Finite Group Databasebeta

← C2×#21429341 #28759083

Subgroups — C2×#21429341 #28759083

Order 15104.

2614 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21429341C2116yesmaximal, direct product factor
2C2×#16837344C211yesmaximal, characteristic, complemented
3C2×#16837318C211yesmaximal, characteristic
4C2×#16837313C211yesmaximal, characteristic, complemented
5C2×#16837309C211yesmaximal, characteristic, complemented
6C2×#16837296C211yesmaximal, characteristic, complemented
7C2×#16837291C211yesmaximal, characteristic, complemented
8C2×#16837279C211yesmaximal, characteristic
9C2×#16837278C211yesmaximal, characteristic
10C2×#16837269C211yesmaximal, characteristic, complemented
11C2×#16837269C211yesmaximal, characteristic, complemented
12C2×#16837264C211yesmaximal, characteristic, complemented
13C2×#16837263C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic59C211yesmaximal, characteristic, complemented
15C2×#16837249C211yesmaximal, characteristic, complemented
16C2×C59×#393C211yesmaximal, characteristic, complemented
17C23×C22⋊D59C2211yescharacteristic
18C24×Dic59C2211yescharacteristic
19C23×C4×D59C2211yescharacteristic
20C22×C4⋊Dic59C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×C22⋊Dic59C2211yescharacteristic
23C22×C22⋊Dic59C2211yescharacteristic
24C22×(C2×D59)⋊C4C2211yescharacteristic
25C22×(C2×D59)⋊C4C2211yescharacteristic
26C22×(C2×D59)⋊C4C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28C22×(C2×D59)⋊C4C2211yescharacteristic
29C22×C4×Dic59C2211yescharacteristic
30C22×C4×Dic59C2211yescharacteristic
31C22×C4×Dic59C2211yescharacteristic
32#16837344C2218yescomplemented
33#16837318C2218yes—
34#16837313C2218yescomplemented
35#16837309C2218yescomplemented
36#16837296C2218yescomplemented
37#16837291C2218yescomplemented
38#16837279C2218yes—
39#16837278C2218yes—
40#16837269C2218yescomplemented
41#16837269C2218yescomplemented
42#16837264C2218yescomplemented
43#16837263C2218yescomplemented
44C22⋊C4×Dic59C2218yescomplemented
45#16837249C2218yescomplemented
46C2×C59⋊#95C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C2×C59⋊#95C2211yescharacteristic
51C2×C59⋊#95C2211yescharacteristic
52C2×C59⋊#95C2211yescharacteristic
53C2×C59⋊#95C2211yescharacteristic
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C23×Q8×C59C2211yescharacteristic
60C22×C22⋊C4×C59C2211yescharacteristic
61C22×C22⋊C4×C59C2211yescharacteristic
62C22×C22⋊C4×C59C2211yescharacteristic
63C59×#393C2218yescomplemented
64C2×#95×C59C2211yescharacteristic
65C2×#95×C59C2211yescharacteristic
66C2×#95×C59C2211yescharacteristic
67C24×D59C2311yescharacteristic
68C22×C22⋊D59—24no—
69C22×C22⋊D59—24no—
70C22×C22⋊D59—42no—
71C22×C22⋊D59C2314yes—
72C23×Dic59—24no—
73C23×Dic59—24no—
74C23×Dic59—42no—
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C23×Dic59C2311yescharacteristic
80C23×Dic59C2314yes—
81C23×Dic59C2311yescharacteristic
82C23×Dic59C2311yescharacteristic
83C22×C4×D59—24no—
84C22×C4×D59—24no—
85C22×C4×D59—42no—
86C22×C4×D59C2314yes—
87C2×C4⋊Dic59—42no—
88C2×C4⋊Dic59C2314yes—
89C2×Dic59⋊C4—42no—
90C2×Dic59⋊C4C2314yes—
91C2×C22⋊Dic59—24no—
92C2×C22⋊Dic59—24no—
93C2×C22⋊Dic59C2314yes—
94C2×C22⋊Dic59C2314yes—
95C2×(C2×D59)⋊C4—24no—
96C2×(C2×D59)⋊C4—24no—
97C2×(C2×D59)⋊C4—24no—
98C2×(C2×D59)⋊C4—42no—
99C2×(C2×D59)⋊C4—42no—
100C2×(C2×D59)⋊C4C2314yes—
101C2×(C2×D59)⋊C4C2314yes—
102C2×(C2×D59)⋊C4C2314yes—
103C2×(C2×D59)⋊C4C2314yes—
104C2×(C2×D59)⋊C4C2314yes—
105C2×C4×Dic59—24no—
106C2×C4×Dic59—24no—
107C2×C4×Dic59—42no—
108C2×C4×Dic59C2314yes—
109C2×C4×Dic59C2314yes—
110C2×C4×Dic59C2314yes—
111C59⋊#95C2314yes—
112C59⋊#95C2314yes—
113C59⋊#95C2314yes—
114C59⋊#95C2314yes—
115C59⋊#95C2314yes—
116C59⋊#95C2314yes—
117C59⋊#95C2314yes—
118C59⋊#95C2314yes—
119C59⋊#95C2314yes—
120C59⋊#95C2314yes—
121C59⋊#95C2314yes—
122C59⋊#95C2314yes—
123C59⋊#95C2314yes—
124C25×C59C2311yescharacteristic
125C22×Q8×C59—24no—
126C22×Q8×C59—42no—
127C22×Q8×C59—42no—
128C22×Q8×C59C2314yes—
129C23×C4×C59C2311yescharacteristic
130C23×C4×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C2×C22⋊C4×C59—24no—
136C2×C22⋊C4×C59—42no—
137C2×C22⋊C4×C59—42no—
138C2×C22⋊C4×C59C2314yes—
139C2×C22⋊C4×C59C2314yes—
140C2×C22⋊C4×C59C2314yes—
141#95×C59C2314yes—
142#95×C59C2314yes—
143#95×C59C2314yes—
144C24×C59—22no—
145C24×C59—22no—
146C24×C59—22no—
147C24×C59—22no—
148C24×C59—22no—
149C24×C59—22no—
150C24×C59#4114yes—
151C24×C59C2412yes—
152C24×C59C2411yescharacteristic
153C23×D59—22no—
154C23×D59—22no—
155C23×D59—22no—
156C23×D59—22no—
157C23×D59—22no—
158C23×D59—22no—
159C23×D59#4114yes—
160C23×D59C2412yes—
161C2×Q8×C59—28no—
162C2×Q8×C59—44no—
163C2×Q8×C59—44no—
164C2×Q8×C59—416no—
165C22×C4×C59—22no—
166C22×C4×C59—22no—
167C22×C4×C59—22no—
168C22×C4×C59—22no—
169C22×C4×C59—22no—
170C22×C4×C59—22no—
171C22×C4×C59—22no—
172C22×C4×C59—22no—
173C22×C4×C59—22no—
174C22×C4×C59—22no—
175C22×C4×C59—22no—
176C22×C4×C59—22no—
177C22×C4×C59—22no—
178C22×C4×C59—22no—
179C22×C4×C59—22no—
180C22×C4×C59—22no—
181C22×C4×C59—22no—
182C22×C4×C59#4114yes—
183C22×C4×C59C2412yes—
184C22×C4×C59C2412yes—
185C22×C4×C59C2412yes—
186C22×C4×C59C2412yes—
187C22×C4×C59C2412yes—
188C22×C4×C59C2412yes—
189C2×C22⋊D59—28no—
190C2×C22⋊D59—28no—
191C2×C22⋊D59—44no—
192C2×C22⋊D59—416no—
193C22×Dic59—22no—
194C22×Dic59—22no—
195C22×Dic59—22no—
196C22×Dic59—22no—
197C22×Dic59—22no—
198C22×Dic59—22no—
199C22×Dic59—22no—
200C22×Dic59—22no—
201C22×Dic59—22no—
202C22×Dic59—22no—
203C22×Dic59—22no—
204C22×Dic59—28no—
205C22×Dic59—22no—
206C22×Dic59—22no—
207C22×Dic59—22no—
208C22×Dic59—22no—
209C22×Dic59—22no—
210C22×Dic59—22no—
211C22×Dic59—22no—
212C22×Dic59—22no—
213C22×Dic59—28no—
214C22×Dic59—44no—
215C22×Dic59—416no—
216C22×Dic59#4114yes—
217C22×Dic59#4114yes—
218C22×Dic59C2412yes—
219C22×Dic59C2412yes—
220C22×Dic59C2412yes—
221C22×Dic59C2412yes—
222C22×Dic59C2412yes—
223C22×Dic59C2412yes—
224C22×Dic59C2412yes—
225C2×C4×D59—28no—
226C2×C4×D59—28no—
227C2×C4×D59—44no—
228C2×C4×D59—416no—
229C22⋊C4×C59—28no—
230C22⋊C4×C59—44no—
231C22⋊C4×C59—44no—
232C22⋊Dic59—28no—
233C22⋊Dic59—28no—
234(C2×D59)⋊C4—28no—
235(C2×D59)⋊C4—28no—
236(C2×D59)⋊C4—28no—
237(C2×D59)⋊C4—44no—
238(C2×D59)⋊C4—44no—
239C4⋊Dic59—44no—
240Dic59⋊C4—44no—
241C4×Dic59—28no—
242C4×Dic59—28no—
243C4×Dic59—44no—
244C23×C59—28no—
245C23×C59—28no—
246C23×C59—28no—
247C23×C59—22no—
248C23×C59—22no—
249C23×C59—22no—
250C23×C59—22no—
251C23×C59—22no—
252C23×C59—22no—
253C23×C59—44no—
254C23×C59—44no—
255C23×C59—44no—
256C23×C59—44no—
257C23×C59C2×#4112yes—
258C23×C59C2×#4112yes—
259C23×C59C2×#4112yes—
260C23×C59C2×#4112yes—
261C23×C59C2×#4114yes—
262C23×C59C2×#4112yes—
263C23×C59H(5,𝔽2)12yes—
264C23×C59H(5,𝔽2)12yes—
265C23×C59C2511yescharacteristic
266C22×D59—28no—
267C22×D59—28no—
268C22×D59—28no—
269C22×D59—22no—
270C22×D59—22no—
271C22×D59—22no—
272C22×D59—22no—
273C22×D59—22no—
274C22×D59—22no—
275C22×D59—44no—
276C22×D59—44no—
277C22×D59—44no—
278C22×D59—44no—
279C22×D59C2×#4114yes—
280Q8×C59—416no—
281C2×C4×C59—28no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—44no—
300C2×C4×C59—44no—
301C2×C4×C59—44no—
302C2×C4×C59—44no—
303C2×C4×C59—44no—
304C2×C4×C59C2×#4114yes—
305C22⋊D59—416no—
306C2×Dic59—28no—
307C2×Dic59—28no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—416no—
328C2×Dic59—44no—
329C2×Dic59—44no—
330C2×Dic59—44no—
331C2×Dic59—44no—
332C2×Dic59—44no—
333C2×Dic59C2×#4114yes—
334C2×Dic59C2×#4114yes—
335C4×D59—416no—
336C2×#2572—591nomaximal, Sylow
337C22×C59—24no—
338C22×C59—24no—
339C22×C59—24no—
340C22×C59—416no—
341C22×C59—42no—
342C22×C59—42no—
343C22×C59—42no—
344C22×C59—42no—
345C22×C59#52914yes—
346C22×C59#52914yes—
347C22×C59#53814yes—
348C22×C59#55114yes—
349C22×C59#55114yes—
350C22×C59#55114yes—
351C22×C59#55514yes—
352C22×C59C22×#4111yescharacteristic
353C22×C59C22×#4111yescharacteristic
354C22×C59C22×#4111yescharacteristic
355C22×C59C22×#4111yescharacteristic
356C22×C59C22×#4111yescharacteristic
357C22×C59C2×H(5,𝔽2)11yescharacteristic
358C22×C59C2×H(5,𝔽2)11yescharacteristic
359C2×D59—24no—
360C2×D59—24no—
361C2×D59—24no—
362C2×D59—416no—
363C2×D59—42no—
364C2×D59—42no—
365C2×D59—42no—
366C2×D59—42no—
367C4×C59—24no—
368C4×C59—42no—
369C4×C59—42no—
370C4×C59—42no—
371C4×C59—42no—
372C4×C59—42no—
373Dic59—24no—
374Dic59—24no—
375Dic59—42no—
376Dic59—42no—
377Dic59—42no—
378Dic59—42no—
379Dic59—42no—
380#2572—5916no—
381C2×#400—591no—
382C2×#394—591no—
383C2×#393—591no—
384C2×#393D5911yescharacteristic, complemented
385C2×#391—591no—
386C2×#388—591no—
387C2×#388—591no—
388C2×#386—591no—
389C2×#386—591no—
390C2×#383—591no—
391C2×#383—591no—
392C2×#381—591no—
393C2×#381—591no—
394C2×C4×C22⋊C4—591no—
395C2×C4×C22⋊C4—591no—
396C2×C59—44no—
397C2×C59#257218yescomplemented
398C2×C59C2×#52911yescharacteristic
399C2×C59C2×#52911yescharacteristic
400C2×C59C2×#53811yescharacteristic
401C2×C59C2×#55111yescharacteristic
402C2×C59C2×#55111yescharacteristic
403C2×C59C2×#55111yescharacteristic
404C2×C59C2×#55511yescharacteristic
405D59—44no—
406C23×Q8C2×D5911yescharacteristic
407C23×D4—591no—
408C24×C4—591no—
409C24×C4—591no—
410C22×C4⋊C4—591no—
411C22×C4⋊C4—591no—
412C22×C22⋊C4—591no—
413C22×C22⋊C4—591no—
414C22×C22⋊C4—591no—
415C22×C22⋊C4—591no—
416C22×C22⋊C4—591no—
417C22×C22⋊C4—591no—
418C22×C22⋊C4—591no—
419C22×C22⋊C4C2×D5911yescharacteristic
420C22×C22⋊C4C2×D5911yescharacteristic
421C22×C22⋊C4C2×D5911yescharacteristic
422C22×C42—591no—
423C22×C42—591no—
424C22×C42—591no—
425#400—598no—
426#394—598no—
427#393—598no—
428#393C2×D5918yescomplemented
429#391—598no—
430#388—598no—
431#388—598no—
432#386—598no—
433#386—598no—
434#383—598no—
435#383—598no—
436#381—598no—
437#381—598no—
438C4×C22⋊C4—598no—
439C4×C22⋊C4—598no—
440C2×#95—591no—
441C2×#95—591no—
442C2×#95—591no—
443C2×#95—591no—
444C2×#95—591no—
445C2×#95—591no—
446C2×#95—591no—
447C2×#95—591no—
448C2×#95—591no—
449C2×#95—591no—
450C2×#95—591no—
451C2×#95—591no—
452C2×#95—591no—
453C2×#95C2×D5911yescharacteristic
454C2×#95C2×D5911yescharacteristic
455C2×#95C2×D5911yescharacteristic
456C59C2×#257211yescharacteristic, complemented, Sylow
457C25—591no—
458C25C22×D5911yescharacteristic
459C22×Q8—24no—
460C22×Q8—42no—
461C22×Q8—42no—
462C22×Q8C22×D5914yes—
463C22×D4—594no—
464C22×D4—1184no—
465C22×D4—1184no—
466C22×D4—2362no—
467C23×C4—591no—
468C23×C4—591no—
469C23×C4—591no—
470C23×C4—591no—
471C23×C4—591no—
472C23×C4—591no—
473C23×C4—591no—
474C23×C4—594no—
475C23×C4—594no—
476C23×C4—1184no—
477C23×C4—1184no—
478C23×C4—1184no—
479C23×C4—1184no—
480C23×C4—2362no—
481C23×C4—2362no—
482C23×C4C22×D5911yescharacteristic
483C23×C4C22×D5911yescharacteristic
484C23×C4C22×D5911yescharacteristic
485C23×C4C22×D5911yescharacteristic
486C23×C4C22×D5911yescharacteristic
487C23×C4C22×D5911yescharacteristic
488C2×C4⋊C4—594no—
489C2×C4⋊C4—594no—
490C2×C4⋊C4—2362no—
491C2×C4⋊C4—2362no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—594no—
496C2×C22⋊C4—594no—
497C2×C22⋊C4—594no—
498C2×C22⋊C4—594no—
499C2×C22⋊C4—594no—
500C2×C22⋊C4—594no—
501C2×C22⋊C4—594no—
502C2×C22⋊C4—1184no—
503C2×C22⋊C4—1184no—
504C2×C22⋊C4—1184no—
505C2×C22⋊C4—1184no—
506C2×C22⋊C4—1184no—
507C2×C22⋊C4—2362no—
508C2×C22⋊C4—2362no—
509C2×C22⋊C4C22×D5914yes—
510C2×C22⋊C4C22×D5914yes—
511C2×C22⋊C4C22×D5914yes—
512C2×C42—594no—
513C2×C42—594no—
514C2×C42—594no—
515C2×C42—1184no—
516C2×C42—1184no—
517C2×C42—2362no—
518#95—594no—
519#95—594no—
520#95—594no—
521#95—594no—
522#95—594no—
523#95—594no—
524#95—594no—
525#95—594no—
526#95—594no—
527#95—594no—
528#95—594no—
529#95—594no—
530#95—594no—
531#95C22×D5914yes—
532#95C22×D5914yes—
533#95C22×D5914yes—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—594no—
541C24—592no—
542C24—1182no—
543C24—1182no—
544C24—1182no—
545C24—1182no—
546C24—1182no—
547C24—1182no—
548C24#1174568914yes—
549C24C23×D5912yes—
550C24C23×D5911yescharacteristic
551C2×Q8—28no—
552C2×Q8—44no—
553C2×Q8—44no—
554C2×Q8—416no—
555C2×D4—1188no—
556C2×D4—1188no—
557C2×D4—2364no—
558C2×D4—23616no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—594no—
577C22×C4—594no—
578C22×C4—592no—
579C22×C4—592no—
580C22×C4—592no—
581C22×C4—592no—
582C22×C4—592no—
583C22×C4—592no—
584C22×C4—592no—
585C22×C4—1188no—
586C22×C4—1188no—
587C22×C4—1188no—
588C22×C4—1182no—
589C22×C4—1182no—
590C22×C4—1182no—
591C22×C4—1182no—
592C22×C4—1182no—
593C22×C4—1182no—
594C22×C4—1182no—
595C22×C4—1182no—
596C22×C4—1182no—
597C22×C4—1182no—
598C22×C4—1182no—
599C22×C4—1182no—
600C22×C4—1182no—
601C22×C4—1188no—
602C22×C4—1182no—
603C22×C4—1182no—
604C22×C4—1182no—
605C22×C4—1182no—
606C22×C4—1182no—
607C22×C4—1182no—
608C22×C4—2364no—
609C22×C4—23616no—
610C22×C4—2364no—
611C22×C4—23616no—
612C22×C4#1174568714yes—
613C22×C4C23×D5912yes—
614C22×C4C23×D5912yes—
615C22×C4C23×D5912yes—
616C22×C4C23×D5912yes—
617C22×C4C23×D5912yes—
618C22×C4C23×D5912yes—
619C4⋊C4—2364no—
620C4⋊C4—2364no—
621C22⋊C4—28no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—1188no—
625C22⋊C4—1188no—
626C22⋊C4—1188no—
627C22⋊C4—1188no—
628C22⋊C4—1188no—
629C22⋊C4—2364no—
630C22⋊C4—2364no—
631C42—1188no—
632C42—1188no—
633C42—2364no—
634C23—28no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—28no—
642C23—28no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—594no—
648C23—1188no—
649C23—1182no—
650C23—1182no—
651C23—1182no—
652C23—1182no—
653C23—1182no—
654C23—1182no—
655C23—1188no—
656C23—1188no—
657C23—2364no—
658C23—2364no—
659C23—2364no—
660C23—2364no—
661C23#41×D5912yes—
662C23#41×D5912yes—
663C23#41×D5912yes—
664C23C2×#1174568712yes—
665C23C2×#1174568914yes—
666C23C2×#1174568912yes—
667C23#1427377212yes—
668C23#1427377212yes—
669C23C24×D5911yescharacteristic
670Q8—416no—
671D4—23616no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—28no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—594no—
696C2×C4—594no—
697C2×C4—1182no—
698C2×C4—1182no—
699C2×C4—1182no—
700C2×C4—1182no—
701C2×C4—1188no—
702C2×C4—1188no—
703C2×C4—1182no—
704C2×C4—1182no—
705C2×C4—1182no—
706C2×C4—1182no—
707C2×C4—1182no—
708C2×C4—1182no—
709C2×C4—1182no—
710C2×C4—1182no—
711C2×C4—1182no—
712C2×C4—1182no—
713C2×C4—1182no—
714C2×C4—1182no—
715C2×C4—1182no—
716C2×C4—1182no—
717C2×C4—1182no—
718C2×C4—23616no—
719C2×C4—23616no—
720C2×C4—2364no—
721C2×C4—2364no—
722C2×C4—2364no—
723C2×C4—2364no—
724C2×C4—2364no—
725C2×C4C2×#1174568714yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—416no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—1184no—
735C22—1184no—
736C22—1184no—
737C22—23616no—
738C22—2362no—
739C22—2362no—
740C22—2362no—
741C22—2362no—
742C22#1683793114yes—
743C22#1683793814yes—
744C22#1683798714yes—
745C22#1683807914yes—
746C22#1683807914yes—
747C22#1683808214yes—
748C22#1683811414yes—
749C22C2×#41×D5911yescharacteristic
750C22C2×#41×D5911yescharacteristic
751C22C2×#41×D5911yescharacteristic
752C22C22×#1174568711yescharacteristic
753C22C22×#1174568911yescharacteristic
754C22C2×#1427377211yescharacteristic
755C22C2×#1427377211yescharacteristic
756C4—24no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—1184no—
763C4—1184no—
764C4—2362no—
765C4—2362no—
766C4—2362no—
767C4—2362no—
768C4—2362no—
769C2—44no—
770C2—2364no—
771C2#2142934118yesdirect product factor
772C2C2×#1683793111yescharacteristic
773C2C2×#1683793811yescharacteristic
774C2C2×#1683798711yescharacteristic
775C2C2×#1683807911yescharacteristic
776C2C2×#1683807911yescharacteristic
777C2C2×#1683808211yescharacteristic
778C2C2×#1683811411yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#393C2
socleC24×C59C24
prime radicalC23×C22⋊D59C22
hypercenterC2×#393D59
hypocenterC59C2×#2572
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. #21429341C2direct (N × H)
2. C2×#16837344C2semidirect
4. C2×#16837313C2semidirect
5. C2×#16837309C2semidirect
6. C2×#16837296C2semidirect
7. C2×#16837291C2semidirect
10. C2×#16837269C2semidirect
11. C2×#16837269C2semidirect
12. C2×#16837264C2semidirect
13. C2×#16837263C2semidirect
14. C2×C22⋊C4×Dic59C2semidirect
15. C2×#16837249C2semidirect
16. C2×C59×#393C2semidirect
32. #16837344C22semidirect
34. #16837313C22semidirect
35. #16837309C22semidirect
36. #16837296C22semidirect
37. #16837291C22semidirect
40. #16837269C22semidirect
41. #16837269C22semidirect
42. #16837264C22semidirect
43. #16837263C22semidirect
44. C22⋊C4×Dic59C22semidirect
45. #16837249C22semidirect
63. C59×#393C22semidirect
384. C2×#393D59semidirect
397. C2×C59#2572semidirect
428. #393C2×D59semidirect
456. C59C2×#2572semidirect
771. C2#21429341direct (N × H)

Maximal subgroups

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

subgroupindex
#214293412
C2×#168373442
C2×#168373182
C2×#168373132
C2×#168373092
C2×#168372962
C2×#168372912
C2×#168372792
C2×#168372782
C2×#168372692
C2×#168372642
C2×#168372632
C2×C22⋊C4×Dic592
C2×#168372492
C2×C59×#3932
C2×#257259