Finite Group Databasebeta

← C2×#21459436 #30587105

Subgroups — C2×#21459436 #30587105

Order 15616.

7706 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459436C2132yesmaximal, direct product factor
2C2×#16840488C211yesmaximal, characteristic, complemented
3C2×#16840484C213yesmaximal, complemented
4C2×#16840453C213yesmaximal, complemented
5C2×#16840447C213yesmaximal, complemented
6C2×Q8×C22⋊D61C211yesmaximal, characteristic, complemented
7C2×#16840424C211yesmaximal, characteristic, complemented
8C2×#16840423C211yesmaximal, characteristic, complemented
9C2×#16840413C213yesmaximal, complemented
10C2×#16840316C213yesmaximal, complemented
11C2×#16840299C213yesmaximal, complemented
12C2×#16840296C213yesmaximal, complemented
13C2×C4×#11758226C211yesmaximal, characteristic, complemented
14C2×C4×#11758222C213yesmaximal, complemented
15C2×C4×Q8×D61C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C61C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758222C2213yes—
19C22×Q8×D61C2211yescharacteristic
20#16840488C22116yescomplemented
21#16840484C22148yescomplemented
22#16840453C22148yescomplemented
23#16840447C22148yescomplemented
24Q8×C22⋊D61C22116yescomplemented
25#16840424C22116yescomplemented
26#16840423C22116yescomplemented
27#16840413C22148yescomplemented
28#16840316C22148yescomplemented
29C2×#14519776C2213yes—
30C2×#14519775C2213yes—
31#16840299C22148yescomplemented
32#16840296C22148yescomplemented
33C2×#14519772C2216yes—
34C2×#14519771C2216yes—
35C2×#14519769C2213yes—
36C2×#14519768C2213yes—
37C2×#14519767C2216yes—
38C2×#14519766C2213yes—
39C2×#14519765C2213yes—
40C2×#14519762C2216yes—
41C2×#14519760C2216yes—
42C2×#14519757C2213yes—
43C2×#14519756C2213yes—
44C2×#14519755C2216yes—
45C2×#14519753C2213yes—
46C2×#14519753C2213yes—
47C2×#14519752C2213yes—
48C2×#14519751C2213yes—
49C4×#11758226C22116yescomplemented
50C4×#11758222C22148yescomplemented
51C2×Q8×Dic61C2211yescharacteristic
52C2×Q8×Dic61C2211yescharacteristic
53C2×C4×Dic122C2213yes—
54C2×C4×Dic122C2213yes—
55C2×C4×Dic122C2213yes—
56C2×#14519742C2213yes—
57C4×Q8×D61C22116yescomplemented
58C2×C4×D244C2213yes—
59C2×C4×D244C2213yes—
60C2×C4×D244C2213yes—
61C2×#14519739C2213yes—
62C2×C4×C22⋊D61C2211yescharacteristic
63C2×C4×C22⋊D61C2213yes—
64C2×C4×C22⋊D61C2213yes—
65C2×C4×C22⋊D61C2213yes—
66C2×#14519736C2213yes—
67C2×#14519735C2213yes—
68C2×#14519734C2213yes—
69C2×#14519734C2213yes—
70C2×#14519734C2216yes—
71C2×C4⋊C4×D61C2213yes—
72C2×C42×D61C2213yes—
73C2×C42×D61C2213yes—
74C23×Q8×C61C2211yescharacteristic
75C2×C4×Q8×C61C2211yescharacteristic
76C2×C4×Q8×C61C2211yescharacteristic
77C2×C4×Q8×C61C2213yes—
78C2×C4×Q8×C61C2213yes—
79C2×C4×Q8×C61C22116yescomplemented
80C22×C4⋊C4×C61C2213yes—
81C22×C42×C61C2213yes—
82C2×#11758226—28no—
83C2×#11758226C2318yes—
84C2×#11758222—224no—
85C2×#11758222C23124yes—
86C22×Dic122C2313yes—
87C22×Dic122C2313yes—
88C2×Q8×D61—28no—
89C2×Q8×D61C2318yes—
90C22×D244C2313yes—
91C22×D244C2313yes—
92C22×C22⋊D61C2313yes—
93C22×C22⋊D61C2311yescharacteristic
94C22×C4×D61C2311yescharacteristic
95C22×C4×D61C2313yes—
96C22×C4×D61C2313yes—
97C22×C4×D61C2313yes—
98C22×C4×D61C2313yes—
99C22×C4×D61C2313yes—
100#14519776C23124yes—
101#14519775C23124yes—
102#14519772C23148yes—
103#14519771C23148yes—
104#14519769C23124yes—
105#14519768C23124yes—
106#14519767C23148yes—
107#14519766C23124yes—
108#14519765C23124yes—
109#14519762C23148yes—
110#14519760C23148yes—
111#14519757C23124yes—
112#14519756C23124yes—
113#14519755C23148yes—
114#14519753C23124yes—
115#14519753C23124yes—
116#14519752C23124yes—
117#14519751C23124yes—
118Q8×Dic61C2318yes—
119Q8×Dic61C2318yes—
120C4×Dic122C23124yes—
121C4×Dic122C23124yes—
122C4×Dic122C23124yes—
123#14519742C23124yes—
124C4×D244C23124yes—
125C4×D244C23124yes—
126C4×D244C23124yes—
127#14519739C23124yes—
128C4×C22⋊D61C2318yes—
129C4×C22⋊D61C23124yes—
130C4×C22⋊D61C23124yes—
131C4×C22⋊D61C23124yes—
132#14519736C23124yes—
133#14519735C23124yes—
134#14519734C23124yes—
135#14519734C23124yes—
136#14519734C23148yes—
137C2×C4⋊Dic61C2313yes—
138C2×C4⋊Dic61C2313yes—
139C2×C4⋊Dic61C2313yes—
140C2×C4⋊Dic61C2313yes—
141C2×#11758196C2316yes—
142C2×#11758196C2311yescharacteristic
143C2×#11758196C2313yes—
144C2×#11758196C2313yes—
145C2×#11758196C2313yes—
146C2×#11758196C2316yes—
147C2×#11758196C2316yes—
148C4⋊C4×D61C23124yes—
149C2×C22⋊Dic61C2311yescharacteristic
150C2×C22⋊Dic61C2313yes—
151C2×#11758198C2311yescharacteristic
152C2×#11758198C2313yes—
153C2×#11758198C2313yes—
154C2×#11758198C2313yes—
155C2×#11758198C2316yes—
156C2×#11758198C2316yes—
157C2×#11758198C2316yes—
158C2×C4×Dic61C2311yescharacteristic
159C2×C4×Dic61C2313yes—
160C2×C4×Dic61C2313yes—
161C2×C4×Dic61C2313yes—
162C2×C4×Dic61C2313yes—
163C2×C4×Dic61C2313yes—
164C42×D61C23124yes—
165C42×D61C23124yes—
166C22×Q8×C61—28no—
167C22×Q8×C61C2313yes—
168C22×Q8×C61C2318yes—
169C22×Q8×C61C2311yescharacteristic
170C23×C4×C61C2313yes—
171C23×C4×C61C2311yescharacteristic
172C23×C4×C61C2313yes—
173C4×Q8×C61C23124yes—
174C4×Q8×C61C2318yes—
175C4×Q8×C61C2318yes—
176C4×Q8×C61C23124yes—
177C2×C4⋊C4×C61C2313yes—
178C2×C4⋊C4×C61C2313yes—
179C2×C4⋊C4×C61C2316yes—
180C2×C4⋊C4×C61C23124yes—
181C2×C42×C61C2313yes—
182C2×C42×C61C2313yes—
183C2×C42×C61C2313yes—
184C2×C42×C61C2313yes—
185C2×C42×C61C23124yes—
186C24×C61C2411yescharacteristic
187C23×D61C2413yes—
188C23×D61C2411yescharacteristic
189C2×Q8×C61—232no—
190C2×Q8×C61—212no—
191C2×Q8×C61#4118yescomplemented
192C2×Q8×C61C24112yes—
193C2×Q8×C61C2414yes—
194C22×C4×C61—212no—
195C22×C4×C61—212no—
196C22×C4×C61—24no—
197C22×C4×C61C2413yes—
198C22×C4×C61C2413yes—
199C22×C4×C61C24112yes—
200C22×C4×C61C2411yescharacteristic
201C22×C4×C61C2414yes—
202C22×C4×C61C2413yes—
203C22×C4×C61C24112yes—
204C22×C4×C61C2413yes—
205C22×C4×C61C2411yescharacteristic
206C2×C22⋊D61—212no—
207C2×C22⋊D61#4118yescomplemented
208C2×C22⋊D61C24112yes—
209C2×C22⋊D61C2414yes—
210C22×Dic61C2411yescharacteristic
211C22×Dic61C2413yes—
212C22×Dic61C2413yes—
213C22×Dic61C2411yescharacteristic
214C22×Dic61C2413yes—
215C22×Dic61C2411yescharacteristic
216#11758226—232no—
217Q8×D61—232no—
218#11758222—296no—
219C2×D244—212no—
220C2×D244—212no—
221C2×D244C24112yes—
222C2×D244C24112yes—
223C2×C4×D61—212no—
224C2×C4×D61—212no—
225C2×C4×D61—212no—
226C2×C4×D61—24no—
227C2×C4×D61—212no—
228C2×C4×D61—212no—
229C2×C4×D61C24112yes—
230C2×C4×D61C24112yes—
231C2×C4×D61C24112yes—
232C2×C4×D61C24112yes—
233C2×C4×D61C2414yes—
234C2×C4×D61C24112yes—
235C2×Dic122—212no—
236C2×Dic122—212no—
237C2×Dic122C24112yes—
238C2×Dic122C24112yes—
239C4⋊C4×C61C24112yes—
240C4⋊C4×C61C24112yes—
241C4⋊C4×C61C24124yes—
242C42×C61C24112yes—
243C42×C61C24112yes—
244C42×C61C24112yes—
245C42×C61C24112yes—
246C22⋊Dic61C2414yes—
247C22⋊Dic61C24112yes—
248#11758198C2414yes—
249#11758198C24112yes—
250#11758198C24112yes—
251#11758198C24112yes—
252#11758198C24124yes—
253#11758198C24124yes—
254#11758198C24124yes—
255C4⋊Dic61C24112yes—
256C4⋊Dic61C24112yes—
257C4⋊Dic61C24112yes—
258C4⋊Dic61C24112yes—
259#11758196C24124yes—
260#11758196C2414yes—
261#11758196C24112yes—
262#11758196C24112yes—
263#11758196C24112yes—
264#11758196C24124yes—
265#11758196C24124yes—
266C4×Dic61C2414yes—
267C4×Dic61C24112yes—
268C4×Dic61C24112yes—
269C4×Dic61C24112yes—
270C4×Dic61C24112yes—
271C4×Dic61C24112yes—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61C2×#4114yes—
275C23×C61C2512yes—
276C23×C61C2511yescharacteristic
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—26no—
280C22×D61—26no—
281C22×D61—26no—
282C22×D61C2×#4114yes—
283C22×D61C2516yes—
284C22×D61C2512yes—
285Q8×C61—224no—
286Q8×C61C2×#41116yescomplemented
287C2×C4×C61—26no—
288C2×C4×C61—26no—
289C2×C4×C61—224no—
290C2×C4×C61—26no—
291C2×C4×C61—22no—
292C2×C4×C61—224no—
293C2×C4×C61—28no—
294C2×C4×C61C2×#41112yes—
295C2×C4×C612−1+414yes—
296C2×C4×C61C2516yes—
297C2×C4×C61C2512yes—
298C2×C4×C61C2516yes—
299C2×C4×C61C2516yes—
300C2×C4×C61C2516yes—
301C2×C4×C61C2512yes—
302C22⋊D61—224no—
303C22⋊D61C2×#41116yescomplemented
304C2×Dic61—26no—
305C2×Dic61—26no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—26no—
309C2×Dic61C2×#4114yes—
310C2×Dic61C2512yes—
311C2×Dic61C2512yes—
312C2×Dic61C2516yes—
313C2×Dic61C2516yes—
314C2×Dic61C2516yes—
315C2×Dic61C2512yes—
316D244—224no—
317D244—224no—
318C4×D61—224no—
319C4×D61—224no—
320C4×D61—224no—
321C4×D61—28no—
322C4×D61—224no—
323C4×D61—224no—
324Dic122—224no—
325Dic122—224no—
326C2×#3482—611nomaximal, Sylow
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—28no—
330C22×C61C22×#4114yes—
331C22×C61C22×#4112yes—
332C22×C61C22×#4112yes—
333C22×C61C2×2−1+412yes—
334C22×C61C2611yescharacteristic
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—28no—
338C2×D61—26no—
339C2×D61—26no—
340C2×D61—26no—
341C2×D61—412no—
342C2×D61C22×#4114yes—
343C4×C61—26no—
344C4×C61—26no—
345C4×C61—26no—
346C4×C61—22no—
347C4×C61C22×#41112yes—
348C4×C61C2×2−1+414yes—
349Dic61—26no—
350Dic61—26no—
351Dic61—22no—
352Dic61—22no—
353Dic61—26no—
354Dic61C22×#4114yes—
355#3482—6132no—
356C2×#557—611no—
357C2×#556—613no—
358C2×#552—613no—
359C2×#552—613no—
360C2×D4×Q8—611no—
361C2×#548—611no—
362C2×#548—611no—
363C2×#547—613no—
364C2×#533—613no—
365C2×#529—613no—
366C2×#529—613no—
367C2×C4×#41—613no—
368C2×C4×#41—611no—
369C22×C4×Q8—611no—
370C22×C4×Q8D6111yescharacteristic, complemented
371C2×C61—24no—
372C2×C61#348214yescomplemented
373C2×C61C23×#4111yescharacteristic
374C2×C61C23×#4111yescharacteristic
375C2×C61C22×2−1+411yescharacteristic
376D61—24no—
377D61—46no—
378C22×#41—611no—
379C22×#41—613no—
380C23×Q8—611no—
381C23×Q8C2×D6111yescharacteristic
382#557—6116no—
383#556—6148no—
384#552—6148no—
385#552—6148no—
386D4×Q8—6116no—
387#548—6116no—
388#548—6116no—
389#547—6148no—
390#533—6148no—
391C2×C4⋊Q8—613no—
392C2×C4⋊Q8—613no—
393#529—6148no—
394#529—6148no—
395C2×#126—616no—
396C2×#126—616no—
397C2×#125—616no—
398C2×#125—613no—
399C2×#125—613no—
400C2×#124—613no—
401C2×#124—613no—
402C2×#123—616no—
403C2×#123—616no—
404C2×C22⋊Q8—613no—
405C2×C22⋊Q8—613no—
406C2×C22⋊Q8—613no—
407C2×C22⋊Q8—616no—
408C2×C22⋊Q8—613no—
409C2×#121—613no—
410C2×#121—613no—
411C4×#41—6116no—
412C4×#41—6148no—
413C2×C4×Q8—611no—
414C2×C4×Q8—611no—
415C2×C4×Q8—6116no—
416C2×C4×Q8—613no—
417C2×C4×Q8—613no—
418C2×C4×Q8—613no—
419C2×C4×Q8—613no—
420C2×C4×Q8C2×D6111yescharacteristic
421C2×C4×Q8C2×D6113yes—
422C2×C4×Q8C2×D6111yescharacteristic
423C2×C4×Q8C2×D6113yes—
424C2×C4×Q8C2×D61116yescomplemented
425C2×C4×D4—611no—
426C2×C4×D4—613no—
427C2×C4×D4—613no—
428C2×C4×D4—613no—
429C2×C4×D4—613no—
430C2×C4×D4—613no—
431C2×C4×D4—613no—
432C2×C4×D4—613no—
433C2×#117—613no—
434C2×#117—613no—
435C2×#117—613no—
436C2×#117—613no—
437C2×#117—616no—
438C22×C4⋊C4—613no—
439C22×C4⋊C4C2×D6113yes—
440C22×C42—613no—
441C22×C42—613no—
442C22×C42C2×D6113yes—
443C61C2×#348211yescharacteristic, complemented, Sylow
444C2×#41—618no—
445C2×#41—6124no—
446C2×#41—12224no—
447C2×#41—1228no—
448C22×Q8—28no—
449C22×Q8—618no—
450C22×Q8—613no—
451C22×Q8—613no—
452C22×Q8—1228no—
453C22×Q8C22×D6113yes—
454C22×Q8C22×D6118yes—
455C22×Q8C22×D6111yescharacteristic
456C22×D4—611no—
457C22×D4—613no—
458C22×D4—613no—
459C22×D4—613no—
460C23×C4—613no—
461C23×C4—613no—
462C23×C4—613no—
463C23×C4—613no—
464C23×C4—613no—
465C23×C4—611no—
466C23×C4C22×D6113yes—
467C23×C4C22×D6113yes—
468C23×C4C22×D6111yescharacteristic
469C4⋊Q8—6124no—
470C4⋊Q8—6124no—
471#126—6148no—
472#126—6148no—
473#125—6124no—
474#125—6148no—
475#125—6124no—
476#124—6124no—
477#124—6124no—
478#123—6148no—
479#123—6148no—
480C22⋊Q8—6124no—
481C22⋊Q8—6124no—
482C22⋊Q8—6124no—
483C22⋊Q8—6148no—
484C22⋊Q8—6124no—
485#121—6124no—
486#121—6124no—
487C4×Q8—618no—
488C4×Q8—618no—
489C4×Q8—6124no—
490C4×Q8—6124no—
491C4×Q8—6124no—
492C4×Q8—6124no—
493C4×Q8C22×D6118yes—
494C4×Q8C22×D61124yes—
495C4×Q8C22×D6118yes—
496C4×Q8C22×D61124yes—
497C4×D4—618no—
498C4×D4—6124no—
499C4×D4—6124no—
500C4×D4—6124no—
501C4×D4—6124no—
502C4×D4—6124no—
503C4×D4—6124no—
504C4×D4—6124no—
505#117—6124no—
506#117—6124no—
507#117—6124no—
508#117—6124no—
509#117—6148no—
510C2×C4⋊C4—613no—
511C2×C4⋊C4—616no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—613no—
514C2×C4⋊C4—613no—
515C2×C4⋊C4—613no—
516C2×C4⋊C4—613no—
517C2×C4⋊C4—613no—
518C2×C4⋊C4—613no—
519C2×C4⋊C4—616no—
520C2×C4⋊C4—616no—
521C2×C4⋊C4—6124no—
522C2×C4⋊C4C22×D6113yes—
523C2×C4⋊C4C22×D6113yes—
524C2×C4⋊C4C22×D6116yes—
525C2×C4⋊C4C22×D61124yes—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—613no—
528C2×C22⋊C4—611no—
529C2×C22⋊C4—613no—
530C2×C22⋊C4—616no—
531C2×C22⋊C4—613no—
532C2×C22⋊C4—613no—
533C2×C22⋊C4—616no—
534C2×C22⋊C4—616no—
535C2×C42—613no—
536C2×C42—613no—
537C2×C42—613no—
538C2×C42—613no—
539C2×C42—613no—
540C2×C42—611no—
541C2×C42—6124no—
542C2×C42—6124no—
543C2×C42C22×D6113yes—
544C2×C42C22×D6113yes—
545C2×C42C22×D61124yes—
546C2×C42C22×D6113yes—
547C2×C42C22×D6113yes—
548C24—611no—
549C24—613no—
550C24C23×D6111yescharacteristic
551#41—12296no—
552#41—12232no—
553C2×Q8—232no—
554C2×Q8—212no—
555C2×Q8—6112no—
556C2×Q8—6112no—
557C2×Q8—12212no—
558C2×Q8—12232no—
559C2×Q8—12212no—
560C2×Q8#1175822218yescomplemented
561C2×Q8C23×D61112yes—
562C2×Q8C23×D6114yes—
563C2×D4—618no—
564C2×D4—614no—
565C2×D4—6112no—
566C2×D4—6112no—
567C2×D4—6112no—
568C2×D4—12212no—
569C2×D4—12212no—
570C2×D4—12212no—
571C22×C4—212no—
572C22×C4—212no—
573C22×C4—24no—
574C22×C4—611no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—613no—
578C22×C4—613no—
579C22×C4—613no—
580C22×C4—614no—
581C22×C4—6112no—
582C22×C4—6112no—
583C22×C4—6112no—
584C22×C4—6112no—
585C22×C4—6112no—
586C22×C4—12212no—
587C22×C4—12212no—
588C22×C4—12212no—
589C22×C4—12212no—
590C22×C4—1224no—
591C22×C4—12212no—
592C22×C4C23×D6113yes—
593C22×C4C23×D6111yescharacteristic
594C22×C4C23×D6114yes—
595C22×C4C23×D6113yes—
596C22×C4C23×D6113yes—
597C22×C4C23×D61112yes—
598C22×C4C23×D61112yes—
599C22×C4C23×D6113yes—
600C22×C4C23×D6111yescharacteristic
601C4⋊C4—6124no—
602C4⋊C4—6112no—
603C4⋊C4—614no—
604C4⋊C4—6112no—
605C4⋊C4—6112no—
606C4⋊C4—6112no—
607C4⋊C4—6124no—
608C4⋊C4—6124no—
609C4⋊C4—6112no—
610C4⋊C4—6112no—
611C4⋊C4—6112no—
612C4⋊C4C23×D61112yes—
613C4⋊C4C23×D61112yes—
614C4⋊C4C23×D61124yes—
615C22⋊C4—614no—
616C22⋊C4—6112no—
617C22⋊C4—614no—
618C22⋊C4—6112no—
619C22⋊C4—6124no—
620C22⋊C4—6112no—
621C22⋊C4—6112no—
622C22⋊C4—6124no—
623C22⋊C4—6124no—
624C42—614no—
625C42—6112no—
626C42—6112no—
627C42—6112no—
628C42—6112no—
629C42—6112no—
630C42C23×D61112yes—
631C42C23×D61112yes—
632C42C23×D61112yes—
633C42C23×D61112yes—
634C23—22no—
635C23—22no—
636C23—614no—
637C23—612no—
638C23—616no—
639C23—1222no—
640C23—1222no—
641C23—1226no—
642C23—1226no—
643C23—1226no—
644C23#41×D6114yes—
645C23C24×D6112yes—
646C23C24×D6111yescharacteristic
647Q8—224no—
648Q8—12224no—
649Q8—12224no—
650Q8C2×#11758222116yescomplemented
651D4—6116no—
652D4—12224no—
653D4—12224no—
654D4—12224no—
655C2×C4—26no—
656C2×C4—26no—
657C2×C4—224no—
658C2×C4—26no—
659C2×C4—22no—
660C2×C4—224no—
661C2×C4—28no—
662C2×C4—614no—
663C2×C4—612no—
664C2×C4—612no—
665C2×C4—612no—
666C2×C4—616no—
667C2×C4—616no—
668C2×C4—616no—
669C2×C4—12224no—
670C2×C4—12224no—
671C2×C4—1226no—
672C2×C4—1222no—
673C2×C4—1226no—
674C2×C4—1222no—
675C2×C4—1226no—
676C2×C4—12224no—
677C2×C4—12224no—
678C2×C4—1228no—
679C2×C4—12224no—
680C2×C4C2×#11758222112yes—
681C2×C4#1451982514yes—
682C2×C4C24×D6116yes—
683C2×C4C24×D6112yes—
684C2×C4C24×D6116yes—
685C2×C4C24×D6116yes—
686C2×C4C24×D6116yes—
687C2×C4C24×D6112yes—
688C22—22no—
689C22—22no—
690C22—28no—
691C22—614no—
692C22—1222no—
693C22—1222no—
694C22—1228no—
695C22—1226no—
696C22—1226no—
697C22—1226no—
698C22—24412no—
699C22C2×#41×D6114yes—
700C22C2×#41×D6112yes—
701C22C22×#1175822212yes—
702C22C2×#1451982512yes—
703C22C25×D6111yescharacteristic
704C4—26no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—614no—
709C4—1226no—
710C4—1222no—
711C4—1226no—
712C4—1222no—
713C4—1226no—
714C4C22×#11758222112yes—
715C4C2×#1451982514yes—
716C2—24no—
717C2—1224no—
718C2—2446no—
719C2#2145943614yesdirect product factor
720C2C22×#41×D6111yescharacteristic
721C2C23×#1175822211yescharacteristic
722C2C22×#1451982511yescharacteristic
subgroupG/H
centerC22×C4C23×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC22×C4×Q8×C61C2
socleC23×C61C25
hypercenterC22×C4×Q8D61
hypocenterC61C2×#3482
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #21459436C2direct (N × H)
2. C2×#16840488C2semidirect
3. C2×#16840484C2semidirect
4. C2×#16840453C2semidirect
5. C2×#16840447C2semidirect
6. C2×Q8×C22⋊D61C2semidirect
7. C2×#16840424C2semidirect
8. C2×#16840423C2semidirect
9. C2×#16840413C2semidirect
10. C2×#16840316C2semidirect
11. C2×#16840299C2semidirect
12. C2×#16840296C2semidirect
13. C2×C4×#11758226C2semidirect
14. C2×C4×#11758222C2semidirect
15. C2×C4×Q8×D61C2semidirect
16. C22×C4×Q8×C61C2semidirect
20. #16840488C22semidirect
21. #16840484C22semidirect
22. #16840453C22semidirect
23. #16840447C22semidirect
24. Q8×C22⋊D61C22semidirect
25. #16840424C22semidirect
26. #16840423C22semidirect
27. #16840413C22semidirect
28. #16840316C22semidirect
31. #16840299C22semidirect
32. #16840296C22semidirect
49. C4×#11758226C22semidirect
50. C4×#11758222C22semidirect
57. C4×Q8×D61C22semidirect
79. C2×C4×Q8×C61C22semidirect
191. C2×Q8×C61#41semidirect
207. C2×C22⋊D61#41semidirect
286. Q8×C61C2×#41semidirect
303. C22⋊D61C2×#41semidirect
370. C22×C4×Q8D61semidirect
372. C2×C61#3482semidirect
424. C2×C4×Q8C2×D61semidirect
443. C61C2×#3482semidirect
560. C2×Q8#11758222semidirect
650. Q8C2×#11758222semidirect
719. C2#21459436direct (N × H)

Maximal subgroups

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

subgroupindex
#214594362
C2×#168404882
C2×#168404842
C2×#168404532
C2×#168404472
C2×Q8×C22⋊D612
C2×#168404242
C2×#168404232
C2×#168404132
C2×#168403162
C2×#168402992
C2×#168402962
C2×C4×#117582262
C2×C4×#117582222
C2×C4×Q8×D612
C22×C4×Q8×C612
C2×#348261