Finite Group Databasebeta

← C2×#21460353 #30587380

Subgroups — C2×#21460353 #30587380

Order 15616.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460353C2132yesmaximal, direct product factor
2C2×#16840516C212yesmaximal, complemented
3C2×#16840510C212yesmaximal, complemented
4C2×#16840468C212yesmaximal, complemented
5C2×#16840465C212yesmaximal, complemented
6C2×#16840460C212yesmaximal, complemented
7C2×#16840413C212yesmaximal, complemented
8C2×#16840413C214yesmaximal, complemented
9C2×#16840392C212yesmaximal, complemented
10C2×#16840368C212yesmaximal, complemented
11C2×#16840360C214yesmaximal, complemented
12C2×#16840359C212yesmaximal, complemented
13C2×#16840343C212yesmaximal, complemented
14C2×#16840312C211yesmaximal, characteristic, complemented
15C2×#16840296C211yesmaximal, characteristic, complemented
16C22×#125×C61C211yesmaximal, characteristic, complemented
17C22×#11758222C2212yes—
18C22×#11758222C2214yes—
19#16840516C22132yescomplemented
20#16840510C22132yescomplemented
21#16840468C22132yescomplemented
22#16840465C22132yescomplemented
23#16840460C22132yescomplemented
24#16840413C22164yescomplemented
25#16840413C22132yescomplemented
26#16840392C22132yescomplemented
27#16840368C22132yescomplemented
28#16840360C22164yescomplemented
29#16840359C22132yescomplemented
30#16840343C22132yescomplemented
31#16840312C22116yescomplemented
32C2×#14519777C2211yescharacteristic
33C2×#14519776C2212yes—
34C2×#14519776C2214yes—
35C2×#14519774C2211yescharacteristic
36#16840296C22116yescomplemented
37C2×#14519772C2214yes—
38C2×#14519772C2214yes—
39C2×#14519771C2212yes—
40C2×#14519769C2211yescharacteristic
41C2×#14519768C2212yes—
42C2×#14519767C2214yes—
43C2×#14519765C2211yescharacteristic
44C2×#14519765C2212yes—
45C2×#14519762C2214yes—
46C2×#14519762C2214yes—
47C2×#14519762C2214yes—
48C2×#14519762C2214yes—
49C2×#14519762C2214yes—
50C2×#14519760C2212yes—
51C2×#14519760C2214yes—
52C2×#14519757C2214yes—
53C2×#14519757C2214yes—
54C2×#14519756C2211yescharacteristic
55C2×#14519755C2214yes—
56C2×#14519755C2214yes—
57C2×#14519755C2214yes—
58C2×#14519755C2214yes—
59C2×#14519752C2212yes—
60C2×#14519752C2214yes—
61C2×#14519752C2212yes—
62C2×#14519752C2214yes—
63C2×#14519752C2214yes—
64C2×#14519751C2212yes—
65C2×#14519751C2214yes—
66C2×#14519751C2211yescharacteristic
67C2×#14519751C2212yes—
68C2×C4×Dic122C2211yescharacteristic
69C2×C4×D244C2211yescharacteristic
70C2×C4×D244C2212yes—
71C2×C4×D244C2212yes—
72C2×#14519739C2214yes—
73C2×#14519739C2212yes—
74C2×#14519739C2212yes—
75C2×C4×C22⋊D61C2212yes—
76C2×C4×C22⋊D61C2214yes—
77C2×#14519735C2212yes—
78C2×#14519734C2212yes—
79C2×C4⋊C4×D61C2212yes—
80C2×C4⋊C4×D61C2214yes—
81C2×#125×C61C2212yes—
82C2×#125×C61C2212yes—
83C2×#125×C61C2212yes—
84C2×#125×C61C2212yes—
85C2×#125×C61C22116yescomplemented
86C22×C4⋊C4×C61C2211yescharacteristic
87C22×C4⋊C4×C61C2212yes—
88C22×C4⋊C4×C61C2211yescharacteristic
89C22×C4⋊C4×C61C2212yes—
90C22×C42×C61C2211yescharacteristic
91C2×#11758222—48no—
92C2×#11758222—416no—
93C2×#11758222C23116yes—
94C2×#11758222C23132yes—
95C22×Dic122C2311yescharacteristic
96C22×Dic122C2314yes—
97C22×Dic122C2312yes—
98C22×D244C2312yes—
99C22×D244C2314yes—
100C22×D244C2311yescharacteristic
101C22×D244C2312yes—
102C22×D244C2314yes—
103C22×D244C2312yes—
104C22×C22⋊D61C2312yes—
105C22×C22⋊D61C2314yes—
106C22×C4×D61C2312yes—
107C22×C4×D61C2314yes—
108C22×C4×D61C2314yes—
109C22×C4×D61C2314yes—
110C22×C4×D61C2314yes—
111#14519777C2318yes—
112#14519776C23116yes—
113#14519776C23132yes—
114#14519774C2318yes—
115#14519772C23132yes—
116#14519772C23132yes—
117#14519771C23116yes—
118#14519769C2318yes—
119#14519768C23116yes—
120#14519767C23132yes—
121#14519765C2318yes—
122#14519765C23116yes—
123#14519762C23132yes—
124#14519762C23132yes—
125#14519762C23132yes—
126#14519762C23132yes—
127#14519762C23132yes—
128#14519760C23116yes—
129#14519760C23132yes—
130#14519757C23132yes—
131#14519757C23132yes—
132#14519756C2318yes—
133#14519755C23132yes—
134#14519755C23132yes—
135#14519755C23132yes—
136#14519755C23132yes—
137#14519752C23116yes—
138#14519752C23132yes—
139#14519752C23116yes—
140#14519752C23132yes—
141#14519752C23132yes—
142#14519751C23116yes—
143#14519751C23132yes—
144#14519751C2318yes—
145#14519751C23116yes—
146C4×Dic122C2318yes—
147C4×D244C2318yes—
148C4×D244C23116yes—
149C4×D244C23116yes—
150#14519739C23116yes—
151#14519739C23132yes—
152#14519739C23116yes—
153C4×C22⋊D61C23116yes—
154C4×C22⋊D61C23132yes—
155#14519735C23116yes—
156#14519734C23116yes—
157C2×C4⋊Dic61C2312yes—
158C2×C4⋊Dic61C2314yes—
159C2×C4⋊Dic61C2312yes—
160C2×C4⋊Dic61C2311yescharacteristic
161C2×C4⋊Dic61C2311yescharacteristic
162C2×#11758196C2312yes—
163C2×#11758196C2314yes—
164C2×#11758196C2314yes—
165C2×#11758196C2312yes—
166C2×#11758196C2312yes—
167C2×#11758196C2314yes—
168C2×#11758196C2312yes—
169C4⋊C4×D61C23116yes—
170C4⋊C4×D61C23132yes—
171C2×C22⋊Dic61C2312yes—
172C2×#11758198C2312yes—
173C2×#11758198C2312yes—
174C2×#11758198C2314yes—
175C2×#11758198C2314yes—
176C2×#11758198C2312yes—
177C2×#11758198C2312yes—
178C2×#11758198C2314yes—
179C2×#11758198C2314yes—
180C2×#11758198C2314yes—
181C2×#11758198C2314yes—
182C2×#11758198C2314yes—
183C2×C4×Dic61C2312yes—
184C2×C4×Dic61C2314yes—
185C23×C4×C61C2311yescharacteristic
186C23×C4×C61C2311yescharacteristic
187C23×C4×C61C2312yes—
188C23×C4×C61C2312yes—
189C23×C4×C61C2311yescharacteristic
190#125×C61C23116yes—
191#125×C61C23116yes—
192#125×C61C23116yes—
193#125×C61C23116yes—
194C2×C4⋊C4×C61C2318yes—
195C2×C4⋊C4×C61C2312yes—
196C2×C4⋊C4×C61C2314yes—
197C2×C4⋊C4×C61C2312yes—
198C2×C4⋊C4×C61C2314yes—
199C2×C4⋊C4×C61C2314yes—
200C2×C4⋊C4×C61C2314yes—
201C2×C4⋊C4×C61C2312yes—
202C2×C4⋊C4×C61C2312yes—
203C2×C4⋊C4×C61C23116yes—
204C2×C4⋊C4×C61C2318yes—
205C2×C4⋊C4×C61C23116yes—
206C2×C42×C61C2311yescharacteristic
207C2×C42×C61C2311yescharacteristic
208C2×C42×C61C2311yescharacteristic
209C2×C42×C61C2311yescharacteristic
210C2×C42×C61C2318yes—
211C24×C61C2411yescharacteristic
212C23×D61C2412yes—
213C23×D61C2414yes—
214C22×C4×C61—24no—
215C22×C4×C61—28no—
216C22×C4×C61—24no—
217C22×C4×C61—42no—
218C22×C4×C61—44no—
219C22×C4×C61C2411yescharacteristic
220C22×C4×C61C2414yes—
221C22×C4×C61C2414yes—
222C22×C4×C61C2411yescharacteristic
223C22×C4×C61C2411yescharacteristic
224C22×C4×C61C2411yescharacteristic
225C22×C4×C61C2414yes—
226C22×C4×C61C2418yes—
227C22×C4×C61C2411yescharacteristic
228C22×C4×C61C2414yes—
229C22×C4×C61C2414yes—
230C22×C4×C61C2418yes—
231C22×C4×C61C2411yescharacteristic
232C2×C22⋊D61—28no—
233C2×C22⋊D61—216no—
234C2×C22⋊D61C24116yes—
235C2×C22⋊D61C2418yes—
236C22×Dic61C2414yes—
237C22×Dic61C2412yes—
238C22×Dic61C2412yes—
239C22×Dic61C2412yes—
240#11758222—432no—
241#11758222—464no—
242C2×D244—28no—
243C2×D244—42no—
244C2×D244—48no—
245C2×D244—44no—
246C2×D244—44no—
247C2×D244—48no—
248C2×D244C2418yes—
249C2×D244C24116yes—
250C2×D244C2418yes—
251C2×D244C24116yes—
252C2×D244C2414yes—
253C2×D244C2418yes—
254C2×C4×D61—28no—
255C2×C4×D61—48no—
256C2×C4×D61—48no—
257C2×C4×D61—48no—
258C2×C4×D61—48no—
259C2×C4×D61C2418yes—
260C2×C4×D61C24116yes—
261C2×C4×D61C24116yes—
262C2×C4×D61C24116yes—
263C2×C4×D61C24116yes—
264C2×Dic122—42no—
265C2×Dic122—44no—
266C2×Dic122—48no—
267C2×Dic122C24116yes—
268C2×Dic122C2418yes—
269C2×Dic122C2414yes—
270C4⋊C4×C61C2418yes—
271C4⋊C4×C61C24116yes—
272C4⋊C4×C61C2418yes—
273C4⋊C4×C61C24116yes—
274C4⋊C4×C61C24116yes—
275C4⋊C4×C61C24116yes—
276C4⋊C4×C61C2418yes—
277C4⋊C4×C61C2418yes—
278C42×C61C2414yes—
279C42×C61C2414yes—
280C42×C61C2414yes—
281C42×C61C2414yes—
282C22⋊Dic61C2418yes—
283#11758198C2418yes—
284#11758198C2418yes—
285#11758198C24116yes—
286#11758198C24116yes—
287#11758198C2418yes—
288#11758198C2418yes—
289#11758198C24116yes—
290#11758198C24116yes—
291#11758198C24116yes—
292#11758198C24116yes—
293#11758198C24116yes—
294C4⋊Dic61C2418yes—
295C4⋊Dic61C24116yes—
296C4⋊Dic61C2418yes—
297C4⋊Dic61C2414yes—
298C4⋊Dic61C2414yes—
299#11758196C2418yes—
300#11758196C24116yes—
301#11758196C24116yes—
302#11758196C2418yes—
303#11758196C2418yes—
304#11758196C24116yes—
305#11758196C2418yes—
306C4×Dic61C2418yes—
307C4×Dic61C24116yes—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61H(5,𝔽2)14yes—
311C23×C61C2512yes—
312C23×C61C2511yescharacteristic
313C22×D61—24no—
314C22×D61—28no—
315C22×D61—24no—
316C22×D61—28no—
317C22×D61—28no—
318C22×D61—24no—
319C22×D61C2514yes—
320C22×D61C2518yes—
321C2×C4×C61—22no—
322C2×C4×C61—28no—
323C2×C4×C61—22no—
324C2×C4×C61—28no—
325C2×C4×C61—216no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—28no—
329C2×C4×C61—22no—
330C2×C4×C61—28no—
331C2×C4×C61—44no—
332C2×C4×C61—48no—
333C2×C4×C612−1+414yes—
334C2×C4×C61C2518yes—
335C2×C4×C61C2512yes—
336C2×C4×C61C2512yes—
337C2×C4×C61C2512yes—
338C2×C4×C61C2512yes—
339C2×C4×C61C2518yes—
340C2×C4×C61C2512yes—
341C2×C4×C61C2512yes—
342C22⋊D61—232no—
343C22⋊D61—216no—
344C2×Dic61—28no—
345C2×Dic61—24no—
346C2×Dic61—24no—
347C2×Dic61—24no—
348C2×Dic61C2514yes—
349C2×Dic61C2514yes—
350C2×Dic61C2514yes—
351C2×Dic61C2518yes—
352D244—216no—
353D244—44no—
354D244—416no—
355D244—48no—
356D244—48no—
357D244—416no—
358C4×D61—216no—
359C4×D61—416no—
360C4×D61—416no—
361C4×D61—416no—
362C4×D61—416no—
363Dic122—44no—
364Dic122—48no—
365Dic122—416no—
366C2×#3559—611nomaximal, Sylow
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—28no—
370C22×C61C2×H(5,𝔽2)14yes—
371C22×C61C2×H(5,𝔽2)12yes—
372C22×C61C2×2−1+412yes—
373C22×C61#58512yes—
374C22×C61C2611yescharacteristic
375C2×D61—24no—
376C2×D61—28no—
377C2×D61—24no—
378C2×D61—28no—
379C2×D61—28no—
380C2×D61—24no—
381C2×D61—48no—
382C2×D61—416no—
383C4×C61—22no—
384C4×C61—28no—
385C4×C61—22no—
386C4×C61—22no—
387C4×C61—22no—
388C4×C61—28no—
389C4×C61—22no—
390C4×C61C2×2−1+414yes—
391Dic61—28no—
392Dic61—24no—
393Dic61—24no—
394Dic61—24no—
395#3559—6132no—
396C2×#563—612no—
397C2×#562—612no—
398C2×#554—612no—
399C2×#553—612no—
400C2×#553—612no—
401C2×#547—614no—
402C2×#547—612no—
403C2×#544—612no—
404C2×#540—612no—
405C2×#539—614no—
406C2×#539—612no—
407C2×#537—612no—
408C2×#532—611no—
409C2×#529—611no—
410C22×#125D6111yescharacteristic, complemented
411C2×C61—24no—
412C2×C61#355914yescomplemented
413C2×C61C22×H(5,𝔽2)11yescharacteristic
414C2×C61C22×2−1+411yescharacteristic
415C2×C61C2×#58511yescharacteristic
416D61—44no—
417D61—48no—
418C22×#41—612no—
419C22×#41—614no—
420#563—6132no—
421#562—6132no—
422#554—6132no—
423#553—6132no—
424#553—6132no—
425#547—6164no—
426#547—6132no—
427#544—6132no—
428#540—6132no—
429#539—6164no—
430#539—6132no—
431#537—6132no—
432#532—6116no—
433C2×C4⋊Q8—612no—
434C2×C4⋊Q8—614no—
435C2×C4⋊Q8—611no—
436C2×#127—611no—
437#529—6116no—
438C2×#126—614no—
439C2×#126—614no—
440C2×#126—612no—
441C2×#125—614no—
442C2×#125—612no—
443C2×#125—611no—
444C2×#125C2×D6112yes—
445C2×#125C2×D6112yes—
446C2×#125C2×D6112yes—
447C2×#125C2×D6112yes—
448C2×#125C2×D61116yescomplemented
449C2×#124—611no—
450C2×#124—612no—
451C2×#123—612no—
452C2×#123—614no—
453C2×#123—614no—
454C2×#123—614no—
455C2×#123—614no—
456C2×#123—614no—
457C2×#123—614no—
458C2×C22⋊Q8—611no—
459C2×C22⋊Q8—614no—
460C2×C22⋊Q8—614no—
461C2×C22⋊Q8—614no—
462C2×C22⋊Q8—614no—
463C2×C22⋊Q8—614no—
464C2×C22⋊Q8—614no—
465C2×#121—611no—
466C2×#121—612no—
467C2×#121—612no—
468C2×#121—614no—
469C2×#121—614no—
470C2×#121—614no—
471C2×#121—612no—
472C2×#121—614no—
473C2×#121—612no—
474C2×C4×Q8—611no—
475C2×C4×D4—612no—
476C2×C4×D4—614no—
477C2×C4×D4—614no—
478C2×C4×D4—612no—
479C2×C4×D4—612no—
480C2×C4×D4—611no—
481C2×C4×D4—612no—
482C2×C4×D4—612no—
483C2×#117—612no—
484C2×#117—612no—
485C22×C4⋊C4—614no—
486C22×C4⋊C4—612no—
487C22×C4⋊C4C2×D6112yes—
488C22×C4⋊C4C2×D6111yescharacteristic
489C22×C4⋊C4C2×D6112yes—
490C22×C4⋊C4C2×D6111yescharacteristic
491C22×C42C2×D6111yescharacteristic
492C61C2×#355911yescharacteristic, complemented, Sylow
493C2×#41—6116no—
494C2×#41—6132no—
495C2×#41—2448no—
496C2×#41—24416no—
497C22×Q8—611no—
498C22×Q8—614no—
499C22×Q8—612no—
500C22×D4—612no—
501C22×D4—614no—
502C22×D4—612no—
503C22×D4—614no—
504C22×D4—611no—
505C22×D4—612no—
506C22×D4—614no—
507C22×D4—612no—
508C23×C4—612no—
509C23×C4—614no—
510C23×C4—614no—
511C23×C4—614no—
512C23×C4—614no—
513C23×C4C22×D6112yes—
514C23×C4C22×D6111yescharacteristic
515C23×C4C22×D6111yescharacteristic
516C23×C4C22×D6112yes—
517C23×C4C22×D6111yescharacteristic
518C4⋊Q8—6116no—
519C4⋊Q8—6132no—
520C4⋊Q8—618no—
521#127—618no—
522#126—6132no—
523#126—6132no—
524#126—6116no—
525#125—6132no—
526#125—6116no—
527#125—618no—
528#125C22×D61116yes—
529#125C22×D61116yes—
530#125C22×D61116yes—
531#125C22×D61116yes—
532#124—618no—
533#124—6116no—
534#123—6116no—
535#123—6132no—
536#123—6132no—
537#123—6132no—
538#123—6132no—
539#123—6132no—
540#123—6132no—
541C22⋊Q8—618no—
542C22⋊Q8—6132no—
543C22⋊Q8—6132no—
544C22⋊Q8—6132no—
545C22⋊Q8—6132no—
546C22⋊Q8—6132no—
547C22⋊Q8—6132no—
548#121—618no—
549#121—6116no—
550#121—6116no—
551#121—6132no—
552#121—6132no—
553#121—6132no—
554#121—6116no—
555#121—6132no—
556#121—6116no—
557C4×Q8—618no—
558C4×D4—6116no—
559C4×D4—6132no—
560C4×D4—6132no—
561C4×D4—6116no—
562C4×D4—6116no—
563C4×D4—618no—
564C4×D4—6116no—
565C4×D4—6116no—
566#117—6116no—
567#117—6116no—
568C2×C4⋊C4—612no—
569C2×C4⋊C4—612no—
570C2×C4⋊C4—614no—
571C2×C4⋊C4—614no—
572C2×C4⋊C4—614no—
573C2×C4⋊C4—612no—
574C2×C4⋊C4—612no—
575C2×C4⋊C4—612no—
576C2×C4⋊C4—614no—
577C2×C4⋊C4—612no—
578C2×C4⋊C4—611no—
579C2×C4⋊C4—611no—
580C2×C4⋊C4—6132no—
581C2×C4⋊C4—6116no—
582C2×C4⋊C4C22×D6112yes—
583C2×C4⋊C4C22×D6114yes—
584C2×C4⋊C4C22×D6112yes—
585C2×C4⋊C4C22×D6114yes—
586C2×C4⋊C4C22×D6114yes—
587C2×C4⋊C4C22×D6114yes—
588C2×C4⋊C4C22×D6112yes—
589C2×C4⋊C4C22×D6112yes—
590C2×C4⋊C4C22×D61116yes—
591C2×C4⋊C4C22×D6118yes—
592C2×C4⋊C4C22×D61116yes—
593C2×C4⋊C4C22×D6118yes—
594C2×C22⋊C4—612no—
595C2×C22⋊C4—612no—
596C2×C22⋊C4—614no—
597C2×C22⋊C4—612no—
598C2×C22⋊C4—612no—
599C2×C22⋊C4—614no—
600C2×C22⋊C4—614no—
601C2×C22⋊C4—614no—
602C2×C22⋊C4—614no—
603C2×C22⋊C4—614no—
604C2×C22⋊C4—614no—
605C2×C22⋊C4—612no—
606C2×C42—612no—
607C2×C42—614no—
608C2×C42C22×D6111yescharacteristic
609C2×C42C22×D6111yescharacteristic
610C2×C42C22×D6111yescharacteristic
611C2×C42C22×D6111yescharacteristic
612C2×C42C22×D6118yes—
613C24—612no—
614C24—614no—
615C24C23×D6111yescharacteristic
616#41—24432no—
617#41—24464no—
618C2×Q8—614no—
619C2×Q8—6116no—
620C2×Q8—618no—
621C2×Q8—2442no—
622C2×Q8—2448no—
623C2×Q8—2444no—
624C2×D4—618no—
625C2×D4—6116no—
626C2×D4—618no—
627C2×D4—6116no—
628C2×D4—614no—
629C2×D4—618no—
630C2×D4—6116no—
631C2×D4—618no—
632C2×D4—1228no—
633C2×D4—12216no—
634C2×D4—1228no—
635C2×D4—2448no—
636C2×D4—2444no—
637C2×D4—2448no—
638C2×D4—2444no—
639C2×D4—2442no—
640C22×C4—24no—
641C22×C4—28no—
642C22×C4—24no—
643C22×C4—44no—
644C22×C4—42no—
645C22×C4—612no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—614no—
649C22×C4—618no—
650C22×C4—6116no—
651C22×C4—6116no—
652C22×C4—6116no—
653C22×C4—6116no—
654C22×C4—1228no—
655C22×C4—2448no—
656C22×C4—2448no—
657C22×C4—2448no—
658C22×C4—2448no—
659C22×C4C23×D6114yes—
660C22×C4C23×D6114yes—
661C22×C4C23×D6118yes—
662C22×C4C23×D6114yes—
663C22×C4C23×D6111yescharacteristic
664C22×C4C23×D6111yescharacteristic
665C22×C4C23×D6111yescharacteristic
666C22×C4C23×D6111yescharacteristic
667C22×C4C23×D6111yescharacteristic
668C22×C4C23×D6114yes—
669C22×C4C23×D6114yes—
670C22×C4C23×D6118yes—
671C22×C4C23×D6111yescharacteristic
672C4⋊C4—618no—
673C4⋊C4—6116no—
674C4⋊C4—6116no—
675C4⋊C4—618no—
676C4⋊C4—6116no—
677C4⋊C4—618no—
678C4⋊C4—618no—
679C4⋊C4—6116no—
680C4⋊C4—618no—
681C4⋊C4—618no—
682C4⋊C4—614no—
683C4⋊C4—614no—
684C4⋊C4C23×D6118yes—
685C4⋊C4C23×D61116yes—
686C4⋊C4C23×D6118yes—
687C4⋊C4C23×D61116yes—
688C4⋊C4C23×D61116yes—
689C4⋊C4C23×D61116yes—
690C4⋊C4C23×D6118yes—
691C4⋊C4C23×D6118yes—
692C22⋊C4—618no—
693C22⋊C4—618no—
694C22⋊C4—6116no—
695C22⋊C4—618no—
696C22⋊C4—618no—
697C22⋊C4—6116no—
698C22⋊C4—6116no—
699C22⋊C4—6116no—
700C22⋊C4—6116no—
701C22⋊C4—6116no—
702C22⋊C4—6116no—
703C22⋊C4—618no—
704C42—618no—
705C42—6116no—
706C42C23×D6114yes—
707C42C23×D6114yes—
708C42C23×D6114yes—
709C42C23×D6114yes—
710C23—22no—
711C23—22no—
712C23—614no—
713C23—618no—
714C23—1224no—
715C23—1228no—
716C23—1224no—
717C23—1228no—
718C23—1228no—
719C23—1224no—
720C23#1451982314yes—
721C23C24×D6112yes—
722C23C24×D6111yescharacteristic
723Q8—2444no—
724Q8—24416no—
725Q8—2448no—
726D4—12216no—
727D4—12232no—
728D4—12216no—
729D4—24416no—
730D4—2448no—
731D4—2444no—
732D4—24416no—
733D4—2448no—
734C2×C4—22no—
735C2×C4—28no—
736C2×C4—22no—
737C2×C4—28no—
738C2×C4—216no—
739C2×C4—22no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—28no—
744C2×C4—48no—
745C2×C4—44no—
746C2×C4—614no—
747C2×C4—614no—
748C2×C4—614no—
749C2×C4—618no—
750C2×C4—1224no—
751C2×C4—1228no—
752C2×C4—1224no—
753C2×C4—1224no—
754C2×C4—12216no—
755C2×C4—24416no—
756C2×C4—24416no—
757C2×C4—24416no—
758C2×C4—24416no—
759C2×C4#1451982514yes—
760C2×C4C24×D6118yes—
761C2×C4C24×D6112yes—
762C2×C4C24×D6112yes—
763C2×C4C24×D6112yes—
764C2×C4C24×D6112yes—
765C2×C4C24×D6112yes—
766C2×C4C24×D6118yes—
767C2×C4C24×D6112yes—
768C22—28no—
769C22—22no—
770C22—22no—
771C22—1224no—
772C22—1228no—
773C22—1224no—
774C22—1228no—
775C22—1228no—
776C22—1224no—
777C22—2448no—
778C22—24416no—
779C22C2×#1451982314yes—
780C22C2×#1451982312yes—
781C22C2×#1451982512yes—
782C22#1684059812yes—
783C22C25×D6111yescharacteristic
784C4—22no—
785C4—28no—
786C4—22no—
787C4—22no—
788C4—28no—
789C4—22no—
790C4—22no—
791C4—1224no—
792C4—1228no—
793C4—1224no—
794C4—1224no—
795C4C2×#1451982514yes—
796C2—24no—
797C2—2444no—
798C2—2448no—
799C2#2146035314yesdirect product factor
800C2C22×#1451982311yescharacteristic
801C2C22×#1451982511yescharacteristic
802C2C2×#1684059811yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC22×#125×C61C2
socleC23×C61C25
hypercenterC22×#125D61
hypocenterC61C2×#3559
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. #21460353C2direct (N × H)
2. C2×#16840516C2semidirect
3. C2×#16840510C2semidirect
4. C2×#16840468C2semidirect
5. C2×#16840465C2semidirect
6. C2×#16840460C2semidirect
7. C2×#16840413C2semidirect
8. C2×#16840413C2semidirect
9. C2×#16840392C2semidirect
10. C2×#16840368C2semidirect
11. C2×#16840360C2semidirect
12. C2×#16840359C2semidirect
13. C2×#16840343C2semidirect
14. C2×#16840312C2semidirect
15. C2×#16840296C2semidirect
16. C22×#125×C61C2semidirect
19. #16840516C22semidirect
20. #16840510C22semidirect
21. #16840468C22semidirect
22. #16840465C22semidirect
23. #16840460C22semidirect
24. #16840413C22semidirect
25. #16840413C22semidirect
26. #16840392C22semidirect
27. #16840368C22semidirect
28. #16840360C22semidirect
29. #16840359C22semidirect
30. #16840343C22semidirect
31. #16840312C22semidirect
36. #16840296C22semidirect
85. C2×#125×C61C22semidirect
410. C22×#125D61semidirect
412. C2×C61#3559semidirect
448. C2×#125C2×D61semidirect
492. C61C2×#3559semidirect
799. C2#21460353direct (N × H)

Maximal subgroups

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

subgroupindex
#214603532
C2×#168405162
C2×#168405102
C2×#168404682
C2×#168404652
C2×#168404602
C2×#168404132
C2×#168403922
C2×#168403682
C2×#168403602
C2×#168403592
C2×#168403432
C2×#168403122
C2×#168402962
C22×#125×C612
C2×#355961