Finite Group Databasebeta

← C2×#21434289 #29456930

Subgroups — C2×#21434289 #29456930

Order 15104.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837882C211yesmaximal, characteristic, complemented
2#21434289C2116yesmaximal, direct product factor
3C2×#16837718C211yesmaximal, characteristic, complemented
4C2×#16837713C211yesmaximal, characteristic, complemented
5C2×#16837706C211yesmaximal, characteristic, complemented
6C2×#16837699C211yesmaximal, characteristic, complemented
7C2×#16837599C211yesmaximal, characteristic, complemented
8C2×#16837594C211yesmaximal, characteristic, complemented
9C2×#16837545C211yesmaximal, characteristic, complemented
10C2×#16837545C211yesmaximal, characteristic, complemented
11C2×#16837512C211yesmaximal, characteristic, complemented
12C2×#16837502C211yesmaximal, characteristic, complemented
13C2×C4×#11745670C211yesmaximal, characteristic, complemented
14C2×C4×#11745669C211yesmaximal, characteristic, complemented
15C2×#16837463C211yesmaximal, characteristic, complemented
16C2×C59×#540C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×#11745670C2211yescharacteristic
19C22×#11745670C2211yescharacteristic
20C22×#11745669C2211yescharacteristic
21C22×#11745669C2211yescharacteristic
22#16837882—24no—
23#16837882C2218yescomplemented
24C2×C4×Dic118C2211yescharacteristic
25C2×C4×Dic118C2211yescharacteristic
26C2×C4×D236C2211yescharacteristic
27C2×C4×D236C2211yescharacteristic
28C2×(C22⋊D59)⋊C4—21no—
29C2×(C22⋊D59)⋊C4—21no—
30C2×#14273685—21no—
31C22×C4⋊Dic59C2211yescharacteristic
32C2×C4⋊C4×D59—21no—
33#16837718C2218yescomplemented
34#16837713C2218yescomplemented
35#16837706C2218yescomplemented
36#16837699C2218yescomplemented
37#16837599C2218yescomplemented
38#16837594C2218yescomplemented
39#16837545C2218yescomplemented
40#16837545C2218yescomplemented
41#16837512C2218yescomplemented
42#16837502C2218yescomplemented
43C4×#11745670C2218yescomplemented
44C4×#11745669C2218yescomplemented
45#16837463C2218yescomplemented
46C2×#14273660C2211yescharacteristic
47C2×#14273660C2211yescharacteristic
48C2×#14273658C2211yescharacteristic
49C2×#14273658C2211yescharacteristic
50C2×C4⋊(C59⋊C8)C2211yescharacteristic
51C2×C4⋊(C59⋊C8)C2211yescharacteristic
52C2×#14273650C2211yescharacteristic
53C2×#14273650C2211yescharacteristic
54C2×#14273648C2211yescharacteristic
55C2×#14273648C2211yescharacteristic
56C2×#14273648C2211yescharacteristic
57C2×#14273648C2211yescharacteristic
58C2×#14273647C2211yescharacteristic
59C2×#14273647C2211yescharacteristic
60C2×C22⋊(C59⋊C8)C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×#14273638C2211yescharacteristic
63C2×C4×C59⋊C8C2211yescharacteristic
64C59×#540—24no—
65C59×#540C2218yescomplemented
66C2×#127×C59C2211yescharacteristic
67C2×#125×C59C2211yescharacteristic
68C2×#123×C59—21no—
69C2×#123×C59—21no—
70C2×#121×C59—21no—
71C2×#121×C59—21no—
72C2×#121×C59C2211yescharacteristic
73C2×#121×C59C2211yescharacteristic
74C2×C4×D4×C59C2211yescharacteristic
75C2×C4×D4×C59C2211yescharacteristic
76C2×#117×C59C2211yescharacteristic
77C2×#11745685—22no—
78C2×#11745685—24no—
79C2×#11745685—24no—
80C2×#11745685C2314yes—
81C22×Dic118C2311yescharacteristic
82C22×D236C2311yescharacteristic
83C22×C22⋊D59—21no—
84C23×Dic59—21no—
85C22×C4×D59—21no—
86C22×C4×D59—21no—
87C22×C4×D59—21no—
88C2×#11745670—24no—
89C2×#11745670—24no—
90C2×#11745670C2314yes—
91C2×#11745670C2314yes—
92C2×#11745669—24no—
93C2×#11745669—24no—
94C2×#11745669C2314yes—
95C2×#11745669C2314yes—
96C22×C59⋊C8C2311yescharacteristic
97C22×C59⋊C8C2311yescharacteristic
98C22×C59⋊C8C2311yescharacteristic
99C22×C59⋊C8C2311yescharacteristic
100C4×Dic118—22no—
101C4×Dic118—22no—
102C4×Dic118C2314yes—
103C4×Dic118C2314yes—
104C4×D236—22no—
105C4×D236—22no—
106C4×D236C2314yes—
107C4×D236C2314yes—
108(C22⋊D59)⋊C4—28no—
109(C22⋊D59)⋊C4—28no—
110#14273685—28no—
111C2×C4⋊Dic59—21no—
112C2×C4⋊Dic59—22no—
113C2×C4⋊Dic59C2311yescharacteristic
114C2×C4⋊Dic59C2311yescharacteristic
115C2×C4⋊Dic59C2314yes—
116C2×Dic59⋊C4—21no—
117C2×Dic59⋊C4—21no—
118C4⋊C4×D59—28no—
119C2×(C2×D59)⋊C4—21no—
120C2×(C2×D59)⋊C4—21no—
121C2×C4×Dic59—21no—
122C2×C4×Dic59—21no—
123#14273660C2314yes—
124#14273660C2314yes—
125#14273658C2314yes—
126#14273658C2314yes—
127C4⋊(C59⋊C8)C2314yes—
128C4⋊(C59⋊C8)C2314yes—
129#14273650C2314yes—
130#14273650C2314yes—
131#14273648C2314yes—
132#14273648C2314yes—
133#14273648C2314yes—
134#14273648C2314yes—
135#14273647C2314yes—
136#14273647C2314yes—
137C22⋊(C59⋊C8)C2314yes—
138C22⋊(C59⋊C8)C2314yes—
139#14273638C2314yes—
140C4×C59⋊C8C2314yes—
141C22×D4×C59—21no—
142C22×D4×C59—21no—
143C22×D4×C59—21no—
144C22×D4×C59—21no—
145C22×D4×C59C2311yescharacteristic
146C22×D4×C59C2311yescharacteristic
147C23×C4×C59—21no—
148C23×C4×C59—21no—
149C23×C4×C59C2311yescharacteristic
150#127×C59—22no—
151#127×C59C2314yes—
152#125×C59—22no—
153#125×C59C2314yes—
154#123×C59—28no—
155#123×C59—28no—
156#121×C59—22no—
157#121×C59—22no—
158#121×C59—28no—
159#121×C59—28no—
160#121×C59C2314yes—
161#121×C59C2314yes—
162C4×D4×C59—22no—
163C4×D4×C59—22no—
164C4×D4×C59C2314yes—
165C4×D4×C59C2314yes—
166#117×C59D414yes—
167#117×C59C2314yes—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59—21no—
170C2×C4⋊C4×C59D411yescharacteristic
171C2×C4⋊C4×C59D411yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176C2×C22⋊C4×C59—21no—
177C2×C22⋊C4×C59—21no—
178C2×C22⋊C4×C59D411yescharacteristic
179C2×C22⋊C4×C59D411yescharacteristic
180C2×C42×C59C2311yescharacteristic
181C2×C42×C59C2311yescharacteristic
182C24×C59—21no—
183C24×C59—21no—
184C24×C59C2×D411yescharacteristic
185C23×D59—21no—
186C2×D4×C59—24no—
187C2×D4×C59—24no—
188C2×D4×C59—21no—
189C2×D4×C59—21no—
190C2×D4×C59—24no—
191C2×D4×C59—24no—
192C2×D4×C59—22no—
193C2×D4×C59—22no—
194C2×D4×C59—22no—
195C2×D4×C59—22no—
196C2×D4×C59—82no—
197C2×D4×C59—82no—
198C2×D4×C59—82no—
199C2×D4×C59—82no—
200C2×D4×C59C2412yes—
201C2×D4×C59C2412yes—
202C22×C4×C59—22no—
203C22×C4×C59—22no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—24no—
207C22×C4×C59—24no—
208C22×C4×C59—82no—
209C22×C4×C59—82no—
210C22×C4×C59C2×D411yescharacteristic
211C22×C4×C59C2×D411yescharacteristic
212C22×C4×C59C2×D411yescharacteristic
213C22×C4×C59C2×D411yescharacteristic
214C22×C4×C59C2×D411yescharacteristic
215C22×C4×C59C2×D412yes—
216C22×C4×C59C2412yes—
217C22×C4×C59C2411yescharacteristic
218C2×C22⋊D59—28no—
219C2×C22⋊D59—24no—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—21no—
223C22×Dic59—24no—
224C22×Dic59—82no—
225#11745685—216no—
226#11745685—28no—
227#11745685—28no—
228C2×D236—21no—
229C2×D236—22no—
230C2×D236#4114yes—
231C2×D236C2412yes—
232C2×C4×D59—28no—
233C2×C4×D59—24no—
234C2×C4×D59—24no—
235C2×C4×D59—24no—
236C2×C4×D59—82no—
237C2×C4×D59—82no—
238C2×Dic118—21no—
239C2×Dic118—22no—
240C2×Dic118#4114yes—
241C2×Dic118C2412yes—
242C4⋊C4×C59—24no—
243C4⋊C4×C59—24no—
244C4⋊C4×C59—21no—
245C4⋊C4×C59—21no—
246C4⋊C4×C59C2×D414yes—
247C4⋊C4×C59C2×D414yes—
248C4⋊C4×C59C2412yes—
249C4⋊C4×C59C2412yes—
250C22⋊C4×C59—24no—
251C22⋊C4×C59—24no—
252C22⋊C4×C59—24no—
253C22⋊C4×C59—24no—
254C22⋊C4×C59C2×D414yes—
255C22⋊C4×C59C2×D414yes—
256C42×C59C2×D412yes—
257C42×C59C2×D412yes—
258C42×C59C2412yes—
259C42×C59C2412yes—
260#11745670—28no—
261#11745670—28no—
262#11745669—28no—
263#11745669—28no—
264(C2×D59)⋊C4—24no—
265(C2×D59)⋊C4—24no—
266C4⋊Dic59—24no—
267C4⋊Dic59—21no—
268C4⋊Dic59—21no—
269C4⋊Dic59C2412yes—
270C4⋊Dic59C2412yes—
271Dic59⋊C4—24no—
272Dic59⋊C4—24no—
273C4×Dic59—24no—
274C4×Dic59—24no—
275C2×C59⋊C8—22no—
276C2×C59⋊C8—22no—
277C2×C59⋊C8—22no—
278C2×C59⋊C8—22no—
279C2×C59⋊C8C2412yes—
280C2×C59⋊C8C2412yes—
281C2×C59⋊C8C2412yes—
282C2×C59⋊C8C2412yes—
283C23×C59—22no—
284C23×C59—22no—
285C23×C59—22no—
286C23×C59—22no—
287C23×C59—22no—
288C23×C59—42no—
289C23×C59—42no—
290C23×C59—42no—
291C23×C59—42no—
292C23×C59—42no—
293C23×C59—42no—
294C23×C59C22×D412yes—
295C23×C59C22×D411yescharacteristic
296C22×D59—24no—
297C22×D59—22no—
298C22×D59—42no—
299C22×D59—42no—
300D4×C59—22no—
301D4×C59—22no—
302D4×C59—22no—
303D4×C59—22no—
304D4×C59—42no—
305D4×C59—42no—
306D4×C59—84no—
307D4×C59—84no—
308D4×C59—84no—
309D4×C59—84no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—24no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—42no—
321C2×C4×C59—42no—
322C2×C4×C59—84no—
323C2×C4×C59—84no—
324C2×C4×C59C22×D412yes—
325C2×C4×C59C22×D412yes—
326C2×C4×C59C22×D412yes—
327C2×C4×C59C22×D412yes—
328C2×C4×C59C22×D412yes—
329C2×C4×C59C22×D411yescharacteristic
330C2×C4×C59C2×#4112yes—
331C2×C4×C59C2×#4112yes—
332C2×C4×C59C2511yescharacteristic
333C22⋊D59—216no—
334C2×Dic59—24no—
335C2×Dic59—22no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—42no—
339C2×Dic59—42no—
340C2×Dic59—84no—
341D236—24no—
342D236—22no—
343D236C2×#4114yes—
344C4×D59—216no—
345C4×D59—84no—
346C4×D59—84no—
347Dic118—24no—
348Dic118—22no—
349Dic118C2×#4114yes—
350C59⋊C8—22no—
351C59⋊C8—22no—
352C59⋊C8—22no—
353C59⋊C8—22no—
354C2×#3119—591nomaximal, Sylow
355C22×C59—22no—
356C22×C59—22no—
357C22×C59—22no—
358C22×C59—44no—
359C22×C59—42no—
360C22×C59—42no—
361C22×C59—42no—
362C22×C59—42no—
363C22×C59—42no—
364C22×C59—42no—
365C22×C59—84no—
366C22×C59—84no—
367C22×C59#52512yes—
368C22×C59#57612yes—
369C22×C59#57712yes—
370C22×C59C23×D411yescharacteristic
371C2×D59—24no—
372C2×D59—48no—
373C2×D59—42no—
374C2×D59—42no—
375C4×C59—22no—
376C4×C59—22no—
377C4×C59—22no—
378C4×C59—22no—
379C4×C59—22no—
380C4×C59—42no—
381C4×C59—42no—
382C4×C59#52512yes—
383C4×C59C22×#4111yescharacteristic
384C4×C59C22×#4111yescharacteristic
385Dic59—24no—
386Dic59—42no—
387Dic59—42no—
388C2×#540D5911yescharacteristic, complemented
389C2×#520—591no—
390#3119—5916no—
391C2×#481—591no—
392C2×#480—591no—
393C2×#479—591no—
394C2×#478—591no—
395C2×#460—591no—
396C2×#459—591no—
397C2×#449—591no—
398C2×#449—591no—
399C2×#442—591no—
400C2×#440—591no—
401C2×C4×SD16—591no—
402C2×C4×D8—591no—
403C2×#433—591no—
404C2×C59—42no—
405C2×C59—82no—
406C2×C59—82no—
407C2×C59#311914yescomplemented
408C2×C59C2×#52511yescharacteristic
409C2×C59C2×#57611yescharacteristic
410C2×C59C2×#57711yescharacteristic
411D59—44no—
412C22×#41—591no—
413C22×SD16—591no—
414C22×SD16—591no—
415C22×D8—591no—
416C22×D8—591no—
417#540—24no—
418#540C2×D5918yescomplemented
419C2×#127C2×D5911yescharacteristic
420C2×#125C2×D5911yescharacteristic
421C2×#123—21no—
422C2×#123—21no—
423C2×#121—21no—
424C2×#121—21no—
425C2×#121C2×D5911yescharacteristic
426C2×#121C2×D5911yescharacteristic
427#520—598no—
428#520—1184no—
429C2×C4×Q8—591no—
430C2×C4×Q8—591no—
431C2×C4×D4—591no—
432C2×C4×D4—591no—
433C2×C4×D4—1181no—
434C2×C4×D4—1181no—
435C2×C4×D4C2×D5911yescharacteristic
436C2×C4×D4C2×D5911yescharacteristic
437C2×#117—1181no—
438C2×#117C2×D5911yescharacteristic
439C22×C4⋊C4—591no—
440C22×C4⋊C4—1181no—
441#481—598no—
442#480—598no—
443#479—598no—
444#478—598no—
445#460—598no—
446#459—598no—
447#449—598no—
448#449—598no—
449#442—598no—
450#440—598no—
451C4×SD16—598no—
452C4×D8—598no—
453#433—598no—
454C2×#107—591no—
455C2×#107—591no—
456C2×#106—591no—
457C2×#106—591no—
458C2×C4⋊C8—591no—
459C2×C4⋊C8—591no—
460C2×#103—591no—
461C2×#103—591no—
462C2×#102—591no—
463C2×#102—591no—
464C2×#102—591no—
465C2×#102—591no—
466C2×#102—591no—
467C2×#102—591no—
468C2×C22⋊C8—591no—
469C2×C22⋊C8—591no—
470C2×#97—591no—
471C2×C4×C8—591no—
472C59C2×#311911yescharacteristic, complemented, Sylow
473C2×#41—594no—
474C2×#41—1184no—
475C2×#41—1184no—
476C2×#41—1182no—
477C22×Q8—591no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4—591no—
483C22×D4—1181no—
484C22×D4C22×D5911yescharacteristic
485C22×D4C22×D5911yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—1181no—
489C23×C4—1181no—
490C23×C4—1181no—
491C23×C4—1181no—
492C23×C4C22×D5911yescharacteristic
493C2×SD16—594no—
494C2×SD16—594no—
495C2×SD16—1184no—
496C2×SD16—1184no—
497C2×D8—594no—
498C2×D8—594no—
499C2×D8—1184no—
500C2×D8—1184no—
501C22×C8—591no—
502C22×C8—591no—
503C22×C8—591no—
504C22×C8—591no—
505#127—22no—
506#127C22×D5914yes—
507#125—22no—
508#125C22×D5914yes—
509#123—28no—
510#123—28no—
511#121—22no—
512#121—22no—
513#121—28no—
514#121—28no—
515#121C22×D5914yes—
516#121C22×D5914yes—
517C4×Q8—594no—
518C4×Q8—594no—
519C4×Q8—1182no—
520C4×Q8—1182no—
521C4×D4—22no—
522C4×D4—22no—
523C4×D4—594no—
524C4×D4—594no—
525C4×D4—1188no—
526C4×D4—1188no—
527C4×D4—1182no—
528C4×D4—1182no—
529C4×D4C22×D5914yes—
530C4×D4C22×D5914yes—
531#117—1188no—
532#117C22⋊D5914yes—
533#117C22×D5914yes—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—591no—
537C2×C4⋊C4—591no—
538C2×C4⋊C4—594no—
539C2×C4⋊C4—1181no—
540C2×C4⋊C4—1182no—
541C2×C4⋊C4—1181no—
542C2×C4⋊C4—1181no—
543C2×C4⋊C4—1188no—
544C2×C4⋊C4C22⋊D5911yescharacteristic
545C2×C4⋊C4C22⋊D5911yescharacteristic
546C2×C4⋊C4C22×D5911yescharacteristic
547C2×C4⋊C4C22×D5911yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—1181no—
553C2×C22⋊C4—1181no—
554C2×C22⋊C4C22⋊D5911yescharacteristic
555C2×C22⋊C4C22⋊D5911yescharacteristic
556C2×C42—1181no—
557C2×C42—1181no—
558C2×C42C22×D5911yescharacteristic
559C2×C42C22×D5911yescharacteristic
560#107—594no—
561#107—594no—
562#106—594no—
563#106—594no—
564C4⋊C8—594no—
565C4⋊C8—594no—
566#103—594no—
567#103—594no—
568#102—594no—
569#102—594no—
570#102—594no—
571#102—594no—
572#102—594no—
573#102—594no—
574C22⋊C8—594no—
575C22⋊C8—594no—
576#97—594no—
577C4×C8—594no—
578C24—21no—
579C24—21no—
580C24—1181no—
581C24C2×C22⋊D5911yescharacteristic
582#41—1188no—
583#41—1188no—
584#41—11816no—
585C2×Q8—594no—
586C2×Q8—592no—
587C2×Q8—1181no—
588C2×Q8—1182no—
589C2×D4—24no—
590C2×D4—24no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—24no—
594C2×D4—24no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—82no—
600C2×D4—82no—
601C2×D4—82no—
602C2×D4—82no—
603C2×D4—594no—
604C2×D4—592no—
605C2×D4—1188no—
606C2×D4—1184no—
607C2×D4—1181no—
608C2×D4—1182no—
609C2×D4C23×D5912yes—
610C2×D4C23×D5912yes—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4—1188no—
620C22×C4—1181no—
621C22×C4—1184no—
622C22×C4—1184no—
623C22×C4—1181no—
624C22×C4—1181no—
625C22×C4—1184no—
626C22×C4—1184no—
627C22×C4—4722no—
628C22×C4—4722no—
629C22×C4—4722no—
630C22×C4C2×C22⋊D5912yes—
631C22×C4C2×C22⋊D5911yescharacteristic
632C22×C4C2×C22⋊D5911yescharacteristic
633C22×C4C2×C22⋊D5911yescharacteristic
634C22×C4C2×C22⋊D5911yescharacteristic
635C22×C4C2×C22⋊D5911yescharacteristic
636C22×C4C23×D5912yes—
637C22×C4C23×D5911yescharacteristic
638SD16—1188no—
639SD16—1188no—
640D8—1188no—
641D8—1188no—
642C2×C8—592no—
643C2×C8—592no—
644C2×C8—592no—
645C2×C8—592no—
646C2×C8—1182no—
647C2×C8—1182no—
648C2×C8—1182no—
649C2×C8—1182no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—592no—
655C4⋊C4—592no—
656C4⋊C4—1184no—
657C4⋊C4—1181no—
658C4⋊C4—1181no—
659C4⋊C4—1184no—
660C4⋊C4—1184no—
661C4⋊C4C2×C22⋊D5914yes—
662C4⋊C4C2×C22⋊D5914yes—
663C4⋊C4C23×D5912yes—
664C4⋊C4C23×D5912yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—1184no—
670C22⋊C4—1184no—
671C22⋊C4C2×C22⋊D5914yes—
672C22⋊C4C2×C22⋊D5914yes—
673C42—1184no—
674C42—1184no—
675C42C2×C22⋊D5912yes—
676C42C2×C22⋊D5912yes—
677C42C23×D5912yes—
678C42C23×D5912yes—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—1184no—
691C23—1182no—
692C23—2362no—
693C23—2362no—
694C23C22×C22⋊D5912yes—
695C23C22×C22⋊D5911yescharacteristic
696Q8—594no—
697Q8—1184no—
698Q8—1182no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—22no—
703D4—42no—
704D4—42no—
705D4—84no—
706D4—84no—
707D4—84no—
708D4—84no—
709D4—594no—
710D4—11816no—
711D4—1184no—
712D4—1182no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4—11816no—
728C2×C4—1184no—
729C2×C4—1182no—
730C2×C4—1182no—
731C2×C4—1182no—
732C2×C4—4724no—
733C2×C4—4724no—
734C2×C4—4724no—
735C2×C4—2362no—
736C2×C4—2362no—
737C2×C4C22×C22⋊D5912yes—
738C2×C4C22×C22⋊D5912yes—
739C2×C4C22×C22⋊D5912yes—
740C2×C4C22×C22⋊D5912yes—
741C2×C4C22×C22⋊D5912yes—
742C2×C4C22×C22⋊D5911yescharacteristic
743C2×C4#41×D5912yes—
744C2×C4#41×D5912yes—
745C2×C4C24×D5911yescharacteristic
746C8—1182no—
747C8—1182no—
748C8—1182no—
749C8—1182no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—84no—
762C22—1184no—
763C22—2362no—
764C22—2362no—
765C22—2368no—
766C22#1683790912yes—
767C22#1683820512yes—
768C22#1683821312yes—
769C22C23×C22⋊D5911yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—42no—
776C4—42no—
777C4—1184no—
778C4—2362no—
779C4—2362no—
780C4#1683790912yes—
781C4C2×#41×D5911yescharacteristic
782C4C2×#41×D5911yescharacteristic
783C2—42no—
784C2—82no—
785C2—82no—
786C2—2364no—
787C2#2143428914yesdirect product factor
788C2C2×#1683790911yescharacteristic
789C2C2×#1683820511yescharacteristic
790C2C2×#1683821311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#540C2
socleC23×C59C22×D4
hypercenterC2×#540D59
hypocenterC59C2×#3119
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#16837882C2semidirect
2. #21434289C2direct (N × H)
3. C2×#16837718C2semidirect
4. C2×#16837713C2semidirect
5. C2×#16837706C2semidirect
6. C2×#16837699C2semidirect
7. C2×#16837599C2semidirect
8. C2×#16837594C2semidirect
9. C2×#16837545C2semidirect
10. C2×#16837545C2semidirect
11. C2×#16837512C2semidirect
12. C2×#16837502C2semidirect
13. C2×C4×#11745670C2semidirect
14. C2×C4×#11745669C2semidirect
15. C2×#16837463C2semidirect
16. C2×C59×#540C2semidirect
23. #16837882C22semidirect
33. #16837718C22semidirect
34. #16837713C22semidirect
35. #16837706C22semidirect
36. #16837699C22semidirect
37. #16837599C22semidirect
38. #16837594C22semidirect
39. #16837545C22semidirect
40. #16837545C22semidirect
41. #16837512C22semidirect
42. #16837502C22semidirect
43. C4×#11745670C22semidirect
44. C4×#11745669C22semidirect
45. #16837463C22semidirect
65. C59×#540C22semidirect
388. C2×#540D59semidirect
407. C2×C59#3119semidirect
418. #540C2×D59semidirect
472. C59C2×#3119semidirect
787. C2#21434289direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168378822
#214342892
C2×#168377182
C2×#168377132
C2×#168377062
C2×#168376992
C2×#168375992
C2×#168375942
C2×#168375452
C2×#168375122
C2×#168375022
C2×C4×#117456702
C2×C4×#117456692
C2×#168374632
C2×C59×#5402
C2×#311959