Finite Group Databasebeta

← C2×#21460301 #30587729

Subgroups — C2×#21460301 #30587729

Order 15616.

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#21460301C2132yesmaximal, direct product factor
2C2×#16840513C214yesmaximal, complemented
3C2×#16840492C211yesmaximal, characteristic, complemented
4C2×#16840488C212yesmaximal, complemented
5C2×#16840487C211yesmaximal, characteristic, complemented
6C2×#16840486C211yesmaximal, characteristic, complemented
7C2×#16840484C212yesmaximal, complemented
8C2×#16840480C212yesmaximal, complemented
9C2×#16840473C211yesmaximal, characteristic, complemented
10C2×#16840451C212yesmaximal, complemented
11C2×#16840392C212yesmaximal, complemented
12C2×#16840385C212yesmaximal
13C2×#16840375C212yesmaximal, complemented
14C2×#16840372C212yesmaximal, complemented
15C2×#16840370C214yesmaximal, complemented
16C2×#16840319C211yesmaximal, characteristic, complemented
17C2×#16840296C211yesmaximal, characteristic
18C2×C61×#533C211yesmaximal, characteristic, complemented
19#16840513C22164yescomplemented
20#16840492C22116yescomplemented
21#16840488C22132yescomplemented
22#16840487C22116yescomplemented
23#16840486C22116yescomplemented
24#16840484C22132yescomplemented
25#16840480C22132yescomplemented
26#16840473C22116yescomplemented
27#16840451C22132yescomplemented
28#16840392C22132yescomplemented
29#16840385C22132yes—
30#16840375C22132yescomplemented
31#16840372C22132yescomplemented
32#16840370C22164yescomplemented
33#16840319C22116yescomplemented
34C2×#14519777C2211yescharacteristic
35C2×#14519777C2211yescharacteristic
36C2×#14519776C2212yes—
37C2×#14519776C2214yes—
38C2×#14519776C2212yes—
39C2×#14519775C2212yes—
40C2×#14519775C2214yes—
41#16840296C22116yes—
42C2×#14519772C2214yes—
43C2×#14519772C2214yes—
44C2×#14519772C2214yes—
45C2×#14519771C2212yes—
46C2×#14519771C2214yes—
47C2×#14519770C2214yes—
48C2×#14519770C2214yes—
49C2×#14519769C2214yes—
50C2×#14519769C2211yescharacteristic
51C2×#14519769C2212yes—
52C2×#14519768C2212yes—
53C2×#14519768C2212yes—
54C2×#14519768C2214yes—
55C2×#14519768C2214yes—
56C2×#14519767C2214yes—
57C2×#14519767C2214yes—
58C2×#14519766C2212yes—
59C2×#14519765C2211yescharacteristic
60C2×#14519763C2214yes—
61C2×#14519760C2212yes—
62C2×#14519759C2214yes—
63C2×#14519757C2214yes—
64C2×#14519757C2212yes—
65C2×#14519757C2212yes—
66C2×#14519756C2211yescharacteristic
67C2×#14519756C2211yescharacteristic
68C2×#14519756C2211yescharacteristic
69C2×#14519756C2212yes—
70C2×#14519755C2214yes—
71C2×#14519753C2214yes—
72C2×#14519751C2211yescharacteristic
73C2×Q8×Dic61C2212yes—
74C2×Q8×Dic61C2212yes—
75C2×C4×Dic122C2211yescharacteristic
76C2×C4×Dic122C2211yescharacteristic
77C2×C4×Dic122C2214yes—
78C2×C4×Dic122C2212yes—
79C2×C4×Dic122C2211yescharacteristic
80C2×#14519742C2212yes—
81C2×#14519742C2212yes—
82C2×#14519742C2212yes—
83C2×C4×D244C2211yescharacteristic
84C2×#14519739C2212yes—
85C2×C4×C22⋊D61C2212yes—
86C2×#14519736C2212yes—
87C2×#14519735C2212yes—
88C2×#14519734C2212yes—
89C2×#14519734C2214yes—
90C2×C4⋊C4×D61C2212yes—
91C61×#533C22116yescomplemented
92C2×C4⋊Q8×C61C2211yescharacteristic
93C2×C4⋊Q8×C61C2211yescharacteristic
94C2×#125×C61C2212yes—
95C2×C22⋊Q8×C61C2212yes—
96C2×C22⋊Q8×C61C2212yes—
97C2×C4×Q8×C61C2212yes—
98C2×C4×Q8×C61C2212yes—
99C2×#117×C61C2212yes—
100C22×C42×C61C2211yescharacteristic
101C22×Dic122C2311yescharacteristic
102C22×Dic122C2311yescharacteristic
103C22×Dic122C2311yescharacteristic
104C22×Dic122C2312yes—
105C22×Dic122C2314yes—
106C22×D244C2311yescharacteristic
107C22×C22⋊D61C2312yes—
108C22×C4×D61C2312yes—
109C22×C4×D61C2314yes—
110#14519777C2318yes—
111#14519777C2318yes—
112#14519776C23116yes—
113#14519776C23116yes—
114#14519776C23132yes—
115#14519775C23116yes—
116#14519775C23132yes—
117#14519772C23132yes—
118#14519772C23132yes—
119#14519772C23132yes—
120#14519771C23132yes—
121#14519771C23116yes—
122#14519770C23132yes—
123#14519770C23132yes—
124#14519769C23132yes—
125#14519769C2318yes—
126#14519769C23116yes—
127#14519768C23116yes—
128#14519768C23116yes—
129#14519768C23132yes—
130#14519768C23132yes—
131#14519767C23132yes—
132#14519767C23132yes—
133#14519766C23116yes—
134#14519765C2318yes—
135#14519763C23132yes—
136#14519760C23116yes—
137#14519759C23132yes—
138#14519757C23116yes—
139#14519757C23116yes—
140#14519757C23132yes—
141#14519756C2318yes—
142#14519756C2318yes—
143#14519756C23116yes—
144#14519756C2318yes—
145#14519755C23132yes—
146#14519753C23132yes—
147#14519751C2318yes—
148Q8×Dic61C23116yes—
149Q8×Dic61C23116yes—
150C4×Dic122C2318yes—
151C4×Dic122C23132yes—
152C4×Dic122C23116yes—
153C4×Dic122C2318yes—
154C4×Dic122C2318yes—
155#14519742C23116yes—
156#14519742C23116yes—
157#14519742C23116yes—
158C4×D244C2318yes—
159#14519739C23116yes—
160C4×C22⋊D61C23116yes—
161#14519736C23116yes—
162#14519735C23116yes—
163#14519734C23132yes—
164#14519734C23116yes—
165C2×C4⋊Dic61C2311yescharacteristic
166C2×C4⋊Dic61C2311yescharacteristic
167C2×C4⋊Dic61C2312yes—
168C2×C4⋊Dic61C2312yes—
169C2×C4⋊Dic61C2311yescharacteristic
170C2×C4⋊Dic61C2311yescharacteristic
171C2×C4⋊Dic61C2314yes—
172C2×C4⋊Dic61C2312yes—
173C2×C4⋊Dic61C2314yes—
174C2×C4⋊Dic61C2314yes—
175C2×#11758196C2314yes—
176C2×#11758196C2312yes—
177C2×#11758196C2314yes—
178C2×#11758196C2312yes—
179C2×#11758196C2312yes—
180C2×#11758196C2312yes—
181C2×#11758196C2314yes—
182C2×#11758196C2314yes—
183C2×#11758196C2314yes—
184C2×#11758196C2312yes—
185C2×#11758196C2312yes—
186C2×#11758196C2312yes—
187C2×#11758196C2312yes—
188C4⋊C4×D61C23116yes—
189C2×C22⋊Dic61C2312yes—
190C2×C22⋊Dic61C2312yes—
191C2×C22⋊Dic61C2312yes—
192C2×#11758198C2312yes—
193C2×#11758198C2312yes—
194C2×#11758198C2312yes—
195C2×#11758198C2314yes—
196C2×#11758198C2314yes—
197C2×#11758198C2314yes—
198C2×#11758198C2312yes—
199C2×C4×Dic61C2312yes—
200C2×C4×Dic61C2314yes—
201C2×C4×Dic61C2314yes—
202C2×C4×Dic61C2312yes—
203C2×C4×Dic61C2312yes—
204C2×C4×Dic61C2314yes—
205C22×Q8×C61C2312yes—
206C22×Q8×C61C2312yes—
207C23×C4×C61C2311yescharacteristic
208C23×C4×C61C2311yescharacteristic
209C23×C4×C61C2311yescharacteristic
210C4⋊Q8×C61C2318yes—
211C4⋊Q8×C61C2318yes—
212#125×C61C23116yes—
213C22⋊Q8×C61C23116yes—
214C22⋊Q8×C61C23116yes—
215C4×Q8×C61C23116yes—
216C4×Q8×C61C23116yes—
217#117×C61C23116yes—
218C2×C4⋊C4×C61C2312yes—
219C2×C4⋊C4×C61C2312yes—
220C2×C4⋊C4×C61C2312yes—
221C2×C4⋊C4×C61C2312yes—
222C2×C4⋊C4×C61C2314yes—
223C2×C4⋊C4×C61C2314yes—
224C2×C22⋊C4×C61C2314yes—
225C2×C42×C61C2311yescharacteristic
226C2×C42×C61C2318yes—
227C2×C42×C61C2311yescharacteristic
228C2×C42×C61C2314yes—
229C2×C42×C61C2311yescharacteristic
230C2×C42×C61C2311yescharacteristic
231C24×C61C2411yescharacteristic
232C23×D61C2412yes—
233C2×Q8×C61—28no—
234C2×Q8×C61—44no—
235C2×Q8×C61C2418yes—
236C2×Q8×C61C2418yes—
237C22×C4×C61—24no—
238C22×C4×C61—24no—
239C22×C4×C61—42no—
240C22×C4×C61C2414yes—
241C22×C4×C61C2411yescharacteristic
242C22×C4×C61C2411yescharacteristic
243C22×C4×C61C2411yescharacteristic
244C22×C4×C61C2411yescharacteristic
245C22×C4×C61C2414yes—
246C22×C4×C61C2414yes—
247C22×C4×C61C2414yes—
248C22×C4×C61C2414yes—
249C22×C4×C61C2411yescharacteristic
250C22×C4×C61C2411yescharacteristic
251C2×C22⋊D61—44no—
252C2×C22⋊D61C2418yes—
253C22×Dic61C2412yes—
254C22×Dic61C2412yes—
255C22×Dic61C2412yes—
256C22×Dic61C2412yes—
257C22×Dic61C2412yes—
258C22×Dic61C2412yes—
259C22×Dic61C2412yes—
260C2×D244—24no—
261C2×D244C2414yes—
262C2×C4×D61—28no—
263C2×C4×D61—48no—
264C2×C4×D61C2418yes—
265C2×C4×D61C24116yes—
266C2×Dic122—24no—
267C2×Dic122—24no—
268C2×Dic122—24no—
269C2×Dic122—48no—
270C2×Dic122—44no—
271C2×Dic122C2414yes—
272C2×Dic122C2414yes—
273C2×Dic122C2414yes—
274C2×Dic122C2418yes—
275C2×Dic122C24116yes—
276C4⋊C4×C61C2418yes—
277C4⋊C4×C61C2418yes—
278C4⋊C4×C61C24116yes—
279C4⋊C4×C61C24116yes—
280C4⋊C4×C61C2418yes—
281C4⋊C4×C61C2418yes—
282C22⋊C4×C61C24116yes—
283C42×C61C2414yes—
284C42×C61C2414yes—
285C42×C61C2414yes—
286C42×C61C2414yes—
287C42×C61C24116yes—
288C22⋊Dic61C2418yes—
289C22⋊Dic61C2418yes—
290C22⋊Dic61C2418yes—
291#11758198C2418yes—
292#11758198C2418yes—
293#11758198C2418yes—
294#11758198C24116yes—
295#11758198C24116yes—
296#11758198C24116yes—
297#11758198C2418yes—
298C4⋊Dic61C2414yes—
299C4⋊Dic61C2414yes—
300C4⋊Dic61C2418yes—
301C4⋊Dic61C2418yes—
302C4⋊Dic61C2414yes—
303C4⋊Dic61C2414yes—
304C4⋊Dic61C24116yes—
305C4⋊Dic61C2418yes—
306C4⋊Dic61C24116yes—
307C4⋊Dic61C24116yes—
308#11758196C24116yes—
309#11758196C2418yes—
310#11758196C24116yes—
311#11758196C2418yes—
312#11758196C2418yes—
313#11758196C2418yes—
314#11758196C24116yes—
315#11758196C24116yes—
316#11758196C24116yes—
317#11758196C2418yes—
318#11758196C2418yes—
319#11758196C2418yes—
320#11758196C2418yes—
321C4×Dic61C2418yes—
322C4×Dic61C24116yes—
323C4×Dic61C24116yes—
324C4×Dic61C2418yes—
325C4×Dic61C2418yes—
326C4×Dic61C24116yes—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61C2512yes—
331C23×C61C2511yescharacteristic
332C22×D61—24no—
333C22×D61—24no—
334C22×D61—24no—
335C22×D61C2514yes—
336Q8×C61—216no—
337Q8×C61—48no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—28no—
341C2×C4×C61—22no—
342C2×C4×C61—28no—
343C2×C4×C61—22no—
344C2×C4×C61—28no—
345C2×C4×C61—28no—
346C2×C4×C61—44no—
347C2×C4×C612−1+414yes—
348C2×C4×C612−1+414yes—
349C2×C4×C61C2518yes—
350C2×C4×C61C2518yes—
351C2×C4×C61C2512yes—
352C2×C4×C61C2512yes—
353C2×C4×C61C2512yes—
354C2×C4×C61C2512yes—
355C2×C4×C61C2512yes—
356C2×C4×C61C2512yes—
357C22⋊D61—48no—
358C2×Dic61—24no—
359C2×Dic61—24no—
360C2×Dic61—24no—
361C2×Dic61—24no—
362C2×Dic61—24no—
363C2×Dic61—24no—
364C2×Dic61—24no—
365C2×Dic61C2514yes—
366C2×Dic61C2514yes—
367C2×Dic61C2514yes—
368C2×Dic61C2514yes—
369C2×Dic61C2514yes—
370C2×Dic61C2514yes—
371C2×Dic61C2514yes—
372D244—28no—
373C4×D61—216no—
374C4×D61—416no—
375Dic122—28no—
376Dic122—28no—
377Dic122—28no—
378Dic122—416no—
379Dic122—48no—
380C2×#3555—611nomaximal, Sylow
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—44no—
385C22×C61C2×2−1+412yes—
386C22×C61C2×2−1+412yes—
387C22×C61#58512yes—
388C22×C61C2611yescharacteristic
389C2×D61—24no—
390C2×D61—24no—
391C2×D61—24no—
392C2×D61—48no—
393C4×C61—22no—
394C4×C61—22no—
395C4×C61—28no—
396C4×C61—22no—
397C4×C61—28no—
398C4×C61—22no—
399C4×C61C2×2−1+414yes—
400C4×C61C2×2−1+414yes—
401Dic61—24no—
402Dic61—24no—
403Dic61—24no—
404Dic61—24no—
405Dic61—24no—
406Dic61—24no—
407Dic61—24no—
408#3555—6132no—
409C2×#563—614no—
410C2×Q82—611no—
411C2×#557—611no—
412C2×#557—612no—
413C2×#556—611no—
414C2×#556—612no—
415C2×#556—612no—
416C2×#554—611no—
417C2×#552—612no—
418C2×#544—612no—
419C2×#542—612no—
420C2×#541—612no—
421C2×#541—612no—
422C2×#541—614no—
423C2×#533—611no—
424C2×#533D6111yescharacteristic, complemented
425C2×#529—611no—
426C2×C61—42no—
427C2×C61#355514yescomplemented
428C2×C61C22×2−1+411yescharacteristic
429C2×C61C22×2−1+411yescharacteristic
430C2×C61C2×#58511yescharacteristic
431D61—44no—
432#563—6164no—
433Q82—6116no—
434#557—6116no—
435#557—6132no—
436#556—6116no—
437#556—6132no—
438#556—6132no—
439#554—6116no—
440#552—6132no—
441#544—6132no—
442#542—6132no—
443#541—6132no—
444#541—6132no—
445#541—6164no—
446#533—6116no—
447#533C2×D61116yescomplemented
448C2×C4⋊Q8—612no—
449C2×C4⋊Q8—614no—
450C2×C4⋊Q8—612no—
451C2×C4⋊Q8—612no—
452C2×C4⋊Q8—614no—
453C2×C4⋊Q8—611no—
454C2×C4⋊Q8—611no—
455C2×C4⋊Q8C2×D6111yescharacteristic
456C2×C4⋊Q8C2×D6111yescharacteristic
457#529—6116no—
458C2×#126—614no—
459C2×#126—614no—
460C2×#126—614no—
461C2×#126—614no—
462C2×#126—614no—
463C2×#126—612no—
464C2×#126—614no—
465C2×#125—614no—
466C2×#125—614no—
467C2×#125—614no—
468C2×#125—612no—
469C2×#125—614no—
470C2×#125—612no—
471C2×#125—611no—
472C2×#125—612no—
473C2×#125—614no—
474C2×#125C2×D6112yes—
475C2×#124—612no—
476C2×#124—614no—
477C2×#124—611no—
478C2×#123—612no—
479C2×#123—614no—
480C2×C22⋊Q8—614no—
481C2×C22⋊Q8—611no—
482C2×C22⋊Q8—611no—
483C2×C22⋊Q8—611no—
484C2×C22⋊Q8—612no—
485C2×C22⋊Q8—614no—
486C2×C22⋊Q8—614no—
487C2×C22⋊Q8—612no—
488C2×C22⋊Q8—612no—
489C2×C22⋊Q8C2×D6112yes—
490C2×C22⋊Q8C2×D6112yes—
491C2×#121—611no—
492C2×C4×Q8—612no—
493C2×C4×Q8—612no—
494C2×C4×Q8—612no—
495C2×C4×Q8—612no—
496C2×C4×Q8—612no—
497C2×C4×Q8—611no—
498C2×C4×Q8—611no—
499C2×C4×Q8—612no—
500C2×C4×Q8—611no—
501C2×C4×Q8—614no—
502C2×C4×Q8C2×D6112yes—
503C2×C4×Q8C2×D6112yes—
504C2×C4×D4—612no—
505C2×C4×D4—612no—
506C2×C4×D4—611no—
507C2×#117—612no—
508C2×#117—612no—
509C2×#117—612no—
510C2×#117—614no—
511C2×#117C2×D6112yes—
512C22×C4⋊C4—612no—
513C22×C42C2×D6111yescharacteristic
514C61C2×#355511yescharacteristic, complemented, Sylow
515C22×Q8—611no—
516C22×Q8—611no—
517C22×Q8—611no—
518C22×Q8—612no—
519C22×Q8—614no—
520C22×Q8C22×D6112yes—
521C22×Q8C22×D6112yes—
522C22×D4—612no—
523C22×D4—611no—
524C23×C4—612no—
525C23×C4—614no—
526C23×C4C22×D6111yescharacteristic
527C23×C4C22×D6111yescharacteristic
528C23×C4C22×D6111yescharacteristic
529C4⋊Q8—6116no—
530C4⋊Q8—6132no—
531C4⋊Q8—6116no—
532C4⋊Q8—6116no—
533C4⋊Q8—6132no—
534C4⋊Q8—618no—
535C4⋊Q8—618no—
536C4⋊Q8C22×D6118yes—
537C4⋊Q8C22×D6118yes—
538#126—6132no—
539#126—6132no—
540#126—6132no—
541#126—6132no—
542#126—6132no—
543#126—6116no—
544#126—6132no—
545#125—6132no—
546#125—6132no—
547#125—6116no—
548#125—6132no—
549#125—6132no—
550#125—6116no—
551#125—618no—
552#125—6116no—
553#125—6132no—
554#125C22×D61116yes—
555#124—6116no—
556#124—6132no—
557#124—618no—
558#123—6116no—
559#123—6132no—
560C22⋊Q8—6132no—
561C22⋊Q8—618no—
562C22⋊Q8—618no—
563C22⋊Q8—618no—
564C22⋊Q8—6116no—
565C22⋊Q8—6132no—
566C22⋊Q8—6116no—
567C22⋊Q8—6116no—
568C22⋊Q8—6132no—
569C22⋊Q8C22×D61116yes—
570C22⋊Q8C22×D61116yes—
571#121—618no—
572C4×Q8—6116no—
573C4×Q8—6116no—
574C4×Q8—6116no—
575C4×Q8—6116no—
576C4×Q8—6116no—
577C4×Q8—618no—
578C4×Q8—618no—
579C4×Q8—6116no—
580C4×Q8—618no—
581C4×Q8—6132no—
582C4×Q8C22×D61116yes—
583C4×Q8C22×D61116yes—
584C4×D4—6116no—
585C4×D4—6116no—
586C4×D4—618no—
587#117—6116no—
588#117—6116no—
589#117—6116no—
590#117—6132no—
591#117C22×D61116yes—
592C2×C4⋊C4—611no—
593C2×C4⋊C4—614no—
594C2×C4⋊C4—612no—
595C2×C4⋊C4—611no—
596C2×C4⋊C4—612no—
597C2×C4⋊C4—612no—
598C2×C4⋊C4—614no—
599C2×C4⋊C4—612no—
600C2×C4⋊C4—612no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—612no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—612no—
605C2×C4⋊C4—612no—
606C2×C4⋊C4—614no—
607C2×C4⋊C4—614no—
608C2×C4⋊C4—614no—
609C2×C4⋊C4—612no—
610C2×C4⋊C4—614no—
611C2×C4⋊C4—612no—
612C2×C4⋊C4—614no—
613C2×C4⋊C4—612no—
614C2×C4⋊C4—614no—
615C2×C4⋊C4—6116no—
616C2×C4⋊C4C22×D6112yes—
617C2×C4⋊C4C22×D6112yes—
618C2×C4⋊C4C22×D6112yes—
619C2×C4⋊C4C22×D6114yes—
620C2×C4⋊C4C22×D6114yes—
621C2×C4⋊C4C22×D6112yes—
622C2×C22⋊C4—612no—
623C2×C22⋊C4—612no—
624C2×C22⋊C4—612no—
625C2×C22⋊C4—612no—
626C2×C22⋊C4—612no—
627C2×C22⋊C4—612no—
628C2×C22⋊C4—614no—
629C2×C22⋊C4—614no—
630C2×C22⋊C4—612no—
631C2×C22⋊C4—614no—
632C2×C22⋊C4C22×D6114yes—
633C2×C42—612no—
634C2×C42—612no—
635C2×C42—612no—
636C2×C42—614no—
637C2×C42—614no—
638C2×C42—614no—
639C2×C42C22×D6111yescharacteristic
640C2×C42C22×D6114yes—
641C2×C42C22×D6111yescharacteristic
642C2×C42C22×D6111yescharacteristic
643C2×C42C22×D6111yescharacteristic
644C2×C42C22×D6118yes—
645C24—612no—
646C24C23×D6111yescharacteristic
647C2×Q8—28no—
648C2×Q8—44no—
649C2×Q8—614no—
650C2×Q8—614no—
651C2×Q8—614no—
652C2×Q8—618no—
653C2×Q8—6116no—
654C2×Q8—1224no—
655C2×Q8—1224no—
656C2×Q8—1224no—
657C2×Q8—2444no—
658C2×Q8—2448no—
659C2×Q8C23×D6118yes—
660C2×Q8C23×D6118yes—
661C2×D4—618no—
662C2×D4—614no—
663C2×D4—1224no—
664C2×D4—2444no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—42no—
668C22×C4—612no—
669C22×C4—612no—
670C22×C4—612no—
671C22×C4—612no—
672C22×C4—612no—
673C22×C4—612no—
674C22×C4—612no—
675C22×C4—618no—
676C22×C4—6116no—
677C22×C4—1228no—
678C22×C4—2448no—
679C22×C4C23×D6114yes—
680C22×C4C23×D6114yes—
681C22×C4C23×D6114yes—
682C22×C4C23×D6114yes—
683C22×C4C23×D6111yescharacteristic
684C22×C4C23×D6111yescharacteristic
685C22×C4C23×D6111yescharacteristic
686C22×C4C23×D6111yescharacteristic
687C22×C4C23×D6114yes—
688C22×C4C23×D6111yescharacteristic
689C22×C4C23×D6111yescharacteristic
690C4⋊C4—614no—
691C4⋊C4—6116no—
692C4⋊C4—618no—
693C4⋊C4—618no—
694C4⋊C4—6116no—
695C4⋊C4—618no—
696C4⋊C4—618no—
697C4⋊C4—618no—
698C4⋊C4—618no—
699C4⋊C4—6116no—
700C4⋊C4—618no—
701C4⋊C4—6116no—
702C4⋊C4—618no—
703C4⋊C4—6116no—
704C4⋊C4—614no—
705C4⋊C4—618no—
706C4⋊C4—618no—
707C4⋊C4—614no—
708C4⋊C4—614no—
709C4⋊C4—6116no—
710C4⋊C4—6116no—
711C4⋊C4—6116no—
712C4⋊C4—618no—
713C4⋊C4C23×D6118yes—
714C4⋊C4C23×D6118yes—
715C4⋊C4C23×D6118yes—
716C4⋊C4C23×D61116yes—
717C4⋊C4C23×D61116yes—
718C4⋊C4C23×D6118yes—
719C22⋊C4—618no—
720C22⋊C4—618no—
721C22⋊C4—618no—
722C22⋊C4—618no—
723C22⋊C4—618no—
724C22⋊C4—618no—
725C22⋊C4—6116no—
726C22⋊C4—6116no—
727C22⋊C4—618no—
728C22⋊C4—6116no—
729C22⋊C4C23×D61116yes—
730C42—618no—
731C42—618no—
732C42—618no—
733C42—6116no—
734C42—6116no—
735C42—6116no—
736C42C23×D6114yes—
737C42C23×D6114yes—
738C42C23×D6114yes—
739C42C23×D6114yes—
740C42C23×D61116yes—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—614no—
745C23—1224no—
746C23—1224no—
747C23—1224no—
748C23C24×D6112yes—
749C23C24×D6111yescharacteristic
750Q8—216no—
751Q8—48no—
752Q8—1228no—
753Q8—1228no—
754Q8—1228no—
755Q8—2448no—
756Q8—24416no—
757D4—1228no—
758D4—2448no—
759C2×C4—22no—
760C2×C4—28no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—44no—
768C2×C4—614no—
769C2×C4—614no—
770C2×C4—614no—
771C2×C4—614no—
772C2×C4—614no—
773C2×C4—614no—
774C2×C4—614no—
775C2×C4—1224no—
776C2×C4—1224no—
777C2×C4—1224no—
778C2×C4—1224no—
779C2×C4—1224no—
780C2×C4—1224no—
781C2×C4—1224no—
782C2×C4—12216no—
783C2×C4—24416no—
784C2×C4#1451982414yes—
785C2×C4#1451982514yes—
786C2×C4C24×D6118yes—
787C2×C4C24×D6118yes—
788C2×C4C24×D6112yes—
789C2×C4C24×D6112yes—
790C2×C4C24×D6112yes—
791C2×C4C24×D6112yes—
792C2×C4C24×D6112yes—
793C2×C4C24×D6112yes—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—1224no—
799C22—1224no—
800C22—1224no—
801C22—2448no—
802C22C2×#1451982412yes—
803C22C2×#1451982512yes—
804C22#1684059812yes—
805C22C25×D6111yescharacteristic
806C4—22no—
807C4—28no—
808C4—22no—
809C4—22no—
810C4—22no—
811C4—28no—
812C4—1224no—
813C4—1224no—
814C4—1224no—
815C4—1224no—
816C4—1224no—
817C4—1224no—
818C4—1224no—
819C4C2×#1451982414yes—
820C4C2×#1451982514yes—
821C2—42no—
822C2—2444no—
823C2#2146030114yesdirect product factor
824C2C22×#1451982411yescharacteristic
825C2C22×#1451982511yescharacteristic
826C2C2×#1684059811yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#533C2
socleC23×C61C25
prime radicalC2×#14519751C22
hypercenterC2×#533D61
hypocenterC61C2×#3555
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #21460301C2direct (N × H)
2. C2×#16840513C2semidirect
3. C2×#16840492C2semidirect
4. C2×#16840488C2semidirect
5. C2×#16840487C2semidirect
6. C2×#16840486C2semidirect
7. C2×#16840484C2semidirect
8. C2×#16840480C2semidirect
9. C2×#16840473C2semidirect
10. C2×#16840451C2semidirect
11. C2×#16840392C2semidirect
13. C2×#16840375C2semidirect
14. C2×#16840372C2semidirect
15. C2×#16840370C2semidirect
16. C2×#16840319C2semidirect
18. C2×C61×#533C2semidirect
19. #16840513C22semidirect
20. #16840492C22semidirect
21. #16840488C22semidirect
22. #16840487C22semidirect
23. #16840486C22semidirect
24. #16840484C22semidirect
25. #16840480C22semidirect
26. #16840473C22semidirect
27. #16840451C22semidirect
28. #16840392C22semidirect
30. #16840375C22semidirect
31. #16840372C22semidirect
32. #16840370C22semidirect
33. #16840319C22semidirect
91. C61×#533C22semidirect
424. C2×#533D61semidirect
427. C2×C61#3555semidirect
447. #533C2×D61semidirect
514. C61C2×#3555semidirect
823. C2#21460301direct (N × H)

Maximal subgroups

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

subgroupindex
#214603012
C2×#168405132
C2×#168404922
C2×#168404882
C2×#168404872
C2×#168404862
C2×#168404842
C2×#168404802
C2×#168404732
C2×#168404512
C2×#168403922
C2×#168403852
C2×#168403752
C2×#168403722
C2×#168403702
C2×#168403192
C2×#168402962
C2×C61×#5332
C2×#355561