Finite Group Databasebeta

← C2×#21438074 #29496803

Subgroups — C2×#21438074 #29496803

Order 15104.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438074C2132yesmaximal, direct product factor
2C2×#16838130C211yesmaximal, characteristic, complemented
3C2×#16838112C211yesmaximal, characteristic, complemented
4C2×#16838109C211yesmaximal, characteristic, complemented
5C2×#16838098C212yesmaximal, complemented
6C2×#16838092C212yesmaximal, complemented
7C2×#16838091C212yesmaximal, complemented
8C2×#16838085C214yesmaximal, complemented
9C2×#16838056C211yesmaximal, characteristic, complemented
10C2×#16838051C212yesmaximal, complemented
11C2×#16838010C212yesmaximal, complemented
12C2×#16837994C214yesmaximal, complemented
13C2×#16837959C211yesmaximal, characteristic, complemented
14C2×#16837936C212yesmaximal, complemented
15C2×#16837936C211yesmaximal, characteristic, complemented
16C22×#14273719C212yesmaximal, complemented
17C2×#16837881C212yesmaximal, complemented
18C2×C4×#41×C59C211yesmaximal, characteristic, complemented
19C22×#11745687C2212yes—
20#16838130C22116yescomplemented
21#16838112C22116yescomplemented
22#16838109C22116yescomplemented
23#16838098C22132yescomplemented
24#16838092C22132yescomplemented
25#16838091C22132yescomplemented
26#16838085C22164yescomplemented
27#16838056C22116yescomplemented
28#16838051C22132yescomplemented
29#16838010C22132yescomplemented
30#16837994C22164yescomplemented
31#16837959C22116yescomplemented
32C2×#14273727C2211yescharacteristic
33C2×#14273727C2211yescharacteristic
34C2×#14273725C2212yes—
35#16837936C22132yescomplemented
36#16837936C22116yescomplemented
37C2×#14273722C2214yes—
38C2×#14273721C2214yes—
39C2×#14273721C2212yes—
40C2×#14273720C2214yes—
41C2×#14273719C2214yes—
42C2×#14273719C2214yes—
43C2×#14273719C2211yescharacteristic
44C2×#14273719C2212yes—
45C2×#14273719C2212yes—
46C2×#14273719C2212yes—
47C2×#14273719C22132yescomplemented
48C2×#14273718C2212yes—
49C2×#14273717C2214yes—
50C2×#14273717C2214yes—
51C2×#14273715C2211yescharacteristic
52C2×#14273711C2214yes—
53C2×#14273710C2212yes—
54C2×#14273710C2214yes—
55C2×#14273709C2214yes—
56C2×#14273708C2214yes—
57C2×#14273707C2212yes—
58C2×#14273706C2212yes—
59C2×#14273706C2212yes—
60C2×#14273706C2211yescharacteristic
61C2×#14273706C2212yes—
62C2×#14273705C2214yes—
63C2×#14273704C2214yes—
64C2×#14273703C2212yes—
65C2×#14273701C2212yes—
66C2×#14273701C2211yescharacteristic
67C2×#14273699C2214yes—
68#16837881C22132yescomplemented
69C2×C4×Dic118C2212yes—
70C2×C4×Dic118C2212yes—
71C2×C4×Dic118C2212yes—
72C2×C4×Dic118C2211yescharacteristic
73C2×#14273692C2212yes—
74C2×C4×D236C2211yescharacteristic
75C2×C4×D236C2212yes—
76C2×D4×Dic59C2212yes—
77C2×C4×C22⋊D59C2214yes—
78C2×C4×C22⋊D59C2212yes—
79C2×(C22⋊D59)⋊C4C2214yes—
80C2×#14273686C2212yes—
81C2×#14273684C2212yes—
82C2×#14273684C2214yes—
83C2×#14273683C2214yes—
84C22×C4⋊Dic59C2212yes—
85C22×C4⋊Dic59C2212yes—
86C22×Dic59⋊C4C2214yes—
87C22×Dic59⋊C4C2214yes—
88C2×C4⋊C4×D59C2212yes—
89C22×#41×C59C2211yescharacteristic
90C4×#41×C59C22116yescomplemented
91C2×C4×Q8×C59C2211yescharacteristic
92C2×C4×Q8×C59C2211yescharacteristic
93C2×C4×D4×C59C2212yes—
94C2×C4×D4×C59C2211yescharacteristic
95C2×C4×D4×C59C2211yescharacteristic
96C2×C4×D4×C59C2212yes—
97C2×#117×C59C2212yes—
98C2×#117×C59C2211yescharacteristic
99C22×C42×C59C2212yes—
100C22×C42×C59C2211yescharacteristic
101C2×#11745687—216no—
102C2×#11745687C23116yes—
103C22×Dic118C2311yescharacteristic
104C22×Dic118C2312yes—
105C22×Dic118C2312yes—
106C22×D236C2311yescharacteristic
107C22×C22⋊D59C2314yes—
108C22×C22⋊D59C2312yes—
109C23×Dic59C2314yes—
110C23×Dic59C2314yes—
111C22×C4×D59C2312yes—
112C22×C4×D59C2314yes—
113#14273727C2318yes—
114#14273727C2318yes—
115#14273725C23116yes—
116#14273722C23132yes—
117#14273721C23132yes—
118#14273721C23116yes—
119#14273720C23132yes—
120#14273719C2318yes—
121#14273719C23116yes—
122#14273719C23132yes—
123#14273719C23132yes—
124#14273719C23116yes—
125#14273719C23116yes—
126#14273718C23116yes—
127#14273717C23132yes—
128#14273717C23132yes—
129#14273715C2318yes—
130#14273711C23132yes—
131#14273710C23116yes—
132#14273710C23132yes—
133#14273709C23132yes—
134#14273708C23132yes—
135#14273707C23116yes—
136#14273706C2318yes—
137#14273706C23116yes—
138#14273706C23116yes—
139#14273706C23116yes—
140#14273705C23132yes—
141#14273704C23132yes—
142#14273703C23116yes—
143#14273701C23116yes—
144#14273701C2318yes—
145#14273699C23132yes—
146C4×Dic118C23116yes—
147C4×Dic118C2318yes—
148C4×Dic118C23116yes—
149C4×Dic118C23116yes—
150#14273692C23116yes—
151C4×D236C2318yes—
152C4×D236C23116yes—
153D4×Dic59C23116yes—
154C4×C22⋊D59C23132yes—
155C4×C22⋊D59C23116yes—
156(C22⋊D59)⋊C4C23132yes—
157#14273686C23116yes—
158#14273684C23116yes—
159#14273684C23132yes—
160#14273683C23132yes—
161C2×C4⋊Dic59C2311yescharacteristic
162C2×C4⋊Dic59C2312yes—
163C2×C4⋊Dic59C2312yes—
164C2×C4⋊Dic59C2314yes—
165C2×C4⋊Dic59C2312yes—
166C2×C4⋊Dic59C2311yescharacteristic
167C2×C4⋊Dic59C2312yes—
168C2×C4⋊Dic59C2314yes—
169C2×C4⋊Dic59C23116yes—
170C2×C4⋊Dic59C23116yes—
171C2×Dic59⋊C4C2314yes—
172C2×Dic59⋊C4C2314yes—
173C2×Dic59⋊C4C2312yes—
174C2×Dic59⋊C4C2314yes—
175C2×Dic59⋊C4C2314yes—
176C2×Dic59⋊C4C2314yes—
177C2×Dic59⋊C4C2312yes—
178C2×Dic59⋊C4C2314yes—
179C2×Dic59⋊C4C2314yes—
180C2×Dic59⋊C4C2314yes—
181C2×Dic59⋊C4C2312yes—
182C2×Dic59⋊C4C2312yes—
183C2×Dic59⋊C4C23132yes—
184C2×Dic59⋊C4C23132yes—
185C4⋊C4×D59C23116yes—
186C2×C22⋊Dic59C2314yes—
187C2×C22⋊Dic59C2314yes—
188C2×C22⋊Dic59C2312yes—
189C2×(C2×D59)⋊C4C2314yes—
190C2×(C2×D59)⋊C4C2314yes—
191C2×(C2×D59)⋊C4C2312yes—
192C2×(C2×D59)⋊C4C2312yes—
193C2×(C2×D59)⋊C4C2312yes—
194C2×(C2×D59)⋊C4C2312yes—
195C2×C4×Dic59C2314yes—
196C2×C4×Dic59C2314yes—
197C2×C4×Dic59C2312yes—
198C2×#41×C59—28no—
199C2×#41×C59C2318yes—
200C22×Q8×C59C2311yescharacteristic
201C22×D4×C59C2312yes—
202C22×D4×C59C2311yescharacteristic
203C23×C4×C59C2312yes—
204C23×C4×C59C2311yescharacteristic
205C23×C4×C59C2311yescharacteristic
206C23×C4×C59C2312yes—
207C23×C4×C59C2311yescharacteristic
208C23×C4×C59C2312yes—
209C4×Q8×C59C2318yes—
210C4×Q8×C59C2318yes—
211C4×D4×C59C23116yes—
212C4×D4×C59C2318yes—
213C4×D4×C59C23116yes—
214C4×D4×C59C2318yes—
215#117×C59C23116yes—
216#117×C59C2318yes—
217C2×C4⋊C4×C59C2312yes—
218C2×C4⋊C4×C59C2311yescharacteristic
219C2×C4⋊C4×C59C2312yes—
220C2×C4⋊C4×C59C2311yescharacteristic
221C2×C22⋊C4×C59C2312yes—
222C2×C22⋊C4×C59C2312yes—
223C2×C22⋊C4×C59C2312yes—
224C2×C42×C59C2311yescharacteristic
225C2×C42×C59C2312yes—
226C2×C42×C59C2312yes—
227C2×C42×C59C2312yes—
228C2×C42×C59C23116yes—
229C2×C42×C59C2311yescharacteristic
230C2×C42×C59C2318yes—
231C2×C42×C59C2311yescharacteristic
232C2×C42×C59C2311yescharacteristic
233C24×C59C2411yescharacteristic
234C24×C59C2412yes—
235C23×D59C2412yes—
236#41×C59—232no—
237C2×Q8×C59—24no—
238C2×Q8×C59C2414yes—
239C2×D4×C59—28no—
240C2×D4×C59#4118yes—
241C2×D4×C59C2418yes—
242C2×D4×C59C2414yes—
243C22×C4×C59—28no—
244C22×C4×C59—24no—
245C22×C4×C59—28no—
246C22×C4×C59—24no—
247C22×C4×C59—42no—
248C22×C4×C59—44no—
249C22×C4×C59C2411yescharacteristic
250C22×C4×C59C2411yescharacteristic
251C22×C4×C59C2411yescharacteristic
252C22×C4×C59C2412yes—
253C22×C4×C59C2412yes—
254C22×C4×C59C2411yescharacteristic
255C22×C4×C59C2412yes—
256C22×C4×C59C2418yes—
257C22×C4×C59C2414yes—
258C22×C4×C59C2418yes—
259C22×C4×C59C2414yes—
260C22×C4×C59C2418yes—
261C22×C4×C59C2414yes—
262C22×C4×C59C2411yescharacteristic
263C22×C4×C59C2411yescharacteristic
264C2×C22⋊D59—216no—
265C2×C22⋊D59—44no—
266C2×C22⋊D59C24116yes—
267C2×C22⋊D59C2418yes—
268C22×Dic59—216no—
269C22×Dic59—48no—
270C22×Dic59C2412yes—
271C22×Dic59C2414yes—
272C22×Dic59C2414yes—
273C22×Dic59C2412yes—
274C22×Dic59C2412yes—
275C22×Dic59C24116yes—
276C22×Dic59C24116yes—
277#11745687—264no—
278C2×D236—24no—
279C2×D236C2414yes—
280C2×C4×D59—28no—
281C2×C4×D59—48no—
282C2×C4×D59C2418yes—
283C2×C4×D59C24116yes—
284C2×Dic118—28no—
285C2×Dic118—24no—
286C2×Dic118—44no—
287C2×Dic118C2418yes—
288C2×Dic118C2414yes—
289C2×Dic118C2418yes—
290C4⋊C4×C59C2414yes—
291C4⋊C4×C59C2418yes—
292C4⋊C4×C59C2414yes—
293C4⋊C4×C59C2418yes—
294C22⋊C4×C59C2418yes—
295C22⋊C4×C59C2418yes—
296C22⋊C4×C59C2418yes—
297C42×C59C2414yes—
298C42×C59C2418yes—
299C42×C59C2414yes—
300C42×C59C2414yes—
301C42×C59C2418yes—
302C42×C59C2414yes—
303C42×C59C2418yes—
304C22⋊Dic59C24116yes—
305C22⋊Dic59C24116yes—
306C22⋊Dic59C2418yes—
307(C2×D59)⋊C4C2418yes—
308(C2×D59)⋊C4C2418yes—
309(C2×D59)⋊C4C2418yes—
310(C2×D59)⋊C4C24116yes—
311(C2×D59)⋊C4C24116yes—
312(C2×D59)⋊C4C2418yes—
313C4⋊Dic59C2418yes—
314C4⋊Dic59C2414yes—
315C4⋊Dic59C2414yes—
316C4⋊Dic59C2418yes—
317C4⋊Dic59C2418yes—
318C4⋊Dic59C24116yes—
319C4⋊Dic59C24116yes—
320C4⋊Dic59C2418yes—
321Dic59⋊C4C24116yes—
322Dic59⋊C4C2418yes—
323Dic59⋊C4C2418yes—
324Dic59⋊C4C24116yes—
325Dic59⋊C4C24116yes—
326Dic59⋊C4C24116yes—
327Dic59⋊C4C24116yes—
328Dic59⋊C4C24116yes—
329Dic59⋊C4C2418yes—
330Dic59⋊C4C24116yes—
331Dic59⋊C4C2418yes—
332Dic59⋊C4C24116yes—
333C4×Dic59C24116yes—
334C4×Dic59C24116yes—
335C4×Dic59C2418yes—
336C23×C59—24no—
337C23×C59—24no—
338C23×C59—22no—
339C23×C59—22no—
340C23×C59—22no—
341C23×C59C2×#4118yes—
342C23×C59C2512yes—
343C23×C59C2514yes—
344C23×C59C2511yescharacteristic
345C22×D59—24no—
346C22×D59—24no—
347C22×D59—24no—
348C22×D59C2514yes—
349Q8×C59—28no—
350D4×C59—216no—
351D4×C59C2×#41116yes—
352C2×C4×C59—22no—
353C2×C4×C59—24no—
354C2×C4×C59—216no—
355C2×C4×C59—22no—
356C2×C4×C59—24no—
357C2×C4×C59—22no—
358C2×C4×C59—24no—
359C2×C4×C59—22no—
360C2×C4×C59—28no—
361C2×C4×C59—216no—
362C2×C4×C59—28no—
363C2×C4×C59—44no—
364C2×C4×C59—48no—
365C2×C4×C59C2×#4114yes—
366C2×C4×C592−1+414yes—
367C2×C4×C59C2512yes—
368C2×C4×C59C2514yes—
369C2×C4×C59C2512yes—
370C2×C4×C59C2512yes—
371C2×C4×C59C2514yes—
372C2×C4×C59C2514yes—
373C2×C4×C59C2512yes—
374C2×C4×C59C2512yes—
375C2×C4×C59C2512yes—
376C22⋊D59—232no—
377C22⋊D59—48no—
378C2×Dic59—28no—
379C2×Dic59—24no—
380C2×Dic59—232no—
381C2×Dic59—24no—
382C2×Dic59—28no—
383C2×Dic59—24no—
384C2×Dic59—416no—
385C2×Dic59C2514yes—
386C2×Dic59C2518yes—
387C2×Dic59C2514yes—
388C2×Dic59C2518yes—
389C2×Dic59C2514yes—
390D236—28no—
391C4×D59—216no—
392C4×D59—416no—
393Dic118—216no—
394Dic118—28no—
395Dic118—48no—
396C2×#3515—591nomaximal, Sylow
397C22×C59—24no—
398C22×C59—24no—
399C22×C59—216no—
400C22×C59—22no—
401C22×C59—22no—
402C22×C59—22no—
403C22×C59—44no—
404C22×C59C22×#4118yes—
405C22×C59C22×#4112yes—
406C22×C59C2×2−1+412yes—
407C22×C59#58512yes—
408C22×C59C2611yescharacteristic
409C2×D59—24no—
410C2×D59—24no—
411C2×D59—24no—
412C2×D59—48no—
413C4×C59—22no—
414C4×C59—24no—
415C4×C59—22no—
416C4×C59—24no—
417C4×C59—22no—
418C4×C59—24no—
419C4×C59—22no—
420C4×C59C22×#4114yes—
421C4×C59C2×2−1+414yes—
422Dic59—28no—
423Dic59—24no—
424Dic59—24no—
425Dic59—28no—
426Dic59—24no—
427#3515—5932no—
428C2×#557—591no—
429C2×#554—591no—
430C2×#554—591no—
431C2×#553—592no—
432C2×#552—592no—
433C2×#552—594no—
434C2×#552—592no—
435C2×#547—592no—
436C2×#547—591no—
437C2×#541—592no—
438C2×#539—594no—
439C2×#533—591no—
440C2×#529—591no—
441C2×#529—592no—
442C22×#125—592no—
443C2×#520—592no—
444C2×C4×#41D5911yescharacteristic, complemented
445C2×C59—28no—
446C2×C59—42no—
447C2×C59#351514yescomplemented
448C2×C59C23×#4111yescharacteristic
449C2×C59C22×2−1+411yescharacteristic
450C2×C59C2×#58511yescharacteristic
451D59—44no—
452C22×#41—592no—
453C22×#41C2×D5911yescharacteristic
454#557—5916no—
455#554—5916no—
456#554—5916no—
457#553—5932no—
458#552—5932no—
459#552—5964no—
460#552—5932no—
461#547—5932no—
462#547—5916no—
463#541—5932no—
464#539—5964no—
465#533—5916no—
466C2×C4⋊Q8—592no—
467C2×C4⋊Q8—591no—
468C2×C4⋊Q8—591no—
469#529—5932no—
470#529—5916no—
471C2×#126—594no—
472C2×#126—594no—
473C2×#126—594no—
474C2×#126—592no—
475C2×#125—594no—
476C2×#125—594no—
477C2×#125—592no—
478C2×#125—591no—
479C2×#125—592no—
480C2×#125—594no—
481C2×#125—594no—
482C2×#125—592no—
483C2×#125—592no—
484C2×#125—5932no—
485C2×#124—591no—
486C2×#123—594no—
487C2×#123—592no—
488C2×#123—594no—
489C2×#123—594no—
490C2×#123—594no—
491C2×C22⋊Q8—592no—
492C2×C22⋊Q8—591no—
493C2×C22⋊Q8—592no—
494C2×C22⋊Q8—592no—
495C2×C22⋊Q8—592no—
496C2×C22⋊Q8—594no—
497C2×C22⋊Q8—592no—
498C2×C22⋊Q8—594no—
499C2×#121—594no—
500C2×#121—592no—
501C2×#121—591no—
502#520—5932no—
503C4×#41C2×D59116yescomplemented
504C2×C4×Q8—592no—
505C2×C4×Q8—592no—
506C2×C4×Q8—592no—
507C2×C4×Q8—591no—
508C2×C4×Q8—592no—
509C2×C4×Q8C2×D5911yescharacteristic
510C2×C4×Q8C2×D5911yescharacteristic
511C2×C4×D4—592no—
512C2×C4×D4—594no—
513C2×C4×D4—592no—
514C2×C4×D4—594no—
515C2×C4×D4—591no—
516C2×C4×D4—592no—
517C2×C4×D4C2×D5911yescharacteristic
518C2×C4×D4C2×D5912yes—
519C2×C4×D4C2×D5911yescharacteristic
520C2×C4×D4C2×D5912yes—
521C2×#117—592no—
522C2×#117—594no—
523C2×#117—592no—
524C2×#117—594no—
525C2×#117C2×D5911yescharacteristic
526C2×#117C2×D5912yes—
527C22×C4⋊C4—594no—
528C22×C4⋊C4—594no—
529C22×C4⋊C4—592no—
530C22×C4⋊C4—592no—
531C22×C4⋊C4—592no—
532C22×C42C2×D5912yes—
533C22×C42C2×D5911yescharacteristic
534C59C2×#351511yescharacteristic, complemented, Sylow
535C2×#41—28no—
536C2×#41—5916no—
537C2×#41—11816no—
538C2×#41C22×D5918yes—
539C22×Q8—591no—
540C22×Q8—592no—
541C22×Q8—592no—
542C22×Q8C22×D5911yescharacteristic
543C22×D4—594no—
544C22×D4—592no—
545C22×D4—591no—
546C22×D4C22×D5912yes—
547C22×D4C22×D5911yescharacteristic
548C23×C4—594no—
549C23×C4—594no—
550C23×C4—592no—
551C23×C4—594no—
552C23×C4C22×D5912yes—
553C23×C4C22×D5912yes—
554C23×C4C22×D5911yescharacteristic
555C23×C4C22×D5911yescharacteristic
556C23×C4C22×D5912yes—
557C23×C4C22×D5911yescharacteristic
558C4⋊Q8—5916no—
559C4⋊Q8—598no—
560C4⋊Q8—598no—
561#126—5932no—
562#126—5932no—
563#126—5932no—
564#126—5916no—
565#125—5932no—
566#125—5932no—
567#125—5916no—
568#125—598no—
569#125—5916no—
570#125—5932no—
571#125—5932no—
572#125—5916no—
573#125—5916no—
574#124—598no—
575#123—5932no—
576#123—5916no—
577#123—5932no—
578#123—5932no—
579#123—5932no—
580C22⋊Q8—5916no—
581C22⋊Q8—598no—
582C22⋊Q8—5916no—
583C22⋊Q8—5916no—
584C22⋊Q8—5916no—
585C22⋊Q8—5932no—
586C22⋊Q8—5916no—
587C22⋊Q8—5932no—
588#121—5932no—
589#121—5916no—
590#121—598no—
591C4×Q8—5916no—
592C4×Q8—5916no—
593C4×Q8—5916no—
594C4×Q8—598no—
595C4×Q8—5916no—
596C4×Q8C22×D5918yes—
597C4×Q8C22×D5918yes—
598C4×D4—5916no—
599C4×D4—5932no—
600C4×D4—5916no—
601C4×D4—5932no—
602C4×D4—598no—
603C4×D4—5916no—
604C4×D4C22×D5918yes—
605C4×D4C22×D59116yes—
606C4×D4C22×D5918yes—
607C4×D4C22×D59116yes—
608#117—5916no—
609#117—5932no—
610#117—5916no—
611#117—5932no—
612#117C22×D5918yes—
613#117C22×D59116yes—
614C2×C4⋊C4—594no—
615C2×C4⋊C4—592no—
616C2×C4⋊C4—591no—
617C2×C4⋊C4—592no—
618C2×C4⋊C4—591no—
619C2×C4⋊C4—592no—
620C2×C4⋊C4—592no—
621C2×C4⋊C4—594no—
622C2×C4⋊C4—592no—
623C2×C4⋊C4—594no—
624C2×C4⋊C4—594no—
625C2×C4⋊C4—5932no—
626C2×C4⋊C4—594no—
627C2×C4⋊C4—594no—
628C2×C4⋊C4—594no—
629C2×C4⋊C4—594no—
630C2×C4⋊C4—5932no—
631C2×C4⋊C4—5916no—
632C2×C4⋊C4—5916no—
633C2×C4⋊C4—592no—
634C2×C4⋊C4—594no—
635C2×C4⋊C4—592no—
636C2×C4⋊C4—592no—
637C2×C4⋊C4—594no—
638C2×C4⋊C4—5916no—
639C2×C4⋊C4C22×D5911yescharacteristic
640C2×C4⋊C4C22×D5912yes—
641C2×C4⋊C4C22×D5911yescharacteristic
642C2×C4⋊C4C22×D5912yes—
643C2×C22⋊C4—594no—
644C2×C22⋊C4—594no—
645C2×C22⋊C4—592no—
646C2×C22⋊C4—592no—
647C2×C22⋊C4—592no—
648C2×C22⋊C4—592no—
649C2×C22⋊C4—594no—
650C2×C22⋊C4—594no—
651C2×C22⋊C4—592no—
652C2×C22⋊C4C22×D5912yes—
653C2×C22⋊C4C22×D5912yes—
654C2×C22⋊C4C22×D5912yes—
655C2×C42—594no—
656C2×C42—594no—
657C2×C42—592no—
658C2×C42C22×D5912yes—
659C2×C42C22×D5911yescharacteristic
660C2×C42C22×D5911yescharacteristic
661C2×C42C22×D5912yes—
662C2×C42C22×D5911yescharacteristic
663C2×C42C22×D5912yes—
664C2×C42C22×D59116yes—
665C2×C42C22×D5918yes—
666C2×C42C22×D5911yescharacteristic
667C24—592no—
668C24C23×D5911yescharacteristic
669C24C23×D5912yes—
670#41—232no—
671#41—11864no—
672C2×Q8—24no—
673C2×Q8—594no—
674C2×Q8—598no—
675C2×Q8—598no—
676C2×Q8—1188no—
677C2×Q8—1184no—
678C2×Q8—2364no—
679C2×Q8C23×D5914yes—
680C2×D4—28no—
681C2×D4—5916no—
682C2×D4—598no—
683C2×D4—594no—
684C2×D4—11816no—
685C2×D4—1184no—
686C2×D4—2364no—
687C2×D4#1174568518yes—
688C2×D4C23×D5918yes—
689C2×D4C23×D5914yes—
690C22×C4—28no—
691C22×C4—24no—
692C22×C4—28no—
693C22×C4—24no—
694C22×C4—44no—
695C22×C4—42no—
696C22×C4—5916no—
697C22×C4—592no—
698C22×C4—594no—
699C22×C4—594no—
700C22×C4—592no—
701C22×C4—592no—
702C22×C4—5916no—
703C22×C4—598no—
704C22×C4—5916no—
705C22×C4—11816no—
706C22×C4—1188no—
707C22×C4—2368no—
708C22×C4—2368no—
709C22×C4C23×D5918yes—
710C22×C4C23×D5918yes—
711C22×C4C23×D5914yes—
712C22×C4C23×D5914yes—
713C22×C4C23×D5911yescharacteristic
714C22×C4C23×D5912yes—
715C22×C4C23×D5911yescharacteristic
716C22×C4C23×D5911yescharacteristic
717C22×C4C23×D5912yes—
718C22×C4C23×D5911yescharacteristic
719C22×C4C23×D5912yes—
720C22×C4C23×D5918yes—
721C22×C4C23×D5914yes—
722C22×C4C23×D5911yescharacteristic
723C22×C4C23×D5911yescharacteristic
724C4⋊C4—5916no—
725C4⋊C4—598no—
726C4⋊C4—594no—
727C4⋊C4—598no—
728C4⋊C4—594no—
729C4⋊C4—598no—
730C4⋊C4—598no—
731C4⋊C4—5916no—
732C4⋊C4—598no—
733C4⋊C4—5916no—
734C4⋊C4—5916no—
735C4⋊C4—5916no—
736C4⋊C4—5916no—
737C4⋊C4—5916no—
738C4⋊C4—5916no—
739C4⋊C4—598no—
740C4⋊C4—5916no—
741C4⋊C4—598no—
742C4⋊C4—598no—
743C4⋊C4—5916no—
744C4⋊C4C23×D5914yes—
745C4⋊C4C23×D5918yes—
746C4⋊C4C23×D5914yes—
747C4⋊C4C23×D5918yes—
748C22⋊C4—5916no—
749C22⋊C4—5916no—
750C22⋊C4—598no—
751C22⋊C4—598no—
752C22⋊C4—598no—
753C22⋊C4—598no—
754C22⋊C4—5916no—
755C22⋊C4—5916no—
756C22⋊C4—598no—
757C22⋊C4C23×D5918yes—
758C22⋊C4C23×D5918yes—
759C22⋊C4C23×D5918yes—
760C42—5916no—
761C42—5916no—
762C42—598no—
763C42C23×D5914yes—
764C42C23×D5918yes—
765C42C23×D5914yes—
766C42C23×D5914yes—
767C42C23×D5918yes—
768C42C23×D5914yes—
769C42C23×D5918yes—
770C23—24no—
771C23—24no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—594no—
776C23—1184no—
777C23—1184no—
778C23—1184no—
779C23C2×#1174568518yes—
780C23C24×D5912yes—
781C23C24×D5914yes—
782C23C24×D5911yescharacteristic
783Q8—28no—
784Q8—11816no—
785Q8—1188no—
786Q8—2368no—
787D4—216no—
788D4—11832no—
789D4—1188no—
790D4—2368no—
791D4C2×#11745685116yes—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—216no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—28no—
801C2×C4—216no—
802C2×C4—28no—
803C2×C4—48no—
804C2×C4—44no—
805C2×C4—594no—
806C2×C4—598no—
807C2×C4—598no—
808C2×C4—594no—
809C2×C4—594no—
810C2×C4—1184no—
811C2×C4—1188no—
812C2×C4—11832no—
813C2×C4—1184no—
814C2×C4—1184no—
815C2×C4—1188no—
816C2×C4—11816no—
817C2×C4—23616no—
818C2×C4—23616no—
819C2×C4C2×#1174568514yes—
820C2×C4#1427377414yes—
821C2×C4C24×D5912yes—
822C2×C4C24×D5914yes—
823C2×C4C24×D5912yes—
824C2×C4C24×D5912yes—
825C2×C4C24×D5914yes—
826C2×C4C24×D5912yes—
827C2×C4C24×D5914yes—
828C2×C4C24×D5912yes—
829C2×C4C24×D5912yes—
830C22—216no—
831C22—24no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—44no—
837C22—1184no—
838C22—1184no—
839C22—1184no—
840C22—2368no—
841C22C22×#1174568518yes—
842C22C22×#1174568512yes—
843C22C2×#1427377412yes—
844C22#1683823812yes—
845C22C25×D5911yescharacteristic
846C4—22no—
847C4—24no—
848C4—22no—
849C4—24no—
850C4—22no—
851C4—24no—
852C4—22no—
853C4—1184no—
854C4—1188no—
855C4—1184no—
856C4—1184no—
857C4—1188no—
858C4C22×#1174568514yes—
859C4C2×#1427377414yes—
860C2—28no—
861C2—42no—
862C2—2364no—
863C2#2143807414yesdirect product factor
864C2C23×#1174568511yescharacteristic
865C2C22×#1427377411yescharacteristic
866C2C2×#1683823811yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C4×#41×C59C2
socleC23×C59C25
hypercenterC2×C4×#41D59
hypocenterC59C2×#3515
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #21438074C2direct (N × H)
2. C2×#16838130C2semidirect
3. C2×#16838112C2semidirect
4. C2×#16838109C2semidirect
5. C2×#16838098C2semidirect
6. C2×#16838092C2semidirect
7. C2×#16838091C2semidirect
8. C2×#16838085C2semidirect
9. C2×#16838056C2semidirect
10. C2×#16838051C2semidirect
11. C2×#16838010C2semidirect
12. C2×#16837994C2semidirect
13. C2×#16837959C2semidirect
14. C2×#16837936C2semidirect
15. C2×#16837936C2semidirect
16. C22×#14273719C2semidirect
17. C2×#16837881C2semidirect
18. C2×C4×#41×C59C2semidirect
20. #16838130C22semidirect
21. #16838112C22semidirect
22. #16838109C22semidirect
23. #16838098C22semidirect
24. #16838092C22semidirect
25. #16838091C22semidirect
26. #16838085C22semidirect
27. #16838056C22semidirect
28. #16838051C22semidirect
29. #16838010C22semidirect
30. #16837994C22semidirect
31. #16837959C22semidirect
35. #16837936C22semidirect
36. #16837936C22semidirect
47. C2×#14273719C22semidirect
68. #16837881C22semidirect
90. C4×#41×C59C22semidirect
444. C2×C4×#41D59semidirect
447. C2×C59#3515semidirect
503. C4×#41C2×D59semidirect
534. C59C2×#3515semidirect
863. C2#21438074direct (N × H)

Maximal subgroups

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

subgroupindex
#214380742
C2×#168381302
C2×#168381122
C2×#168381092
C2×#168380982
C2×#168380922
C2×#168380912
C2×#168380852
C2×#168380562
C2×#168380512
C2×#168380102
C2×#168379942
C2×#168379592
C2×#168379362
C22×#142737192
C2×#168378812
C2×C4×#41×C592
C2×#351559