Finite Group Databasebeta

← C2×#21437954 #29496762

Subgroups — C2×#21437954 #29496762

Order 15104.

7130 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437954C2132yesmaximal, direct product factor
2C2×#16838135C212yesmaximal, complemented
3C2×#16838130C212yesmaximal, complemented
4C2×#16838124C212yesmaximal, complemented
5C2×#16838122C212yesmaximal, complemented
6C2×#16838120C212yesmaximal, complemented
7C2×#16838107C212yesmaximal, complemented
8C2×#16838091C212yesmaximal, complemented
9C2×#16838087C212yesmaximal, complemented
10C2×#16837994C214yesmaximal, complemented
11C2×#16837978C211yesmaximal, characteristic, complemented
12C2×#16837973C211yesmaximal, characteristic, complemented
13C2×#16837955C211yesmaximal, characteristic, complemented
14C2×#16837948C211yesmaximal, characteristic
15C2×#16837932C214yesmaximal, complemented
16C2×#16837883C211yesmaximal, characteristic, complemented
17C22×#14273692C211yesmaximal, characteristic, complemented
18C2×C59×#520C211yesmaximal, characteristic, complemented
19C22×#11745685C2211yescharacteristic
20C23×Dic118C2211yescharacteristic
21#16838135C22132yescomplemented
22#16838130C22132yescomplemented
23#16838124C22132yescomplemented
24#16838122C22132yescomplemented
25#16838120C22132yescomplemented
26#16838107C22132yescomplemented
27#16838091C22132yescomplemented
28#16838087C22132yescomplemented
29#16837994C22164yescomplemented
30#16837978C22116yescomplemented
31#16837973C22116yescomplemented
32#16837955C22116yescomplemented
33#16837948C22116yes—
34C2×#14273727C2212yes—
35C2×#14273726C2211yescharacteristic
36C2×#14273726C2211yescharacteristic
37C2×#14273725C2211yescharacteristic
38C2×#14273725C2212yes—
39C2×#14273723C2211yescharacteristic
40#16837932C22164yescomplemented
41C2×#14273722C2214yes—
42C2×#14273721C2214yes—
43C2×#14273720C2214yes—
44C2×#14273720C2214yes—
45C2×#14273719C2214yes—
46C2×#14273718C2211yescharacteristic
47C2×#14273718C2211yescharacteristic
48C2×#14273717C2214yes—
49C2×#14273717C2214yes—
50C2×#14273716C2211yescharacteristic
51C2×#14273715C2212yes—
52C2×#14273714C2211yescharacteristic
53C2×#14273714C2212yes—
54C2×#14273713C2214yes—
55C2×#14273711C2214yes—
56C2×#14273710C2214yes—
57C2×#14273709C2214yes—
58C2×#14273708C2214yes—
59C2×#14273707C2212yes—
60C2×#14273707C2212yes—
61C2×#14273706C2214yes—
62C2×#14273706C2212yes—
63C2×#14273706C2212yes—
64C2×#14273705C2214yes—
65C2×#14273704C2212yes—
66C2×#14273704C2212yes—
67C2×#14273699C2212yes—
68C2×#14273699C2212yes—
69#16837883C22116yescomplemented
70C2×C4×Dic118C2214yes—
71C2×C4×Dic118C2212yes—
72C2×C4×Dic118C2212yes—
73C2×#14273692C2212yes—
74C2×#14273692C2212yes—
75C2×#14273692C2212yes—
76C2×#14273692C2212yes—
77C2×#14273692C2212yes—
78C2×#14273692C22116yescomplemented
79C2×#14273689C2212yes—
80C2×C4×C22⋊D59C2214yes—
81C2×C4×C22⋊D59C2212yes—
82C2×C4×C22⋊D59C2214yes—
83C2×C4×C22⋊D59C2212yes—
84C2×#14273686C2211yescharacteristic
85C2×#14273686C2214yes—
86C2×#14273685C2212yes—
87C2×#14273684C2214yes—
88C22×Dic59⋊C4C2212yes—
89C2×C4⋊C4×D59C2212yes—
90C22×C4×Dic59C2212yes—
91C22×C4×Dic59C2211yescharacteristic
92C22×#41×C59C2211yescharacteristic
93C59×#520C22116yescomplemented
94C2×C4×Q8×C59C2212yes—
95C2×C4×D4×C59C2214yes—
96C2×C4×D4×C59C2212yes—
97C2×#117×C59C2212yes—
98C2×#117×C59C2211yescharacteristic
99C22×C4⋊C4×C59C2211yescharacteristic
100C22×C4⋊C4×C59C2212yes—
101C2×#11745685—28no—
102C2×#11745685C2318yes—
103C22×Dic118—28no—
104C22×Dic118C2312yes—
105C22×Dic118C2312yes—
106C22×Dic118C2312yes—
107C22×Dic118C2311yescharacteristic
108C22×Dic118C2318yes—
109C22×Dic118C2312yes—
110C22×D236C2311yescharacteristic
111C22×C22⋊D59C2312yes—
112C22×C22⋊D59C2312yes—
113C22×C22⋊D59C2312yes—
114C23×Dic59C2311yescharacteristic
115C23×Dic59C2312yes—
116C23×Dic59C2311yescharacteristic
117C22×C4×D59C2312yes—
118C22×C4×D59C2314yes—
119#14273727C23116yes—
120#14273726C2318yes—
121#14273726C2318yes—
122#14273725C2318yes—
123#14273725C23116yes—
124#14273723C2318yes—
125#14273722C23132yes—
126#14273721C23132yes—
127#14273720C23132yes—
128#14273720C23132yes—
129#14273719C23132yes—
130#14273718C2318yes—
131#14273718C2318yes—
132#14273717C23132yes—
133#14273717C23132yes—
134#14273716C2318yes—
135#14273715C23116yes—
136#14273714C2318yes—
137#14273714C23116yes—
138#14273713C23132yes—
139#14273711C23132yes—
140#14273710C23132yes—
141#14273709C23132yes—
142#14273708C23132yes—
143#14273707C23116yes—
144#14273707C23116yes—
145#14273706C23116yes—
146#14273706C23116yes—
147#14273706C23132yes—
148#14273705C23132yes—
149#14273704C23116yes—
150#14273704C23116yes—
151#14273699C23116yes—
152#14273699C23116yes—
153C4×Dic118C23132yes—
154C4×Dic118C23116yes—
155C4×Dic118C23116yes—
156#14273692C23116yes—
157#14273692C23116yes—
158#14273692C23116yes—
159#14273692C23116yes—
160#14273692C23116yes—
161#14273689C23116yes—
162C4×C22⋊D59C23132yes—
163C4×C22⋊D59C23132yes—
164C4×C22⋊D59C23116yes—
165C4×C22⋊D59C23116yes—
166#14273686C23132yes—
167#14273686C2318yes—
168#14273685C23116yes—
169#14273684C23132yes—
170C2×C4⋊Dic59C2312yes—
171C2×C4⋊Dic59C2312yes—
172C2×C4⋊Dic59C2311yescharacteristic
173C2×C4⋊Dic59C2311yescharacteristic
174C2×C4⋊Dic59C2314yes—
175C2×C4⋊Dic59C2314yes—
176C2×Dic59⋊C4C2312yes—
177C2×Dic59⋊C4C2312yes—
178C2×Dic59⋊C4C2312yes—
179C2×Dic59⋊C4C2312yes—
180C2×Dic59⋊C4C2312yes—
181C2×Dic59⋊C4C2312yes—
182C2×Dic59⋊C4C2314yes—
183C2×Dic59⋊C4C2314yes—
184C2×Dic59⋊C4C2314yes—
185C2×Dic59⋊C4C2314yes—
186C2×Dic59⋊C4C2314yes—
187C2×Dic59⋊C4C23116yes—
188C4⋊C4×D59C23116yes—
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)⋊C4C2314yes—
199C2×C4×Dic59C2314yes—
200C2×C4×Dic59C2311yescharacteristic
201C2×C4×Dic59C2312yes—
202C2×C4×Dic59C2314yes—
203C2×C4×Dic59C2311yescharacteristic
204C2×C4×Dic59C2314yes—
205C2×C4×Dic59C23116yes—
206C2×C4×Dic59C2311yescharacteristic
207C2×C4×Dic59C2311yescharacteristic
208C2×C4×Dic59C2318yes—
209C2×#41×C59—28no—
210C2×#41×C59C2318yes—
211C22×Q8×C59C2311yescharacteristic
212C22×D4×C59C2312yes—
213C22×D4×C59C2311yescharacteristic
214C23×C4×C59C2312yes—
215C23×C4×C59C2314yes—
216C23×C4×C59C2312yes—
217C23×C4×C59C2311yescharacteristic
218C4×Q8×C59C23116yes—
219C4×D4×C59C23132yes—
220C4×D4×C59C23116yes—
221#117×C59C2318yes—
222#117×C59C23116yes—
223C2×C4⋊C4×C59C2314yes—
224C2×C4⋊C4×C59C2311yescharacteristic
225C2×C4⋊C4×C59C2311yescharacteristic
226C2×C4⋊C4×C59C2312yes—
227C2×C4⋊C4×C59C2312yes—
228C2×C4⋊C4×C59C23116yes—
229C2×C4⋊C4×C59C2318yes—
230C2×C22⋊C4×C59C2312yes—
231C2×C22⋊C4×C59C2314yes—
232C2×C42×C59C2312yes—
233C2×C42×C59C2314yes—
234C24×C59C2412yes—
235C24×C59C2411yescharacteristic
236C23×D59C2412yes—
237#41×C59—232no—
238C2×Q8×C59—24no—
239C2×Q8×C59C2414yes—
240C2×D4×C59—28no—
241C2×D4×C59—24no—
242C2×D4×C59C2418yes—
243C2×D4×C59C2414yes—
244C22×C4×C59—28no—
245C22×C4×C59—48no—
246C22×C4×C59—44no—
247C22×C4×C59#4118yes—
248C22×C4×C59C2412yes—
249C22×C4×C59C2412yes—
250C22×C4×C59C2414yes—
251C22×C4×C59C2412yes—
252C22×C4×C59C2418yes—
253C22×C4×C59C2418yes—
254C22×C4×C59C24116yes—
255C22×C4×C59C2411yescharacteristic
256C22×C4×C59C2411yescharacteristic
257C22×C4×C59C2414yes—
258C2×C22⋊D59—28no—
259C2×C22⋊D59—28no—
260C2×C22⋊D59—44no—
261C2×C22⋊D59C2418yes—
262C2×C22⋊D59C2418yes—
263C2×C22⋊D59C2418yes—
264C22×Dic59—28no—
265C22×Dic59—24no—
266C22×Dic59—42no—
267C22×Dic59C2411yescharacteristic
268C22×Dic59C2414yes—
269C22×Dic59C2412yes—
270C22×Dic59C2411yescharacteristic
271C22×Dic59C2414yes—
272C22×Dic59C2412yes—
273C22×Dic59C2411yescharacteristic
274C22×Dic59C2418yes—
275C22×Dic59C2412yes—
276C22×Dic59C2414yes—
277C22×Dic59C2411yescharacteristic
278#11745685—232no—
279C2×D236—24no—
280C2×D236C2414yes—
281C2×C4×D59—28no—
282C2×C4×D59—48no—
283C2×C4×D59C2418yes—
284C2×C4×D59C24116yes—
285C2×Dic118—28no—
286C2×Dic118—28no—
287C2×Dic118—232no—
288C2×Dic118—24no—
289C2×Dic118—28no—
290C2×Dic118—44no—
291C2×Dic118C2418yes—
292C2×Dic118C2418yes—
293C2×Dic118C2414yes—
294C2×Dic118C2418yes—
295C2×Dic118C2418yes—
296C4⋊C4×C59C2418yes—
297C4⋊C4×C59C2414yes—
298C4⋊C4×C59C2418yes—
299C4⋊C4×C59C24116yes—
300C4⋊C4×C59C2414yes—
301C22⋊C4×C59C2418yes—
302C22⋊C4×C59C24116yes—
303C42×C59C24116yes—
304C42×C59C2418yes—
305C22⋊Dic59C2418yes—
306C22⋊Dic59C2418yes—
307C22⋊Dic59C24116yes—
308C22⋊Dic59C2418yes—
309C22⋊Dic59C24116yes—
310(C2×D59)⋊C4C2418yes—
311(C2×D59)⋊C4C24116yes—
312(C2×D59)⋊C4C24116yes—
313(C2×D59)⋊C4C2418yes—
314(C2×D59)⋊C4C24116yes—
315C4⋊Dic59C2414yes—
316C4⋊Dic59C2414yes—
317C4⋊Dic59C2418yes—
318C4⋊Dic59C24116yes—
319C4⋊Dic59C2418yes—
320C4⋊Dic59C24116yes—
321Dic59⋊C4C24116yes—
322Dic59⋊C4C24116yes—
323Dic59⋊C4C24116yes—
324Dic59⋊C4C2418yes—
325Dic59⋊C4C24116yes—
326Dic59⋊C4C2418yes—
327Dic59⋊C4C2418yes—
328Dic59⋊C4C2418yes—
329Dic59⋊C4C2418yes—
330Dic59⋊C4C2418yes—
331Dic59⋊C4C24116yes—
332C4×Dic59C24116yes—
333C4×Dic59C2414yes—
334C4×Dic59C2414yes—
335C4×Dic59C24116yes—
336C4×Dic59C2414yes—
337C4×Dic59C2414yes—
338C4×Dic59C24116yes—
339C4×Dic59C2418yes—
340C23×C59—22no—
341C23×C59—22no—
342C23×C59—24no—
343C23×C59—24no—
344C23×C59—24no—
345C23×C59C2×#4114yes—
346C23×C59C2514yes—
347C23×C59C2512yes—
348C23×C59C2511yescharacteristic
349C22×D59—24no—
350C22×D59—24no—
351C22×D59—24no—
352C22×D59C2514yes—
353Q8×C59—28no—
354D4×C59—216no—
355D4×C59—28no—
356C2×C4×C59—24no—
357C2×C4×C59—24no—
358C2×C4×C59—24no—
359C2×C4×C59—28no—
360C2×C4×C59—216no—
361C2×C4×C59—416no—
362C2×C4×C59—48no—
363C2×C4×C59C2×#4114yes—
364C2×C4×C59C2×#4114yes—
365C2×C4×C59C2×#41116yes—
366C2×C4×C59C2518yes—
367C2×C4×C59C2514yes—
368C2×C4×C59C2514yes—
369C2×C4×C59C2514yes—
370C2×C4×C59C2512yes—
371C2×C4×C59C2512yes—
372C22⋊D59—216no—
373C22⋊D59—216no—
374C22⋊D59—48no—
375C2×Dic59—216no—
376C2×Dic59—28no—
377C2×Dic59—24no—
378C2×Dic59—24no—
379C2×Dic59—22no—
380C2×Dic59—22no—
381C2×Dic59—24no—
382C2×Dic59—22no—
383C2×Dic59—28no—
384C2×Dic59—44no—
385C2×Dic592−1+414yes—
386C2×Dic59C2512yes—
387C2×Dic59C2514yes—
388C2×Dic59C2512yes—
389C2×Dic59C2512yes—
390C2×Dic59C2514yes—
391C2×Dic59C2518yes—
392C2×Dic59C2514yes—
393C2×Dic59C2512yes—
394D236—28no—
395C4×D59—216no—
396C4×D59—416no—
397Dic118—216no—
398Dic118—216no—
399Dic118—28no—
400Dic118—216no—
401Dic118—48no—
402C2×#3507—591nomaximal, Sylow
403C22×C59—22no—
404C22×C59—22no—
405C22×C59—28no—
406C22×C59—24no—
407C22×C59—24no—
408C22×C59—24no—
409C22×C59—48no—
410C22×C59C22×#4114yes—
411C22×C59C22×#4112yes—
412C22×C59C2×2−1+412yes—
413C22×C59#58512yes—
414C22×C59C2611yescharacteristic
415C2×D59—24no—
416C2×D59—24no—
417C2×D59—24no—
418C2×D59—48no—
419C4×C59—24no—
420C4×C59—24no—
421C4×C59—24no—
422C4×C59—28no—
423C4×C59C22×#4114yes—
424C4×C59C22×#4114yes—
425Dic59—28no—
426Dic59—24no—
427Dic59—24no—
428Dic59—22no—
429Dic59—22no—
430Dic59—24no—
431Dic59—22no—
432Dic59C2×2−1+414yes—
433#3507—5932no—
434C2×#559—592no—
435C2×#557—592no—
436C2×#556—592no—
437C2×#556—592no—
438C2×#556—592no—
439C2×#554—592no—
440C2×#552—592no—
441C2×#552—592no—
442C2×#539—594no—
443C2×#536—591no—
444C2×#536—591no—
445C2×#533—591no—
446C2×#532—591no—
447C2×#529—594no—
448C2×#520—591no—
449C2×#520D5911yescharacteristic, complemented
450C22×C4×Q8—591no—
451C2×C59—24no—
452C2×C59—44no—
453C2×C59#350714yescomplemented
454C2×C59C23×#4111yescharacteristic
455C2×C59C22×2−1+411yescharacteristic
456C2×C59C2×#58511yescharacteristic
457D59—44no—
458C22×#41—591no—
459C22×#41C2×D5911yescharacteristic
460C23×Q8—591no—
461#559—5932no—
462#557—5932no—
463#556—5932no—
464#556—5932no—
465#556—5932no—
466#554—5932no—
467#552—5932no—
468#552—5932no—
469#539—5964no—
470#536—5916no—
471#536—5916no—
472#533—5916no—
473#532—5916no—
474C2×C4⋊Q8—591no—
475C2×C4⋊Q8—592no—
476C2×C4⋊Q8—591no—
477C2×C4⋊Q8—591no—
478C2×C4⋊Q8—592no—
479C2×#127—591no—
480#529—5964no—
481C2×#126—594no—
482C2×#126—594no—
483C2×#126—594no—
484C2×#126—594no—
485C2×#125—594no—
486C2×#125—594no—
487C2×#125—591no—
488C2×#125—591no—
489C2×#125—594no—
490C2×#124—591no—
491C2×#124—591no—
492C2×#124—592no—
493C2×#124—594no—
494C2×#124—592no—
495C2×#123—594no—
496C2×#123—594no—
497C2×#123—594no—
498C2×#123—594no—
499C2×C22⋊Q8—592no—
500C2×C22⋊Q8—592no—
501C2×C22⋊Q8—594no—
502C2×C22⋊Q8—594no—
503C2×C22⋊Q8—592no—
504C2×C22⋊Q8—592no—
505C2×C22⋊Q8—592no—
506C2×C22⋊Q8—592no—
507C2×#121—592no—
508C2×#121—592no—
509#520—5916no—
510#520C2×D59116yescomplemented
511C2×C4×Q8—592no—
512C2×C4×Q8—592no—
513C2×C4×Q8—592no—
514C2×C4×Q8—592no—
515C2×C4×Q8—5916no—
516C2×C4×Q8—592no—
517C2×C4×Q8—594no—
518C2×C4×Q8—592no—
519C2×C4×Q8—592no—
520C2×C4×Q8C2×D5912yes—
521C2×C4×D4—594no—
522C2×C4×D4—594no—
523C2×C4×D4—592no—
524C2×C4×D4—592no—
525C2×C4×D4—592no—
526C2×C4×D4C2×D5914yes—
527C2×C4×D4C2×D5912yes—
528C2×#117—591no—
529C2×#117—594no—
530C2×#117—592no—
531C2×#117—594no—
532C2×#117C2×D5911yescharacteristic
533C2×#117C2×D5912yes—
534C22×C4⋊C4—592no—
535C22×C4⋊C4—592no—
536C22×C4⋊C4C2×D5911yescharacteristic
537C22×C4⋊C4C2×D5912yes—
538C22×C42—592no—
539C22×C42—591no—
540C59C2×#350711yescharacteristic, complemented, Sylow
541C2×#41—28no—
542C2×#41—598no—
543C2×#41—1188no—
544C2×#41C22×D5918yes—
545C22×Q8—592no—
546C22×Q8—592no—
547C22×Q8—592no—
548C22×Q8—591no—
549C22×Q8—598no—
550C22×Q8—592no—
551C22×Q8—1188no—
552C22×Q8C22×D5911yescharacteristic
553C22×D4—592no—
554C22×D4—592no—
555C22×D4—592no—
556C22×D4—591no—
557C22×D4C22×D5912yes—
558C22×D4C22×D5911yescharacteristic
559C23×C4—592no—
560C23×C4—591no—
561C23×C4—591no—
562C23×C4—592no—
563C23×C4—594no—
564C23×C4C22×D5912yes—
565C23×C4C22×D5912yes—
566C23×C4C22×D5914yes—
567C23×C4C22×D5911yescharacteristic
568C4⋊Q8—598no—
569C4⋊Q8—5916no—
570C4⋊Q8—598no—
571C4⋊Q8—598no—
572C4⋊Q8—5916no—
573#127—598no—
574#126—5932no—
575#126—5932no—
576#126—5932no—
577#126—5932no—
578#125—5932no—
579#125—598no—
580#125—598no—
581#125—5932no—
582#125—5932no—
583#124—598no—
584#124—598no—
585#124—5916no—
586#124—5932no—
587#124—5916no—
588#123—5932no—
589#123—5932no—
590#123—5932no—
591#123—5932no—
592C22⋊Q8—5916no—
593C22⋊Q8—5916no—
594C22⋊Q8—5932no—
595C22⋊Q8—5916no—
596C22⋊Q8—5916no—
597C22⋊Q8—5932no—
598C22⋊Q8—5916no—
599C22⋊Q8—5916no—
600#121—5916no—
601#121—5916no—
602C4×Q8—5916no—
603C4×Q8—5916no—
604C4×Q8—5916no—
605C4×Q8—5916no—
606C4×Q8—5916no—
607C4×Q8—5932no—
608C4×Q8—5916no—
609C4×Q8—5916no—
610C4×Q8C22×D59116yes—
611C4×D4—5932no—
612C4×D4—5932no—
613C4×D4—5916no—
614C4×D4—5916no—
615C4×D4—5916no—
616C4×D4C22×D59132yes—
617C4×D4C22×D59116yes—
618#117—598no—
619#117—5932no—
620#117—5916no—
621#117—5932no—
622#117C22×D5918yes—
623#117C22×D59116yes—
624C2×C4⋊C4—591no—
625C2×C4⋊C4—594no—
626C2×C4⋊C4—594no—
627C2×C4⋊C4—594no—
628C2×C4⋊C4—5916no—
629C2×C4⋊C4—591no—
630C2×C4⋊C4—592no—
631C2×C4⋊C4—592no—
632C2×C4⋊C4—594no—
633C2×C4⋊C4—594no—
634C2×C4⋊C4—592no—
635C2×C4⋊C4—592no—
636C2×C4⋊C4—592no—
637C2×C4⋊C4—592no—
638C2×C4⋊C4—592no—
639C2×C4⋊C4—594no—
640C2×C4⋊C4—594no—
641C2×C4⋊C4—592no—
642C2×C4⋊C4—5916no—
643C2×C4⋊C4C22×D5912yes—
644C2×C4⋊C4C22×D5911yescharacteristic
645C2×C4⋊C4C22×D5912yes—
646C2×C4⋊C4C22×D5914yes—
647C2×C4⋊C4C22×D5918yes—
648C2×C4⋊C4C22×D59116yes—
649C2×C4⋊C4C22×D5911yescharacteristic
650C2×C22⋊C4—592no—
651C2×C22⋊C4—592no—
652C2×C22⋊C4—594no—
653C2×C22⋊C4—592no—
654C2×C22⋊C4—594no—
655C2×C22⋊C4—592no—
656C2×C22⋊C4—594no—
657C2×C22⋊C4—594no—
658C2×C22⋊C4—592no—
659C2×C22⋊C4—594no—
660C2×C22⋊C4C22×D5912yes—
661C2×C22⋊C4C22×D5914yes—
662C2×C42—594no—
663C2×C42—594no—
664C2×C42—592no—
665C2×C42—591no—
666C2×C42—591no—
667C2×C42—594no—
668C2×C42—591no—
669C2×C42—591no—
670C2×C42—5916no—
671C2×C42—598no—
672C2×C42C22×D5914yes—
673C2×C42C22×D5912yes—
674C24—592no—
675C24C23×D5912yes—
676C24C23×D5911yescharacteristic
677#41—232no—
678#41—11832no—
679C2×Q8—24no—
680C2×Q8—598no—
681C2×Q8—598no—
682C2×Q8—598no—
683C2×Q8—594no—
684C2×Q8—598no—
685C2×Q8—1188no—
686C2×Q8—1188no—
687C2×Q8—1188no—
688C2×Q8—11832no—
689C2×Q8—1184no—
690C2×Q8—2364no—
691C2×Q8C23×D5914yes—
692C2×D4—28no—
693C2×D4—24no—
694C2×D4—598no—
695C2×D4—598no—
696C2×D4—598no—
697C2×D4—594no—
698C2×D4—1188no—
699C2×D4—1188no—
700C2×D4—1184no—
701C2×D4—2364no—
702C2×D4C23×D5918yes—
703C2×D4C23×D5914yes—
704C22×C4—28no—
705C22×C4—44no—
706C22×C4—48no—
707C22×C4—591no—
708C22×C4—594no—
709C22×C4—598no—
710C22×C4—591no—
711C22×C4—592no—
712C22×C4—594no—
713C22×C4—591no—
714C22×C4—592no—
715C22×C4—591no—
716C22×C4—592no—
717C22×C4—594no—
718C22×C4—598no—
719C22×C4—5916no—
720C22×C4—1184no—
721C22×C4—1188no—
722C22×C4—1188no—
723C22×C4—2368no—
724C22×C4—2362no—
725C22×C4#1174568518yes—
726C22×C4C23×D5918yes—
727C22×C4C23×D5914yes—
728C22×C4C23×D5912yes—
729C22×C4C23×D5912yes—
730C22×C4C23×D5912yes—
731C22×C4C23×D5918yes—
732C22×C4C23×D59116yes—
733C22×C4C23×D5914yes—
734C22×C4C23×D5911yescharacteristic
735C22×C4C23×D5911yescharacteristic
736C4⋊C4—594no—
737C4⋊C4—5916no—
738C4⋊C4—5916no—
739C4⋊C4—5916no—
740C4⋊C4—594no—
741C4⋊C4—598no—
742C4⋊C4—598no—
743C4⋊C4—5916no—
744C4⋊C4—5916no—
745C4⋊C4—598no—
746C4⋊C4—598no—
747C4⋊C4—598no—
748C4⋊C4—598no—
749C4⋊C4—598no—
750C4⋊C4—5916no—
751C4⋊C4—5916no—
752C4⋊C4—598no—
753C4⋊C4C23×D5918yes—
754C4⋊C4C23×D5914yes—
755C4⋊C4C23×D5918yes—
756C4⋊C4C23×D59116yes—
757C4⋊C4C23×D5914yes—
758C22⋊C4—598no—
759C22⋊C4—598no—
760C22⋊C4—5916no—
761C22⋊C4—598no—
762C22⋊C4—5916no—
763C22⋊C4—598no—
764C22⋊C4—5916no—
765C22⋊C4—5916no—
766C22⋊C4—598no—
767C22⋊C4—5916no—
768C22⋊C4C23×D5918yes—
769C22⋊C4C23×D59116yes—
770C42—5916no—
771C42—594no—
772C42—594no—
773C42—5916no—
774C42—594no—
775C42—594no—
776C42—5916no—
777C42—598no—
778C42C23×D59116yes—
779C42C23×D5918yes—
780C23—22no—
781C23—22no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—594no—
786C23—1184no—
787C23—1184no—
788C23—1184no—
789C23C2×#1174568514yes—
790C23C24×D5914yes—
791C23C24×D5912yes—
792C23C24×D5911yescharacteristic
793Q8—28no—
794Q8—11816no—
795Q8—11816no—
796Q8—11816no—
797Q8—1188no—
798Q8—2368no—
799D4—216no—
800D4—28no—
801D4—11816no—
802D4—11816no—
803D4—1188no—
804D4—2368no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—28no—
808C2×C4—24no—
809C2×C4—216no—
810C2×C4—48no—
811C2×C4—416no—
812C2×C4—594no—
813C2×C4—592no—
814C2×C4—592no—
815C2×C4—594no—
816C2×C4—598no—
817C2×C4—592no—
818C2×C4—594no—
819C2×C4—592no—
820C2×C4—594no—
821C2×C4—1188no—
822C2×C4—1184no—
823C2×C4—11816no—
824C2×C4—1188no—
825C2×C4—1182no—
826C2×C4—1184no—
827C2×C4—1184no—
828C2×C4—1182no—
829C2×C4—1182no—
830C2×C4—11816no—
831C2×C4—23616no—
832C2×C4—2364no—
833C2×C4C2×#1174568514yes—
834C2×C4C2×#1174568514yes—
835C2×C4C2×#11745685116yes—
836C2×C4C24×D5918yes—
837C2×C4C24×D5914yes—
838C2×C4C24×D5914yes—
839C2×C4C24×D5914yes—
840C2×C4C24×D5912yes—
841C2×C4C24×D5912yes—
842C22—28no—
843C22—22no—
844C22—22no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—48no—
849C22—1184no—
850C22—1184no—
851C22—1184no—
852C22—2368no—
853C22C22×#1174568514yes—
854C22C22×#1174568512yes—
855C222−1+4×D5912yes—
856C22#1683823712yes—
857C22C25×D5911yescharacteristic
858C4—24no—
859C4—24no—
860C4—28no—
861C4—24no—
862C4—594no—
863C4—1184no—
864C4—1188no—
865C4—1182no—
866C4—1184no—
867C4—1184no—
868C4—1182no—
869C4—1182no—
870C4C22×#1174568514yes—
871C4C22×#1174568514yes—
872C2—24no—
873C2—44no—
874C2—2364no—
875C2#2143795414yesdirect product factor
876C2C23×#1174568511yescharacteristic
877C2C2×2−1+4×D5911yescharacteristic
878C2C2×#1683823711yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#520C2
socleC23×C59C25
prime radicalC2×#16837948C2
hypercenterC2×#520D59
hypocenterC59C2×#3507
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #21437954C2direct (N × H)
2. C2×#16838135C2semidirect
3. C2×#16838130C2semidirect
4. C2×#16838124C2semidirect
5. C2×#16838122C2semidirect
6. C2×#16838120C2semidirect
7. C2×#16838107C2semidirect
8. C2×#16838091C2semidirect
9. C2×#16838087C2semidirect
10. C2×#16837994C2semidirect
11. C2×#16837978C2semidirect
12. C2×#16837973C2semidirect
13. C2×#16837955C2semidirect
15. C2×#16837932C2semidirect
16. C2×#16837883C2semidirect
17. C22×#14273692C2semidirect
18. C2×C59×#520C2semidirect
21. #16838135C22semidirect
22. #16838130C22semidirect
23. #16838124C22semidirect
24. #16838122C22semidirect
25. #16838120C22semidirect
26. #16838107C22semidirect
27. #16838091C22semidirect
28. #16838087C22semidirect
29. #16837994C22semidirect
30. #16837978C22semidirect
31. #16837973C22semidirect
32. #16837955C22semidirect
40. #16837932C22semidirect
69. #16837883C22semidirect
78. C2×#14273692C22semidirect
93. C59×#520C22semidirect
449. C2×#520D59semidirect
453. C2×C59#3507semidirect
510. #520C2×D59semidirect
540. C59C2×#3507semidirect
875. C2#21437954direct (N × H)

Maximal subgroups

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

subgroupindex
#214379542
C2×#168381352
C2×#168381302
C2×#168381242
C2×#168381222
C2×#168381202
C2×#168381072
C2×#168380912
C2×#168380872
C2×#168379942
C2×#168379782
C2×#168379732
C2×#168379552
C2×#168379482
C2×#168379322
C2×#168378832
C22×#142736922
C2×C59×#5202
C2×#350759