Finite Group Databasebeta

← #28611122

Subgroups — #28611122

Order 15104.

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×#16837602C211yesmaximal, characteristic
2C2×#16837500C211yesmaximal, characteristic, complemented
3C2×C4×#11745671C211yesmaximal, characteristic, complemented
4#21427160C211yesmaximal, characteristic
5#21424919C211yesmaximal, characteristic
6#21424862C211yesmaximal, characteristic, complemented
7#21424792C211yesmaximal, characteristic, complemented
8#21424778C211yesmaximal, characteristic, complemented
9#21424451C211yesmaximal, characteristic, complemented
10#21424451C211yesmaximal, characteristic, complemented
11#21424356C211yesmaximal, characteristic, complemented
12#21424342C211yesmaximal, characteristic, complemented
13#21423971C211yesmaximal, characteristic, complemented
14#21423926C211yesmaximal, characteristic, complemented
15C59×#2351C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic
17C22×#11745671C2211yescharacteristic
18C2×#14273724C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic
21C2×#14273689—21no—
22#16837602C418yescomplemented
23#16837500—24no—
24C4×#11745671—24no—
25C2×#14273660C2211yescharacteristic
26C2×#14273658C2211yescharacteristic
27C2×C4⋊(C59⋊C8)C2211yescharacteristic
28C2×#14273651C2211yescharacteristic
29C2×#14273651C2211yescharacteristic
30C2×#14273647C2211yescharacteristic
31C2×#14273647C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×#14273647C2211yescharacteristic
36C2×#14273638C2211yescharacteristic
37C2×#14273638C2211yescharacteristic
38C2×C4×C59⋊C8C2211yescharacteristic
39#16837304C2211yescharacteristic
40#16837304C2211yescharacteristic
41#16837303—21no—
42#16837280—21no—
43#16837280—21no—
44C4×C4⋊Dic59C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837157C2211yescharacteristic
51C2×C4×Q8×C59C2211yescharacteristic
52C2×C4×Q8×C59C2211yescharacteristic
53C2×C4×Q8×C59C2211yescharacteristic
54C59×#389—21no—
55C59×#389—21no—
56C59×#389C2211yescharacteristic
57C59×#389C2211yescharacteristic
58C59×#382—21no—
59C59×#382C2211yescharacteristic
60C4×C4⋊C4×C59—21no—
61C4×C4⋊C4×C59C2211yescharacteristic
62C22×D236—21no—
63C22×D236—21no—
64C22×D236C2311yescharacteristic
65C22×D236C2311yescharacteristic
66C22×C4×D59—21no—
67C22×C4×D59—21no—
68C2×#11745671—22no—
69C2×#11745671—22no—
70C2×#11745671—22no—
71C2×#11745671—22no—
72C2×#11745671C2×C414yescomplemented
73C2×#11745671C2×C414yescomplemented
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78#14273724—22no—
79#14273724C2×C414yes—
80C4×D236—22no—
81C4×D236—22no—
82C4×D236—41no—
83C4×D236—41no—
84#14273689—44no—
85C2×C4⋊Dic59C2311yescharacteristic
86C2×C4⋊Dic59C2311yescharacteristic
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×(C2×D59)⋊C4—21no—
92C2×(C2×D59)⋊C4—21no—
93C2×C4×Dic59—21no—
94#14273660—22no—
95#14273658—22no—
96C4⋊(C59⋊C8)C2×C414yescomplemented
97#14273651—22no—
98#14273651D414yescomplemented
99#14273647—22no—
100#14273647—22no—
101#14273647—41no—
102#14273647—41no—
103#14273647C2×C414yescomplemented
104#14273647C2×C414yescomplemented
105#14273638—22no—
106#14273638—22no—
107C4×C59⋊C8—22no—
108C59⋊#95—21no—
109C22×Q8×C59C2311yescharacteristic
110C4×Q8×C59—22no—
111C4×Q8×C59—22no—
112C4×Q8×C59—22no—
113C4×Q8×C59—41no—
114C4×Q8×C59—41no—
115C4×Q8×C59C2×C414yescomplemented
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59—21no—
121C2×C4⋊C4×C59D411yescharacteristic
122C2×C4⋊C4×C59D411yescharacteristic
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C4⋊C4×C59C2311yescharacteristic
125C2×C4⋊C4×C59C2311yescharacteristic
126C2×C42×C59—21no—
127C2×C42×C59—21no—
128C2×C42×C59—21no—
129C2×C42×C59C2311yescharacteristic
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
138C23×D59—21no—
139C23×D59—21no—
140C2×Q8×C59—21no—
141C2×Q8×C59—21no—
142C2×Q8×C59—21no—
143C2×Q8×C59C22×C412yes—
144C2×Q8×C59C2×D412yes—
145C2×Q8×C59#4112yes—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59C2×D411yescharacteristic
151C22×C4×C59C2×D411yescharacteristic
152C22×C4×C59C2×D411yescharacteristic
153C22×C4×C59C2×D411yescharacteristic
154C22×C4×C59C2×D411yescharacteristic
155C22×C4×C59C2×D411yescharacteristic
156C22×C4×C59C2411yescharacteristic
157C22×Dic59—21no—
158C22×Dic59—21no—
159C2×D236—21no—
160C2×D236—21no—
161C2×D236—21no—
162C2×D236—21no—
163C2×D236—21no—
164C2×D236—21no—
165C2×D236—21no—
166C2×D236—21no—
167C2×D236—24no—
168C2×D236—21no—
169C2×D236—21no—
170C2×D236—24no—
171C2×D236—42no—
172C2×D236—42no—
173C2×D236—81no—
174C2×D236—81no—
175C2×D236C22×C412yes—
176C2×D236C22×C412yes—
177C2×C4×D59—42no—
178C2×C4×D59—42no—
179C2×C4×D59—42no—
180C2×C4×D59—42no—
181C2×C4×D59—81no—
182C2×C4×D59—81no—
183C4⋊C4×C59—24no—
184C4⋊C4×C59—22no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—41no—
191C4⋊C4×C59—42no—
192C4⋊C4×C59—42no—
193C4⋊C4×C59—42no—
194C4⋊C4×C59—42no—
195C4⋊C4×C59C22×C412yes—
196C42×C59—24no—
197C42×C59—21no—
198C42×C59—21no—
199C42×C59—21no—
200C42×C59—21no—
201C42×C59—42no—
202C42×C59—42no—
203C42×C59C22×C412yes—
204C42×C59#4112yes—
205#11745671—28no—
206#11745671—28no—
207(C2×D59)⋊C4—42no—
208(C2×D59)⋊C4—42no—
209(C2×D59)⋊C4—42no—
210(C2×D59)⋊C4—42no—
211(C2×D59)⋊C4—81no—
212(C2×D59)⋊C4—81no—
213C4⋊Dic59—21no—
214C4⋊Dic59—21no—
215C4⋊Dic59—21no—
216C4⋊Dic59C2×D412yes—
217C4×Dic59—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⋊C8C22×C412yes—
228C2×C59⋊C8C22×C412yes—
229C2×C59⋊C8C2×D412yes—
230C23×C59C22×D411yescharacteristic
231C22×D59—22no—
232C22×D59—22no—
233C22×D59—41no—
234C22×D59—41no—
235C22×D59—41no—
236C22×D59—41no—
237C22×D59—41no—
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—22no—
248Q8×C59C4×D414yescomplemented
249C2×C4×C59—22no—
250C2×C4×C59—21no—
251C2×C4×C59—22no—
252C2×C4×C59—22no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
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—21no—
267C2×C4×C59—21no—
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×C59C4×D412yes—
277C2×C4×C59C4×D412yes—
278C2×C4×C59AGL(1,ℤ/8)12yes—
279C2×C4×C59C23×C411yescharacteristic
280C2×C4×C59C22×D411yescharacteristic
281C2×C4×C59C2×#4111yescharacteristic
282C2×C4×C59C2×#4111yescharacteristic
283C2×C4×C59H(5,𝔽2)11yescharacteristic
284C2×C4×C592−1+411yescharacteristic
285C2×Dic59—22no—
286C2×Dic59—41no—
287C2×Dic59—41no—
288C2×Dic59—41no—
289C2×Dic59—41no—
290C2×Dic59—41no—
291D236—22no—
292D236—22no—
293D236—22no—
294D236—22no—
295D236—48no—
296D236—41no—
297D236—41no—
298D236—41no—
299D236—41no—
300D236—84no—
301C4×D59—84no—
302C4×D59—84no—
303C59⋊C8—22no—
304C59⋊C8—22no—
305C59⋊C8—22no—
306C59⋊C8—41no—
307#23010—591nomaximal, Sylow
308C22×C59C2×C4×D411yescharacteristic
309C22×C59D4211yescharacteristic
310C22×C59#54811yescharacteristic
311C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C59#57511yescharacteristic
313C22×C59#57711yescharacteristic
314C22×C59#57711yescharacteristic
315C2×D59—42no—
316C2×D59—42no—
317C2×D59—42no—
318C2×D59—42no—
319C2×D59—42no—
320C2×D59—42no—
321C2×D59—81no—
322C2×D59—81no—
323C2×D59—81no—
324C2×D59—81no—
325C2×D59—81no—
326C2×D59—81no—
327C2×D59—81no—
328C2×D59—81no—
329C4×C59—24no—
330C4×C59—22no—
331C4×C59—22no—
332C4×C59—22no—
333C4×C59—42no—
334C4×C59—41no—
335C4×C59—41no—
336C4×C59—41no—
337C4×C59—81no—
338C4×C59—81no—
339C4×C59C2×C4×D411yescharacteristic
340C4×C59#52011yescharacteristic
341C4×C59#54711yescharacteristic
342C4×C59#55311yescharacteristic
343Dic59—42no—
344Dic59—81no—
345C2×#460—591no—
346C2×#440—591no—
347C2×C4×SD16—591no—
348#2366—591no—
349#2351D5911yescharacteristic, complemented
350#1961—591no—
351#1949—591no—
352#1936—591no—
353#1934—591no—
354#1880—591no—
355#1880—591no—
356#1864—591no—
357#1862—591no—
358#1771—591no—
359#1763—591no—
360C2×C59#236111yescharacteristic
361C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
362C2×C59#294911yescharacteristic
363C2×C59#326511yescharacteristic
364C2×C59#327111yescharacteristic
365C2×C59#336811yescharacteristic
366C2×C59#337111yescharacteristic
367D59—82no—
368D59—82no—
369C22×SD16—591no—
370C22×SD16—591no—
371C2×#127—591no—
372C2×C4×Q8C2×D5911yescharacteristic
373C2×C4×Q8C2×D5911yescharacteristic
374C2×C4×Q8C2×D5911yescharacteristic
375C2×C4×D4—591no—
376C2×C4×D4—591no—
377C2×C4×D4—1181no—
378#460—598no—
379#440—1184no—
380C4×SD16—1184no—
381C2×#107—591no—
382C2×#106—591no—
383C2×C4⋊C8—591no—
384C2×#103—591no—
385C2×#103—591no—
386C2×#102—591no—
387C2×#102—591no—
388C2×#102—591no—
389C2×#102—591no—
390C2×#102—591no—
391C2×#102—591no—
392C2×#97—591no—
393C2×#97—591no—
394C2×C4×C8—591no—
395#390—591no—
396#390—591no—
397#390—1181no—
398#389—21no—
399#389—21no—
400#389C2×D5911yescharacteristic
401#389C2×D5911yescharacteristic
402#386—1181no—
403#386—1181no—
404#382—21no—
405#382C2×D5911yescharacteristic
406C4×C4⋊C4—21no—
407C4×C4⋊C4—591no—
408C4×C4⋊C4C2×D5911yescharacteristic
409#340—591no—
410#340—591no—
411#340—591no—
412#340—591no—
413#336—591no—
414#336—591no—
415C59#2301011yescharacteristic, complemented, Sylow
416C22×Q8C22×D5911yescharacteristic
417C22×D4—591no—
418C22×D4—591no—
419C22×D4—1181no—
420C22×D4—1181no—
421C23×C4—1181no—
422C23×C4—1181no—
423C2×SD16—594no—
424C2×SD16—594no—
425C2×SD16—1182no—
426C2×SD16—1182no—
427C2×SD16—1182no—
428C2×SD16—1182no—
429C22×C8—591no—
430C22×C8—591no—
431C22×C8—591no—
432C22×C8—591no—
433#127—594no—
434#127—1182no—
435C4×Q8—22no—
436C4×Q8—22no—
437C4×Q8—22no—
438C4×Q8—41no—
439C4×Q8—41no—
440C4×Q8C4×D5914yescomplemented
441C4×D4—1182no—
442C4×D4—1182no—
443C4×D4—2361no—
444C4×D4—2361no—
445C4×D4—2364no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—591no—
452C2×C4⋊C4—591no—
453C2×C4⋊C4C22⋊D5911yescharacteristic
454C2×C4⋊C4C22⋊D5911yescharacteristic
455C2×C4⋊C4C22×D5911yescharacteristic
456C2×C4⋊C4C22×D5911yescharacteristic
457C2×C4⋊C4C22×D5911yescharacteristic
458C2×C22⋊C4—1181no—
459C2×C22⋊C4—1181no—
460C2×C22⋊C4—1181no—
461C2×C22⋊C4—1181no—
462C2×C22⋊C4—1181no—
463C2×C22⋊C4—1181no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—1181no—
468C2×C42C22×D5911yescharacteristic
469C2×C42C22×D5911yescharacteristic
470C2×C42C22×D5911yescharacteristic
471#107—1182no—
472#106—1182no—
473C4⋊C8—594no—
474#103—594no—
475#103—1182no—
476#102—594no—
477#102—594no—
478#102—1182no—
479#102—1182no—
480#102—2361no—
481#102—2361no—
482#97—1182no—
483#97—1182no—
484C4×C8—1182no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—1181no—
490#95C22⋊D5911yescharacteristic
491#95C22⋊D5911yescharacteristic
492C24—1181no—
493C24—1181no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8C2×C4×D5912yes—
498C2×Q8D4×D5912yes—
499C2×Q8#1174568912yes—
500C2×D4—592no—
501C2×D4—592no—
502C2×D4—1184no—
503C2×D4—1184no—
504C2×D4—1181no—
505C2×D4—1181no—
506C2×D4—1181no—
507C2×D4—1181no—
508C2×D4—1181no—
509C2×D4—1181no—
510C2×D4—1181no—
511C2×D4—1181no—
512C2×D4—1181no—
513C2×D4—1181no—
514C2×D4—4721no—
515C2×D4—4721no—
516C2×D4—2362no—
517C2×D4—2362no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—1181no—
523C22×C4—1181no—
524C22×C4—4721no—
525C22×C4—4721no—
526C22×C4—2362no—
527C22×C4—2362no—
528C22×C4—2362no—
529C22×C4—2362no—
530C22×C4C2×C22⋊D5911yescharacteristic
531C22×C4C2×C22⋊D5911yescharacteristic
532C22×C4C2×C22⋊D5911yescharacteristic
533C22×C4C2×C22⋊D5911yescharacteristic
534C22×C4C2×C22⋊D5911yescharacteristic
535C22×C4C2×C22⋊D5911yescharacteristic
536C22×C4C23×D5911yescharacteristic
537SD16—1188no—
538SD16—1188no—
539C2×C8—592no—
540C2×C8—592no—
541C2×C8—592no—
542C2×C8—1181no—
543C2×C8—1181no—
544C2×C8—1181no—
545C2×C8—1181no—
546C2×C8—1181no—
547C2×C8—1181no—
548C2×C8—1181no—
549C2×C8—1181no—
550C2×C8—1181no—
551C4⋊C4—24no—
552C4⋊C4—22no—
553C4⋊C4—21no—
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—592no—
564C4⋊C4—1181no—
565C4⋊C4—1181no—
566C4⋊C4—1181no—
567C4⋊C4C2×C4×D5912yes—
568C22⋊C4—4721no—
569C22⋊C4—4721no—
570C22⋊C4—2362no—
571C22⋊C4—2362no—
572C22⋊C4—2362no—
573C22⋊C4—2362no—
574C42—24no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—42no—
581C42—2362no—
582C42C2×C4×D5912yes—
583C42#1174568512yes—
584C23—1182no—
585C23—1182no—
586C23—2361no—
587C23—2361no—
588C23—2361no—
589C23—2361no—
590C23—2361no—
591C23—2361no—
592C23—2361no—
593C23—2361no—
594C23—2361no—
595C23—2361no—
596C23—2361no—
597C23—2361no—
598C23C22×C22⋊D5911yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—22no—
602Q8#1427368914yescomplemented
603D4—1182no—
604D4—1182no—
605D4—1182no—
606D4—1182no—
607D4—4724no—
608D4—2368no—
609D4—2361no—
610D4—2361no—
611D4—2361no—
612D4—2361no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
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—1182no—
641C2×C4—4724no—
642C2×C4—4724no—
643C2×C4—2361no—
644C2×C4—2361no—
645C2×C4—2361no—
646C2×C4—2361no—
647C2×C4—2361no—
648C2×C4C4×C22⋊D5912yes—
649C2×C4C4×C22⋊D5912yes—
650C2×C4#1427375212yes—
651C2×C4C22×C4×D5911yescharacteristic
652C2×C4C2×D4×D5911yescharacteristic
653C2×C4C2×#1174568511yescharacteristic
654C2×C4C2×#1174568911yescharacteristic
655C2×C4#1427377211yescharacteristic
656C2×C4#1427377511yescharacteristic
657C8—1182no—
658C8—1182no—
659C8—1182no—
660C8—2361no—
661C22—4721no—
662C22—4721no—
663C22—4721no—
664C22—4721no—
665C22—4721no—
666C22—4721no—
667C22—4721no—
668C22—4721no—
669C22—2362no—
670C22—2362no—
671C22—2362no—
672C22—2362no—
673C22—2362no—
674C22—2362no—
675C22C2×C4×C22⋊D5911yescharacteristic
676C22D4×C22⋊D5911yescharacteristic
677C22#1683806311yescharacteristic
678C22C2×#1427375211yescharacteristic
679C22#1683820011yescharacteristic
680C22#1683821011yescharacteristic
681C22#1683821011yescharacteristic
682C4—22no—
683C4—22no—
684C4—24no—
685C4—22no—
686C4—41no—
687C4—41no—
688C4—42no—
689C4—41no—
690C4—81no—
691C4—81no—
692C4—4721no—
693C4—2362no—
694C4C2×#1427368911yescharacteristic
695C4#1683788311yescharacteristic
696C4#1683805311yescharacteristic
697C4#1683810011yescharacteristic
698C2—4722no—
699C2—4722no—
700C2#2142711211yescharacteristic
701C2C4×#1427375211yescharacteristic
702C2#2143295511yescharacteristic
703C2#2143559211yescharacteristic
704C2#2143568211yescharacteristic
705C2#2143682511yescharacteristic
706C2#2143686411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2351C2
socleC23×C59C22×D4
prime radicalC2×#14273724C22
cosocleC22×C4×C59C24
hypercenter#2351D59
hypocenterC59#23010
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2351

Complements

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

NH ≅ G/Ntype
2. C2×#16837500C2semidirect
3. C2×C4×#11745671C2semidirect
6. #21424862C2semidirect
7. #21424792C2semidirect
8. #21424778C2semidirect
9. #21424451C2semidirect
10. #21424451C2semidirect
11. #21424356C2semidirect
12. #21424342C2semidirect
13. #21423971C2semidirect
14. #21423926C2semidirect
15. C59×#2351C2semidirect
22. #16837602C4semidirect
72. C2×#11745671C2×C4semidirect
73. C2×#11745671C2×C4semidirect
96. C4⋊(C59⋊C8)C2×C4semidirect
98. #14273651D4semidirect
103. #14273647C2×C4semidirect
104. #14273647C2×C4semidirect
115. C4×Q8×C59C2×C4semidirect
248. Q8×C59C4×D4semidirect
349. #2351D59semidirect
415. C59#23010semidirect
440. C4×Q8C4×D59semidirect
602. Q8#14273689semidirect

Maximal subgroups

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

subgroupindex
C2×#168376022
C2×#168375002
C2×C4×#117456712
#214271602
#214249192
#214248622
#214247922
#214247782
#214244512
#214243562
#214243422
#214239712
#214239262
C59×#23512
#2301059