Finite Group Databasebeta

← #28622827

Subgroups — #28622827

Order 15104.

1174 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837699C211yesmaximal, characteristic, complemented
2C2×#16837500C211yesmaximal, characteristic, complemented
3#21429009C211yesmaximal, characteristic
4#21425296C211yesmaximal, characteristic, complemented
5#21425289C211yesmaximal, characteristic, complemented
6#21425097C211yesmaximal, characteristic, complemented
7#21425097C211yesmaximal, characteristic, complemented
8#21425066C211yesmaximal, characteristic, complemented
9#21424895C211yesmaximal, characteristic, complemented
10#21424418C211yesmaximal, characteristic, complemented
11#21424413C211yesmaximal, characteristic, complemented
12#21424295C211yesmaximal, characteristic, complemented
13#21424284C211yesmaximal, characteristic, complemented
14#21424101C211yesmaximal, characteristic, complemented
15C2×C59×#552C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic
17C2×#14273701C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×#14273698—21no—
20C2×C4×D236C2211yescharacteristic
21#16837699—24no—
22#16837500—24no—
23C2×#14273660C2211yescharacteristic
24C2×#14273660C2211yescharacteristic
25C2×#14273658C2211yescharacteristic
26C2×C4⋊(C59⋊C8)C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273651C2211yescharacteristic
29C2×#14273651C2211yescharacteristic
30C2×#14273647C2211yescharacteristic
31C2×#14273647C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37C2×#14273638C2211yescharacteristic
38#16837318—21no—
39#16837318—21no—
40#16837272C2211yescharacteristic
41#16837262C2211yescharacteristic
42#16837262C2211yescharacteristic
43#16837259—21no—
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50C59×#552—24no—
51C59×#552—24no—
52C2×#126×C59—21no—
53C2×#125×C59—21no—
54C2×#125×C59C2211yescharacteristic
55C2×#123×C59—21no—
56C2×C22⋊Q8×C59C2211yescharacteristic
57C2×C22⋊Q8×C59C2211yescharacteristic
58C2×C4×Q8×C59C2211yescharacteristic
59C2×C4×D4×C59C2211yescharacteristic
60C2×#117×C59—21no—
61C2×#117×C59C2211yescharacteristic
62C22×C4⋊C4×C59C2211yescharacteristic
63C22×D236C2311yescharacteristic
64C22×C22⋊D59—21no—
65C22×C22⋊D59—21no—
66C22×C4×D59—21no—
67C2×#11745671—22no—
68C2×#11745671—22no—
69C2×#11745671—22no—
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74#14273701—22no—
75#14273701—22no—
76#14273701—41no—
77#14273701—41no—
78#14273698—44no—
79C4×D236—22no—
80C4×D236—22no—
81C2×C4⋊Dic59—21no—
82C2×C4⋊Dic59—21no—
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×C22⋊Dic59—21no—
87C2×C22⋊Dic59—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91#14273660—22no—
92#14273660—22no—
93#14273658—22no—
94C4⋊(C59⋊C8)—22no—
95#14273651—22no—
96#14273651—41no—
97#14273651—41no—
98#14273647—22no—
99#14273647—22no—
100#14273647—22no—
101C22⋊(C59⋊C8)—22no—
102C22⋊(C59⋊C8)—22no—
103C22⋊(C59⋊C8)—41no—
104C22⋊(C59⋊C8)—41no—
105#14273638—22no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C22×Q8×C59C2311yescharacteristic
109C22×D4×C59D411yescharacteristic
110C23×C4×C59—21no—
111C23×C4×C59C2311yescharacteristic
112C23×C4×C59C2311yescharacteristic
113#126×C59—28no—
114#125×C59—28no—
115#125×C59—22no—
116#125×C59D414yescomplemented
117#123×C59—28no—
118C22⋊Q8×C59—22no—
119C22⋊Q8×C59—22no—
120C22⋊Q8×C59—22no—
121C22⋊Q8×C59—22no—
122C4×Q8×C59—22no—
123C4×Q8×C59D414yescomplemented
124C4×D4×C59—22no—
125C4×D4×C59—22no—
126#117×C59—28no—
127#117×C59—22no—
128#117×C59—22no—
129C2×C4⋊C4×C59—21no—
130C2×C4⋊C4×C59—21no—
131C2×C4⋊C4×C59—21no—
132C2×C4⋊C4×C59—21no—
133C2×C4⋊C4×C59—21no—
134C2×C4⋊C4×C59—21no—
135C2×C4⋊C4×C59—22no—
136C2×C4⋊C4×C59—22no—
137C2×C4⋊C4×C59D411yescharacteristic
138C2×C4⋊C4×C59C2311yescharacteristic
139C2×C4⋊C4×C59C2311yescharacteristic
140C2×C4⋊C4×C59C2311yescharacteristic
141C2×C22⋊C4×C59—21no—
142C2×C22⋊C4×C59—21no—
143C2×C22⋊C4×C59—21no—
144C2×C22⋊C4×C59D411yescharacteristic
145C2×C22⋊C4×C59D411yescharacteristic
146C2×C42×C59—21no—
147C2×C42×C59—21no—
148C2×C42×C59C2311yescharacteristic
149C24×C59C2×D411yescharacteristic
150C24×C59C2×D411yescharacteristic
151C23×D59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59—21no—
156C2×Q8×C59—21no—
157C2×Q8×C59C2×D412yes—
158C2×D4×C59—22no—
159C2×D4×C59—22no—
160C2×D4×C59—41no—
161C22×C4×C59—24no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—42no—
179C22×C4×C59—42no—
180C22×C4×C59C2×D411yescharacteristic
181C22×C4×C59C2×D411yescharacteristic
182C22×C4×C59C2×D411yescharacteristic
183C22×C4×C59C2×D411yescharacteristic
184C22×C4×C59C2411yescharacteristic
185C2×C22⋊D59—42no—
186C2×C22⋊D59—42no—
187C2×C22⋊D59—42no—
188C2×C22⋊D59—42no—
189C2×C22⋊D59—81no—
190C2×C22⋊D59—81no—
191C22×Dic59—21no—
192C22×Dic59—21no—
193C22×Dic59—21no—
194C2×D236—21no—
195C2×D236—21no—
196C2×D236—21no—
197C2×D236—21no—
198C2×D236—21no—
199C2×D236#4112yes—
200C2×C4×D59—42no—
201C2×C4×D59—42no—
202C2×C4×D59—42no—
203C4⋊C4×C59—24no—
204C4⋊C4×C59—24no—
205C4⋊C4×C59—24no—
206C4⋊C4×C59—24no—
207C4⋊C4×C59—24no—
208C4⋊C4×C59—24no—
209C4⋊C4×C59—22no—
210C4⋊C4×C59—21no—
211C4⋊C4×C59—21no—
212C4⋊C4×C59—21no—
213C4⋊C4×C59C2×D412yes—
214C4⋊C4×C59C2×D412yes—
215C4⋊C4×C59C2×D412yes—
216C22⋊C4×C59—24no—
217C22⋊C4×C59—24no—
218C22⋊C4×C59—24no—
219C22⋊C4×C59—22no—
220C22⋊C4×C59—22no—
221C42×C59—24no—
222C42×C59—24no—
223C42×C59C2×D412yes—
224C42×C59C2×D412yes—
225C22⋊Dic59—42no—
226C22⋊Dic59—42no—
227#11745671—28no—
228(C2×D59)⋊C4—42no—
229(C2×D59)⋊C4—42no—
230(C2×D59)⋊C4—42no—
231C4⋊Dic59—21no—
232C4⋊Dic59—21no—
233C4⋊Dic59—21no—
234C4⋊Dic59—21no—
235C4⋊Dic59—21no—
236C4⋊Dic59—21no—
237C4⋊Dic59—42no—
238C4⋊Dic59—81no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—21no—
241C2×C59⋊C8—21no—
242C2×C59⋊C8—21no—
243C2×C59⋊C8—21no—
244C2×C59⋊C8—21no—
245C2×C59⋊C8—21no—
246C2×C59⋊C8—21no—
247C2×C59⋊C8—21no—
248C2×C59⋊C8—21no—
249C2×C59⋊C8—21no—
250C2×C59⋊C8#4112yes—
251C23×C59—21no—
252C23×C59—21no—
253C23×C59—21no—
254C23×C59—21no—
255C23×C59—21no—
256C23×C59—21no—
257C23×C59—21no—
258C23×C59—21no—
259C23×C59—21no—
260C23×C59—21no—
261C23×C59—21no—
262C23×C59—21no—
263C23×C59—21no—
264C23×C59AGL(1,ℤ/8)12yes—
265C23×C59C22×D411yescharacteristic
266C22×D59—22no—
267C22×D59—41no—
268C22×D59—41no—
269C22×D59—41no—
270C22×D59—41no—
271C22×D59—41no—
272C22×D59—41no—
273Q8×C59—22no—
274Q8×C59—22no—
275Q8×C59—41no—
276Q8×C59—41no—
277D4×C59—44no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—21no—
281C2×C4×C59—21no—
282C2×C4×C59—21no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—21no—
287C2×C4×C59—22no—
288C2×C4×C59—21no—
289C2×C4×C59—21no—
290C2×C4×C59—21no—
291C2×C4×C59—21no—
292C2×C4×C59—48no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59—41no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59—41no—
302C2×C4×C59—41no—
303C2×C4×C59—41no—
304C2×C4×C59—41no—
305C2×C4×C59—41no—
306C2×C4×C59—41no—
307C2×C4×C59—41no—
308C2×C4×C59—41no—
309C2×C4×C59#12012yes—
310C2×C4×C59#12012yes—
311C2×C4×C59C22×D411yescharacteristic
312C2×C4×C59C22×D411yescharacteristic
313C2×C4×C59C2×#4111yescharacteristic
314C2×C4×C59C2×#4111yescharacteristic
315C2×C4×C59H(5,𝔽2)11yescharacteristic
316C2×C4×C592−1+411yescharacteristic
317C22⋊D59—84no—
318C22⋊D59—84no—
319C2×Dic59—41no—
320C2×Dic59—41no—
321C2×Dic59—41no—
322C2×Dic59—41no—
323C2×Dic59—41no—
324C2×Dic59—41no—
325C2×Dic59—41no—
326C2×Dic59—41no—
327C2×Dic59—41no—
328D236—22no—
329D236—22no—
330D236—41no—
331D236—41no—
332C4×D59—84no—
333C59⋊C8—22no—
334C59⋊C8—41no—
335C59⋊C8—41no—
336C59⋊C8—41no—
337#24137—591nomaximal, Sylow
338C22×C59—22no—
339C22×C59—22no—
340C22×C59—22no—
341C22×C59—41no—
342C22×C59—41no—
343C22×C59—41no—
344C22×C59—41no—
345C22×C59—41no—
346C22×C59—41no—
347C22×C59—41no—
348C22×C59—41no—
349C22×C59—41no—
350C22×C59—41no—
351C22×C59—41no—
352C22×C59C2×#12011yescharacteristic
353C22×C59#54611yescharacteristic
354C22×C59#54711yescharacteristic
355C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C59#57511yescharacteristic
357C22×C59#57711yescharacteristic
358C22×C59#57811yescharacteristic
359C2×D59—42no—
360C2×D59—42no—
361C2×D59—42no—
362C2×D59—81no—
363C2×D59—81no—
364C2×D59—81no—
365C2×D59—81no—
366C4×C59—22no—
367C4×C59—22no—
368C4×C59—41no—
369C4×C59—41no—
370C4×C59—42no—
371C4×C59—42no—
372C4×C59—42no—
373C4×C59—42no—
374C4×C59#52511yescharacteristic
375C4×C59#53711yescharacteristic
376C4×C59#54811yescharacteristic
377C4×C59#55011yescharacteristic
378Dic59—81no—
379Dic59—81no—
380Dic59—81no—
381C2×#552D5911yescharacteristic, complemented
382C2×#478—591no—
383C2×#440—591no—
384#2537—591no—
385#2036—591no—
386#2035—591no—
387#2000—591no—
388#2000—591no—
389#1992—591no—
390#1955—591no—
391#1875—591no—
392#1874—591no—
393#1854—591no—
394#1852—591no—
395#1803—591no—
396C2×C59—42no—
397C2×C59—81no—
398C2×C59#240711yescharacteristic
399C2×C59#300611yescharacteristic
400C2×C59#301311yescharacteristic
401C2×C59#331011yescharacteristic
402C2×C59#331511yescharacteristic
403C2×C59#334311yescharacteristic
404C2×C59#334811yescharacteristic
405D59—82no—
406C22×SD16—591no—
407#552—24no—
408#552—24no—
409C2×#126—21no—
410C2×#125—21no—
411C2×#125C2×D5911yescharacteristic
412C2×#123—21no—
413C2×C22⋊Q8C2×D5911yescharacteristic
414C2×C22⋊Q8C2×D5911yescharacteristic
415C2×#121—591no—
416C2×#121—591no—
417C2×#121—1181no—
418C2×C4×Q8C2×D5911yescharacteristic
419C2×C4×D4—591no—
420C2×C4×D4C2×D5911yescharacteristic
421C2×#117—21no—
422C2×#117C2×D5911yescharacteristic
423C22×C4⋊C4C2×D5911yescharacteristic
424#478—1184no—
425#440—1184no—
426C2×#107—591no—
427C2×#107—591no—
428C2×#106—591no—
429C2×C4⋊C8—591no—
430C2×#103—591no—
431C2×#103—591no—
432C2×#103—591no—
433C2×#102—591no—
434C2×#102—591no—
435C2×#102—591no—
436C2×C22⋊C8—591no—
437C2×C22⋊C8—591no—
438C2×C22⋊C8—591no—
439C2×C22⋊C8—591no—
440C2×#97—591no—
441#394—1181no—
442#394—1181no—
443#384—591no—
444#380—591no—
445#380—591no—
446#380—1181no—
447#340—591no—
448#340—591no—
449#340—591no—
450#340—591no—
451#340—591no—
452#340—591no—
453C59#2413711yescharacteristic, complemented, Sylow
454C22×Q8C22×D5911yescharacteristic
455C22×D4—591no—
456C22×D4—1181no—
457C22×D4—1181no—
458C22×D4C22⋊D5911yescharacteristic
459C23×C4—21no—
460C23×C4—1181no—
461C23×C4C22×D5911yescharacteristic
462C23×C4C22×D5911yescharacteristic
463C2×SD16—1182no—
464C2×SD16—1182no—
465C2×SD16—1182no—
466C22×C8—591no—
467C22×C8—591no—
468C22×C8—591no—
469C22×C8—591no—
470#126—28no—
471#125—28no—
472#125—22no—
473#125C22⋊D5914yescomplemented
474#123—28no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479#121—1182no—
480#121—1182no—
481#121—2361no—
482#121—2361no—
483#121—2364no—
484C4×Q8—22no—
485C4×Q8C22⋊D5914yescomplemented
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—1182no—
489C4×D4—1182no—
490#117—28no—
491#117—22no—
492#117—22no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—591no—
502C2×C4⋊C4—591no—
503C2×C4⋊C4—591no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4—1181no—
506C2×C4⋊C4C22⋊D5911yescharacteristic
507C2×C4⋊C4C22×D5911yescharacteristic
508C2×C4⋊C4C22×D5911yescharacteristic
509C2×C4⋊C4C22×D5911yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—1181no—
514C2×C22⋊C4—1181no—
515C2×C22⋊C4—1181no—
516C2×C22⋊C4—1181no—
517C2×C22⋊C4—1181no—
518C2×C22⋊C4C22⋊D5911yescharacteristic
519C2×C22⋊C4C22⋊D5911yescharacteristic
520C2×C42—21no—
521C2×C42—21no—
522C2×C42C22×D5911yescharacteristic
523#107—1182no—
524#107—1182no—
525#106—1182no—
526C4⋊C8—1182no—
527#103—1182no—
528#103—2361no—
529#103—2361no—
530#102—1182no—
531#102—1182no—
532#102—1182no—
533C22⋊C8—1182no—
534C22⋊C8—1182no—
535C22⋊C8—2361no—
536C22⋊C8—2361no—
537#97—1182no—
538#95—1181no—
539#95—1181no—
540C24—1181no—
541C24C2×C22⋊D5911yescharacteristic
542C24C2×C22⋊D5911yescharacteristic
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×C22⋊D5912yes—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—41no—
552C2×D4—592no—
553C2×D4—1181no—
554C2×D4—1181no—
555C2×D4—1181no—
556C2×D4—1181no—
557C2×D4—1181no—
558C2×D4—4721no—
559C2×D4—4721no—
560C2×D4—2362no—
561C2×D4—2362no—
562C2×D4—2362no—
563C2×D4—2362no—
564C22×C4—24no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—1181no—
584C22×C4—1181no—
585C22×C4—1181no—
586C22×C4—2362no—
587C22×C4—2362no—
588C22×C4—2362no—
589C22×C4C2×C22⋊D5911yescharacteristic
590C22×C4C2×C22⋊D5911yescharacteristic
591C22×C4C2×C22⋊D5911yescharacteristic
592C22×C4C2×C22⋊D5911yescharacteristic
593C22×C4C23×D5911yescharacteristic
594SD16—1188no—
595C2×C8—592no—
596C2×C8—1181no—
597C2×C8—1181no—
598C2×C8—1181no—
599C2×C8—1181no—
600C2×C8—1181no—
601C2×C8—1181no—
602C2×C8—1181no—
603C2×C8—1181no—
604C2×C8—1181no—
605C2×C8—1181no—
606C2×C8—1181no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—1181no—
618C4⋊C4—1181no—
619C4⋊C4—1181no—
620C4⋊C4—1181no—
621C4⋊C4—1181no—
622C4⋊C4—1181no—
623C4⋊C4—4721no—
624C4⋊C4—2362no—
625C4⋊C4C2×C22⋊D5912yes—
626C4⋊C4C2×C22⋊D5912yes—
627C4⋊C4C2×C22⋊D5912yes—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—2362no—
634C22⋊C4—2362no—
635C22⋊C4—2362no—
636C22⋊C4—2362no—
637C22⋊C4—2362no—
638C42—24no—
639C42—24no—
640C42C2×C22⋊D5912yes—
641C42C2×C22⋊D5912yes—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—1182no—
656C23—2361no—
657C23—2361no—
658C23—2361no—
659C23—2361no—
660C23—2361no—
661C23—2361no—
662C23#1427375212yes—
663C23C22×C22⋊D5911yescharacteristic
664Q8—22no—
665Q8—22no—
666Q8—41no—
667Q8—41no—
668D4—44no—
669D4—1182no—
670D4—1182no—
671D4—4724no—
672D4—4724no—
673D4—2361no—
674D4—2361no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—48no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—4724no—
707C2×C4—2361no—
708C2×C4—2361no—
709C2×C4—2361no—
710C2×C4—2361no—
711C2×C4—2361no—
712C2×C4—2361no—
713C2×C4—2361no—
714C2×C4—2361no—
715C2×C4—2361no—
716C2×C4#1427369612yes—
717C2×C4#1427369612yes—
718C2×C4C22×C22⋊D5911yescharacteristic
719C2×C4C22×C22⋊D5911yescharacteristic
720C2×C4#41×D5911yescharacteristic
721C2×C4#41×D5911yescharacteristic
722C2×C4#1427377311yescharacteristic
723C2×C4#1427377411yescharacteristic
724C8—1182no—
725C8—2361no—
726C8—2361no—
727C8—2361no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—4721no—
743C22—4721no—
744C22—4721no—
745C22—4721no—
746C22—2362no—
747C22—2362no—
748C22—2362no—
749C22C2×#1427369611yescharacteristic
750C22#1683804011yescharacteristic
751C22#1683805111yescharacteristic
752C22C2×#1427375211yescharacteristic
753C22#1683820011yescharacteristic
754C22#1683821011yescharacteristic
755C22#1683821711yescharacteristic
756C4—22no—
757C4—22no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—4721no—
765C4—4721no—
766C4—4721no—
767C4#1683790911yescharacteristic
768C4#1683798011yescharacteristic
769C4#1683805911yescharacteristic
770C4#1683807111yescharacteristic
771C2—42no—
772C2—81no—
773C2—4722no—
774C2#2142743511yescharacteristic
775C2#2143334811yescharacteristic
776C2#2143341111yescharacteristic
777C2#2143611111yescharacteristic
778C2#2143618611yescharacteristic
779C2#2143653611yescharacteristic
780C2#2143660511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#552C2
socleC23×C59C22×D4
prime radical#21429009C2
hypercenterC2×#552D59
hypocenterC59#24137
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#16837699C2semidirect
2. C2×#16837500C2semidirect
4. #21425296C2semidirect
5. #21425289C2semidirect
6. #21425097C2semidirect
7. #21425097C2semidirect
8. #21425066C2semidirect
9. #21424895C2semidirect
10. #21424418C2semidirect
11. #21424413C2semidirect
12. #21424295C2semidirect
13. #21424284C2semidirect
14. #21424101C2semidirect
15. C2×C59×#552C2semidirect
116. #125×C59D4semidirect
123. C4×Q8×C59D4semidirect
381. C2×#552D59semidirect
453. C59#24137semidirect
473. #125C22⋊D59semidirect
485. C4×Q8C22⋊D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168376992
C2×#168375002
#214290092
#214252962
#214252892
#214250972
#214250662
#214248952
#214244182
#214244132
#214242952
#214242842
#214241012
C2×C59×#5522
#2413759