Finite Group Databasebeta

← C2×#21437976 #29497126

Subgroups — C2×#21437976 #29497126

Order 15104.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437976C2132yesmaximal, direct product factor
2C2×#16838131C211yesmaximal, characteristic, complemented
3C2×#16838130C212yesmaximal, complemented
4C2×#16838127C211yesmaximal, characteristic, complemented
5C2×#16838122C211yesmaximal, characteristic, complemented
6C2×#16838121C212yesmaximal, complemented
7C2×#16838091C212yesmaximal, complemented
8C2×#16838088C214yesmaximal, complemented
9C2×#16838086C212yesmaximal, complemented
10C2×#16838009C214yesmaximal, complemented
11C2×#16837972C212yesmaximal
12C2×#16837956C211yesmaximal, characteristic, complemented
13C2×#16837955C212yesmaximal, complemented
14C2×#16837954C212yesmaximal, complemented
15C2×C4⋊Q8×D59C211yesmaximal, characteristic, complemented
16C2×#16837878C212yesmaximal, complemented
17C2×C4×#11745687C211yesmaximal, characteristic
18C2×C59×#556C211yesmaximal, characteristic, complemented
19C22×#11745687C2211yescharacteristic
20C22×Q8×D59C2212yes—
21#16838131C22116yescomplemented
22#16838130C22132yescomplemented
23#16838127C22116yescomplemented
24#16838122C22116yescomplemented
25#16838121C22132yescomplemented
26#16838091C22132yescomplemented
27#16838088C22164yescomplemented
28#16838086C22132yescomplemented
29#16838009C22164yescomplemented
30#16837972C22132yes—
31#16837956C22116yescomplemented
32#16837955C22132yescomplemented
33#16837954C22132yescomplemented
34C2×#14273727C2211yescharacteristic
35C2×#14273727C2212yes—
36C2×#14273726C2212yes—
37C2×#14273726C2212yes—
38C2×#14273726C2211yescharacteristic
39C2×#14273725C2212yes—
40C2×#14273725C2211yescharacteristic
41C2×#14273725C2212yes—
42C4⋊Q8×D59C22116yescomplemented
43C2×#14273720C2214yes—
44C2×#14273720C2214yes—
45C2×#14273720C2214yes—
46C2×#14273719C2214yes—
47C2×#14273718C2214yes—
48C2×#14273718C2212yes—
49C2×#14273718C2212yes—
50C2×#14273717C2212yes—
51C2×#14273717C2214yes—
52C2×#14273717C2214yes—
53C2×#14273717C2214yes—
54C2×#14273714C2212yes—
55C2×#14273709C2214yes—
56C2×#14273709C2214yes—
57C2×#14273707C2211yescharacteristic
58C2×#14273706C2212yes—
59C2×#14273705C2212yes—
60C2×#14273704C2214yes—
61C2×#14273704C2214yes—
62C2×#14273704C2214yes—
63C2×#14273703C2211yescharacteristic
64#16837878C22132yescomplemented
65C4×#11745687C22116yes—
66C2×Q8×Dic59C2212yes—
67C2×Q8×Dic59C2212yes—
68C2×C4×Dic118C2214yes—
69C2×C4×Dic118C2211yescharacteristic
70C2×C4×Dic118C2212yes—
71C2×C4×Dic118C2214yes—
72C2×C4×Dic118C2212yes—
73C2×C4×Dic118C2211yescharacteristic
74C2×#14273692C2214yes—
75C2×#14273692C2211yescharacteristic
76C2×#14273692C2212yes—
77C2×#14273692C2212yes—
78C2×D4×Dic59C2211yescharacteristic
79C2×C4×C22⋊D59C2212yes—
80C2×(C22⋊D59)⋊C4C2212yes—
81C2×#14273686C2212yes—
82C2×#14273685C2211yescharacteristic
83C2×#14273685C2214yes—
84C2×#14273684C2214yes—
85C2×#14273684C2212yes—
86C2×#14273683C2212yes—
87C2×#14273683C2214yes—
88C2×C4⋊C4×D59C2212yes—
89C2×C4⋊C4×D59C2212yes—
90C22×C4×Dic59C2212yes—
91C2×C42×D59C2211yescharacteristic
92C59×#556C22116yescomplemented
93C2×C4⋊Q8×C59C2211yescharacteristic
94C2×#126×C59C2214yes—
95C2×#124×C59C2212yes—
96C2×C22⋊Q8×C59C2212yes—
97C2×C4×Q8×C59C2212yes—
98C2×C4×Q8×C59C2211yescharacteristic
99C2×C4×D4×C59C2211yescharacteristic
100C2×#117×C59C2212yes—
101C2×#11745687—28no—
102C2×#11745687C2318yes—
103C22×Dic118C2312yes—
104C22×Dic118C2314yes—
105C22×Dic118C2311yescharacteristic
106C22×Dic118C2312yes—
107C22×Dic118C2311yescharacteristic
108C2×Q8×D59—216no—
109C2×Q8×D59C23116yes—
110C22×C22⋊D59C2312yes—
111C23×Dic59C2312yes—
112C23×Dic59C2312yes—
113C22×C4×D59C2311yescharacteristic
114C22×C4×D59C2311yescharacteristic
115C22×C4×D59C2314yes—
116C22×C4×D59C2311yescharacteristic
117#14273727C2318yes—
118#14273727C23116yes—
119#14273726C23116yes—
120#14273726C23116yes—
121#14273726C2318yes—
122#14273725C23116yes—
123#14273725C2318yes—
124#14273725C23116yes—
125#14273720C23132yes—
126#14273720C23132yes—
127#14273720C23132yes—
128#14273719C23132yes—
129#14273718C23116yes—
130#14273718C23116yes—
131#14273718C23132yes—
132#14273717C23132yes—
133#14273717C23116yes—
134#14273717C23132yes—
135#14273717C23132yes—
136#14273714C23116yes—
137#14273709C23132yes—
138#14273709C23132yes—
139#14273707C2318yes—
140#14273706C23116yes—
141#14273705C23116yes—
142#14273704C23132yes—
143#14273704C23132yes—
144#14273704C23132yes—
145#14273703C2318yes—
146Q8×Dic59C23116yes—
147Q8×Dic59C23116yes—
148C4×Dic118C23132yes—
149C4×Dic118C23132yes—
150C4×Dic118C23116yes—
151C4×Dic118C2318yes—
152C4×Dic118C23116yes—
153C4×Dic118C2318yes—
154#14273692C23132yes—
155#14273692C23116yes—
156#14273692C23116yes—
157#14273692C2318yes—
158D4×Dic59C2318yes—
159C4×C22⋊D59C23116yes—
160(C22⋊D59)⋊C4C23116yes—
161#14273686C23116yes—
162#14273685C23132yes—
163#14273685C2318yes—
164#14273684C23116yes—
165#14273684C23132yes—
166#14273683C23132yes—
167#14273683C23116yes—
168C2×C4⋊Dic59C2311yescharacteristic
169C2×C4⋊Dic59C2314yes—
170C2×C4⋊Dic59C2314yes—
171C2×C4⋊Dic59C2314yes—
172C2×C4⋊Dic59C2312yes—
173C2×C4⋊Dic59C2312yes—
174C2×C4⋊Dic59C2312yes—
175C2×C4⋊Dic59C2311yescharacteristic
176C2×Dic59⋊C4C2312yes—
177C2×Dic59⋊C4C2312yes—
178C2×Dic59⋊C4C2312yes—
179C2×Dic59⋊C4C2314yes—
180C2×Dic59⋊C4C2314yes—
181C2×Dic59⋊C4C2314yes—
182C2×Dic59⋊C4C2314yes—
183C2×Dic59⋊C4C2312yes—
184C2×Dic59⋊C4C2312yes—
185C2×Dic59⋊C4C2314yes—
186C2×Dic59⋊C4C2312yes—
187C2×Dic59⋊C4C2312yes—
188C2×Dic59⋊C4C2314yes—
189C4⋊C4×D59C23116yes—
190C4⋊C4×D59C23116yes—
191C2×C22⋊Dic59C2314yes—
192C2×C22⋊Dic59C2314yes—
193C2×C22⋊Dic59C2312yes—
194C2×(C2×D59)⋊C4C2312yes—
195C2×(C2×D59)⋊C4C2312yes—
196C2×(C2×D59)⋊C4C2312yes—
197C2×C4×Dic59C2312yes—
198C2×C4×Dic59C2311yescharacteristic
199C2×C4×Dic59C2312yes—
200C2×C4×Dic59C2314yes—
201C2×C4×Dic59C2314yes—
202C2×C4×Dic59C2312yes—
203C2×C4×Dic59C2314yes—
204C2×C4×Dic59C2311yescharacteristic
205C2×C4×Dic59C2311yescharacteristic
206C2×C4×Dic59C23116yes—
207C2×C4×Dic59C2312yes—
208C42×D59C2318yes—
209C22×Q8×C59C2311yescharacteristic
210C22×Q8×C59C2312yes—
211C22×D4×C59C2311yescharacteristic
212C23×C4×C59C2312yes—
213C4⋊Q8×C59C2318yes—
214#126×C59C23132yes—
215#124×C59C23116yes—
216C22⋊Q8×C59C23116yes—
217C4×Q8×C59C2318yes—
218C4×Q8×C59C23116yes—
219C4×D4×C59C2318yes—
220#117×C59C23116yes—
221C2×C4⋊C4×C59C2312yes—
222C2×C4⋊C4×C59C2311yescharacteristic
223C2×C4⋊C4×C59C2312yes—
224C2×C4⋊C4×C59C2314yes—
225C2×C4⋊C4×C59C2312yes—
226C2×C4⋊C4×C59C2311yescharacteristic
227C2×C22⋊C4×C59C2314yes—
228C2×C22⋊C4×C59C2314yes—
229C2×C22⋊C4×C59C2312yes—
230C2×C42×C59C2314yes—
231C2×C42×C59C2311yescharacteristic
232C2×C42×C59C2312yes—
233C24×C59C2412yes—
234C23×D59C2411yescharacteristic
235C2×Q8×C59—28no—
236C2×Q8×C59—24no—
237C2×Q8×C59C2414yes—
238C2×Q8×C59C2418yes—
239C2×D4×C59—24no—
240C2×D4×C59C2414yes—
241C22×C4×C59—28no—
242C22×C4×C59C2412yes—
243C22×C4×C59C2412yes—
244C22×C4×C59C2411yescharacteristic
245C22×C4×C59C2412yes—
246C22×C4×C59C2414yes—
247C22×C4×C59C2418yes—
248C22×C4×C59C2411yescharacteristic
249C22×C4×C59C2411yescharacteristic
250C2×C22⋊D59—28no—
251C2×C22⋊D59C2418yes—
252C22×Dic59—28no—
253C22×Dic59—28no—
254C22×Dic59C2412yes—
255C22×Dic59C2412yes—
256C22×Dic59C2412yes—
257C22×Dic59C2411yescharacteristic
258C22×Dic59C2414yes—
259C22×Dic59C2412yes—
260C22×Dic59C2418yes—
261C22×Dic59C2418yes—
262C22×Dic59C2411yescharacteristic
263C22×Dic59C2411yescharacteristic
264Q8×D59—264no—
265#11745687—232no—
266C2×C4×D59—216no—
267C2×C4×D59—24no—
268C2×C4×D59—24no—
269C2×C4×D59#4118yes—
270C2×C4×D59C2414yes—
271C2×C4×D59C2414yes—
272C2×C4×D59C24116yes—
273C2×C4×D59C2414yes—
274C2×Dic118—28no—
275C2×Dic118—24no—
276C2×Dic118—24no—
277C2×Dic118—216no—
278C2×Dic118—28no—
279C2×Dic118C2414yes—
280C2×Dic118C24116yes—
281C2×Dic118C2418yes—
282C2×Dic118C2414yes—
283C2×Dic118C2418yes—
284C4⋊C4×C59C2414yes—
285C4⋊C4×C59C2418yes—
286C4⋊C4×C59C2414yes—
287C4⋊C4×C59C24116yes—
288C4⋊C4×C59C2418yes—
289C4⋊C4×C59C2418yes—
290C22⋊C4×C59C24116yes—
291C22⋊C4×C59C2418yes—
292C22⋊C4×C59C24116yes—
293C42×C59C24116yes—
294C42×C59C2414yes—
295C42×C59C2418yes—
296C22⋊Dic59C2418yes—
297C22⋊Dic59C24116yes—
298C22⋊Dic59C24116yes—
299(C2×D59)⋊C4C2418yes—
300(C2×D59)⋊C4C2418yes—
301(C2×D59)⋊C4C2418yes—
302C4⋊Dic59C2418yes—
303C4⋊Dic59C2418yes—
304C4⋊Dic59C2414yes—
305C4⋊Dic59C24116yes—
306C4⋊Dic59C2414yes—
307C4⋊Dic59C24116yes—
308C4⋊Dic59C2418yes—
309C4⋊Dic59C24116yes—
310Dic59⋊C4C24116yes—
311Dic59⋊C4C24116yes—
312Dic59⋊C4C2418yes—
313Dic59⋊C4C2418yes—
314Dic59⋊C4C2418yes—
315Dic59⋊C4C2418yes—
316Dic59⋊C4C24116yes—
317Dic59⋊C4C2418yes—
318Dic59⋊C4C24116yes—
319Dic59⋊C4C24116yes—
320Dic59⋊C4C2418yes—
321Dic59⋊C4C24116yes—
322Dic59⋊C4C2418yes—
323C4×Dic59C2414yes—
324C4×Dic59C2414yes—
325C4×Dic59C2414yes—
326C4×Dic59C2418yes—
327C4×Dic59C2418yes—
328C4×Dic59C2418yes—
329C4×Dic59C24116yes—
330C4×Dic59C24116yes—
331C4×Dic59C2418yes—
332C4×Dic59C24116yes—
333C23×C59—24no—
334C23×C59—24no—
335C23×C59—24no—
336C23×C59C2514yes—
337C23×C59C2511yescharacteristic
338C22×D59—22no—
339C22×D59—22no—
340C22×D59C2×#4114yes—
341C22×D59C2512yes—
342Q8×C59—216no—
343Q8×C59—28no—
344D4×C59—28no—
345C2×C4×C59—28no—
346C2×C4×C59—24no—
347C2×C4×C59—22no—
348C2×C4×C59—24no—
349C2×C4×C59—24no—
350C2×C4×C59—216no—
351C2×C4×C59C2×#4114yes—
352C2×C4×C592−1+414yes—
353C2×C4×C59C2514yes—
354C2×C4×C59C2514yes—
355C2×C4×C59C2512yes—
356C2×C4×C59C2518yes—
357C2×C4×C59C2514yes—
358C2×C4×C59C2512yes—
359C2×C4×C59C2512yes—
360C22⋊D59—216no—
361C2×Dic59—28no—
362C2×Dic59—24no—
363C2×Dic59—24no—
364C2×Dic59—24no—
365C2×Dic59—22no—
366C2×Dic59—24no—
367C2×Dic59—216no—
368C2×Dic59—216no—
369C2×Dic59C2×#4114yes—
370C2×Dic592−1+414yes—
371C2×Dic59C2514yes—
372C2×Dic59C2514yes—
373C2×Dic59C2514yes—
374C2×Dic59C2512yes—
375C2×Dic59C2514yes—
376C2×Dic59C2518yes—
377C2×Dic59C2512yes—
378C2×Dic59C2512yes—
379C4×D59—232no—
380C4×D59—28no—
381C4×D59—28no—
382C4×D59C2×#41116yes—
383Dic118—28no—
384Dic118—216no—
385Dic118—28no—
386Dic118—232no—
387Dic118—216no—
388C2×#3509—591nomaximal, Sylow
389C22×C59—24no—
390C22×C59—24no—
391C22×C59—24no—
392C22×C59—48no—
393C22×C59C22×#4112yes—
394C22×C59C2×2−1+412yes—
395C22×C59C2×2−1+412yes—
396C22×C59C2611yescharacteristic
397C2×D59—22no—
398C2×D59—22no—
399C2×D59—28no—
400C2×D59C22×#4114yes—
401C4×C59—28no—
402C4×C59—24no—
403C4×C59—22no—
404C4×C59—24no—
405C4×C59—24no—
406C4×C59C22×#4114yes—
407C4×C59C2×2−1+414yes—
408Dic59—28no—
409Dic59—24no—
410Dic59—24no—
411Dic59—24no—
412Dic59—22no—
413Dic59—24no—
414Dic59C22×#4114yes—
415Dic59C2×2−1+414yes—
416#3509—5932no—
417C2×#557—591no—
418C2×#557—592no—
419C2×#557—591no—
420C2×#556—592no—
421C2×#556—591no—
422C2×#556D5911yescharacteristic, complemented
423C2×#552—594no—
424C2×#552—592no—
425C2×#552—592no—
426C2×#541—594no—
427C2×#536—592no—
428C2×#533—592no—
429C2×#533—591no—
430C2×#533—592no—
431C22×C4⋊Q8—591no—
432C2×#519—592no—
433C2×C4×#41—591no—
434C2×C59—44no—
435C2×C59#350914yescomplemented
436C2×C59C23×#4111yescharacteristic
437C2×C59C22×2−1+411yescharacteristic
438C2×C59C22×2−1+411yescharacteristic
439D59—24no—
440C22×#41—591no—
441C23×Q8—592no—
442#557—5916no—
443#557—5932no—
444#557—5916no—
445#556—5932no—
446#556—5916no—
447#556C2×D59116yescomplemented
448#552—5964no—
449#552—5932no—
450#552—5932no—
451#541—5964no—
452#536—5932no—
453#533—5932no—
454#533—5916no—
455#533—5932no—
456C2×C4⋊Q8—592no—
457C2×C4⋊Q8—591no—
458C2×C4⋊Q8—592no—
459C2×C4⋊Q8—5916no—
460C2×C4⋊Q8—592no—
461C2×C4⋊Q8—592no—
462C2×C4⋊Q8—591no—
463C2×C4⋊Q8—591no—
464C2×C4⋊Q8—592no—
465C2×C4⋊Q8C2×D5911yescharacteristic
466C2×#126—594no—
467C2×#126—594no—
468C2×#126—594no—
469C2×#126C2×D5914yes—
470C2×#125—592no—
471C2×#125—594no—
472C2×#125—594no—
473C2×#125—594no—
474C2×#125—592no—
475C2×#125—592no—
476C2×#125—594no—
477C2×#125—594no—
478C2×#124—592no—
479C2×#124C2×D5912yes—
480C2×#123—594no—
481C2×#123—594no—
482C2×C22⋊Q8—591no—
483C2×C22⋊Q8—592no—
484C2×C22⋊Q8—592no—
485C2×C22⋊Q8—591no—
486C2×C22⋊Q8—594no—
487C2×C22⋊Q8—594no—
488C2×C22⋊Q8—594no—
489C2×C22⋊Q8C2×D5912yes—
490#519—5932no—
491C4×#41—5916no—
492C2×C4×Q8—592no—
493C2×C4×Q8—592no—
494C2×C4×Q8—591no—
495C2×C4×Q8—594no—
496C2×C4×Q8—592no—
497C2×C4×Q8—592no—
498C2×C4×Q8—591no—
499C2×C4×Q8—594no—
500C2×C4×Q8—592no—
501C2×C4×Q8—594no—
502C2×C4×Q8—591no—
503C2×C4×Q8—592no—
504C2×C4×Q8C2×D5912yes—
505C2×C4×Q8C2×D5911yescharacteristic
506C2×C4×D4—591no—
507C2×C4×D4—592no—
508C2×C4×D4—592no—
509C2×C4×D4C2×D5911yescharacteristic
510C2×#117—592no—
511C2×#117—591no—
512C2×#117—594no—
513C2×#117—592no—
514C2×#117—594no—
515C2×#117—592no—
516C2×#117—594no—
517C2×#117C2×D5912yes—
518C22×C4⋊C4—592no—
519C22×C4⋊C4—592no—
520C22×C42—592no—
521C22×C42—591no—
522C59C2×#350911yescharacteristic, complemented, Sylow
523C2×#41—598no—
524C2×#41—1188no—
525C22×Q8—5916no—
526C22×Q8—592no—
527C22×Q8—591no—
528C22×Q8—594no—
529C22×Q8—592no—
530C22×Q8—591no—
531C22×Q8—11816no—
532C22×Q8C22×D5911yescharacteristic
533C22×Q8C22×D5912yes—
534C22×D4—592no—
535C22×D4C22×D5911yescharacteristic
536C23×C4—591no—
537C23×C4—592no—
538C23×C4—592no—
539C23×C4—594no—
540C23×C4—591no—
541C23×C4—591no—
542C23×C4C22×D5912yes—
543C4⋊Q8—5916no—
544C4⋊Q8—598no—
545C4⋊Q8—5916no—
546C4⋊Q8—5916no—
547C4⋊Q8—5916no—
548C4⋊Q8—598no—
549C4⋊Q8—598no—
550C4⋊Q8—5916no—
551C4⋊Q8C22×D5918yes—
552#126—5932no—
553#126—5932no—
554#126—5932no—
555#126C22×D59132yes—
556#125—5916no—
557#125—5932no—
558#125—5916no—
559#125—5916no—
560#125—5932no—
561#125—5932no—
562#125—5932no—
563#125—5932no—
564#124—5916no—
565#124C22×D59116yes—
566#123—5932no—
567#123—5932no—
568C22⋊Q8—598no—
569C22⋊Q8—5916no—
570C22⋊Q8—5916no—
571C22⋊Q8—598no—
572C22⋊Q8—5932no—
573C22⋊Q8—5932no—
574C22⋊Q8—5932no—
575C22⋊Q8C22×D59116yes—
576C4×Q8—5916no—
577C4×Q8—5916no—
578C4×Q8—598no—
579C4×Q8—5932no—
580C4×Q8—5916no—
581C4×Q8—5916no—
582C4×Q8—598no—
583C4×Q8—5932no—
584C4×Q8—5916no—
585C4×Q8—5932no—
586C4×Q8—5916no—
587C4×Q8—598no—
588C4×Q8C22×D59116yes—
589C4×Q8C22×D5918yes—
590C4×D4—598no—
591C4×D4—5916no—
592C4×D4—5916no—
593C4×D4C22×D5918yes—
594#117—5916no—
595#117—598no—
596#117—5932no—
597#117—5916no—
598#117—5932no—
599#117—5916no—
600#117—5932no—
601#117C22×D59116yes—
602C2×C4⋊C4—594no—
603C2×C4⋊C4—592no—
604C2×C4⋊C4—594no—
605C2×C4⋊C4—592no—
606C2×C4⋊C4—592no—
607C2×C4⋊C4—591no—
608C2×C4⋊C4—591no—
609C2×C4⋊C4—592no—
610C2×C4⋊C4—592no—
611C2×C4⋊C4—592no—
612C2×C4⋊C4—592no—
613C2×C4⋊C4—594no—
614C2×C4⋊C4—594no—
615C2×C4⋊C4—594no—
616C2×C4⋊C4—594no—
617C2×C4⋊C4—594no—
618C2×C4⋊C4—594no—
619C2×C4⋊C4—594no—
620C2×C4⋊C4—592no—
621C2×C4⋊C4—592no—
622C2×C4⋊C4—592no—
623C2×C4⋊C4—5916no—
624C2×C4⋊C4—5916no—
625C2×C4⋊C4C22×D5912yes—
626C2×C4⋊C4C22×D5912yes—
627C2×C4⋊C4C22×D5911yescharacteristic
628C2×C4⋊C4C22×D5914yes—
629C2×C4⋊C4C22×D5911yescharacteristic
630C2×C4⋊C4C22×D5912yes—
631C2×C22⋊C4—592no—
632C2×C22⋊C4—594no—
633C2×C22⋊C4—594no—
634C2×C22⋊C4—592no—
635C2×C22⋊C4—592no—
636C2×C22⋊C4—592no—
637C2×C22⋊C4C22×D5912yes—
638C2×C22⋊C4C22×D5914yes—
639C2×C22⋊C4C22×D5914yes—
640C2×C42—592no—
641C2×C42—594no—
642C2×C42—594no—
643C2×C42—594no—
644C2×C42—591no—
645C2×C42—592no—
646C2×C42—592no—
647C2×C42—592no—
648C2×C42—591no—
649C2×C42—5916no—
650C2×C42—591no—
651C2×C42—598no—
652C2×C42C22×D5914yes—
653C2×C42C22×D5912yes—
654C2×C42C22×D5911yescharacteristic
655C24—591no—
656C24C23×D5912yes—
657#41—11832no—
658C2×Q8—28no—
659C2×Q8—24no—
660C2×Q8—598no—
661C2×Q8—594no—
662C2×Q8—5916no—
663C2×Q8—598no—
664C2×Q8—594no—
665C2×Q8—11816no—
666C2×Q8—1188no—
667C2×Q8—11864no—
668C2×Q8—1188no—
669C2×Q8—1184no—
670C2×Q8—1184no—
671C2×Q8C23×D5914yes—
672C2×Q8C23×D5918yes—
673C2×D4—24no—
674C2×D4—598no—
675C2×D4—1188no—
676C2×D4C23×D5914yes—
677C22×C4—28no—
678C22×C4—591no—
679C22×C4—591no—
680C22×C4—598no—
681C22×C4—594no—
682C22×C4—598no—
683C22×C4—598no—
684C22×C4—592no—
685C22×C4—592no—
686C22×C4—592no—
687C22×C4—591no—
688C22×C4—594no—
689C22×C4—592no—
690C22×C4—594no—
691C22×C4—594no—
692C22×C4—5916no—
693C22×C4—1184no—
694C22×C4—11816no—
695C22×C4—1188no—
696C22×C4—1188no—
697C22×C4—1184no—
698C22×C4C23×D5918yes—
699C22×C4C23×D5912yes—
700C22×C4C23×D5912yes—
701C22×C4C23×D5911yescharacteristic
702C22×C4C23×D5914yes—
703C22×C4C23×D5912yes—
704C22×C4C23×D5911yescharacteristic
705C22×C4C23×D5911yescharacteristic
706C4⋊C4—5916no—
707C4⋊C4—598no—
708C4⋊C4—5916no—
709C4⋊C4—598no—
710C4⋊C4—598no—
711C4⋊C4—594no—
712C4⋊C4—594no—
713C4⋊C4—598no—
714C4⋊C4—598no—
715C4⋊C4—598no—
716C4⋊C4—598no—
717C4⋊C4—5916no—
718C4⋊C4—5916no—
719C4⋊C4—5916no—
720C4⋊C4—5916no—
721C4⋊C4—5916no—
722C4⋊C4—5916no—
723C4⋊C4—5916no—
724C4⋊C4—598no—
725C4⋊C4—598no—
726C4⋊C4—598no—
727C4⋊C4C23×D5918yes—
728C4⋊C4C23×D5918yes—
729C4⋊C4C23×D5914yes—
730C4⋊C4C23×D59116yes—
731C4⋊C4C23×D5914yes—
732C4⋊C4C23×D5918yes—
733C22⋊C4—598no—
734C22⋊C4—5916no—
735C22⋊C4—5916no—
736C22⋊C4—598no—
737C22⋊C4—598no—
738C22⋊C4—598no—
739C22⋊C4C23×D5918yes—
740C22⋊C4C23×D59116yes—
741C22⋊C4C23×D59116yes—
742C42—594no—
743C42—598no—
744C42—594no—
745C42—598no—
746C42—598no—
747C42—594no—
748C42—5916no—
749C42—5916no—
750C42—5916no—
751C42—598no—
752C42C23×D5914yes—
753C42C23×D59116yes—
754C42C23×D5918yes—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—594no—
759C23—592no—
760C23—1182no—
761C23—1182no—
762C23C24×D5914yes—
763C23C24×D5911yescharacteristic
764Q8—216no—
765Q8—28no—
766Q8—11816no—
767Q8—11832no—
768Q8—11816no—
769Q8—1188no—
770Q8—1188no—
771D4—28no—
772D4—11816no—
773C2×C4—28no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—216no—
779C2×C4—594no—
780C2×C4—594no—
781C2×C4—592no—
782C2×C4—592no—
783C2×C4—5916no—
784C2×C4—594no—
785C2×C4—594no—
786C2×C4—594no—
787C2×C4—592no—
788C2×C4—598no—
789C2×C4—594no—
790C2×C4—1188no—
791C2×C4—11832no—
792C2×C4—11816no—
793C2×C4—11816no—
794C2×C4—1184no—
795C2×C4—1188no—
796C2×C4—1184no—
797C2×C4—1184no—
798C2×C4—1182no—
799C2×C4—1184no—
800C2×C4—1188no—
801C2×C4#41×D5914yes—
802C2×C4#1427377414yes—
803C2×C4C24×D5914yes—
804C2×C4C24×D5914yes—
805C2×C4C24×D5912yes—
806C2×C4C24×D5918yes—
807C2×C4C24×D5914yes—
808C2×C4C24×D5912yes—
809C2×C4C24×D5912yes—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—48no—
814C22—594no—
815C22—1188no—
816C22—1182no—
817C22—1182no—
818C22C2×#41×D5912yes—
819C222−1+4×D5912yes—
820C22C2×#1427377412yes—
821C22C25×D5911yescharacteristic
822C4—28no—
823C4—22no—
824C4—24no—
825C4—24no—
826C4—24no—
827C4—594no—
828C4—594no—
829C4—1184no—
830C4—1188no—
831C4—1184no—
832C4—1184no—
833C4—1182no—
834C4—1184no—
835C4C2×#41×D5914yes—
836C4C2×#1427377414yes—
837C2—44no—
838C2—1184no—
839C2#2143797614yesdirect product factor
840C2C22×#41×D5911yescharacteristic
841C2C2×2−1+4×D5911yescharacteristic
842C2C22×#1427377411yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#556C2
socleC23×C59C25
prime radicalC22×#11745687C22
hypercenterC2×#556D59
hypocenterC59C2×#3509
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #21437976C2direct (N × H)
2. C2×#16838131C2semidirect
3. C2×#16838130C2semidirect
4. C2×#16838127C2semidirect
5. C2×#16838122C2semidirect
6. C2×#16838121C2semidirect
7. C2×#16838091C2semidirect
8. C2×#16838088C2semidirect
9. C2×#16838086C2semidirect
10. C2×#16838009C2semidirect
12. C2×#16837956C2semidirect
13. C2×#16837955C2semidirect
14. C2×#16837954C2semidirect
15. C2×C4⋊Q8×D59C2semidirect
16. C2×#16837878C2semidirect
18. C2×C59×#556C2semidirect
21. #16838131C22semidirect
22. #16838130C22semidirect
23. #16838127C22semidirect
24. #16838122C22semidirect
25. #16838121C22semidirect
26. #16838091C22semidirect
27. #16838088C22semidirect
28. #16838086C22semidirect
29. #16838009C22semidirect
31. #16837956C22semidirect
32. #16837955C22semidirect
33. #16837954C22semidirect
42. C4⋊Q8×D59C22semidirect
64. #16837878C22semidirect
92. C59×#556C22semidirect
422. C2×#556D59semidirect
435. C2×C59#3509semidirect
447. #556C2×D59semidirect
522. C59C2×#3509semidirect
839. C2#21437976direct (N × H)

Maximal subgroups

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

subgroupindex
#214379762
C2×#168381312
C2×#168381302
C2×#168381272
C2×#168381222
C2×#168381212
C2×#168380912
C2×#168380882
C2×#168380862
C2×#168380092
C2×#168379722
C2×#168379562
C2×#168379552
C2×#168379542
C2×C4⋊Q8×D592
C2×#168378782
C2×C4×#117456872
C2×C59×#5562
C2×#350959