Finite Group Databasebeta

← #34306605

Subgroups — #34306605

Order 20224.

1086 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098673C211yesmaximal, characteristic
2C2×#19098673C211yesmaximal, characteristic
3C2×C4×#11929609C211yesmaximal, characteristic
4C4⋊C4×D316C211yesmaximal, characteristic, complemented
5#23764140C211yesmaximal, characteristic, complemented
6#23764125C211yesmaximal, characteristic, complemented
7#23763661C211yesmaximal, characteristic, complemented
8#23763660C211yesmaximal, characteristic, complemented
9#23763647C211yesmaximal, characteristic, complemented
10#23763646C211yesmaximal, characteristic, complemented
11#23763569C211yesmaximal, characteristic, complemented
12#23763407C211yesmaximal, characteristic, complemented
13#23763400C211yesmaximal, characteristic, complemented
14#23763275C211yesmaximal, characteristic, complemented
15C79×#2349C211yesmaximal, characteristic, complemented
16C22×#11929609C2211yescharacteristic
17C2×C4×D316C2211yescharacteristic
18C2×C4×D316C2211yescharacteristic
19C2×C4×D316C2211yescharacteristic
20C2×C4⋊C4×D79—21no—
21#19098673—24no—
22#19098673C418yescomplemented
23C4×#11929609—24no—
24C2×#14579094C2211yescharacteristic
25C2×#14579094C2211yescharacteristic
26C2×#14579092C2211yescharacteristic
27C2×#14579092C2211yescharacteristic
28C2×#14579092C2211yescharacteristic
29C2×C4⋊(C79⋊C8)C2211yescharacteristic
30C2×#14579082C2211yescharacteristic
31C2×#14579082C2211yescharacteristic
32C2×#14579082C2211yescharacteristic
33C2×#14579081C2211yescharacteristic
34C2×#14579081C2211yescharacteristic
35C2×#14579081C2211yescharacteristic
36C2×#14579072C2211yescharacteristic
37C2×#14579072C2211yescharacteristic
38C2×C4×C79⋊C8C2211yescharacteristic
39#19098461C2211yescharacteristic
40#19098461C2211yescharacteristic
41#19098437—21no—
42#19098437—21no—
43#19098433C2211yescharacteristic
44#19098420—21no—
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098318C2211yescharacteristic
50#19098318C2211yescharacteristic
51C2×C4×D4×C79C2211yescharacteristic
52C2×C4×D4×C79C2211yescharacteristic
53C2×C4×D4×C79C2211yescharacteristic
54#389×C79C2211yescharacteristic
55#389×C79C2211yescharacteristic
56#385×C79—21no—
57#385×C79—21no—
58#382×C79C2211yescharacteristic
59#380×C79—21no—
60C4×C4⋊C4×C79C2211yescharacteristic
61C2×#95×C79—21no—
62C22×D316C2311yescharacteristic
63C22×C4×D79—21no—
64C22×C4×D79—21no—
65C22×C4×D79—21no—
66C2×#11929609C2×C414yes—
67C2×#11929609D414yes—
68C2×#11929609Q814yes—
69C22×C79⋊C8C2311yescharacteristic
70C22×C79⋊C8C2311yescharacteristic
71C22×C79⋊C8C2311yescharacteristic
72C22×C79⋊C8C2311yescharacteristic
73C4×D316—22no—
74C4×D316—22no—
75C4×D316—22no—
76C4×D316—41no—
77C4×D316—41no—
78C4×D316C2×C414yescomplemented
79C2×C4⋊Dic79—21no—
80C2×C4⋊Dic79—21no—
81C2×C4⋊Dic79C2311yescharacteristic
82C2×C4⋊Dic79C2311yescharacteristic
83C2×C4⋊Dic79C2311yescharacteristic
84C2×Dic79⋊C4—21no—
85C2×Dic79⋊C4—21no—
86C4⋊C4×D79—44no—
87C2×(C2×D79)⋊C4—21no—
88C2×(C2×D79)⋊C4—21no—
89C2×(C2×D79)⋊C4—21no—
90#14579094—22no—
91#14579094—41no—
92#14579092—22no—
93#14579092—41no—
94#14579092C2×C414yescomplemented
95C4⋊(C79⋊C8)—22no—
96#14579082—22no—
97#14579082—22no—
98#14579082C2×C414yescomplemented
99#14579081—22no—
100#14579081—22no—
101#14579081C2×C414yescomplemented
102#14579072—22no—
103#14579072C2×C414yescomplemented
104C4×C79⋊C8—22no—
105C79⋊#95—21no—
106C79⋊#95—21no—
107C22×D4×C79C2311yescharacteristic
108C23×C4×C79—21no—
109C23×C4×C79—21no—
110C23×C4×C79—21no—
111C4×D4×C79—22no—
112C4×D4×C79—22no—
113C4×D4×C79—22no—
114C4×D4×C79—41no—
115C4×D4×C79—41no—
116C4×D4×C79C2×C414yescomplemented
117C2×C4⋊C4×C79—21no—
118C2×C4⋊C4×C79—21no—
119C2×C4⋊C4×C79D411yescharacteristic
120C2×C4⋊C4×C79D411yescharacteristic
121C2×C4⋊C4×C79C2311yescharacteristic
122C2×C4⋊C4×C79C2311yescharacteristic
123C2×C4⋊C4×C79C2311yescharacteristic
124C2×C22⋊C4×C79—21no—
125C2×C22⋊C4×C79—21no—
126C2×C22⋊C4×C79—21no—
127C2×C42×C79C2311yescharacteristic
128C2×C42×C79C2311yescharacteristic
129C2×C42×C79C2311yescharacteristic
130#95×C79—21no—
131#95×C79—21no—
132#95×C79—21no—
133#95×C79—21no—
134#95×C79D411yescharacteristic
135#95×C79D411yescharacteristic
136C23×D79—21no—
137C2×D316—21no—
138C2×D316—21no—
139C2×D316—21no—
140C2×D316C22×C412yes—
141C2×D316C2×D412yes—
142C2×D316C2×Q812yes—
143C22×Dic79—21no—
144C22×Dic79—21no—
145C22×Dic79—21no—
146C2×C4×D79—24no—
147C2×C4×D79—42no—
148C2×C4×D79—42no—
149C2×C4×D79—42no—
150C2×C4×D79—42no—
151C2×C4×D79—42no—
152C2×C4×D79—42no—
153C2×C4×D79—81no—
154C2×C4×D79—81no—
155#11929609C4⋊C4116yescomplemented
156C2×C79⋊C8—21no—
157C2×C79⋊C8—21no—
158C2×C79⋊C8—21no—
159C2×C79⋊C8—21no—
160C2×C79⋊C8—21no—
161C2×C79⋊C8—21no—
162C2×C79⋊C8—21no—
163C2×C79⋊C8—21no—
164C2×C79⋊C8C22×C412yes—
165C2×C79⋊C8C22×C412yes—
166C2×C79⋊C8C2×D412yes—
167C2×C79⋊C8C2×Q812yes—
168C4⋊Dic79—21no—
169C4⋊Dic79—21no—
170C4⋊Dic79—21no—
171C4⋊Dic79—21no—
172C4⋊Dic79—21no—
173C4⋊Dic79—42no—
174C4⋊Dic79—81no—
175C4⋊Dic79C22×C412yes—
176Dic79⋊C4—42no—
177Dic79⋊C4—42no—
178(C2×D79)⋊C4—24no—
179(C2×D79)⋊C4—42no—
180(C2×D79)⋊C4—42no—
181C24×C79—21no—
182C2×D4×C79—21no—
183C2×D4×C79—21no—
184C2×D4×C79—21no—
185C2×D4×C79C22×C412yes—
186C2×D4×C79C2×D412yes—
187C2×D4×C79C2×Q812yes—
188C22×C4×C79—21no—
189C22×C4×C79—24no—
190C22×C4×C79—21no—
191C22×C4×C79—21no—
192C22×C4×C79—42no—
193C22×C4×C79—42no—
194C22×C4×C79—42no—
195C22×C4×C79—42no—
196C22×C4×C79—81no—
197C22×C4×C79—81no—
198C22×C4×C79—81no—
199C22×C4×C79—81no—
200C22×C4×C79C2×D411yescharacteristic
201C22×C4×C79C2×D411yescharacteristic
202C22×C4×C79C2×D411yescharacteristic
203C22×C4×C79C2×D411yescharacteristic
204C22×C4×C79C2×D411yescharacteristic
205C22×C4×C79C2×D411yescharacteristic
206C22×C4×C79C2411yescharacteristic
207C4⋊C4×C79—22no—
208C4⋊C4×C79—21no—
209C4⋊C4×C79—21no—
210C4⋊C4×C79—21no—
211C4⋊C4×C79—21no—
212C4⋊C4×C79—21no—
213C4⋊C4×C79—41no—
214C4⋊C4×C79—81no—
215C4⋊C4×C79—81no—
216C4⋊C4×C79C22×C412yes—
217C22⋊C4×C79—24no—
218C22⋊C4×C79—42no—
219C22⋊C4×C79—42no—
220C42×C79—21no—
221C42×C79—21no—
222C42×C79—21no—
223C42×C79—21no—
224C42×C79C22×C412yes—
225C42×C79#4112yes—
226C23×C79—22no—
227C23×C79—22no—
228C23×C79—22no—
229C23×C79—41no—
230C23×C79—41no—
231C23×C79—41no—
232C23×C79—41no—
233C23×C79C22×D411yescharacteristic
234C22×D79—22no—
235C22×D79—22no—
236C22×D79—22no—
237C22×D79—41no—
238C22×D79—41no—
239C22×D79—41no—
240C22×D79—41no—
241D4×C79—22no—
242D4×C79—22no—
243D4×C79—22no—
244D4×C79C2×C4⋊C414yescomplemented
245C2×C4×C79—21no—
246C2×C4×C79—21no—
247C2×C4×C79—21no—
248C2×C4×C79—21no—
249C2×C4×C79—21no—
250C2×C4×C79—21no—
251C2×C4×C79—22no—
252C2×C4×C79—21no—
253C2×C4×C79—21no—
254C2×C4×C79—21no—
255C2×C4×C79—21no—
256C2×C4×C79—21no—
257C2×C4×C79—21no—
258C2×C4×C79—21no—
259C2×C4×C79—21no—
260C2×C4×C79—21no—
261C2×C4×C79—41no—
262C2×C4×C79—41no—
263C2×C4×C79—41no—
264C2×C4×C79—41no—
265C2×C4×C79—41no—
266C2×C4×C79—41no—
267C2×C4×C79—41no—
268C2×C4×C79—41no—
269C2×C4×C79—84no—
270C2×C4×C79—84no—
271C2×C4×C79—84no—
272C2×C4×C79C4×D412yes—
273C2×C4×C79C4×D412yes—
274C2×C4×C79AGL(1,ℤ/8)12yes—
275C2×C4×C79C23×C411yescharacteristic
276C2×C4×C79C22×D411yescharacteristic
277C2×C4×C79C22×Q811yescharacteristic
278C2×C4×C79C2×#4111yescharacteristic
279C2×C4×C79H(5,𝔽2)11yescharacteristic
280C2×C4×C792−1+411yescharacteristic
281C2×Dic79—22no—
282C2×Dic79—41no—
283C2×Dic79—41no—
284C2×Dic79—41no—
285C2×Dic79—41no—
286C2×Dic79—41no—
287C2×Dic79—41no—
288C2×Dic79—41no—
289C2×Dic79—41no—
290D316—22no—
291D316—22no—
292D316—22no—
293D316C2×C4⋊C414yes—
294C4×D79—48no—
295C4×D79—84no—
296C4×D79—84no—
297C79⋊C8—22no—
298C79⋊C8—41no—
299C79⋊C8—41no—
300C79⋊C8C2×C4⋊C414yescomplemented
301C22×C79—24no—
302C22×C79—42no—
303C22×C79—42no—
304C22×C79—42no—
305C22×C79—42no—
306C22×C79—42no—
307C22×C79—42no—
308C22×C79C2×C4×D411yescharacteristic
309C22×C79D4211yescharacteristic
310C22×C79D4×Q811yescharacteristic
311C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C79#57511yescharacteristic
313C22×C79#57611yescharacteristic
314C22×C79#57711yescharacteristic
315C2×D79—24no—
316C2×D79—42no—
317C2×D79—42no—
318C2×D79—42no—
319C2×D79—42no—
320C2×D79—42no—
321C2×D79—42no—
322C4×C79—22no—
323C4×C79—22no—
324C4×C79—22no—
325C4×C79—42no—
326C4×C79—41no—
327C4×C79—41no—
328C4×C79—41no—
329C4×C79—81no—
330C4×C79—81no—
331C4×C79C22×C4⋊C411yescharacteristic
332C4×C79#52011yescharacteristic
333C4×C79#54711yescharacteristic
334C4×C79#55411yescharacteristic
335Dic79—42no—
336Dic79—81no—
337Dic79—81no—
338#22676—791nomaximal, Sylow
339C2×C79—44no—
340C2×C79D4×C4⋊C411yescharacteristic
341C2×C79C4×AGL(1,ℤ/8)11yescharacteristic
342C2×C79#294611yescharacteristic
343C2×C79#326411yescharacteristic
344C2×C79#326711yescharacteristic
345C2×C79#338411yescharacteristic
346C2×C79#338911yescharacteristic
347D79—44no—
348C2×#442—791no—
349C2×#442—791no—
350C2×C4×D8—791no—
351#2349D7911yescharacteristic, complemented
352D4×C4⋊C4—791no—
353#1944—791no—
354#1941—791no—
355#1864—791no—
356#1864—791no—
357#1862—791no—
358#1862—791no—
359#1847—791no—
360#1804—791no—
361#1802—791no—
362#1771—791no—
363C79#2267611yescharacteristic, complemented, Sylow
364C22×D8—791no—
365C2×C4×D4—791no—
366C2×C4×D4—791no—
367C2×C4×D4—791no—
368C2×C4×D4C2×D7911yescharacteristic
369C2×C4×D4C2×D7911yescharacteristic
370C2×C4×D4C2×D7911yescharacteristic
371C22×C4⋊C4—1581no—
372#442—798no—
373#442—1584no—
374C4×D8—1584no—
375C2×#107—791no—
376C2×#107—791no—
377C2×#106—791no—
378C2×#106—791no—
379C2×#106—791no—
380C2×C4⋊C8—791no—
381C2×#102—791no—
382C2×#102—791no—
383C2×#102—791no—
384C2×#102—791no—
385C2×#102—791no—
386C2×#102—791no—
387C2×#97—791no—
388C2×#97—791no—
389C2×C4×C8—791no—
390#389—791no—
391#389—791no—
392#389C2×D7911yescharacteristic
393#389C2×D7911yescharacteristic
394#385—21no—
395#385—21no—
396#385—1581no—
397#385—1581no—
398#384—791no—
399#382C2×D7911yescharacteristic
400#380—21no—
401#380—1581no—
402C4×C4⋊C4C2×D7911yescharacteristic
403C2×#95—21no—
404#340—791no—
405#340—791no—
406#340—791no—
407#340—791no—
408#336—791no—
409#336—791no—
410C22×D4—791no—
411C22×D4C22×D7911yescharacteristic
412C23×C4—21no—
413C23×C4—21no—
414C23×C4—21no—
415C23×C4—1581no—
416C23×C4—1581no—
417C23×C4—1581no—
418C2×D8—794no—
419C2×D8—794no—
420C2×D8—794no—
421C22×C8—791no—
422C22×C8—791no—
423C22×C8—791no—
424C22×C8—791no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—22no—
428C4×D4—41no—
429C4×D4—41no—
430C4×D4—3161no—
431C4×D4—3161no—
432C4×D4—794no—
433C4×D4—1582no—
434C4×D4—1582no—
435C4×D4—1582no—
436C4×D4C4×D7914yescomplemented
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—3164no—
440C2×C4⋊C4—791no—
441C2×C4⋊C4—791no—
442C2×C4⋊C4—791no—
443C2×C4⋊C4—1581no—
444C2×C4⋊C4—1581no—
445C2×C4⋊C4—1581no—
446C2×C4⋊C4—1581no—
447C2×C4⋊C4C22⋊D7911yescharacteristic
448C2×C4⋊C4C22⋊D7911yescharacteristic
449C2×C4⋊C4C22×D7911yescharacteristic
450C2×C4⋊C4C22×D7911yescharacteristic
451C2×C4⋊C4C22×D7911yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—1581no—
456C2×C22⋊C4—1581no—
457C2×C22⋊C4—1581no—
458C2×C42C22×D7911yescharacteristic
459C2×C42C22×D7911yescharacteristic
460C2×C42C22×D7911yescharacteristic
461#107—3161no—
462#107—1582no—
463#106—3161no—
464#106—794no—
465#106—1582no—
466C4⋊C8—1582no—
467#102—794no—
468#102—794no—
469#102—1582no—
470#102—1582no—
471#102—1582no—
472#102—1582no—
473#97—794no—
474#97—1582no—
475C4×C8—1582no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—1581no—
481#95—1581no—
482#95C22⋊D7911yescharacteristic
483#95C22⋊D7911yescharacteristic
484C24—21no—
485C24—1581no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—792no—
490C2×D4—792no—
491C2×D4—792no—
492C2×D4—1581no—
493C2×D4—1581no—
494C2×D4—1581no—
495C2×D4C2×C4×D7912yes—
496C2×D4D4×D7912yes—
497C2×D4Q8×D7912yes—
498C22×C4—21no—
499C22×C4—24no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4—81no—
509C22×C4—81no—
510C22×C4—3162no—
511C22×C4—3162no—
512C22×C4—3162no—
513C22×C4—3162no—
514C22×C4—3162no—
515C22×C4—3162no—
516C22×C4—6321no—
517C22×C4—6321no—
518C22×C4—1581no—
519C22×C4—1581no—
520C22×C4—1581no—
521C22×C4—1584no—
522C22×C4C2×C22⋊D7911yescharacteristic
523C22×C4C2×C22⋊D7911yescharacteristic
524C22×C4C2×C22⋊D7911yescharacteristic
525C22×C4C2×C22⋊D7911yescharacteristic
526C22×C4C2×C22⋊D7911yescharacteristic
527C22×C4C2×C22⋊D7911yescharacteristic
528C22×C4C23×D7911yescharacteristic
529D8—7916no—
530C2×C8—792no—
531C2×C8—792no—
532C2×C8—792no—
533C2×C8—792no—
534C2×C8—1581no—
535C2×C8—1581no—
536C2×C8—1581no—
537C2×C8—1581no—
538C2×C8—1581no—
539C2×C8—1581no—
540C2×C8—1581no—
541C2×C8—1581no—
542C4⋊C4—21no—
543C4⋊C4—22no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—41no—
549C4⋊C4—81no—
550C4⋊C4—81no—
551C4⋊C4—3162no—
552C4⋊C4—3162no—
553C4⋊C4—3162no—
554C4⋊C4—792no—
555C4⋊C4—6321no—
556C4⋊C4—1581no—
557C4⋊C4—1581no—
558C4⋊C4—1581no—
559C4⋊C4—1581no—
560C4⋊C4—1581no—
561C4⋊C4C2×C4×D7912yes—
562C22⋊C4—24no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—3162no—
566C22⋊C4—3162no—
567C22⋊C4—1584no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42C2×C4×D7912yes—
573C42#1192962412yes—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—3161no—
582C23—3161no—
583C23—3161no—
584C23—3161no—
585C23—1582no—
586C23—1582no—
587C23—1582no—
588C23C22×C22⋊D7911yescharacteristic
589D4—22no—
590D4—22no—
591D4—22no—
592D4—794no—
593D4—1582no—
594D4—1582no—
595D4—1582no—
596D4C4⋊C4×D7914yescomplemented
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—84no—
622C2×C4—84no—
623C2×C4—84no—
624C2×C4—3168no—
625C2×C4—3161no—
626C2×C4—3161no—
627C2×C4—3161no—
628C2×C4—3161no—
629C2×C4—3161no—
630C2×C4—3161no—
631C2×C4—3161no—
632C2×C4—3161no—
633C2×C4—6324no—
634C2×C4—6324no—
635C2×C4—1582no—
636C2×C4C4×C22⋊D7912yes—
637C2×C4C4×C22⋊D7912yes—
638C2×C4#1457918612yes—
639C2×C4C22×C4×D7911yescharacteristic
640C2×C4C2×D4×D7911yescharacteristic
641C2×C4C2×Q8×D7911yescharacteristic
642C2×C4C2×#1192962411yescharacteristic
643C2×C4#1457920611yescharacteristic
644C2×C4#1457920911yescharacteristic
645C8—3161no—
646C8—3161no—
647C8—794no—
648C8—1582no—
649C22—24no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—3162no—
657C22—3162no—
658C22—3162no—
659C22—3162no—
660C22—3162no—
661C22—3162no—
662C22—1584no—
663C22C2×C4×C22⋊D7911yescharacteristic
664C22D4×C22⋊D7911yescharacteristic
665C22Q8×C22⋊D7911yescharacteristic
666C22C2×#1457918611yescharacteristic
667C22#1909936111yescharacteristic
668C22#1909936611yescharacteristic
669C22#1909937411yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—42no—
674C4—41no—
675C4—41no—
676C4—41no—
677C4—81no—
678C4—81no—
679C4—3162no—
680C4—6321no—
681C4—6321no—
682C4C2×C4⋊C4×D7911yescharacteristic
683C4#1909904411yescharacteristic
684C4#1909921411yescharacteristic
685C4#1909926811yescharacteristic
686C2—44no—
687C2—3164no—
688C2C4⋊C4×C22⋊D7911yescharacteristic
689C2C4×#1457918611yescharacteristic
690C2#2377223211yescharacteristic
691C2#2377488111yescharacteristic
692C2#2377492111yescharacteristic
693C2#2377629911yescharacteristic
694C2#2377635411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2349C2
socleC23×C79C22×D4
prime radicalC22×#11929609C22
cosocleC22×C4×C79C24
hypercenter#2349D79
hypocenterC79#22676
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2349

Complements

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

NH ≅ G/Ntype
4. C4⋊C4×D316C2semidirect
5. #23764140C2semidirect
6. #23764125C2semidirect
7. #23763661C2semidirect
8. #23763660C2semidirect
9. #23763647C2semidirect
10. #23763646C2semidirect
11. #23763569C2semidirect
12. #23763407C2semidirect
13. #23763400C2semidirect
14. #23763275C2semidirect
15. C79×#2349C2semidirect
22. #19098673C4semidirect
78. C4×D316C2×C4semidirect
94. #14579092C2×C4semidirect
98. #14579082C2×C4semidirect
101. #14579081C2×C4semidirect
103. #14579072C2×C4semidirect
116. C4×D4×C79C2×C4semidirect
155. #11929609C4⋊C4semidirect
244. D4×C79C2×C4⋊C4semidirect
300. C79⋊C8C2×C4⋊C4semidirect
351. #2349D79semidirect
363. C79#22676semidirect
436. C4×D4C4×D79semidirect
596. D4C4⋊C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190986732
C2×C4×#119296092
C4⋊C4×D3162
#237641402
#237641252
#237636612
#237636602
#237636472
#237636462
#237635692
#237634072
#237634002
#237632752
C79×#23492
#2267679