Finite Group Databasebeta

← C2×#21459702 #30588452

Subgroups — C2×#21459702 #30588452

Order 15616.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459702C2132yesmaximal, direct product factor
2C2×#16840490C211yesmaximal, characteristic, complemented
3C2×#16840487C212yesmaximal, complemented
4C2×#16840486C211yesmaximal, characteristic, complemented
5C2×#16840485C211yesmaximal, characteristic, complemented
6C2×#16840484C212yesmaximal, complemented
7C2×#16840453C212yesmaximal, complemented
8C2×#16840450C212yesmaximal, complemented
9C2×#16840444C214yesmaximal, complemented
10C2×#16840371C214yesmaximal, complemented
11C2×#16840337C212yesmaximal
12C2×#16840318C212yesmaximal, complemented
13C2×#16840316C211yesmaximal, characteristic, complemented
14C2×#16840316C212yesmaximal, complemented
15C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
16C2×#16840238C212yesmaximal, complemented
17C2×C4×#11758226C211yesmaximal, characteristic
18C2×C61×#557C211yesmaximal, characteristic, complemented
19C22×#11758226C2211yescharacteristic
20C22×Q8×D61C2212yes—
21#16840490C22116yescomplemented
22#16840487C22132yescomplemented
23#16840486C22116yescomplemented
24#16840485C22116yescomplemented
25#16840484C22132yescomplemented
26#16840453C22132yescomplemented
27#16840450C22132yescomplemented
28#16840444C22164yescomplemented
29#16840371C22164yescomplemented
30#16840337C22132yes—
31#16840318C22132yescomplemented
32#16840316C22132yescomplemented
33#16840316C22116yescomplemented
34C2×#14519777C2211yescharacteristic
35C2×#14519776C2212yes—
36C2×#14519776C2212yes—
37C2×#14519776C2211yescharacteristic
38C2×#14519775C2212yes—
39C2×#14519775C2211yescharacteristic
40C2×#14519775C2212yes—
41C4⋊Q8×D61C22116yescomplemented
42C2×#14519772C2214yes—
43C2×#14519772C2214yes—
44C2×#14519772C2214yes—
45C2×#14519771C2214yes—
46C2×#14519769C2212yes—
47C2×#14519768C2214yes—
48C2×#14519767C2214yes—
49C2×#14519767C2214yes—
50C2×#14519767C2214yes—
51C2×#14519767C2212yes—
52C2×#14519766C2212yes—
53C2×#14519765C2212yes—
54C2×#14519762C2214yes—
55C2×#14519762C2214yes—
56C2×#14519757C2211yescharacteristic
57C2×#14519757C2212yes—
58C2×#14519755C2212yes—
59C2×#14519755C2214yes—
60C2×#14519755C2214yes—
61C2×#14519755C2214yes—
62C2×#14519753C2211yescharacteristic
63C2×#14519753C2212yes—
64#16840238C22132yescomplemented
65C4×#11758226C22116yes—
66C2×Q8×Dic61C2211yescharacteristic
67C2×Q8×Dic61C2212yes—
68C2×C4×Dic122C2214yes—
69C2×C4×Dic122C2212yes—
70C2×C4×Dic122C2212yes—
71C2×C4×Dic122C2212yes—
72C2×C4×Dic122C2211yescharacteristic
73C2×#14519742C2214yes—
74C2×#14519742C2212yes—
75C2×#14519742C2214yes—
76C2×C4×D244C2212yes—
77C2×C4×D244C2211yescharacteristic
78C2×#14519739C2212yes—
79C2×#14519739C2211yescharacteristic
80C2×#14519735C2211yescharacteristic
81C2×#14519735C2212yes—
82C2×#14519735C2214yes—
83C2×#14519735C2212yes—
84C2×#14519735C2212yes—
85C2×#14519734C2214yes—
86C2×#14519734C2212yes—
87C2×#14519734C2214yes—
88C2×C4⋊C4×D61C2212yes—
89C2×C4⋊C4×D61C2212yes—
90C2×C42×D61C2211yescharacteristic
91C2×C42×D61C2212yes—
92C61×#557C22116yescomplemented
93C2×C4⋊Q8×C61C2211yescharacteristic
94C2×C4⋊Q8×C61C2212yes—
95C2×#125×C61C2214yes—
96C2×#125×C61C2212yes—
97C2×C4×Q8×C61C2211yescharacteristic
98C2×C4×Q8×C61C2212yes—
99C2×C4×Q8×C61C2212yes—
100C2×C4×Q8×C61C2211yescharacteristic
101C2×#11758226—28no—
102C2×#11758226C2318yes—
103C22×Dic122C2312yes—
104C22×Dic122C2314yes—
105C22×Dic122C2312yes—
106C22×Dic122C2311yescharacteristic
107C2×Q8×D61—216no—
108C2×Q8×D61C23116yes—
109C22×D244C2312yes—
110C22×D244C2311yescharacteristic
111C22×C4×D61C2311yescharacteristic
112C22×C4×D61C2311yescharacteristic
113C22×C4×D61C2312yes—
114C22×C4×D61C2312yes—
115C22×C4×D61C2312yes—
116C22×C4×D61C2314yes—
117C22×C4×D61C2311yescharacteristic
118#14519777C2318yes—
119#14519776C23116yes—
120#14519776C23116yes—
121#14519776C2318yes—
122#14519775C23116yes—
123#14519775C23116yes—
124#14519775C2318yes—
125#14519772C23132yes—
126#14519772C23132yes—
127#14519772C23132yes—
128#14519771C23132yes—
129#14519769C23116yes—
130#14519768C23132yes—
131#14519767C23132yes—
132#14519767C23132yes—
133#14519767C23132yes—
134#14519767C23116yes—
135#14519766C23116yes—
136#14519765C23116yes—
137#14519762C23132yes—
138#14519762C23132yes—
139#14519757C2318yes—
140#14519757C23116yes—
141#14519755C23132yes—
142#14519755C23132yes—
143#14519755C23116yes—
144#14519755C23132yes—
145#14519753C2318yes—
146#14519753C23116yes—
147Q8×Dic61C23116yes—
148Q8×Dic61C2318yes—
149C4×Dic122C23116yes—
150C4×Dic122C23116yes—
151C4×Dic122C23116yes—
152C4×Dic122C2318yes—
153C4×Dic122C23132yes—
154#14519742C23116yes—
155#14519742C23132yes—
156#14519742C23132yes—
157C4×D244C23116yes—
158C4×D244C2318yes—
159#14519739C2318yes—
160#14519739C23116yes—
161#14519735C23116yes—
162#14519735C23132yes—
163#14519735C23116yes—
164#14519735C2318yes—
165#14519735C23116yes—
166#14519734C23132yes—
167#14519734C23132yes—
168#14519734C23116yes—
169C2×C4⋊Dic61C2312yes—
170C2×C4⋊Dic61C2312yes—
171C2×C4⋊Dic61C2311yescharacteristic
172C2×C4⋊Dic61C2311yescharacteristic
173C2×C4⋊Dic61C2312yes—
174C2×C4⋊Dic61C2314yes—
175C2×C4⋊Dic61C2312yes—
176C2×#11758196C2314yes—
177C2×#11758196C2314yes—
178C2×#11758196C2312yes—
179C2×#11758196C2312yes—
180C2×#11758196C2314yes—
181C2×#11758196C2314yes—
182C2×#11758196C2312yes—
183C2×#11758196C2314yes—
184C2×#11758196C2312yes—
185C2×#11758196C2314yes—
186C2×#11758196C2312yes—
187C4⋊C4×D61C23116yes—
188C4⋊C4×D61C23116yes—
189C2×#11758198C2312yes—
190C2×#11758198C2312yes—
191C2×#11758198C2312yes—
192C2×#11758198C2314yes—
193C2×#11758198C2314yes—
194C2×#11758198C2312yes—
195C2×#11758198C2312yes—
196C2×#11758198C2314yes—
197C2×#11758198C2314yes—
198C2×C4×Dic61C2311yescharacteristic
199C2×C4×Dic61C2312yes—
200C2×C4×Dic61C2311yescharacteristic
201C2×C4×Dic61C2312yes—
202C2×C4×Dic61C2311yescharacteristic
203C2×C4×Dic61C2314yes—
204C2×C4×Dic61C2314yes—
205C2×C4×Dic61C2312yes—
206C2×C4×Dic61C2314yes—
207C42×D61C2318yes—
208C42×D61C23116yes—
209C22×Q8×C61C2312yes—
210C22×Q8×C61C2311yescharacteristic
211C22×Q8×C61C2311yescharacteristic
212C4⋊Q8×C61C2318yes—
213C4⋊Q8×C61C23116yes—
214#125×C61C23116yes—
215#125×C61C23132yes—
216C4×Q8×C61C23116yes—
217C4×Q8×C61C23116yes—
218C4×Q8×C61C2318yes—
219C4×Q8×C61C2318yes—
220C2×C4⋊C4×C61C2312yes—
221C2×C4⋊C4×C61C2312yes—
222C2×C4⋊C4×C61C2314yes—
223C2×C4⋊C4×C61C2314yes—
224C2×C4⋊C4×C61C2311yescharacteristic
225C2×C4⋊C4×C61C2311yescharacteristic
226C2×C4⋊C4×C61C2312yes—
227C2×C4⋊C4×C61C2314yes—
228C2×C4⋊C4×C61C2312yes—
229C2×C42×C61C2311yescharacteristic
230C2×C42×C61C2312yes—
231C2×C42×C61C2312yes—
232C2×C42×C61C2314yes—
233C23×D61C2412yes—
234C23×D61C2411yescharacteristic
235C2×Q8×C61—28no—
236C2×Q8×C61—24no—
237C2×Q8×C61—24no—
238C2×Q8×C61C2418yes—
239C2×Q8×C61C2414yes—
240C2×Q8×C61C2414yes—
241C22×C4×C61C2412yes—
242C22×C4×C61C2414yes—
243C22×C4×C61C2412yes—
244C22×C4×C61C2411yescharacteristic
245C22×C4×C61C2412yes—
246C22×C4×C61C2412yes—
247C22×C4×C61C2411yescharacteristic
248C22×C4×C61C2411yescharacteristic
249C22×Dic61C2414yes—
250C22×Dic61C2412yes—
251C22×Dic61C2411yescharacteristic
252C22×Dic61C2412yes—
253C22×Dic61C2412yes—
254C22×Dic61C2411yescharacteristic
255C22×Dic61C2411yescharacteristic
256#11758226—232no—
257Q8×D61—264no—
258C2×D244—28no—
259C2×D244—24no—
260C2×D244C2418yes—
261C2×D244C2414yes—
262C2×C4×D61—216no—
263C2×C4×D61—24no—
264C2×C4×D61—28no—
265C2×C4×D61—28no—
266C2×C4×D61—24no—
267C2×C4×D61—28no—
268C2×C4×D61#4118yes—
269C2×C4×D61C24116yes—
270C2×C4×D61C2418yes—
271C2×C4×D61C2414yes—
272C2×C4×D61C2414yes—
273C2×C4×D61C2418yes—
274C2×C4×D61C2418yes—
275C2×C4×D61C2414yes—
276C2×Dic122—28no—
277C2×Dic122—24no—
278C2×Dic122—216no—
279C2×Dic122—28no—
280C2×Dic122C24116yes—
281C2×Dic122C2418yes—
282C2×Dic122C2418yes—
283C2×Dic122C2414yes—
284C4⋊C4×C61C2414yes—
285C4⋊C4×C61C2414yes—
286C4⋊C4×C61C2418yes—
287C4⋊C4×C61C24116yes—
288C4⋊C4×C61C2418yes—
289C4⋊C4×C61C2418yes—
290C4⋊C4×C61C24116yes—
291C4⋊C4×C61C2418yes—
292C4⋊C4×C61C24116yes—
293C42×C61C2418yes—
294C42×C61C24116yes—
295C42×C61C2414yes—
296C42×C61C2418yes—
297#11758198C2418yes—
298#11758198C2418yes—
299#11758198C2418yes—
300#11758198C24116yes—
301#11758198C24116yes—
302#11758198C2418yes—
303#11758198C2418yes—
304#11758198C24116yes—
305#11758198C24116yes—
306C4⋊Dic61C2418yes—
307C4⋊Dic61C2418yes—
308C4⋊Dic61C2414yes—
309C4⋊Dic61C2414yes—
310C4⋊Dic61C2418yes—
311C4⋊Dic61C24116yes—
312C4⋊Dic61C2418yes—
313#11758196C24116yes—
314#11758196C24116yes—
315#11758196C2418yes—
316#11758196C2418yes—
317#11758196C24116yes—
318#11758196C24116yes—
319#11758196C2418yes—
320#11758196C24116yes—
321#11758196C2418yes—
322#11758196C24116yes—
323#11758196C2418yes—
324C4×Dic61C2414yes—
325C4×Dic61C2418yes—
326C4×Dic61C2414yes—
327C4×Dic61C2418yes—
328C4×Dic61C2414yes—
329C4×Dic61C24116yes—
330C4×Dic61C24116yes—
331C4×Dic61C2418yes—
332C4×Dic61C24116yes—
333C23×C61C2511yescharacteristic
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—24no—
337C22×D61—24no—
338C22×D61—24no—
339C22×D61C2×#4114yes—
340C22×D61C2514yes—
341C22×D61C2512yes—
342Q8×C61—216no—
343Q8×C61—28no—
344Q8×C61—28no—
345C2×C4×C61—28no—
346C2×C4×C61—24no—
347C2×C4×C61—24no—
348C2×C4×C61—24no—
349C2×C4×C61—22no—
350C2×C4×C61—24no—
351C2×C4×C61C2×#4114yes—
352C2×C4×C612−1+414yes—
353C2×C4×C61C2514yes—
354C2×C4×C61C2514yes—
355C2×C4×C61C2514yes—
356C2×C4×C61C2512yes—
357C2×C4×C61C2518yes—
358C2×C4×C61C2514yes—
359C2×C4×C61C2512yes—
360C2×C4×C61C2512yes—
361C2×Dic61—28no—
362C2×Dic61—24no—
363C2×Dic61—24no—
364C2×Dic61—24no—
365C2×Dic61—22no—
366C2×Dic61C2×#4114yes—
367C2×Dic612−1+414yes—
368C2×Dic61C2514yes—
369C2×Dic61C2514yes—
370C2×Dic61C2514yes—
371C2×Dic61C2512yes—
372C2×Dic61C2518yes—
373C2×Dic61C2512yes—
374C2×Dic61C2512yes—
375D244—216no—
376D244—28no—
377C4×D61—232no—
378C4×D61—28no—
379C4×D61—216no—
380C4×D61—216no—
381C4×D61—28no—
382C4×D61—216no—
383C4×D61C2×#41116yes—
384Dic122—216no—
385Dic122—28no—
386Dic122—232no—
387Dic122—216no—
388C2×#3509—611nomaximal, Sylow
389C22×C61C22×#4112yes—
390C22×C61C2×2−1+412yes—
391C22×C61C2×2−1+412yes—
392C22×C61C2611yescharacteristic
393C2×D61—22no—
394C2×D61—22no—
395C2×D61—28no—
396C2×D61—24no—
397C2×D61—24no—
398C2×D61—24no—
399C2×D61—48no—
400C2×D61C22×#4114yes—
401C4×C61—28no—
402C4×C61—24no—
403C4×C61—24no—
404C4×C61—24no—
405C4×C61—22no—
406C4×C61—24no—
407C4×C61C22×#4114yes—
408C4×C61C2×2−1+414yes—
409Dic61—28no—
410Dic61—24no—
411Dic61—24no—
412Dic61—24no—
413Dic61—22no—
414Dic61C22×#4114yes—
415Dic61C2×2−1+414yes—
416#3509—6132no—
417C2×#557—612no—
418C2×#557—611no—
419C2×#557D6111yescharacteristic, complemented
420C2×#556—611no—
421C2×#556—612no—
422C2×#556—611no—
423C2×#552—614no—
424C2×#552—612no—
425C2×#552—612no—
426C2×#541—614no—
427C2×#536—612no—
428C2×#533—612no—
429C2×#533—611no—
430C2×#533—612no—
431C22×C4⋊Q8—611no—
432C2×#519—612no—
433C2×C4×#41—611no—
434C2×C61#350914yescomplemented
435C2×C61C23×#4111yescharacteristic
436C2×C61C22×2−1+411yescharacteristic
437C2×C61C22×2−1+411yescharacteristic
438D61—24no—
439D61—44no—
440C22×#41—611no—
441C23×Q8—612no—
442#557—6132no—
443#557—6116no—
444#557C2×D61116yescomplemented
445#556—6116no—
446#556—6132no—
447#556—6116no—
448#552—6132no—
449#552—6164no—
450#552—6132no—
451#541—6164no—
452#536—6132no—
453#533—6132no—
454#533—6116no—
455#533—6132no—
456C2×C4⋊Q8—612no—
457C2×C4⋊Q8—611no—
458C2×C4⋊Q8—612no—
459C2×C4⋊Q8—6116no—
460C2×C4⋊Q8—612no—
461C2×C4⋊Q8—612no—
462C2×C4⋊Q8—611no—
463C2×C4⋊Q8—611no—
464C2×C4⋊Q8C2×D6111yescharacteristic
465C2×C4⋊Q8C2×D6112yes—
466C2×#126—614no—
467C2×#126—614no—
468C2×#126—614no—
469C2×#126—614no—
470C2×#125—612no—
471C2×#125—614no—
472C2×#125—614no—
473C2×#125—614no—
474C2×#125—614no—
475C2×#125—612no—
476C2×#125C2×D6112yes—
477C2×#125C2×D6114yes—
478C2×#124—612no—
479C2×#124—612no—
480C2×#123—614no—
481C2×#123—614no—
482C2×C22⋊Q8—611no—
483C2×C22⋊Q8—612no—
484C2×C22⋊Q8—614no—
485C2×C22⋊Q8—614no—
486C2×C22⋊Q8—612no—
487C2×C22⋊Q8—614no—
488C2×C22⋊Q8—611no—
489C2×C22⋊Q8—612no—
490#519—6132no—
491C4×#41—6116no—
492C2×C4×Q8—611no—
493C2×C4×Q8—612no—
494C2×C4×Q8—614no—
495C2×C4×Q8—612no—
496C2×C4×Q8—614no—
497C2×C4×Q8—614no—
498C2×C4×Q8—612no—
499C2×C4×Q8—612no—
500C2×C4×Q8—611no—
501C2×C4×Q8—612no—
502C2×C4×Q8C2×D6111yescharacteristic
503C2×C4×Q8C2×D6112yes—
504C2×C4×Q8C2×D6112yes—
505C2×C4×Q8C2×D6111yescharacteristic
506C2×C4×D4—612no—
507C2×C4×D4—611no—
508C2×C4×D4—612no—
509C2×C4×D4—611no—
510C2×#117—611no—
511C2×#117—612no—
512C2×#117—614no—
513C2×#117—612no—
514C2×#117—612no—
515C2×#117—612no—
516C2×#117—614no—
517C2×#117—614no—
518C22×C4⋊C4—612no—
519C22×C4⋊C4—612no—
520C22×C42—611no—
521C22×C42—612no—
522C61C2×#350911yescharacteristic, complemented, Sylow
523C2×#41—618no—
524C2×#41—1228no—
525C22×Q8—6116no—
526C22×Q8—612no—
527C22×Q8—611no—
528C22×Q8—614no—
529C22×Q8—612no—
530C22×Q8—12216no—
531C22×Q8C22×D6112yes—
532C22×Q8C22×D6111yescharacteristic
533C22×Q8C22×D6111yescharacteristic
534C22×D4—612no—
535C22×D4—611no—
536C23×C4—611no—
537C23×C4—614no—
538C23×C4—611no—
539C23×C4—611no—
540C23×C4—612no—
541C23×C4—612no—
542C23×C4—612no—
543C4⋊Q8—6116no—
544C4⋊Q8—618no—
545C4⋊Q8—6116no—
546C4⋊Q8—6116no—
547C4⋊Q8—6116no—
548C4⋊Q8—618no—
549C4⋊Q8—618no—
550C4⋊Q8C22×D6118yes—
551C4⋊Q8C22×D61116yes—
552#126—6132no—
553#126—6132no—
554#126—6132no—
555#126—6132no—
556#125—6116no—
557#125—6132no—
558#125—6132no—
559#125—6132no—
560#125—6132no—
561#125—6116no—
562#125C22×D61116yes—
563#125C22×D61132yes—
564#124—6116no—
565#124—6116no—
566#123—6132no—
567#123—6132no—
568C22⋊Q8—618no—
569C22⋊Q8—6116no—
570C22⋊Q8—6132no—
571C22⋊Q8—6132no—
572C22⋊Q8—6116no—
573C22⋊Q8—618no—
574C22⋊Q8—6132no—
575C22⋊Q8—6116no—
576C4×Q8—618no—
577C4×Q8—6116no—
578C4×Q8—6132no—
579C4×Q8—6116no—
580C4×Q8—6132no—
581C4×Q8—6132no—
582C4×Q8—6116no—
583C4×Q8—6116no—
584C4×Q8—6116no—
585C4×Q8—618no—
586C4×Q8C22×D6118yes—
587C4×Q8C22×D61116yes—
588C4×Q8C22×D61116yes—
589C4×Q8C22×D6118yes—
590C4×D4—6116no—
591C4×D4—618no—
592C4×D4—6116no—
593C4×D4—618no—
594#117—618no—
595#117—6116no—
596#117—6132no—
597#117—6116no—
598#117—6116no—
599#117—6116no—
600#117—6132no—
601#117—6132no—
602C2×C4⋊C4—614no—
603C2×C4⋊C4—612no—
604C2×C4⋊C4—614no—
605C2×C4⋊C4—612no—
606C2×C4⋊C4—612no—
607C2×C4⋊C4—611no—
608C2×C4⋊C4—611no—
609C2×C4⋊C4—612no—
610C2×C4⋊C4—612no—
611C2×C4⋊C4—612no—
612C2×C4⋊C4—614no—
613C2×C4⋊C4—614no—
614C2×C4⋊C4—614no—
615C2×C4⋊C4—614no—
616C2×C4⋊C4—614no—
617C2×C4⋊C4—612no—
618C2×C4⋊C4—612no—
619C2×C4⋊C4—612no—
620C2×C4⋊C4—6116no—
621C2×C4⋊C4—6116no—
622C2×C4⋊C4C22×D6112yes—
623C2×C4⋊C4C22×D6112yes—
624C2×C4⋊C4C22×D6111yescharacteristic
625C2×C4⋊C4C22×D6111yescharacteristic
626C2×C4⋊C4C22×D6112yes—
627C2×C4⋊C4C22×D6114yes—
628C2×C4⋊C4C22×D6114yes—
629C2×C4⋊C4C22×D6114yes—
630C2×C4⋊C4C22×D6112yes—
631C2×C22⋊C4—612no—
632C2×C22⋊C4—612no—
633C2×C22⋊C4—612no—
634C2×C22⋊C4—612no—
635C2×C22⋊C4—612no—
636C2×C22⋊C4—614no—
637C2×C22⋊C4—614no—
638C2×C22⋊C4—614no—
639C2×C22⋊C4—614no—
640C2×C42—612no—
641C2×C42—614no—
642C2×C42—614no—
643C2×C42—614no—
644C2×C42—611no—
645C2×C42—612no—
646C2×C42—612no—
647C2×C42—611no—
648C2×C42—611no—
649C2×C42—618no—
650C2×C42—6116no—
651C2×C42C22×D6114yes—
652C2×C42C22×D6112yes—
653C2×C42C22×D6112yes—
654C2×C42C22×D6111yescharacteristic
655C24—611no—
656C24—612no—
657#41—12232no—
658C2×Q8—28no—
659C2×Q8—24no—
660C2×Q8—24no—
661C2×Q8—618no—
662C2×Q8—614no—
663C2×Q8—6116no—
664C2×Q8—618no—
665C2×Q8—1228no—
666C2×Q8—12216no—
667C2×Q8—12264no—
668C2×Q8—1228no—
669C2×Q8—1224no—
670C2×Q8C23×D6118yes—
671C2×Q8C23×D6114yes—
672C2×Q8C23×D6114yes—
673C2×D4—618no—
674C2×D4—614no—
675C2×D4—1228no—
676C2×D4—1224no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—618no—
680C22×C4—614no—
681C22×C4—612no—
682C22×C4—612no—
683C22×C4—612no—
684C22×C4—611no—
685C22×C4—614no—
686C22×C4—614no—
687C22×C4—614no—
688C22×C4—618no—
689C22×C4—618no—
690C22×C4—618no—
691C22×C4—6116no—
692C22×C4—1224no—
693C22×C4—1228no—
694C22×C4—1228no—
695C22×C4—12216no—
696C22×C4—1224no—
697C22×C4—1228no—
698C22×C4C23×D6112yes—
699C22×C4C23×D6112yes—
700C22×C4C23×D6111yescharacteristic
701C22×C4C23×D6114yes—
702C22×C4C23×D6112yes—
703C22×C4C23×D6112yes—
704C22×C4C23×D6111yescharacteristic
705C22×C4C23×D6111yescharacteristic
706C4⋊C4—6116no—
707C4⋊C4—6116no—
708C4⋊C4—618no—
709C4⋊C4—618no—
710C4⋊C4—618no—
711C4⋊C4—618no—
712C4⋊C4—618no—
713C4⋊C4—6116no—
714C4⋊C4—6116no—
715C4⋊C4—6116no—
716C4⋊C4—6116no—
717C4⋊C4—618no—
718C4⋊C4—618no—
719C4⋊C4—614no—
720C4⋊C4—614no—
721C4⋊C4—618no—
722C4⋊C4—6116no—
723C4⋊C4—618no—
724C4⋊C4C23×D6118yes—
725C4⋊C4C23×D6118yes—
726C4⋊C4C23×D6114yes—
727C4⋊C4C23×D6114yes—
728C4⋊C4C23×D6118yes—
729C4⋊C4C23×D61116yes—
730C4⋊C4C23×D61116yes—
731C4⋊C4C23×D61116yes—
732C4⋊C4C23×D6118yes—
733C22⋊C4—618no—
734C22⋊C4—618no—
735C22⋊C4—618no—
736C22⋊C4—618no—
737C22⋊C4—618no—
738C22⋊C4—6116no—
739C22⋊C4—6116no—
740C22⋊C4—6116no—
741C22⋊C4—6116no—
742C42—614no—
743C42—618no—
744C42—614no—
745C42—618no—
746C42—614no—
747C42—6116no—
748C42—6116no—
749C42—6116no—
750C42—618no—
751C42C23×D6118yes—
752C42C23×D6114yes—
753C42C23×D61116yes—
754C42C23×D6118yes—
755C23—614no—
756C23—612no—
757C23—614no—
758C23—1222no—
759C23—1222no—
760C23—1224no—
761C23—1224no—
762C23—1224no—
763C23C24×D6111yescharacteristic
764Q8—216no—
765Q8—28no—
766Q8—28no—
767Q8—12216no—
768Q8—12232no—
769Q8—12216no—
770Q8—1228no—
771D4—12216no—
772D4—1228no—
773C2×C4—24no—
774C2×C4—28no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—614no—
780C2×C4—614no—
781C2×C4—612no—
782C2×C4—612no—
783C2×C4—6116no—
784C2×C4—614no—
785C2×C4—614no—
786C2×C4—614no—
787C2×C4—612no—
788C2×C4—618no—
789C2×C4—1228no—
790C2×C4—12216no—
791C2×C4—12216no—
792C2×C4—12232no—
793C2×C4—1228no—
794C2×C4—1224no—
795C2×C4—1224no—
796C2×C4—1222no—
797C2×C4—1224no—
798C2×C4—1228no—
799C2×C4—12216no—
800C2×C4#41×D6114yes—
801C2×C4#1451982514yes—
802C2×C4C24×D6114yes—
803C2×C4C24×D6114yes—
804C2×C4C24×D6112yes—
805C2×C4C24×D6118yes—
806C2×C4C24×D6114yes—
807C2×C4C24×D6114yes—
808C2×C4C24×D6112yes—
809C2×C4C24×D6112yes—
810C22—614no—
811C22—1222no—
812C22—1222no—
813C22—1228no—
814C22—1224no—
815C22—1224no—
816C22—1224no—
817C22—2448no—
818C22C2×#41×D6112yes—
819C222−1+4×D6112yes—
820C22C2×#1451982512yes—
821C22C25×D6111yescharacteristic
822C4—24no—
823C4—28no—
824C4—24no—
825C4—22no—
826C4—24no—
827C4—24no—
828C4—614no—
829C4—614no—
830C4—1228no—
831C4—1224no—
832C4—1224no—
833C4—1222no—
834C4—1224no—
835C4C2×#41×D6114yes—
836C4C2×#1451982514yes—
837C2—1224no—
838C2—2444no—
839C2#2145970214yesdirect product factor
840C2C22×#41×D6111yescharacteristic
841C2C2×2−1+4×D6111yescharacteristic
842C2C22×#1451982511yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#557C2
socleC23×C61C25
prime radicalC22×#11758226C22
hypercenterC2×#557D61
hypocenterC61C2×#3509
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #21459702C2direct (N × H)
2. C2×#16840490C2semidirect
3. C2×#16840487C2semidirect
4. C2×#16840486C2semidirect
5. C2×#16840485C2semidirect
6. C2×#16840484C2semidirect
7. C2×#16840453C2semidirect
8. C2×#16840450C2semidirect
9. C2×#16840444C2semidirect
10. C2×#16840371C2semidirect
12. C2×#16840318C2semidirect
13. C2×#16840316C2semidirect
14. C2×#16840316C2semidirect
15. C2×C4⋊Q8×D61C2semidirect
16. C2×#16840238C2semidirect
18. C2×C61×#557C2semidirect
21. #16840490C22semidirect
22. #16840487C22semidirect
23. #16840486C22semidirect
24. #16840485C22semidirect
25. #16840484C22semidirect
26. #16840453C22semidirect
27. #16840450C22semidirect
28. #16840444C22semidirect
29. #16840371C22semidirect
31. #16840318C22semidirect
32. #16840316C22semidirect
33. #16840316C22semidirect
41. C4⋊Q8×D61C22semidirect
64. #16840238C22semidirect
92. C61×#557C22semidirect
419. C2×#557D61semidirect
434. C2×C61#3509semidirect
444. #557C2×D61semidirect
522. C61C2×#3509semidirect
839. C2#21459702direct (N × H)

Maximal subgroups

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

subgroupindex
#214597022
C2×#168404902
C2×#168404872
C2×#168404862
C2×#168404852
C2×#168404842
C2×#168404532
C2×#168404502
C2×#168404442
C2×#168403712
C2×#168403372
C2×#168403182
C2×#168403162
C2×C4⋊Q8×D612
C2×#168402382
C2×C4×#117582262
C2×C61×#5572
C2×#350961