Finite Group Databasebeta

← C2×#21459496 #30588413

Subgroups — C2×#21459496 #30588413

Order 15616.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519825C211yesmaximal, characteristic, complemented
2C23×#11758226C211yesmaximal, characteristic, complemented
3#21459496C2132yesmaximal, direct product factor
4C2×Q8×C22⋊D61C211yesmaximal, characteristic, complemented
5C2×#16840424C211yesmaximal, characteristic, complemented
6C2×#16840423C211yesmaximal, characteristic, complemented
7C2×#16840415C213yesmaximal, complemented
8C2×#16840414C213yesmaximal, complemented
9C2×#16840408C213yesmaximal, complemented
10C2×#16840403C213yesmaximal, complemented
11C2×#16840342C213yesmaximal, complemented
12C2×#16840337C213yesmaximal, complemented
13C2×#16840271C213yesmaximal, complemented
14C2×C22⋊Q8×D61C213yesmaximal, complemented
15C2×#16840244C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C61C211yesmaximal, characteristic, complemented
17C2×#14519825—216no—
18C2×#14519825C22116yescomplemented
19C22×#11758226—216no—
20C22×#11758226C2213yes—
21C22×#11758226C2211yescharacteristic
22C22×#11758226C2213yes—
23C22×#11758226C2211yescharacteristic
24C22×#11758226C22116yescomplemented
25C22×#11758226C2213yescomplemented
26C22×#11758222C2213yescomplemented
27C22×#11758222C2213yescomplemented
28C22×Q8×D61C2211yescharacteristic, complemented
29C22×Q8×D61C2213yescomplemented
30C23×D244C2213yes—
31C23×C4×D61C2213yes—
32Q8×C22⋊D61C22116yescomplemented
33#16840424C22116yescomplemented
34#16840423C22116yescomplemented
35#16840415C22148yescomplemented
36#16840414C22148yescomplemented
37#16840408C22148yescomplemented
38#16840403C22148yescomplemented
39#16840342C22148yescomplemented
40#16840337C22148yescomplemented
41C2×#14519775C2213yescomplemented
42C2×#14519766C2213yescomplemented
43C2×#14519765C2213yescomplemented
44#16840271C22148yescomplemented
45C2×#14519762C2216yescomplemented
46C2×#14519762C2216yescomplemented
47C2×#14519762C2213yescomplemented
48C2×#14519759C2213yescomplemented
49C2×#14519757C2213yescomplemented
50C2×#14519756C2213yes—
51C2×#14519755C2216yescomplemented
52C2×#14519755C2213yescomplemented
53C2×#14519754C2213yes—
54C2×#14519753C2213yescomplemented
55C2×#14519753C2213yescomplemented
56C22⋊Q8×D61C22148yescomplemented
57C2×#14519752C2216yescomplemented
58C2×#14519752C2213yescomplemented
59C2×#14519751C2213yescomplemented
60C2×#14519750C2216yescomplemented
61C2×#14519750C2213yescomplemented
62C2×#14519749C2211yescharacteristic
63C2×#14519747C2213yes—
64C2×#14519745C2213yes—
65#16840244C22116yescomplemented
66C2×Q8×Dic61C2211yescharacteristic, complemented
67C2×C4×D244C2213yescomplemented
68C2×C4×D244C2213yescomplemented
69C2×#14519739C2213yescomplemented
70C2×C4×C22⋊D61C2213yes—
71C2×C4×C22⋊D61C2213yescomplemented
72C2×#14519734C2213yescomplemented
73C2×C4⋊C4×D61C2213yescomplemented
74C2×C4⋊C4×D61C2216yescomplemented
75C2×C22⋊C4×D61C2216yes—
76C23×Q8×C61C2211yescharacteristic
77C23×Q8×C61C2211yescharacteristic, complemented
78D4×Q8×C61C22116yescomplemented
79C2×C4⋊Q8×C61C2213yescomplemented
80C2×C22⋊Q8×C61C2213yes—
81C2×C22⋊Q8×C61C2213yescomplemented
82C2×C4×Q8×C61C2211yescharacteristic, complemented
83C2×C4×D4×C61C2213yes—
84C24×D61C2313yes—
85#14519825—2128no—
86C2×#11758226—28no—
87C2×#11758226—2128no—
88C2×#11758226—224no—
89C2×#11758226—224no—
90C2×#11758226—224no—
91C2×#11758226D4116yescomplemented
92C2×#11758226C23124yes—
93C2×#11758226C23124yes—
94C2×#11758226C2318yes—
95C2×#11758226C2318yes—
96C2×#11758226C23124yescomplemented
97C2×#11758222—224no—
98C2×#11758222—224no—
99C2×#11758222C23124yescomplemented
100C2×#11758222C23124yescomplemented
101C22×Dic122C2313yes—
102C22×Dic122C2313yes—
103C2×Q8×D61—28no—
104C2×Q8×D61—224no—
105C2×Q8×D61C23124yescomplemented
106C2×Q8×D61C2318yescomplemented
107C22×D244—224no—
108C22×D244C2313yes—
109C22×D244C2316yes—
110C22×D244C2313yes—
111C22×D244C23124yes—
112C22×D244C2313yes—
113C22×D244C2313yes—
114C22×C22⋊D61C2311yescharacteristic
115C22×C22⋊D61C2313yes—
116C22×C22⋊D61C2311yescharacteristic
117C22×C22⋊D61C2313yes—
118C23×Dic61C2311yescharacteristic
119C22×C4×D61—224no—
120C22×C4×D61C2316yes—
121C22×C4×D61C2313yes—
122C22×C4×D61C2313yes—
123C22×C4×D61C2313yes—
124C22×C4×D61C2313yes—
125C22×C4×D61C23124yes—
126C22×C4×D61C2316yes—
127C22×C4×D61C2313yes—
128#14519775C23124yescomplemented
129#14519766C23124yescomplemented
130#14519765C23124yescomplemented
131#14519762C23124yescomplemented
132#14519762C23148yescomplemented
133#14519762C23148yescomplemented
134#14519759C23124yescomplemented
135#14519757C23124yescomplemented
136#14519756C23124yes—
137#14519755C23148yescomplemented
138#14519755C23124yescomplemented
139#14519754C23124yes—
140#14519753C23124yescomplemented
141#14519753C23124yescomplemented
142#14519752C23148yescomplemented
143#14519752C23124yescomplemented
144#14519751C23124yescomplemented
145#14519750C23124yescomplemented
146#14519750C23148yescomplemented
147#14519749C2318yes—
148#14519747C23124yes—
149#14519745C23124yes—
150Q8×Dic61C2318yescomplemented
151C4×D244C23124yescomplemented
152C4×D244C23124yescomplemented
153#14519739C23124yescomplemented
154C4×C22⋊D61C23124yes—
155C4×C22⋊D61C23124yescomplemented
156#14519734C23124yescomplemented
157C2×C4⋊Dic61C2313yes—
158C2×C4⋊Dic61C2313yes—
159C2×#11758196C2313yes—
160C2×#11758196C2313yes—
161C2×#11758196C2316yes—
162C2×#11758196C2311yescharacteristic
163C2×#11758196C2313yes—
164C4⋊C4×D61C23124yescomplemented
165C4⋊C4×D61C23148yescomplemented
166C2×C22⋊Dic61C2313yes—
167C2×C22⋊Dic61C2311yescharacteristic
168C2×#11758198C2316yes—
169C2×#11758198C2316yes—
170C2×#11758198C2313yes—
171C2×#11758198C2313yes—
172C2×#11758198C2313yes—
173C2×#11758198C2313yes—
174C2×#11758198C2311yescharacteristic
175C2×#11758198C2313yes—
176C22⋊C4×D61C23148yes—
177C2×C4×Dic61C2313yes—
178C22×Q8×C61—28no—
179C22×Q8×C61—28no—
180C22×Q8×C61C2313yes—
181C22×Q8×C61C2313yes—
182C22×Q8×C61C2318yes—
183C22×Q8×C61C2311yescharacteristic
184C22×Q8×C61C2318yescomplemented
185C22×D4×C61C2311yescharacteristic
186C23×C4×C61C2313yes—
187C23×C4×C61C2313yes—
188C4⋊Q8×C61C23124yescomplemented
189C22⋊Q8×C61C23124yes—
190C22⋊Q8×C61C23124yescomplemented
191C4×Q8×C61C2318yescomplemented
192C4×D4×C61C23124yes—
193C2×C4⋊C4×C61C2313yes—
194C2×C4⋊C4×C61C2316yes—
195C2×C4⋊C4×C61C2313yes—
196C2×C22⋊C4×C61C2313yes—
197C2×C22⋊C4×C61C2313yes—
198C2×C42×C61C2313yes—
199C24×C61C2411yescharacteristic
200C24×C61C2411yescharacteristic
201C23×D61—212no—
202C23×D61—212no—
203C23×D61—46no—
204C23×D61C2411yescharacteristic
205C23×D61C2413yes—
206C23×D61C24112yes—
207C23×D61C2413yes—
208C2×Q8×C61—232no—
209C2×Q8×C61—232no—
210C2×Q8×C61—212no—
211C2×Q8×C61—212no—
212C2×Q8×C61C2×D418yes—
213C2×Q8×C61C24112yes—
214C2×Q8×C61C24112yes—
215C2×Q8×C61C2414yes—
216C2×D4×C61—24no—
217C2×D4×C61C2414yes—
218C22×C4×C61—212no—
219C22×C4×C61—212no—
220C22×C4×C61C2413yes—
221C22×C4×C61C24112yes—
222C22×C4×C61C2413yes—
223C22×C4×C61C2413yes—
224C22×C4×C61C24112yes—
225C22×C4×C61C2411yescharacteristic
226C22×C4×C61C2413yes—
227C2×C22⋊D61—24no—
228C2×C22⋊D61—212no—
229C2×C22⋊D61—24no—
230C2×C22⋊D61—46no—
231C2×C22⋊D61C24112yes—
232C2×C22⋊D61C2414yes—
233C2×C22⋊D61C2414yes—
234C2×C22⋊D61C24112yes—
235C22×Dic61—24no—
236C22×Dic61C2411yescharacteristic
237C22×Dic61C2414yes—
238C22×Dic61C2413yes—
239C22×Dic61C2413yes—
240C22×Dic61C2411yescharacteristic
241C22×Dic61C2411yescharacteristic
242#11758226—232no—
243#11758226—296no—
244#11758226—296no—
245#11758226—296no—
246#11758226C2×D4164yescomplemented
247Q8×D61—232no—
248Q8×D61—296no—
249#11758222—296no—
250#11758222—296no—
251C2×D244—224no—
252C2×D244—212no—
253C2×D244—212no—
254C2×D244—296no—
255C2×D244—46no—
256C2×D244C2×D4124yes—
257C2×D244C24124yes—
258C2×D244C24112yes—
259C2×D244C24112yes—
260C2×D244C24112yes—
261C2×D244C24112yes—
262C2×C4×D61—212no—
263C2×C4×D61—224no—
264C2×C4×D61—212no—
265C2×C4×D61—212no—
266C2×C4×D61—212no—
267C2×C4×D61—296no—
268C2×C4×D61—412no—
269C2×C4×D61C2×D4124yes—
270C2×C4×D61C24112yes—
271C2×C4×D61C24112yes—
272C2×C4×D61C24112yes—
273C2×C4×D61C24124yes—
274C2×C4×D61C24112yes—
275C2×C4×D61C24124yes—
276C2×C4×D61C24112yes—
277C2×Dic122—212no—
278C2×Dic122—212no—
279C2×Dic122C24112yes—
280C2×Dic122C24112yes—
281C4⋊C4×C61C24112yes—
282C4⋊C4×C61C24112yes—
283C4⋊C4×C61C24124yes—
284C22⋊C4×C61C24112yes—
285C22⋊C4×C61C24112yes—
286C42×C61C24112yes—
287C22⋊Dic61C24112yes—
288C22⋊Dic61C2414yes—
289#11758198C24124yes—
290#11758198C24124yes—
291#11758198C24112yes—
292#11758198C24112yes—
293#11758198C24112yes—
294#11758198C24112yes—
295#11758198C2414yes—
296#11758198C24112yes—
297C4⋊Dic61C24112yes—
298C4⋊Dic61C24112yes—
299#11758196C24112yes—
300#11758196C24112yes—
301#11758196C24124yes—
302#11758196C2414yes—
303#11758196C24112yes—
304C4×Dic61C24112yes—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C612−1+414yescomplemented
311C23×C61C2512yes—
312C23×C61C2512yes—
313C23×C61C2511yescharacteristic
314C22×D61—26no—
315C22×D61—26no—
316C22×D61—22no—
317C22×D61—26no—
318C22×D61—22no—
319C22×D61—26no—
320C22×D61—224no—
321C22×D61—22no—
322C22×D61—26no—
323C22×D61—224no—
324C22×D61—412no—
325C22×D61—448no—
326C22×D61C22×D4112yes—
327C22×D61C2516yes—
328C22×D61C2512yes—
329C22×D61C2516yes—
330Q8×C61—224no—
331Q8×C61—224no—
332Q8×C61C22×D4116yes—
333D4×C61—28no—
334C2×C4×C61—26no—
335C2×C4×C61—26no—
336C2×C4×C61—22no—
337C2×C4×C61—26no—
338C2×C4×C61—224no—
339C2×C4×C61—224no—
340C2×C4×C61C22×D4112yes—
341C2×C4×C61C2516yes—
342C2×C4×C61C2516yes—
343C2×C4×C61C2512yes—
344C2×C4×C61C2516yes—
345C2×C4×C61C2516yes—
346C22⋊D61—28no—
347C22⋊D61—224no—
348C22⋊D61—28no—
349C22⋊D61—412no—
350C2×Dic61—26no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—26no—
354C2×Dic61—28no—
355C2×Dic61C22×D414yes—
356C2×Dic61C2512yes—
357C2×Dic61C2516yes—
358C2×Dic61C2512yes—
359C2×Dic61C2516yes—
360C2×Dic61C2512yes—
361D244—248no—
362D244—224no—
363D244—224no—
364D244—412no—
365D244C22×D4148yes—
366C4×D61—224no—
367C4×D61—248no—
368C4×D61—224no—
369C4×D61—224no—
370C4×D61—224no—
371C4×D61—424no—
372C4×D61C22×D4148yes—
373Dic122—224no—
374Dic122—224no—
375C2×#3489—611nomaximal, Sylow
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—28no—
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—44no—
383C22×C61C23×D412yes—
384C22×C61C2×2−1+412yes—
385C22×C61C2×2−1+414yescomplemented
386C22×C61#58512yes—
387C22×C61C2611yescharacteristic
388C2×D61—26no—
389C2×D61—26no—
390C2×D61—224no—
391C2×D61—22no—
392C2×D61—26no—
393C2×D61—22no—
394C2×D61—26no—
395C2×D61—22no—
396C2×D61—26no—
397C2×D61—448no—
398C2×D61—44no—
399C2×D61—412no—
400C2×D61C23×D4112yes—
401C4×C61—26no—
402C4×C61—26no—
403C4×C61—22no—
404C4×C61—26no—
405C4×C61C23×D4112yes—
406Dic61—26no—
407Dic61—22no—
408Dic61—22no—
409Dic61—26no—
410Dic61C23×D414yes—
411C22×2−1+4—611no—
412C23×#41—611no—
413#3489—6132no—
414C2×D4×Q8—611no—
415C2×D4×Q8D6111yescharacteristic, complemented
416C2×#548—611no—
417C2×#548—611no—
418C2×#547—613no—
419C2×#547—613no—
420C2×#546—613no—
421C2×#546—613no—
422C2×#537—613no—
423C2×#536—613no—
424C2×#525—613no—
425C22×C22⋊Q8—613no—
426C2×#520—611no—
427C2×C61—24no—
428C2×C61—42no—
429C2×C61#348914yescomplemented
430C2×C61C24×D411yescharacteristic
431C2×C61C22×2−1+411yescharacteristic
432C2×C61C2×#58511yescharacteristic
433D61—212no—
434D61—42no—
435D61—46no—
436C2×2−1+4—6116no—
437C2×2−1+4—12216no—
438C22×#41—611no—
439C22×#41—613no—
440C22×#41—613no—
441C22×#41—611no—
442C22×#41—6116no—
443C22×#41—613no—
444C22×#41—613no—
445C22×#41—613no—
446C22×#41—12216no—
447C23×Q8—613no—
448C23×Q8—611no—
449C23×Q8C2×D6111yescharacteristic
450C23×Q8C2×D6111yescharacteristic, complemented
451C23×D4—613no—
452C24×C4—613no—
453D4×Q8—6116no—
454D4×Q8C2×D61116yescomplemented
455#548—6116no—
456#548—6116no—
457#547—6148no—
458#547—6148no—
459#546—6148no—
460#546—6148no—
461#537—6148no—
462#536—6148no—
463C2×C4⋊Q8—613no—
464C2×C4⋊Q8C2×D6113yescomplemented
465C2×#124—613no—
466C2×#124—613no—
467#525—6148no—
468C2×#123—613no—
469C2×#123—616no—
470C2×#123—616no—
471C2×#123—613no—
472C2×C22⋊Q8—613no—
473C2×C22⋊Q8—613no—
474C2×C22⋊Q8—613no—
475C2×C22⋊Q8—6148no—
476C2×C22⋊Q8—616no—
477C2×C22⋊Q8—613no—
478C2×C22⋊Q8—613no—
479C2×C22⋊Q8—613no—
480C2×C22⋊Q8C2×D6113yes—
481C2×C22⋊Q8C2×D6113yescomplemented
482C2×#121—611no—
483C2×#121—613no—
484C2×#121—616no—
485C2×#121—613no—
486C2×#121—613no—
487C2×#121—616no—
488C2×#120—613no—
489C2×#120—613no—
490#520—6116no—
491C2×C4×Q8—611no—
492C2×C4×Q8C2×D6111yescharacteristic, complemented
493C2×C4×D4—613no—
494C2×C4×D4—613no—
495C2×C4×D4—613no—
496C2×C4×D4—613no—
497C2×C4×D4—613no—
498C2×C4×D4C2×D6113yes—
499C2×#117—613no—
500C22×C4⋊C4—613no—
501C22×C4⋊C4—616no—
502C22×C22⋊C4—616no—
503C61C2×#348911yescharacteristic, complemented, Sylow
504C25—613no—
5052−1+4—122128no—
506C2×#41—6116no—
507C2×#41—618no—
508C2×#41—6124no—
509C2×#41—6124no—
510C2×#41—618no—
511C2×#41—6124no—
512C2×#41—6124no—
513C2×#41—6124no—
514C2×#41—12224no—
515C2×#41—12224no—
516C2×#41—12224no—
517C2×#41—12224no—
518C2×#41—12224no—
519C2×#41—122128no—
520C2×#41—1228no—
521C22×Q8—28no—
522C22×Q8—28no—
523C22×Q8—6124no—
524C22×Q8—618no—
525C22×Q8—613no—
526C22×Q8—613no—
527C22×Q8—12224no—
528C22×Q8—1228no—
529C22×Q8C22×D6113yes—
530C22×Q8C22×D6113yes—
531C22×Q8C22×D6118yes—
532C22×Q8C22×D6111yescharacteristic
533C22×Q8C22×D6118yescomplemented
534C22×D4—611no—
535C22×D4—613no—
536C22×D4—611no—
537C22×D4—613no—
538C22×D4—613no—
539C22×D4—613no—
540C22×D4—616no—
541C22×D4—613no—
542C22×D4—6124no—
543C22×D4—613no—
544C22×D4—12224no—
545C22×D4C22×D6111yescharacteristic
546C23×C4—613no—
547C23×C4—611no—
548C23×C4—616no—
549C23×C4—613no—
550C23×C4—613no—
551C23×C4—613no—
552C23×C4—613no—
553C23×C4—6124no—
554C23×C4—616no—
555C23×C4—12224no—
556C23×C4C22×D6113yes—
557C23×C4C22×D6113yes—
558C4⋊Q8—6124no—
559C4⋊Q8C22×D61124yescomplemented
560#124—6124no—
561#124—6124no—
562#123—6124no—
563#123—6148no—
564#123—6148no—
565#123—6124no—
566C22⋊Q8—6124no—
567C22⋊Q8—6124no—
568C22⋊Q8—6124no—
569C22⋊Q8—6148no—
570C22⋊Q8—6124no—
571C22⋊Q8—6124no—
572C22⋊Q8—6124no—
573C22⋊Q8C22×D61124yes—
574C22⋊Q8C22×D61124yescomplemented
575#121—618no—
576#121—6124no—
577#121—6148no—
578#121—6124no—
579#121—6124no—
580#121—6148no—
581#120—6124no—
582#120—6124no—
583C4×Q8—618no—
584C4×Q8C22×D6118yescomplemented
585C4×D4—6124no—
586C4×D4—6124no—
587C4×D4—6124no—
588C4×D4—6124no—
589C4×D4—6124no—
590C4×D4C22×D61124yes—
591#117—6124no—
592C2×C4⋊C4—613no—
593C2×C4⋊C4—613no—
594C2×C4⋊C4—613no—
595C2×C4⋊C4—613no—
596C2×C4⋊C4—616no—
597C2×C4⋊C4—611no—
598C2×C4⋊C4—613no—
599C2×C4⋊C4—6124no—
600C2×C4⋊C4—6148no—
601C2×C4⋊C4C22×D6113yes—
602C2×C4⋊C4C22×D6116yes—
603C2×C4⋊C4C22×D6113yes—
604C2×C22⋊C4—613no—
605C2×C22⋊C4—611no—
606C2×C22⋊C4—616no—
607C2×C22⋊C4—616no—
608C2×C22⋊C4—613no—
609C2×C22⋊C4—613no—
610C2×C22⋊C4—611no—
611C2×C22⋊C4—613no—
612C2×C22⋊C4—613no—
613C2×C22⋊C4—613no—
614C2×C22⋊C4—6148no—
615C2×C22⋊C4C22×D6113yes—
616C2×C22⋊C4C22×D6113yes—
617C2×C42—613no—
618C2×C42C22×D6113yes—
619C24—613no—
620C24—613no—
621C24—611no—
622C24—6112no—
623C24—12212no—
624C24—12212no—
625C24—2446no—
626C24C23×D6111yescharacteristic
627C24C23×D6111yescharacteristic
628#41—6164no—
629#41—12296no—
630#41—12296no—
631#41—12296no—
632#41—12296no—
633#41—12296no—
634#41—12232no—
635C2×Q8—232no—
636C2×Q8—232no—
637C2×Q8—212no—
638C2×Q8—212no—
639C2×Q8—6112no—
640C2×Q8—6112no—
641C2×Q8—12212no—
642C2×Q8—12296no—
643C2×Q8—12232no—
644C2×Q8—12212no—
645C2×Q8D4×D6118yes—
646C2×Q8C23×D61112yes—
647C2×Q8C23×D61112yes—
648C2×Q8C23×D6114yes—
649C2×D4—24no—
650C2×D4—614no—
651C2×D4—6112no—
652C2×D4—614no—
653C2×D4—6112no—
654C2×D4—6124no—
655C2×D4—6112no—
656C2×D4—6112no—
657C2×D4—6124no—
658C2×D4—6112no—
659C2×D4—6112no—
660C2×D4—12296no—
661C2×D4—12224no—
662C2×D4—12212no—
663C2×D4—1224no—
664C2×D4—12212no—
665C2×D4—1224no—
666C2×D4—12212no—
667C2×D4—2446no—
668C2×D4—2446no—
669C2×D4C23×D6114yes—
670C22×C4—212no—
671C22×C4—212no—
672C22×C4—611no—
673C22×C4—6124no—
674C22×C4—6112no—
675C22×C4—614no—
676C22×C4—611no—
677C22×C4—613no—
678C22×C4—613no—
679C22×C4—611no—
680C22×C4—6124no—
681C22×C4—6112no—
682C22×C4—6112no—
683C22×C4—6112no—
684C22×C4—6112no—
685C22×C4—6124no—
686C22×C4—12212no—
687C22×C4—12296no—
688C22×C4—12212no—
689C22×C4—12224no—
690C22×C4—1224no—
691C22×C4—12212no—
692C22×C4—12212no—
693C22×C4—24412no—
694C22×C4C23×D61112yes—
695C22×C4C23×D61112yes—
696C22×C4C23×D6111yescharacteristic
697C22×C4C23×D6113yes—
698C22×C4C23×D6113yes—
699C22×C4C23×D6113yes—
700C22×C4C23×D6113yes—
701C4⋊C4—6112no—
702C4⋊C4—6112no—
703C4⋊C4—6112no—
704C4⋊C4—6124no—
705C4⋊C4—6112no—
706C4⋊C4—614no—
707C4⋊C4—6112no—
708C4⋊C4C23×D61112yes—
709C4⋊C4C23×D61124yes—
710C4⋊C4C23×D61112yes—
711C22⋊C4—6112no—
712C22⋊C4—614no—
713C22⋊C4—6124no—
714C22⋊C4—6124no—
715C22⋊C4—6112no—
716C22⋊C4—6112no—
717C22⋊C4—614no—
718C22⋊C4—6112no—
719C22⋊C4—6112no—
720C22⋊C4—6112no—
721C22⋊C4C23×D61112yes—
722C22⋊C4C23×D61112yes—
723C42—6112no—
724C42C23×D61112yes—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—6112no—
731C23—616no—
732C23—616no—
733C23—612no—
734C23—12224no—
735C23—1226no—
736C23—1226no—
737C23—1222no—
738C23—1226no—
739C23—1222no—
740C23—1226no—
741C23—12224no—
742C23—1222no—
743C23—1226no—
744C23—24412no—
745C23—24448no—
746C23#1451982514yescomplemented
747C23C24×D6112yes—
748C23C24×D6112yes—
749C23C24×D6111yescharacteristic
750Q8—224no—
751Q8—224no—
752Q8—12224no—
753Q8—12224no—
754Q8C2×D4×D61116yes—
755D4—28no—
756D4—6148no—
757D4—12248no—
758D4—12224no—
759D4—1228no—
760D4—12224no—
761D4—1228no—
762D4—12224no—
763D4—24412no—
764D4—24412no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—22no—
768C2×C4—26no—
769C2×C4—224no—
770C2×C4—224no—
771C2×C4—614no—
772C2×C4—612no—
773C2×C4—6148no—
774C2×C4—612no—
775C2×C4—616no—
776C2×C4—616no—
777C2×C4—612no—
778C2×C4—12224no—
779C2×C4—12224no—
780C2×C4—12248no—
781C2×C4—1228no—
782C2×C4—1222no—
783C2×C4—1226no—
784C2×C4—1222no—
785C2×C4—1226no—
786C2×C4—12224no—
787C2×C4—12224no—
788C2×C4—24424no—
789C2×C4C2×D4×D61112yes—
790C2×C4C24×D6112yes—
791C2×C4C24×D6116yes—
792C2×C4C24×D6116yes—
793C2×C4C24×D6116yes—
794C2×C4C24×D6116yes—
795C22—28no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—6112no—
803C22—12224no—
804C22—1226no—
805C22—1226no—
806C22—1222no—
807C22—1226no—
808C22—1222no—
809C22—1226no—
810C22—1222no—
811C22—1226no—
812C22—24448no—
813C22—2444no—
814C22—24412no—
815C22C22×D4×D6112yes—
816C22C2×#1451982512yes—
817C22C2×#1451982514yescomplemented
818C22#1684059912yes—
819C22C25×D6111yescharacteristic
820C4—26no—
821C4—26no—
822C4—22no—
823C4—26no—
824C4—614no—
825C4—1222no—
826C4—1226no—
827C4—1222no—
828C4—1226no—
829C4C22×D4×D61112yes—
830C2—24no—
831C2—42no—
832C2—12212no—
833C2—2446no—
834C2—2442no—
835C2#2145949614yesdirect product factor
836C2C23×D4×D6111yescharacteristic
837C2C22×#1451982511yescharacteristic
838C2C2×#1684059911yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×D4×Q8×C61C2
socleC23×C61C25
hypercenterC2×D4×Q8D61
hypocenterC61C2×#3489
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14519825C2semidirect
2. C23×#11758226C2semidirect
3. #21459496C2direct (N × H)
4. C2×Q8×C22⋊D61C2semidirect
5. C2×#16840424C2semidirect
6. C2×#16840423C2semidirect
7. C2×#16840415C2semidirect
8. C2×#16840414C2semidirect
9. C2×#16840408C2semidirect
10. C2×#16840403C2semidirect
11. C2×#16840342C2semidirect
12. C2×#16840337C2semidirect
13. C2×#16840271C2semidirect
14. C2×C22⋊Q8×D61C2semidirect
15. C2×#16840244C2semidirect
16. C2×D4×Q8×C61C2semidirect
18. C2×#14519825C22semidirect
24. C22×#11758226C22semidirect
25. C22×#11758226C22semidirect
26. C22×#11758222C22semidirect
27. C22×#11758222C22semidirect
28. C22×Q8×D61C22semidirect
29. C22×Q8×D61C22semidirect
32. Q8×C22⋊D61C22semidirect
33. #16840424C22semidirect
34. #16840423C22semidirect
35. #16840415C22semidirect
36. #16840414C22semidirect
37. #16840408C22semidirect
38. #16840403C22semidirect
39. #16840342C22semidirect
40. #16840337C22semidirect
41. C2×#14519775C22semidirect
42. C2×#14519766C22semidirect
43. C2×#14519765C22semidirect
44. #16840271C22semidirect
45. C2×#14519762C22semidirect
46. C2×#14519762C22semidirect
47. C2×#14519762C22semidirect
48. C2×#14519759C22semidirect
49. C2×#14519757C22semidirect
51. C2×#14519755C22semidirect
52. C2×#14519755C22semidirect
54. C2×#14519753C22semidirect
55. C2×#14519753C22semidirect
56. C22⋊Q8×D61C22semidirect
57. C2×#14519752C22semidirect
58. C2×#14519752C22semidirect
59. C2×#14519751C22semidirect
60. C2×#14519750C22semidirect
61. C2×#14519750C22semidirect
65. #16840244C22semidirect
66. C2×Q8×Dic61C22semidirect
67. C2×C4×D244C22semidirect
68. C2×C4×D244C22semidirect
69. C2×#14519739C22semidirect
71. C2×C4×C22⋊D61C22semidirect
72. C2×#14519734C22semidirect
73. C2×C4⋊C4×D61C22semidirect
74. C2×C4⋊C4×D61C22semidirect
77. C23×Q8×C61C22semidirect
78. D4×Q8×C61C22semidirect
79. C2×C4⋊Q8×C61C22semidirect
81. C2×C22⋊Q8×C61C22semidirect
82. C2×C4×Q8×C61C22semidirect
91. C2×#11758226D4semidirect
96. C2×#11758226C23semidirect
99. C2×#11758222C23semidirect
100. C2×#11758222C23semidirect
105. C2×Q8×D61C23semidirect
106. C2×Q8×D61C23semidirect
128. #14519775C23semidirect
129. #14519766C23semidirect
130. #14519765C23semidirect
131. #14519762C23semidirect
132. #14519762C23semidirect
133. #14519762C23semidirect
134. #14519759C23semidirect
135. #14519757C23semidirect
137. #14519755C23semidirect
138. #14519755C23semidirect
140. #14519753C23semidirect
141. #14519753C23semidirect
142. #14519752C23semidirect
143. #14519752C23semidirect
144. #14519751C23semidirect
145. #14519750C23semidirect
146. #14519750C23semidirect
150. Q8×Dic61C23semidirect
151. C4×D244C23semidirect
152. C4×D244C23semidirect
153. #14519739C23semidirect
155. C4×C22⋊D61C23semidirect
156. #14519734C23semidirect
164. C4⋊C4×D61C23semidirect
165. C4⋊C4×D61C23semidirect
184. C22×Q8×C61C23semidirect
188. C4⋊Q8×C61C23semidirect
190. C22⋊Q8×C61C23semidirect
191. C4×Q8×C61C23semidirect
246. #11758226C2×D4semidirect
310. C23×C612−1+4semidirect
385. C22×C61C2×2−1+4semidirect
415. C2×D4×Q8D61semidirect
429. C2×C61#3489semidirect
450. C23×Q8C2×D61semidirect
454. D4×Q8C2×D61semidirect
464. C2×C4⋊Q8C2×D61semidirect
481. C2×C22⋊Q8C2×D61semidirect
492. C2×C4×Q8C2×D61semidirect
503. C61C2×#3489semidirect
533. C22×Q8C22×D61semidirect
559. C4⋊Q8C22×D61semidirect
574. C22⋊Q8C22×D61semidirect
584. C4×Q8C22×D61semidirect
746. C23#14519825semidirect
817. C22C2×#14519825semidirect
835. C2#21459496direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198252
C23×#117582262
#214594962
C2×Q8×C22⋊D612
C2×#168404242
C2×#168404232
C2×#168404152
C2×#168404142
C2×#168404082
C2×#168404032
C2×#168403422
C2×#168403372
C2×#168402712
C2×C22⋊Q8×D612
C2×#168402442
C2×D4×Q8×C612
C2×#348961