Finite Group Databasebeta

← C2×#21438569 #29496310

Subgroups — C2×#21438569 #29496310

Order 15104.

7182 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#21438569C2132yesmaximal, direct product factor
2C2×#16838149C214yesmaximal, complemented
3C2×#16838137C211yesmaximal, characteristic, complemented
4C2×#16838134C212yesmaximal, complemented
5C2×#16838131C211yesmaximal, characteristic, complemented
6C2×#16838108C212yesmaximal, complemented
7C2×#16838073C211yesmaximal, characteristic, complemented
8C2×D4×Dic118C211yesmaximal, characteristic, complemented
9C2×#16838061C212yesmaximal, complemented
10C2×#16838057C212yesmaximal, complemented
11C2×#16838025C212yesmaximal, complemented
12C2×#16838023C212yesmaximal, complemented
13C2×#16838005C212yesmaximal, complemented
14C2×#16837993C214yesmaximal, complemented
15C2×#16837978C212yesmaximal, complemented
16C2×#16837959C211yesmaximal, characteristic, complemented
17C2×#16837952C211yesmaximal, characteristic, complemented
18C2×C59×#529C211yesmaximal, characteristic, complemented
19C22×#11745685C2212yes—
20C22×#11745685C2212yes—
21C23×Dic118C2212yes—
22#16838149C22164yescomplemented
23#16838137C22116yescomplemented
24#16838134C22132yescomplemented
25#16838131C22116yescomplemented
26#16838108C22132yescomplemented
27#16838073C22116yescomplemented
28D4×Dic118C22116yescomplemented
29#16838061C22132yescomplemented
30#16838057C22132yescomplemented
31#16838025C22132yescomplemented
32#16838023C22132yescomplemented
33#16838005C22132yescomplemented
34#16837993C22164yescomplemented
35#16837978C22132yescomplemented
36#16837959C22116yescomplemented
37#16837952C22116yescomplemented
38C2×#14273727C2211yescharacteristic
39C2×#14273727C2212yes—
40C2×#14273727C2211yescharacteristic
41C2×#14273727C2211yescharacteristic
42C2×#14273726C2212yes—
43C2×#14273724C2211yescharacteristic
44C2×#14273723C2212yes—
45C2×#14273722C2214yes—
46C2×#14273719C2212yes—
47C2×#14273718C2214yes—
48C2×#14273718C2212yes—
49C2×#14273716C2212yes—
50C2×#14273715C2212yes—
51C2×#14273715C2212yes—
52C2×#14273713C2214yes—
53C2×#14273713C2214yes—
54C2×#14273712C2214yes—
55C2×#14273711C2214yes—
56C2×#14273711C2214yes—
57C2×#14273709C2214yes—
58C2×#14273709C2214yes—
59C2×#14273709C2214yes—
60C2×#14273707C2214yes—
61C2×#14273707C2214yes—
62C2×#14273706C2212yes—
63C2×#14273706C2212yes—
64C2×#14273706C2211yescharacteristic
65C2×#14273706C2211yescharacteristic
66C2×#14273705C2214yes—
67C2×#14273705C2214yes—
68C2×#14273704C2214yes—
69C2×#14273701C2212yes—
70C2×#14273701C2212yes—
71C2×#14273701C2212yes—
72C2×#14273700C2214yes—
73C2×#14273699C2214yes—
74C2×#14273698C2214yes—
75C2×Q8×Dic59C2212yes—
76C2×C4×Dic118C2212yes—
77C2×C4×Dic118C2211yescharacteristic
78C2×C4×Dic118C2211yescharacteristic
79C2×C4×Dic118C2212yes—
80C2×C4×D236C2212yes—
81C2×C4×D236C2212yes—
82C2×C4×D236C2212yes—
83C2×D4×Dic59C2212yes—
84C2×#14273689C2212yes—
85C2×#14273689C2212yes—
86C2×(C22⋊D59)⋊C4C2214yes—
87C2×#14273686C2212yes—
88C2×C4⋊C4×D59C2214yes—
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×#11745685—48no—
102C2×#11745685—48no—
103C2×#11745685C23116yes—
104C2×#11745685C23116yes—
105C22×Dic118—48no—
106C22×Dic118C2311yescharacteristic
107C22×Dic118C2312yes—
108C22×Dic118C2311yescharacteristic
109C22×Dic118C2314yes—
110C22×Dic118C2312yes—
111C22×Dic118C23116yes—
112C22×D236C2312yes—
113C22×D236C2312yes—
114C22×D236C2312yes—
115C22×C22⋊D59C2314yes—
116C22×C22⋊D59C2314yes—
117C22×C22⋊D59C2314yes—
118C23×Dic59C2314yes—
119C22×C4×D59C2314yes—
120C22×C4×D59C2314yes—
121C22×C4×D59C2314yes—
122#14273727C2318yes—
123#14273727C2318yes—
124#14273727C2318yes—
125#14273727C23116yes—
126#14273726C23116yes—
127#14273724C2318yes—
128#14273723C23116yes—
129#14273722C23132yes—
130#14273719C23116yes—
131#14273718C23132yes—
132#14273718C23116yes—
133#14273716C23116yes—
134#14273715C23116yes—
135#14273715C23116yes—
136#14273713C23132yes—
137#14273713C23132yes—
138#14273712C23132yes—
139#14273711C23132yes—
140#14273711C23132yes—
141#14273709C23132yes—
142#14273709C23132yes—
143#14273709C23132yes—
144#14273707C23132yes—
145#14273707C23132yes—
146#14273706C23116yes—
147#14273706C2318yes—
148#14273706C2318yes—
149#14273706C23116yes—
150#14273705C23132yes—
151#14273705C23132yes—
152#14273704C23132yes—
153#14273701C23116yes—
154#14273701C23116yes—
155#14273701C23116yes—
156#14273700C23132yes—
157#14273699C23132yes—
158#14273698C23132yes—
159Q8×Dic59C23116yes—
160C4×Dic118C2318yes—
161C4×Dic118C2318yes—
162C4×Dic118C23116yes—
163C4×Dic118C23116yes—
164C4×D236C23116yes—
165C4×D236C23116yes—
166C4×D236C23116yes—
167D4×Dic59C23116yes—
168#14273689C23116yes—
169#14273689C23116yes—
170(C22⋊D59)⋊C4C23132yes—
171#14273686C23116yes—
172C2×C4⋊Dic59C2314yes—
173C2×C4⋊Dic59C2311yescharacteristic
174C2×C4⋊Dic59C2312yes—
175C2×C4⋊Dic59C2312yes—
176C2×C4⋊Dic59C2311yescharacteristic
177C2×C4⋊Dic59C2312yes—
178C2×C4⋊Dic59C2312yes—
179C2×C4⋊Dic59C2314yes—
180C2×C4⋊Dic59C2312yes—
181C2×Dic59⋊C4C2314yes—
182C2×Dic59⋊C4C2312yes—
183C2×Dic59⋊C4C2312yes—
184C2×Dic59⋊C4C2314yes—
185C2×Dic59⋊C4C2312yes—
186C2×Dic59⋊C4C2312yes—
187C4⋊C4×D59C23132yes—
188C2×C22⋊Dic59C2312yes—
189C2×C22⋊Dic59C2314yes—
190C2×C22⋊Dic59C2312yes—
191C2×(C2×D59)⋊C4C2314yes—
192C2×(C2×D59)⋊C4C2314yes—
193C2×(C2×D59)⋊C4C2314yes—
194C2×(C2×D59)⋊C4C2314yes—
195C2×(C2×D59)⋊C4C2314yes—
196C2×(C2×D59)⋊C4C2314yes—
197C2×C4×Dic59C2314yes—
198C2×C4×Dic59C2312yes—
199C2×C4×Dic59C2312yes—
200C22×Q8×C59C2311yescharacteristic
201C22×D4×C59C2311yescharacteristic
202C22×D4×C59C2312yes—
203C23×C4×C59C2311yescharacteristic
204C23×C4×C59C2312yes—
205C23×C4×C59C2311yescharacteristic
206C23×C4×C59C2311yescharacteristic
207#126×C59C23116yes—
208#125×C59C2318yes—
209#124×C59C2318yes—
210#123×C59C23116yes—
211C22⋊Q8×C59C2318yes—
212#121×C59C2318yes—
213C4×Q8×C59C2318yes—
214C4×D4×C59C23116yes—
215C4×D4×C59C2318yes—
216#117×C59C23116yes—
217C2×C4⋊C4×C59C2312yes—
218C2×C4⋊C4×C59C2312yes—
219C2×C4⋊C4×C59C2312yes—
220C2×C4⋊C4×C59C2312yes—
221C2×C4⋊C4×C59C2311yescharacteristic
222C2×C4⋊C4×C59C2311yescharacteristic
223C2×C22⋊C4×C59C2312yes—
224C2×C22⋊C4×C59C2312yes—
225C2×C22⋊C4×C59C2312yes—
226C2×C22⋊C4×C59C2312yes—
227C2×C22⋊C4×C59C2312yes—
228C2×C42×C59C2311yescharacteristic
229C2×C42×C59C2312yes—
230C2×C42×C59C2311yescharacteristic
231C2×C42×C59C2311yescharacteristic
232C2×C42×C59C2318yes—
233C2×C42×C59C2311yescharacteristic
234C24×C59C2412yes—
235C24×C59C2411yescharacteristic
236C23×D59C2414yes—
237C2×Q8×C59—24no—
238C2×Q8×C59C2414yes—
239C2×D4×C59—24no—
240C2×D4×C59—44no—
241C2×D4×C59C2414yes—
242C2×D4×C59C2418yes—
243C22×C4×C59—28no—
244C22×C4×C59—24no—
245C22×C4×C59—24no—
246C22×C4×C59—42no—
247C22×C4×C59C2411yescharacteristic
248C22×C4×C59C2411yescharacteristic
249C22×C4×C59C2411yescharacteristic
250C22×C4×C59C2411yescharacteristic
251C22×C4×C59C2414yes—
252C22×C4×C59C2414yes—
253C22×C4×C59C2412yes—
254C22×C4×C59C2412yes—
255C22×C4×C59C2412yes—
256C22×C4×C59C2418yes—
257C22×C4×C59C2414yes—
258C22×C4×C59C2411yescharacteristic
259C22×C4×C59C2411yescharacteristic
260C2×C22⋊D59—48no—
261C2×C22⋊D59—48no—
262C2×C22⋊D59—48no—
263C2×C22⋊D59C24116yes—
264C2×C22⋊D59C24116yes—
265C2×C22⋊D59C24116yes—
266C22×Dic59—48no—
267C22×Dic59C2412yes—
268C22×Dic59C2412yes—
269C22×Dic59C2412yes—
270C22×Dic59C2414yes—
271C22×Dic59C2412yes—
272C22×Dic59C24116yes—
273#11745685—432no—
274#11745685—432no—
275C2×D236—28no—
276C2×D236—28no—
277C2×D236—44no—
278C2×D236C2418yes—
279C2×D236C2418yes—
280C2×D236C2418yes—
281C2×C4×D59—48no—
282C2×C4×D59—48no—
283C2×C4×D59—48no—
284C2×C4×D59C24116yes—
285C2×C4×D59C24116yes—
286C2×C4×D59C24116yes—
287C2×Dic118—24no—
288C2×Dic118—28no—
289C2×Dic118—24no—
290C2×Dic118—432no—
291C2×Dic118—48no—
292C2×Dic118—44no—
293C2×Dic118C2414yes—
294C2×Dic118C2418yes—
295C2×Dic118C2414yes—
296C2×Dic118C2418yes—
297C2×Dic118C24116yes—
298C4⋊C4×C59C2418yes—
299C4⋊C4×C59C2418yes—
300C4⋊C4×C59C2414yes—
301C4⋊C4×C59C2418yes—
302C4⋊C4×C59C2414yes—
303C4⋊C4×C59C2418yes—
304C22⋊C4×C59C2418yes—
305C22⋊C4×C59C2418yes—
306C22⋊C4×C59C2418yes—
307C22⋊C4×C59C2418yes—
308C22⋊C4×C59C2418yes—
309C42×C59C2414yes—
310C42×C59C2414yes—
311C42×C59C2414yes—
312C42×C59C2414yes—
313C42×C59C2418yes—
314C22⋊Dic59C2418yes—
315C22⋊Dic59C2418yes—
316C22⋊Dic59C24116yes—
317(C2×D59)⋊C4C24116yes—
318(C2×D59)⋊C4C24116yes—
319(C2×D59)⋊C4C24116yes—
320(C2×D59)⋊C4C24116yes—
321(C2×D59)⋊C4C24116yes—
322(C2×D59)⋊C4C24116yes—
323C4⋊Dic59C24116yes—
324C4⋊Dic59C2418yes—
325C4⋊Dic59C2418yes—
326C4⋊Dic59C2418yes—
327C4⋊Dic59C2414yes—
328C4⋊Dic59C2418yes—
329C4⋊Dic59C2414yes—
330C4⋊Dic59C2418yes—
331C4⋊Dic59C24116yes—
332Dic59⋊C4C2418yes—
333Dic59⋊C4C24116yes—
334Dic59⋊C4C2418yes—
335Dic59⋊C4C24116yes—
336Dic59⋊C4C2418yes—
337Dic59⋊C4C2418yes—
338C4×Dic59C2418yes—
339C4×Dic59C2418yes—
340C4×Dic59C24116yes—
341C23×C59—24no—
342C23×C59—22no—
343C23×C59—22no—
344C23×C59—24no—
345C23×C59—24no—
346C23×C59—22no—
347C23×C59C2512yes—
348C23×C59C2514yes—
349C23×C59C2511yescharacteristic
350C22×D59—28no—
351C22×D59—28no—
352C22×D59—28no—
353C22×D59C2518yes—
354Q8×C59—28no—
355D4×C59—28no—
356D4×C59—48no—
357C2×C4×C59—24no—
358C2×C4×C59—22no—
359C2×C4×C59—22no—
360C2×C4×C59—24no—
361C2×C4×C59—22no—
362C2×C4×C59—24no—
363C2×C4×C59—22no—
364C2×C4×C59—216no—
365C2×C4×C59—28no—
366C2×C4×C59—28no—
367C2×C4×C59—44no—
368C2×C4×C59H(5,𝔽2)14yes—
369C2×C4×C592−1+414yes—
370C2×C4×C59C2514yes—
371C2×C4×C59C2512yes—
372C2×C4×C59C2512yes—
373C2×C4×C59C2514yes—
374C2×C4×C59C2514yes—
375C2×C4×C59C2512yes—
376C2×C4×C59C2512yes—
377C2×C4×C59C2512yes—
378C2×C4×C59C2512yes—
379C22⋊D59—416no—
380C22⋊D59—416no—
381C22⋊D59—416no—
382C2×Dic59—24no—
383C2×Dic59—28no—
384C2×Dic59—24no—
385C2×Dic59—24no—
386C2×Dic59—24no—
387C2×Dic59—416no—
388C2×Dic59C2514yes—
389C2×Dic59C2514yes—
390C2×Dic59C2514yes—
391C2×Dic59C2518yes—
392C2×Dic59C2514yes—
393D236—216no—
394D236—216no—
395D236—48no—
396C4×D59—416no—
397C4×D59—416no—
398C4×D59—416no—
399Dic118—28no—
400Dic118—216no—
401Dic118—28no—
402Dic118—416no—
403Dic118—48no—
404C2×#3554—591nomaximal, Sylow
405C22×C59—24no—
406C22×C59—22no—
407C22×C59—22no—
408C22×C59—24no—
409C22×C59—24no—
410C22×C59—22no—
411C22×C59—48no—
412C22×C59—44no—
413C22×C59C2×H(5,𝔽2)12yes—
414C22×C59C2×2−1+412yes—
415C22×C59#58512yes—
416C22×C59C2611yescharacteristic
417C2×D59—28no—
418C2×D59—28no—
419C2×D59—28no—
420C2×D59—416no—
421C4×C59—24no—
422C4×C59—22no—
423C4×C59—22no—
424C4×C59—24no—
425C4×C59—22no—
426C4×C59—24no—
427C4×C59—22no—
428C4×C59C2×H(5,𝔽2)14yes—
429C4×C59C2×2−1+414yes—
430Dic59—24no—
431Dic59—28no—
432Dic59—24no—
433Dic59—24no—
434Dic59—24no—
435#3554—5932no—
436C2×#562—594no—
437C2×#559—592no—
438C2×#559—591no—
439C2×#557—591no—
440C2×#554—592no—
441C2×#550—591no—
442C2×D4×Q8—591no—
443C2×#548—592no—
444C2×#547—592no—
445C2×#542—592no—
446C2×#542—592no—
447C2×#540—592no—
448C2×#539—594no—
449C2×#536—592no—
450C2×#533—591no—
451C2×#532—591no—
452C2×#529D5911yescharacteristic, complemented
453C2×C59—44no—
454C2×C59—42no—
455C2×C59#355414yescomplemented
456C2×C59C22×H(5,𝔽2)11yescharacteristic
457C2×C59C22×2−1+411yescharacteristic
458C2×C59C2×#58511yescharacteristic
459D59—48no—
460C22×#41—592no—
461C22×#41—592no—
462C23×Q8—592no—
463#562—5964no—
464#559—5932no—
465#559—5916no—
466#557—5916no—
467#554—5932no—
468#550—5916no—
469D4×Q8—5916no—
470#548—5932no—
471#547—5932no—
472#542—5932no—
473#542—5932no—
474#540—5932no—
475#539—5964no—
476#536—5932no—
477#533—5916no—
478#532—5916no—
479C2×C4⋊Q8—592no—
480C2×C4⋊Q8—591no—
481C2×C4⋊Q8—591no—
482C2×C4⋊Q8—591no—
483C2×C4⋊Q8—592no—
484C2×#127—592no—
485C2×#127—591no—
486#529C2×D59116yescomplemented
487C2×#126—594no—
488C2×#126C2×D5912yes—
489C2×#125—594no—
490C2×#125—592no—
491C2×#125—592no—
492C2×#125C2×D5911yescharacteristic
493C2×#124—592no—
494C2×#124—594no—
495C2×#124—594no—
496C2×#124—592no—
497C2×#124—592no—
498C2×#124C2×D5911yescharacteristic
499C2×#123—594no—
500C2×#123—594no—
501C2×#123—594no—
502C2×#123—594no—
503C2×#123—594no—
504C2×#123—594no—
505C2×#123C2×D5912yes—
506C2×C22⋊Q8—591no—
507C2×C22⋊Q8—591no—
508C2×C22⋊Q8—592no—
509C2×C22⋊Q8—592no—
510C2×C22⋊Q8—594no—
511C2×C22⋊Q8—594no—
512C2×C22⋊Q8—594no—
513C2×C22⋊Q8—594no—
514C2×C22⋊Q8—594no—
515C2×C22⋊Q8C2×D5911yescharacteristic
516C2×#121—594no—
517C2×#121—594no—
518C2×#121—592no—
519C2×#121—592no—
520C2×#121—592no—
521C2×#121—594no—
522C2×#121C2×D5911yescharacteristic
523C2×C4×Q8—592no—
524C2×C4×Q8—591no—
525C2×C4×Q8—591no—
526C2×C4×Q8—592no—
527C2×C4×Q8—592no—
528C2×C4×Q8C2×D5911yescharacteristic
529C2×C4×D4—592no—
530C2×C4×D4—592no—
531C2×C4×D4—592no—
532C2×C4×D4—594no—
533C2×C4×D4—592no—
534C2×C4×D4—592no—
535C2×C4×D4—592no—
536C2×C4×D4C2×D5912yes—
537C2×C4×D4C2×D5911yescharacteristic
538C2×#117—592no—
539C2×#117C2×D5912yes—
540C22×C4⋊C4—594no—
541C22×C42C2×D5911yescharacteristic
542C59C2×#355411yescharacteristic, complemented, Sylow
543C2×#41—5916no—
544C2×#41—5916no—
545C2×#41—2368no—
546C2×#41—2368no—
547C22×Q8—591no—
548C22×Q8—592no—
549C22×Q8—591no—
550C22×Q8—592no—
551C22×Q8—594no—
552C22×Q8—5916no—
553C22×Q8—2368no—
554C22×Q8C22×D5911yescharacteristic
555C22×D4—594no—
556C22×D4—594no—
557C22×D4—594no—
558C22×D4—592no—
559C22×D4—592no—
560C22×D4—592no—
561C22×D4C22×D5911yescharacteristic
562C22×D4C22×D5912yes—
563C23×C4—594no—
564C23×C4—594no—
565C23×C4—594no—
566C23×C4—594no—
567C23×C4C22×D5911yescharacteristic
568C23×C4C22×D5912yes—
569C23×C4C22×D5911yescharacteristic
570C23×C4C22×D5911yescharacteristic
571C4⋊Q8—5916no—
572C4⋊Q8—598no—
573C4⋊Q8—598no—
574C4⋊Q8—598no—
575C4⋊Q8—5916no—
576#127—5916no—
577#127—598no—
578#126—5932no—
579#126C22×D59116yes—
580#125—5932no—
581#125—5916no—
582#125—5916no—
583#125C22×D5918yes—
584#124—5916no—
585#124—5932no—
586#124—5932no—
587#124—5916no—
588#124—5916no—
589#124C22×D5918yes—
590#123—5932no—
591#123—5932no—
592#123—5932no—
593#123—5932no—
594#123—5932no—
595#123—5932no—
596#123C22×D59116yes—
597C22⋊Q8—598no—
598C22⋊Q8—598no—
599C22⋊Q8—5916no—
600C22⋊Q8—5916no—
601C22⋊Q8—5932no—
602C22⋊Q8—5932no—
603C22⋊Q8—5932no—
604C22⋊Q8—5932no—
605C22⋊Q8—5932no—
606C22⋊Q8C22×D5918yes—
607#121—5932no—
608#121—5932no—
609#121—5916no—
610#121—5916no—
611#121—5916no—
612#121—5932no—
613#121C22×D5918yes—
614C4×Q8—5916no—
615C4×Q8—598no—
616C4×Q8—598no—
617C4×Q8—5916no—
618C4×Q8—5916no—
619C4×Q8C22×D5918yes—
620C4×D4—5916no—
621C4×D4—5916no—
622C4×D4—5916no—
623C4×D4—5932no—
624C4×D4—5916no—
625C4×D4—5916no—
626C4×D4—5916no—
627C4×D4C22×D59116yes—
628C4×D4C22×D5918yes—
629#117—5916no—
630#117C22×D59116yes—
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—591no—
639C2×C4⋊C4—592no—
640C2×C4⋊C4—591no—
641C2×C4⋊C4—592no—
642C2×C4⋊C4—594no—
643C2×C4⋊C4—592no—
644C2×C4⋊C4—592no—
645C2×C4⋊C4—594no—
646C2×C4⋊C4—5932no—
647C2×C4⋊C4C22×D5912yes—
648C2×C4⋊C4C22×D5912yes—
649C2×C4⋊C4C22×D5912yes—
650C2×C4⋊C4C22×D5911yescharacteristic
651C2×C4⋊C4C22×D5911yescharacteristic
652C2×C4⋊C4C22×D5912yes—
653C2×C22⋊C4—592no—
654C2×C22⋊C4—592no—
655C2×C22⋊C4—594no—
656C2×C22⋊C4—594no—
657C2×C22⋊C4—594no—
658C2×C22⋊C4—594no—
659C2×C22⋊C4—594no—
660C2×C22⋊C4—594no—
661C2×C22⋊C4—594no—
662C2×C22⋊C4C22×D5912yes—
663C2×C22⋊C4C22×D5912yes—
664C2×C22⋊C4C22×D5912yes—
665C2×C22⋊C4C22×D5912yes—
666C2×C22⋊C4C22×D5912yes—
667C2×C42—592no—
668C2×C42—592no—
669C2×C42—594no—
670C2×C42C22×D5911yescharacteristic
671C2×C42C22×D5912yes—
672C2×C42C22×D5911yescharacteristic
673C2×C42C22×D5911yescharacteristic
674C2×C42C22×D5911yescharacteristic
675C2×C42C22×D5918yes—
676C24—594no—
677C24C23×D5911yescharacteristic
678C24C23×D5912yes—
679#41—23632no—
680#41—23632no—
681C2×Q8—24no—
682C2×Q8—594no—
683C2×Q8—598no—
684C2×Q8—594no—
685C2×Q8—598no—
686C2×Q8—5916no—
687C2×Q8—1184no—
688C2×Q8—1188no—
689C2×Q8—1184no—
690C2×Q8—2368no—
691C2×Q8—2364no—
692C2×Q8—23632no—
693C2×Q8C23×D5914yes—
694C2×D4—24no—
695C2×D4—44no—
696C2×D4—5916no—
697C2×D4—5916no—
698C2×D4—5916no—
699C2×D4—598no—
700C2×D4—598no—
701C2×D4—598no—
702C2×D4—1188no—
703C2×D4—1188no—
704C2×D4—2364no—
705C2×D4—2368no—
706C2×D4—2368no—
707C2×D4—2368no—
708C2×D4C23×D5914yes—
709C2×D4C23×D5918yes—
710C22×C4—28no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—42no—
714C22×C4—592no—
715C22×C4—592no—
716C22×C4—592no—
717C22×C4—594no—
718C22×C4—592no—
719C22×C4—5916no—
720C22×C4—5916no—
721C22×C4—5916no—
722C22×C4—5916no—
723C22×C4—2368no—
724C22×C4—2368no—
725C22×C4—2368no—
726C22×C4—2368no—
727C22×C4C23×D5914yes—
728C22×C4C23×D5914yes—
729C22×C4C23×D5918yes—
730C22×C4C23×D5912yes—
731C22×C4C23×D5911yescharacteristic
732C22×C4C23×D5911yescharacteristic
733C22×C4C23×D5911yescharacteristic
734C22×C4C23×D5911yescharacteristic
735C22×C4C23×D5912yes—
736C22×C4C23×D5912yes—
737C22×C4C23×D5914yes—
738C22×C4C23×D5911yescharacteristic
739C22×C4C23×D5911yescharacteristic
740C4⋊C4—598no—
741C4⋊C4—5916no—
742C4⋊C4—5916no—
743C4⋊C4—598no—
744C4⋊C4—598no—
745C4⋊C4—598no—
746C4⋊C4—598no—
747C4⋊C4—594no—
748C4⋊C4—598no—
749C4⋊C4—594no—
750C4⋊C4—598no—
751C4⋊C4—5916no—
752C4⋊C4—598no—
753C4⋊C4—598no—
754C4⋊C4—5916no—
755C4⋊C4C23×D5918yes—
756C4⋊C4C23×D5918yes—
757C4⋊C4C23×D5918yes—
758C4⋊C4C23×D5914yes—
759C4⋊C4C23×D5914yes—
760C4⋊C4C23×D5918yes—
761C22⋊C4—598no—
762C22⋊C4—598no—
763C22⋊C4—5916no—
764C22⋊C4—5916no—
765C22⋊C4—5916no—
766C22⋊C4—5916no—
767C22⋊C4—5916no—
768C22⋊C4—5916no—
769C22⋊C4—5916no—
770C22⋊C4C23×D5918yes—
771C22⋊C4C23×D5918yes—
772C22⋊C4C23×D5918yes—
773C22⋊C4C23×D5918yes—
774C22⋊C4C23×D5918yes—
775C42—598no—
776C42—598no—
777C42—5916no—
778C42C23×D5914yes—
779C42C23×D5914yes—
780C42C23×D5914yes—
781C42C23×D5914yes—
782C42C23×D5918yes—
783C23—24no—
784C23—22no—
785C23—22no—
786C23—24no—
787C23—22no—
788C23—24no—
789C23—598no—
790C23—1188no—
791C23—1188no—
792C23—1188no—
793C23C24×D5912yes—
794C23C24×D5914yes—
795C23C24×D5911yescharacteristic
796Q8—28no—
797Q8—1188no—
798Q8—11816no—
799Q8—1188no—
800Q8—2368no—
801Q8—23616no—
802D4—28no—
803D4—48no—
804D4—11816no—
805D4—11816no—
806D4—2368no—
807D4—23616no—
808D4—23616no—
809D4—23616no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—216no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—44no—
821C2×C4—594no—
822C2×C4—594no—
823C2×C4—594no—
824C2×C4—598no—
825C2×C4—594no—
826C2×C4—1184no—
827C2×C4—1188no—
828C2×C4—1184no—
829C2×C4—1184no—
830C2×C4—1184no—
831C2×C4—23616no—
832C2×C4—23616no—
833C2×C4—23616no—
834C2×C4—23616no—
835C2×C4#1427377314yes—
836C2×C4#1427377414yes—
837C2×C4C24×D5914yes—
838C2×C4C24×D5912yes—
839C2×C4C24×D5912yes—
840C2×C4C24×D5912yes—
841C2×C4C24×D5912yes—
842C2×C4C24×D5914yes—
843C2×C4C24×D5914yes—
844C2×C4C24×D5912yes—
845C2×C4C24×D5912yes—
846C22—24no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—24no—
852C22—48no—
853C22—44no—
854C22—1188no—
855C22—1188no—
856C22—1188no—
857C22—23616no—
858C22C2×#1427377312yes—
859C22C2×#1427377412yes—
860C22#1683823812yes—
861C22C25×D5911yescharacteristic
862C4—22no—
863C4—24no—
864C4—22no—
865C4—24no—
866C4—22no—
867C4—22no—
868C4—24no—
869C4—1184no—
870C4—1188no—
871C4—1184no—
872C4—1184no—
873C4—1184no—
874C4C2×#1427377314yes—
875C4C2×#1427377414yes—
876C2—44no—
877C2—42no—
878C2—2368no—
879C2#2143856914yesdirect product factor
880C2C22×#1427377311yescharacteristic
881C2C22×#1427377411yescharacteristic
882C2C2×#1683823811yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#529C2
socleC23×C59C25
hypercenterC2×#529D59
hypocenterC59C2×#3554
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #21438569C2direct (N × H)
2. C2×#16838149C2semidirect
3. C2×#16838137C2semidirect
4. C2×#16838134C2semidirect
5. C2×#16838131C2semidirect
6. C2×#16838108C2semidirect
7. C2×#16838073C2semidirect
8. C2×D4×Dic118C2semidirect
9. C2×#16838061C2semidirect
10. C2×#16838057C2semidirect
11. C2×#16838025C2semidirect
12. C2×#16838023C2semidirect
13. C2×#16838005C2semidirect
14. C2×#16837993C2semidirect
15. C2×#16837978C2semidirect
16. C2×#16837959C2semidirect
17. C2×#16837952C2semidirect
18. C2×C59×#529C2semidirect
22. #16838149C22semidirect
23. #16838137C22semidirect
24. #16838134C22semidirect
25. #16838131C22semidirect
26. #16838108C22semidirect
27. #16838073C22semidirect
28. D4×Dic118C22semidirect
29. #16838061C22semidirect
30. #16838057C22semidirect
31. #16838025C22semidirect
32. #16838023C22semidirect
33. #16838005C22semidirect
34. #16837993C22semidirect
35. #16837978C22semidirect
36. #16837959C22semidirect
37. #16837952C22semidirect
89. C59×#529C22semidirect
452. C2×#529D59semidirect
455. C2×C59#3554semidirect
486. #529C2×D59semidirect
542. C59C2×#3554semidirect
879. C2#21438569direct (N × H)

Maximal subgroups

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

subgroupindex
#214385692
C2×#168381492
C2×#168381372
C2×#168381342
C2×#168381312
C2×#168381082
C2×#168380732
C2×D4×Dic1182
C2×#168380612
C2×#168380572
C2×#168380252
C2×#168380232
C2×#168380052
C2×#168379932
C2×#168379782
C2×#168379592
C2×#168379522
C2×C59×#5292
C2×#355459