Finite Group Databasebeta

← #14770328

Subgroups — #14770328

Order 2816.

1114 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071493C212yesmaximal, complemented
2#13069602C212yesmaximal, complemented
3#13069602C214yesmaximal, complemented
4#13068604C212yesmaximal
5#13068604C211yesmaximal, characteristic
6C4×#66898C211yesmaximal, characteristic
7C4×#66898C212yesmaximal
8C2×C11×#554C211yesmaximal, characteristic
9C11×#554—22no—
10C11×#554—24no—
11C11×#554—22no—
12C2×C11×C4⋊Q8C411yescharacteristic, complemented
13C2×C11×#125C412yescomplemented
14C2×C11×C22⋊Q8C412yescomplemented
15C2×C11×C22⋊Q8C411yescharacteristic, complemented
16C2×C11×C22⋊Q8C2212yes—
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C411yescharacteristic, complemented
19C2×C4×D4×C11C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4C411yescharacteristic, complemented
22C22×C11×C4⋊C4C2211yescharacteristic
23C2×#66898C2211yescharacteristic
24C2×#66898C2212yes—
25C2×#66898C2211yescharacteristic
26#10622825C2214yes—
27#10622825C2212yes—
28C4×C22⋊Dic11C2212yes—
29C4×C22⋊Dic11C2214yes—
30#10622598—22no—
31#10622594—24no—
32C4⋊C4×Dic11—22no—
33#10622164C2214yes—
34#10622164C2212yes—
35#10622164C2214yes—
36#10622164C2212yes—
37C22×Q8×C11C2×C411yescharacteristic
38C22×Q8×C11C2×C412yes—
39C22×D4×C11C2311yescharacteristic
40C23×C4×C11C2×C411yescharacteristic
41C23×C4×C11C2×C412yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C11×C4⋊Q8—22no—
45C11×C4⋊Q8—22no—
46C11×#125—24no—
47C11×#125—24no—
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—24no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C4×D4×C11—24no—
60C4×D4×C11—24no—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2×C412yes—
67C2×C11×C4⋊C4C2×C411yescharacteristic
68C2×C11×C4⋊C4C2×C411yescharacteristic
69C2×C11×C4⋊C4C2×C412yes—
70C2×C11×C4⋊C4C2×C412yes—
71C2×C11×C4⋊C4C2×C412yes—
72C2×C11×C4⋊C4C2×C412yes—
73C2×C11×C4⋊C4C2×C411yescharacteristic
74C2×C11×C4⋊C4C2×C412yes—
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C11×C4⋊C4D412yes—
77C2×C11×C4⋊C4D414yes—
78C2×C11×C4⋊C4D412yes—
79C2×C11×C22⋊C4C2×C412yes—
80C2×C11×C22⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2312yes—
82C2×C11×C22⋊C4C2311yescharacteristic
83C2×C42×C11C2×C412yes—
84C2×C42×C11C2×C411yescharacteristic
85C2×C22⋊Dic11C2312yes—
86C2×C22⋊Dic11C2314yes—
87C2×C22⋊Dic11C2312yes—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—24no—
90C2×C4×Dic11—22no—
91C2×C4×Dic11—24no—
92#66898—22no—
93#66898—24no—
94#66898Q814yescomplemented
95C11⋊#95—22no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—22no—
99#22513—111nomaximal, Sylow
100C24×C11C22×C411yescharacteristic
101C24×C11C2411yescharacteristic
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—24no—
105C2×Q8×C11—42no—
106C2×Q8×C11—82no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11C2×Q812yes—
110C2×D4×C11#4112yes—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—82no—
118C22×C4×C11—82no—
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C412yes—
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D414yes—
131C22×C4×C11C2×D414yes—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—24no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4C22⋊C412yes—
146C11×C4⋊C4C22⋊C411yescharacteristic
147C11×C4⋊C4C22⋊C411yescharacteristic
148C11×C4⋊C4C22⋊C414yes—
149C11×C4⋊C4C22⋊C414yes—
150C11×C4⋊C4C22⋊C412yes—
151C11×C4⋊C4C22⋊C412yes—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—22no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11—21no—
159C42×C11—21no—
160C22⋊Dic11—22no—
161C22⋊Dic11—24no—
162C22⋊Dic11—22no—
163C22⋊Dic11—22no—
164C22⋊Dic11—24no—
165C22⋊Dic11C2×Q814yes—
166C4⋊Dic11—44no—
167C4⋊Dic11—84no—
168C4×Dic11—44no—
169C4×Dic11—84no—
170C2×#554D1111yescharacteristic
171#2345—112no—
172#1996—114no—
173#1996—112no—
174#1799—112no—
175#1799—111no—
176C4×#99—112no—
177C4×#99—111no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11C4×Q812yes—
185C23×C11C23×C411yescharacteristic
186C23×C11C22×D412yes—
187C23×C11C22×Q811yescharacteristic
188C23×C11C2×#4111yescharacteristic
189C23×C112−1+412yes—
190Q8×C11—42no—
191Q8×C11—42no—
192Q8×C11—84no—
193D4×C11—24no—
194D4×C11—24no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—24no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—44no—
204C2×C4×C11—44no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—82no—
216C2×C4×C11—82no—
217C2×C4×C11C2×C22⋊C412yes—
218C2×C4×C11C2×C22⋊C412yes—
219C2×C4×C11C2×C22⋊C411yescharacteristic
220C2×C4×C11C2×C22⋊C412yes—
221C2×C4×C11C2×C22⋊C414yes—
222C2×C4×C11C2×C22⋊C411yescharacteristic
223C2×C4×C11C4×Q812yes—
224C2×Dic11—24no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—44no—
229C2×Dic11—44no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—44no—
233#554—22no—
234#554—24no—
235#554—22no—
236C2×C4⋊Q8Dic1111yescharacteristic, complemented
237C2×#125Dic1112yescomplemented
238C2×C22⋊Q8Dic1112yescomplemented
239C2×C22⋊Q8Dic1111yescharacteristic, complemented
240C2×C22⋊Q8C2×D1112yes—
241C2×C22⋊Q8C2×D1111yescharacteristic
242C2×C4×Q8Dic1111yescharacteristic, complemented
243C2×C4×D4C2×D1112yes—
244C2×C4×D4C2×D1111yescharacteristic
245C22×C4⋊C4Dic1111yescharacteristic, complemented
246C22×C4⋊C4C2×D1111yescharacteristic
247C2×#99—111no—
248C2×#99—111no—
249C2×#99—112no—
250#389—222no—
251#387—224no—
252#380—114no—
253#380—112no—
254C4×C4⋊C4—222no—
255C4×C22⋊C4—112no—
256C4×C22⋊C4—114no—
257#342—114no—
258#342—112no—
259#342—114no—
260#342—112no—
261C22×C11—21no—
262C22×C11—22no—
263C22×C11—21no—
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—41no—
267C22×C11—41no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—41no—
272C22×C11—41no—
273C22×C11C22×C22⋊C411yescharacteristic
274C22×C11C2×C4×Q811yescharacteristic
275C22×C11#51911yescharacteristic
276C22×C11#54812yes—
277C22×C11D4×Q812yes—
278C4×C11—22no—
279C4×C11—21no—
280C4×C11—22no—
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—24no—
284C4×C11—41no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—41no—
288C4×C11#41012yes—
289Dic11—44no—
290Dic11—82no—
291Dic11—84no—
292C22×Q8C2×Dic1111yescharacteristic
293C22×Q8C2×Dic1112yes—
294C22×D4C22×D1111yescharacteristic
295C23×C4C2×Dic1111yescharacteristic
296C23×C4C2×Dic1112yes—
297C23×C4C22×D1111yescharacteristic
298C23×C4C22×D1112yes—
299C4⋊Q8—22no—
300C4⋊Q8—22no—
301#125—24no—
302#125—24no—
303C22⋊Q8—24no—
304C22⋊Q8—24no—
305C22⋊Q8—22no—
306C22⋊Q8—22no—
307C22⋊Q8—24no—
308C22⋊Q8—24no—
309C22⋊Q8—22no—
310C22⋊Q8—22no—
311C4×Q8—22no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×D4—24no—
315C4×D4—24no—
316C4×D4—22no—
317C4×D4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4—224no—
323C2×C4⋊C4C2×Dic1112yes—
324C2×C4⋊C4C2×Dic1111yescharacteristic
325C2×C4⋊C4C2×Dic1111yescharacteristic
326C2×C4⋊C4C2×Dic1112yes—
327C2×C4⋊C4C2×Dic1112yes—
328C2×C4⋊C4C2×Dic1112yes—
329C2×C4⋊C4C2×Dic1112yes—
330C2×C4⋊C4C2×Dic1111yescharacteristic
331C2×C4⋊C4C2×Dic1112yes—
332C2×C4⋊C4C2×Dic1111yescharacteristic
333C2×C4⋊C4C22⋊D1112yes—
334C2×C4⋊C4C22⋊D1114yes—
335C2×C4⋊C4C22⋊D1112yes—
336C2×C22⋊C4—112no—
337C2×C22⋊C4—112no—
338C2×C22⋊C4—114no—
339C2×C22⋊C4C2×Dic1112yes—
340C2×C22⋊C4C2×Dic1111yescharacteristic
341C2×C22⋊C4C22×D1112yes—
342C2×C22⋊C4C22×D1111yescharacteristic
343C2×C42—222no—
344C2×C42—224no—
345C2×C42C2×Dic1112yes—
346C2×C42C2×Dic1111yescharacteristic
347#99—114no—
348#99—222no—
349#99—224no—
350#95—222no—
351#95—224no—
352#95—224no—
353#95—222no—
354C2×C11—22no—
355C2×C11—22no—
356C2×C11—21no—
357C2×C11—21no—
358C2×C11—42no—
359C2×C11Q8×C22⋊C411yescharacteristic
360C2×C11C2×#41011yescharacteristic
361C2×C11#288311yescharacteristic
362C24C22×Dic1111yescharacteristic
363C24C23×D1111yescharacteristic
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—24no—
367C2×Q8—42no—
368C2×Q8—82no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4Q8×D1112yes—
372C2×D4#434312yes—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—82no—
380C22×C4—82no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—224no—
384C22×C4C22×Dic1111yescharacteristic
385C22×C4C22×Dic1111yescharacteristic
386C22×C4C22×Dic1112yes—
387C22×C4C22×Dic1111yescharacteristic
388C22×C4C22×Dic1111yescharacteristic
389C22×C4C22×Dic1112yes—
390C22×C4C22×Dic1112yes—
391C22×C4C22×Dic1111yescharacteristic
392C22×C4C22×Dic1112yes—
393C22×C4C2×C22⋊D1112yes—
394C22×C4C2×C22⋊D1112yes—
395C22×C4C2×C22⋊D1114yes—
396C22×C4C2×C22⋊D1114yes—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4—444no—
408C4⋊C4—884no—
409C4⋊C4C22⋊Dic1112yes—
410C4⋊C4C22⋊Dic1111yescharacteristic
411C4⋊C4C22⋊Dic1111yescharacteristic
412C4⋊C4C22⋊Dic1114yes—
413C4⋊C4C22⋊Dic1114yes—
414C4⋊C4C22⋊Dic1112yes—
415C4⋊C4C22⋊Dic1112yes—
416C22⋊C4—24no—
417C22⋊C4—22no—
418C22⋊C4—24no—
419C22⋊C4—22no—
420C22⋊C4—114no—
421C22⋊C4—222no—
422C22⋊C4—222no—
423C22⋊C4—224no—
424C22⋊C4—222no—
425C22⋊C4—224no—
426C42—22no—
427C42—22no—
428C42—21no—
429C42—21no—
430C42—444no—
431C42—884no—
432C11#2251311yescharacteristic, complemented, Sylow
433C23—21no—
434C23—21no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23Q8×Dic1112yes—
440C23C2×Q8×D1111yescharacteristic
441C23C2×#434311yescharacteristic
442C23#6704012yes—
443C23C23×Dic1111yescharacteristic
444C23C22×C22⋊D1112yes—
445Q8—42no—
446Q8—42no—
447Q8—84no—
448D4—24no—
449D4—24no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—22no—
458C2×C4—44no—
459C2×C4—44no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—82no—
471C2×C4—82no—
472C2×C4—224no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—444no—
477C2×C4—444no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—444no—
481C2×C4Q8×Dic1112yes—
482C2×C4C2×C22⋊Dic1112yes—
483C2×C4C2×C22⋊Dic1112yes—
484C2×C4C2×C22⋊Dic1111yescharacteristic
485C2×C4C2×C22⋊Dic1112yes—
486C2×C4C2×C22⋊Dic1114yes—
487C2×C4C2×C22⋊Dic1111yescharacteristic
488C22—21no—
489C22—22no—
490C22—21no—
491C22—22no—
492C22—22no—
493C22—41no—
494C22—41no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—41no—
499C22—41no—
500C22C2×Q8×Dic1111yescharacteristic
501C22#1062334311yescharacteristic
502C22Q8×C22⋊D1112yes—
503C22#1062334812yes—
504C22C22×C22⋊Dic1111yescharacteristic
505C4—21no—
506C4—22no—
507C4—22no—
508C4—22no—
509C4—24no—
510C4—22no—
511C4—41no—
512C4—42no—
513C4—42no—
514C4—41no—
515C4—444no—
516C4—882no—
517C4—884no—
518C4#1062285312yes—
519C2—22no—
520C2—22no—
521C2—21no—
522C2—21no—
523C2—42no—
524C2Q8×C22⋊Dic1111yescharacteristic
525C2C2×#1062285311yescharacteristic
526C2#1307707711yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC2×C11×#554C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×C11C23
cosocleC24×C11C24
hypercenterC2×#554D11
hypocenterC11#22513
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #13071493C2semidirect
2. #13069602C2semidirect
3. #13069602C2semidirect
12. C2×C11×C4⋊Q8C4semidirect
13. C2×C11×#125C4semidirect
14. C2×C11×C22⋊Q8C4semidirect
15. C2×C11×C22⋊Q8C4semidirect
18. C2×C4×Q8×C11C4semidirect
21. C22×C11×C4⋊C4C4semidirect
94. #66898Q8semidirect
236. C2×C4⋊Q8Dic11semidirect
237. C2×#125Dic11semidirect
238. C2×C22⋊Q8Dic11semidirect
239. C2×C22⋊Q8Dic11semidirect
242. C2×C4×Q8Dic11semidirect
245. C22×C4⋊C4Dic11semidirect
432. C11#22513semidirect

Maximal subgroups

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

subgroupindex
#130714932
#130696022
#130686042
C4×#668982
C2×C11×#5542
#2251311