C4×C79C2×D411yescharacteristic
202C22×C4×C79C2×D411yescharacteristic
203C22×C4×C79C2×D411yescharacteristic
204C22×C4×C79C2×D411yescharacteristic
205C22×C4×C79C2×D411yescharacteristic
206C22×C4×C79C2×D411yescharacteristic
207C22×C4×C79C2411yescharacteristic
208C4⋊C4×C79—24no—
209C4⋊C4×C79—22no—
210C4⋊C4×C79—21no—
211C4⋊C4×C79—21no—
212C4⋊C4×C79—21no—
213C4⋊C4×C79—21no—
214C4⋊C4×C79—21no—
215C4⋊C4×C79—41no—
216C4⋊C4×C79—42no—
217C4⋊C4×C79—42no—
218C4⋊C4×C79—42no—
219C4⋊C4×C79—42no—
220C4⋊C4×C79C22×C412yes—
221C42×C79—24no—
222C42×C79—21no—
223C42×C79—21no—
224C42×C79—21no—
225C42×C79—21no—
226C42×C79—42no—
227C42×C79—42no—
228C42×C79C22×C412yes—
229C42×C79#4112yes—
230C23×C79C22×D411yescharacteristic
231C22×D79—22no—
232C22×D79—22no—
233C22×D79—41no—
234C22×D79—41no—
235C22×D79—41no—
236C22×D79—41no—
237C22×D79—41no—
238C22×D79—41no—
239C22×D79—41no—
240C22×D79—41no—
241C22×D79—41no—
242C22×D79—41no—
243C22×D79—41no—
244C22×D79—41no—
245Q8×C79—22no—
246Q8×C79—22no—
247Q8×C79—22no—
248Q8×C79C4×D414yescomplemented
249C2×C4×C79—22no—
250C2×C4×C79—21no—
251C2×C4×C79—22no—
252C2×C4×C79—22no—
253C2×C4×C79—21no—
254C2×C4×C79—21no—
255C2×C4×C79—21no—
256C2×C4×C79—21no—
257C2×C4×C79—21no—
258C2×C4×C79—22no—
259C2×C4×C79—21no—
260C2×C4×C79—21no—
261C2×C4×C79—21no—
262C2×C4×C79—21no—
263C2×C4×C79—21no—
264C2×C4×C79—21no—
265C2×C4×C79—21no—
266C2×C4×C79—21no—
267C2×C4×C79—21no—
268C2×C4×C79—41no—
269C2×C4×C79—41no—
270C2×C4×C79—41no—
271C2×C4×C79—41no—
272C2×C4×C79—41no—
273C2×C4×C79—41no—
274C2×C4×C79—41no—
275C2×C4×C79—41no—
276C2×C4×C79C4×D412yes—
277C2×C4×C79C4×D412yes—
278C2×C4×C79AGL(1,ℤ/8)12yes—
279C2×C4×C79C23×C411yescharacteristic
280C2×C4×C79C22×D411yescharacteristic
281C2×C4×C79C2×#4111yescharacteristic
282C2×C4×C79C2×#4111yescharacteristic
283C2×C4×C79H(5,𝔽2)11yescharacteristic
284C2×C4×C792−1+411yescharacteristic
285C2×Dic79—22no—
286C2×Dic79—41no—
287C2×Dic79—41no—
288C2×Dic79—41no—
289C2×Dic79—41no—
290C2×Dic79—41no—
291D316—22no—
292D316—22no—
293D316—22no—
294D316—22no—
295D316—48no—
296D316—41no—
297D316—41no—
298D316—41no—
299D316—41no—
300D316—84no—
301C4×D79—84no—
302C4×D79—84no—
303C79⋊C8—22no—
304C79⋊C8—22no—
305C79⋊C8—22no—
306C79⋊C8—41no—
307C22×C79C2×C4×D411yescharacteristic
308C22×C79D4211yescharacteristic
309C22×C79#54811yescharacteristic
310C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
311C22×C79#57511yescharacteristic
312C22×C79#57711yescharacteristic
313C22×C79#57711yescharacteristic
314C2×D79—42no—
315C2×D79—42no—
316C2×D79—42no—
317C2×D79—42no—
318C2×D79—42no—
319C2×D79—42no—
320C2×D79—81no—
321C2×D79—81no—
322C2×D79—81no—
323C2×D79—81no—
324C2×D79—81no—
325C2×D79—81no—
326C2×D79—81no—
327C2×D79—81no—
328C4×C79—24no—
329C4×C79—22no—
330C4×C79—22no—
331C4×C79—22no—
332C4×C79—42no—
333C4×C79—41no—
334C4×C79—41no—
335C4×C79—41no—
336C4×C79—81no—
337C4×C79—81no—
338C4×C79C2×C4×D411yescharacteristic
339C4×C79#52011yescharacteristic
340C4×C79#54711yescharacteristic
341C4×C79#55311yescharacteristic
342Dic79—42no—
343Dic79—81no—
344#23010—791nomaximal, Sylow
345C2×C79#236111yescharacteristic
346C2×C79C4×AGL(1,ℤ/8)11yescharacteristic
347C2×C79#294911yescharacteristic
348C2×C79#326511yescharacteristic
349C2×C79#327111yescharacteristic
350C2×C79#336811yescharacteristic
351C2×C79#337111yescharacteristic
352D79—82no—
353D79—82no—
354C2×#460—791no—
355C2×#440—791no—
356C2×C4×SD16—791no—
357#2366—791no—
358#2351D7911yescharacteristic, complemented
359#1961—791no—
360#1949—791no—
361#1936—791no—
362#1934—791no—
363#1880—791no—
364#1880—791no—
365#1864—791no—
366#1862—791no—
367#1771—791no—
368#1763—791no—
369C79#2301011yescharacteristic, complemented, Sylow
370C22×SD16—791no—
371C22×SD16—791no—
372C2×#127—791no—
373C2×C4×Q8C2×D7911yescharacteristic
374C2×C4×Q8C2×D7911yescharacteristic
375C2×C4×Q8C2×D7911yescharacteristic
376C2×C4×D4—791no—
377C2×C4×D4—791no—
378C2×C4×D4—1581no—
379#460—798no—
380#440—1584no—
381C4×SD16—1584no—
382C2×#107—791no—
383C2×#106—791no—
384C2×C4⋊C8—791no—
385C2×#103—791no—
386C2×#103—791no—
387C2×#102—791no—
388C2×#102—791no—
389C2×#102—791no—
390C2×#102—791no—
391C2×#102—791no—
392C2×#102—791no—
393C2×#97—791no—
394C2×#97—791no—
395C2×C4×C8—791no—
396#390—791no—
397#390—791no—
398#390—1581no—
399#389—21no—
400#389—21no—
401#389C2×D7911yescharacteristic
402#389C2×D7911yescharacteristic
403#386—1581no—
404#386—1581no—
405#382—21no—
406#382C2×D7911yescharacteristic
407C4×C4⋊C4—21no—
408C4×C4⋊C4—791no—
409C4×C4⋊C4C2×D7911yescharacteristic
410#340—791no—
411#340—791no—
412#340—791no—
413#340—791no—
414#336—791no—
415#336—791no—
416C22×Q8C22×D7911yescharacteristic
417C22×D4—791no—
418C22×D4—791no—
419C22×D4—1581no—
420C22×D4—1581no—
421C23×C4—1581no—
422C23×C4—1581no—
423C2×SD16—794no—
424C2×SD16—794no—
425C2×SD16—1582no—
426C2×SD16—1582no—
427C2×SD16—1582no—
428C2×SD16—1582no—
429C22×C8—791no—
430C22×C8—791no—
431C22×C8—791no—
432C22×C8—791no—
433#127—794no—
434#127—1582no—
435C4×Q8—22no—
436C4×Q8—22no—
437C4×Q8—22no—
438C4×Q8—41no—
439C4×Q8—41no—
440C4×Q8C4×D7914yescomplemented
441C4×D4—3161no—
442C4×D4—3161no—
443C4×D4—3164no—
444C4×D4—1582no—
445C4×D4—1582no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—791no—
452C2×C4⋊C4—791no—
453C2×C4⋊C4C22⋊D7911yescharacteristic
454C2×C4⋊C4C22⋊D7911yescharacteristic
455C2×C4⋊C4C22×D7911yescharacteristic
456C2×C4⋊C4C22×D7911yescharacteristic
457C2×C4⋊C4C22×D7911yescharacteristic
458C2×C22⋊C4—1581no—
459C2×C22⋊C4—1581no—
460C2×C22⋊C4—1581no—
461C2×C22⋊C4—1581no—
462C2×C22⋊C4—1581no—
463C2×C22⋊C4—1581no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—1581no—
468C2×C42C22×D7911yescharacteristic
469C2×C42C22×D7911yescharacteristic
470C2×C42C22×D7911yescharacteristic
471#107—1582no—
472#106—1582no—
473C4⋊C8—794no—
474#103—794no—
475#103—1582no—
476#102—3161no—
477#102—3161no—
478#102—794no—
479#102—794no—
480#102—1582no—
481#102—1582no—
482#97—1582no—
483#97—1582no—
484C4×C8—1582no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—1581no—
490#95C22⋊D7911yescharacteristic
491#95C22⋊D7911yescharacteristic
492C24—1581no—
493C24—1581no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8C2×C4×D7912yes—
498C2×Q8D4×D7912yes—
499C2×Q8#1192962512yes—
500C2×D4—3162no—
501C2×D4—3162no—
502C2×D4—792no—
503C2×D4—792no—
504C2×D4—6321no—
505C2×D4—6321no—
506C2×D4—1581no—
507C2×D4—1581no—
508C2×D4—1581no—
509C2×D4—1581no—
510C2×D4—1581no—
511C2×D4—1581no—
512C2×D4—1581no—
513C2×D4—1581no—
514C2×D4—1584no—
515C2×D4—1584no—
516C2×D4—1581no—
517C2×D4—1581no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—3162no—
523C22×C4—3162no—
524C22×C4—3162no—
525C22×C4—3162no—
526C22×C4—6321no—
527C22×C4—6321no—
528C22×C4—1581no—
529C22×C4—1581no—
530C22×C4C2×C22⋊D7911yescharacteristic
531C22×C4C2×C22⋊D7911yescharacteristic
532C22×C4C2×C22⋊D7911yescharacteristic
533C22×C4C2×C22⋊D7911yescharacteristic
534C22×C4C2×C22⋊D7911yescharacteristic
535C22×C4C2×C22⋊D7911yescharacteristic
536C22×C4C23×D7911yescharacteristic
537SD16—1588no—
538SD16—1588no—
539C2×C8—792no—
540C2×C8—792no—
541C2×C8—792no—
542C2×C8—1581no—
543C2×C8—1581no—
544C2×C8—1581no—
545C2×C8—1581no—
546C2×C8—1581no—
547C2×C8—1581no—
548C2×C8—1581no—
549C2×C8—1581no—
550C2×C8—1581no—
551C4⋊C4—21no—
552C4⋊C4—24no—
553C4⋊C4—22no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—41no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—792no—
564C4⋊C4—1581no—
565C4⋊C4—1581no—
566C4⋊C4—1581no—
567C4⋊C4C2×C4×D7912yes—
568C22⋊C4—3162no—
569C22⋊C4—3162no—
570C22⋊C4—3162no—
571C22⋊C4—3162no—
572C22⋊C4—6321no—
573C22⋊C4—6321no—
574C42—21no—
575C42—21no—
576C42—24no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—42no—
581C42—3162no—
582C42C2×C4×D7912yes—
583C42#1192962412yes—
584C23—3161no—
585C23—3161no—
586C23—3161no—
587C23—3161no—
588C23—3161no—
589C23—3161no—
590C23—3161no—
591C23—3161no—
592C23—3161no—
593C23—3161no—
594C23—3161no—
595C23—3161no—
596C23—1582no—
597C23—1582no—
598C23C22×C22⋊D7911yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—22no—
602Q8#1457912314yescomplemented
603D4—3168no—
604D4—3161no—
605D4—3161no—
606D4—3161no—
607D4—3161no—
608D4—6324no—
609D4—1582no—
610D4—1582no—
611D4—1582no—
612D4—1582no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—3161no—
641C2×C4—3161no—
642C2×C4—3161no—
643C2×C4—3161no—
644C2×C4—3161no—
645C2×C4—6324no—
646C2×C4—6324no—
647C2×C4—1582no—
648C2×C4C4×C22⋊D7912yes—
649C2×C4C4×C22⋊D7912yes—
650C2×C4#1457918612yes—
651C2×C4C22×C4×D7911yescharacteristic
652C2×C4C2×D4×D7911yescharacteristic
653C2×C4C2×#1192962411yescharacteristic
654C2×C4C2×#1192962511yescharacteristic
655C2×C4#1457920611yescharacteristic
656C2×C4#1457920911yescharacteristic
657C8—3161no—
658C8—1582no—
659C8—1582no—
660C8—1582no—
661C22—3162no—
662C22—3162no—
663C22—3162no—
664C22—3162no—
665C22—3162no—
666C22—3162no—
667C22—6321no—
668C22—6321no—
669C22—6321no—
670C22—6321no—
671C22—6321no—
672C22—6321no—
673C22—6321no—
674C22—6321no—
675C22C2×C4×C22⋊D7911yescharacteristic
676C22D4×C22⋊D7911yescharacteristic
677C22#1909922411yescharacteristic
678C22C2×#1457918611yescharacteristic
679C22#1909936111yescharacteristic
680C22#1909937111yescharacteristic
681C22#1909937111yescharacteristic
682C4—22no—
683C4—22no—
684C4—24no—
685C4—22no—
686C4—41no—
687C4—41no—
688C4—42no—
689C4—41no—
690C4—81no—
691C4—81no—
692C4—3162no—
693C4—6321no—
694C4C2×#1457912311yescharacteristic
695C4#1909904411yescharacteristic
696C4#1909921411yescharacteristic
697C4#1909926111yescharacteristic
698C2—6322no—
699C2—6322no—
700C2#2376641611yescharacteristic
701C2C4×#1457918611yescharacteristic
702C2#2377225911yescharacteristic
703C2#2377489611yescharacteristic
704C2#2377498611yescharacteristic
705C2#2377612911yescharacteristic
706C2#2377616811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2351C2
socleC23×C79C22×D4
prime radicalC2×#14579158C22
cosocleC22×C4×C79C24
hypercenter#2351D79
hypocenterC79#23010
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2351

Complements

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

NH ≅ G/Ntype
2. C2×#19098661C2semidirect
3. C2×C4×#11929611C2semidirect
6. #23764166C2semidirect
7. #23764096C2semidirect
8. #23764082C2semidirect
9. #23763755C2semidirect
10. #23763755C2semidirect
11. #23763660C2semidirect
12. #23763646C2semidirect
13. #23763275C2semidirect
14. #23763230C2semidirect
15. C79×#2351C2semidirect
22. #19098763C4semidirect
72. C2×#11929611C2×C4semidirect
73. C2×#11929611C2×C4semidirect
96. C4⋊(C79⋊C8)C2×C4semidirect
98. #14579085D4semidirect
103. #14579081C2×C4semidirect
104. #14579081C2×C4semidirect
115. C4×Q8×C79C2×C4semidirect
248. Q8×C79C4×D4semidirect
358. #2351D79semidirect
369. C79#23010semidirect
440. C4×Q8C4×D79semidirect
602. Q8#14579123semidirect

Maximal subgroups

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

subgroupindex
C2×#190987632
C2×#190986612
C2×C4×#119296112
#237664642
#237642232
#237641662
#237640962
#237640822
#237637552
#237636602
#237636462
#237632752
#237632302
C79×#23512
#2301079