Finite Group Databasebeta

← C2×#21437975 #29497125

Subgroups — C2×#21437975 #29497125

Order 15104.

7022 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437975C2132yesmaximal, direct product factor
2C2×#16838129C212yesmaximal, complemented
3C2×#16838128C212yesmaximal, complemented
4C2×#16838123C212yesmaximal, complemented
5C2×#16838120C212yesmaximal, complemented
6C2×#16838093C212yesmaximal, complemented
7C2×#16838091C212yesmaximal, complemented
8C2×#16838090C212yesmaximal, complemented
9C2×#16838086C212yesmaximal, complemented
10C2×#16838012C212yesmaximal, complemented
11C2×#16838010C212yesmaximal, complemented
12C2×#16837975C212yesmaximal
13C2×#16837959C211yesmaximal, characteristic, complemented
14C2×#16837957C211yesmaximal, characteristic, complemented
15C2×#16837957C211yesmaximal, characteristic, complemented
16C2×#16837957C211yesmaximal, characteristic, complemented
17C2×C4⋊Q8×D59C211yesmaximal, characteristic, complemented
18C2×#16837878C212yesmaximal, complemented
19C2×C4×#11745685C211yesmaximal, characteristic
20C2×C59×#533C211yesmaximal, characteristic, complemented
21C22×#11745685C2211yescharacteristic
22C22×Q8×D59C2212yes—
23#16838129C22132yescomplemented
24#16838128C22132yescomplemented
25#16838123C22132yescomplemented
26#16838120C22132yescomplemented
27#16838093C22132yescomplemented
28#16838091C22132yescomplemented
29#16838090C22132yescomplemented
30#16838086C22132yescomplemented
31#16838012C22132yescomplemented
32#16838010C22132yescomplemented
33#16837975C22132yes—
34#16837959C22116yescomplemented
35#16837957C22116yescomplemented
36#16837957C22116yescomplemented
37#16837957C22116yescomplemented
38C2×#14273727C2211yescharacteristic
39C2×#14273727C2211yescharacteristic
40C2×#14273726C2212yes—
41C2×#14273726C2212yes—
42C2×#14273726C2214yes—
43C2×#14273725C2212yes—
44C4⋊Q8×D59C22116yescomplemented
45C2×#14273722C2214yes—
46C2×#14273721C2214yes—
47C2×#14273720C2214yes—
48C2×#14273720C2214yes—
49C2×#14273719C2214yes—
50C2×#14273719C2212yes—
51C2×#14273718C2212yes—
52C2×#14273718C2214yes—
53C2×#14273718C2212yes—
54C2×#14273718C2212yes—
55C2×#14273717C2214yes—
56C2×#14273717C2214yes—
57C2×#14273713C2214yes—
58C2×#14273712C2214yes—
59C2×#14273709C2214yes—
60C2×#14273707C2212yes—
61C2×#14273707C2212yes—
62C2×#14273707C2212yes—
63C2×#14273706C2212yes—
64C2×#14273706C2212yes—
65C2×#14273703C2212yes—
66C2×#14273703C2212yes—
67C2×#14273703C2212yes—
68#16837878C22132yescomplemented
69C4×#11745685C22116yes—
70C2×Q8×Dic59C2212yes—
71C2×Q8×Dic59C2212yes—
72C2×Q8×Dic59C2212yes—
73C2×C4×Dic118C2212yes—
74C2×C4×Dic118C2211yescharacteristic
75C2×C4×Dic118C2211yescharacteristic
76C2×C4×Dic118C2214yes—
77C2×C4×Dic118C2212yes—
78C2×#14273692C2212yes—
79C2×#14273692C2214yes—
80C2×#14273692C2212yes—
81C2×#14273692C2212yes—
82C2×C4×D236C2211yescharacteristic
83C2×C4×D236C2211yescharacteristic
84C2×C4×C22⋊D59C2211yescharacteristic
85C2×C4×C22⋊D59C2211yescharacteristic
86C2×C4×C22⋊D59C2211yescharacteristic
87C2×C4×C22⋊D59C2211yescharacteristic
88C2×#14273686C2211yescharacteristic
89C2×#14273686C2212yes—
90C2×#14273685C2214yes—
91C2×#14273685C2212yes—
92C2×#14273685C2212yes—
93C2×#14273685C2212yes—
94C2×#14273684C2211yescharacteristic
95C2×#14273684C2211yescharacteristic
96C2×#14273684C2214yes—
97C2×C4⋊C4×D59C2212yes—
98C2×C4⋊C4×D59C2212yes—
99C2×C42×D59C2211yescharacteristic
100C2×C42×D59C2211yescharacteristic
101C59×#533C22116yescomplemented
102C2×C4⋊Q8×C59C2211yescharacteristic
103C2×C4⋊Q8×C59C2211yescharacteristic
104C2×#125×C59C2212yes—
105C2×C22⋊Q8×C59C2212yes—
106C2×C22⋊Q8×C59C2212yes—
107C2×C4×Q8×C59C2212yes—
108C2×C4×Q8×C59C2212yes—
109C2×#117×C59C2212yes—
110C22×C42×C59C2211yescharacteristic
111C2×#11745685—28no—
112C2×#11745685C2318yes—
113C22×Dic118C2312yes—
114C22×Dic118C2312yes—
115C22×Dic118C2314yes—
116C22×Dic118C2311yescharacteristic
117C2×Q8×D59—216no—
118C2×Q8×D59C23116yes—
119C22×D236C2311yescharacteristic
120C22×C22⋊D59C2311yescharacteristic
121C22×C22⋊D59C2311yescharacteristic
122C22×C4×D59C2311yescharacteristic
123C22×C4×D59C2311yescharacteristic
124C22×C4×D59C2311yescharacteristic
125C22×C4×D59C2311yescharacteristic
126C22×C4×D59C2311yescharacteristic
127C22×C4×D59C2314yes—
128C22×C4×D59C2311yescharacteristic
129#14273727C2318yes—
130#14273727C2318yes—
131#14273726C23116yes—
132#14273726C23116yes—
133#14273726C23132yes—
134#14273725C23116yes—
135#14273722C23132yes—
136#14273721C23132yes—
137#14273720C23132yes—
138#14273720C23132yes—
139#14273719C23116yes—
140#14273719C23132yes—
141#14273718C23116yes—
142#14273718C23116yes—
143#14273718C23116yes—
144#14273718C23132yes—
145#14273717C23132yes—
146#14273717C23132yes—
147#14273713C23132yes—
148#14273712C23132yes—
149#14273709C23132yes—
150#14273707C23116yes—
151#14273707C23116yes—
152#14273707C23116yes—
153#14273706C23116yes—
154#14273706C23116yes—
155#14273703C23116yes—
156#14273703C23116yes—
157#14273703C23116yes—
158Q8×Dic59C23116yes—
159Q8×Dic59C23116yes—
160Q8×Dic59C23116yes—
161C4×Dic118C23116yes—
162C4×Dic118C23116yes—
163C4×Dic118C23132yes—
164C4×Dic118C2318yes—
165C4×Dic118C2318yes—
166#14273692C23116yes—
167#14273692C23116yes—
168#14273692C23116yes—
169#14273692C23132yes—
170C4×D236C2318yes—
171C4×D236C2318yes—
172C4×C22⋊D59C2318yes—
173C4×C22⋊D59C2318yes—
174C4×C22⋊D59C2318yes—
175C4×C22⋊D59C2318yes—
176#14273686C23116yes—
177#14273686C2318yes—
178#14273685C23116yes—
179#14273685C23116yes—
180#14273685C23116yes—
181#14273685C23132yes—
182#14273684C2318yes—
183#14273684C23132yes—
184#14273684C2318yes—
185C2×C4⋊Dic59C2312yes—
186C2×C4⋊Dic59C2312yes—
187C2×C4⋊Dic59C2312yes—
188C2×C4⋊Dic59C2312yes—
189C2×C4⋊Dic59C2314yes—
190C2×C4⋊Dic59C2314yes—
191C2×C4⋊Dic59C2314yes—
192C2×C4⋊Dic59C2311yescharacteristic
193C2×C4⋊Dic59C2311yescharacteristic
194C2×Dic59⋊C4C2314yes—
195C2×Dic59⋊C4C2314yes—
196C2×Dic59⋊C4C2314yes—
197C2×Dic59⋊C4C2314yes—
198C2×Dic59⋊C4C2314yes—
199C2×Dic59⋊C4C2311yescharacteristic
200C2×Dic59⋊C4C2314yes—
201C2×Dic59⋊C4C2314yes—
202C2×Dic59⋊C4C2311yescharacteristic
203C2×Dic59⋊C4C2311yescharacteristic
204C2×Dic59⋊C4C2311yescharacteristic
205C4⋊C4×D59C23116yes—
206C4⋊C4×D59C23116yes—
207C2×C22⋊Dic59C2314yes—
208C2×C22⋊Dic59C2311yescharacteristic
209C2×C22⋊Dic59C2311yescharacteristic
210C2×(C2×D59)⋊C4C2314yes—
211C2×(C2×D59)⋊C4C2314yes—
212C2×(C2×D59)⋊C4C2314yes—
213C2×(C2×D59)⋊C4C2311yescharacteristic
214C2×(C2×D59)⋊C4C2311yescharacteristic
215C2×(C2×D59)⋊C4C2311yescharacteristic
216C2×(C2×D59)⋊C4C2311yescharacteristic
217C2×C4×Dic59C2314yes—
218C2×C4×Dic59C2314yes—
219C2×C4×Dic59C2314yes—
220C2×C4×Dic59C2311yescharacteristic
221C2×C4×Dic59C2311yescharacteristic
222C2×C4×Dic59C2311yescharacteristic
223C2×C4×Dic59C2314yes—
224C2×C4×Dic59C2311yescharacteristic
225C2×C4×Dic59C2311yescharacteristic
226C2×C4×Dic59C2311yescharacteristic
227C42×D59C2318yes—
228C42×D59C2318yes—
229C22×Q8×C59C2312yes—
230C22×Q8×C59C2312yes—
231C23×C4×C59C2311yescharacteristic
232C23×C4×C59C2311yescharacteristic
233C23×C4×C59C2311yescharacteristic
234C4⋊Q8×C59C2318yes—
235C4⋊Q8×C59C2318yes—
236#125×C59C23116yes—
237C22⋊Q8×C59C23116yes—
238C22⋊Q8×C59C23116yes—
239C4×Q8×C59C23116yes—
240C4×Q8×C59C23116yes—
241#117×C59C23116yes—
242C2×C4⋊C4×C59C2312yes—
243C2×C4⋊C4×C59C2312yes—
244C2×C4⋊C4×C59C2312yes—
245C2×C4⋊C4×C59C2314yes—
246C2×C4⋊C4×C59C2314yes—
247C2×C4⋊C4×C59C2312yes—
248C2×C22⋊C4×C59C2314yes—
249C2×C42×C59C2311yescharacteristic
250C2×C42×C59C2314yes—
251C2×C42×C59C2311yescharacteristic
252C2×C42×C59C2318yes—
253C2×C42×C59C2311yescharacteristic
254C2×C42×C59C2311yescharacteristic
255C24×C59C2411yescharacteristic
256C23×D59C2411yescharacteristic
257C23×D59C2411yescharacteristic
258C2×Q8×C59—28no—
259C2×Q8×C59—28no—
260C2×Q8×C59C2418yes—
261C2×Q8×C59C2418yes—
262C22×C4×C59—24no—
263C22×C4×C59—24no—
264C22×C4×C59—24no—
265C22×C4×C59C2411yescharacteristic
266C22×C4×C59C2411yescharacteristic
267C22×C4×C59C2411yescharacteristic
268C22×C4×C59C2414yes—
269C22×C4×C59C2414yes—
270C22×C4×C59C2414yes—
271C22×C4×C59C2414yes—
272C22×C4×C59C2414yes—
273C22×C4×C59C2411yescharacteristic
274C22×C4×C59C2411yescharacteristic
275C22×C4×C59C2411yescharacteristic
276C2×C22⋊D59—24no—
277C2×C22⋊D59—24no—
278C2×C22⋊D59C2414yes—
279C2×C22⋊D59C2414yes—
280C22×Dic59C2411yescharacteristic
281C22×Dic59C2411yescharacteristic
282C22×Dic59C2414yes—
283C22×Dic59C2411yescharacteristic
284C22×Dic59C2411yescharacteristic
285C22×Dic59C2414yes—
286C22×Dic59C2411yescharacteristic
287C22×Dic59C2411yescharacteristic
288Q8×D59—264no—
289#11745685—232no—
290C2×D236—24no—
291C2×D236C2414yes—
292C2×C4×D59—216no—
293C2×C4×D59—24no—
294C2×C4×D59—24no—
295C2×C4×D59—24no—
296C2×C4×D59—24no—
297C2×C4×D59—24no—
298C2×C4×D59#4118yes—
299C2×C4×D59C2414yes—
300C2×C4×D59C2414yes—
301C2×C4×D59C2414yes—
302C2×C4×D59C2414yes—
303C2×C4×D59C2414yes—
304C2×C4×D59C24116yes—
305C2×C4×D59C2414yes—
306C2×Dic118—28no—
307C2×Dic118—28no—
308C2×Dic118—216no—
309C2×Dic118—24no—
310C2×Dic118C2418yes—
311C2×Dic118C2418yes—
312C2×Dic118C24116yes—
313C2×Dic118C2414yes—
314C4⋊C4×C59C2418yes—
315C4⋊C4×C59C2418yes—
316C4⋊C4×C59C24116yes—
317C4⋊C4×C59C24116yes—
318C4⋊C4×C59C2418yes—
319C4⋊C4×C59C2418yes—
320C22⋊C4×C59C24116yes—
321C42×C59C2414yes—
322C42×C59C2414yes—
323C42×C59C2414yes—
324C42×C59C2414yes—
325C42×C59C24116yes—
326C22⋊Dic59C2414yes—
327C22⋊Dic59C2414yes—
328C22⋊Dic59C24116yes—
329(C2×D59)⋊C4C2414yes—
330(C2×D59)⋊C4C2414yes—
331(C2×D59)⋊C4C24116yes—
332(C2×D59)⋊C4C2414yes—
333(C2×D59)⋊C4C2414yes—
334(C2×D59)⋊C4C24116yes—
335(C2×D59)⋊C4C24116yes—
336C4⋊Dic59C2418yes—
337C4⋊Dic59C2418yes—
338C4⋊Dic59C2418yes—
339C4⋊Dic59C2418yes—
340C4⋊Dic59C24116yes—
341C4⋊Dic59C2414yes—
342C4⋊Dic59C2414yes—
343C4⋊Dic59C24116yes—
344C4⋊Dic59C24116yes—
345Dic59⋊C4C24116yes—
346Dic59⋊C4C24116yes—
347Dic59⋊C4C2414yes—
348Dic59⋊C4C2414yes—
349Dic59⋊C4C2414yes—
350Dic59⋊C4C2414yes—
351Dic59⋊C4C24116yes—
352Dic59⋊C4C24116yes—
353Dic59⋊C4C24116yes—
354Dic59⋊C4C24116yes—
355Dic59⋊C4C24116yes—
356C4×Dic59C2414yes—
357C4×Dic59C2414yes—
358C4×Dic59C2414yes—
359C4×Dic59C2414yes—
360C4×Dic59C2414yes—
361C4×Dic59C2414yes—
362C4×Dic59C24116yes—
363C4×Dic59C24116yes—
364C4×Dic59C24116yes—
365C4×Dic59C24116yes—
366C23×C59—22no—
367C23×C59—22no—
368C23×C59—22no—
369C23×C59C2512yes—
370C23×C59C2511yescharacteristic
371C22×D59—22no—
372C22×D59—22no—
373C22×D59—22no—
374C22×D59—22no—
375C22×D59—22no—
376C22×D59C2×#4114yes—
377C22×D59C2512yes—
378C22×D59C2512yes—
379Q8×C59—216no—
380Q8×C59—216no—
381C2×C4×C59—28no—
382C2×C4×C59—22no—
383C2×C4×C59—22no—
384C2×C4×C59—22no—
385C2×C4×C59—28no—
386C2×C4×C59—28no—
387C2×C4×C59—28no—
388C2×C4×C59—28no—
389C2×C4×C59C2×#4114yes—
390C2×C4×C592−1+414yes—
391C2×C4×C592−1+414yes—
392C2×C4×C59C2512yes—
393C2×C4×C59C2518yes—
394C2×C4×C59C2518yes—
395C2×C4×C59C2512yes—
396C2×C4×C59C2512yes—
397C2×C4×C59C2512yes—
398C2×C4×C59C2512yes—
399C2×C4×C59C2512yes—
400C22⋊D59—28no—
401C22⋊D59—28no—
402C2×Dic59—28no—
403C2×Dic59—22no—
404C2×Dic59—28no—
405C2×Dic59—22no—
406C2×Dic59—22no—
407C2×Dic59—22no—
408C2×Dic59—22no—
409C2×Dic59C2×#4114yes—
410C2×Dic59C2512yes—
411C2×Dic59C2512yes—
412C2×Dic59C2518yes—
413C2×Dic59C2512yes—
414C2×Dic59C2512yes—
415C2×Dic59C2512yes—
416C2×Dic59C2518yes—
417C2×Dic59C2512yes—
418D236—28no—
419C4×D59—232no—
420C4×D59—28no—
421C4×D59—28no—
422C4×D59—28no—
423C4×D59—28no—
424C4×D59—28no—
425C4×D59C2×#41116yes—
426Dic118—216no—
427Dic118—216no—
428Dic118—28no—
429Dic118—232no—
430C2×#3509—591nomaximal, Sylow
431C22×C59—22no—
432C22×C59—22no—
433C22×C59—22no—
434C22×C59—44no—
435C22×C59C22×#4112yes—
436C22×C59C2×2−1+412yes—
437C22×C59C2×2−1+412yes—
438C22×C59C2611yescharacteristic
439C2×D59—22no—
440C2×D59—22no—
441C2×D59—28no—
442C2×D59—22no—
443C2×D59—22no—
444C2×D59—22no—
445C2×D59—44no—
446C2×D59C22×#4114yes—
447C4×C59—28no—
448C4×C59—22no—
449C4×C59—22no—
450C4×C59—22no—
451C4×C59—28no—
452C4×C59C22×#4114yes—
453C4×C59C2×2−1+414yes—
454C4×C59C2×2−1+414yes—
455Dic59—28no—
456Dic59—22no—
457Dic59—28no—
458Dic59—22no—
459Dic59—22no—
460Dic59—22no—
461Dic59—22no—
462Dic59C22×#4114yes—
463#3509—5932no—
464C2×#557—592no—
465C2×#557—592no—
466C2×#556—592no—
467C2×#556—592no—
468C2×#552—592no—
469C2×#552—592no—
470C2×#552—592no—
471C2×#552—592no—
472C2×#541—592no—
473C2×#541—592no—
474C2×#536—592no—
475C2×#533—591no—
476C2×#533—591no—
477C2×#533—591no—
478C2×#533—591no—
479C2×#533D5911yescharacteristic, complemented
480C22×C4⋊Q8—591no—
481C2×#519—592no—
482C2×C4×#41—591no—
483C2×C59—42no—
484C2×C59#350914yescomplemented
485C2×C59C23×#4111yescharacteristic
486C2×C59C22×2−1+411yescharacteristic
487C2×C59C22×2−1+411yescharacteristic
488D59—24no—
489D59—42no—
490C22×#41—591no—
491C23×Q8—592no—
492#557—5932no—
493#557—5932no—
494#556—5932no—
495#556—5932no—
496#552—5932no—
497#552—5932no—
498#552—5932no—
499#552—5932no—
500#541—5932no—
501#541—5932no—
502#536—5932no—
503#533—5916no—
504#533—5916no—
505#533—5916no—
506#533—5916no—
507#533C2×D59116yescomplemented
508C2×C4⋊Q8—592no—
509C2×C4⋊Q8—5916no—
510C2×C4⋊Q8—592no—
511C2×C4⋊Q8—592no—
512C2×C4⋊Q8—594no—
513C2×C4⋊Q8—591no—
514C2×C4⋊Q8—591no—
515C2×C4⋊Q8C2×D5911yescharacteristic
516C2×C4⋊Q8C2×D5911yescharacteristic
517C2×#126—594no—
518C2×#126—594no—
519C2×#126—594no—
520C2×#126—594no—
521C2×#125—594no—
522C2×#125—594no—
523C2×#125—592no—
524C2×#125—592no—
525C2×#125—592no—
526C2×#125—594no—
527C2×#125—592no—
528C2×#125—594no—
529C2×#125C2×D5912yes—
530C2×#124—594no—
531C2×#123—594no—
532C2×#123—594no—
533C2×C22⋊Q8—592no—
534C2×C22⋊Q8—592no—
535C2×C22⋊Q8—592no—
536C2×C22⋊Q8—592no—
537C2×C22⋊Q8—592no—
538C2×C22⋊Q8—592no—
539C2×C22⋊Q8—592no—
540C2×C22⋊Q8—592no—
541C2×C22⋊Q8C2×D5912yes—
542C2×C22⋊Q8C2×D5912yes—
543#519—5932no—
544C4×#41—5916no—
545C2×C4×Q8—592no—
546C2×C4×Q8—592no—
547C2×C4×Q8—592no—
548C2×C4×Q8—592no—
549C2×C4×Q8—594no—
550C2×C4×Q8—592no—
551C2×C4×Q8—592no—
552C2×C4×Q8—591no—
553C2×C4×Q8—591no—
554C2×C4×Q8—592no—
555C2×C4×Q8—594no—
556C2×C4×Q8—592no—
557C2×C4×Q8C2×D5912yes—
558C2×C4×Q8C2×D5912yes—
559C2×C4×D4—591no—
560C2×C4×D4—591no—
561C2×C4×D4—591no—
562C2×C4×D4—591no—
563C2×C4×D4—591no—
564C2×C4×D4—591no—
565C2×#117—591no—
566C2×#117—592no—
567C2×#117—592no—
568C2×#117—594no—
569C2×#117—592no—
570C2×#117—592no—
571C2×#117—591no—
572C2×#117—591no—
573C2×#117—594no—
574C2×#117C2×D5912yes—
575C22×C4⋊C4—592no—
576C22×C4⋊C4—592no—
577C22×C42—591no—
578C22×C42—591no—
579C22×C42C2×D5911yescharacteristic
580C59C2×#350911yescharacteristic, complemented, Sylow
581C2×#41—598no—
582C2×#41—1188no—
583C22×Q8—5916no—
584C22×Q8—592no—
585C22×Q8—592no—
586C22×Q8—594no—
587C22×Q8—591no—
588C22×Q8—11816no—
589C22×Q8C22×D5912yes—
590C22×Q8C22×D5912yes—
591C22×D4—591no—
592C22×D4—591no—
593C22×D4—591no—
594C23×C4—591no—
595C23×C4—594no—
596C23×C4—591no—
597C23×C4—591no—
598C23×C4—591no—
599C23×C4—591no—
600C23×C4—591no—
601C23×C4C22×D5911yescharacteristic
602C23×C4C22×D5911yescharacteristic
603C23×C4C22×D5911yescharacteristic
604C4⋊Q8—5916no—
605C4⋊Q8—5916no—
606C4⋊Q8—5916no—
607C4⋊Q8—5932no—
608C4⋊Q8—598no—
609C4⋊Q8—598no—
610C4⋊Q8C22×D5918yes—
611C4⋊Q8C22×D5918yes—
612#126—5932no—
613#126—5932no—
614#126—5932no—
615#126—5932no—
616#125—5916no—
617#125—5916no—
618#125—5916no—
619#125—5932no—
620#125—5932no—
621#125—5932no—
622#125—5916no—
623#125—5932no—
624#125C22×D59116yes—
625#124—5932no—
626#123—5932no—
627#123—5932no—
628C22⋊Q8—5916no—
629C22⋊Q8—5916no—
630C22⋊Q8—5916no—
631C22⋊Q8—5916no—
632C22⋊Q8—5916no—
633C22⋊Q8—5916no—
634C22⋊Q8—5916no—
635C22⋊Q8—5916no—
636C22⋊Q8C22×D59116yes—
637C22⋊Q8C22×D59116yes—
638C4×Q8—5916no—
639C4×Q8—5916no—
640C4×Q8—5916no—
641C4×Q8—5916no—
642C4×Q8—5932no—
643C4×Q8—5916no—
644C4×Q8—5916no—
645C4×Q8—598no—
646C4×Q8—598no—
647C4×Q8—5916no—
648C4×Q8—5932no—
649C4×Q8—5916no—
650C4×Q8C22×D59116yes—
651C4×Q8C22×D59116yes—
652C4×D4—598no—
653C4×D4—598no—
654C4×D4—598no—
655C4×D4—598no—
656C4×D4—598no—
657C4×D4—598no—
658#117—598no—
659#117—5916no—
660#117—5916no—
661#117—5932no—
662#117—5916no—
663#117—5916no—
664#117—598no—
665#117—598no—
666#117—5932no—
667#117C22×D59116yes—
668C2×C4⋊C4—592no—
669C2×C4⋊C4—592no—
670C2×C4⋊C4—594no—
671C2×C4⋊C4—594no—
672C2×C4⋊C4—592no—
673C2×C4⋊C4—591no—
674C2×C4⋊C4—591no—
675C2×C4⋊C4—591no—
676C2×C4⋊C4—591no—
677C2×C4⋊C4—591no—
678C2×C4⋊C4—591no—
679C2×C4⋊C4—592no—
680C2×C4⋊C4—594no—
681C2×C4⋊C4—594no—
682C2×C4⋊C4—594no—
683C2×C4⋊C4—594no—
684C2×C4⋊C4—594no—
685C2×C4⋊C4—594no—
686C2×C4⋊C4—594no—
687C2×C4⋊C4—594no—
688C2×C4⋊C4—5916no—
689C2×C4⋊C4—5916no—
690C2×C4⋊C4C22×D5912yes—
691C2×C4⋊C4C22×D5912yes—
692C2×C4⋊C4C22×D5912yes—
693C2×C4⋊C4C22×D5912yes—
694C2×C4⋊C4C22×D5914yes—
695C2×C4⋊C4C22×D5914yes—
696C2×C22⋊C4—591no—
697C2×C22⋊C4—591no—
698C2×C22⋊C4—594no—
699C2×C22⋊C4—591no—
700C2×C22⋊C4—591no—
701C2×C22⋊C4—594no—
702C2×C22⋊C4—591no—
703C2×C22⋊C4—591no—
704C2×C22⋊C4—594no—
705C2×C22⋊C4—594no—
706C2×C22⋊C4C22×D5914yes—
707C2×C42—591no—
708C2×C42—594no—
709C2×C42—594no—
710C2×C42—594no—
711C2×C42—591no—
712C2×C42—594no—
713C2×C42—591no—
714C2×C42—591no—
715C2×C42—591no—
716C2×C42—591no—
717C2×C42—598no—
718C2×C42—598no—
719C2×C42C22×D5911yescharacteristic
720C2×C42C22×D5914yes—
721C2×C42C22×D5911yescharacteristic
722C2×C42C22×D5911yescharacteristic
723C2×C42C22×D5918yes—
724C2×C42C22×D5911yescharacteristic
725C24—591no—
726C24—591no—
727C24C23×D5911yescharacteristic
728#41—11832no—
729C2×Q8—28no—
730C2×Q8—28no—
731C2×Q8—598no—
732C2×Q8—598no—
733C2×Q8—5916no—
734C2×Q8—594no—
735C2×Q8—11816no—
736C2×Q8—1184no—
737C2×Q8—11864no—
738C2×Q8—1188no—
739C2×Q8—1188no—
740C2×Q8C23×D5918yes—
741C2×Q8C23×D5918yes—
742C2×D4—594no—
743C2×D4—594no—
744C2×D4—594no—
745C2×D4—1184no—
746C2×D4—1184no—
747C2×D4—1184no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—591no—
752C22×C4—598no—
753C22×C4—594no—
754C22×C4—591no—
755C22×C4—591no—
756C22×C4—594no—
757C22×C4—591no—
758C22×C4—591no—
759C22×C4—594no—
760C22×C4—591no—
761C22×C4—594no—
762C22×C4—594no—
763C22×C4—594no—
764C22×C4—594no—
765C22×C4—594no—
766C22×C4—5916no—
767C22×C4—11816no—
768C22×C4—1184no—
769C22×C4—1184no—
770C22×C4—1184no—
771C22×C4—1184no—
772C22×C4—1184no—
773C22×C4C23×D5914yes—
774C22×C4C23×D5914yes—
775C22×C4C23×D5914yes—
776C22×C4C23×D5911yescharacteristic
777C22×C4C23×D5914yes—
778C22×C4C23×D5914yes—
779C22×C4C23×D5911yescharacteristic
780C22×C4C23×D5911yescharacteristic
781C22×C4C23×D5911yescharacteristic
782C22×C4C23×D5911yescharacteristic
783C22×C4C23×D5911yescharacteristic
784C4⋊C4—598no—
785C4⋊C4—598no—
786C4⋊C4—5916no—
787C4⋊C4—5916no—
788C4⋊C4—598no—
789C4⋊C4—594no—
790C4⋊C4—594no—
791C4⋊C4—594no—
792C4⋊C4—594no—
793C4⋊C4—594no—
794C4⋊C4—594no—
795C4⋊C4—598no—
796C4⋊C4—5916no—
797C4⋊C4—5916no—
798C4⋊C4—5916no—
799C4⋊C4—5916no—
800C4⋊C4—5916no—
801C4⋊C4—5916no—
802C4⋊C4—5916no—
803C4⋊C4—5916no—
804C4⋊C4C23×D5918yes—
805C4⋊C4C23×D5918yes—
806C4⋊C4C23×D5918yes—
807C4⋊C4C23×D5918yes—
808C4⋊C4C23×D59116yes—
809C4⋊C4C23×D59116yes—
810C22⋊C4—594no—
811C22⋊C4—594no—
812C22⋊C4—5916no—
813C22⋊C4—594no—
814C22⋊C4—594no—
815C22⋊C4—5916no—
816C22⋊C4—594no—
817C22⋊C4—594no—
818C22⋊C4—5916no—
819C22⋊C4—5916no—
820C22⋊C4C23×D59116yes—
821C42—594no—
822C42—594no—
823C42—594no—
824C42—594no—
825C42—594no—
826C42—594no—
827C42—5916no—
828C42—5916no—
829C42—5916no—
830C42—5916no—
831C42C23×D5914yes—
832C42C23×D5914yes—
833C42C23×D5914yes—
834C42C23×D5914yes—
835C42C23×D59116yes—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—594no—
840C23—592no—
841C23—592no—
842C23—1182no—
843C23—1182no—
844C23—1182no—
845C23—1182no—
846C23—1182no—
847C23C24×D5912yes—
848C23C24×D5911yescharacteristic
849Q8—216no—
850Q8—216no—
851Q8—11832no—
852Q8—1188no—
853Q8—11816no—
854Q8—11816no—
855D4—1188no—
856D4—1188no—
857D4—1188no—
858C2×C4—22no—
859C2×C4—28no—
860C2×C4—22no—
861C2×C4—28no—
862C2×C4—22no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—28no—
866C2×C4—594no—
867C2×C4—592no—
868C2×C4—5916no—
869C2×C4—592no—
870C2×C4—592no—
871C2×C4—598no—
872C2×C4—592no—
873C2×C4—592no—
874C2×C4—598no—
875C2×C4—592no—
876C2×C4—11832no—
877C2×C4—1182no—
878C2×C4—1188no—
879C2×C4—1182no—
880C2×C4—1182no—
881C2×C4—1182no—
882C2×C4—1182no—
883C2×C4—1188no—
884C2×C4—1188no—
885C2×C4—1188no—
886C2×C4—1188no—
887C2×C4—1188no—
888C2×C4—1188no—
889C2×C4#41×D5914yes—
890C2×C4#1427377414yes—
891C2×C4#1427377514yes—
892C2×C4C24×D5912yes—
893C2×C4C24×D5918yes—
894C2×C4C24×D5918yes—
895C2×C4C24×D5912yes—
896C2×C4C24×D5912yes—
897C2×C4C24×D5912yes—
898C2×C4C24×D5912yes—
899C2×C4C24×D5912yes—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—44no—
904C22—594no—
905C22—1188no—
906C22—1182no—
907C22—1182no—
908C22—1182no—
909C22—1182no—
910C22—1182no—
911C22—2364no—
912C22C2×#41×D5912yes—
913C22C2×#1427377412yes—
914C22C2×#1427377512yes—
915C22C25×D5911yescharacteristic
916C4—22no—
917C4—28no—
918C4—22no—
919C4—28no—
920C4—22no—
921C4—594no—
922C4—1182no—
923C4—1188no—
924C4—1182no—
925C4—1182no—
926C4—1182no—
927C4—1182no—
928C4—1188no—
929C4C2×#41×D5914yes—
930C4C2×#1427377414yes—
931C4C2×#1427377514yes—
932C2—42no—
933C2—1184no—
934C2—2362no—
935C2#2143797514yesdirect product factor
936C2C22×#41×D5911yescharacteristic
937C2C22×#1427377411yescharacteristic
938C2C22×#1427377511yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#533C2
socleC23×C59C25
prime radicalC22×#11745685C22
hypercenterC2×#533D59
hypocenterC59C2×#3509
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #21437975C2direct (N × H)
2. C2×#16838129C2semidirect
3. C2×#16838128C2semidirect
4. C2×#16838123C2semidirect
5. C2×#16838120C2semidirect
6. C2×#16838093C2semidirect
7. C2×#16838091C2semidirect
8. C2×#16838090C2semidirect
9. C2×#16838086C2semidirect
10. C2×#16838012C2semidirect
11. C2×#16838010C2semidirect
13. C2×#16837959C2semidirect
14. C2×#16837957C2semidirect
15. C2×#16837957C2semidirect
16. C2×#16837957C2semidirect
17. C2×C4⋊Q8×D59C2semidirect
18. C2×#16837878C2semidirect
20. C2×C59×#533C2semidirect
23. #16838129C22semidirect
24. #16838128C22semidirect
25. #16838123C22semidirect
26. #16838120C22semidirect
27. #16838093C22semidirect
28. #16838091C22semidirect
29. #16838090C22semidirect
30. #16838086C22semidirect
31. #16838012C22semidirect
32. #16838010C22semidirect
34. #16837959C22semidirect
35. #16837957C22semidirect
36. #16837957C22semidirect
37. #16837957C22semidirect
44. C4⋊Q8×D59C22semidirect
68. #16837878C22semidirect
101. C59×#533C22semidirect
479. C2×#533D59semidirect
484. C2×C59#3509semidirect
507. #533C2×D59semidirect
580. C59C2×#3509semidirect
935. C2#21437975direct (N × H)

Maximal subgroups

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

subgroupindex
#214379752
C2×#168381292
C2×#168381282
C2×#168381232
C2×#168381202
C2×#168380932
C2×#168380912
C2×#168380902
C2×#168380862
C2×#168380122
C2×#168380102
C2×#168379752
C2×#168379592
C2×#168379572
C2×C4⋊Q8×D592
C2×#168378782
C2×C4×#117456852
C2×C59×#5332
C2×#350959