Finite Group Databasebeta

← C2×#21438584 #29496409

Subgroups — C2×#21438584 #29496409

Order 15104.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438584C2132yesmaximal, direct product factor
2C2×#16838153C214yesmaximal, complemented
3C2×Q8×Dic118C211yesmaximal, characteristic, complemented
4C2×#16838131C211yesmaximal, characteristic, complemented
5C2×#16838130C212yesmaximal, complemented
6C2×#16838125C212yesmaximal, complemented
7C2×#16838125C211yesmaximal, characteristic, complemented
8C2×#16838123C212yesmaximal, complemented
9C2×#16838112C211yesmaximal, characteristic, complemented
10C2×#16838086C212yesmaximal, complemented
11C2×#16838029C212yesmaximal, complemented
12C2×#16838023C212yesmaximal
13C2×#16838014C212yesmaximal, complemented
14C2×#16838013C212yesmaximal, complemented
15C2×#16838011C214yesmaximal, complemented
16C2×#16837959C211yesmaximal, characteristic, complemented
17C2×#16837936C211yesmaximal, characteristic
18C2×C59×#533C211yesmaximal, characteristic, complemented
19#16838153C22164yescomplemented
20Q8×Dic118C22116yescomplemented
21#16838131C22116yescomplemented
22#16838130C22132yescomplemented
23#16838125C22132yescomplemented
24#16838125C22116yescomplemented
25#16838123C22132yescomplemented
26#16838112C22116yescomplemented
27#16838086C22132yescomplemented
28#16838029C22132yescomplemented
29#16838023C22132yes—
30#16838014C22132yescomplemented
31#16838013C22132yescomplemented
32#16838011C22164yescomplemented
33#16837959C22116yescomplemented
34C2×#14273727C2212yes—
35C2×#14273727C2212yes—
36C2×#14273727C2211yescharacteristic
37C2×#14273727C2211yescharacteristic
38C2×#14273726C2214yes—
39C2×#14273726C2212yes—
40C2×#14273725C2214yes—
41#16837936C22116yes—
42C2×#14273722C2214yes—
43C2×#14273722C2214yes—
44C2×#14273722C2214yes—
45C2×#14273722C2214yes—
46C2×#14273721C2212yes—
47C2×#14273720C2214yes—
48C2×#14273720C2214yes—
49C2×#14273719C2212yes—
50C2×#14273719C2212yes—
51C2×#14273719C2211yescharacteristic
52C2×#14273718C2214yes—
53C2×#14273718C2212yes—
54C2×#14273717C2214yes—
55C2×#14273717C2214yes—
56C2×#14273717C2214yes—
57C2×#14273717C2214yes—
58C2×#14273715C2212yes—
59C2×#14273715C2211yescharacteristic
60C2×#14273713C2214yes—
61C2×#14273710C2212yes—
62C2×#14273709C2214yes—
63C2×#14273706C2212yes—
64C2×#14273706C2211yescharacteristic
65C2×#14273706C2212yes—
66C2×#14273705C2214yes—
67C2×#14273705C2214yes—
68C2×#14273703C2214yes—
69C2×#14273703C2212yes—
70C2×#14273703C2212yes—
71C2×#14273701C2211yescharacteristic
72C2×Q8×Dic59C2212yes—
73C2×Q8×Dic59C2212yes—
74C2×C4×Dic118C2212yes—
75C2×C4×Dic118C2212yes—
76C2×C4×Dic118C2212yes—
77C2×C4×Dic118C2212yes—
78C2×C4×Dic118C2211yescharacteristic
79C2×C4×Dic118C2212yes—
80C2×#14273692C2214yes—
81C2×C4×D236C2212yes—
82C2×C4×D236C2211yescharacteristic
83C2×C4×C22⋊D59C2212yes—
84C2×#14273686C2212yes—
85C2×#14273685C2214yes—
86C2×#14273685C2212yes—
87C2×#14273684C2212yes—
88C2×C4⋊C4×D59C2212yes—
89C59×#533C22116yescomplemented
90C2×C4⋊Q8×C59C2211yescharacteristic
91C2×C4⋊Q8×C59C2211yescharacteristic
92C2×#125×C59C2212yes—
93C2×C22⋊Q8×C59C2212yes—
94C2×C22⋊Q8×C59C2211yescharacteristic
95C2×C22⋊Q8×C59C2211yescharacteristic
96C2×C4×Q8×C59C2211yescharacteristic
97C2×C4×Q8×C59C2212yes—
98C2×C4×Q8×C59C2211yescharacteristic
99C2×#117×C59C2212yes—
100C22×C42×C59C2211yescharacteristic
101C22×Dic118C2311yescharacteristic
102C22×Dic118C2312yes—
103C22×Dic118C2312yes—
104C22×Dic118C2314yes—
105C22×D236C2311yescharacteristic
106C22×C22⋊D59C2312yes—
107C22×C4×D59C2312yes—
108C22×C4×D59C2314yes—
109#14273727C2318yes—
110#14273727C2318yes—
111#14273727C23116yes—
112#14273727C23116yes—
113#14273726C23132yes—
114#14273726C23116yes—
115#14273725C23132yes—
116#14273722C23132yes—
117#14273722C23132yes—
118#14273722C23132yes—
119#14273722C23132yes—
120#14273721C23116yes—
121#14273720C23132yes—
122#14273720C23132yes—
123#14273719C2318yes—
124#14273719C23116yes—
125#14273719C23116yes—
126#14273718C23132yes—
127#14273718C23116yes—
128#14273717C23132yes—
129#14273717C23132yes—
130#14273717C23132yes—
131#14273717C23132yes—
132#14273715C2318yes—
133#14273715C23116yes—
134#14273713C23132yes—
135#14273710C23116yes—
136#14273709C23132yes—
137#14273706C23116yes—
138#14273706C2318yes—
139#14273706C23116yes—
140#14273705C23132yes—
141#14273705C23132yes—
142#14273703C23132yes—
143#14273703C23116yes—
144#14273703C23116yes—
145#14273701C2318yes—
146Q8×Dic59C23116yes—
147Q8×Dic59C23116yes—
148C4×Dic118C2318yes—
149C4×Dic118C23116yes—
150C4×Dic118C23116yes—
151C4×Dic118C23116yes—
152C4×Dic118C23116yes—
153C4×Dic118C23116yes—
154#14273692C23132yes—
155C4×D236C2318yes—
156C4×D236C23116yes—
157C4×C22⋊D59C23116yes—
158#14273686C23116yes—
159#14273685C23132yes—
160#14273685C23116yes—
161#14273684C23116yes—
162C2×C4⋊Dic59C2311yescharacteristic
163C2×C4⋊Dic59C2314yes—
164C2×C4⋊Dic59C2312yes—
165C2×C4⋊Dic59C2312yes—
166C2×C4⋊Dic59C2312yes—
167C2×C4⋊Dic59C2311yescharacteristic
168C2×C4⋊Dic59C2312yes—
169C2×C4⋊Dic59C2314yes—
170C2×C4⋊Dic59C2314yes—
171C2×Dic59⋊C4C2314yes—
172C2×Dic59⋊C4C2314yes—
173C2×Dic59⋊C4C2314yes—
174C2×Dic59⋊C4C2314yes—
175C2×Dic59⋊C4C2314yes—
176C2×Dic59⋊C4C2314yes—
177C2×Dic59⋊C4C2314yes—
178C2×Dic59⋊C4C2312yes—
179C2×Dic59⋊C4C2312yes—
180C2×Dic59⋊C4C2312yes—
181C2×Dic59⋊C4C2312yes—
182C4⋊C4×D59C23116yes—
183C2×C22⋊Dic59C2314yes—
184C2×C22⋊Dic59C2312yes—
185C2×(C2×D59)⋊C4C2312yes—
186C2×(C2×D59)⋊C4C2312yes—
187C2×(C2×D59)⋊C4C2314yes—
188C2×(C2×D59)⋊C4C2314yes—
189C2×(C2×D59)⋊C4C2314yes—
190C2×(C2×D59)⋊C4C2312yes—
191C2×(C2×D59)⋊C4C2312yes—
192C2×C4×Dic59C2314yes—
193C2×C4×Dic59C2314yes—
194C2×C4×Dic59C2314yes—
195C2×C4×Dic59C2314yes—
196C2×C4×Dic59C2312yes—
197C22×Q8×C59C2311yescharacteristic
198C22×Q8×C59C2311yescharacteristic
199C22×Q8×C59C2312yes—
200C23×C4×C59C2311yescharacteristic
201C23×C4×C59C2311yescharacteristic
202C23×C4×C59C2311yescharacteristic
203C4⋊Q8×C59C2318yes—
204C4⋊Q8×C59C2318yes—
205#125×C59C23116yes—
206C22⋊Q8×C59C23116yes—
207C22⋊Q8×C59C2318yes—
208C22⋊Q8×C59C2318yes—
209C4×Q8×C59C2318yes—
210C4×Q8×C59C23116yes—
211C4×Q8×C59C2318yes—
212#117×C59C23116yes—
213C2×C4⋊C4×C59C2312yes—
214C2×C4⋊C4×C59C2312yes—
215C2×C4⋊C4×C59C2312yes—
216C2×C4⋊C4×C59C2312yes—
217C2×C4⋊C4×C59C2312yes—
218C2×C4⋊C4×C59C2311yescharacteristic
219C2×C4⋊C4×C59C2312yes—
220C2×C4⋊C4×C59C2312yes—
221C2×C4⋊C4×C59C2311yescharacteristic
222C2×C22⋊C4×C59C2312yes—
223C2×C22⋊C4×C59C2312yes—
224C2×C42×C59C2311yescharacteristic
225C2×C42×C59C2312yes—
226C2×C42×C59C2311yescharacteristic
227C2×C42×C59C2312yes—
228C2×C42×C59C2311yescharacteristic
229C2×C42×C59C2318yes—
230C2×C42×C59C2311yescharacteristic
231C24×C59C2411yescharacteristic
232C23×D59C2412yes—
233C2×Q8×C59—24no—
234C2×Q8×C59—24no—
235C2×Q8×C59—44no—
236C2×Q8×C59C2414yes—
237C2×Q8×C59C2414yes—
238C2×Q8×C59C2418yes—
239C22×C4×C59—24no—
240C22×C4×C59—24no—
241C22×C4×C59—42no—
242C22×C4×C59C2411yescharacteristic
243C22×C4×C59C2411yescharacteristic
244C22×C4×C59C2411yescharacteristic
245C22×C4×C59C2411yescharacteristic
246C22×C4×C59C2414yes—
247C22×C4×C59C2414yes—
248C22×C4×C59C2412yes—
249C22×C4×C59C2412yes—
250C22×C4×C59C2412yes—
251C22×C4×C59C2412yes—
252C22×C4×C59C2414yes—
253C22×C4×C59C2411yescharacteristic
254C22×C4×C59C2411yescharacteristic
255C2×C22⋊D59—44no—
256C2×C22⋊D59C2418yes—
257C22×Dic59C2414yes—
258C22×Dic59C2412yes—
259C22×Dic59C2412yes—
260C22×Dic59C2412yes—
261C22×Dic59C2414yes—
262C2×D236—24no—
263C2×D236C2414yes—
264C2×C4×D59—28no—
265C2×C4×D59—48no—
266C2×C4×D59C2418yes—
267C2×C4×D59C24116yes—
268C2×Dic118—24no—
269C2×Dic118—28no—
270C2×Dic118—44no—
271C2×Dic118—48no—
272C2×Dic118C2414yes—
273C2×Dic118C2418yes—
274C2×Dic118C24116yes—
275C2×Dic118C2418yes—
276C4⋊C4×C59C2418yes—
277C4⋊C4×C59C2418yes—
278C4⋊C4×C59C2418yes—
279C4⋊C4×C59C2418yes—
280C4⋊C4×C59C2418yes—
281C4⋊C4×C59C2418yes—
282C4⋊C4×C59C2414yes—
283C4⋊C4×C59C2414yes—
284C4⋊C4×C59C2418yes—
285C22⋊C4×C59C2418yes—
286C22⋊C4×C59C2418yes—
287C42×C59C2414yes—
288C42×C59C2414yes—
289C42×C59C2414yes—
290C42×C59C2414yes—
291C42×C59C2418yes—
292C42×C59C2418yes—
293C22⋊Dic59C24116yes—
294C22⋊Dic59C2418yes—
295(C2×D59)⋊C4C2418yes—
296(C2×D59)⋊C4C2418yes—
297(C2×D59)⋊C4C2418yes—
298(C2×D59)⋊C4C24116yes—
299(C2×D59)⋊C4C24116yes—
300(C2×D59)⋊C4C24116yes—
301(C2×D59)⋊C4C2418yes—
302C4⋊Dic59C2418yes—
303C4⋊Dic59C2418yes—
304C4⋊Dic59C24116yes—
305C4⋊Dic59C2414yes—
306C4⋊Dic59C2418yes—
307C4⋊Dic59C2414yes—
308C4⋊Dic59C2418yes—
309C4⋊Dic59C24116yes—
310C4⋊Dic59C24116yes—
311Dic59⋊C4C24116yes—
312Dic59⋊C4C2418yes—
313Dic59⋊C4C2418yes—
314Dic59⋊C4C2418yes—
315Dic59⋊C4C24116yes—
316Dic59⋊C4C24116yes—
317Dic59⋊C4C24116yes—
318Dic59⋊C4C24116yes—
319Dic59⋊C4C24116yes—
320Dic59⋊C4C24116yes—
321Dic59⋊C4C2418yes—
322C4×Dic59C2418yes—
323C4×Dic59C24116yes—
324C4×Dic59C24116yes—
325C4×Dic59C24116yes—
326C4×Dic59C24116yes—
327C23×C59—22no—
328C23×C59—22no—
329C23×C59—22no—
330C23×C59C2512yes—
331C23×C59C2511yescharacteristic
332C22×D59—24no—
333C22×D59—24no—
334C22×D59—24no—
335C22×D59C2514yes—
336Q8×C59—28no—
337Q8×C59—28no—
338Q8×C59—48no—
339C2×C4×C59—22no—
340C2×C4×C59—22no—
341C2×C4×C59—24no—
342C2×C4×C59—24no—
343C2×C4×C59—22no—
344C2×C4×C59—24no—
345C2×C4×C59—24no—
346C2×C4×C59—22no—
347C2×C4×C59—28no—
348C2×C4×C59—28no—
349C2×C4×C59—44no—
350C2×C4×C592−1+414yes—
351C2×C4×C592−1+414yes—
352C2×C4×C59C2512yes—
353C2×C4×C59C2514yes—
354C2×C4×C59C2514yes—
355C2×C4×C59C2514yes—
356C2×C4×C59C2512yes—
357C2×C4×C59C2512yes—
358C2×C4×C59C2514yes—
359C2×C4×C59C2512yes—
360C2×C4×C59C2512yes—
361C2×C4×C59C2512yes—
362C22⋊D59—48no—
363C2×Dic59—28no—
364C2×Dic59—24no—
365C2×Dic59—24no—
366C2×Dic59—28no—
367C2×Dic59—24no—
368C2×Dic59C2514yes—
369C2×Dic59C2514yes—
370C2×Dic59C2518yes—
371C2×Dic59C2514yes—
372C2×Dic59C2518yes—
373D236—28no—
374C4×D59—216no—
375C4×D59—416no—
376Dic118—28no—
377Dic118—216no—
378Dic118—48no—
379Dic118—416no—
380C2×#3555—591nomaximal, Sylow
381C22×C59—22no—
382C22×C59—22no—
383C22×C59—22no—
384C22×C59—44no—
385C22×C59C2×2−1+412yes—
386C22×C59C2×2−1+412yes—
387C22×C59#58512yes—
388C22×C59C2611yescharacteristic
389C2×D59—24no—
390C2×D59—24no—
391C2×D59—24no—
392C2×D59—48no—
393C4×C59—22no—
394C4×C59—22no—
395C4×C59—24no—
396C4×C59—24no—
397C4×C59—22no—
398C4×C59—24no—
399C4×C59—24no—
400C4×C59—22no—
401C4×C59C2×2−1+414yes—
402C4×C59C2×2−1+414yes—
403Dic59—24no—
404Dic59—28no—
405Dic59—24no—
406Dic59—28no—
407Dic59—24no—
408#3555—5932no—
409C2×#563—594no—
410C2×Q82—591no—
411C2×#557—592no—
412C2×#557—591no—
413C2×#556—592no—
414C2×#556—592no—
415C2×#556—591no—
416C2×#554—591no—
417C2×#552—592no—
418C2×#544—592no—
419C2×#542—592no—
420C2×#541—592no—
421C2×#541—594no—
422C2×#541—592no—
423C2×#533—591no—
424C2×#533D5911yescharacteristic, complemented
425C2×#529—591no—
426C2×C59—42no—
427C2×C59#355514yescomplemented
428C2×C59C22×2−1+411yescharacteristic
429C2×C59C22×2−1+411yescharacteristic
430C2×C59C2×#58511yescharacteristic
431D59—44no—
432#563—5964no—
433Q82—5916no—
434#557—5932no—
435#557—5916no—
436#556—5932no—
437#556—5932no—
438#556—5916no—
439#554—5916no—
440#552—5932no—
441#544—5932no—
442#542—5932no—
443#541—5932no—
444#541—5964no—
445#541—5932no—
446#533—5916no—
447#533C2×D59116yescomplemented
448C2×C4⋊Q8—594no—
449C2×C4⋊Q8—594no—
450C2×C4⋊Q8—592no—
451C2×C4⋊Q8—591no—
452C2×C4⋊Q8—591no—
453C2×C4⋊Q8—592no—
454C2×C4⋊Q8—592no—
455C2×C4⋊Q8C2×D5911yescharacteristic
456C2×C4⋊Q8C2×D5911yescharacteristic
457#529—5916no—
458C2×#126—594no—
459C2×#126—594no—
460C2×#126—594no—
461C2×#126—594no—
462C2×#126—594no—
463C2×#126—594no—
464C2×#126—592no—
465C2×#125—594no—
466C2×#125—594no—
467C2×#125—594no—
468C2×#125—594no—
469C2×#125—594no—
470C2×#125—592no—
471C2×#125—591no—
472C2×#125—592no—
473C2×#125—592no—
474C2×#125C2×D5912yes—
475C2×#124—594no—
476C2×#124—591no—
477C2×#124—592no—
478C2×#123—592no—
479C2×#123—594no—
480C2×C22⋊Q8—592no—
481C2×C22⋊Q8—592no—
482C2×C22⋊Q8—594no—
483C2×C22⋊Q8—591no—
484C2×C22⋊Q8—592no—
485C2×C22⋊Q8—592no—
486C2×C22⋊Q8—594no—
487C2×C22⋊Q8—594no—
488C2×C22⋊Q8C2×D5911yescharacteristic
489C2×C22⋊Q8C2×D5911yescharacteristic
490C2×C22⋊Q8C2×D5912yes—
491C2×#121—591no—
492C2×C4×Q8—592no—
493C2×C4×Q8—592no—
494C2×C4×Q8—594no—
495C2×C4×Q8—591no—
496C2×C4×Q8—592no—
497C2×C4×Q8—592no—
498C2×C4×Q8—592no—
499C2×C4×Q8—592no—
500C2×C4×Q8—592no—
501C2×C4×Q8C2×D5911yescharacteristic
502C2×C4×Q8C2×D5912yes—
503C2×C4×Q8C2×D5911yescharacteristic
504C2×C4×D4—592no—
505C2×C4×D4—591no—
506C2×C4×D4—592no—
507C2×#117—592no—
508C2×#117—594no—
509C2×#117—592no—
510C2×#117—592no—
511C2×#117C2×D5912yes—
512C22×C4⋊C4—592no—
513C22×C42C2×D5911yescharacteristic
514C59C2×#355511yescharacteristic, complemented, Sylow
515C22×Q8—591no—
516C22×Q8—592no—
517C22×Q8—592no—
518C22×Q8—594no—
519C22×Q8C22×D5911yescharacteristic
520C22×Q8C22×D5911yescharacteristic
521C22×Q8C22×D5912yes—
522C22×D4—592no—
523C22×D4—591no—
524C23×C4—592no—
525C23×C4—594no—
526C23×C4C22×D5911yescharacteristic
527C23×C4C22×D5911yescharacteristic
528C23×C4C22×D5911yescharacteristic
529C4⋊Q8—5932no—
530C4⋊Q8—5932no—
531C4⋊Q8—5916no—
532C4⋊Q8—598no—
533C4⋊Q8—598no—
534C4⋊Q8—5916no—
535C4⋊Q8—5916no—
536C4⋊Q8C22×D5918yes—
537C4⋊Q8C22×D5918yes—
538#126—5932no—
539#126—5932no—
540#126—5932no—
541#126—5932no—
542#126—5932no—
543#126—5932no—
544#126—5916no—
545#125—5932no—
546#125—5932no—
547#125—5932no—
548#125—5932no—
549#125—5932no—
550#125—5916no—
551#125—598no—
552#125—5916no—
553#125—5916no—
554#125C22×D59116yes—
555#124—5932no—
556#124—598no—
557#124—5916no—
558#123—5916no—
559#123—5932no—
560C22⋊Q8—5916no—
561C22⋊Q8—5916no—
562C22⋊Q8—5932no—
563C22⋊Q8—598no—
564C22⋊Q8—5916no—
565C22⋊Q8—5916no—
566C22⋊Q8—5932no—
567C22⋊Q8—5932no—
568C22⋊Q8C22×D5918yes—
569C22⋊Q8C22×D5918yes—
570C22⋊Q8C22×D59116yes—
571#121—598no—
572C4×Q8—5916no—
573C4×Q8—5916no—
574C4×Q8—5932no—
575C4×Q8—598no—
576C4×Q8—5916no—
577C4×Q8—5916no—
578C4×Q8—5916no—
579C4×Q8—5916no—
580C4×Q8—5916no—
581C4×Q8C22×D5918yes—
582C4×Q8C22×D59116yes—
583C4×Q8C22×D5918yes—
584C4×D4—5916no—
585C4×D4—598no—
586C4×D4—5916no—
587#117—5916no—
588#117—5932no—
589#117—5916no—
590#117—5916no—
591#117C22×D59116yes—
592C2×C4⋊C4—592no—
593C2×C4⋊C4—594no—
594C2×C4⋊C4—592no—
595C2×C4⋊C4—592no—
596C2×C4⋊C4—594no—
597C2×C4⋊C4—592no—
598C2×C4⋊C4—591no—
599C2×C4⋊C4—592no—
600C2×C4⋊C4—592no—
601C2×C4⋊C4—591no—
602C2×C4⋊C4—594no—
603C2×C4⋊C4—594no—
604C2×C4⋊C4—594no—
605C2×C4⋊C4—594no—
606C2×C4⋊C4—594no—
607C2×C4⋊C4—592no—
608C2×C4⋊C4—594no—
609C2×C4⋊C4—592no—
610C2×C4⋊C4—594no—
611C2×C4⋊C4—594no—
612C2×C4⋊C4—5916no—
613C2×C4⋊C4C22×D5911yescharacteristic
614C2×C4⋊C4C22×D5912yes—
615C2×C4⋊C4C22×D5911yescharacteristic
616C2×C4⋊C4C22×D5912yes—
617C2×C4⋊C4C22×D5912yes—
618C2×C4⋊C4C22×D5912yes—
619C2×C4⋊C4C22×D5912yes—
620C2×C4⋊C4C22×D5912yes—
621C2×C4⋊C4C22×D5912yes—
622C2×C22⋊C4—594no—
623C2×C22⋊C4—592no—
624C2×C22⋊C4—592no—
625C2×C22⋊C4—592no—
626C2×C22⋊C4—592no—
627C2×C22⋊C4—594no—
628C2×C22⋊C4—594no—
629C2×C22⋊C4—592no—
630C2×C22⋊C4—594no—
631C2×C22⋊C4C22×D5912yes—
632C2×C22⋊C4C22×D5912yes—
633C2×C42—594no—
634C2×C42—592no—
635C2×C42—594no—
636C2×C42—594no—
637C2×C42—594no—
638C2×C42C22×D5911yescharacteristic
639C2×C42C22×D5912yes—
640C2×C42C22×D5912yes—
641C2×C42C22×D5911yescharacteristic
642C2×C42C22×D5911yescharacteristic
643C2×C42C22×D5911yescharacteristic
644C2×C42C22×D5918yes—
645C24—592no—
646C24C23×D5911yescharacteristic
647C2×Q8—24no—
648C2×Q8—24no—
649C2×Q8—44no—
650C2×Q8—594no—
651C2×Q8—598no—
652C2×Q8—598no—
653C2×Q8—5916no—
654C2×Q8—1184no—
655C2×Q8—1188no—
656C2×Q8—2364no—
657C2×Q8—2368no—
658C2×Q8C23×D5914yes—
659C2×Q8C23×D5914yes—
660C2×Q8C23×D5918yes—
661C2×D4—598no—
662C2×D4—594no—
663C2×D4—1184no—
664C2×D4—2364no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—42no—
668C22×C4—594no—
669C22×C4—592no—
670C22×C4—592no—
671C22×C4—592no—
672C22×C4—594no—
673C22×C4—598no—
674C22×C4—5916no—
675C22×C4—1188no—
676C22×C4—2368no—
677C22×C4C23×D5914yes—
678C22×C4C23×D5914yes—
679C22×C4C23×D5911yescharacteristic
680C22×C4C23×D5912yes—
681C22×C4C23×D5912yes—
682C22×C4C23×D5912yes—
683C22×C4C23×D5911yescharacteristic
684C22×C4C23×D5911yescharacteristic
685C22×C4C23×D5911yescharacteristic
686C22×C4C23×D5912yes—
687C22×C4C23×D5914yes—
688C22×C4C23×D5911yescharacteristic
689C22×C4C23×D5911yescharacteristic
690C4⋊C4—598no—
691C4⋊C4—5916no—
692C4⋊C4—598no—
693C4⋊C4—598no—
694C4⋊C4—5916no—
695C4⋊C4—598no—
696C4⋊C4—594no—
697C4⋊C4—598no—
698C4⋊C4—598no—
699C4⋊C4—594no—
700C4⋊C4—5916no—
701C4⋊C4—5916no—
702C4⋊C4—5916no—
703C4⋊C4—5916no—
704C4⋊C4—5916no—
705C4⋊C4—598no—
706C4⋊C4—5916no—
707C4⋊C4—598no—
708C4⋊C4—5916no—
709C4⋊C4—5916no—
710C4⋊C4C23×D5914yes—
711C4⋊C4C23×D5918yes—
712C4⋊C4C23×D5914yes—
713C4⋊C4C23×D5918yes—
714C4⋊C4C23×D5918yes—
715C4⋊C4C23×D5918yes—
716C4⋊C4C23×D5918yes—
717C4⋊C4C23×D5918yes—
718C4⋊C4C23×D5918yes—
719C22⋊C4—5916no—
720C22⋊C4—598no—
721C22⋊C4—598no—
722C22⋊C4—598no—
723C22⋊C4—598no—
724C22⋊C4—5916no—
725C22⋊C4—5916no—
726C22⋊C4—598no—
727C22⋊C4—5916no—
728C22⋊C4C23×D5918yes—
729C22⋊C4C23×D5918yes—
730C42—5916no—
731C42—598no—
732C42—5916no—
733C42—5916no—
734C42—5916no—
735C42C23×D5914yes—
736C42C23×D5914yes—
737C42C23×D5914yes—
738C42C23×D5914yes—
739C42C23×D5918yes—
740C42C23×D5918yes—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—594no—
745C23—1184no—
746C23—1184no—
747C23—1184no—
748C23C24×D5912yes—
749C23C24×D5911yescharacteristic
750Q8—28no—
751Q8—28no—
752Q8—48no—
753Q8—1188no—
754Q8—11816no—
755Q8—2368no—
756Q8—23616no—
757D4—1188no—
758D4—2368no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—44no—
770C2×C4—598no—
771C2×C4—594no—
772C2×C4—594no—
773C2×C4—594no—
774C2×C4—598no—
775C2×C4—1184no—
776C2×C4—1188no—
777C2×C4—1184no—
778C2×C4—1188no—
779C2×C4—1184no—
780C2×C4—11816no—
781C2×C4—23616no—
782C2×C4#1427377414yes—
783C2×C4#1427377514yes—
784C2×C4C24×D5912yes—
785C2×C4C24×D5914yes—
786C2×C4C24×D5914yes—
787C2×C4C24×D5914yes—
788C2×C4C24×D5912yes—
789C2×C4C24×D5912yes—
790C2×C4C24×D5912yes—
791C2×C4C24×D5914yes—
792C2×C4C24×D5912yes—
793C2×C4C24×D5912yes—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—1184no—
799C22—1184no—
800C22—1184no—
801C22—2368no—
802C22C2×#1427377412yes—
803C22C2×#1427377512yes—
804C22#1683823812yes—
805C22C25×D5911yescharacteristic
806C4—22no—
807C4—24no—
808C4—24no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—24no—
813C4—24no—
814C4—1184no—
815C4—1188no—
816C4—1184no—
817C4—1188no—
818C4—1184no—
819C4C2×#1427377414yes—
820C4C2×#1427377514yes—
821C2—42no—
822C2—2364no—
823C2#2143858414yesdirect product factor
824C2C22×#1427377411yescharacteristic
825C2C22×#1427377511yescharacteristic
826C2C2×#1683823811yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#533C2
socleC23×C59C25
prime radicalC2×#14273701C22
hypercenterC2×#533D59
hypocenterC59C2×#3555
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #21438584C2direct (N × H)
2. C2×#16838153C2semidirect
3. C2×Q8×Dic118C2semidirect
4. C2×#16838131C2semidirect
5. C2×#16838130C2semidirect
6. C2×#16838125C2semidirect
7. C2×#16838125C2semidirect
8. C2×#16838123C2semidirect
9. C2×#16838112C2semidirect
10. C2×#16838086C2semidirect
11. C2×#16838029C2semidirect
13. C2×#16838014C2semidirect
14. C2×#16838013C2semidirect
15. C2×#16838011C2semidirect
16. C2×#16837959C2semidirect
18. C2×C59×#533C2semidirect
19. #16838153C22semidirect
20. Q8×Dic118C22semidirect
21. #16838131C22semidirect
22. #16838130C22semidirect
23. #16838125C22semidirect
24. #16838125C22semidirect
25. #16838123C22semidirect
26. #16838112C22semidirect
27. #16838086C22semidirect
28. #16838029C22semidirect
30. #16838014C22semidirect
31. #16838013C22semidirect
32. #16838011C22semidirect
33. #16837959C22semidirect
89. C59×#533C22semidirect
424. C2×#533D59semidirect
427. C2×C59#3555semidirect
447. #533C2×D59semidirect
514. C59C2×#3555semidirect
823. C2#21438584direct (N × H)

Maximal subgroups

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

subgroupindex
#214385842
C2×#168381532
C2×Q8×Dic1182
C2×#168381312
C2×#168381302
C2×#168381252
C2×#168381232
C2×#168381122
C2×#168380862
C2×#168380292
C2×#168380232
C2×#168380142
C2×#168380132
C2×#168380112
C2×#168379592
C2×#168379362
C2×C59×#5332
C2×#355559