Finite Group Databasebeta

← C2×#21438436 #29496371

Subgroups — C2×#21438436 #29496371

Order 15104.

7086 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#21438436C2132yesmaximal, direct product factor
2C2×#16838154C214yesmaximal, complemented
3C2×Q8×Dic118C211yesmaximal, characteristic, complemented
4C2×#16838117C211yesmaximal, characteristic, complemented
5C2×#16838112C211yesmaximal, characteristic, complemented
6C2×#16838109C211yesmaximal, characteristic, complemented
7C2×#16838094C212yesmaximal, complemented
8C2×#16838092C212yesmaximal, complemented
9C2×#16838056C212yesmaximal, complemented
10C2×#16838052C212yesmaximal, complemented
11C2×#16838032C212yesmaximal, complemented
12C2×#16838030C212yesmaximal, complemented
13C2×#16838023C212yesmaximal, complemented
14C2×#16838021C212yesmaximal, complemented
15C2×#16837974C214yesmaximal, complemented
16C22×#14273727C211yesmaximal, characteristic, complemented
17C2×#16837936C211yesmaximal, characteristic, complemented
18C2×C59×#529C211yesmaximal, characteristic, complemented
19C22×#11745687C2214yes—
20C23×Dic118C2212yes—
21#16838154C22164yescomplemented
22Q8×Dic118C22116yescomplemented
23#16838117C22116yescomplemented
24#16838112C22116yescomplemented
25#16838109C22116yescomplemented
26#16838094C22132yescomplemented
27#16838092C22132yescomplemented
28#16838056C22132yescomplemented
29#16838052C22132yescomplemented
30#16838032C22132yescomplemented
31#16838030C22132yescomplemented
32#16838023C22132yescomplemented
33#16838021C22132yescomplemented
34#16837974C22164yescomplemented
35C2×#14273727C2212yes—
36C2×#14273727C2212yes—
37C2×#14273727C2212yes—
38C2×#14273727C2212yes—
39C2×#14273727C2211yescharacteristic
40C2×#14273727C2211yescharacteristic
41C2×#14273727C22116yescomplemented
42C2×#14273726C2214yes—
43C2×#14273726C2214yes—
44C2×#14273726C2212yes—
45#16837936C22116yescomplemented
46C2×#14273722C2214yes—
47C2×#14273721C2212yes—
48C2×#14273720C2214yes—
49C2×#14273719C2211yescharacteristic
50C2×#14273719C2212yes—
51C2×#14273718C2214yes—
52C2×#14273718C2212yes—
53C2×#14273717C2214yes—
54C2×#14273715C2211yescharacteristic
55C2×#14273713C2214yes—
56C2×#14273713C2214yes—
57C2×#14273711C2214yes—
58C2×#14273711C2214yes—
59C2×#14273710C2212yes—
60C2×#14273709C2214yes—
61C2×#14273708C2214yes—
62C2×#14273707C2214yes—
63C2×#14273706C2212yes—
64C2×#14273706C2211yescharacteristic
65C2×#14273705C2214yes—
66C2×#14273705C2214yes—
67C2×#14273704C2214yes—
68C2×#14273704C2214yes—
69C2×#14273704C2214yes—
70C2×#14273703C2212yes—
71C2×#14273701C2212yes—
72C2×#14273701C2211yescharacteristic
73C2×#14273698C2212yes—
74C2×Q8×Dic59C2212yes—
75C2×C4×Dic118C2212yes—
76C2×C4×Dic118C2211yescharacteristic
77C2×C4×D236C2212yes—
78C2×C4×D236C2211yescharacteristic
79C2×D4×Dic59C2212yes—
80C2×C4×C22⋊D59C2212yes—
81C2×#14273686C2212yes—
82C2×#14273685C2212yes—
83C2×#14273684C2212yes—
84C2×#14273683C2214yes—
85C22×C4⋊Dic59C2212yes—
86C22×C4⋊Dic59C2212yes—
87C22×C4⋊Dic59C2212yes—
88C2×C4⋊C4×D59C2212yes—
89C59×#529C22116yescomplemented
90C2×#126×C59C2212yes—
91C2×#125×C59C2211yescharacteristic
92C2×#124×C59C2211yescharacteristic
93C2×#123×C59C2212yes—
94C2×C22⋊Q8×C59C2211yescharacteristic
95C2×#121×C59C2211yescharacteristic
96C2×C4×Q8×C59C2211yescharacteristic
97C2×C4×D4×C59C2212yes—
98C2×C4×D4×C59C2211yescharacteristic
99C2×#117×C59C2212yes—
100C22×C42×C59C2211yescharacteristic
101C2×#11745687—416no—
102C2×#11745687C23132yes—
103C22×Dic118—48no—
104C22×Dic118C2311yescharacteristic
105C22×Dic118C2312yes—
106C22×Dic118C2314yes—
107C22×Dic118C2314yes—
108C22×Dic118C2312yes—
109C22×Dic118C23116yes—
110C22×D236C2311yescharacteristic
111C22×C22⋊D59C2312yes—
112C22×C22⋊D59C2314yes—
113C23×Dic59C2314yes—
114C23×Dic59C2314yes—
115C22×C4×D59C2312yes—
116C22×C4×D59C2314yes—
117#14273727C23116yes—
118#14273727C23116yes—
119#14273727C23116yes—
120#14273727C2318yes—
121#14273727C2318yes—
122#14273727C23116yes—
123#14273726C23132yes—
124#14273726C23132yes—
125#14273726C23116yes—
126#14273722C23132yes—
127#14273721C23116yes—
128#14273720C23132yes—
129#14273719C2318yes—
130#14273719C23116yes—
131#14273718C23132yes—
132#14273718C23116yes—
133#14273717C23132yes—
134#14273715C2318yes—
135#14273713C23132yes—
136#14273713C23132yes—
137#14273711C23132yes—
138#14273711C23132yes—
139#14273710C23116yes—
140#14273709C23132yes—
141#14273708C23132yes—
142#14273707C23132yes—
143#14273706C2318yes—
144#14273706C23116yes—
145#14273705C23132yes—
146#14273705C23132yes—
147#14273704C23132yes—
148#14273704C23132yes—
149#14273704C23132yes—
150#14273703C23116yes—
151#14273701C2318yes—
152#14273701C23116yes—
153#14273698C23116yes—
154Q8×Dic59C23116yes—
155C4×Dic118C2318yes—
156C4×Dic118C23116yes—
157C4×D236C2318yes—
158C4×D236C23116yes—
159D4×Dic59C23116yes—
160C4×C22⋊D59C23116yes—
161#14273686C23116yes—
162#14273685C23116yes—
163#14273684C23116yes—
164#14273683C23132yes—
165C2×C4⋊Dic59C2312yes—
166C2×C4⋊Dic59C2311yescharacteristic
167C2×C4⋊Dic59C2312yes—
168C2×C4⋊Dic59C2312yes—
169C2×C4⋊Dic59C2314yes—
170C2×C4⋊Dic59C2314yes—
171C2×C4⋊Dic59C2314yes—
172C2×C4⋊Dic59C2311yescharacteristic
173C2×C4⋊Dic59C2312yes—
174C2×C4⋊Dic59C2314yes—
175C2×C4⋊Dic59C23116yes—
176C2×C4⋊Dic59C23116yes—
177C2×C4⋊Dic59C23116yes—
178C2×Dic59⋊C4C2314yes—
179C2×Dic59⋊C4C2312yes—
180C2×Dic59⋊C4C2312yes—
181C2×Dic59⋊C4C2312yes—
182C2×Dic59⋊C4C2314yes—
183C2×Dic59⋊C4C2314yes—
184C2×Dic59⋊C4C2314yes—
185C2×Dic59⋊C4C2312yes—
186C4⋊C4×D59C23116yes—
187C2×C22⋊Dic59C2314yes—
188C2×C22⋊Dic59C2314yes—
189C2×C22⋊Dic59C2312yes—
190C2×(C2×D59)⋊C4C2314yes—
191C2×(C2×D59)⋊C4C2312yes—
192C2×(C2×D59)⋊C4C2314yes—
193C2×(C2×D59)⋊C4C2312yes—
194C2×(C2×D59)⋊C4C2312yes—
195C2×(C2×D59)⋊C4C2312yes—
196C2×C4×Dic59C2314yes—
197C2×C4×Dic59C2314yes—
198C2×C4×Dic59C2312yes—
199C22×Q8×C59C2311yescharacteristic
200C22×D4×C59C2311yescharacteristic
201C22×D4×C59C2312yes—
202C23×C4×C59C2311yescharacteristic
203C23×C4×C59C2312yes—
204C23×C4×C59C2311yescharacteristic
205C23×C4×C59C2311yescharacteristic
206#126×C59C23116yes—
207#125×C59C2318yes—
208#124×C59C2318yes—
209#123×C59C23116yes—
210C22⋊Q8×C59C2318yes—
211#121×C59C2318yes—
212C4×Q8×C59C2318yes—
213C4×D4×C59C23116yes—
214C4×D4×C59C2318yes—
215#117×C59C23116yes—
216C2×C4⋊C4×C59C2312yes—
217C2×C4⋊C4×C59C2312yes—
218C2×C4⋊C4×C59C2312yes—
219C2×C4⋊C4×C59C2312yes—
220C2×C4⋊C4×C59C2311yescharacteristic
221C2×C4⋊C4×C59C2311yescharacteristic
222C2×C22⋊C4×C59C2312yes—
223C2×C22⋊C4×C59C2312yes—
224C2×C22⋊C4×C59C2312yes—
225C2×C22⋊C4×C59C2312yes—
226C2×C22⋊C4×C59C2312yes—
227C2×C42×C59C2311yescharacteristic
228C2×C42×C59C2312yes—
229C2×C42×C59C2311yescharacteristic
230C2×C42×C59C2318yes—
231C2×C42×C59C2311yescharacteristic
232C2×C42×C59C2311yescharacteristic
233C24×C59C2412yes—
234C24×C59C2411yescharacteristic
235C23×D59C2412yes—
236C2×Q8×C59—24no—
237C2×Q8×C59C2414yes—
238C2×D4×C59—28no—
239C2×D4×C59—24no—
240C2×D4×C59C2418yes—
241C2×D4×C59C2414yes—
242C22×C4×C59—24no—
243C22×C4×C59—24no—
244C22×C4×C59—28no—
245C22×C4×C59—24no—
246C22×C4×C59C2411yescharacteristic
247C22×C4×C59C2411yescharacteristic
248C22×C4×C59C2411yescharacteristic
249C22×C4×C59C2411yescharacteristic
250C22×C4×C59C2414yes—
251C22×C4×C59C2414yes—
252C22×C4×C59C2414yes—
253C22×C4×C59C2412yes—
254C22×C4×C59C2412yes—
255C22×C4×C59C2412yes—
256C22×C4×C59C2418yes—
257C22×C4×C59C2411yescharacteristic
258C22×C4×C59C2411yescharacteristic
259C2×C22⋊D59—28no—
260C2×C22⋊D59—48no—
261C2×C22⋊D59C2418yes—
262C2×C22⋊D59C24116yes—
263C22×Dic59—216no—
264C22×Dic59—48no—
265C22×Dic59C2412yes—
266C22×Dic59C2412yes—
267C22×Dic59C2414yes—
268C22×Dic59C2412yes—
269C22×Dic59C2414yes—
270C22×Dic59C24116yes—
271C22×Dic59C24116yes—
272#11745687—464no—
273C2×D236—24no—
274C2×D236C2414yes—
275C2×C4×D59—28no—
276C2×C4×D59—48no—
277C2×C4×D59C2418yes—
278C2×C4×D59C24116yes—
279C2×Dic118—24no—
280C2×Dic118—44no—
281C2×Dic118—48no—
282C2×Dic118—44no—
283C2×Dic118—432no—
284C2×Dic118—48no—
285C2×Dic118C2414yes—
286C2×Dic118C2418yes—
287C2×Dic118C24116yes—
288C2×Dic118C24116yes—
289C2×Dic118C2418yes—
290C4⋊C4×C59C2418yes—
291C4⋊C4×C59C2418yes—
292C4⋊C4×C59C2414yes—
293C4⋊C4×C59C2418yes—
294C4⋊C4×C59C2414yes—
295C4⋊C4×C59C2418yes—
296C22⋊C4×C59C2418yes—
297C22⋊C4×C59C2418yes—
298C22⋊C4×C59C2418yes—
299C22⋊C4×C59C2418yes—
300C22⋊C4×C59C2418yes—
301C42×C59C2414yes—
302C42×C59C2414yes—
303C42×C59C2414yes—
304C42×C59C2414yes—
305C42×C59C2418yes—
306C22⋊Dic59C2418yes—
307C22⋊Dic59C24116yes—
308C22⋊Dic59C24116yes—
309(C2×D59)⋊C4C2418yes—
310(C2×D59)⋊C4C2418yes—
311(C2×D59)⋊C4C24116yes—
312(C2×D59)⋊C4C2418yes—
313(C2×D59)⋊C4C24116yes—
314(C2×D59)⋊C4C2418yes—
315C4⋊Dic59C2418yes—
316C4⋊Dic59C2418yes—
317C4⋊Dic59C2414yes—
318C4⋊Dic59C2418yes—
319C4⋊Dic59C2418yes—
320C4⋊Dic59C24116yes—
321C4⋊Dic59C24116yes—
322C4⋊Dic59C24116yes—
323C4⋊Dic59C2414yes—
324C4⋊Dic59C24116yes—
325Dic59⋊C4C24116yes—
326Dic59⋊C4C24116yes—
327Dic59⋊C4C24116yes—
328Dic59⋊C4C2418yes—
329Dic59⋊C4C2418yes—
330Dic59⋊C4C2418yes—
331Dic59⋊C4C2418yes—
332Dic59⋊C4C24116yes—
333C4×Dic59C24116yes—
334C4×Dic59C24116yes—
335C4×Dic59C2418yes—
336C23×C59—22no—
337C23×C59—22no—
338C23×C59—24no—
339C23×C59—24no—
340C23×C59—24no—
341C23×C59H(5,𝔽2)14yes—
342C23×C59C2514yes—
343C23×C59C2512yes—
344C23×C59C2511yescharacteristic
345C22×D59—24no—
346C22×D59—24no—
347C22×D59—24no—
348C22×D59C2514yes—
349Q8×C59—28no—
350D4×C59—216no—
351D4×C59—28no—
352C2×C4×C59—28no—
353C2×C4×C59—22no—
354C2×C4×C59—22no—
355C2×C4×C59—24no—
356C2×C4×C59—22no—
357C2×C4×C59—22no—
358C2×C4×C59—24no—
359C2×C4×C59—24no—
360C2×C4×C59—28no—
361C2×C4×C59—216no—
362C2×C4×C59—28no—
363C2×C4×C592−1+414yes—
364C2×C4×C592−1+414yes—
365C2×C4×C59C2514yes—
366C2×C4×C59C2514yes—
367C2×C4×C59C2514yes—
368C2×C4×C59C2512yes—
369C2×C4×C59C2512yes—
370C2×C4×C59C2512yes—
371C2×C4×C59C2512yes—
372C2×C4×C59C2512yes—
373C2×C4×C59C2512yes—
374C22⋊D59—216no—
375C22⋊D59—416no—
376C2×Dic59—28no—
377C2×Dic59—28no—
378C2×Dic59—232no—
379C2×Dic59—24no—
380C2×Dic59—24no—
381C2×Dic59—24no—
382C2×Dic59—416no—
383C2×Dic59C2514yes—
384C2×Dic59C2514yes—
385C2×Dic59C2518yes—
386C2×Dic59C2514yes—
387C2×Dic59C2518yes—
388D236—28no—
389C4×D59—216no—
390C4×D59—416no—
391Dic118—28no—
392Dic118—48no—
393Dic118—416no—
394Dic118—48no—
395Dic118—416no—
396C2×#3544—591nomaximal, Sylow
397C22×C59—22no—
398C22×C59—22no—
399C22×C59—28no—
400C22×C59—24no—
401C22×C59—24no—
402C22×C59—24no—
403C22×C59—48no—
404C22×C59C2×H(5,𝔽2)14yes—
405C22×C59C2×H(5,𝔽2)12yes—
406C22×C59C2×2−1+412yes—
407C22×C59C2×2−1+412yes—
408C22×C59C2611yescharacteristic
409C2×D59—24no—
410C2×D59—24no—
411C2×D59—24no—
412C2×D59—48no—
413C4×C59—22no—
414C4×C59—22no—
415C4×C59—24no—
416C4×C59—24no—
417C4×C59—22no—
418C4×C59—22no—
419C4×C59—24no—
420C4×C59C2×2−1+414yes—
421C4×C59C2×2−1+414yes—
422Dic59—28no—
423Dic59—28no—
424Dic59—24no—
425Dic59—24no—
426Dic59—24no—
427#3544—5932no—
428C2×#563—594no—
429C2×Q82—591no—
430C2×#555—591no—
431C2×#554—591no—
432C2×#554—591no—
433C2×#552—592no—
434C2×#552—592no—
435C2×#547—592no—
436C2×#547—592no—
437C2×#544—592no—
438C2×#544—592no—
439C2×#542—592no—
440C2×#542—592no—
441C2×#536—594no—
442C22×C4⋊Q8—591no—
443C2×#529—591no—
444C2×#529D5911yescharacteristic, complemented
445C2×C59—24no—
446C2×C59—44no—
447C2×C59#354414yescomplemented
448C2×C59C22×H(5,𝔽2)11yescharacteristic
449C2×C59C22×2−1+411yescharacteristic
450C2×C59C22×2−1+411yescharacteristic
451D59—44no—
452C22×#41—594no—
453C23×Q8—592no—
454#563—5964no—
455Q82—5916no—
456#555—5916no—
457#554—5916no—
458#554—5916no—
459#552—5932no—
460#552—5932no—
461#547—5932no—
462#547—5932no—
463#544—5932no—
464#544—5932no—
465#542—5932no—
466#542—5932no—
467#536—5964no—
468C2×C4⋊Q8—594no—
469C2×C4⋊Q8—594no—
470C2×C4⋊Q8—592no—
471C2×C4⋊Q8—592no—
472C2×C4⋊Q8—592no—
473C2×C4⋊Q8—591no—
474C2×C4⋊Q8—591no—
475C2×C4⋊Q8—592no—
476C2×C4⋊Q8—592no—
477C2×C4⋊Q8—5916no—
478#529—5916no—
479#529C2×D59116yescomplemented
480C2×#126—594no—
481C2×#126—594no—
482C2×#126—592no—
483C2×#126C2×D5912yes—
484C2×#125—594no—
485C2×#125—592no—
486C2×#125—594no—
487C2×#125—591no—
488C2×#125—592no—
489C2×#125C2×D5911yescharacteristic
490C2×#124—594no—
491C2×#124—594no—
492C2×#124—591no—
493C2×#124C2×D5911yescharacteristic
494C2×#123—594no—
495C2×#123—592no—
496C2×#123—594no—
497C2×#123—594no—
498C2×#123—594no—
499C2×#123C2×D5912yes—
500C2×C22⋊Q8—592no—
501C2×C22⋊Q8—591no—
502C2×C22⋊Q8—592no—
503C2×C22⋊Q8—594no—
504C2×C22⋊Q8—594no—
505C2×C22⋊Q8—594no—
506C2×C22⋊Q8—594no—
507C2×C22⋊Q8—594no—
508C2×C22⋊Q8—594no—
509C2×C22⋊Q8C2×D5911yescharacteristic
510C2×#121—592no—
511C2×#121—591no—
512C2×#121—592no—
513C2×#121C2×D5911yescharacteristic
514C2×C4×Q8—592no—
515C2×C4×Q8—591no—
516C2×C4×Q8—592no—
517C2×C4×Q8C2×D5911yescharacteristic
518C2×C4×D4—592no—
519C2×C4×D4—592no—
520C2×C4×D4—591no—
521C2×C4×D4—592no—
522C2×C4×D4C2×D5912yes—
523C2×C4×D4C2×D5911yescharacteristic
524C2×#117—592no—
525C2×#117—592no—
526C2×#117—594no—
527C2×#117—592no—
528C2×#117C2×D5912yes—
529C22×C4⋊C4—592no—
530C22×C4⋊C4—592no—
531C22×C4⋊C4—592no—
532C22×C4⋊C4—592no—
533C22×C42C2×D5911yescharacteristic
534C59C2×#354411yescharacteristic, complemented, Sylow
535C2×#41—5932no—
536C2×#41—23616no—
537C22×Q8—591no—
538C22×Q8—592no—
539C22×Q8—594no—
540C22×Q8—594no—
541C22×Q8—592no—
542C22×Q8—5916no—
543C22×Q8—2368no—
544C22×Q8C22×D5911yescharacteristic
545C22×D4—592no—
546C22×D4—594no—
547C22×D4—591no—
548C22×D4C22×D5911yescharacteristic
549C22×D4C22×D5912yes—
550C23×C4—594no—
551C23×C4—594no—
552C23×C4—592no—
553C23×C4—594no—
554C23×C4C22×D5911yescharacteristic
555C23×C4C22×D5911yescharacteristic
556C23×C4C22×D5912yes—
557C23×C4C22×D5911yescharacteristic
558C4⋊Q8—5932no—
559C4⋊Q8—5932no—
560C4⋊Q8—5916no—
561C4⋊Q8—5916no—
562C4⋊Q8—5916no—
563C4⋊Q8—598no—
564C4⋊Q8—598no—
565C4⋊Q8—5916no—
566C4⋊Q8—5916no—
567#126—5932no—
568#126—5932no—
569#126—5916no—
570#126C22×D59116yes—
571#125—5916no—
572#125—5932no—
573#125—5932no—
574#125—598no—
575#125—5916no—
576#125C22×D5918yes—
577#124—5932no—
578#124—5932no—
579#124—598no—
580#124C22×D5918yes—
581#123—5932no—
582#123—5916no—
583#123—5932no—
584#123—5932no—
585#123—5932no—
586#123C22×D59116yes—
587C22⋊Q8—5916no—
588C22⋊Q8—598no—
589C22⋊Q8—5916no—
590C22⋊Q8—5932no—
591C22⋊Q8—5932no—
592C22⋊Q8—5932no—
593C22⋊Q8—5932no—
594C22⋊Q8—5932no—
595C22⋊Q8—5932no—
596C22⋊Q8C22×D5918yes—
597#121—5916no—
598#121—598no—
599#121—5916no—
600#121C22×D5918yes—
601C4×Q8—5916no—
602C4×Q8—598no—
603C4×Q8—5916no—
604C4×Q8C22×D5918yes—
605C4×D4—5916no—
606C4×D4—5916no—
607C4×D4—598no—
608C4×D4—5916no—
609C4×D4C22×D59116yes—
610C4×D4C22×D5918yes—
611#117—5916no—
612#117—5916no—
613#117—5932no—
614#117—5916no—
615#117C22×D59116yes—
616C2×C4⋊C4—592no—
617C2×C4⋊C4—592no—
618C2×C4⋊C4—591no—
619C2×C4⋊C4—592no—
620C2×C4⋊C4—592no—
621C2×C4⋊C4—594no—
622C2×C4⋊C4—594no—
623C2×C4⋊C4—594no—
624C2×C4⋊C4—594no—
625C2×C4⋊C4—5916no—
626C2×C4⋊C4—5916no—
627C2×C4⋊C4—5916no—
628C2×C4⋊C4—591no—
629C2×C4⋊C4—594no—
630C2×C4⋊C4—594no—
631C2×C4⋊C4—592no—
632C2×C4⋊C4—592no—
633C2×C4⋊C4—592no—
634C2×C4⋊C4—592no—
635C2×C4⋊C4—594no—
636C2×C4⋊C4—594no—
637C2×C4⋊C4—5916no—
638C2×C4⋊C4C22×D5911yescharacteristic
639C2×C4⋊C4C22×D5911yescharacteristic
640C2×C4⋊C4C22×D5912yes—
641C2×C4⋊C4C22×D5912yes—
642C2×C4⋊C4C22×D5912yes—
643C2×C4⋊C4C22×D5912yes—
644C2×C22⋊C4—592no—
645C2×C22⋊C4—594no—
646C2×C22⋊C4—594no—
647C2×C22⋊C4—592no—
648C2×C22⋊C4—594no—
649C2×C22⋊C4—592no—
650C2×C22⋊C4—594no—
651C2×C22⋊C4—592no—
652C2×C22⋊C4—592no—
653C2×C22⋊C4C22×D5912yes—
654C2×C22⋊C4C22×D5912yes—
655C2×C22⋊C4C22×D5912yes—
656C2×C22⋊C4C22×D5912yes—
657C2×C22⋊C4C22×D5912yes—
658C2×C42—594no—
659C2×C42—592no—
660C2×C42—594no—
661C2×C42C22×D5911yescharacteristic
662C2×C42C22×D5911yescharacteristic
663C2×C42C22×D5912yes—
664C2×C42C22×D5911yescharacteristic
665C2×C42C22×D5911yescharacteristic
666C2×C42C22×D5918yes—
667C24—592no—
668C24C23×D5912yes—
669C24C23×D5911yescharacteristic
670#41—23664no—
671C2×Q8—24no—
672C2×Q8—594no—
673C2×Q8—598no—
674C2×Q8—5916no—
675C2×Q8—5916no—
676C2×Q8—598no—
677C2×Q8—1184no—
678C2×Q8—2364no—
679C2×Q8—2368no—
680C2×Q8—2364no—
681C2×Q8—23632no—
682C2×Q8—2368no—
683C2×Q8C23×D5914yes—
684C2×D4—28no—
685C2×D4—24no—
686C2×D4—598no—
687C2×D4—5916no—
688C2×D4—594no—
689C2×D4—1188no—
690C2×D4—1184no—
691C2×D4—2368no—
692C2×D4C23×D5914yes—
693C2×D4C23×D5918yes—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—28no—
697C22×C4—24no—
698C22×C4—5916no—
699C22×C4—592no—
700C22×C4—592no—
701C22×C4—594no—
702C22×C4—592no—
703C22×C4—594no—
704C22×C4—5916no—
705C22×C4—598no—
706C22×C4—5916no—
707C22×C4—11816no—
708C22×C4—1188no—
709C22×C4—2368no—
710C22×C4—2368no—
711C22×C4C23×D5914yes—
712C22×C4C23×D5914yes—
713C22×C4C23×D5914yes—
714C22×C4C23×D5918yes—
715C22×C4C23×D5912yes—
716C22×C4C23×D5912yes—
717C22×C4C23×D5911yescharacteristic
718C22×C4C23×D5911yescharacteristic
719C22×C4C23×D5911yescharacteristic
720C22×C4C23×D5911yescharacteristic
721C22×C4C23×D5912yes—
722C22×C4C23×D5911yescharacteristic
723C22×C4C23×D5911yescharacteristic
724C4⋊C4—598no—
725C4⋊C4—598no—
726C4⋊C4—594no—
727C4⋊C4—598no—
728C4⋊C4—598no—
729C4⋊C4—5916no—
730C4⋊C4—5916no—
731C4⋊C4—5916no—
732C4⋊C4—5916no—
733C4⋊C4—594no—
734C4⋊C4—5916no—
735C4⋊C4—5916no—
736C4⋊C4—598no—
737C4⋊C4—598no—
738C4⋊C4—598no—
739C4⋊C4—598no—
740C4⋊C4—5916no—
741C4⋊C4—5916no—
742C4⋊C4C23×D5914yes—
743C4⋊C4C23×D5914yes—
744C4⋊C4C23×D5918yes—
745C4⋊C4C23×D5918yes—
746C4⋊C4C23×D5918yes—
747C4⋊C4C23×D5918yes—
748C22⋊C4—598no—
749C22⋊C4—5916no—
750C22⋊C4—5916no—
751C22⋊C4—598no—
752C22⋊C4—5916no—
753C22⋊C4—598no—
754C22⋊C4—5916no—
755C22⋊C4—598no—
756C22⋊C4—598no—
757C22⋊C4C23×D5918yes—
758C22⋊C4C23×D5918yes—
759C22⋊C4C23×D5918yes—
760C22⋊C4C23×D5918yes—
761C22⋊C4C23×D5918yes—
762C42—5916no—
763C42—598no—
764C42—5916no—
765C42C23×D5914yes—
766C42C23×D5914yes—
767C42C23×D5914yes—
768C42C23×D5914yes—
769C42C23×D5918yes—
770C23—22no—
771C23—22no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—594no—
776C23—1184no—
777C23—1184no—
778C23—1184no—
779C23#1427377314yes—
780C23C24×D5914yes—
781C23C24×D5912yes—
782C23C24×D5911yescharacteristic
783Q8—28no—
784Q8—1188no—
785Q8—2368no—
786Q8—23616no—
787Q8—2368no—
788Q8—23616no—
789D4—216no—
790D4—28no—
791D4—11816no—
792D4—1188no—
793D4—23616no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—28no—
803C2×C4—216no—
804C2×C4—28no—
805C2×C4—594no—
806C2×C4—594no—
807C2×C4—598no—
808C2×C4—594no—
809C2×C4—598no—
810C2×C4—1188no—
811C2×C4—1188no—
812C2×C4—11832no—
813C2×C4—1184no—
814C2×C4—1184no—
815C2×C4—1184no—
816C2×C4—11816no—
817C2×C4—23616no—
818C2×C4—23616no—
819C2×C4#1427377414yes—
820C2×C4#1427377414yes—
821C2×C4C24×D5914yes—
822C2×C4C24×D5914yes—
823C2×C4C24×D5912yes—
824C2×C4C24×D5912yes—
825C2×C4C24×D5912yes—
826C2×C4C24×D5912yes—
827C2×C4C24×D5914yes—
828C2×C4C24×D5912yes—
829C2×C4C24×D5912yes—
830C22—22no—
831C22—22no—
832C22—28no—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—48no—
837C22—1184no—
838C22—1184no—
839C22—1184no—
840C22—2368no—
841C22C2×#1427377314yes—
842C22C2×#1427377312yes—
843C22C2×#1427377412yes—
844C22C2×#1427377412yes—
845C22C25×D5911yescharacteristic
846C4—22no—
847C4—22no—
848C4—24no—
849C4—24no—
850C4—22no—
851C4—22no—
852C4—24no—
853C4—1188no—
854C4—1188no—
855C4—1184no—
856C4—1184no—
857C4—1184no—
858C4C2×#1427377414yes—
859C4C2×#1427377414yes—
860C2—24no—
861C2—44no—
862C2—2364no—
863C2#2143843614yesdirect product factor
864C2C22×#1427377311yescharacteristic
865C2C22×#1427377411yescharacteristic
866C2C22×#1427377411yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#529C2
socleC23×C59C25
hypercenterC2×#529D59
hypocenterC59C2×#3544
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #21438436C2direct (N × H)
2. C2×#16838154C2semidirect
3. C2×Q8×Dic118C2semidirect
4. C2×#16838117C2semidirect
5. C2×#16838112C2semidirect
6. C2×#16838109C2semidirect
7. C2×#16838094C2semidirect
8. C2×#16838092C2semidirect
9. C2×#16838056C2semidirect
10. C2×#16838052C2semidirect
11. C2×#16838032C2semidirect
12. C2×#16838030C2semidirect
13. C2×#16838023C2semidirect
14. C2×#16838021C2semidirect
15. C2×#16837974C2semidirect
16. C22×#14273727C2semidirect
17. C2×#16837936C2semidirect
18. C2×C59×#529C2semidirect
21. #16838154C22semidirect
22. Q8×Dic118C22semidirect
23. #16838117C22semidirect
24. #16838112C22semidirect
25. #16838109C22semidirect
26. #16838094C22semidirect
27. #16838092C22semidirect
28. #16838056C22semidirect
29. #16838052C22semidirect
30. #16838032C22semidirect
31. #16838030C22semidirect
32. #16838023C22semidirect
33. #16838021C22semidirect
34. #16837974C22semidirect
41. C2×#14273727C22semidirect
45. #16837936C22semidirect
89. C59×#529C22semidirect
444. C2×#529D59semidirect
447. C2×C59#3544semidirect
479. #529C2×D59semidirect
534. C59C2×#3544semidirect
863. C2#21438436direct (N × H)

Maximal subgroups

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

subgroupindex
#214384362
C2×#168381542
C2×Q8×Dic1182
C2×#168381172
C2×#168381122
C2×#168381092
C2×#168380942
C2×#168380922
C2×#168380562
C2×#168380522
C2×#168380322
C2×#168380302
C2×#168380232
C2×#168380212
C2×#168379742
C22×#142737272
C2×#168379362
C2×C59×#5292
C2×#354459