Finite Group Databasebeta

← C2×#21437715 #29495784

Subgroups — C2×#21437715 #29495784

Order 15104.

7706 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437715C2132yesmaximal, direct product factor
2C2×#16838130C211yesmaximal, characteristic, complemented
3C2×#16838120C212yesmaximal, complemented
4C2×#16838093C212yesmaximal, complemented
5C2×#16838088C214yesmaximal, complemented
6C2×#16838067C211yesmaximal, characteristic, complemented
7C2×#16838060C212yesmaximal, complemented
8C2×#16838057C211yesmaximal, characteristic, complemented
9C2×#16838054C212yesmaximal, complemented
10C2×#16837957C211yesmaximal, characteristic, complemented
11C2×#16837954C212yesmaximal, complemented
12C2×#16837935C214yesmaximal, complemented
13C2×#16837931C212yesmaximal, complemented
14C2×C4×#11745689C211yesmaximal, characteristic, complemented
15C2×#16837870C212yesmaximal, complemented
16C2×C4×#11745687C211yesmaximal, characteristic, complemented
17C2×C4×Q8×D59C212yesmaximal, complemented
18C2×C59×#556C211yesmaximal, characteristic, complemented
19C22×#11745689C2211yescharacteristic
20C22×#11745685C2212yes—
21C22×#11745687C2211yescharacteristic
22C22×Q8×D59C2212yes—
23#16838130C22116yescomplemented
24#16838120C22132yescomplemented
25#16838093C22132yescomplemented
26#16838088C22164yescomplemented
27#16838067C22116yescomplemented
28#16838060C22132yescomplemented
29#16838057C22116yescomplemented
30#16838054C22132yescomplemented
31#16837957C22116yescomplemented
32#16837954C22132yescomplemented
33C2×#14273727C2211yescharacteristic
34C2×#14273726C2212yes—
35C2×#14273725C2212yes—
36#16837935C22164yescomplemented
37#16837931C22132yescomplemented
38C2×#14273721C2214yes—
39C2×#14273720C2214yes—
40C2×#14273719C2212yes—
41C2×#14273718C2212yes—
42C2×#14273717C2214yes—
43C2×#14273717C2214yes—
44C2×#14273713C2214yes—
45C2×#14273712C2214yes—
46C2×#14273709C2214yes—
47C2×#14273709C2214yes—
48C2×#14273707C2212yes—
49C2×#14273706C2212yes—
50C2×#14273705C2214yes—
51C2×#14273704C2214yes—
52C2×#14273703C2212yes—
53C2×#14273703C2212yes—
54C2×#14273700C2214yes—
55C2×#14273698C2212yes—
56C4×#11745689C22116yescomplemented
57#16837870C22132yescomplemented
58C4×#11745687C22116yescomplemented
59C2×Q8×Dic59C2212yes—
60C2×Q8×Dic59C2211yescharacteristic
61C2×C4×Dic118C2212yes—
62C2×C4×Dic118C2214yes—
63C2×C4×Dic118C2211yescharacteristic
64C2×#14273692C2211yescharacteristic
65C2×#14273692C2214yes—
66C2×#14273692C2212yes—
67C2×#14273692C2212yes—
68C4×Q8×D59C22132yescomplemented
69C2×C4×D236C2211yescharacteristic
70C2×C4×D236C2212yes—
71C2×D4×Dic59C2211yescharacteristic
72C2×#14273689C2211yescharacteristic
73C2×#14273689C2212yes—
74C2×#14273689C2212yes—
75C2×C4×C22⋊D59C2212yes—
76C2×(C22⋊D59)⋊C4C2212yes—
77C2×(C22⋊D59)⋊C4C2214yes—
78C2×(C22⋊D59)⋊C4C2214yes—
79C2×#14273685C2211yescharacteristic
80C2×#14273685C2212yes—
81C2×#14273685C2211yescharacteristic
82C2×#14273685C2212yes—
83C2×#14273684C2214yes—
84C2×#14273683C2212yes—
85C2×#14273683C2214yes—
86C2×C4⋊C4×D59C2214yes—
87C2×C4⋊C4×D59C2212yes—
88C22×C4×Dic59C2212yes—
89C2×C42×D59C2214yes—
90C2×C42×D59C2212yes—
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×#11745689—28no—
102C2×#11745689C2318yes—
103C2×#11745685—216no—
104C2×#11745685C23116yes—
105C2×#11745687—28no—
106C2×#11745687C2318yes—
107C22×Dic118C2314yes—
108C22×Dic118C2312yes—
109C22×Dic118C2311yescharacteristic
110C2×Q8×D59—216no—
111C2×Q8×D59C23116yes—
112C22×D236C2312yes—
113C22×D236C2311yescharacteristic
114C22×C22⋊D59C2314yes—
115C22×C22⋊D59C2312yes—
116C23×Dic59C2312yes—
117C23×Dic59C2312yes—
118C22×C4×D59C2312yes—
119C22×C4×D59C2314yes—
120C22×C4×D59C2311yescharacteristic
121C22×C4×D59C2311yescharacteristic
122C22×C4×D59C2312yes—
123C22×C4×D59C2314yes—
124C22×C4×D59C2312yes—
125C22×C4×D59C2311yescharacteristic
126#14273727C2318yes—
127#14273726C23116yes—
128#14273725C23116yes—
129#14273721C23132yes—
130#14273720C23132yes—
131#14273719C23116yes—
132#14273718C23116yes—
133#14273717C23132yes—
134#14273717C23132yes—
135#14273713C23132yes—
136#14273712C23132yes—
137#14273709C23132yes—
138#14273709C23132yes—
139#14273707C23116yes—
140#14273706C23116yes—
141#14273705C23132yes—
142#14273704C23132yes—
143#14273703C23116yes—
144#14273703C23116yes—
145#14273700C23132yes—
146#14273698C23116yes—
147Q8×Dic59C23116yes—
148Q8×Dic59C2318yes—
149C4×Dic118C23116yes—
150C4×Dic118C2318yes—
151C4×Dic118C23132yes—
152#14273692C23132yes—
153#14273692C23116yes—
154#14273692C23116yes—
155#14273692C2318yes—
156C4×D236C2318yes—
157C4×D236C23116yes—
158D4×Dic59C2318yes—
159#14273689C23116yes—
160#14273689C23116yes—
161#14273689C2318yes—
162C4×C22⋊D59C23116yes—
163(C22⋊D59)⋊C4C23132yes—
164(C22⋊D59)⋊C4C23116yes—
165(C22⋊D59)⋊C4C23132yes—
166#14273685C23116yes—
167#14273685C23116yes—
168#14273685C2318yes—
169#14273685C2318yes—
170#14273684C23132yes—
171#14273683C23132yes—
172#14273683C23116yes—
173C2×C4⋊Dic59C2312yes—
174C2×C4⋊Dic59C2311yescharacteristic
175C2×C4⋊Dic59C2312yes—
176C2×C4⋊Dic59C2311yescharacteristic
177C2×C4⋊Dic59C2314yes—
178C2×C4⋊Dic59C2312yes—
179C2×Dic59⋊C4C2314yes—
180C2×Dic59⋊C4C2314yes—
181C2×Dic59⋊C4C2314yes—
182C2×Dic59⋊C4C2312yes—
183C2×Dic59⋊C4C2314yes—
184C2×Dic59⋊C4C2314yes—
185C2×Dic59⋊C4C2314yes—
186C2×Dic59⋊C4C2312yes—
187C4⋊C4×D59C23132yes—
188C4⋊C4×D59C23116yes—
189C2×C22⋊Dic59C2314yes—
190C2×C22⋊Dic59C2312yes—
191C2×(C2×D59)⋊C4C2314yes—
192C2×(C2×D59)⋊C4C2314yes—
193C2×(C2×D59)⋊C4C2312yes—
194C2×(C2×D59)⋊C4C2312yes—
195C2×(C2×D59)⋊C4C2312yes—
196C2×(C2×D59)⋊C4C2312yes—
197C2×C4×Dic59C2314yes—
198C2×C4×Dic59C2312yes—
199C2×C4×Dic59C2311yescharacteristic
200C2×C4×Dic59C2312yes—
201C2×C4×Dic59C2312yes—
202C2×C4×Dic59C23116yes—
203C2×C4×Dic59C2311yescharacteristic
204C2×C4×Dic59C2312yes—
205C2×C4×Dic59C2311yescharacteristic
206C2×C4×Dic59C2312yes—
207C2×C4×Dic59C2314yes—
208C42×D59C23116yes—
209C42×D59C23132yes—
210C42×D59C2318yes—
211C22×Q8×C59C2312yes—
212C22×Q8×C59C2311yescharacteristic
213C22×D4×C59C2311yescharacteristic
214C23×C4×C59C2312yes—
215C4⋊Q8×C59C2318yes—
216#126×C59C23132yes—
217#124×C59C23116yes—
218C22⋊Q8×C59C23116yes—
219C4×Q8×C59C23116yes—
220C4×Q8×C59C2318yes—
221C4×D4×C59C2318yes—
222#117×C59C23116yes—
223C2×C4⋊C4×C59C2312yes—
224C2×C4⋊C4×C59C2312yes—
225C2×C4⋊C4×C59C2314yes—
226C2×C4⋊C4×C59C2312yes—
227C2×C4⋊C4×C59C2311yescharacteristic
228C2×C4⋊C4×C59C2311yescharacteristic
229C2×C22⋊C4×C59C2314yes—
230C2×C22⋊C4×C59C2312yes—
231C2×C22⋊C4×C59C2314yes—
232C2×C42×C59C2312yes—
233C2×C42×C59C2314yes—
234C2×C42×C59C2311yescharacteristic
235C24×C59C2412yes—
236C23×D59C2411yescharacteristic
237C23×D59C2412yes—
238C2×Q8×C59—28no—
239C2×Q8×C59—24no—
240C2×Q8×C59C2414yes—
241C2×Q8×C59C2418yes—
242C2×D4×C59—24no—
243C2×D4×C59C2414yes—
244C22×C4×C59—28no—
245C22×C4×C59C2412yes—
246C22×C4×C59C2412yes—
247C22×C4×C59C2411yescharacteristic
248C22×C4×C59C2414yes—
249C22×C4×C59C2412yes—
250C22×C4×C59C2418yes—
251C22×C4×C59C2411yescharacteristic
252C22×C4×C59C2411yescharacteristic
253C2×C22⋊D59—216no—
254C2×C22⋊D59—28no—
255C2×C22⋊D59C24116yes—
256C2×C22⋊D59C2418yes—
257C22×Dic59—28no—
258C22×Dic59—28no—
259C22×Dic59C2411yescharacteristic
260C22×Dic59C2411yescharacteristic
261C22×Dic59C2412yes—
262C22×Dic59C2412yes—
263C22×Dic59C2414yes—
264C22×Dic59C2418yes—
265C22×Dic59C2418yes—
266C22×Dic59C2412yes—
267C22×Dic59C2411yescharacteristic
268#11745689—232no—
269Q8×D59—264no—
270#11745687—232no—
271#11745685—264no—
272C2×D236—28no—
273C2×D236#4118yescomplemented
274C2×D236C2418yes—
275C2×D236C2414yes—
276C2×C4×D59—216no—
277C2×C4×D59—28no—
278C2×C4×D59—28no—
279C2×C4×D59—24no—
280C2×C4×D59—24no—
281C2×C4×D59—216no—
282C2×C4×D59—28no—
283C2×C4×D59—24no—
284C2×C4×D59C2418yes—
285C2×C4×D59C24116yes—
286C2×C4×D59C2418yes—
287C2×C4×D59C24116yes—
288C2×C4×D59C2418yes—
289C2×C4×D59C2414yes—
290C2×C4×D59C2414yes—
291C2×C4×D59C2414yes—
292C2×Dic118—28no—
293C2×Dic118—216no—
294C2×Dic118#4118yescomplemented
295C2×Dic118C2418yes—
296C2×Dic118C24116yes—
297C2×Dic118C2414yes—
298C4⋊C4×C59C2414yes—
299C4⋊C4×C59C2418yes—
300C4⋊C4×C59C2414yes—
301C4⋊C4×C59C24116yes—
302C4⋊C4×C59C2418yes—
303C4⋊C4×C59C2418yes—
304C22⋊C4×C59C24116yes—
305C22⋊C4×C59C2418yes—
306C22⋊C4×C59C24116yes—
307C42×C59C24116yes—
308C42×C59C2414yes—
309C42×C59C2418yes—
310C22⋊Dic59C2418yes—
311C22⋊Dic59C24116yes—
312(C2×D59)⋊C4C2418yes—
313(C2×D59)⋊C4C24116yes—
314(C2×D59)⋊C4C2418yes—
315(C2×D59)⋊C4C2418yes—
316(C2×D59)⋊C4C2418yes—
317(C2×D59)⋊C4C24116yes—
318C4⋊Dic59C2418yes—
319C4⋊Dic59C24116yes—
320C4⋊Dic59C2414yes—
321C4⋊Dic59C2418yes—
322C4⋊Dic59C2414yes—
323C4⋊Dic59C2418yes—
324Dic59⋊C4C2418yes—
325Dic59⋊C4C24116yes—
326Dic59⋊C4C24116yes—
327Dic59⋊C4C2418yes—
328Dic59⋊C4C24116yes—
329Dic59⋊C4C24116yes—
330Dic59⋊C4C24116yes—
331Dic59⋊C4C24116yes—
332C4×Dic59C2414yes—
333C4×Dic59C2418yes—
334C4×Dic59C2414yes—
335C4×Dic59C2414yes—
336C4×Dic59C2418yes—
337C4×Dic59C24116yes—
338C4×Dic59C2418yes—
339C4×Dic59C24116yes—
340C4×Dic59C2418yes—
341C4×Dic59C2418yes—
342C23×C59—24no—
343C23×C59—24no—
344C23×C59—24no—
345C23×C59C2514yes—
346C23×C59C2511yescharacteristic
347C22×D59—24no—
348C22×D59—24no—
349C22×D59—22no—
350C22×D59—22no—
351C22×D59—22no—
352C22×D59C2×#4118yes—
353C22×D59C2512yes—
354C22×D59C2514yes—
355Q8×C59—216no—
356Q8×C59—28no—
357D4×C59—28no—
358C2×C4×C59—28no—
359C2×C4×C59—24no—
360C2×C4×C59—24no—
361C2×C4×C59—24no—
362C2×C4×C59—22no—
363C2×C4×C59—216no—
364C2×C4×C59C2×#4114yes—
365C2×C4×C59C2×#4114yes—
366C2×C4×C59C2514yes—
367C2×C4×C59C2514yes—
368C2×C4×C59C2514yes—
369C2×C4×C59C2512yes—
370C2×C4×C59C2518yes—
371C2×C4×C59C2512yes—
372C2×C4×C59C2512yes—
373C22⋊D59—232no—
374C22⋊D59—216no—
375C2×Dic59—24no—
376C2×Dic59—28no—
377C2×Dic59—22no—
378C2×Dic59—22no—
379C2×Dic59—24no—
380C2×Dic59—216no—
381C2×Dic59—216no—
382C2×Dic59C2×#4118yes—
383C2×Dic592−1+414yes—
384C2×Dic59C2512yes—
385C2×Dic59C2512yes—
386C2×Dic59C2514yes—
387C2×Dic59C2518yes—
388C2×Dic59C2514yes—
389C2×Dic59C2514yes—
390C2×Dic59C2512yes—
391D236—216no—
392D236C2×#41116yescomplemented
393C4×D59—232no—
394C4×D59—216no—
395C4×D59—28no—
396C4×D59—216no—
397C4×D59—28no—
398C4×D59—232no—
399C4×D59—216no—
400C4×D59—28no—
401Dic118—216no—
402Dic118—232no—
403Dic118C2×#41116yescomplemented
404C2×#3482—591nomaximal, Sylow
405C22×C59—24no—
406C22×C59—24no—
407C22×C59—24no—
408C22×C59—48no—
409C22×C59C22×#4112yes—
410C22×C59C22×#4112yes—
411C22×C59C2×2−1+412yes—
412C22×C59C2611yescharacteristic
413C2×D59—24no—
414C2×D59—24no—
415C2×D59—216no—
416C2×D59—22no—
417C2×D59—22no—
418C2×D59—22no—
419C2×D59—44no—
420C2×D59C22×#4118yes—
421C4×C59—28no—
422C4×C59—24no—
423C4×C59—24no—
424C4×C59—24no—
425C4×C59—22no—
426C4×C59C22×#4114yes—
427C4×C59C22×#4114yes—
428Dic59—24no—
429Dic59—28no—
430Dic59—22no—
431Dic59—22no—
432Dic59—24no—
433Dic59C22×#4118yes—
434Dic59C2×2−1+414yes—
435#3482—5932no—
436C2×#557—591no—
437C2×#556—592no—
438C2×#556D5911yescharacteristic, complemented
439C2×#552—594no—
440C2×#552—592no—
441C2×D4×Q8—591no—
442C2×#548—592no—
443C2×#547—592no—
444C2×#547—591no—
445C2×#533—591no—
446C2×#533—592no—
447C2×#529—594no—
448C2×#529—592no—
449C2×C4×#41—591no—
450C2×C4×#41—591no—
451C2×C4×#41—592no—
452C22×C4×Q8—592no—
453C2×C59—44no—
454C2×C59#348214yescomplemented
455C2×C59C23×#4111yescharacteristic
456C2×C59C23×#4111yescharacteristic
457C2×C59C22×2−1+411yescharacteristic
458D59—28no—
459D59—42no—
460C22×#41—591no—
461C22×#41—591no—
462C22×#41—592no—
463C23×Q8—592no—
464#557—5916no—
465#556—5932no—
466#556C2×D59116yescomplemented
467#552—5964no—
468#552—5932no—
469D4×Q8—5916no—
470#548—5932no—
471#547—5932no—
472#547—5916no—
473#533—5916no—
474#533—5932no—
475C2×C4⋊Q8—592no—
476C2×C4⋊Q8—592no—
477C2×C4⋊Q8—591no—
478C2×C4⋊Q8C2×D5911yescharacteristic
479#529—5964no—
480#529—5932no—
481C2×#126—594no—
482C2×#126—594no—
483C2×#126C2×D5914yes—
484C2×#125—594no—
485C2×#125—594no—
486C2×#125—592no—
487C2×#125—592no—
488C2×#124—594no—
489C2×#124C2×D5912yes—
490C2×#123—594no—
491C2×#123—594no—
492C2×#123—594no—
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×C22⋊Q8C2×D5912yes—
500C2×#121—592no—
501C2×#121—594no—
502C4×#41—5916no—
503C4×#41—5916no—
504C4×#41—5932no—
505C2×C4×Q8—592no—
506C2×C4×Q8—591no—
507C2×C4×Q8—5932no—
508C2×C4×Q8—591no—
509C2×C4×Q8—594no—
510C2×C4×Q8—592no—
511C2×C4×Q8—592no—
512C2×C4×Q8—592no—
513C2×C4×Q8—594no—
514C2×C4×Q8—591no—
515C2×C4×Q8C2×D5912yes—
516C2×C4×Q8C2×D5911yescharacteristic
517C2×C4×D4—591no—
518C2×C4×D4—592no—
519C2×C4×D4—591no—
520C2×C4×D4—592no—
521C2×C4×D4—592no—
522C2×C4×D4—594no—
523C2×C4×D4—592no—
524C2×C4×D4—594no—
525C2×C4×D4—591no—
526C2×C4×D4—592no—
527C2×C4×D4C2×D5911yescharacteristic
528C2×#117—591no—
529C2×#117—592no—
530C2×#117—591no—
531C2×#117—592no—
532C2×#117—592no—
533C2×#117—594no—
534C2×#117—594no—
535C2×#117C2×D5912yes—
536C22×C4⋊C4—594no—
537C22×C4⋊C4—592no—
538C22×C42—592no—
539C22×C42—592no—
540C22×C42—594no—
541C22×C42—591no—
542C59C2×#348211yescharacteristic, complemented, Sylow
543C2×#41—598no—
544C2×#41—598no—
545C2×#41—5916no—
546C2×#41—11816no—
547C2×#41—1188no—
548C2×#41—1188no—
549C22×Q8—5916no—
550C22×Q8—591no—
551C22×Q8—594no—
552C22×Q8—592no—
553C22×Q8—11816no—
554C22×Q8C22×D5912yes—
555C22×Q8C22×D5911yescharacteristic
556C22×D4—594no—
557C22×D4—592no—
558C22×D4—591no—
559C22×D4—592no—
560C22×D4C22×D5911yescharacteristic
561C23×C4—592no—
562C23×C4—592no—
563C23×C4—592no—
564C23×C4—594no—
565C23×C4—594no—
566C23×C4—592no—
567C23×C4—591no—
568C23×C4—591no—
569C23×C4—591no—
570C23×C4—592no—
571C23×C4C22×D5912yes—
572C4⋊Q8—5916no—
573C4⋊Q8—5916no—
574C4⋊Q8—598no—
575C4⋊Q8C22×D5918yes—
576#126—5932no—
577#126—5932no—
578#126C22×D59132yes—
579#125—5932no—
580#125—5932no—
581#125—5916no—
582#125—5916no—
583#124—5932no—
584#124C22×D59116yes—
585#123—5932no—
586#123—5932no—
587#123—5932no—
588C22⋊Q8—5916no—
589C22⋊Q8—5916no—
590C22⋊Q8—5916no—
591C22⋊Q8—5932no—
592C22⋊Q8—5916no—
593C22⋊Q8—5932no—
594C22⋊Q8C22×D59116yes—
595#121—5916no—
596#121—5932no—
597C4×Q8—5916no—
598C4×Q8—598no—
599C4×Q8—598no—
600C4×Q8—5932no—
601C4×Q8—5916no—
602C4×Q8—5916no—
603C4×Q8—5916no—
604C4×Q8—5932no—
605C4×Q8—598no—
606C4×Q8C22×D59116yes—
607C4×Q8C22×D5918yes—
608C4×D4—598no—
609C4×D4—5916no—
610C4×D4—598no—
611C4×D4—5916no—
612C4×D4—5916no—
613C4×D4—5916no—
614C4×D4—5932no—
615C4×D4—5932no—
616C4×D4—598no—
617C4×D4—5916no—
618C4×D4C22×D5918yes—
619#117—598no—
620#117—5916no—
621#117—598no—
622#117—5916no—
623#117—5916no—
624#117—5932no—
625#117—5932no—
626#117C22×D59116yes—
627C2×C4⋊C4—592no—
628C2×C4⋊C4—594no—
629C2×C4⋊C4—592no—
630C2×C4⋊C4—594no—
631C2×C4⋊C4—594no—
632C2×C4⋊C4—592no—
633C2×C4⋊C4—594no—
634C2×C4⋊C4—592no—
635C2×C4⋊C4—591no—
636C2×C4⋊C4—591no—
637C2×C4⋊C4—594no—
638C2×C4⋊C4—594no—
639C2×C4⋊C4—594no—
640C2×C4⋊C4—592no—
641C2×C4⋊C4—5932no—
642C2×C4⋊C4—5916no—
643C2×C4⋊C4C22×D5911yescharacteristic
644C2×C4⋊C4C22×D5914yes—
645C2×C4⋊C4C22×D5911yescharacteristic
646C2×C4⋊C4C22×D5912yes—
647C2×C4⋊C4C22×D5912yes—
648C2×C4⋊C4C22×D5912yes—
649C2×C22⋊C4—592no—
650C2×C22⋊C4—594no—
651C2×C22⋊C4—592no—
652C2×C22⋊C4—594no—
653C2×C22⋊C4—592no—
654C2×C22⋊C4—592no—
655C2×C22⋊C4—592no—
656C2×C22⋊C4—594no—
657C2×C22⋊C4C22×D5912yes—
658C2×C22⋊C4C22×D5914yes—
659C2×C22⋊C4C22×D5914yes—
660C2×C42—591no—
661C2×C42—592no—
662C2×C42—592no—
663C2×C42—594no—
664C2×C42—592no—
665C2×C42—592no—
666C2×C42—594no—
667C2×C42—592no—
668C2×C42—591no—
669C2×C42—591no—
670C2×C42—5916no—
671C2×C42—5916no—
672C2×C42—5932no—
673C2×C42—598no—
674C2×C42C22×D5914yes—
675C2×C42C22×D5911yescharacteristic
676C2×C42C22×D5912yes—
677C24—592no—
678C24—591no—
679C24C23×D5912yes—
680#41—11864no—
681#41—11832no—
682#41—11832no—
683C2×Q8—28no—
684C2×Q8—24no—
685C2×Q8—598no—
686C2×Q8—594no—
687C2×Q8—5916no—
688C2×Q8—598no—
689C2×Q8—11816no—
690C2×Q8—11864no—
691C2×Q8—1188no—
692C2×Q8C23×D5918yes—
693C2×Q8C23×D5914yes—
694C2×D4—24no—
695C2×D4—5916no—
696C2×D4—598no—
697C2×D4—598no—
698C2×D4—594no—
699C2×D4—598no—
700C2×D4—1188no—
701C2×D4—1188no—
702C2×D4—11816no—
703C2×D4C23×D5914yes—
704C22×C4—28no—
705C22×C4—591no—
706C22×C4—592no—
707C22×C4—598no—
708C22×C4—598no—
709C22×C4—591no—
710C22×C4—591no—
711C22×C4—592no—
712C22×C4—592no—
713C22×C4—594no—
714C22×C4—598no—
715C22×C4—598no—
716C22×C4—5916no—
717C22×C4—5916no—
718C22×C4—598no—
719C22×C4—594no—
720C22×C4—594no—
721C22×C4—594no—
722C22×C4—11816no—
723C22×C4—1188no—
724C22×C4—1184no—
725C22×C4—11816no—
726C22×C4—1188no—
727C22×C4—1188no—
728C22×C4—1188no—
729C22×C4—1188no—
730C22×C4—1184no—
731C22×C4—1184no—
732C22×C4C23×D5918yes—
733C22×C4C23×D5912yes—
734C22×C4C23×D5912yes—
735C22×C4C23×D5911yescharacteristic
736C22×C4C23×D5914yes—
737C22×C4C23×D5912yes—
738C22×C4C23×D5911yescharacteristic
739C22×C4C23×D5911yescharacteristic
740C4⋊C4—598no—
741C4⋊C4—5916no—
742C4⋊C4—598no—
743C4⋊C4—5916no—
744C4⋊C4—5916no—
745C4⋊C4—598no—
746C4⋊C4—5916no—
747C4⋊C4—598no—
748C4⋊C4—594no—
749C4⋊C4—594no—
750C4⋊C4—5916no—
751C4⋊C4—5916no—
752C4⋊C4—5916no—
753C4⋊C4—598no—
754C4⋊C4C23×D5914yes—
755C4⋊C4C23×D59116yes—
756C4⋊C4C23×D5914yes—
757C4⋊C4C23×D5918yes—
758C4⋊C4C23×D5918yes—
759C4⋊C4C23×D5918yes—
760C22⋊C4—598no—
761C22⋊C4—5916no—
762C22⋊C4—598no—
763C22⋊C4—5916no—
764C22⋊C4—598no—
765C22⋊C4—598no—
766C22⋊C4—598no—
767C22⋊C4—5916no—
768C22⋊C4C23×D5918yes—
769C22⋊C4C23×D59116yes—
770C22⋊C4C23×D59116yes—
771C42—598no—
772C42—594no—
773C42—594no—
774C42—594no—
775C42—598no—
776C42—598no—
777C42—5916no—
778C42—598no—
779C42—598no—
780C42—5916no—
781C42C23×D59116yes—
782C42C23×D5914yes—
783C42C23×D5918yes—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—598no—
788C23—594no—
789C23—592no—
790C23—1184no—
791C23—1184no—
792C23—1182no—
793C23—1182no—
794C23—1182no—
795C23C24×D5914yes—
796C23C24×D5911yescharacteristic
797Q8—216no—
798Q8—28no—
799Q8—5916no—
800Q8—11832no—
801Q8—11816no—
802D4—28no—
803D4—5916no—
804D4—11816no—
805D4—11816no—
806D4—11832no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—28no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—216no—
813C2×C4—598no—
814C2×C4—594no—
815C2×C4—592no—
816C2×C4—594no—
817C2×C4—592no—
818C2×C4—592no—
819C2×C4—594no—
820C2×C4—594no—
821C2×C4—598no—
822C2×C4—11816no—
823C2×C4—1188no—
824C2×C4—11832no—
825C2×C4—11832no—
826C2×C4—11816no—
827C2×C4—11816no—
828C2×C4—11816no—
829C2×C4—1182no—
830C2×C4—1182no—
831C2×C4—1188no—
832C2×C4—1184no—
833C2×C4—1184no—
834C2×C4—11816no—
835C2×C4—1188no—
836C2×C4—1188no—
837C2×C4#41×D5914yes—
838C2×C4#41×D5914yes—
839C2×C4C24×D5914yes—
840C2×C4C24×D5914yes—
841C2×C4C24×D5912yes—
842C2×C4C24×D5918yes—
843C2×C4C24×D5914yes—
844C2×C4C24×D5912yes—
845C2×C4C24×D5912yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—48no—
850C22—598no—
851C22—11816no—
852C22—1184no—
853C22—1184no—
854C22—1182no—
855C22—1182no—
856C22—1182no—
857C22—2364no—
858C22C2×#41×D5912yes—
859C22C2×#41×D5912yes—
860C222−1+4×D5912yes—
861C22C25×D5911yescharacteristic
862C4—24no—
863C4—24no—
864C4—28no—
865C4—24no—
866C4—22no—
867C4—598no—
868C4—594no—
869C4—1182no—
870C4—1182no—
871C4—1188no—
872C4—1184no—
873C4—1184no—
874C4C2×#41×D5914yes—
875C4C2×#41×D5914yes—
876C2—44no—
877C2—1188no—
878C2—2362no—
879C2#2143771514yesdirect product factor
880C2C22×#41×D5911yescharacteristic
881C2C22×#41×D5911yescharacteristic
882C2C2×2−1+4×D5911yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#556C2
socleC23×C59C25
hypercenterC2×#556D59
hypocenterC59C2×#3482
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #21437715C2direct (N × H)
2. C2×#16838130C2semidirect
3. C2×#16838120C2semidirect
4. C2×#16838093C2semidirect
5. C2×#16838088C2semidirect
6. C2×#16838067C2semidirect
7. C2×#16838060C2semidirect
8. C2×#16838057C2semidirect
9. C2×#16838054C2semidirect
10. C2×#16837957C2semidirect
11. C2×#16837954C2semidirect
12. C2×#16837935C2semidirect
13. C2×#16837931C2semidirect
14. C2×C4×#11745689C2semidirect
15. C2×#16837870C2semidirect
16. C2×C4×#11745687C2semidirect
17. C2×C4×Q8×D59C2semidirect
18. C2×C59×#556C2semidirect
23. #16838130C22semidirect
24. #16838120C22semidirect
25. #16838093C22semidirect
26. #16838088C22semidirect
27. #16838067C22semidirect
28. #16838060C22semidirect
29. #16838057C22semidirect
30. #16838054C22semidirect
31. #16837957C22semidirect
32. #16837954C22semidirect
36. #16837935C22semidirect
37. #16837931C22semidirect
56. C4×#11745689C22semidirect
57. #16837870C22semidirect
58. C4×#11745687C22semidirect
68. C4×Q8×D59C22semidirect
92. C59×#556C22semidirect
273. C2×D236#41semidirect
294. C2×Dic118#41semidirect
392. D236C2×#41semidirect
403. Dic118C2×#41semidirect
438. C2×#556D59semidirect
454. C2×C59#3482semidirect
466. #556C2×D59semidirect
542. C59C2×#3482semidirect
879. C2#21437715direct (N × H)

Maximal subgroups

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

subgroupindex
#214377152
C2×#168381302
C2×#168381202
C2×#168380932
C2×#168380882
C2×#168380672
C2×#168380602
C2×#168380572
C2×#168380542
C2×#168379572
C2×#168379542
C2×#168379352
C2×#168379312
C2×C4×#117456892
C2×#168378702
C2×C4×#117456872
C2×C4×Q8×D592
C2×C59×#5562
C2×#348259