Finite Group Databasebeta

← #28611521

Subgroups — #28611521

Order 15104.

1026 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837650C211yesmaximal, characteristic
2C2×#16837500C211yesmaximal, characteristic, complemented
3C2×#16837445C211yesmaximal, characteristic, complemented
4#21427110C211yesmaximal, characteristic
5#21424953C211yesmaximal, characteristic, complemented
6#21424831C211yesmaximal, characteristic, complemented
7#21424727C211yesmaximal, characteristic, complemented
8#21424716C211yesmaximal, characteristic, complemented
9#21424418C211yesmaximal, characteristic
10#21424404C211yesmaximal, characteristic, complemented
11#21424356C211yesmaximal, characteristic, complemented
12#21424350C211yesmaximal, characteristic, complemented
13C4×#14273660C211yesmaximal, characteristic, complemented
14#21423880C211yesmaximal, characteristic, complemented
15C59×#2362C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic
17C22×#11745664C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic
20C2×(C22⋊D59)⋊C4—21no—
21C22×C4⋊Dic59C2211yescharacteristic
22#16837650C418yescomplemented
23#16837500—24no—
24#16837445—24no—
25C2×#14273660C2211yescharacteristic
26C2×#14273660C2211yescharacteristic
27C2×#14273660C2211yescharacteristic
28C2×#14273658C2211yescharacteristic
29C2×#14273658C2211yescharacteristic
30C2×#14273651C2211yescharacteristic
31C2×#14273651C2211yescharacteristic
32C2×#14273651C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×#14273647C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37C2×#14273638C2211yescharacteristic
38C2×C4×C59⋊C8C2211yescharacteristic
39#16837304C2211yescharacteristic
40#16837300C2211yescharacteristic
41#16837294—21no—
42#16837279—21no—
43#16837276—21no—
44C4×C4⋊Dic59C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837157C2211yescharacteristic
51C2×C22⋊Q8×C59C2211yescharacteristic
52C2×C4×Q8×C59C2211yescharacteristic
53C2×#117×C59C2211yescharacteristic
54C59×#391C2211yescharacteristic
55C59×#389C2211yescharacteristic
56C59×#388—21no—
57C59×#388—21no—
58C59×#387—21no—
59C4×C4⋊C4×C59—21no—
60C4×C4⋊C4×C59C2211yescharacteristic
61C4×C22⋊C4×C59C2211yescharacteristic
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C23×Dic59—21no—
65C22×C4×D59—21no—
66C2×#11745671—22no—
67C2×#11745671—22no—
68C2×#11745671C2×C414yescomplemented
69C2×#11745664—22no—
70C2×#11745664—22no—
71C2×#11745664C2×C414yescomplemented
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76#14273701—22no—
77#14273701C2×C414yes—
78C4×D236—22no—
79C4×D236—41no—
80(C22⋊D59)⋊C4—44no—
81C2×C4⋊Dic59—22no—
82C2×C4⋊Dic59—21no—
83C2×C4⋊Dic59—41no—
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×C4⋊Dic59C2311yescharacteristic
87C2×Dic59⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×(C2×D59)⋊C4—21no—
92C2×C4×Dic59—21no—
93#14273660—22no—
94#14273660C2×C414yescomplemented
95#14273660D414yescomplemented
96#14273658—22no—
97#14273658—22no—
98#14273651—22no—
99#14273651—41no—
100#14273651C2×C414yescomplemented
101#14273647—22no—
102#14273647—41no—
103#14273647C2×C414yescomplemented
104C22⋊(C59⋊C8)—22no—
105#14273638—22no—
106C4×C59⋊C8—22no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C22×Q8×C59C2311yescharacteristic
110C23×C4×C59C2311yescharacteristic
111C22⋊Q8×C59—22no—
112C22⋊Q8×C59C2×C414yescomplemented
113C4×Q8×C59—22no—
114C4×Q8×C59—41no—
115#117×C59—22no—
116#117×C59—41no—
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×C22⋊C4×C59D411yescharacteristic
126C2×C22⋊C4×C59D411yescharacteristic
127C2×C42×C59—21no—
128C2×C42×C59—21no—
129C2×C42×C59—21no—
130C2×C42×C59C2311yescharacteristic
131C2×C42×C59C2311yescharacteristic
132#95×C59—21no—
133#95×C59—21no—
134#95×C59—21no—
135#95×C59—21no—
136#95×C59D411yescharacteristic
137#95×C59D411yescharacteristic
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×C59C22×C412yes—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59C22×C412yes—
155C22×C4×C59C2×D411yescharacteristic
156C22×C4×C59C2×D411yescharacteristic
157C22×C4×C59C2×D411yescharacteristic
158C22×C4×C59C2×D411yescharacteristic
159C22×C4×C59C2×D411yescharacteristic
160C22×C4×C59#4112yes—
161C22×C4×C59C2411yescharacteristic
162C2×C22⋊D59—24no—
163C2×C22⋊D59—42no—
164C2×C22⋊D59—42no—
165C22×Dic59—21no—
166C22×Dic59—21no—
167C22×Dic59—21no—
168C22×Dic59—42no—
169C22×Dic59—42no—
170C22×Dic59—81no—
171C2×D236—21no—
172C2×D236—21no—
173C2×D236—21no—
174C2×D236—21no—
175C2×D236—21no—
176C2×D236C22×C412yes—
177C2×C4×D59—42no—
178C2×C4×D59—42no—
179C2×C4×D59—81no—
180C4⋊C4×C59—24no—
181C4⋊C4×C59—21no—
182C4⋊C4×C59—21no—
183C4⋊C4×C59—21no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—42no—
186C4⋊C4×C59—42no—
187C4⋊C4×C59C22×C412yes—
188C4⋊C4×C59C2×D412yes—
189C22⋊C4×C59—24no—
190C22⋊C4×C59—22no—
191C22⋊C4×C59—41no—
192C22⋊C4×C59—42no—
193C42×C59—21no—
194C42×C59—21no—
195C42×C59—21no—
196C42×C59—21no—
197C42×C59—42no—
198C42×C59—42no—
199C42×C59—42no—
200#11745671—28no—
201(C2×D59)⋊C4—24no—
202(C2×D59)⋊C4—42no—
203(C2×D59)⋊C4—42no—
204(C2×D59)⋊C4—81no—
205C4⋊Dic59—21no—
206C4⋊Dic59—21no—
207C4⋊Dic59—21no—
208C4⋊Dic59—21no—
209C4⋊Dic59—42no—
210C4⋊Dic59C22×C412yes—
211C4⋊Dic59C2×D412yes—
212Dic59⋊C4—42no—
213C4×Dic59—42no—
214#11745664—28no—
215C2×C59⋊C8—21no—
216C2×C59⋊C8—21no—
217C2×C59⋊C8—21no—
218C2×C59⋊C8—21no—
219C2×C59⋊C8—21no—
220C2×C59⋊C8—21no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8C22×C412yes—
224C2×C59⋊C8C22×C412yes—
225C2×C59⋊C8C2×D412yes—
226C2×C59⋊C8#4112yes—
227C23×C59—21no—
228C23×C59—21no—
229C23×C59—21no—
230C23×C59—21no—
231C23×C59—21no—
232C23×C59—21no—
233C23×C59C4×D412yes—
234C23×C59C22×D411yescharacteristic
235C22×D59—22no—
236C22×D59—41no—
237C22×D59—41no—
238C22×D59—41no—
239C22×D59—41no—
240C22×D59—41no—
241C22×D59—41no—
242Q8×C59—22no—
243Q8×C59—22no—
244Q8×C59—41no—
245Q8×C59—41no—
246C2×C4×C59—21no—
247C2×C4×C59—21no—
248C2×C4×C59—21no—
249C2×C4×C59—21no—
250C2×C4×C59—22no—
251C2×C4×C59—22no—
252C2×C4×C59—22no—
253C2×C4×C59—22no—
254C2×C4×C59—22no—
255C2×C4×C59—22no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—22no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
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×C59C4×D412yes—
276C2×C4×C59AGL(1,ℤ/8)12yes—
277C2×C4×C59C23×C411yescharacteristic
278C2×C4×C59C22×D411yescharacteristic
279C2×C4×C59C2×#4111yescharacteristic
280C2×C4×C59C2×#4111yescharacteristic
281C2×C4×C59H(5,𝔽2)11yescharacteristic
282C2×C4×C592−1+411yescharacteristic
283C22⋊D59—48no—
284C2×Dic59—22no—
285C2×Dic59—22no—
286C2×Dic59—41no—
287C2×Dic59—41no—
288C2×Dic59—41no—
289C2×Dic59—41no—
290C2×Dic59—41no—
291C2×Dic59—41no—
292C2×Dic59—41no—
293C2×Dic59—84no—
294D236—22no—
295D236—22no—
296D236—41no—
297D236—41no—
298C4×D59—84no—
299C59⋊C8—22no—
300C59⋊C8—41no—
301C59⋊C8—41no—
302C59⋊C8C4×D414yescomplemented
303#23040—591nomaximal, Sylow
304C22×C59—22no—
305C22×C59—22no—
306C22×C59—22no—
307C22×C59—41no—
308C22×C59—41no—
309C22×C59—41no—
310C22×C59—41no—
311C22×C59C2×C4×D411yescharacteristic
312C22×C59D4211yescharacteristic
313C22×C59#54711yescharacteristic
314C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C59#57511yescharacteristic
316C22×C59#57711yescharacteristic
317C22×C59#57811yescharacteristic
318C2×D59—42no—
319C2×D59—42no—
320C2×D59—42no—
321C2×D59—81no—
322C2×D59—81no—
323C2×D59—81no—
324C2×D59—81no—
325C4×C59—22no—
326C4×C59—22no—
327C4×C59—41no—
328C4×C59—42no—
329C4×C59—42no—
330C4×C59—41no—
331C4×C59—42no—
332C4×C59—41no—
333C4×C59—81no—
334C4×C59C2×C4×D411yescharacteristic
335C4×C59#52011yescharacteristic
336C4×C59#54811yescharacteristic
337C4×C59#55311yescharacteristic
338Dic59—42no—
339Dic59—42no—
340Dic59—81no—
341C2×#468—591no—
342C2×#440—591no—
343C2×#428—591no—
344#2362D5911yescharacteristic, complemented
345#2361—591no—
346#1968—591no—
347#1943—591no—
348#1927—591no—
349#1925—591no—
350#1875—591no—
351#1872—591no—
352#1864—591no—
353#1863—591no—
354C4×#107—591no—
355#1753—591no—
356C2×C59—42no—
357C2×C59#236111yescharacteristic
358C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
359C2×C59#294711yescharacteristic
360C2×C59#327211yescharacteristic
361C2×C59#327711yescharacteristic
362C2×C59#334311yescharacteristic
363C2×C59#335011yescharacteristic
364D59—82no—
365C22×SD16—591no—
366C22×M16—591no—
367C2×C22⋊Q8C2×D5911yescharacteristic
368C2×#121—591no—
369C2×C4×Q8C2×D5911yescharacteristic
370C2×C4×D4—591no—
371C2×C4×D4—1181no—
372C2×#117C2×D5911yescharacteristic
373C22×C4⋊C4—591no—
374#468—598no—
375#440—1184no—
376#428—1184no—
377C2×#107—591no—
378C2×#107—591no—
379C2×#107—591no—
380C2×#106—591no—
381C2×#106—591no—
382C2×#103—591no—
383C2×#103—591no—
384C2×#103—591no—
385C2×#102—591no—
386C2×#102—591no—
387C2×#102—591no—
388C2×C22⋊C8—591no—
389C2×#97—591no—
390C2×C4×C8—591no—
391#391C2×D5911yescharacteristic
392#390—591no—
393#389—591no—
394#389C2×D5911yescharacteristic
395#388—21no—
396#388—21no—
397#388—1181no—
398#387—21no—
399#386—1181no—
400#385—1181no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4—591no—
403C4×C4⋊C4C2×D5911yescharacteristic
404C4×C22⋊C4C2×D5911yescharacteristic
405#340—591no—
406#340—591no—
407#340—591no—
408#340—591no—
409#336—591no—
410#336—591no—
411C59#2304011yescharacteristic, complemented, Sylow
412C22×Q8C22×D5911yescharacteristic
413C22×D4—591no—
414C22×D4—1181no—
415C23×C4—1181no—
416C23×C4—1181no—
417C23×C4C22×D5911yescharacteristic
418C2×SD16—594no—
419C2×SD16—1182no—
420C2×SD16—1182no—
421C2×M16—594no—
422C2×M16—1182no—
423C2×M16—1182no—
424C22×C8—591no—
425C22×C8—591no—
426C22×C8—591no—
427C22×C8—591no—
428C22⋊Q8—22no—
429C22⋊Q8C4×D5914yescomplemented
430#121—594no—
431#121—1182no—
432C4×Q8—22no—
433C4×Q8—41no—
434C4×D4—1182no—
435C4×D4—2361no—
436C4×D4—2364no—
437#117—22no—
438#117—41no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—591no—
443C2×C4⋊C4—591no—
444C2×C4⋊C4—591no—
445C2×C4⋊C4—1182no—
446C2×C4⋊C4—1181no—
447C2×C4⋊C4—1181no—
448C2×C4⋊C4—2361no—
449C2×C4⋊C4C22×D5911yescharacteristic
450C2×C4⋊C4C22×D5911yescharacteristic
451C2×C4⋊C4C22×D5911yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—1181no—
455C2×C22⋊C4—1181no—
456C2×C22⋊C4—1181no—
457C2×C22⋊C4—1181no—
458C2×C22⋊C4C22⋊D5911yescharacteristic
459C2×C22⋊C4C22⋊D5911yescharacteristic
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—1181no—
464C2×C42C22×D5911yescharacteristic
465C2×C42C22×D5911yescharacteristic
466#107—594no—
467#107—594no—
468#107—1182no—
469#106—1182no—
470#106—1182no—
471#103—594no—
472#103—1182no—
473#103—2361no—
474#102—594no—
475#102—1182no—
476#102—2361no—
477C22⋊C8—1182no—
478#97—1182no—
479C4×C8—1182no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—1181no—
485#95—1181no—
486#95C22⋊D5911yescharacteristic
487#95C22⋊D5911yescharacteristic
488C24—1181no—
489C24C2×C22⋊D5911yescharacteristic
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8C2×C4×D5912yes—
496C2×D4—592no—
497C2×D4—1184no—
498C2×D4—1181no—
499C2×D4—1181no—
500C2×D4—1181no—
501C2×D4—1181no—
502C2×D4—1181no—
503C2×D4—2362no—
504C2×D4—2362no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—1181no—
514C22×C4—1181no—
515C22×C4—1181no—
516C22×C4—4721no—
517C22×C4—4721no—
518C22×C4—2362no—
519C22×C4—2362no—
520C22×C4—2362no—
521C22×C4—2362no—
522C22×C4C2×C4×D5912yes—
523C22×C4#1174568512yes—
524C22×C4C2×C22⋊D5911yescharacteristic
525C22×C4C2×C22⋊D5911yescharacteristic
526C22×C4C2×C22⋊D5911yescharacteristic
527C22×C4C2×C22⋊D5911yescharacteristic
528C22×C4C2×C22⋊D5911yescharacteristic
529C22×C4C23×D5911yescharacteristic
530SD16—1188no—
531M16—1188no—
532C2×C8—592no—
533C2×C8—592no—
534C2×C8—592no—
535C2×C8—592no—
536C2×C8—1181no—
537C2×C8—1181no—
538C2×C8—1181no—
539C2×C8—1181no—
540C2×C8—1181no—
541C2×C8—1181no—
542C2×C8—1181no—
543C2×C8—1181no—
544C4⋊C4—24no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—592no—
552C4⋊C4—592no—
553C4⋊C4—1181no—
554C4⋊C4—1181no—
555C4⋊C4—1181no—
556C4⋊C4—1181no—
557C4⋊C4—2362no—
558C4⋊C4—2362no—
559C4⋊C4C2×C4×D5912yes—
560C4⋊C4D4×D5912yes—
561C22⋊C4—24no—
562C22⋊C4—22no—
563C22⋊C4—41no—
564C22⋊C4—42no—
565C22⋊C4—1184no—
566C22⋊C4—4721no—
567C22⋊C4—2362no—
568C22⋊C4—2362no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—42no—
574C42—42no—
575C42—42no—
576C42—2362no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—1182no—
584C23—2361no—
585C23—2361no—
586C23—2361no—
587C23—2361no—
588C23—2361no—
589C23—2361no—
590C23C4×C22⋊D5912yes—
591C23C22×C22⋊D5911yescharacteristic
592Q8—22no—
593Q8—22no—
594Q8—41no—
595Q8—41no—
596D4—1182no—
597D4—1182no—
598D4—2368no—
599D4—2361no—
600D4—2361no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—1182no—
631C2×C4—1182no—
632C2×C4—4724no—
633C2×C4—4724no—
634C2×C4—2361no—
635C2×C4—2361no—
636C2×C4—2361no—
637C2×C4—2361no—
638C2×C4—2361no—
639C2×C4—2361no—
640C2×C4—2361no—
641C2×C4C4×C22⋊D5912yes—
642C2×C4#1427375212yes—
643C2×C4C22×C4×D5911yescharacteristic
644C2×C4C2×D4×D5911yescharacteristic
645C2×C4#41×D5911yescharacteristic
646C2×C4C2×#1174568511yescharacteristic
647C2×C4#1427377211yescharacteristic
648C2×C4#1427377411yescharacteristic
649C8—594no—
650C8—1182no—
651C8—2361no—
652C8—2361no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—4721no—
661C22—4721no—
662C22—4721no—
663C22—4721no—
664C22—2362no—
665C22—2362no—
666C22—2362no—
667C22C2×C4×C22⋊D5911yescharacteristic
668C22D4×C22⋊D5911yescharacteristic
669C22#1683805111yescharacteristic
670C22C2×#1427375211yescharacteristic
671C22#1683820011yescharacteristic
672C22#1683821011yescharacteristic
673C22#1683821711yescharacteristic
674C4—22no—
675C4—22no—
676C4—41no—
677C4—42no—
678C4—42no—
679C4—41no—
680C4—42no—
681C4—41no—
682C4—81no—
683C4—4721no—
684C4—2362no—
685C4—2362no—
686C4C4×D4×D5911yescharacteristic
687C4#1683788111yescharacteristic
688C4#1683806111yescharacteristic
689C4#1683810111yescharacteristic
690C2—42no—
691C2—4722no—
692C2#2142711311yescharacteristic
693C2C4×#1427375211yescharacteristic
694C2#2143293911yescharacteristic
695C2#2143569611yescharacteristic
696C2#2143574911yescharacteristic
697C2#2143653611yescharacteristic
698C2#2143664111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2362C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
cosocleC22×C4×C59C24
hypercenter#2362D59
hypocenterC59#23040
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2362

Complements

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

NH ≅ G/Ntype
2. C2×#16837500C2semidirect
3. C2×#16837445C2semidirect
5. #21424953C2semidirect
6. #21424831C2semidirect
7. #21424727C2semidirect
8. #21424716C2semidirect
10. #21424404C2semidirect
11. #21424356C2semidirect
12. #21424350C2semidirect
13. C4×#14273660C2semidirect
14. #21423880C2semidirect
15. C59×#2362C2semidirect
22. #16837650C4semidirect
68. C2×#11745671C2×C4semidirect
71. C2×#11745664C2×C4semidirect
94. #14273660C2×C4semidirect
95. #14273660D4semidirect
100. #14273651C2×C4semidirect
103. #14273647C2×C4semidirect
112. C22⋊Q8×C59C2×C4semidirect
302. C59⋊C8C4×D4semidirect
344. #2362D59semidirect
411. C59#23040semidirect
429. C22⋊Q8C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168376502
C2×#168375002
C2×#168374452
#214271102
#214249532
#214248312
#214247272
#214247162
#214244182
#214244042
#214243562
#214243502
C4×#142736602
#214238802
C59×#23622
#2304059