Finite Group Databasebeta

← C2×#21437849 #29497121

Subgroups — C2×#21437849 #29497121

Order 15104.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437849C2132yesmaximal, direct product factor
2C2×#16838120C212yesmaximal, complemented
3C2×#16838107C212yesmaximal, complemented
4C2×#16838092C214yesmaximal, complemented
5C2×#16838091C212yesmaximal, complemented
6C2×#16838087C212yesmaximal, complemented
7C2×#16838081C214yesmaximal, complemented
8C2×#16838033C211yesmaximal, characteristic, complemented
9C2×#16838017C212yesmaximal, complemented
10C2×#16838010C212yesmaximal, complemented
11C2×#16837973C211yesmaximal, characteristic, complemented
12C2×#16837956C212yesmaximal, complemented
13C2×#16837934C212yesmaximal, complemented
14C2×#16837909C211yesmaximal, characteristic
15C22×#14273707C211yesmaximal, characteristic, complemented
16C2×#16837879C211yesmaximal, characteristic, complemented
17C2×#117×D59C211yesmaximal, characteristic, complemented
18C2×C59×#520C211yesmaximal, characteristic, complemented
19C23×Dic118C2211yescharacteristic
20C23×C4×D59C2211yescharacteristic
21#16838120C22132yescomplemented
22#16838107C22132yescomplemented
23#16838092C22164yescomplemented
24#16838091C22132yescomplemented
25#16838087C22132yescomplemented
26#16838081C22164yescomplemented
27#16838033C22116yescomplemented
28#16838017C22132yescomplemented
29#16838010C22132yescomplemented
30#16837973C22116yescomplemented
31#16837956C22132yescomplemented
32C2×#14273726C2212yescomplemented
33C2×#14273726C2212yescomplemented
34C2×#14273725C2212yescomplemented
35#16837934C22132yescomplemented
36C2×#14273722C2214yes—
37C2×#14273721C2214yes—
38C2×#14273720C2214yescomplemented
39C2×#14273720C2214yescomplemented
40C2×#14273719C2214yescomplemented
41C2×#14273718C2212yescomplemented
42C2×#14273718C2212yescomplemented
43C2×#14273717C2214yescomplemented
44C2×#14273717C2214yescomplemented
45C2×#14273714C2212yescomplemented
46C2×#14273713C2214yes—
47#16837909C22116yes—
48C2×#14273710C2214yes—
49C2×#14273709C2214yes—
50C2×#14273708C2212yes—
51C2×#14273708C2214yes—
52C2×#14273707C2212yes—
53C2×#14273707C2212yes—
54C2×#14273707C2212yes—
55C2×#14273707C2212yes—
56C2×#14273707C22116yescomplemented
57C2×#14273706C2214yes—
58C2×#14273706C2214yescomplemented
59C2×#14273706C2212yescomplemented
60C2×#14273706C2212yescomplemented
61C2×#14273705C2214yes—
62C2×#14273703C2211yescharacteristic
63C2×#14273703C2211yescharacteristic
64C2×#14273698C2211yescharacteristic
65C2×#14273698C2211yescharacteristic
66C2×#14273695C2212yes—
67#16837879C22116yescomplemented
68C2×C4×Dic118C2212yescomplemented
69C2×C4×Dic118C2212yescomplemented
70C2×C4×Dic118C2214yescomplemented
71C2×#14273692C2212yescomplemented
72C2×#14273692C2212yescomplemented
73C2×C4×C22⋊D59C2212yes—
74C2×C4×C22⋊D59C2212yes—
75C2×C4×C22⋊D59C2214yes—
76C2×#14273686C2211yescharacteristic
77C2×#14273686C2211yescharacteristic
78C2×#14273686C2214yescomplemented
79C2×#14273685C2211yescharacteristic
80C2×#14273685C2211yescharacteristic
81C2×#14273684C2212yes—
82C2×#14273684C2214yes—
83C2×#14273683C2212yes—
84C2×#14273683C2214yes—
85#117×D59C22116yescomplemented
86C22×C4⋊Dic59C2212yes—
87C2×C4⋊C4×D59C2211yescharacteristic
88C2×C4⋊C4×D59C2211yescharacteristic
89C22×(C2×D59)⋊C4C2212yes—
90C2×C22⋊C4×D59C2212yes—
91C2×C42×D59C2212yes—
92C22×#41×C59C2211yescharacteristic
93C59×#520C22116yescomplemented
94C2×C4×Q8×C59C2212yescomplemented
95C2×C4×D4×C59C2214yes—
96C2×C4×D4×C59C2212yescomplemented
97C2×#117×C59C2211yescharacteristic
98C2×#117×C59C2212yescomplemented
99C22×C4⋊C4×C59C2211yescharacteristic
100C22×C4⋊C4×C59C2212yescomplemented
101C24×D59C2311yescharacteristic
102C22×Dic118—28no—
103C22×Dic118C2312yes—
104C22×Dic118C2312yes—
105C22×Dic118C2318yes—
106C22×Dic118C2314yes—
107C22×C22⋊D59C2312yes—
108C22×C22⋊D59C2312yes—
109C23×Dic59C2311yescharacteristic
110C23×Dic59C2312yes—
111C22×C4×D59—28no—
112C22×C4×D59C2311yescharacteristic
113C22×C4×D59C2311yescharacteristic
114C22×C4×D59C2311yescharacteristic
115C22×C4×D59C2311yescharacteristic
116C22×C4×D59C2318yes—
117C22×C4×D59C2312yes—
118C22×C4×D59C2312yes—
119#14273726C23116yescomplemented
120#14273726C23116yescomplemented
121#14273725C23116yescomplemented
122#14273722C23132yes—
123#14273721C23132yes—
124#14273720C23132yescomplemented
125#14273720C23132yescomplemented
126#14273719C23132yescomplemented
127#14273718C23116yescomplemented
128#14273718C23116yescomplemented
129#14273717C23132yescomplemented
130#14273717C23132yescomplemented
131#14273714C23116yescomplemented
132#14273713C23132yes—
133#14273710C23132yes—
134#14273709C23132yes—
135#14273708C23116yes—
136#14273708C23132yes—
137#14273707C23116yes—
138#14273707C23116yes—
139#14273707C23116yes—
140#14273707C23116yes—
141#14273706C23132yes—
142#14273706C23116yescomplemented
143#14273706C23116yescomplemented
144#14273706C23132yescomplemented
145#14273705C23132yes—
146#14273703C2318yes—
147#14273703C2318yes—
148#14273698C2318yes—
149#14273698C2318yes—
150#14273695C23116yes—
151C4×Dic118C23116yescomplemented
152C4×Dic118C23116yescomplemented
153C4×Dic118C23132yescomplemented
154#14273692C23116yescomplemented
155#14273692C23116yescomplemented
156C4×C22⋊D59C23116yes—
157C4×C22⋊D59C23116yes—
158C4×C22⋊D59C23132yes—
159#14273686C2318yes—
160#14273686C2318yes—
161#14273686C23132yescomplemented
162#14273685C2318yes—
163#14273685C2318yes—
164#14273684C23132yes—
165#14273684C23116yes—
166#14273683C23132yes—
167#14273683C23116yes—
168C2×C4⋊Dic59C2311yescharacteristic
169C2×C4⋊Dic59C2311yescharacteristic
170C2×C4⋊Dic59C2314yes—
171C2×C4⋊Dic59C2311yescharacteristic
172C2×C4⋊Dic59C2311yescharacteristic
173C2×C4⋊Dic59C2314yes—
174C2×C4⋊Dic59C2314yes—
175C2×C4⋊Dic59C23116yes—
176C2×Dic59⋊C4C2312yes—
177C2×Dic59⋊C4C2312yes—
178C2×Dic59⋊C4C2314yes—
179C2×Dic59⋊C4C2314yes—
180C2×Dic59⋊C4C2314yes—
181C2×Dic59⋊C4C2314yes—
182C2×Dic59⋊C4C2312yes—
183C2×Dic59⋊C4C2314yes—
184C2×Dic59⋊C4C2314yes—
185C2×Dic59⋊C4C2312yes—
186C4⋊C4×D59C2318yes—
187C4⋊C4×D59C2318yes—
188C2×C22⋊Dic59C2312yes—
189C2×C22⋊Dic59C2312yes—
190C2×C22⋊Dic59C2312yes—
191C2×C22⋊Dic59C2312yes—
192C2×C22⋊Dic59C2314yes—
193C2×C22⋊Dic59C2314yes—
194C2×(C2×D59)⋊C4C2312yes—
195C2×(C2×D59)⋊C4C2312yes—
196C2×(C2×D59)⋊C4C2314yes—
197C2×(C2×D59)⋊C4C2314yes—
198C2×(C2×D59)⋊C4C23116yes—
199C2×(C2×D59)⋊C4C2312yes—
200C2×(C2×D59)⋊C4C2312yes—
201C22⋊C4×D59C23116yes—
202C2×C4×Dic59C2314yes—
203C2×C4×Dic59C2312yes—
204C2×C4×Dic59C2312yes—
205C2×C4×Dic59C2314yes—
206C2×C4×Dic59C2312yes—
207C2×C4×Dic59C2312yes—
208C42×D59C23116yes—
209C2×#41×C59—28no—
210C2×#41×C59C2318yes—
211C22×Q8×C59C2311yescharacteristic
212C22×D4×C59C2311yescharacteristic
213C22×D4×C59C2312yes—
214C23×C4×C59C2312yes—
215C23×C4×C59C2312yes—
216C23×C4×C59C2314yes—
217C23×C4×C59C2311yescharacteristic
218C4×Q8×C59C23116yescomplemented
219C4×D4×C59C23132yes—
220C4×D4×C59C23116yescomplemented
221#117×C59C2318yes—
222#117×C59C23116yescomplemented
223C2×C4⋊C4×C59C2314yes—
224C2×C4⋊C4×C59C2312yes—
225C2×C4⋊C4×C59C2312yes—
226C2×C4⋊C4×C59C2318yes—
227C2×C4⋊C4×C59C2311yescharacteristic
228C2×C4⋊C4×C59C2311yescharacteristic
229C2×C4⋊C4×C59C23116yescomplemented
230C2×C22⋊C4×C59C2314yes—
231C2×C22⋊C4×C59C2312yes—
232C2×C42×C59C2314yes—
233C2×C42×C59C2312yes—
234C24×C59C2412yes—
235C24×C59C2411yescharacteristic
236C23×D59—24no—
237C23×D59—24no—
238C23×D59—42no—
239C23×D59C2411yescharacteristic
240C23×D59C2414yes—
241C23×D59C2411yescharacteristic
242#41×C59—232no—
243C2×Q8×C59—24no—
244C2×Q8×C59C2414yes—
245C2×D4×C59—28no—
246C2×D4×C59—24no—
247C2×D4×C59C2418yes—
248C2×D4×C59C2414yes—
249C22×C4×C59—28no—
250C22×C4×C59—44no—
251C22×C4×C59—48no—
252C22×C4×C59#4118yes—
253C22×C4×C59C2412yes—
254C22×C4×C59C2412yes—
255C22×C4×C59C2412yes—
256C22×C4×C59C2414yes—
257C22×C4×C59C2418yes—
258C22×C4×C59C2418yes—
259C22×C4×C59C24116yes—
260C22×C4×C59C2411yescharacteristic
261C22×C4×C59C2411yescharacteristic
262C22×C4×C59C2414yes—
263C2×C22⋊D59—28no—
264C2×C22⋊D59—44no—
265C2×C22⋊D59C2418yes—
266C2×C22⋊D59C2418yes—
267C22×Dic59—24no—
268C22×Dic59—28no—
269C22×Dic59C2411yescharacteristic
270C22×Dic59C2412yes—
271C22×Dic59C2412yes—
272C22×Dic59C2414yes—
273C22×Dic59C2412yes—
274C22×Dic59C2412yes—
275C22×Dic59C2418yes—
276C22×Dic59C2411yescharacteristic
277C22×Dic59C2414yes—
278C2×C4×D59—28no—
279C2×C4×D59—24no—
280C2×C4×D59—24no—
281C2×C4×D59—24no—
282C2×C4×D59—24no—
283C2×C4×D59—232no—
284C2×C4×D59—44no—
285C2×C4×D59C2414yes—
286C2×C4×D59C2418yes—
287C2×C4×D59C2414yes—
288C2×C4×D59C2414yes—
289C2×C4×D59C2414yes—
290C2×C4×D59C2418yes—
291C2×Dic118—28no—
292C2×Dic118—28no—
293C2×Dic118—232no—
294C2×Dic118—48no—
295C2×Dic118C2418yes—
296C2×Dic118C2418yes—
297C2×Dic118C24116yes—
298C4⋊C4×C59C2418yes—
299C4⋊C4×C59C2418yes—
300C4⋊C4×C59C2414yes—
301C4⋊C4×C59C24116yes—
302C4⋊C4×C59C2414yes—
303C22⋊C4×C59C2418yes—
304C22⋊C4×C59C24116yes—
305C42×C59C2418yes—
306C42×C59C24116yes—
307C22⋊Dic59C2418yes—
308C22⋊Dic59C2418yes—
309C22⋊Dic59C2418yes—
310C22⋊Dic59C24116yes—
311C22⋊Dic59C2418yes—
312C22⋊Dic59C24116yes—
313(C2×D59)⋊C4C2418yes—
314(C2×D59)⋊C4C2418yes—
315(C2×D59)⋊C4C24116yes—
316(C2×D59)⋊C4C24116yes—
317(C2×D59)⋊C4C2418yes—
318(C2×D59)⋊C4C2418yes—
319C4⋊Dic59C2414yes—
320C4⋊Dic59C2414yes—
321C4⋊Dic59C24116yes—
322C4⋊Dic59C24116yes—
323C4⋊Dic59C2414yes—
324C4⋊Dic59C2414yes—
325C4⋊Dic59C24116yes—
326Dic59⋊C4C2418yes—
327Dic59⋊C4C2418yes—
328Dic59⋊C4C24116yes—
329Dic59⋊C4C24116yes—
330Dic59⋊C4C24116yes—
331Dic59⋊C4C24116yes—
332Dic59⋊C4C2418yes—
333Dic59⋊C4C2418yes—
334Dic59⋊C4C24116yes—
335Dic59⋊C4C24116yes—
336C4×Dic59C2418yes—
337C4×Dic59C2418yes—
338C4×Dic59C2418yes—
339C4×Dic59C24116yes—
340C4×Dic59C24116yes—
341C4×Dic59C2418yes—
342C23×C59—22no—
343C23×C59—22no—
344C23×C59—24no—
345C23×C59—24no—
346C23×C59—24no—
347C23×C59C2×#4114yes—
348C23×C59C2514yes—
349C23×C59C2512yes—
350C23×C59C2511yescharacteristic
351C22×D59—22no—
352C22×D59—22no—
353C22×D59—28no—
354C22×D59—22no—
355C22×D59—22no—
356C22×D59—22no—
357C22×D59—28no—
358C22×D59—44no—
359C22×D59—416no—
360C22×D592−1+414yes—
361C22×D59C2512yes—
362C22×D59C2512yes—
363Q8×C59—28no—
364D4×C59—216no—
365D4×C59—28no—
366C2×C4×C59—24no—
367C2×C4×C59—24no—
368C2×C4×C59—28no—
369C2×C4×C59—24no—
370C2×C4×C59—216no—
371C2×C4×C59—48no—
372C2×C4×C59—416no—
373C2×C4×C59C2×#4114yes—
374C2×C4×C59C2×#4114yes—
375C2×C4×C59C2×#41116yes—
376C2×C4×C59C2514yes—
377C2×C4×C59C2514yes—
378C2×C4×C59C2514yes—
379C2×C4×C59C2518yes—
380C2×C4×C59C2512yes—
381C2×C4×C59C2512yes—
382C22⋊D59—216no—
383C22⋊D59—48no—
384C2×Dic59—216no—
385C2×Dic59—28no—
386C2×Dic59—28no—
387C2×Dic59—22no—
388C2×Dic59—22no—
389C2×Dic59—24no—
390C2×Dic59—24no—
391C2×Dic59—24no—
392C2×Dic59—24no—
393C2×Dic59C2512yes—
394C2×Dic59C2514yes—
395C2×Dic59C2514yes—
396C2×Dic59C2514yes—
397C2×Dic59C2514yes—
398C2×Dic59C2518yes—
399C2×Dic59C2512yes—
400C4×D59—216no—
401C4×D59—28no—
402C4×D59—28no—
403C4×D59—28no—
404C4×D59—28no—
405C4×D59—48no—
406Dic118—216no—
407Dic118—216no—
408Dic118—416no—
409C2×#3495—591nomaximal, Sylow
410C22×C59—22no—
411C22×C59—22no—
412C22×C59—28no—
413C22×C59—24no—
414C22×C59—24no—
415C22×C59—24no—
416C22×C59—48no—
417C22×C59C22×#4114yes—
418C22×C59C22×#4112yes—
419C22×C59C2×2−1+412yes—
420C22×C59#58512yes—
421C22×C59C2611yescharacteristic
422C2×D59—22no—
423C2×D59—22no—
424C2×D59—28no—
425C2×D59—22no—
426C2×D59—22no—
427C2×D59—22no—
428C2×D59—416no—
429C2×D59—44no—
430C2×D59C2×2−1+414yes—
431C4×C59—24no—
432C4×C59—24no—
433C4×C59—28no—
434C4×C59—24no—
435C4×C59C22×#4114yes—
436C4×C59C22×#4114yes—
437Dic59—28no—
438Dic59—22no—
439Dic59—22no—
440Dic59—24no—
441Dic59—24no—
442Dic59—24no—
443Dic59—24no—
444#3495—5932no—
445C2×#556—592no—
446C2×#554—592no—
447C2×#552—594no—
448C2×#552—592no—
449C2×#552—592no—
450C2×#551—594no—
451C2×#544—591no—
452C2×#542—592no—
453C2×#541—592no—
454C2×#536—591no—
455C2×#533—592no—
456C2×#529—592no—
457C2×#525—591no—
458C22×C22⋊Q8—591no—
459C2×#520D5911yescharacteristic, complemented
460C2×#519—591no—
461C22×#117—591no—
462C2×C59—24no—
463C2×C59—44no—
464C2×C59#349514yescomplemented
465C2×C59C23×#4111yescharacteristic
466C2×C59C22×2−1+411yescharacteristic
467C2×C59C2×#58511yescharacteristic
468D59—24no—
469D59—42no—
470C22×#41C2×D5911yescharacteristic
471C23×Q8—591no—
472C24×C4—591no—
473#556—5932no—
474#554—5932no—
475#552—5964no—
476#552—5932no—
477#552—5932no—
478#551—5964no—
479#544—5916no—
480#542—5932no—
481#541—5932no—
482#536—5916no—
483#533—5932no—
484C2×C4⋊Q8—592no—
485C2×C4⋊Q8—592no—
486C2×C4⋊Q8—592no—
487#529—5932no—
488C2×#126—594no—
489C2×#126—594no—
490C2×#126—594no—
491C2×#126—594no—
492C2×#125—594no—
493C2×#125—594no—
494C2×#125—592no—
495C2×#125—592no—
496C2×#125—594no—
497C2×#124—592no—
498C2×#124—594no—
499#525—5916no—
500C2×#123—592no—
501C2×#123—594no—
502C2×#123—594no—
503C2×#123—594no—
504C2×C22⋊Q8—591no—
505C2×C22⋊Q8—591no—
506C2×C22⋊Q8—594no—
507C2×C22⋊Q8—592no—
508C2×C22⋊Q8—592no—
509C2×C22⋊Q8—594no—
510C2×C22⋊Q8—594no—
511C2×C22⋊Q8—592no—
512C2×C22⋊Q8—592no—
513C2×C22⋊Q8—592no—
514C2×C22⋊Q8—592no—
515C2×C22⋊Q8—5916no—
516C2×#121—591no—
517C2×#121—591no—
518C2×#120—592no—
519#520C2×D59116yescomplemented
520#519—5916no—
521C2×C4×Q8—592no—
522C2×C4×Q8—592no—
523C2×C4×Q8—592no—
524C2×C4×Q8—592no—
525C2×C4×Q8—594no—
526C2×C4×Q8C2×D5912yescomplemented
527C2×C4×D4—592no—
528C2×C4×D4—592no—
529C2×C4×D4—594no—
530C2×C4×D4C2×D5914yes—
531C2×C4×D4C2×D5912yescomplemented
532C2×#117—591no—
533C2×#117—591no—
534C2×#117—594no—
535C2×#117—5916no—
536C2×#117—591no—
537C2×#117—591no—
538C2×#117—592no—
539C2×#117—594no—
540C2×#117—592no—
541C2×#117—594no—
542C2×#117C2×D5911yescharacteristic
543C2×#117C2×D5912yescomplemented
544C22×C4⋊C4—592no—
545C22×C4⋊C4—591no—
546C22×C4⋊C4—591no—
547C22×C4⋊C4C2×D5911yescharacteristic
548C22×C4⋊C4C2×D5912yescomplemented
549C22×C22⋊C4—592no—
550C22×C22⋊C4—592no—
551C22×C42—592no—
552C59C2×#349511yescharacteristic, complemented, Sylow
553C25—591no—
554C2×#41—28no—
555C2×#41C22×D5918yes—
556C22×Q8—592no—
557C22×Q8—592no—
558C22×Q8—598no—
559C22×Q8—594no—
560C22×Q8—1188no—
561C22×Q8C22×D5911yescharacteristic
562C22×D4—592no—
563C22×D4—592no—
564C22×D4C22×D5912yes—
565C22×D4C22×D5911yescharacteristic
566C23×C4—592no—
567C23×C4—591no—
568C23×C4—592no—
569C23×C4—591no—
570C23×C4—591no—
571C23×C4—591no—
572C23×C4—598no—
573C23×C4—591no—
574C23×C4—592no—
575C23×C4—1188no—
576C23×C4C22×D5912yes—
577C23×C4C22×D5912yes—
578C23×C4C22×D5914yes—
579C23×C4C22×D5911yescharacteristic
580C4⋊Q8—5916no—
581C4⋊Q8—5916no—
582C4⋊Q8—5916no—
583#126—5932no—
584#126—5932no—
585#126—5932no—
586#126—5932no—
587#125—5916no—
588#125—5932no—
589#125—5932no—
590#125—5916no—
591#125—5932no—
592#124—5916no—
593#124—5932no—
594#123—5916no—
595#123—5932no—
596#123—5932no—
597#123—5932no—
598C22⋊Q8—598no—
599C22⋊Q8—598no—
600C22⋊Q8—5916no—
601C22⋊Q8—5916no—
602C22⋊Q8—5932no—
603C22⋊Q8—5932no—
604C22⋊Q8—5916no—
605C22⋊Q8—5916no—
606C22⋊Q8—5916no—
607C22⋊Q8—5916no—
608C22⋊Q8—5932no—
609#121—598no—
610#121—598no—
611#120—5916no—
612C4×Q8—5916no—
613C4×Q8—5916no—
614C4×Q8—5916no—
615C4×Q8—5916no—
616C4×Q8—5932no—
617C4×Q8C22×D59116yescomplemented
618C4×D4—5916no—
619C4×D4—5916no—
620C4×D4—5932no—
621C4×D4C22×D59132yes—
622C4×D4C22×D59116yescomplemented
623#117—598no—
624#117—598no—
625#117—5932no—
626#117—598no—
627#117—598no—
628#117—5916no—
629#117—5932no—
630#117—5916no—
631#117—5932no—
632#117C22×D5918yes—
633#117C22×D59116yescomplemented
634C2×C4⋊C4—592no—
635C2×C4⋊C4—591no—
636C2×C4⋊C4—591no—
637C2×C4⋊C4—592no—
638C2×C4⋊C4—594no—
639C2×C4⋊C4—594no—
640C2×C4⋊C4—5916no—
641C2×C4⋊C4—591no—
642C2×C4⋊C4—591no—
643C2×C4⋊C4—594no—
644C2×C4⋊C4—594no—
645C2×C4⋊C4—594no—
646C2×C4⋊C4—594no—
647C2×C4⋊C4—594no—
648C2×C4⋊C4—592no—
649C2×C4⋊C4—592no—
650C2×C4⋊C4—594no—
651C2×C4⋊C4—594no—
652C2×C4⋊C4—598no—
653C2×C4⋊C4—598no—
654C2×C4⋊C4C22×D5911yescharacteristic
655C2×C4⋊C4C22×D5911yescharacteristic
656C2×C4⋊C4C22×D5912yes—
657C2×C4⋊C4C22×D5912yes—
658C2×C4⋊C4C22×D5918yes—
659C2×C4⋊C4C22×D5914yes—
660C2×C4⋊C4C22×D59116yescomplemented
661C2×C22⋊C4—592no—
662C2×C22⋊C4—592no—
663C2×C22⋊C4—592no—
664C2×C22⋊C4—594no—
665C2×C22⋊C4—592no—
666C2×C22⋊C4—594no—
667C2×C22⋊C4—592no—
668C2×C22⋊C4—592no—
669C2×C22⋊C4—594no—
670C2×C22⋊C4—594no—
671C2×C22⋊C4—5916no—
672C2×C22⋊C4—592no—
673C2×C22⋊C4—592no—
674C2×C22⋊C4—5916no—
675C2×C22⋊C4C22×D5912yes—
676C2×C22⋊C4C22×D5914yes—
677C2×C42—592no—
678C2×C42—594no—
679C2×C42—594no—
680C2×C42—592no—
681C2×C42—592no—
682C2×C42—592no—
683C2×C42—5916no—
684C2×C42C22×D5912yes—
685C2×C42C22×D5914yes—
686C24—591no—
687C24—591no—
688C24—594no—
689C24—1184no—
690C24—1184no—
691C24—2362no—
692C24C23×D5912yes—
693C24C23×D5911yescharacteristic
694#41—232no—
695C2×Q8—24no—
696C2×Q8—598no—
697C2×Q8—598no—
698C2×Q8—5916no—
699C2×Q8—1188no—
700C2×Q8—1188no—
701C2×Q8—11832no—
702C2×Q8—2368no—
703C2×Q8C23×D5914yes—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—598no—
707C2×D4—598no—
708C2×D4—1188no—
709C2×D4—2364no—
710C2×D4C23×D5918yes—
711C2×D4C23×D5914yes—
712C22×C4—28no—
713C22×C4—48no—
714C22×C4—44no—
715C22×C4—598no—
716C22×C4—594no—
717C22×C4—591no—
718C22×C4—592no—
719C22×C4—592no—
720C22×C4—592no—
721C22×C4—594no—
722C22×C4—592no—
723C22×C4—591no—
724C22×C4—594no—
725C22×C4—598no—
726C22×C4—594no—
727C22×C4—594no—
728C22×C4—594no—
729C22×C4—598no—
730C22×C4—1188no—
731C22×C4—1184no—
732C22×C4—1188no—
733C22×C4—1184no—
734C22×C4—1184no—
735C22×C4—1184no—
736C22×C4—1184no—
737C22×C4—11832no—
738C22×C4—2364no—
739C22×C4#1174568518yes—
740C22×C4C23×D5918yes—
741C22×C4C23×D5912yes—
742C22×C4C23×D5912yes—
743C22×C4C23×D5912yes—
744C22×C4C23×D5914yes—
745C22×C4C23×D5918yes—
746C22×C4C23×D59116yes—
747C22×C4C23×D5914yes—
748C22×C4C23×D5911yescharacteristic
749C22×C4C23×D5911yescharacteristic
750C4⋊C4—598no—
751C4⋊C4—594no—
752C4⋊C4—594no—
753C4⋊C4—598no—
754C4⋊C4—5916no—
755C4⋊C4—5916no—
756C4⋊C4—594no—
757C4⋊C4—594no—
758C4⋊C4—5916no—
759C4⋊C4—5916no—
760C4⋊C4—5916no—
761C4⋊C4—5916no—
762C4⋊C4—5916no—
763C4⋊C4—598no—
764C4⋊C4—598no—
765C4⋊C4—5916no—
766C4⋊C4—5916no—
767C4⋊C4C23×D5914yes—
768C4⋊C4C23×D5914yes—
769C4⋊C4C23×D5918yes—
770C4⋊C4C23×D5918yes—
771C4⋊C4C23×D59116yes—
772C22⋊C4—598no—
773C22⋊C4—598no—
774C22⋊C4—598no—
775C22⋊C4—5916no—
776C22⋊C4—598no—
777C22⋊C4—5916no—
778C22⋊C4—598no—
779C22⋊C4—598no—
780C22⋊C4—5916no—
781C22⋊C4—5916no—
782C22⋊C4—598no—
783C22⋊C4—598no—
784C22⋊C4C23×D5918yes—
785C22⋊C4C23×D59116yes—
786C42—598no—
787C42—598no—
788C42—598no—
789C42—5916no—
790C42—5916no—
791C42—598no—
792C42C23×D5918yes—
793C42C23×D59116yes—
794C23—22no—
795C23—22no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—594no—
800C23—592no—
801C23—592no—
802C23—1188no—
803C23—1182no—
804C23—1182no—
805C23—1188no—
806C23—1182no—
807C23—1182no—
808C23—1182no—
809C23—2364no—
810C23—23616no—
811C23C2×#1174568514yes—
812C23C24×D5914yes—
813C23C24×D5912yes—
814C23C24×D5911yescharacteristic
815Q8—28no—
816Q8—11816no—
817Q8—11816no—
818Q8—23616no—
819D4—216no—
820D4—28no—
821D4—11816no—
822D4—2368no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—28no—
827C2×C4—216no—
828C2×C4—416no—
829C2×C4—48no—
830C2×C4—592no—
831C2×C4—594no—
832C2×C4—594no—
833C2×C4—594no—
834C2×C4—598no—
835C2×C4—594no—
836C2×C4—592no—
837C2×C4—11816no—
838C2×C4—1188no—
839C2×C4—1182no—
840C2×C4—1182no—
841C2×C4—11816no—
842C2×C4—1188no—
843C2×C4—1184no—
844C2×C4—1184no—
845C2×C4—1184no—
846C2×C4—1184no—
847C2×C4—1188no—
848C2×C4—1188no—
849C2×C4—1188no—
850C2×C4—1188no—
851C2×C4—2368no—
852C2×C4C2×#1174568514yes—
853C2×C4C2×#1174568514yes—
854C2×C4C2×#11745685116yes—
855C2×C4C24×D5914yes—
856C2×C4C24×D5914yes—
857C2×C4C24×D5914yes—
858C2×C4C24×D5918yes—
859C2×C4C24×D5912yes—
860C2×C4C24×D5912yes—
861C22—28no—
862C22—22no—
863C22—22no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—48no—
868C22—594no—
869C22—1188no—
870C22—1182no—
871C22—1182no—
872C22—1182no—
873C22—1182no—
874C22—1182no—
875C22—23616no—
876C22—2364no—
877C22C22×#1174568514yes—
878C22C22×#1174568512yes—
879C222−1+4×D5912yes—
880C22#1683823712yes—
881C22C25×D5911yescharacteristic
882C4—24no—
883C4—24no—
884C4—24no—
885C4—28no—
886C4—1182no—
887C4—1182no—
888C4—1188no—
889C4—1184no—
890C4—1184no—
891C4—1184no—
892C4—1184no—
893C4C22×#1174568514yes—
894C4C22×#1174568514yes—
895C2—24no—
896C2—44no—
897C2—1184no—
898C2—2362no—
899C2#2143784914yesdirect product factor
900C2C23×#1174568511yescharacteristic
901C2C2×2−1+4×D5911yescharacteristic
902C2C2×#1683823711yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#520C2
socleC23×C59C25
prime radicalC2×#16837909C2
hypercenterC2×#520D59
hypocenterC59C2×#3495
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #21437849C2direct (N × H)
2. C2×#16838120C2semidirect
3. C2×#16838107C2semidirect
4. C2×#16838092C2semidirect
5. C2×#16838091C2semidirect
6. C2×#16838087C2semidirect
7. C2×#16838081C2semidirect
8. C2×#16838033C2semidirect
9. C2×#16838017C2semidirect
10. C2×#16838010C2semidirect
11. C2×#16837973C2semidirect
12. C2×#16837956C2semidirect
13. C2×#16837934C2semidirect
15. C22×#14273707C2semidirect
16. C2×#16837879C2semidirect
17. C2×#117×D59C2semidirect
18. C2×C59×#520C2semidirect
21. #16838120C22semidirect
22. #16838107C22semidirect
23. #16838092C22semidirect
24. #16838091C22semidirect
25. #16838087C22semidirect
26. #16838081C22semidirect
27. #16838033C22semidirect
28. #16838017C22semidirect
29. #16838010C22semidirect
30. #16837973C22semidirect
31. #16837956C22semidirect
32. C2×#14273726C22semidirect
33. C2×#14273726C22semidirect
34. C2×#14273725C22semidirect
35. #16837934C22semidirect
38. C2×#14273720C22semidirect
39. C2×#14273720C22semidirect
40. C2×#14273719C22semidirect
41. C2×#14273718C22semidirect
42. C2×#14273718C22semidirect
43. C2×#14273717C22semidirect
44. C2×#14273717C22semidirect
45. C2×#14273714C22semidirect
56. C2×#14273707C22semidirect
58. C2×#14273706C22semidirect
59. C2×#14273706C22semidirect
60. C2×#14273706C22semidirect
67. #16837879C22semidirect
68. C2×C4×Dic118C22semidirect
69. C2×C4×Dic118C22semidirect
70. C2×C4×Dic118C22semidirect
71. C2×#14273692C22semidirect
72. C2×#14273692C22semidirect
78. C2×#14273686C22semidirect
85. #117×D59C22semidirect
93. C59×#520C22semidirect
94. C2×C4×Q8×C59C22semidirect
96. C2×C4×D4×C59C22semidirect
98. C2×#117×C59C22semidirect
100. C22×C4⋊C4×C59C22semidirect
119. #14273726C23semidirect
120. #14273726C23semidirect
121. #14273725C23semidirect
124. #14273720C23semidirect
125. #14273720C23semidirect
126. #14273719C23semidirect
127. #14273718C23semidirect
128. #14273718C23semidirect
129. #14273717C23semidirect
130. #14273717C23semidirect
131. #14273714C23semidirect
142. #14273706C23semidirect
143. #14273706C23semidirect
144. #14273706C23semidirect
151. C4×Dic118C23semidirect
152. C4×Dic118C23semidirect
153. C4×Dic118C23semidirect
154. #14273692C23semidirect
155. #14273692C23semidirect
161. #14273686C23semidirect
218. C4×Q8×C59C23semidirect
220. C4×D4×C59C23semidirect
222. #117×C59C23semidirect
229. C2×C4⋊C4×C59C23semidirect
459. C2×#520D59semidirect
464. C2×C59#3495semidirect
519. #520C2×D59semidirect
526. C2×C4×Q8C2×D59semidirect
531. C2×C4×D4C2×D59semidirect
543. C2×#117C2×D59semidirect
548. C22×C4⋊C4C2×D59semidirect
552. C59C2×#3495semidirect
617. C4×Q8C22×D59semidirect
622. C4×D4C22×D59semidirect
633. #117C22×D59semidirect
660. C2×C4⋊C4C22×D59semidirect
899. C2#21437849direct (N × H)

Maximal subgroups

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

subgroupindex
#214378492
C2×#168381202
C2×#168381072
C2×#168380922
C2×#168380912
C2×#168380872
C2×#168380812
C2×#168380332
C2×#168380172
C2×#168380102
C2×#168379732
C2×#168379562
C2×#168379342
C2×#168379092
C22×#142737072
C2×#168378792
C2×#117×D592
C2×C59×#5202
C2×#349559