Finite Group Databasebeta

← #28629329

Subgroups — #28629329

Order 15104.

902 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837624C211yesmaximal, characteristic, complemented
2C2×#16837459C211yesmaximal, characteristic, complemented
3#21432397C211yesmaximal, characteristic
4#21425299C211yesmaximal, characteristic, complemented
5#21425285C211yesmaximal, characteristic
6#21425104C211yesmaximal, characteristic, complemented
7#21425097C211yesmaximal, characteristic
8#21425028C211yesmaximal, characteristic, complemented
9#21424980C211yesmaximal, characteristic, complemented
10#21424966C211yesmaximal, characteristic, complemented
11#21424864C211yesmaximal, characteristic, complemented
12#21424792C211yesmaximal, characteristic, complemented
13#21424785C211yesmaximal, characteristic, complemented
14#21424111C211yesmaximal, characteristic, complemented
15C4×C22⋊Q8×C59C211yesmaximal, characteristic, complemented
16C22×#11745672C2211yescharacteristic
17C22×#11745671C2211yescharacteristic
18C2×#14273715C2211yescharacteristic
19C2×#14273706C2211yescharacteristic
20C2×#14273701C2211yescharacteristic
21#16837624—24no—
22#16837459—24no—
23C2×#14273660C2211yescharacteristic
24C2×#14273658C2211yescharacteristic
25C2×C4⋊(C59⋊C8)C2211yescharacteristic
26C2×C4⋊(C59⋊C8)C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273651C2211yescharacteristic
29C2×#14273650C2211yescharacteristic
30C2×#14273650C2211yescharacteristic
31C2×#14273650C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37C2×#14273638C2211yescharacteristic
38C2×#14273638C2211yescharacteristic
39#16837308C2211yescharacteristic
40#16837304C2211yescharacteristic
41#16837293—21no—
42#16837293—21no—
43#16837281—21no—
44#16837281—21no—
45#16837268C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50C2×C22⋊Q8×C59C2211yescharacteristic
51C2×C4×Q8×C59C2211yescharacteristic
52C22×C42×C59C2211yescharacteristic
53C59×#391C2211yescharacteristic
54C59×#389C2211yescharacteristic
55C59×#387—21no—
56C59×#385—21no—
57C59×#380C2211yescharacteristic
58C4×C4⋊C4×C59—21no—
59C4×C4⋊C4×C59C2211yescharacteristic
60C4×C22⋊C4×C59—21no—
61C22×Dic118C2311yescharacteristic
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C2×#11745672—22no—
65C2×#11745672—22no—
66C2×#11745672—41no—
67C2×#11745671—22no—
68C2×#11745671—22no—
69C2×#11745671—41no—
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74#14273715—22no—
75#14273715—22no—
76#14273706—41no—
77#14273706—41no—
78#14273701—41no—
79#14273701—41no—
80C2×C4⋊Dic59C2311yescharacteristic
81C2×C4⋊Dic59C2311yescharacteristic
82C2×Dic59⋊C4—21no—
83C2×C22⋊Dic59—21no—
84C2×(C2×D59)⋊C4—21no—
85C2×(C2×D59)⋊C4—21no—
86C2×(C2×D59)⋊C4—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89#14273660—41no—
90#14273658—41no—
91C4⋊(C59⋊C8)—22no—
92C4⋊(C59⋊C8)D414yescomplemented
93#14273651—41no—
94#14273651—41no—
95#14273650—22no—
96#14273650—22no—
97#14273650—41no—
98#14273647—22no—
99#14273647—22no—
100#14273647—41no—
101C22⋊(C59⋊C8)—22no—
102C22⋊(C59⋊C8)—22no—
103#14273638—22no—
104#14273638—22no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C22×Q8×C59C2311yescharacteristic
110C23×C4×C59D411yescharacteristic
111C23×C4×C59D411yescharacteristic
112C23×C4×C59C2311yescharacteristic
113C22⋊Q8×C59—22no—
114C22⋊Q8×C59—22no—
115C4×Q8×C59—22no—
116C4×Q8×C59—22no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C22⋊C4×C59—21no—
124C2×C22⋊C4×C59—21no—
125C2×C42×C59—22no—
126C2×C42×C59—22no—
127C2×C42×C59—21no—
128C2×C42×C59—21no—
129C2×C42×C59D411yescharacteristic
130C2×C42×C59D411yescharacteristic
131C2×C42×C59C2311yescharacteristic
132C2×C42×C59C2311yescharacteristic
133#95×C59—21no—
134#95×C59—21no—
135#95×C59—21no—
136#95×C59—21no—
137#95×C59—21no—
138C24×C59C2×D411yescharacteristic
139C23×D59—21no—
140C2×Q8×C59—21no—
141C2×Q8×C59—21no—
142C2×Q8×C59—21no—
143C2×Q8×C59—21no—
144C2×Q8×C59—21no—
145C2×Q8×C59#4112yes—
146C22×C4×C59—22no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—22no—
150C22×C4×C59—22no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—41no—
160C22×C4×C59—41no—
161C22×C4×C59—41no—
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2×D411yescharacteristic
166C22×C4×C59C2×D411yescharacteristic
167C22×C4×C59C2411yescharacteristic
168C2×C22⋊D59—42no—
169C2×C22⋊D59—42no—
170C2×C22⋊D59—42no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173C22×Dic59—21no—
174C2×D236—21no—
175C2×D236—21no—
176C2×D236—21no—
177C2×D236—21no—
178C2×D236—21no—
179C2×D236—21no—
180C2×Dic118—21no—
181C2×Dic118—21no—
182C2×Dic118—21no—
183C2×Dic118—21no—
184C2×Dic118—21no—
185C2×Dic118—21no—
186C4⋊C4×C59—24no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59—42no—
193C4⋊C4×C59—42no—
194C4⋊C4×C59#4112yes—
195C22⋊C4×C59—24no—
196C22⋊C4×C59—42no—
197C42×C59—22no—
198C42×C59—22no—
199C42×C59—21no—
200C42×C59—21no—
201C42×C59—42no—
202C42×C59—42no—
203C42×C59C2×D412yes—
204C42×C59#4112yes—
205C22⋊Dic59—42no—
206#11745672—44no—
207#11745671—44no—
208(C2×D59)⋊C4—42no—
209(C2×D59)⋊C4—42no—
210(C2×D59)⋊C4—42no—
211(C2×D59)⋊C4—42no—
212(C2×D59)⋊C4—42no—
213C4⋊Dic59—21no—
214C4⋊Dic59—21no—
215C4⋊Dic59—21no—
216C4⋊Dic59—21no—
217Dic59⋊C4—42no—
218C2×C59⋊C8—21no—
219C2×C59⋊C8—21no—
220C2×C59⋊C8—21no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8C2×D412yes—
229C2×C59⋊C8C2×D412yes—
230C23×C59—21no—
231C23×C59—21no—
232C23×C59—21no—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59#13712yes—
237C23×C59C22×D411yescharacteristic
238C22×D59—41no—
239C22×D59—41no—
240C22×D59—41no—
241C22×D59—41no—
242C22×D59—41no—
243C22×D59—41no—
244C22×D59—41no—
245Q8×C59—22no—
246Q8×C59—22no—
247Q8×C59—41no—
248Q8×C59—41no—
249C2×C4×C59—21no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—21no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—22no—
257C2×C4×C59—22no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—44no—
265C2×C4×C59—44no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
271C2×C4×C59—41no—
272C2×C4×C59—41no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59—41no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59#12112yes—
281C2×C4×C59#12112yes—
282C2×C4×C59C22×D411yescharacteristic
283C2×C4×C59C2×#4111yescharacteristic
284C2×C4×C59C2×#4111yescharacteristic
285C2×C4×C59C2×#4111yescharacteristic
286C2×C4×C59H(5,𝔽2)11yescharacteristic
287C2×C4×C59H(5,𝔽2)11yescharacteristic
288C22⋊D59—84no—
289C2×Dic59—41no—
290C2×Dic59—41no—
291C2×Dic59—41no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298D236—41no—
299D236—41no—
300D236—41no—
301D236—41no—
302Dic118—41no—
303Dic118—41no—
304Dic118—41no—
305Dic118—41no—
306C59⋊C8—22no—
307C59⋊C8—22no—
308C59⋊C8—41no—
309C59⋊C8—41no—
310#24657—591nomaximal, Sylow
311C22×C59—22no—
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—41no—
315C22×C59—41no—
316C22×C59—41no—
317C22×C59—41no—
318C22×C59C2×#12111yescharacteristic
319C22×C59#52511yescharacteristic
320C22×C59#53511yescharacteristic
321C22×C59C2×#13711yescharacteristic
322C22×C59#57511yescharacteristic
323C22×C59#57511yescharacteristic
324C22×C59#57511yescharacteristic
325C2×D59—81no—
326C2×D59—81no—
327C2×D59—81no—
328C2×D59—81no—
329C2×D59—81no—
330C2×D59—81no—
331C2×D59—81no—
332C4×C59—22no—
333C4×C59—22no—
334C4×C59—42no—
335C4×C59—41no—
336C4×C59—42no—
337C4×C59—41no—
338C4×C59—41no—
339C4×C59—81no—
340C4×C59—81no—
341C4×C59#54611yescharacteristic
342C4×C59#55011yescharacteristic
343C4×C59#55311yescharacteristic
344C4×C59#55511yescharacteristic
345Dic59—81no—
346Dic59—81no—
347Dic59—81no—
348C2×#464—591no—
349C2×#432—591no—
350#2850—591no—
351C4×C22⋊Q8D5911yescharacteristic, complemented
352#2036—591no—
353#2034—591no—
354#2001—591no—
355#2000—591no—
356#1983—591no—
357#1973—591no—
358#1971—591no—
359#1949—591no—
360#1936—591no—
361#1935—591no—
362#1805—591no—
363C2×C59—42no—
364C2×C59#241411yescharacteristic
365C2×C59#305411yescharacteristic
366C2×C59#305611yescharacteristic
367C2×C59#311111yescharacteristic
368C2×C59#311711yescharacteristic
369C2×C59#321511yescharacteristic
370C2×C59#321911yescharacteristic
371D59—161no—
372C22×Q16—591no—
373C22×SD16—591no—
374C2×#124—591no—
375C2×C22⋊Q8—591no—
376C2×C22⋊Q8C2×D5911yescharacteristic
377C2×#121—591no—
378C2×C4×Q8C2×D5911yescharacteristic
379C22×C42C2×D5911yescharacteristic
380#464—1184no—
381#432—1184no—
382C2×#107—591no—
383C2×#106—591no—
384C2×C4⋊C8—591no—
385C2×C4⋊C8—591no—
386C2×#103—591no—
387C2×#103—591no—
388C2×#103—591no—
389C2×#103—591no—
390C2×#103—591no—
391C2×#102—591no—
392C2×#102—591no—
393C2×#102—591no—
394C2×C22⋊C8—591no—
395C2×C22⋊C8—591no—
396C2×#97—591no—
397C2×#97—591no—
398#391—591no—
399#391C2×D5911yescharacteristic
400#390—591no—
401#389C2×D5911yescharacteristic
402#388—1181no—
403#388—1181no—
404#387—21no—
405#386—1181no—
406#386—1181no—
407#385—21no—
408#382—591no—
409#380C2×D5911yescharacteristic
410C4×C4⋊C4—21no—
411C4×C4⋊C4C2×D5911yescharacteristic
412C4×C22⋊C4—21no—
413#340—591no—
414#340—591no—
415#340—591no—
416#340—591no—
417C59#2465711yescharacteristic, complemented, Sylow
418C22×Q8—591no—
419C22×Q8C22×D5911yescharacteristic
420C22×D4—591no—
421C22×D4—1181no—
422C23×C4C22⋊D5911yescharacteristic
423C23×C4C22⋊D5911yescharacteristic
424C23×C4C22×D5911yescharacteristic
425C2×Q16—1182no—
426C2×Q16—1182no—
427C2×Q16—2361no—
428C2×SD16—1182no—
429C2×SD16—1182no—
430C2×SD16—2361no—
431C22×C8—591no—
432C22×C8—591no—
433C22×C8—591no—
434C22×C8—591no—
435#124—1182no—
436#124—1182no—
437C22⋊Q8—22no—
438C22⋊Q8—22no—
439C22⋊Q8—2361no—
440C22⋊Q8—2361no—
441#121—2361no—
442#121—2361no—
443C4×Q8—22no—
444C4×Q8—22no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—591no—
449C2×C4⋊C4—591no—
450C2×C4⋊C4—1181no—
451C2×C4⋊C4C22×D5911yescharacteristic
452C2×C4⋊C4C22×D5911yescharacteristic
453C2×C4⋊C4C22×D5911yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—1181no—
457C2×C22⋊C4—1181no—
458C2×C22⋊C4—1181no—
459C2×C22⋊C4—1181no—
460C2×C22⋊C4—1181no—
461C2×C22⋊C4—1181no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42C22⋊D5911yescharacteristic
467C2×C42C22⋊D5911yescharacteristic
468C2×C42C22×D5911yescharacteristic
469C2×C42C22×D5911yescharacteristic
470#107—2361no—
471#106—2361no—
472C4⋊C8—594no—
473C4⋊C8—1182no—
474#103—1182no—
475#103—1182no—
476#103—2361no—
477#103—2361no—
478#103—2361no—
479#102—1182no—
480#102—1182no—
481#102—2361no—
482C22⋊C8—1182no—
483C22⋊C8—1182no—
484#97—1182no—
485#97—1182no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—1181no—
492#95—1181no—
493#95—1181no—
494#95—1181no—
495C24—1181no—
496C24C2×C22⋊D5911yescharacteristic
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—1181no—
503C2×Q8—1181no—
504C2×Q8—1181no—
505C2×Q8—1181no—
506C2×Q8—1181no—
507C2×Q8—1181no—
508C2×Q8#1174568512yes—
509C2×D4—1181no—
510C2×D4—1181no—
511C2×D4—1181no—
512C2×D4—1181no—
513C2×D4—1181no—
514C2×D4—1181no—
515C2×D4—2362no—
516C2×D4—2362no—
517C2×D4—2362no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—1181no—
535C22×C4—1181no—
536C22×C4—1181no—
537C22×C4C2×C22⋊D5911yescharacteristic
538C22×C4C2×C22⋊D5911yescharacteristic
539C22×C4C2×C22⋊D5911yescharacteristic
540C22×C4C2×C22⋊D5911yescharacteristic
541C22×C4C2×C22⋊D5911yescharacteristic
542C22×C4C23×D5911yescharacteristic
543Q16—2364no—
544SD16—2364no—
545C2×C8—592no—
546C2×C8—592no—
547C2×C8—1181no—
548C2×C8—1181no—
549C2×C8—1181no—
550C2×C8—1181no—
551C2×C8—1181no—
552C2×C8—1181no—
553C2×C8—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C2×C8—1181no—
557C4⋊C4—24no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—1181no—
566C4⋊C4—1181no—
567C4⋊C4—1181no—
568C4⋊C4—1181no—
569C4⋊C4—2362no—
570C4⋊C4#1174568512yes—
571C22⋊C4—24no—
572C22⋊C4—42no—
573C22⋊C4—2362no—
574C22⋊C4—2362no—
575C22⋊C4—2362no—
576C22⋊C4—2362no—
577C22⋊C4—2362no—
578C22⋊C4—2362no—
579C42—22no—
580C42—22no—
581C42—21no—
582C42—21no—
583C42—42no—
584C42—42no—
585C42D4×D5912yes—
586C42#1174568712yes—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—2361no—
594C23—2361no—
595C23—2361no—
596C23—2361no—
597C23—2361no—
598C23—2361no—
599C23—2361no—
600C23#1427375812yes—
601C23C22×C22⋊D5911yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606Q8—2361no—
607Q8—2361no—
608Q8—2361no—
609Q8—2361no—
610D4—4724no—
611D4—2361no—
612D4—2361no—
613D4—2361no—
614D4—2361no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—44no—
631C2×C4—44no—
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—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—2361no—
647C2×C4—2361no—
648C2×C4—2361no—
649C2×C4—2361no—
650C2×C4—2361no—
651C2×C4—2361no—
652C2×C4—2361no—
653C2×C4—2361no—
654C2×C4—2361no—
655C2×C4#1427369912yes—
656C2×C4#1427369912yes—
657C2×C4C2×D4×D5911yescharacteristic
658C2×C4C2×#1174568711yescharacteristic
659C2×C4C2×#1174568511yescharacteristic
660C2×C4C2×#1174568511yescharacteristic
661C2×C4#1427377311yescharacteristic
662C2×C4#1427377311yescharacteristic
663C8—1182no—
664C8—1182no—
665C8—2361no—
666C8—2361no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—4721no—
675C22—4721no—
676C22—4721no—
677C22—4721no—
678C22—4721no—
679C22—4721no—
680C22—4721no—
681C22C2×#1427369911yescharacteristic
682C22#1683791311yescharacteristic
683C22#1683796611yescharacteristic
684C22C2×#1427375811yescharacteristic
685C22#1683820011yescharacteristic
686C22#1683820011yescharacteristic
687C22#1683820011yescharacteristic
688C4—22no—
689C4—22no—
690C4—41no—
691C4—42no—
692C4—42no—
693C4—41no—
694C4—41no—
695C4—81no—
696C4—81no—
697C4—4721no—
698C4—4721no—
699C4—4721no—
700C4#1683804811yescharacteristic
701C4#1683807311yescharacteristic
702C4#1683809811yescharacteristic
703C4#1683811711yescharacteristic
704C2—42no—
705C2—9441no—
706C2#2142751411yescharacteristic
707C2#2143370211yescharacteristic
708C2#2143372211yescharacteristic
709C2#2143420511yescharacteristic
710C2#2143426711yescharacteristic
711C2#2143509511yescharacteristic
712C2#2143512911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC4×C22⋊Q8×C59C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
hypercenterC4×C22⋊Q8D59
hypocenterC59#24657
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16837624C2semidirect
2. C2×#16837459C2semidirect
4. #21425299C2semidirect
6. #21425104C2semidirect
8. #21425028C2semidirect
9. #21424980C2semidirect
10. #21424966C2semidirect
11. #21424864C2semidirect
12. #21424792C2semidirect
13. #21424785C2semidirect
14. #21424111C2semidirect
15. C4×C22⋊Q8×C59C2semidirect
92. C4⋊(C59⋊C8)D4semidirect
351. C4×C22⋊Q8D59semidirect
417. C59#24657semidirect

Maximal subgroups

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

subgroupindex
C2×#168376242
C2×#168374592
#214323972
#214252992
#214252852
#214251042
#214250972
#214250282
#214249802
#214249662
#214248642
#214247922
#214247852
#214241112
C4×C22⋊Q8×C592
#2465759