Finite Group Databasebeta

← #14769117

Subgroups — #14769117

Order 2816.

1474 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623086C211yesmaximal, characteristic
2C2×#10622353C212yesmaximal, complemented
3#13071483C212yesmaximal, complemented
4#13069452C212yesmaximal, complemented
5#13069073C214yesmaximal, complemented
6#13068604C211yesmaximal, characteristic, complemented
7#13068532C212yesmaximal, complemented
8C4×C11×#99C211yesmaximal, characteristic, complemented
9C22×#4341C2212yes—
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66983C411yescharacteristic, complemented
12C2×#66983C2211yescharacteristic
13C22×C4⋊Dic11C411yescharacteristic, complemented
14C22×C4⋊Dic11C2211yescharacteristic
15#10623086—24no—
16#10623086—22no—
17#10623086—22no—
18C2×#66950C412yescomplemented
19C2×#66939C412yescomplemented
20C2×#66939C2212yes—
21C2×#66930C2214yes—
22C2×C4×D44C411yescharacteristic, complemented
23C2×#66922C411yescharacteristic, complemented
24C2×C11×#99C2211yescharacteristic
25C2×C11×#99C2211yescharacteristic
26C4×C11×C22⋊C4C2212yes—
27C2×#66898C2212yes—
28#10622825C2212yes—
29C2×#66870C2214yes—
30C2×#66870C2214yes—
31#10622556C2214yes—
32C4×C4⋊Dic11—22no—
33#10622541—22no—
34#10622353—28no—
35#10622266—24no—
36C11×#342C2212yes—
37#10622164C2212yes—
38C22×D4×C11C2311yescharacteristic
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11C2×C412yes—
42C22×C22⋊D11C2312yes—
43C23×Dic11C2×C412yes—
44C23×Dic11C2312yes—
45C2×#4341—24no—
46C2×#4341—24no—
47C2×#4341—24no—
48C2×#4341—24no—
49C2×#4341—44no—
50C22×D44C2×C411yescharacteristic
51C22×C4×D11C2×C412yes—
52C22×Dic22C2×C412yes—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C2×C11×C4⋊C4C2×C411yescharacteristic
56C2×C11×C22⋊C4C2×C411yescharacteristic
57C2×C11×C22⋊C4C2312yes—
58C2×C11×C22⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4C2312yes—
60C2×C42×C11—22no—
61C2×C42×C11C2×C411yescharacteristic
62C2×C22⋊Dic11C2314yes—
63#66983—22no—
64#66983—22no—
65#66983—22no—
66#66983—22no—
67C2×(C2×D11)⋊C4C2×C412yes—
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11C2×C412yes—
75C2×C4⋊Dic11C2×C411yescharacteristic
76C2×C4⋊Dic11C2×C412yes—
77C2×C4⋊Dic11C2×C411yescharacteristic
78C2×C4⋊Dic11C2×C411yescharacteristic
79C2×C4⋊Dic11C2×C412yes—
80C2×C4⋊Dic11D414yes—
81C2×C4⋊Dic11D412yes—
82C2×C4⋊Dic11D412yes—
83C2×Dic11⋊C4—24no—
84C2×C4×Dic11—24no—
85#66950—24no—
86#66950—24no—
87#66939—24no—
88#66939—24no—
89#66939—24no—
90#66939—24no—
91#66930—28no—
92#66930—44no—
93C4×D44—22no—
94C4×D44—21no—
95C4×D44—21no—
96#66922—22no—
97#66922—22no—
98C11×#99—22no—
99C11×#99D414yescomplemented
100C11×#95—22no—
101#66898—24no—
102C11⋊#95—22no—
103C11⋊#95—24no—
104C11⋊#95—24no—
105#66870—28no—
106#66870—44no—
107#22406—111nomaximal, Sylow
108C24×C11C22×C411yescharacteristic
109C24×C11C2411yescharacteristic
110C23×D11C22×C412yes—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11C2×D412yes—
114C2×D4×C11#4112yes—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C2×C22⋊D11—24no—
129C2×C22⋊D11—24no—
130C2×C22⋊D11—22no—
131C2×C22⋊D11—24no—
132C2×C22⋊D11—22no—
133C2×C22⋊D11—24no—
134C2×C22⋊D11—42no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—42no—
143C22×Dic11C22×C412yes—
144C22×Dic11C22×C412yes—
145C22×Dic11C22×C412yes—
146C22×Dic11C2×D414yes—
147C22×Dic11C2×D414yes—
148#4341—48no—
149#4341—48no—
150#4341—48no—
151#4341—48no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—42no—
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—24no—
158C2×C4×D11—42no—
159C2×Dic22—24no—
160C2×Dic22—24no—
161C2×Dic22—42no—
162C11×C4⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4C2×D414yes—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—44no—
172C22⋊Dic11—24no—
173C22⋊Dic11—24no—
174(C2×D11)⋊C4—22no—
175(C2×D11)⋊C4—22no—
176(C2×D11)⋊C4—24no—
177(C2×D11)⋊C4—24no—
178C4⋊Dic11—24no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—44no—
184C4⋊Dic11C22⋊C412yes—
185C4⋊Dic11C22⋊C412yes—
186C4⋊Dic11C22⋊C412yes—
187C4⋊Dic11C22⋊C411yescharacteristic
188C4⋊Dic11C22⋊C411yescharacteristic
189C4⋊Dic11C22⋊C414yes—
190C4⋊Dic11C22⋊C414yes—
191Dic11⋊C4—48no—
192C4×Dic11—48no—
193C2×#547—111no—
194C2×#410—112no—
195#2344—112no—
196#1964—112no—
197#1899—114no—
198#1799—111no—
199#1782—112no—
200C4×#99D1111yescharacteristic, complemented
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11C4×D412yes—
208C23×C11C23×C411yescharacteristic
209C23×C11C22×D411yescharacteristic
210C23×C11C22×D412yes—
211C23×C11C2×#4111yescharacteristic
212C23×C11H(5,𝔽2)12yes—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—42no—
217C22×D11—42no—
218D4×C11—24no—
219D4×C11—24no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—24no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11C2×C22⋊C411yescharacteristic
239C2×C4×C11C2×C22⋊C412yes—
240C2×C4×C11C2×C22⋊C411yescharacteristic
241C2×C4×C11C4×D412yes—
242C22⋊D11—48no—
243C22⋊D11—44no—
244C22⋊D11—44no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—44no—
257C2×Dic11—44no—
258C2×Dic11—44no—
259C2×Dic11—44no—
260C2×Dic11—44no—
261C2×Dic11C2×C22⋊C414yes—
262C2×Dic11C2×C22⋊C412yes—
263C2×Dic11C2×C22⋊C412yes—
264D44—42no—
265D44—42no—
266C4×D11—44no—
267C4×D11—44no—
268Dic22—48no—
269C22×#41—112no—
270#547—222no—
271#547—224no—
272#547—222no—
273C2×C4⋊Q8—111no—
274C2×#123—112no—
275C2×#123—112no—
276C2×C22⋊Q8—112no—
277C2×#121—111no—
278C2×#121—111no—
279C2×C4×D4—111no—
280C2×C4×D4C2×D1111yescharacteristic
281C2×#117—114no—
282C22×C4⋊C4—111no—
283C22×C4⋊C4—111no—
284#410—228no—
285C2×#99—112no—
286C2×#99—114no—
287C2×#99—114no—
288C2×#99C2×D1111yescharacteristic
289C2×#99C2×D1111yescharacteristic
290#389—222no—
291#387—224no—
292#381—114no—
293#380—112no—
294C4×C4⋊C4—222no—
295C4×C22⋊C4C2×D1112yes—
296#342—112no—
297#342C2×D1112yes—
298C22×C11—22no—
299C22×C11—21no—
300C22×C11—22no—
301C22×C11—21no—
302C22×C11—22no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—41no—
309C22×C11—41no—
310C22×C11C22×C22⋊C411yescharacteristic
311C22×C11C2×C4×D411yescharacteristic
312C22×C11#51811yescharacteristic
313C22×C11D4212yes—
314C22×C11#54612yes—
315C2×D11—42no—
316C2×D11—42no—
317C2×D11—42no—
318C2×D11—82no—
319C2×D11—82no—
320C4×C11—22no—
321C4×C11—21no—
322C4×C11—22no—
323C4×C11—44no—
324C4×C11—41no—
325C4×C11—41no—
326C4×C11—82no—
327C4×C11#41012yescomplemented
328Dic11—24no—
329Dic11—22no—
330Dic11—22no—
331Dic11—42no—
332Dic11—84no—
333C2×#41—224no—
334C2×#41—224no—
335C2×#41—224no—
336C2×#41—224no—
337C2×#41—444no—
338C22×Q8—112no—
339C22×D4—112no—
340C22×D4—112no—
341C22×D4—111no—
342C22×D4C22×D1111yescharacteristic
343C23×C4—112no—
344C23×C4—112no—
345C23×C4—112no—
346C23×C4C4×D1111yescharacteristic
347C23×C4C22×D1111yescharacteristic
348C4⋊Q8—222no—
349C4⋊Q8—222no—
350#123—224no—
351#123—224no—
352#123—224no—
353#123—224no—
354C22⋊Q8—224no—
355C22⋊Q8—224no—
356#121—222no—
357#121—222no—
358#121—222no—
359#121—222no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—222no—
363C4×D4—221no—
364C4×D4—221no—
365#117—228no—
366#117—444no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—112no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—112no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—112no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4C4×D1111yescharacteristic
382C2×C22⋊C4—112no—
383C2×C22⋊C4—112no—
384C2×C22⋊C4—112no—
385C2×C22⋊C4—114no—
386C2×C22⋊C4C4×D1111yescharacteristic
387C2×C22⋊C4C22×D1112yes—
388C2×C22⋊C4C22×D1111yescharacteristic
389C2×C22⋊C4C22×D1112yes—
390C2×C42—22no—
391C2×C42—224no—
392C2×C42C4×D1111yescharacteristic
393#99—22no—
394#99—224no—
395#99—228no—
396#99—444no—
397#99D4414yescomplemented
398#95—22no—
399#95—224no—
400#95—224no—
401#95—222no—
402C2×C11—22no—
403C2×C11—22no—
404C2×C11—21no—
405C2×C11—21no—
406C2×C11—42no—
407C2×C11D4×C22⋊C411yescharacteristic
408C2×C11C2×#41011yescharacteristic
409C2×C11#288411yescharacteristic
410D11—82no—
411C24—112no—
412C24C2×C4×D1111yescharacteristic
413C24C23×D1111yescharacteristic
414#41—448no—
415#41—448no—
416#41—448no—
417#41—448no—
418C2×Q8—224no—
419C2×Q8—224no—
420C2×Q8—442no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—224no—
424C2×D4—224no—
425C2×D4—222no—
426C2×D4—222no—
427C2×D4—224no—
428C2×D4—224no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—442no—
432C2×D4—442no—
433C2×D4C2×D4412yes—
434C2×D4#433912yes—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—112no—
442C22×C4—112no—
443C22×C4—114no—
444C22×C4—114no—
445C22×C4—112no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—224no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—442no—
457C22×C4—442no—
458C22×C4C2×C4×D1111yescharacteristic
459C22×C4C2×C4×D1111yescharacteristic
460C22×C4C2×C4×D1111yescharacteristic
461C22×C4C2×C4×D1111yescharacteristic
462C22×C4C2×C4×D1111yescharacteristic
463C22×C4D4×D1112yes—
464C22×C4D4×D1112yes—
465C4⋊C4—22no—
466C4⋊C4—112no—
467C4⋊C4—111no—
468C4⋊C4—111no—
469C4⋊C4—112no—
470C4⋊C4—112no—
471C4⋊C4—114no—
472C4⋊C4—114no—
473C4⋊C4—222no—
474C4⋊C4—222no—
475C4⋊C4—224no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—448no—
479C4⋊C4—444no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—222no—
486C22⋊C4—222no—
487C22⋊C4—224no—
488C22⋊C4—224no—
489C22⋊C4—224no—
490C22⋊C4—224no—
491C22⋊C4C2×D4414yes—
492C42—21no—
493C42—21no—
494C42—44no—
495C42—448no—
496C11#2240611yescharacteristic, complemented, Sylow
497C23—21no—
498C23—21no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—222no—
504C23—222no—
505C23—222no—
506C23—442no—
507C23—442no—
508C23C4×D4412yes—
509C23C22×C4×D1111yescharacteristic
510C23C22×D4411yescharacteristic
511C23C2×#433911yescharacteristic
512C23C2×D4×D1112yes—
513C23#6704212yes—
514Q8—448no—
515D4—24no—
516D4—24no—
517D4—442no—
518D4—448no—
519D4—444no—
520D4—444no—
521D4—442no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—24no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—112no—
541C2×C4—112no—
542C2×C4—114no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—224no—
548C2×C4—224no—
549C2×C4—224no—
550C2×C4—224no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—444no—
555C2×C4—444no—
556C2×C4—444no—
557C2×C4—444no—
558C2×C4—444no—
559C2×C4—444no—
560C2×C4—444no—
561C2×C4C4×D4412yes—
562C2×C4C22⋊C4×D1111yescharacteristic
563C2×C4C22⋊C4×D1112yes—
564C2×C4C22⋊C4×D1111yescharacteristic
565C22—22no—
566C22—21no—
567C22—22no—
568C22—21no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—41no—
576C22—41no—
577C22—442no—
578C22—442no—
579C22—442no—
580C22—882no—
581C22—882no—
582C22C2×C4×D4411yescharacteristic
583C22C2×C22⋊C4×D1111yescharacteristic
584C22#1062305211yescharacteristic
585C22D4×D4412yes—
586C22#1062308112yes—
587C4—22no—
588C4—21no—
589C4—22no—
590C4—44no—
591C4—41no—
592C4—41no—
593C4—82no—
594C4—222no—
595C4—222no—
596C4—224no—
597C4—442no—
598C4—884no—
599C4#1062235312yescomplemented
600C2—22no—
601C2—22no—
602C2—21no—
603C2—21no—
604C2—42no—
605C2—882no—
606C2C22⋊C4×D4411yescharacteristic
607C2C2×#1062235311yescharacteristic
608C2#1307707811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC4×C11×#99C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623086C2
cosocleC24×C11C24
hypercenterC4×#99D11
hypocenterC11#22406
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. C2×#10622353C2semidirect
3. #13071483C2semidirect
4. #13069452C2semidirect
5. #13069073C2semidirect
6. #13068604C2semidirect
7. #13068532C2semidirect
8. C4×C11×#99C2semidirect
11. C2×#66983C4semidirect
13. C22×C4⋊Dic11C4semidirect
18. C2×#66950C4semidirect
19. C2×#66939C4semidirect
22. C2×C4×D44C4semidirect
23. C2×#66922C4semidirect
99. C11×#99D4semidirect
200. C4×#99D11semidirect
327. C4×C11#410semidirect
397. #99D44semidirect
496. C11#22406semidirect
599. C4#10622353semidirect

Maximal subgroups

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

subgroupindex
C2×#106230862
C2×#106223532
#130714832
#130694522
#130690732
#130686042
#130685322
C4×C11×#992
#2240611