Finite Group Databasebeta

← C2×#21438526 #29496301

Subgroups — C2×#21438526 #29496301

Order 15104.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438526C2132yesmaximal, direct product factor
2C2×#16838154C214yesmaximal, complemented
3C2×#16838131C211yesmaximal, characteristic, complemented
4C2×#16838110C212yesmaximal, complemented
5C2×#16838096C212yesmaximal, complemented
6C2×Q8×D236C212yesmaximal, complemented
7C2×#16838067C211yesmaximal, characteristic, complemented
8C2×#16838060C212yesmaximal, complemented
9C2×#16838056C211yesmaximal, characteristic, complemented
10C2×#16838030C212yesmaximal, complemented
11C2×#16838025C212yesmaximal, complemented
12C2×#16838010C212yesmaximal, complemented
13C2×#16837993C214yesmaximal, complemented
14C2×#16837972C212yesmaximal, complemented
15C2×C4⋊Q8×D59C211yesmaximal, characteristic, complemented
16C2×#16837939C211yesmaximal, characteristic, complemented
17C2×#16837934C211yesmaximal, characteristic, complemented
18C2×C59×#556C211yesmaximal, characteristic, complemented
19C22×#11745687C2212yes—
20C22×Q8×D59C2212yes—
21C22×Q8×D59C2212yes—
22#16838154C22164yescomplemented
23#16838131C22116yescomplemented
24#16838110C22132yescomplemented
25#16838096C22132yescomplemented
26Q8×D236C22132yescomplemented
27#16838067C22116yescomplemented
28#16838060C22132yescomplemented
29#16838056C22116yescomplemented
30#16838030C22132yescomplemented
31#16838025C22132yescomplemented
32#16838010C22132yescomplemented
33#16837993C22164yescomplemented
34#16837972C22132yescomplemented
35C2×#14273727C2214yes—
36C2×#14273727C2211yescharacteristic
37C2×#14273727C2212yes—
38C2×#14273726C2212yes—
39C2×#14273726C2212yes—
40C2×#14273726C2212yes—
41C2×#14273725C2212yes—
42C4⋊Q8×D59C22116yescomplemented
43#16837939C22116yescomplemented
44#16837934C22116yescomplemented
45C2×#14273722C2214yes—
46C2×#14273722C2212yes—
47C2×#14273721C2214yes—
48C2×#14273720C2212yes—
49C2×#14273719C2214yes—
50C2×#14273718C2214yes—
51C2×#14273718C2211yescharacteristic
52C2×#14273718C2211yescharacteristic
53C2×#14273718C2212yes—
54C2×#14273717C2214yes—
55C2×#14273716C2211yescharacteristic
56C2×#14273714C2211yescharacteristic
57C2×#14273713C2214yes—
58C2×#14273712C2212yes—
59C2×#14273711C2214yes—
60C2×#14273709C2212yes—
61C2×#14273709C2214yes—
62C2×#14273709C2214yes—
63C2×#14273707C2214yes—
64C2×#14273707C2212yes—
65C2×#14273707C2214yes—
66C2×#14273707C2211yescharacteristic
67C2×#14273705C2214yes—
68C2×#14273704C2214yes—
69C2×#14273704C2214yes—
70C2×#14273704C2214yes—
71C2×#14273703C2212yes—
72C2×#14273703C2211yescharacteristic
73C2×#14273702C2211yescharacteristic
74C2×#14273701C2212yes—
75C2×#14273700C2214yes—
76C2×#14273698C2211yescharacteristic
77C2×Q8×Dic59C2212yes—
78C2×C4×Dic118C2212yes—
79C2×C4×Dic118C2211yescharacteristic
80C2×C4×D236C2214yes—
81C2×C4×D236C2211yescharacteristic
82C2×C4×D236C2212yes—
83C2×#14273689C2212yes—
84C2×C4×C22⋊D59C2212yes—
85C2×(C22⋊D59)⋊C4C2214yes—
86C2×#14273686C2212yes—
87C2×#14273684C2212yes—
88C22×C4⋊Dic59C2212yes—
89C2×C4⋊C4×D59C2212yes—
90C2×C4⋊C4×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×#11745687—48no—
102C2×#11745687C23116yes—
103C22×Dic118C2311yescharacteristic
104C22×Dic118C2312yes—
105C22×Dic118C2314yes—
106C22×Dic118C2314yes—
107C2×Q8×D59—48no—
108C2×Q8×D59—48no—
109C2×Q8×D59C23116yes—
110C2×Q8×D59C23116yes—
111C22×D236C2312yes—
112C22×D236C2311yescharacteristic
113C22×C22⋊D59C2312yes—
114C22×C22⋊D59C2314yes—
115C23×Dic59C2314yes—
116C22×C4×D59C2311yescharacteristic
117C22×C4×D59C2311yescharacteristic
118C22×C4×D59C2312yes—
119C22×C4×D59C2311yescharacteristic
120C22×C4×D59C2314yes—
121C22×C4×D59C2314yes—
122#14273727C23132yes—
123#14273727C2318yes—
124#14273727C23116yes—
125#14273726C23116yes—
126#14273726C23116yes—
127#14273726C23116yes—
128#14273725C23116yes—
129#14273722C23116yes—
130#14273722C23132yes—
131#14273721C23132yes—
132#14273720C23116yes—
133#14273719C23132yes—
134#14273718C23132yes—
135#14273718C2318yes—
136#14273718C2318yes—
137#14273718C23116yes—
138#14273717C23132yes—
139#14273716C2318yes—
140#14273714C2318yes—
141#14273713C23132yes—
142#14273712C23116yes—
143#14273711C23132yes—
144#14273709C23132yes—
145#14273709C23116yes—
146#14273709C23132yes—
147#14273707C23132yes—
148#14273707C2318yes—
149#14273707C23132yes—
150#14273707C23116yes—
151#14273705C23132yes—
152#14273704C23132yes—
153#14273704C23132yes—
154#14273704C23132yes—
155#14273703C2318yes—
156#14273703C23116yes—
157#14273702C2318yes—
158#14273701C23116yes—
159#14273700C23132yes—
160#14273698C2318yes—
161Q8×Dic59C23116yes—
162C4×Dic118C2318yes—
163C4×Dic118C23116yes—
164C4×D236C2318yes—
165C4×D236C23116yes—
166C4×D236C23132yes—
167#14273689C23116yes—
168C4×C22⋊D59C23116yes—
169(C22⋊D59)⋊C4C23132yes—
170#14273686C23116yes—
171#14273684C23116yes—
172C2×C4⋊Dic59C2311yescharacteristic
173C2×C4⋊Dic59C2312yes—
174C2×C4⋊Dic59C2311yescharacteristic
175C2×C4⋊Dic59C2312yes—
176C2×C4⋊Dic59C2314yes—
177C2×C4⋊Dic59C2314yes—
178C2×C4⋊Dic59C2312yes—
179C2×C4⋊Dic59C2314yes—
180C2×C4⋊Dic59C2312yes—
181C2×C4⋊Dic59C2312yes—
182C2×C4⋊Dic59C23116yes—
183C2×Dic59⋊C4C2314yes—
184C2×Dic59⋊C4C2312yes—
185C2×Dic59⋊C4C2314yes—
186C2×Dic59⋊C4C2312yes—
187C2×Dic59⋊C4C2314yes—
188C2×Dic59⋊C4C2314yes—
189C2×Dic59⋊C4C2312yes—
190C2×Dic59⋊C4C2312yes—
191C4⋊C4×D59C23116yes—
192C4⋊C4×D59C23116yes—
193C2×C22⋊Dic59C2312yes—
194C2×C22⋊Dic59C2312yes—
195C2×C22⋊Dic59C2312yes—
196C2×(C2×D59)⋊C4C2314yes—
197C2×(C2×D59)⋊C4C2314yes—
198C2×(C2×D59)⋊C4C2312yes—
199C2×(C2×D59)⋊C4C2312yes—
200C2×(C2×D59)⋊C4C2312yes—
201C2×(C2×D59)⋊C4C2312yes—
202C2×(C2×D59)⋊C4C2312yes—
203C2×(C2×D59)⋊C4C2312yes—
204C2×C4×Dic59C2314yes—
205C2×C4×Dic59C2311yescharacteristic
206C2×C4×Dic59C2311yescharacteristic
207C2×C4×Dic59C2312yes—
208C2×C4×Dic59C2311yescharacteristic
209C42×D59C2318yes—
210C22×Q8×C59C2311yescharacteristic
211C22×Q8×C59C2312yes—
212C22×D4×C59C2311yescharacteristic
213C23×C4×C59C2312yes—
214C4⋊Q8×C59C2318yes—
215#126×C59C23132yes—
216#124×C59C23116yes—
217C22⋊Q8×C59C23116yes—
218C4×Q8×C59C2318yes—
219C4×Q8×C59C23116yes—
220C4×D4×C59C2318yes—
221#117×C59C23116yes—
222C2×C4⋊C4×C59C2311yescharacteristic
223C2×C4⋊C4×C59C2312yes—
224C2×C4⋊C4×C59C2311yescharacteristic
225C2×C4⋊C4×C59C2314yes—
226C2×C4⋊C4×C59C2312yes—
227C2×C4⋊C4×C59C2312yes—
228C2×C22⋊C4×C59C2314yes—
229C2×C22⋊C4×C59C2314yes—
230C2×C22⋊C4×C59C2312yes—
231C2×C42×C59C2314yes—
232C2×C42×C59C2311yescharacteristic
233C2×C42×C59C2312yes—
234C24×C59C2412yes—
235C23×D59C2412yes—
236C23×D59C2411yescharacteristic
237C2×Q8×C59—28no—
238C2×Q8×C59—24no—
239C2×Q8×C59C2414yes—
240C2×Q8×C59C2418yes—
241C2×D4×C59—24no—
242C2×D4×C59C2414yes—
243C22×C4×C59—28no—
244C22×C4×C59C2412yes—
245C22×C4×C59C2412yes—
246C22×C4×C59C2411yescharacteristic
247C22×C4×C59C2412yes—
248C22×C4×C59C2414yes—
249C22×C4×C59C2418yes—
250C22×C4×C59C2411yescharacteristic
251C22×C4×C59C2411yescharacteristic
252C2×C22⋊D59—28no—
253C2×C22⋊D59—48no—
254C2×C22⋊D59C2418yes—
255C2×C22⋊D59C24116yes—
256C22×Dic59—48no—
257C22×Dic59C2412yes—
258C22×Dic59C2411yescharacteristic
259C22×Dic59C2411yescharacteristic
260C22×Dic59C2411yescharacteristic
261C22×Dic59C2412yes—
262C22×Dic59C2414yes—
263C22×Dic59C2412yes—
264C22×Dic59C24116yes—
265Q8×D59—432no—
266Q8×D59—432no—
267#11745687—432no—
268C2×D236—28no—
269C2×D236—24no—
270C2×D236C2414yes—
271C2×D236C2418yes—
272C2×C4×D59—24no—
273C2×C4×D59—24no—
274C2×C4×D59—28no—
275C2×C4×D59—24no—
276C2×C4×D59—48no—
277C2×C4×D59—48no—
278C2×C4×D59C2414yes—
279C2×C4×D59C2414yes—
280C2×C4×D59C2414yes—
281C2×C4×D59C2418yes—
282C2×C4×D59C24116yes—
283C2×C4×D59C24116yes—
284C2×Dic118—24no—
285C2×Dic118—28no—
286C2×Dic118—48no—
287C2×Dic118—48no—
288C2×Dic118C2414yes—
289C2×Dic118C2418yes—
290C2×Dic118C24116yes—
291C2×Dic118C24116yes—
292C4⋊C4×C59C2414yes—
293C4⋊C4×C59C2418yes—
294C4⋊C4×C59C2414yes—
295C4⋊C4×C59C24116yes—
296C4⋊C4×C59C2418yes—
297C4⋊C4×C59C2418yes—
298C22⋊C4×C59C24116yes—
299C22⋊C4×C59C2418yes—
300C22⋊C4×C59C24116yes—
301C42×C59C24116yes—
302C42×C59C2414yes—
303C42×C59C2418yes—
304C22⋊Dic59C2418yes—
305C22⋊Dic59C2418yes—
306C22⋊Dic59C2418yes—
307(C2×D59)⋊C4C2418yes—
308(C2×D59)⋊C4C2418yes—
309(C2×D59)⋊C4C2418yes—
310(C2×D59)⋊C4C2418yes—
311(C2×D59)⋊C4C24116yes—
312(C2×D59)⋊C4C24116yes—
313(C2×D59)⋊C4C2418yes—
314(C2×D59)⋊C4C2418yes—
315C4⋊Dic59C2418yes—
316C4⋊Dic59C2418yes—
317C4⋊Dic59C2414yes—
318C4⋊Dic59C24116yes—
319C4⋊Dic59C2418yes—
320C4⋊Dic59C2418yes—
321C4⋊Dic59C2418yes—
322C4⋊Dic59C24116yes—
323C4⋊Dic59C2414yes—
324C4⋊Dic59C24116yes—
325Dic59⋊C4C24116yes—
326Dic59⋊C4C24116yes—
327Dic59⋊C4C2418yes—
328Dic59⋊C4C2418yes—
329Dic59⋊C4C24116yes—
330Dic59⋊C4C2418yes—
331Dic59⋊C4C24116yes—
332Dic59⋊C4C2418yes—
333C4×Dic59C2414yes—
334C4×Dic59C2414yes—
335C4×Dic59C2414yes—
336C4×Dic59C2418yes—
337C4×Dic59C24116yes—
338C23×C59—24no—
339C23×C59—24no—
340C23×C59—24no—
341C23×C59C2514yes—
342C23×C59C2511yescharacteristic
343C22×D59—22no—
344C22×D59—22no—
345C22×D59—24no—
346C22×D59—24no—
347C22×D59—24no—
348C22×D592−1+414yes—
349C22×D59C2514yes—
350C22×D59C2512yes—
351Q8×C59—216no—
352Q8×C59—28no—
353D4×C59—28no—
354C2×C4×C59—28no—
355C2×C4×C59—22no—
356C2×C4×C59—24no—
357C2×C4×C59—24no—
358C2×C4×C59—24no—
359C2×C4×C59—216no—
360C2×C4×C59H(5,𝔽2)14yes—
361C2×C4×C592−1+414yes—
362C2×C4×C59C2514yes—
363C2×C4×C59C2512yes—
364C2×C4×C59C2514yes—
365C2×C4×C59C2518yes—
366C2×C4×C59C2514yes—
367C2×C4×C59C2512yes—
368C2×C4×C59C2512yes—
369C22⋊D59—216no—
370C22⋊D59—416no—
371C2×Dic59—24no—
372C2×Dic59—28no—
373C2×Dic59—22no—
374C2×Dic59—24no—
375C2×Dic59—22no—
376C2×Dic59—22no—
377C2×Dic59—24no—
378C2×Dic59—416no—
379C2×Dic59C2514yes—
380C2×Dic59C2512yes—
381C2×Dic59C2512yes—
382C2×Dic59C2512yes—
383C2×Dic59C2518yes—
384C2×Dic59C2514yes—
385C2×Dic59C2514yes—
386D236—216no—
387D236—28no—
388C4×D59—28no—
389C4×D59—216no—
390C4×D59—28no—
391C4×D59—28no—
392C4×D59—416no—
393C4×D59—416no—
394Dic118—216no—
395Dic118—28no—
396Dic118—416no—
397Dic118—416no—
398C2×#3552—591nomaximal, Sylow
399C22×C59—24no—
400C22×C59—24no—
401C22×C59—24no—
402C22×C59—48no—
403C22×C59C2×H(5,𝔽2)12yes—
404C22×C59C2×2−1+412yes—
405C22×C59C2×2−1+412yes—
406C22×C59C2611yescharacteristic
407C2×D59—22no—
408C2×D59—22no—
409C2×D59—28no—
410C2×D59—24no—
411C2×D59—24no—
412C2×D59—24no—
413C2×D59—48no—
414C2×D59C2×2−1+414yes—
415C4×C59—28no—
416C4×C59—22no—
417C4×C59—24no—
418C4×C59—24no—
419C4×C59—24no—
420C4×C59C2×H(5,𝔽2)14yes—
421C4×C59C2×2−1+414yes—
422Dic59—24no—
423Dic59—28no—
424Dic59—22no—
425Dic59—24no—
426Dic59—22no—
427Dic59—22no—
428Dic59—24no—
429#3552—5932no—
430C2×#563—594no—
431C2×#557—591no—
432C2×#556D5911yescharacteristic, complemented
433C2×#554—592no—
434C2×#553—592no—
435C2×D4×Q8—591no—
436C2×D4×Q8—592no—
437C2×#548—592no—
438C2×#547—591no—
439C2×#544—592no—
440C2×#542—592no—
441C2×#541—592no—
442C2×#539—594no—
443C2×#536—592no—
444C22×C4⋊Q8—591no—
445C2×#529—591no—
446C2×#529—591no—
447C2×C59—44no—
448C2×C59#355214yescomplemented
449C2×C59C22×H(5,𝔽2)11yescharacteristic
450C2×C59C22×2−1+411yescharacteristic
451C2×C59C22×2−1+411yescharacteristic
452D59—24no—
453D59—44no—
454C22×#41—592no—
455C23×Q8—592no—
456C23×Q8—592no—
457#563—5964no—
458#557—5916no—
459#556C2×D59116yescomplemented
460#554—5932no—
461#553—5932no—
462D4×Q8—5916no—
463D4×Q8—5932no—
464#548—5932no—
465#547—5916no—
466#544—5932no—
467#542—5932no—
468#541—5932no—
469#539—5964no—
470#536—5932no—
471C2×C4⋊Q8—592no—
472C2×C4⋊Q8—5916no—
473C2×C4⋊Q8—592no—
474C2×C4⋊Q8—592no—
475C2×C4⋊Q8—592no—
476C2×C4⋊Q8—591no—
477C2×C4⋊Q8—592no—
478C2×C4⋊Q8—594no—
479C2×C4⋊Q8C2×D5911yescharacteristic
480#529—5916no—
481#529—5916no—
482C2×#126—592no—
483C2×#126—594no—
484C2×#126—592no—
485C2×#126—594no—
486C2×#126C2×D5914yes—
487C2×#125—594no—
488C2×#125—591no—
489C2×#125—591no—
490C2×#125—594no—
491C2×#125—592no—
492C2×#125—594no—
493C2×#124—591no—
494C2×#124—591no—
495C2×#124—594no—
496C2×#124C2×D5912yes—
497C2×#123—592no—
498C2×#123—592no—
499C2×#123—594no—
500C2×#123—594no—
501C2×#123—594no—
502C2×C22⋊Q8—591no—
503C2×C22⋊Q8—592no—
504C2×C22⋊Q8—594no—
505C2×C22⋊Q8—591no—
506C2×C22⋊Q8—594no—
507C2×C22⋊Q8—592no—
508C2×C22⋊Q8—594no—
509C2×C22⋊Q8—594no—
510C2×C22⋊Q8—594no—
511C2×C22⋊Q8—594no—
512C2×C22⋊Q8C2×D5912yes—
513C2×#121—591no—
514C2×#121—592no—
515C2×#121—591no—
516C2×#121—594no—
517C2×C4×Q8—592no—
518C2×C4×Q8—591no—
519C2×C4×Q8—592no—
520C2×C4×Q8C2×D5911yescharacteristic
521C2×C4×Q8C2×D5912yes—
522C2×C4×D4—592no—
523C2×C4×D4—592no—
524C2×C4×D4—594no—
525C2×C4×D4—591no—
526C2×C4×D4—592no—
527C2×C4×D4—594no—
528C2×C4×D4C2×D5911yescharacteristic
529C2×#117—592no—
530C2×#117—592no—
531C2×#117C2×D5912yes—
532C22×C4⋊C4—592no—
533C22×C4⋊C4—592no—
534C22×C4⋊C4—592no—
535C22×C42—591no—
536C59C2×#355211yescharacteristic, complemented, Sylow
537C2×#41—5916no—
538C2×#41—2368no—
539C22×Q8—5916no—
540C22×Q8—5916no—
541C22×Q8—591no—
542C22×Q8—592no—
543C22×Q8—594no—
544C22×Q8—594no—
545C22×Q8—2368no—
546C22×Q8—2368no—
547C22×Q8C22×D5911yescharacteristic
548C22×Q8C22×D5912yes—
549C22×D4—592no—
550C22×D4—594no—
551C22×D4—592no—
552C22×D4—591no—
553C22×D4C22×D5911yescharacteristic
554C23×C4—594no—
555C23×C4—591no—
556C23×C4—591no—
557C23×C4—592no—
558C23×C4—591no—
559C23×C4—594no—
560C23×C4—594no—
561C23×C4C22×D5912yes—
562C4⋊Q8—5916no—
563C4⋊Q8—5916no—
564C4⋊Q8—5916no—
565C4⋊Q8—5916no—
566C4⋊Q8—598no—
567C4⋊Q8—5916no—
568C4⋊Q8—5932no—
569C4⋊Q8C22×D5918yes—
570#126—5916no—
571#126—5932no—
572#126—5916no—
573#126—5932no—
574#126C22×D59132yes—
575#125—598no—
576#125—598no—
577#125—5932no—
578#125—5932no—
579#125—5916no—
580#125—5932no—
581#124—598no—
582#124—598no—
583#124—5932no—
584#124C22×D59116yes—
585#123—5916no—
586#123—5916no—
587#123—5932no—
588#123—5932no—
589#123—5932no—
590C22⋊Q8—598no—
591C22⋊Q8—5916no—
592C22⋊Q8—598no—
593C22⋊Q8—5932no—
594C22⋊Q8—5932no—
595C22⋊Q8—5916no—
596C22⋊Q8—5932no—
597C22⋊Q8—5932no—
598C22⋊Q8—5932no—
599C22⋊Q8—5932no—
600C22⋊Q8C22×D59116yes—
601#121—598no—
602#121—5916no—
603#121—598no—
604#121—5932no—
605C4×Q8—5916no—
606C4×Q8—598no—
607C4×Q8—5916no—
608C4×Q8C22×D5918yes—
609C4×Q8C22×D59116yes—
610C4×D4—5916no—
611C4×D4—5916no—
612C4×D4—5932no—
613C4×D4—598no—
614C4×D4—5916no—
615C4×D4—5932no—
616C4×D4C22×D5918yes—
617#117—5916no—
618#117—5916no—
619#117C22×D59116yes—
620C2×C4⋊C4—591no—
621C2×C4⋊C4—592no—
622C2×C4⋊C4—594no—
623C2×C4⋊C4—594no—
624C2×C4⋊C4—594no—
625C2×C4⋊C4—592no—
626C2×C4⋊C4—5916no—
627C2×C4⋊C4—592no—
628C2×C4⋊C4—592no—
629C2×C4⋊C4—592no—
630C2×C4⋊C4—592no—
631C2×C4⋊C4—594no—
632C2×C4⋊C4—592no—
633C2×C4⋊C4—594no—
634C2×C4⋊C4—592no—
635C2×C4⋊C4—591no—
636C2×C4⋊C4—594no—
637C2×C4⋊C4—594no—
638C2×C4⋊C4—592no—
639C2×C4⋊C4—5916no—
640C2×C4⋊C4—5916no—
641C2×C4⋊C4C22×D5912yes—
642C2×C4⋊C4C22×D5912yes—
643C2×C4⋊C4C22×D5911yescharacteristic
644C2×C4⋊C4C22×D5911yescharacteristic
645C2×C4⋊C4C22×D5914yes—
646C2×C4⋊C4C22×D5912yes—
647C2×C22⋊C4—592no—
648C2×C22⋊C4—592no—
649C2×C22⋊C4—592no—
650C2×C22⋊C4—592no—
651C2×C22⋊C4—592no—
652C2×C22⋊C4—592no—
653C2×C22⋊C4—592no—
654C2×C22⋊C4—594no—
655C2×C22⋊C4—594no—
656C2×C22⋊C4—592no—
657C2×C22⋊C4—592no—
658C2×C22⋊C4C22×D5914yes—
659C2×C22⋊C4C22×D5914yes—
660C2×C22⋊C4C22×D5912yes—
661C2×C42—591no—
662C2×C42—591no—
663C2×C42—592no—
664C2×C42—594no—
665C2×C42—591no—
666C2×C42—598no—
667C2×C42C22×D5912yes—
668C2×C42C22×D5914yes—
669C2×C42C22×D5911yescharacteristic
670C24—591no—
671C24—592no—
672C24C23×D5912yes—
673#41—23632no—
674C2×Q8—28no—
675C2×Q8—24no—
676C2×Q8—594no—
677C2×Q8—598no—
678C2×Q8—5916no—
679C2×Q8—5916no—
680C2×Q8—1184no—
681C2×Q8—1188no—
682C2×Q8—2368no—
683C2×Q8—2368no—
684C2×Q8—23632no—
685C2×Q8—23632no—
686C2×Q8C23×D5914yes—
687C2×Q8C23×D5918yes—
688C2×D4—24no—
689C2×D4—598no—
690C2×D4—5916no—
691C2×D4—598no—
692C2×D4—594no—
693C2×D4—1188no—
694C2×D4—1188no—
695C2×D4—1184no—
696C2×D4—2368no—
697C2×D4C23×D5914yes—
698C22×C4—28no—
699C22×C4—592no—
700C22×C4—591no—
701C22×C4—591no—
702C22×C4—591no—
703C22×C4—592no—
704C22×C4—594no—
705C22×C4—592no—
706C22×C4—5916no—
707C22×C4—594no—
708C22×C4—594no—
709C22×C4—594no—
710C22×C4—598no—
711C22×C4—5916no—
712C22×C4—5916no—
713C22×C4—1184no—
714C22×C4—1184no—
715C22×C4—1188no—
716C22×C4—1184no—
717C22×C4—2368no—
718C22×C4—2368no—
719C22×C4—2368no—
720C22×C4C23×D5918yes—
721C22×C4C23×D5912yes—
722C22×C4C23×D5911yescharacteristic
723C22×C4C23×D5912yes—
724C22×C4C23×D5912yes—
725C22×C4C23×D5914yes—
726C22×C4C23×D5911yescharacteristic
727C22×C4C23×D5911yescharacteristic
728C4⋊C4—594no—
729C4⋊C4—598no—
730C4⋊C4—5916no—
731C4⋊C4—5916no—
732C4⋊C4—5916no—
733C4⋊C4—598no—
734C4⋊C4—598no—
735C4⋊C4—598no—
736C4⋊C4—598no—
737C4⋊C4—598no—
738C4⋊C4—5916no—
739C4⋊C4—598no—
740C4⋊C4—5916no—
741C4⋊C4—598no—
742C4⋊C4—594no—
743C4⋊C4—5916no—
744C4⋊C4—5916no—
745C4⋊C4—598no—
746C4⋊C4C23×D5918yes—
747C4⋊C4C23×D5918yes—
748C4⋊C4C23×D5914yes—
749C4⋊C4C23×D5914yes—
750C4⋊C4C23×D59116yes—
751C4⋊C4C23×D5918yes—
752C22⋊C4—598no—
753C22⋊C4—598no—
754C22⋊C4—598no—
755C22⋊C4—598no—
756C22⋊C4—598no—
757C22⋊C4—598no—
758C22⋊C4—598no—
759C22⋊C4—5916no—
760C22⋊C4—5916no—
761C22⋊C4—598no—
762C22⋊C4—598no—
763C22⋊C4C23×D59116yes—
764C22⋊C4C23×D59116yes—
765C22⋊C4C23×D5918yes—
766C42—594no—
767C42—594no—
768C42—594no—
769C42—598no—
770C42—5916no—
771C42C23×D5914yes—
772C42C23×D5918yes—
773C42C23×D59116yes—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—594no—
778C23—592no—
779C23—594no—
780C23—1182no—
781C23—1182no—
782C23—1184no—
783C23—1184no—
784C23—1184no—
785C23C24×D5914yes—
786C23C24×D5911yescharacteristic
787Q8—216no—
788Q8—28no—
789Q8—1188no—
790Q8—11816no—
791Q8—23616no—
792Q8—23616no—
793D4—28no—
794D4—11816no—
795D4—11816no—
796D4—1188no—
797D4—23616no—
798C2×C4—28no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—216no—
804C2×C4—594no—
805C2×C4—592no—
806C2×C4—592no—
807C2×C4—592no—
808C2×C4—594no—
809C2×C4—598no—
810C2×C4—594no—
811C2×C4—1188no—
812C2×C4—1184no—
813C2×C4—1182no—
814C2×C4—1188no—
815C2×C4—1184no—
816C2×C4—1182no—
817C2×C4—1184no—
818C2×C4—1182no—
819C2×C4—1188no—
820C2×C4—11816no—
821C2×C4—1188no—
822C2×C4—23616no—
823C2×C4—23616no—
824C2×C4—23616no—
825C2×C4#1427377314yes—
826C2×C4#1427377414yes—
827C2×C4C24×D5914yes—
828C2×C4C24×D5912yes—
829C2×C4C24×D5914yes—
830C2×C4C24×D5914yes—
831C2×C4C24×D5918yes—
832C2×C4C24×D5912yes—
833C2×C4C24×D5912yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—48no—
838C22—594no—
839C22—1188no—
840C22—1182no—
841C22—1182no—
842C22—1184no—
843C22—1184no—
844C22—1184no—
845C22—2368no—
846C22C2×#1427377312yes—
847C222−1+4×D5912yes—
848C22C2×#1427377412yes—
849C22C25×D5911yescharacteristic
850C4—28no—
851C4—22no—
852C4—24no—
853C4—24no—
854C4—24no—
855C4—1184no—
856C4—1182no—
857C4—1188no—
858C4—1184no—
859C4—1182no—
860C4—1184no—
861C4—1182no—
862C4C2×#1427377314yes—
863C4C2×#1427377414yes—
864C2—44no—
865C2—1184no—
866C2—2364no—
867C2#2143852614yesdirect product factor
868C2C22×#1427377311yescharacteristic
869C2C2×2−1+4×D5911yescharacteristic
870C2C22×#1427377411yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#556C2
socleC23×C59C25
hypercenterC2×#556D59
hypocenterC59C2×#3552
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #21438526C2direct (N × H)
2. C2×#16838154C2semidirect
3. C2×#16838131C2semidirect
4. C2×#16838110C2semidirect
5. C2×#16838096C2semidirect
6. C2×Q8×D236C2semidirect
7. C2×#16838067C2semidirect
8. C2×#16838060C2semidirect
9. C2×#16838056C2semidirect
10. C2×#16838030C2semidirect
11. C2×#16838025C2semidirect
12. C2×#16838010C2semidirect
13. C2×#16837993C2semidirect
14. C2×#16837972C2semidirect
15. C2×C4⋊Q8×D59C2semidirect
16. C2×#16837939C2semidirect
17. C2×#16837934C2semidirect
18. C2×C59×#556C2semidirect
22. #16838154C22semidirect
23. #16838131C22semidirect
24. #16838110C22semidirect
25. #16838096C22semidirect
26. Q8×D236C22semidirect
27. #16838067C22semidirect
28. #16838060C22semidirect
29. #16838056C22semidirect
30. #16838030C22semidirect
31. #16838025C22semidirect
32. #16838010C22semidirect
33. #16837993C22semidirect
34. #16837972C22semidirect
42. C4⋊Q8×D59C22semidirect
43. #16837939C22semidirect
44. #16837934C22semidirect
92. C59×#556C22semidirect
432. C2×#556D59semidirect
448. C2×C59#3552semidirect
459. #556C2×D59semidirect
536. C59C2×#3552semidirect
867. C2#21438526direct (N × H)

Maximal subgroups

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

subgroupindex
#214385262
C2×#168381542
C2×#168381312
C2×#168381102
C2×#168380962
C2×Q8×D2362
C2×#168380672
C2×#168380602
C2×#168380562
C2×#168380302
C2×#168380252
C2×#168380102
C2×#168379932
C2×#168379722
C2×C4⋊Q8×D592
C2×#168379392
C2×#168379342
C2×C59×#5562
C2×#355259