Finite Group Databasebeta

← C2×#21438570 #29496319

Subgroups — C2×#21438570 #29496319

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#21438570C2132yesmaximal, direct product factor
2C2×#16838150C214yesmaximal, complemented
3C2×#16838137C211yesmaximal, characteristic, complemented
4C2×#16838137C212yesmaximal, complemented
5C2×#16838108C212yesmaximal, complemented
6C2×#16838074C211yesmaximal, characteristic, complemented
7C2×#16838067C211yesmaximal, characteristic, complemented
8C2×#16838064C212yesmaximal, complemented
9C2×#16838055C212yesmaximal, complemented
10C2×#16838024C212yesmaximal, complemented
11C2×#16838024C212yesmaximal, complemented
12C2×#16838008C212yesmaximal, complemented
13C2×#16838000C214yesmaximal, complemented
14C2×#16837977C212yesmaximal, complemented
15C2×#16837956C211yesmaximal, characteristic, complemented
16C2×#16837953C211yesmaximal, characteristic, complemented
17C2×#16837939C211yesmaximal, characteristic, complemented
18C2×C59×#557C211yesmaximal, characteristic, complemented
19C22×#11745689C2212yes—
20C22×#11745689C2212yes—
21C22×Q8×D59C2212yes—
22#16838150C22164yescomplemented
23#16838137C22116yescomplemented
24#16838137C22132yescomplemented
25#16838108C22132yescomplemented
26#16838074C22116yescomplemented
27#16838067C22116yescomplemented
28#16838064C22132yescomplemented
29#16838055C22132yescomplemented
30#16838024C22132yescomplemented
31#16838024C22132yescomplemented
32#16838008C22132yescomplemented
33#16838000C22164yescomplemented
34#16837977C22132yescomplemented
35#16837956C22116yescomplemented
36#16837953C22116yescomplemented
37C2×#14273726C2211yescharacteristic
38C2×#14273726C2212yes—
39C2×#14273725C2211yescharacteristic
40C2×#14273724C2212yes—
41C2×#14273724C2211yescharacteristic
42#16837939C22116yescomplemented
43C2×#14273722C2212yes—
44C2×#14273721C2214yes—
45C2×#14273718C2211yescharacteristic
46C2×#14273717C2212yes—
47C2×#14273716C2212yes—
48C2×#14273716C2212yes—
49C2×#14273716C2211yescharacteristic
50C2×#14273715C2214yes—
51C2×#14273715C2214yes—
52C2×#14273715C2212yes—
53C2×#14273712C2214yes—
54C2×#14273712C2214yes—
55C2×#14273712C2214yes—
56C2×#14273712C2214yes—
57C2×#14273712C2212yes—
58C2×#14273712C2214yes—
59C2×#14273712C2214yes—
60C2×#14273707C2214yes—
61C2×#14273707C2211yescharacteristic
62C2×#14273705C2214yes—
63C2×#14273705C2214yes—
64C2×#14273705C2212yes—
65C2×#14273705C2214yes—
66C2×#14273705C2214yes—
67C2×#14273703C2211yescharacteristic
68C2×#14273703C2212yes—
69C2×#14273703C2211yescharacteristic
70C2×#14273702C2214yes—
71C2×#14273702C2212yes—
72C2×#14273702C2214yes—
73C2×#14273702C2214yes—
74C2×#14273702C2211yescharacteristic
75C2×#14273702C2212yes—
76C2×#14273702C2212yes—
77C2×C4×Dic118C2211yescharacteristic
78C2×C4×Dic118C2212yes—
79C2×C4×D236C2214yes—
80C2×C4×D236C2212yes—
81C2×C4×D236C2212yes—
82C2×C4×D236C2212yes—
83C2×C4×D236C2211yescharacteristic
84C2×#14273689C2212yes—
85C2×#14273689C2212yes—
86C2×#14273689C2212yes—
87C2×#14273689C2212yes—
88C2×#14273684C2212yes—
89C2×#14273684C2212yes—
90C2×C4⋊C4×D59C2214yes—
91C2×C42×D59C2211yescharacteristic
92C59×#557C22116yescomplemented
93C2×C4⋊Q8×C59C2212yes—
94C2×C4⋊Q8×C59C2211yescharacteristic
95C2×#125×C59C2214yes—
96C2×#125×C59C2212yes—
97C2×C4×Q8×C59C2212yes—
98C2×C4×Q8×C59C2212yes—
99C2×C4×Q8×C59C2211yescharacteristic
100C2×C4×Q8×C59C2211yescharacteristic
101C2×#11745689—48no—
102C2×#11745689—48no—
103C2×#11745689C23116yes—
104C2×#11745689C23116yes—
105C22×Dic118C2311yescharacteristic
106C22×Dic118C2314yes—
107C22×Dic118C2312yes—
108C2×Q8×D59—48no—
109C2×Q8×D59C23116yes—
110C22×D236C2312yes—
111C22×D236C2311yescharacteristic
112C22×D236C2312yes—
113C22×D236C2312yes—
114C22×D236C2314yes—
115C22×D236C2312yes—
116C22×D236C2314yes—
117C22×D236C2314yes—
118C22×C4×D59C2311yescharacteristic
119C22×C4×D59C2312yes—
120C22×C4×D59C2311yescharacteristic
121C22×C4×D59C2311yescharacteristic
122C22×C4×D59C2314yes—
123C22×C4×D59C2314yes—
124C22×C4×D59C2314yes—
125C22×C4×D59C2314yes—
126#14273726C2318yes—
127#14273726C23116yes—
128#14273725C2318yes—
129#14273724C2318yes—
130#14273724C23116yes—
131#14273722C23116yes—
132#14273721C23132yes—
133#14273718C2318yes—
134#14273717C23116yes—
135#14273716C2318yes—
136#14273716C23116yes—
137#14273716C23116yes—
138#14273715C23132yes—
139#14273715C23132yes—
140#14273715C23116yes—
141#14273712C23116yes—
142#14273712C23132yes—
143#14273712C23132yes—
144#14273712C23132yes—
145#14273712C23132yes—
146#14273712C23132yes—
147#14273712C23132yes—
148#14273707C2318yes—
149#14273707C23132yes—
150#14273705C23116yes—
151#14273705C23132yes—
152#14273705C23132yes—
153#14273705C23132yes—
154#14273705C23132yes—
155#14273703C2318yes—
156#14273703C2318yes—
157#14273703C23116yes—
158#14273702C23116yes—
159#14273702C23132yes—
160#14273702C23132yes—
161#14273702C23132yes—
162#14273702C2318yes—
163#14273702C23116yes—
164#14273702C23116yes—
165C4×Dic118C2318yes—
166C4×Dic118C23116yes—
167C4×D236C23116yes—
168C4×D236C2318yes—
169C4×D236C23132yes—
170C4×D236C23116yes—
171C4×D236C23116yes—
172#14273689C23116yes—
173#14273689C23116yes—
174#14273689C23116yes—
175#14273689C23116yes—
176#14273684C23116yes—
177#14273684C23116yes—
178C2×C4⋊Dic59C2311yescharacteristic
179C2×C4⋊Dic59C2311yescharacteristic
180C2×C4⋊Dic59C2312yes—
181C2×C4⋊Dic59C2312yes—
182C2×Dic59⋊C4C2314yes—
183C2×Dic59⋊C4C2312yes—
184C2×Dic59⋊C4C2312yes—
185C2×Dic59⋊C4C2312yes—
186C2×Dic59⋊C4C2312yes—
187C2×Dic59⋊C4C2312yes—
188C2×Dic59⋊C4C2312yes—
189C2×Dic59⋊C4C2312yes—
190C4⋊C4×D59C23132yes—
191C2×(C2×D59)⋊C4C2312yes—
192C2×(C2×D59)⋊C4C2312yes—
193C2×(C2×D59)⋊C4C2312yes—
194C2×(C2×D59)⋊C4C2314yes—
195C2×(C2×D59)⋊C4C2314yes—
196C2×(C2×D59)⋊C4C2314yes—
197C2×(C2×D59)⋊C4C2314yes—
198C2×(C2×D59)⋊C4C2314yes—
199C2×(C2×D59)⋊C4C2312yes—
200C2×(C2×D59)⋊C4C2312yes—
201C2×(C2×D59)⋊C4C2314yes—
202C2×(C2×D59)⋊C4C2312yes—
203C2×(C2×D59)⋊C4C2314yes—
204C2×(C2×D59)⋊C4C2312yes—
205C2×C4×Dic59C2311yescharacteristic
206C2×C4×Dic59C2311yescharacteristic
207C2×C4×Dic59C2312yes—
208C2×C4×Dic59C2311yescharacteristic
209C42×D59C2318yes—
210C22×Q8×C59C2311yescharacteristic
211C22×Q8×C59C2312yes—
212C22×Q8×C59C2311yescharacteristic
213C4⋊Q8×C59C2318yes—
214C4⋊Q8×C59C23116yes—
215#125×C59C23132yes—
216#125×C59C23116yes—
217C4×Q8×C59C2318yes—
218C4×Q8×C59C2318yes—
219C4×Q8×C59C23116yes—
220C4×Q8×C59C23116yes—
221C2×C4⋊C4×C59C2312yes—
222C2×C4⋊C4×C59C2311yescharacteristic
223C2×C4⋊C4×C59C2312yes—
224C2×C4⋊C4×C59C2314yes—
225C2×C4⋊C4×C59C2314yes—
226C2×C4⋊C4×C59C2311yescharacteristic
227C2×C4⋊C4×C59C2312yes—
228C2×C4⋊C4×C59C2314yes—
229C2×C4⋊C4×C59C2312yes—
230C2×C42×C59C2314yes—
231C2×C42×C59C2312yes—
232C2×C42×C59C2312yes—
233C2×C42×C59C2311yescharacteristic
234C23×D59C2412yes—
235C23×D59C2411yescharacteristic
236C23×D59C2414yes—
237C2×Q8×C59—28no—
238C2×Q8×C59—24no—
239C2×Q8×C59—24no—
240C2×Q8×C59C2414yes—
241C2×Q8×C59C2418yes—
242C2×Q8×C59C2414yes—
243C22×C4×C59C2412yes—
244C22×C4×C59C2412yes—
245C22×C4×C59C2411yescharacteristic
246C22×C4×C59C2412yes—
247C22×C4×C59C2414yes—
248C22×C4×C59C2412yes—
249C22×C4×C59C2411yescharacteristic
250C22×C4×C59C2411yescharacteristic
251C22×Dic59C2411yescharacteristic
252C22×Dic59C2411yescharacteristic
253C22×Dic59C2411yescharacteristic
254C22×Dic59C2412yes—
255C22×Dic59C2412yes—
256C22×Dic59C2412yes—
257#11745689—432no—
258#11745689—432no—
259Q8×D59—432no—
260C2×D236—28no—
261C2×D236—24no—
262C2×D236—28no—
263C2×D236—48no—
264C2×D236—44no—
265C2×D236—44no—
266C2×D236—48no—
267C2×D236—48no—
268C2×D236C2418yes—
269C2×D236C2414yes—
270C2×D236C2418yes—
271C2×D236C2418yes—
272C2×D236C2418yes—
273C2×D236C24116yes—
274C2×D236C24116yes—
275C2×D236C24116yes—
276C2×C4×D59—28no—
277C2×C4×D59—24no—
278C2×C4×D59—24no—
279C2×C4×D59—42no—
280C2×C4×D59—48no—
281C2×C4×D59—48no—
282C2×C4×D59—48no—
283C2×C4×D59—48no—
284C2×C4×D59C2414yes—
285C2×C4×D59C2414yes—
286C2×C4×D59C2418yes—
287C2×C4×D59C2414yes—
288C2×C4×D59C24116yes—
289C2×C4×D59C24116yes—
290C2×C4×D59C24116yes—
291C2×C4×D59C24116yes—
292C2×Dic118—24no—
293C2×Dic118—48no—
294C2×Dic118—44no—
295C2×Dic118C2414yes—
296C2×Dic118C2418yes—
297C2×Dic118C24116yes—
298C4⋊C4×C59C2414yes—
299C4⋊C4×C59C2414yes—
300C4⋊C4×C59C2418yes—
301C4⋊C4×C59C24116yes—
302C4⋊C4×C59C2418yes—
303C4⋊C4×C59C2418yes—
304C4⋊C4×C59C24116yes—
305C4⋊C4×C59C24116yes—
306C4⋊C4×C59C2418yes—
307C42×C59C2418yes—
308C42×C59C24116yes—
309C42×C59C2414yes—
310C42×C59C2418yes—
311(C2×D59)⋊C4C2418yes—
312(C2×D59)⋊C4C2418yes—
313(C2×D59)⋊C4C2418yes—
314(C2×D59)⋊C4C2418yes—
315(C2×D59)⋊C4C24116yes—
316(C2×D59)⋊C4C24116yes—
317(C2×D59)⋊C4C24116yes—
318(C2×D59)⋊C4C24116yes—
319(C2×D59)⋊C4C2418yes—
320(C2×D59)⋊C4C2418yes—
321(C2×D59)⋊C4C24116yes—
322(C2×D59)⋊C4C2418yes—
323(C2×D59)⋊C4C24116yes—
324(C2×D59)⋊C4C24116yes—
325C4⋊Dic59C2418yes—
326C4⋊Dic59C2414yes—
327C4⋊Dic59C2414yes—
328C4⋊Dic59C2418yes—
329Dic59⋊C4C2418yes—
330Dic59⋊C4C24116yes—
331Dic59⋊C4C2418yes—
332Dic59⋊C4C2418yes—
333Dic59⋊C4C2418yes—
334Dic59⋊C4C2418yes—
335Dic59⋊C4C2418yes—
336Dic59⋊C4C2418yes—
337C4×Dic59C2414yes—
338C4×Dic59C2414yes—
339C4×Dic59C2414yes—
340C4×Dic59C2418yes—
341C23×C59C2511yescharacteristic
342C22×D59—24no—
343C22×D59—22no—
344C22×D59—28no—
345C22×D59—22no—
346C22×D59—24no—
347C22×D59—28no—
348C22×D59—22no—
349C22×D59—28no—
350C22×D59—24no—
351C22×D59C2514yes—
352C22×D59C2512yes—
353C22×D59C2518yes—
354Q8×C59—216no—
355Q8×C59—28no—
356Q8×C59—28no—
357C2×C4×C59—28no—
358C2×C4×C59—24no—
359C2×C4×C59—24no—
360C2×C4×C59—24no—
361C2×C4×C59—24no—
362C2×C4×C59—22no—
363C2×C4×C59H(5,𝔽2)14yes—
364C2×C4×C592−1+414yes—
365C2×C4×C59C2512yes—
366C2×C4×C59C2514yes—
367C2×C4×C59C2514yes—
368C2×C4×C59C2514yes—
369C2×C4×C59C2514yes—
370C2×C4×C59C2518yes—
371C2×C4×C59C2512yes—
372C2×C4×C59C2512yes—
373C2×Dic59—24no—
374C2×Dic59—24no—
375C2×Dic59—22no—
376C2×Dic59—22no—
377C2×Dic59—22no—
378C2×Dic59—24no—
379C2×Dic59C2512yes—
380C2×Dic59C2512yes—
381C2×Dic59C2512yes—
382C2×Dic59C2514yes—
383C2×Dic59C2514yes—
384C2×Dic59C2514yes—
385D236—216no—
386D236—216no—
387D236—28no—
388D236—416no—
389D236—48no—
390D236—48no—
391D236—416no—
392D236—416no—
393C4×D59—216no—
394C4×D59—28no—
395C4×D59—28no—
396C4×D59—44no—
397C4×D59—416no—
398C4×D59—416no—
399C4×D59—416no—
400C4×D59—416no—
401Dic118—28no—
402Dic118—48no—
403Dic118—416no—
404C2×#3554—591nomaximal, Sylow
405C22×C59C2×H(5,𝔽2)12yes—
406C22×C59C2×2−1+412yes—
407C22×C59#58512yes—
408C22×C59C2611yescharacteristic
409C2×D59—24no—
410C2×D59—22no—
411C2×D59—28no—
412C2×D59—22no—
413C2×D59—24no—
414C2×D59—28no—
415C2×D59—22no—
416C2×D59—28no—
417C2×D59—24no—
418C2×D59—48no—
419C2×D59—44no—
420C2×D59—416no—
421C4×C59—28no—
422C4×C59—24no—
423C4×C59—24no—
424C4×C59—24no—
425C4×C59—24no—
426C4×C59—22no—
427C4×C59C2×H(5,𝔽2)14yes—
428C4×C59C2×2−1+414yes—
429Dic59—24no—
430Dic59—24no—
431Dic59—22no—
432Dic59—22no—
433Dic59—22no—
434Dic59—24no—
435#3554—5932no—
436C2×#562—594no—
437C2×#559—592no—
438C2×#559—591no—
439C2×#557D5911yescharacteristic, complemented
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×#529—591no—
453C2×C59#355414yescomplemented
454C2×C59C22×H(5,𝔽2)11yescharacteristic
455C2×C59C22×2−1+411yescharacteristic
456C2×C59C2×#58511yescharacteristic
457D59—44no—
458D59—42no—
459D59—48no—
460C22×#41—592no—
461C22×#41—592no—
462C23×Q8—592no—
463#562—5964no—
464#559—5932no—
465#559—5916no—
466#557C2×D59116yescomplemented
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—591no—
480C2×C4⋊Q8—591no—
481C2×C4⋊Q8—592no—
482C2×C4⋊Q8C2×D5911yescharacteristic
483C2×C4⋊Q8C2×D5912yes—
484C2×#127—591no—
485C2×#127—592no—
486#529—5916no—
487C2×#126—592no—
488C2×#126—594no—
489C2×#125—592no—
490C2×#125—591no—
491C2×#125C2×D5914yes—
492C2×#125C2×D5912yes—
493C2×#124—591no—
494C2×#124—592no—
495C2×#124—592no—
496C2×#124—592no—
497C2×#124—594no—
498C2×#124—594no—
499C2×#123—592no—
500C2×#123—594no—
501C2×#123—594no—
502C2×#123—594no—
503C2×#123—594no—
504C2×#123—594no—
505C2×#123—594no—
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—591no—
515C2×C22⋊Q8—594no—
516C2×#121—591no—
517C2×#121—592no—
518C2×#121—592no—
519C2×#121—594no—
520C2×#121—594no—
521C2×#121—594no—
522C2×#121—592no—
523C2×C4×Q8—591no—
524C2×C4×Q8—592no—
525C2×C4×Q8C2×D5911yescharacteristic
526C2×C4×Q8C2×D5911yescharacteristic
527C2×C4×Q8C2×D5912yes—
528C2×C4×Q8C2×D5912yes—
529C2×C4×D4—592no—
530C2×C4×D4—592no—
531C2×C4×D4—592no—
532C2×C4×D4—592no—
533C2×C4×D4—592no—
534C2×C4×D4—591no—
535C2×C4×D4—594no—
536C2×C4×D4—592no—
537C2×C4×D4—592no—
538C2×#117—592no—
539C2×#117—592no—
540C22×C4⋊C4—594no—
541C22×C42—591no—
542C59C2×#355411yescharacteristic, complemented, Sylow
543C2×#41—5916no—
544C2×#41—5916no—
545C2×#41—2368no—
546C2×#41—2368no—
547C22×Q8—5916no—
548C22×Q8—591no—
549C22×Q8—592no—
550C22×Q8—594no—
551C22×Q8—2368no—
552C22×Q8C22×D5911yescharacteristic
553C22×Q8C22×D5912yes—
554C22×Q8C22×D5911yescharacteristic
555C22×D4—592no—
556C22×D4—591no—
557C22×D4—592no—
558C22×D4—592no—
559C22×D4—592no—
560C22×D4—594no—
561C22×D4—594no—
562C22×D4—594no—
563C23×C4—591no—
564C23×C4—592no—
565C23×C4—591no—
566C23×C4—594no—
567C23×C4—594no—
568C23×C4—594no—
569C23×C4—594no—
570C23×C4—591no—
571C4⋊Q8—598no—
572C4⋊Q8—598no—
573C4⋊Q8—5916no—
574C4⋊Q8C22×D5918yes—
575C4⋊Q8C22×D59116yes—
576#127—598no—
577#127—5916no—
578#126—5916no—
579#126—5932no—
580#125—598no—
581#125—5916no—
582#125C22×D59132yes—
583#125C22×D59116yes—
584#124—598no—
585#124—5916no—
586#124—5916no—
587#124—5916no—
588#124—5932no—
589#124—5932no—
590#123—5916no—
591#123—5932no—
592#123—5932no—
593#123—5932no—
594#123—5932no—
595#123—5932no—
596#123—5932no—
597C22⋊Q8—598no—
598C22⋊Q8—598no—
599C22⋊Q8—5916no—
600C22⋊Q8—598no—
601C22⋊Q8—5916no—
602C22⋊Q8—5932no—
603C22⋊Q8—5932no—
604C22⋊Q8—5932no—
605C22⋊Q8—5932no—
606C22⋊Q8—5932no—
607#121—598no—
608#121—5916no—
609#121—5916no—
610#121—5932no—
611#121—5932no—
612#121—5932no—
613#121—5916no—
614C4×Q8—598no—
615C4×Q8—5916no—
616C4×Q8C22×D5918yes—
617C4×Q8C22×D5918yes—
618C4×Q8C22×D59116yes—
619C4×Q8C22×D59116yes—
620C4×D4—5916no—
621C4×D4—5916no—
622C4×D4—5916no—
623C4×D4—5916no—
624C4×D4—5916no—
625C4×D4—598no—
626C4×D4—5932no—
627C4×D4—5916no—
628C4×D4—5916no—
629#117—5916no—
630#117—5916no—
631C2×C4⋊C4—592no—
632C2×C4⋊C4—592no—
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—592no—
643C2×C4⋊C4—5932no—
644C2×C4⋊C4C22×D5914yes—
645C2×C4⋊C4C22×D5911yescharacteristic
646C2×C4⋊C4C22×D5912yes—
647C2×C4⋊C4C22×D5912yes—
648C2×C4⋊C4C22×D5911yescharacteristic
649C2×C4⋊C4C22×D5912yes—
650C2×C4⋊C4C22×D5914yes—
651C2×C4⋊C4C22×D5914yes—
652C2×C4⋊C4C22×D5912yes—
653C2×C22⋊C4—592no—
654C2×C22⋊C4—592no—
655C2×C22⋊C4—592no—
656C2×C22⋊C4—592no—
657C2×C22⋊C4—592no—
658C2×C22⋊C4—592no—
659C2×C22⋊C4—594no—
660C2×C22⋊C4—594no—
661C2×C22⋊C4—594no—
662C2×C22⋊C4—594no—
663C2×C22⋊C4—594no—
664C2×C22⋊C4—592no—
665C2×C22⋊C4—594no—
666C2×C22⋊C4—594no—
667C2×C42—591no—
668C2×C42—592no—
669C2×C42—591no—
670C2×C42—591no—
671C2×C42—598no—
672C2×C42C22×D5912yes—
673C2×C42C22×D5912yes—
674C2×C42C22×D5911yescharacteristic
675C2×C42C22×D5914yes—
676C24—592no—
677C24—591no—
678C24—594no—
679#41—23632no—
680#41—23632no—
681C2×Q8—28no—
682C2×Q8—24no—
683C2×Q8—24no—
684C2×Q8—594no—
685C2×Q8—598no—
686C2×Q8—5916no—
687C2×Q8—1184no—
688C2×Q8—2368no—
689C2×Q8—2364no—
690C2×Q8—23632no—
691C2×Q8C23×D5914yes—
692C2×Q8C23×D5918yes—
693C2×Q8C23×D5914yes—
694C2×D4—598no—
695C2×D4—594no—
696C2×D4—598no—
697C2×D4—598no—
698C2×D4—598no—
699C2×D4—5916no—
700C2×D4—5916no—
701C2×D4—5916no—
702C2×D4—1188no—
703C2×D4—1188no—
704C2×D4—1184no—
705C2×D4—2368no—
706C2×D4—2368no—
707C2×D4—2364no—
708C2×D4—2364no—
709C2×D4—2368no—
710C22×C4—591no—
711C22×C4—591no—
712C22×C4—591no—
713C22×C4—592no—
714C22×C4—592no—
715C22×C4—592no—
716C22×C4—594no—
717C22×C4—594no—
718C22×C4—598no—
719C22×C4—594no—
720C22×C4—5916no—
721C22×C4—5916no—
722C22×C4—5916no—
723C22×C4—5916no—
724C22×C4—1188no—
725C22×C4—1184no—
726C22×C4—1184no—
727C22×C4—2368no—
728C22×C4—2368no—
729C22×C4—2368no—
730C22×C4—2368no—
731C22×C4—2362no—
732C22×C4C23×D5911yescharacteristic
733C22×C4C23×D5912yes—
734C22×C4C23×D5912yes—
735C22×C4C23×D5912yes—
736C22×C4C23×D5914yes—
737C22×C4C23×D5912yes—
738C22×C4C23×D5911yescharacteristic
739C22×C4C23×D5911yescharacteristic
740C4⋊C4—598no—
741C4⋊C4—598no—
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—598no—
752C4⋊C4C23×D59116yes—
753C4⋊C4C23×D5914yes—
754C4⋊C4C23×D5918yes—
755C4⋊C4C23×D5918yes—
756C4⋊C4C23×D5914yes—
757C4⋊C4C23×D5918yes—
758C4⋊C4C23×D59116yes—
759C4⋊C4C23×D59116yes—
760C4⋊C4C23×D5918yes—
761C22⋊C4—598no—
762C22⋊C4—598no—
763C22⋊C4—598no—
764C22⋊C4—598no—
765C22⋊C4—598no—
766C22⋊C4—598no—
767C22⋊C4—5916no—
768C22⋊C4—5916no—
769C22⋊C4—5916no—
770C22⋊C4—5916no—
771C22⋊C4—5916no—
772C22⋊C4—598no—
773C22⋊C4—5916no—
774C22⋊C4—5916no—
775C42—594no—
776C42—594no—
777C42—594no—
778C42—598no—
779C42C23×D5914yes—
780C42C23×D5918yes—
781C42C23×D5918yes—
782C42C23×D59116yes—
783C23—594no—
784C23—592no—
785C23—598no—
786C23—1184no—
787C23—1182no—
788C23—1188no—
789C23—1182no—
790C23—1184no—
791C23—1188no—
792C23—1182no—
793C23—1188no—
794C23—1184no—
795C23C24×D5911yescharacteristic
796Q8—216no—
797Q8—28no—
798Q8—28no—
799Q8—1188no—
800Q8—2368no—
801Q8—23616no—
802D4—11816no—
803D4—11816no—
804D4—1188no—
805D4—2368no—
806D4—2368no—
807D4—23616no—
808D4—23616no—
809D4—23616no—
810C2×C4—24no—
811C2×C4—28no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—592no—
817C2×C4—592no—
818C2×C4—592no—
819C2×C4—594no—
820C2×C4—594no—
821C2×C4—594no—
822C2×C4—1182no—
823C2×C4—1184no—
824C2×C4—1184no—
825C2×C4—1182no—
826C2×C4—1184no—
827C2×C4—1182no—
828C2×C4—11816no—
829C2×C4—1188no—
830C2×C4—1188no—
831C2×C4—23616no—
832C2×C4—2364no—
833C2×C4—23616no—
834C2×C4—23616no—
835C2×C4—23616no—
836C2×C4#1427377314yes—
837C2×C4#1427377514yes—
838C2×C4C24×D5912yes—
839C2×C4C24×D5914yes—
840C2×C4C24×D5914yes—
841C2×C4C24×D5914yes—
842C2×C4C24×D5918yes—
843C2×C4C24×D5914yes—
844C2×C4C24×D5912yes—
845C2×C4C24×D5912yes—
846C22—1184no—
847C22—1182no—
848C22—1188no—
849C22—1182no—
850C22—1184no—
851C22—1188no—
852C22—1182no—
853C22—1188no—
854C22—1184no—
855C22—2368no—
856C22—2364no—
857C22—23616no—
858C22C2×#1427377312yes—
859C22C2×#1427377512yes—
860C22#1683823912yes—
861C22C25×D5911yescharacteristic
862C4—24no—
863C4—28no—
864C4—24no—
865C4—24no—
866C4—22no—
867C4—24no—
868C4—1182no—
869C4—1184no—
870C4—1184no—
871C4—1182no—
872C4—1184no—
873C4—1182no—
874C4C2×#1427377314yes—
875C4C2×#1427377514yes—
876C2—2364no—
877C2—2362no—
878C2—2368no—
879C2#2143857014yesdirect product factor
880C2C22×#1427377311yescharacteristic
881C2C22×#1427377511yescharacteristic
882C2C2×#1683823911yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#557C2
socleC23×C59C25
hypercenterC2×#557D59
hypocenterC59C2×#3554
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #21438570C2direct (N × H)
2. C2×#16838150C2semidirect
3. C2×#16838137C2semidirect
4. C2×#16838137C2semidirect
5. C2×#16838108C2semidirect
6. C2×#16838074C2semidirect
7. C2×#16838067C2semidirect
8. C2×#16838064C2semidirect
9. C2×#16838055C2semidirect
10. C2×#16838024C2semidirect
11. C2×#16838024C2semidirect
12. C2×#16838008C2semidirect
13. C2×#16838000C2semidirect
14. C2×#16837977C2semidirect
15. C2×#16837956C2semidirect
16. C2×#16837953C2semidirect
17. C2×#16837939C2semidirect
18. C2×C59×#557C2semidirect
22. #16838150C22semidirect
23. #16838137C22semidirect
24. #16838137C22semidirect
25. #16838108C22semidirect
26. #16838074C22semidirect
27. #16838067C22semidirect
28. #16838064C22semidirect
29. #16838055C22semidirect
30. #16838024C22semidirect
31. #16838024C22semidirect
32. #16838008C22semidirect
33. #16838000C22semidirect
34. #16837977C22semidirect
35. #16837956C22semidirect
36. #16837953C22semidirect
42. #16837939C22semidirect
92. C59×#557C22semidirect
439. C2×#557D59semidirect
453. C2×C59#3554semidirect
466. #557C2×D59semidirect
542. C59C2×#3554semidirect
879. C2#21438570direct (N × H)

Maximal subgroups

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

subgroupindex
#214385702
C2×#168381502
C2×#168381372
C2×#168381082
C2×#168380742
C2×#168380672
C2×#168380642
C2×#168380552
C2×#168380242
C2×#168380082
C2×#168380002
C2×#168379772
C2×#168379562
C2×#168379532
C2×#168379392
C2×C59×#5572
C2×#355459