Finite Group Databasebeta

← C2×#21438586 #29496401

Subgroups — C2×#21438586 #29496401

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#21438586C2132yesmaximal, direct product factor
2C2×#16838155C214yesmaximal, complemented
3C2×Q8×Dic118C211yesmaximal, characteristic, complemented
4C2×#16838130C211yesmaximal, characteristic, complemented
5C2×#16838129C212yesmaximal, complemented
6C2×#16838122C211yesmaximal, characteristic, complemented
7C2×#16838122C212yesmaximal, complemented
8C2×#16838121C212yesmaximal, complemented
9C2×#16838109C211yesmaximal, characteristic, complemented
10C2×#16838092C212yesmaximal, complemented
11C2×#16838030C212yesmaximal, complemented
12C2×#16838019C212yesmaximal
13C2×#16838014C212yesmaximal, complemented
14C2×#16838012C212yesmaximal, complemented
15C2×#16838009C214yesmaximal, complemented
16C2×#16837959C211yesmaximal, characteristic, complemented
17C2×#16837959C211yesmaximal, characteristic, complemented
18C2×C59×#529C211yesmaximal, characteristic
19#16838155C22164yescomplemented
20Q8×Dic118C22116yescomplemented
21#16838130C22116yescomplemented
22#16838129C22132yescomplemented
23#16838122C22132yescomplemented
24#16838122C22116yescomplemented
25#16838121C22132yescomplemented
26#16838109C22116yescomplemented
27#16838092C22132yescomplemented
28#16838030C22132yescomplemented
29#16838019C22132yes—
30#16838014C22132yescomplemented
31#16838012C22132yescomplemented
32#16838009C22164yescomplemented
33#16837959C22116yescomplemented
34#16837959C22116yescomplemented
35C2×#14273727C2211yescharacteristic
36C2×#14273727C2211yescharacteristic
37C2×#14273727C2212yes—
38C2×#14273727C2211yescharacteristic
39C2×#14273727C2211yescharacteristic
40C2×#14273726C2214yes—
41C2×#14273726C2214yes—
42C2×#14273726C2212yes—
43C2×#14273725C2212yes—
44C2×#14273720C2214yes—
45C2×#14273720C2214yes—
46C2×#14273720C2214yes—
47C2×#14273720C2214yes—
48C2×#14273720C2214yes—
49C2×#14273720C2214yes—
50C2×#14273719C2212yes—
51C2×#14273719C2212yes—
52C2×#14273719C2212yes—
53C2×#14273718C2214yes—
54C2×#14273718C2212yes—
55C2×#14273717C2214yes—
56C2×#14273717C2214yes—
57C2×#14273717C2214yes—
58C2×#14273717C2214yes—
59C2×#14273714C2214yes—
60C2×#14273714C2212yes—
61C2×#14273708C2214yes—
62C2×#14273706C2212yes—
63C2×#14273706C2212yes—
64C2×#14273706C2212yes—
65C2×#14273706C2212yes—
66C2×#14273706C2212yes—
67C2×#14273706C2211yescharacteristic
68C2×#14273706C2211yescharacteristic
69C2×#14273704C2214yes—
70C2×#14273704C2214yes—
71C2×#14273704C2214yes—
72C2×Q8×Dic59C2212yes—
73C2×C4×Dic118C2212yes—
74C2×C4×Dic118C2212yes—
75C2×C4×Dic118C2212yes—
76C2×C4×Dic118C2211yescharacteristic
77C2×C4×Dic118C2212yes—
78C2×C4×Dic118C2212yes—
79C2×C4×Dic118C2211yescharacteristic
80C2×#14273692C2214yes—
81C2×#14273692C2212yes—
82C2×#14273692C2212yes—
83C2×D4×Dic59C2212yes—
84C2×#14273686C2212yes—
85C2×#14273686C2212yes—
86C2×#14273686C2212yes—
87C2×#14273683C2214yes—
88C22×C4⋊Dic59C2212yes—
89C59×#529C22116yes—
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
101C22×Dic118C2311yescharacteristic
102C22×Dic118C2311yescharacteristic
103C22×Dic118C2312yes—
104C22×Dic118C2312yes—
105C22×Dic118C2312yes—
106C22×Dic118C2314yes—
107C23×Dic59C2314yes—
108#14273727C2318yes—
109#14273727C2318yes—
110#14273727C2318yes—
111#14273727C2318yes—
112#14273727C23116yes—
113#14273726C23132yes—
114#14273726C23132yes—
115#14273726C23116yes—
116#14273725C23116yes—
117#14273720C23132yes—
118#14273720C23132yes—
119#14273720C23132yes—
120#14273720C23132yes—
121#14273720C23132yes—
122#14273720C23132yes—
123#14273719C23116yes—
124#14273719C23116yes—
125#14273719C23116yes—
126#14273718C23132yes—
127#14273718C23116yes—
128#14273717C23132yes—
129#14273717C23132yes—
130#14273717C23132yes—
131#14273717C23132yes—
132#14273714C23132yes—
133#14273714C23116yes—
134#14273708C23132yes—
135#14273706C23116yes—
136#14273706C23116yes—
137#14273706C23116yes—
138#14273706C2318yes—
139#14273706C2318yes—
140#14273706C23116yes—
141#14273706C23116yes—
142#14273704C23132yes—
143#14273704C23132yes—
144#14273704C23132yes—
145Q8×Dic59C23116yes—
146C4×Dic118C23116yes—
147C4×Dic118C2318yes—
148C4×Dic118C23116yes—
149C4×Dic118C23116yes—
150C4×Dic118C2318yes—
151C4×Dic118C23116yes—
152C4×Dic118C23116yes—
153#14273692C23132yes—
154#14273692C23116yes—
155#14273692C23116yes—
156D4×Dic59C23116yes—
157#14273686C23116yes—
158#14273686C23116yes—
159#14273686C23116yes—
160#14273683C23132yes—
161C2×C4⋊Dic59C2312yes—
162C2×C4⋊Dic59C2314yes—
163C2×C4⋊Dic59C2314yes—
164C2×C4⋊Dic59C2312yes—
165C2×C4⋊Dic59C2312yes—
166C2×C4⋊Dic59C2312yes—
167C2×C4⋊Dic59C2311yescharacteristic
168C2×C4⋊Dic59C2312yes—
169C2×C4⋊Dic59C2312yes—
170C2×C4⋊Dic59C2311yescharacteristic
171C2×C4⋊Dic59C2312yes—
172C2×C4⋊Dic59C23116yes—
173C2×Dic59⋊C4C2312yes—
174C2×Dic59⋊C4C2314yes—
175C2×Dic59⋊C4C2314yes—
176C2×Dic59⋊C4C2314yes—
177C2×Dic59⋊C4C2314yes—
178C2×Dic59⋊C4C2314yes—
179C2×Dic59⋊C4C2314yes—
180C2×Dic59⋊C4C2312yes—
181C2×Dic59⋊C4C2312yes—
182C2×Dic59⋊C4C2312yes—
183C2×Dic59⋊C4C2314yes—
184C2×Dic59⋊C4C2314yes—
185C2×C22⋊Dic59C2314yes—
186C2×C22⋊Dic59C2314yes—
187C2×C22⋊Dic59C2312yes—
188C2×C22⋊Dic59C2314yes—
189C2×C22⋊Dic59C2312yes—
190C2×C22⋊Dic59C2314yes—
191C2×C4×Dic59C2314yes—
192C2×C4×Dic59C2312yes—
193C2×C4×Dic59C2314yes—
194C2×C4×Dic59C2314yes—
195C2×C4×Dic59C2314yes—
196C2×C4×Dic59C2312yes—
197C22×Q8×C59C2311yescharacteristic
198C22×D4×C59C2311yescharacteristic
199C22×D4×C59C2312yes—
200C23×C4×C59C2311yescharacteristic
201C23×C4×C59C2311yescharacteristic
202C23×C4×C59C2312yes—
203C23×C4×C59C2311yescharacteristic
204#126×C59C23116yes—
205#125×C59C2318yes—
206#124×C59C2318yes—
207#123×C59C23116yes—
208C22⋊Q8×C59C2318yes—
209#121×C59C2318yes—
210C4×Q8×C59C2318yes—
211C4×D4×C59C23116yes—
212C4×D4×C59C2318yes—
213#117×C59C23116yes—
214C2×C4⋊C4×C59C2312yes—
215C2×C4⋊C4×C59C2312yes—
216C2×C4⋊C4×C59C2312yes—
217C2×C4⋊C4×C59C2312yes—
218C2×C4⋊C4×C59C2311yescharacteristic
219C2×C4⋊C4×C59C2311yescharacteristic
220C2×C22⋊C4×C59C2312yes—
221C2×C22⋊C4×C59C2312yes—
222C2×C22⋊C4×C59C2312yes—
223C2×C22⋊C4×C59C2312yes—
224C2×C22⋊C4×C59C2312yes—
225C2×C42×C59C2311yescharacteristic
226C2×C42×C59C2311yescharacteristic
227C2×C42×C59C2312yes—
228C2×C42×C59C2311yescharacteristic
229C2×C42×C59C2318yes—
230C2×C42×C59C2311yescharacteristic
231C24×C59C2412yes—
232C24×C59C2411yescharacteristic
233C2×Q8×C59—24no—
234C2×Q8×C59C2414yes—
235C2×D4×C59—24no—
236C2×D4×C59—44no—
237C2×D4×C59C2414yes—
238C2×D4×C59C2418yes—
239C22×C4×C59—24no—
240C22×C4×C59—28no—
241C22×C4×C59—24no—
242C22×C4×C59—42no—
243C22×C4×C59C2411yescharacteristic
244C22×C4×C59C2411yescharacteristic
245C22×C4×C59C2411yescharacteristic
246C22×C4×C59C2411yescharacteristic
247C22×C4×C59C2414yes—
248C22×C4×C59C2414yes—
249C22×C4×C59C2412yes—
250C22×C4×C59C2412yes—
251C22×C4×C59C2412yes—
252C22×C4×C59C2418yes—
253C22×C4×C59C2414yes—
254C22×C4×C59C2411yescharacteristic
255C22×C4×C59C2411yescharacteristic
256C22×Dic59—48no—
257C22×Dic59C2412yes—
258C22×Dic59C2414yes—
259C22×Dic59C2412yes—
260C22×Dic59C2412yes—
261C22×Dic59C2414yes—
262C22×Dic59C2412yes—
263C22×Dic59C24116yes—
264C2×Dic118—24no—
265C2×Dic118—24no—
266C2×Dic118—28no—
267C2×Dic118—48no—
268C2×Dic118—44no—
269C2×Dic118—44no—
270C2×Dic118C2418yes—
271C2×Dic118C2414yes—
272C2×Dic118C2414yes—
273C2×Dic118C24116yes—
274C2×Dic118C2418yes—
275C2×Dic118C2418yes—
276C4⋊C4×C59C2418yes—
277C4⋊C4×C59C2418yes—
278C4⋊C4×C59C2414yes—
279C4⋊C4×C59C2418yes—
280C4⋊C4×C59C2414yes—
281C4⋊C4×C59C2418yes—
282C22⋊C4×C59C2418yes—
283C22⋊C4×C59C2418yes—
284C22⋊C4×C59C2418yes—
285C22⋊C4×C59C2418yes—
286C22⋊C4×C59C2418yes—
287C42×C59C2414yes—
288C42×C59C2414yes—
289C42×C59C2414yes—
290C42×C59C2414yes—
291C42×C59C2418yes—
292C22⋊Dic59C24116yes—
293C22⋊Dic59C24116yes—
294C22⋊Dic59C2418yes—
295C22⋊Dic59C24116yes—
296C22⋊Dic59C2418yes—
297C22⋊Dic59C24116yes—
298C4⋊Dic59C2414yes—
299C4⋊Dic59C2418yes—
300C4⋊Dic59C24116yes—
301C4⋊Dic59C2418yes—
302C4⋊Dic59C2414yes—
303C4⋊Dic59C2418yes—
304C4⋊Dic59C2418yes—
305C4⋊Dic59C2418yes—
306C4⋊Dic59C2418yes—
307C4⋊Dic59C2418yes—
308C4⋊Dic59C24116yes—
309Dic59⋊C4C2418yes—
310Dic59⋊C4C24116yes—
311Dic59⋊C4C2418yes—
312Dic59⋊C4C24116yes—
313Dic59⋊C4C24116yes—
314Dic59⋊C4C24116yes—
315Dic59⋊C4C2418yes—
316Dic59⋊C4C24116yes—
317Dic59⋊C4C24116yes—
318Dic59⋊C4C2418yes—
319Dic59⋊C4C24116yes—
320Dic59⋊C4C24116yes—
321C4×Dic59C24116yes—
322C4×Dic59C24116yes—
323C4×Dic59C2418yes—
324C4×Dic59C24116yes—
325C4×Dic59C2418yes—
326C4×Dic59C24116yes—
327C23×C59—24no—
328C23×C59—22no—
329C23×C59—22no—
330C23×C59—24no—
331C23×C59—24no—
332C23×C59—22no—
333C23×C59C2512yes—
334C23×C59C2514yes—
335C23×C59C2511yescharacteristic
336Q8×C59—28no—
337D4×C59—28no—
338D4×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—22no—
345C2×C4×C59—24no—
346C2×C4×C59—28no—
347C2×C4×C59—216no—
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×C59C2512yes—
359C2×C4×C59C2512yes—
360C2×C4×C59C2512yes—
361C2×Dic59—24no—
362C2×Dic59—24no—
363C2×Dic59—28no—
364C2×Dic59—24no—
365C2×Dic59—28no—
366C2×Dic59—24no—
367C2×Dic59—416no—
368C2×Dic59C2518yes—
369C2×Dic59C2514yes—
370C2×Dic59C2514yes—
371C2×Dic59C2514yes—
372C2×Dic59C2518yes—
373C2×Dic59C2514yes—
374Dic118—28no—
375Dic118—28no—
376Dic118—216no—
377Dic118—416no—
378Dic118—48no—
379Dic118—48no—
380C2×#3555—591nomaximal, Sylow
381C22×C59—22no—
382C22×C59—22no—
383C22×C59—24no—
384C22×C59—24no—
385C22×C59—24no—
386C22×C59—22no—
387C22×C59—44no—
388C22×C59—48no—
389C22×C59C2×2−1+412yes—
390C22×C59C2×2−1+412yes—
391C22×C59#58512yes—
392C22×C59C2611yescharacteristic
393C4×C59—22no—
394C4×C59—24no—
395C4×C59—22no—
396C4×C59—24no—
397C4×C59—22no—
398C4×C59—22no—
399C4×C59—24no—
400C4×C59C2×2−1+414yes—
401C4×C59C2×2−1+414yes—
402Dic59—24no—
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—594no—
421C2×#541—592no—
422C2×#541—592no—
423C2×#533—591no—
424C2×#533—591no—
425C2×#529D5911yescharacteristic
426C2×C59—42no—
427C2×C59—44no—
428C2×C59#355514yescomplemented
429C2×C59C22×2−1+411yescharacteristic
430C2×C59C22×2−1+411yescharacteristic
431C2×C59C2×#58511yescharacteristic
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—5964no—
444#541—5932no—
445#541—5932no—
446#533—5916no—
447#533—5916no—
448C2×C4⋊Q8—592no—
449C2×C4⋊Q8—594no—
450C2×C4⋊Q8—592no—
451C2×C4⋊Q8—594no—
452C2×C4⋊Q8—591no—
453C2×C4⋊Q8—591no—
454C2×C4⋊Q8—591no—
455C2×C4⋊Q8—591no—
456C2×C4⋊Q8—592no—
457#529C2×D59116yes—
458C2×#126—594no—
459C2×#126—594no—
460C2×#126—594no—
461C2×#126—594no—
462C2×#126—594no—
463C2×#126—594no—
464C2×#126C2×D5912yes—
465C2×#125—594no—
466C2×#125—594no—
467C2×#125—594no—
468C2×#125—594no—
469C2×#125—594no—
470C2×#125—592no—
471C2×#125—592no—
472C2×#125—592no—
473C2×#125—592no—
474C2×#125C2×D5911yescharacteristic
475C2×#124—592no—
476C2×#124—594no—
477C2×#124C2×D5911yescharacteristic
478C2×#123—594no—
479C2×#123C2×D5912yes—
480C2×C22⋊Q8—592no—
481C2×C22⋊Q8—591no—
482C2×C22⋊Q8—591no—
483C2×C22⋊Q8—592no—
484C2×C22⋊Q8—592no—
485C2×C22⋊Q8—592no—
486C2×C22⋊Q8—592no—
487C2×C22⋊Q8—594no—
488C2×C22⋊Q8—594no—
489C2×C22⋊Q8—594no—
490C2×C22⋊Q8C2×D5911yescharacteristic
491C2×#121C2×D5911yescharacteristic
492C2×C4×Q8—592no—
493C2×C4×Q8—594no—
494C2×C4×Q8—592no—
495C2×C4×Q8—592no—
496C2×C4×Q8—592no—
497C2×C4×Q8—591no—
498C2×C4×Q8—592no—
499C2×C4×Q8—592no—
500C2×C4×Q8—591no—
501C2×C4×Q8—592no—
502C2×C4×Q8—592no—
503C2×C4×Q8C2×D5911yescharacteristic
504C2×C4×D4—592no—
505C2×C4×D4C2×D5912yes—
506C2×C4×D4C2×D5911yescharacteristic
507C2×#117—592no—
508C2×#117—592no—
509C2×#117—592no—
510C2×#117—594no—
511C2×#117C2×D5912yes—
512C22×C4⋊C4—592no—
513C22×C42C2×D5911yescharacteristic
514C59C2×#355511yescharacteristic, complemented, Sylow
515C22×Q8—591no—
516C22×Q8—591no—
517C22×Q8—592no—
518C22×Q8—592no—
519C22×Q8—592no—
520C22×Q8—594no—
521C22×Q8C22×D5911yescharacteristic
522C22×D4C22×D5911yescharacteristic
523C22×D4C22×D5912yes—
524C23×C4—594no—
525C23×C4C22×D5912yes—
526C23×C4C22×D5911yescharacteristic
527C23×C4C22×D5911yescharacteristic
528C23×C4C22×D5911yescharacteristic
529C4⋊Q8—5916no—
530C4⋊Q8—5932no—
531C4⋊Q8—5916no—
532C4⋊Q8—5932no—
533C4⋊Q8—598no—
534C4⋊Q8—598no—
535C4⋊Q8—598no—
536C4⋊Q8—598no—
537C4⋊Q8—5916no—
538#126—5932no—
539#126—5932no—
540#126—5932no—
541#126—5932no—
542#126—5932no—
543#126—5932no—
544#126C22×D59116yes—
545#125—5932no—
546#125—5932no—
547#125—5932no—
548#125—5916no—
549#125—5932no—
550#125—5932no—
551#125—5916no—
552#125—5916no—
553#125—5916no—
554#125C22×D5918yes—
555#124—5916no—
556#124—5932no—
557#124C22×D5918yes—
558#123—5932no—
559#123C22×D59116yes—
560C22⋊Q8—5916no—
561C22⋊Q8—598no—
562C22⋊Q8—598no—
563C22⋊Q8—5916no—
564C22⋊Q8—5916no—
565C22⋊Q8—5916no—
566C22⋊Q8—5916no—
567C22⋊Q8—5932no—
568C22⋊Q8—5932no—
569C22⋊Q8—5932no—
570C22⋊Q8C22×D5918yes—
571#121C22×D5918yes—
572C4×Q8—5916no—
573C4×Q8—5932no—
574C4×Q8—5916no—
575C4×Q8—5916no—
576C4×Q8—5916no—
577C4×Q8—598no—
578C4×Q8—5916no—
579C4×Q8—5916no—
580C4×Q8—598no—
581C4×Q8—5916no—
582C4×Q8—5916no—
583C4×Q8C22×D5918yes—
584C4×D4—5916no—
585C4×D4C22×D59116yes—
586C4×D4C22×D5918yes—
587#117—5916no—
588#117—5916no—
589#117—5916no—
590#117—5932no—
591#117C22×D59116yes—
592C2×C4⋊C4—591no—
593C2×C4⋊C4—592no—
594C2×C4⋊C4—594no—
595C2×C4⋊C4—5916no—
596C2×C4⋊C4—592no—
597C2×C4⋊C4—592no—
598C2×C4⋊C4—591no—
599C2×C4⋊C4—592no—
600C2×C4⋊C4—594no—
601C2×C4⋊C4—592no—
602C2×C4⋊C4—592no—
603C2×C4⋊C4—592no—
604C2×C4⋊C4—592no—
605C2×C4⋊C4—594no—
606C2×C4⋊C4—594no—
607C2×C4⋊C4—594no—
608C2×C4⋊C4—594no—
609C2×C4⋊C4—594no—
610C2×C4⋊C4—592no—
611C2×C4⋊C4—592no—
612C2×C4⋊C4—592no—
613C2×C4⋊C4—594no—
614C2×C4⋊C4—594no—
615C2×C4⋊C4—594no—
616C2×C4⋊C4C22×D5912yes—
617C2×C4⋊C4C22×D5912yes—
618C2×C4⋊C4C22×D5911yescharacteristic
619C2×C4⋊C4C22×D5912yes—
620C2×C4⋊C4C22×D5911yescharacteristic
621C2×C4⋊C4C22×D5912yes—
622C2×C22⋊C4—592no—
623C2×C22⋊C4—594no—
624C2×C22⋊C4—592no—
625C2×C22⋊C4—594no—
626C2×C22⋊C4—594no—
627C2×C22⋊C4—594no—
628C2×C22⋊C4C22×D5912yes—
629C2×C22⋊C4C22×D5912yes—
630C2×C22⋊C4C22×D5912yes—
631C2×C22⋊C4C22×D5912yes—
632C2×C22⋊C4C22×D5912yes—
633C2×C42—594no—
634C2×C42—592no—
635C2×C42—592no—
636C2×C42—594no—
637C2×C42—594no—
638C2×C42—594no—
639C2×C42C22×D5911yescharacteristic
640C2×C42C22×D5912yes—
641C2×C42C22×D5911yescharacteristic
642C2×C42C22×D5911yescharacteristic
643C2×C42C22×D5911yescharacteristic
644C2×C42C22×D5918yes—
645C24C23×D5911yescharacteristic
646C24C23×D5912yes—
647C2×Q8—24no—
648C2×Q8—594no—
649C2×Q8—594no—
650C2×Q8—598no—
651C2×Q8—598no—
652C2×Q8—598no—
653C2×Q8—5916no—
654C2×Q8—1184no—
655C2×Q8—1184no—
656C2×Q8—1188no—
657C2×Q8—2364no—
658C2×Q8—2364no—
659C2×Q8—2368no—
660C2×Q8C23×D5914yes—
661C2×D4—24no—
662C2×D4—44no—
663C2×D4C23×D5914yes—
664C2×D4C23×D5918yes—
665C22×C4—28no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—42no—
669C22×C4—594no—
670C22×C4—592no—
671C22×C4—592no—
672C22×C4—592no—
673C22×C4—594no—
674C22×C4—592no—
675C22×C4—5916no—
676C22×C4—2368no—
677C22×C4C23×D5914yes—
678C22×C4C23×D5914yes—
679C22×C4C23×D5918yes—
680C22×C4C23×D5911yescharacteristic
681C22×C4C23×D5912yes—
682C22×C4C23×D5912yes—
683C22×C4C23×D5912yes—
684C22×C4C23×D5911yescharacteristic
685C22×C4C23×D5911yescharacteristic
686C22×C4C23×D5911yescharacteristic
687C22×C4C23×D5914yes—
688C22×C4C23×D5911yescharacteristic
689C22×C4C23×D5911yescharacteristic
690C4⋊C4—594no—
691C4⋊C4—598no—
692C4⋊C4—5916no—
693C4⋊C4—598no—
694C4⋊C4—598no—
695C4⋊C4—594no—
696C4⋊C4—598no—
697C4⋊C4—5916no—
698C4⋊C4—598no—
699C4⋊C4—598no—
700C4⋊C4—598no—
701C4⋊C4—598no—
702C4⋊C4—5916no—
703C4⋊C4—5916no—
704C4⋊C4—5916no—
705C4⋊C4—5916no—
706C4⋊C4—5916no—
707C4⋊C4—598no—
708C4⋊C4—598no—
709C4⋊C4—598no—
710C4⋊C4—5916no—
711C4⋊C4—5916no—
712C4⋊C4—5916no—
713C4⋊C4C23×D5918yes—
714C4⋊C4C23×D5918yes—
715C4⋊C4C23×D5914yes—
716C4⋊C4C23×D5918yes—
717C4⋊C4C23×D5914yes—
718C4⋊C4C23×D5918yes—
719C22⋊C4—598no—
720C22⋊C4—5916no—
721C22⋊C4—598no—
722C22⋊C4—5916no—
723C22⋊C4—5916no—
724C22⋊C4—5916no—
725C22⋊C4C23×D5918yes—
726C22⋊C4C23×D5918yes—
727C22⋊C4C23×D5918yes—
728C22⋊C4C23×D5918yes—
729C22⋊C4C23×D5918yes—
730C42—5916no—
731C42—598no—
732C42—598no—
733C42—5916no—
734C42—5916no—
735C42—5916no—
736C42C23×D5914yes—
737C42C23×D5914yes—
738C42C23×D5914yes—
739C42C23×D5914yes—
740C42C23×D5918yes—
741C23—22no—
742C23—22no—
743C23—24no—
744C23—24no—
745C23—22no—
746C23—24no—
747C23C24×D5912yes—
748C23C24×D5914yes—
749C23C24×D5911yescharacteristic
750Q8—28no—
751Q8—1188no—
752Q8—1188no—
753Q8—11816no—
754Q8—2368no—
755Q8—2368no—
756Q8—23616no—
757D4—28no—
758D4—48no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—28no—
767C2×C4—216no—
768C2×C4—28no—
769C2×C4—44no—
770C2×C4—598no—
771C2×C4—594no—
772C2×C4—594no—
773C2×C4—594no—
774C2×C4—598no—
775C2×C4—594no—
776C2×C4—1184no—
777C2×C4—1184no—
778C2×C4—1188no—
779C2×C4—1184no—
780C2×C4—1188no—
781C2×C4—1184no—
782C2×C4—23616no—
783C2×C4#1427377414yes—
784C2×C4#1427377414yes—
785C2×C4C24×D5912yes—
786C2×C4C24×D5914yes—
787C2×C4C24×D5914yes—
788C2×C4C24×D5914yes—
789C2×C4C24×D5912yes—
790C2×C4C24×D5912yes—
791C2×C4C24×D5912yes—
792C2×C4C24×D5912yes—
793C2×C4C24×D5912yes—
794C22—22no—
795C22—22no—
796C22—24no—
797C22—24no—
798C22—22no—
799C22—24no—
800C22—44no—
801C22—48no—
802C22C2×#1427377412yes—
803C22C2×#1427377412yes—
804C22#1683823812yes—
805C22C25×D5911yescharacteristic
806C4—22no—
807C4—24no—
808C4—22no—
809C4—24no—
810C4—22no—
811C4—22no—
812C4—24no—
813C4—1184no—
814C4—1184no—
815C4—1188no—
816C4—1184no—
817C4—1188no—
818C4—1184no—
819C4C2×#1427377414yes—
820C4C2×#1427377414yes—
821C2—42no—
822C2—44no—
823C2#2143858614yesdirect product factor
824C2C22×#1427377411yescharacteristic
825C2C22×#1427377411yescharacteristic
826C2C2×#1683823811yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#529C2
socleC23×C59C25
prime radicalC2×#121×C59C22
hypercenterC2×#529D59
hypocenterC59C2×#3555
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #21438586C2direct (N × H)
2. C2×#16838155C2semidirect
3. C2×Q8×Dic118C2semidirect
4. C2×#16838130C2semidirect
5. C2×#16838129C2semidirect
6. C2×#16838122C2semidirect
7. C2×#16838122C2semidirect
8. C2×#16838121C2semidirect
9. C2×#16838109C2semidirect
10. C2×#16838092C2semidirect
11. C2×#16838030C2semidirect
13. C2×#16838014C2semidirect
14. C2×#16838012C2semidirect
15. C2×#16838009C2semidirect
16. C2×#16837959C2semidirect
17. C2×#16837959C2semidirect
19. #16838155C22semidirect
20. Q8×Dic118C22semidirect
21. #16838130C22semidirect
22. #16838129C22semidirect
23. #16838122C22semidirect
24. #16838122C22semidirect
25. #16838121C22semidirect
26. #16838109C22semidirect
27. #16838092C22semidirect
28. #16838030C22semidirect
30. #16838014C22semidirect
31. #16838012C22semidirect
32. #16838009C22semidirect
33. #16837959C22semidirect
34. #16837959C22semidirect
428. C2×C59#3555semidirect
514. C59C2×#3555semidirect
823. C2#21438586direct (N × H)

Maximal subgroups

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

subgroupindex
#214385862
C2×#168381552
C2×Q8×Dic1182
C2×#168381302
C2×#168381292
C2×#168381222
C2×#168381212
C2×#168381092
C2×#168380922
C2×#168380302
C2×#168380192
C2×#168380142
C2×#168380122
C2×#168380092
C2×#168379592
C2×C59×#5292
C2×#355559