Finite Group Databasebeta

← #14772768

Subgroups — #14772768

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622292C211yesmaximal, characteristic
2#13071574C212yesmaximal
3#13069385C212yesmaximal
4#13069384C212yesmaximal
5#13069376C212yesmaximal
6#13068748C212yesmaximal
7#13068747C211yesmaximal, characteristic
8#13068512C212yesmaximal
9C4×C11×#106C211yesmaximal, characteristic
10C2×C4×Dic22C2211yescharacteristic
11C2×C11×#106C2212yes—
12C2×C4×C8×C11C2211yescharacteristic
13C4×C11×C4⋊C4C2212yes—
14C2×#66879C2212yes—
15C2×Dic11⋊C8C2212yes—
16#10622590C2212yes—
17#10622589C2212yes—
18C4⋊C4×Dic11C2212yes—
19C4⋊C4×Dic11C2212yes—
20C2×#66872C2212yes—
21C2×#66871C2212yes—
22#10622549C2212yes—
23#10622546—22no—
24C4×Dic11⋊C4—22no—
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26#10622292C418yescomplemented
27#10622267—22no—
28#10622259—22no—
29C11×#340C2211yescharacteristic
30C11×#340C2211yescharacteristic
31#10622189C2211yescharacteristic
32#10622189C2211yescharacteristic
33#10622189C2212yes—
34#10622167C2212yes—
35#10622167C2212yes—
36C22×Dic22D411yescharacteristic
37C22×C8×C11C2311yescharacteristic
38C22×C8×C11C2311yescharacteristic
39C2×C11×C4⋊C4C2312yes—
40C2×C11×C4⋊C4C2312yes—
41C2×C42×C11—22no—
42C2×C42×C11C2311yescharacteristic
43C2×C4⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11C2312yes—
45C2×C4⋊Dic11C2312yes—
46C2×Dic11⋊C4—22no—
47C2×Dic11⋊C4—22no—
48C2×Dic11⋊C4D412yes—
49C2×C4×Dic11—22no—
50C2×C4×Dic11—22no—
51C2×C4×Dic11C2312yes—
52C22×C11⋊C8C2312yes—
53C4×Dic22C2×C414yes—
54C4×Dic22Q814yes—
55C11×#106—24no—
56C4×C8×C11C2×C414yes—
57C11×#95—22no—
58C11⋊#95—22no—
59C11⋊#95—22no—
60C11⋊#95—22no—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64#66879C2×C418yes—
65Dic11⋊C8C2×C418yes—
66#66872—24no—
67#66871—24no—
68C4⋊(C11⋊C8)C2×C414yes—
69#22745—111nomaximal, Sylow
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2411yescharacteristic
75C22×Dic11—22no—
76C22×Dic11—22no—
77C22×Dic11C2×D412yes—
78C22×Dic11C2×D412yes—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×Dic22C4⋊C414yes—
82C2×C8×C11—22no—
83C2×C8×C11—22no—
84C2×C8×C11C22×C412yes—
85C2×C8×C11C22×C412yes—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4#4114yes—
90C42×C11—82no—
91C42×C11C22×C412yes—
92C42×C11C2×Q812yes—
93C4⋊Dic11—22no—
94C4⋊Dic11—22no—
95C4⋊Dic11—22no—
96C4⋊Dic11—22no—
97C4⋊Dic11C4⋊C414yes—
98Dic11⋊C4—44no—
99Dic11⋊C4—82no—
100Dic11⋊C4C4⋊C418yes—
101C4×Dic11—44no—
102C4×Dic11—82no—
103C4×Dic11C22×C414yes—
104C4×Dic11C2×Q814yes—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8C22×C414yes—
108C2×#446—111no—
109#2355—112no—
110#1949—112no—
111#1949—112no—
112#1948—112no—
113#1836—112no—
114#1835—111no—
115#1776—112no—
116C4×#106D1111yescharacteristic
117C23×C11C22×D411yescharacteristic
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—22no—
121C2×C4×C11—24no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11C2×C4⋊C412yes—
128C2×C4×C11C2×C4⋊C412yes—
129C2×C4×C11C23×C411yescharacteristic
130C2×C4×C11C22×Q811yescharacteristic
131C2×C4×C11C2×#4112yes—
132C2×C4×C112−1+412yes—
133C2×Dic11—22no—
134C2×Dic11—22no—
135C2×Dic11—22no—
136C2×Dic11—22no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143C2×Dic11C2×C4⋊C414yes—
144C2×Dic11C2×C4⋊C414yes—
145Dic22—44no—
146C8×C11—22no—
147C8×C11—22no—
148C11⋊C8—24no—
149C2×C4×Q8—111no—
150#446—118no—
151C2×#107—112no—
152C2×#106—112no—
153C2×#106C2×D1112yes—
154C2×C4⋊C8—112no—
155C2×C4⋊C8—111no—
156C2×#97—112no—
157C2×C4×C8C2×D1111yescharacteristic
158#391—222no—
159#387—222no—
160#387—222no—
161#384—112no—
162#382—112no—
163#382—112no—
164C4×C4⋊C4—112no—
165C4×C4⋊C4—112no—
166C4×C4⋊C4—222no—
167C4×C4⋊C4C2×D1112yes—
168#340—112no—
169#340—111no—
170#340—111no—
171#340—112no—
172#340—112no—
173#340C2×D1111yescharacteristic
174#340C2×D1111yescharacteristic
175C22×C11C22×C4⋊C411yescharacteristic
176C22×C11#54812yes—
177C22×C11#57511yescharacteristic
178C22×C11#57511yescharacteristic
179C22×C11#57712yes—
180C4×C11—22no—
181C4×C11—22no—
182C4×C11—44no—
183C4×C11—82no—
184C4×C11C4×#4111yescharacteristic
185C4×C11#51911yescharacteristic
186C4×C11#55712yes—
187Dic11—24no—
188Dic11—24no—
189Dic11—82no—
190Dic11—82no—
191C22×Q8—111no—
192C22×C8—112no—
193C22×C8C22×D1111yescharacteristic
194C22×C8C22×D1111yescharacteristic
195C4×Q8—114no—
196C4×Q8—114no—
197C2×C4⋊C4—112no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—112no—
200C2×C4⋊C4—112no—
201C2×C4⋊C4—222no—
202C2×C4⋊C4—222no—
203C2×C4⋊C4C22×D1112yes—
204C2×C4⋊C4C22×D1112yes—
205C2×C42—22no—
206C2×C42—112no—
207C2×C42—222no—
208C2×C42—222no—
209C2×C42C22×D1111yescharacteristic
210#107—224no—
211#106—24no—
212#106—224no—
213C4⋊C8—118no—
214C4⋊C8—114no—
215#97—118no—
216C4×C8C4×D1114yes—
217#95—22no—
218#95—222no—
219#95—222no—
220#95—222no—
221#95—222no—
222#95—222no—
223#95—222no—
224C2×C11#235111yescharacteristic
225C2×C11#291111yescharacteristic
226C2×C11#291211yescharacteristic
227C2×C11#337112yes—
228C2×C11#337612yes—
229C2×Q8—114no—
230C2×Q8—441no—
231C2×Q8—441no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—112no—
235C22×C4—112no—
236C22×C4—222no—
237C22×C4—222no—
238C22×C4D4×D1111yescharacteristic
239C22×C4D4×D1111yescharacteristic
240C22×C4C23×D1111yescharacteristic
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—114no—
244C2×C8—222no—
245C2×C8—222no—
246C2×C8C2×C4×D1112yes—
247C2×C8C2×C4×D1112yes—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—118no—
252C4⋊C4—114no—
253C4⋊C4—222no—
254C4⋊C4—222no—
255C4⋊C4—222no—
256C4⋊C4—222no—
257C4⋊C4—444no—
258C4⋊C4—882no—
259C4⋊C4#433914yes—
260C42—82no—
261C42—114no—
262C42—114no—
263C42—444no—
264C42—882no—
265C42C2×C4×D1112yes—
266C42Q8×D1112yes—
267C11#2274511yescharacteristic, complemented, Sylow
268C23C2×D4×D1111yescharacteristic
269Q8—444no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—24no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—114no—
280C2×C4—114no—
281C2×C4—222no—
282C2×C4—222no—
283C2×C4—222no—
284C2×C4—222no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—442no—
290C2×C4—442no—
291C2×C4C4⋊C4×D1112yes—
292C2×C4C4⋊C4×D1112yes—
293C2×C4C22×C4×D1111yescharacteristic
294C2×C4C2×#433912yes—
295C2×C4C2×Q8×D1111yescharacteristic
296C2×C4#6704312yes—
297C8—22no—
298C8—22no—
299C8—224no—
300C22C2×C4⋊C4×D1111yescharacteristic
301C22#1062308312yes—
302C22#1062329312yes—
303C22#1062329911yescharacteristic
304C22#1062329911yescharacteristic
305C4—22no—
306C4—22no—
307C4—44no—
308C4—82no—
309C4—224no—
310C4—224no—
311C4—882no—
312C4—882no—
313C4C4×#433911yescharacteristic
314C4#1062304711yescharacteristic
315C4#1062309812yes—
316C2#1307153611yescharacteristic
317C2#1307720411yescharacteristic
318C2#1307720711yescharacteristic
319C2#1308138012yes—
320C2#1308143912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#106C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC4×#106D11
hypocenterC11#22745
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
26. #10622292C4semidirect
267. C11#22745semidirect

Maximal subgroups

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

subgroupindex
C2×#106222922
#130715742
#130693852
#130693842
#130693762
#130687482
#130687472
#130685122
C4×C11×#1062
#2274511