Finite Group Databasebeta

← #14664498

Subgroups — #14664498

Order 2816.

382 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074437C211yesmaximal, characteristic
2#13066950C211yesmaximal, characteristic
3#13066636C214yesmaximal
4C11×#1820C211yesmaximal, characteristic
5C2×C11×#117C2211yescharacteristic
6C2×#66922C411yescharacteristic, complemented
7C11×#381—21no—
8#10622825—21no—
9#10622599—21no—
10#10622592C412yescomplemented
11#10622562—21no—
12#10622560C2212yes—
13#10622549C411yescharacteristic, complemented
14#10622541—21no—
15#10622539—21no—
16C11×#342—21no—
17C11×#342C2212yes—
18#10622166—21no—
19#10622163C2212yes—
20C23×C4×C11D411yescharacteristic
21C22×Dic22C2×C412yes—
22C11×#117—41no—
23C11×#117—41no—
24C2×C11×C4⋊C4C2×C411yescharacteristic
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C11×C22⋊C4—22no—
27C2×C11×C22⋊C4D411yescharacteristic
28C2×C11×C22⋊C4C2311yescharacteristic
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C22⋊Dic11—22no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×Dic11⋊C4—22no—
36#66922—41no—
37#66922—41no—
38C11×#95—41no—
39C11×#95—41no—
40C11⋊#95—21no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43C11⋊#95C2×C412yes—
44C22⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)—41no—
46#66867—41no—
47#11812—111nomaximal, Sylow
48C24×C11C2×D411yescharacteristic
49C22×C4×C11—22no—
50C22×C4×C11—21no—
51C22×C4×C11—21no—
52C22×C4×C11—41no—
53C22×C4×C11—42no—
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22×C411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—22no—
61C22×Dic11—22no—
62C2×Dic22—42no—
63C2×Dic22—82no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—41no—
66C11×C22⋊C4—41no—
67C11×C22⋊C4—41no—
68C11×C22⋊C4—42no—
69C11×C22⋊C4—42no—
70C42×C11—21no—
71C42×C11—21no—
72C42×C11—21no—
73C42×C11—21no—
74C22⋊Dic11—82no—
75C4⋊Dic11—42no—
76C4⋊Dic11—42no—
77C4⋊Dic11—41no—
78C4⋊Dic11—41no—
79Dic11⋊C4—82no—
80C2×C11⋊C8—42no—
81#2628—111no—
82#1820D1111yescharacteristic
83#1464—111no—
84#1351—114no—
85C23×C11—21no—
86C23×C11—21no—
87C23×C11—41no—
88C23×C11—41no—
89C23×C11C2×C22⋊C411yescharacteristic
90C23×C11#13712yes—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—41no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—82no—
107C2×C4×C11—82no—
108C2×C4×C11—82no—
109C2×C4×C11#9911yescharacteristic
110C2×C4×C11#9911yescharacteristic
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116C2×Dic11—42no—
117Dic22—84no—
118C11⋊C8—82no—
119C2×C4⋊Q8—111no—
120C2×#117C2×D1111yescharacteristic
121#432—221no—
122#400—221no—
123#399—221no—
124#395—112no—
125#393—112no—
126#389—221no—
127#382—111no—
128#381—21no—
129#380—221no—
130#342—21no—
131#342C2×D1112yes—
132#324—221no—
133#323—112no—
134C22×C11—21no—
135C22×C11—21no—
136C22×C11—22no—
137C22×C11—42no—
138C22×C11—41no—
139C22×C11—41no—
140C22×C11—81no—
141C22×C11C2×#9911yescharacteristic
142C22×C11#41911yescharacteristic
143C22×C11#42111yescharacteristic
144C4×C11—21no—
145C4×C11—21no—
146C4×C11—41no—
147C4×C11—41no—
148C4×C11—41no—
149C4×C11—41no—
150C4×C11—41no—
151C4×C11—162no—
152Dic11—82no—
153Dic11—82no—
154C22×Q8—112no—
155C23×C4C22⋊D1111yescharacteristic
156C4⋊Q8—441no—
157C4⋊Q8—441no—
158#117—41no—
159#117—41no—
160C2×C4⋊C4—221no—
161C2×C4⋊C4—221no—
162C2×C4⋊C4—221no—
163C2×C4⋊C4—222no—
164C2×C4⋊C4C4×D1111yescharacteristic
165C2×C4⋊C4D4411yescharacteristic
166C2×C22⋊C4—22no—
167C2×C22⋊C4—222no—
168C2×C22⋊C4C22⋊D1111yescharacteristic
169C2×C22⋊C4C22×D1111yescharacteristic
170C2×C42C4×D1111yescharacteristic
171C2×C42D4411yescharacteristic
172C4⋊C8—441no—
173C22⋊C8—222no—
174#97—441no—
175#95—41no—
176#95—41no—
177#95—112no—
178#95—222no—
179#95—221no—
180#95—222no—
181C2×C11—21no—
182C2×C11—21no—
183C2×C11—42no—
184C2×C11#151111yescharacteristic
185C2×C11#212211yescharacteristic
186C2×C11#212911yescharacteristic
187C24C2×C22⋊D1111yescharacteristic
188C2×Q8—442no—
189C2×Q8—882no—
190C22×C4—22no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—41no—
194C22×C4—42no—
195C22×C4—222no—
196C22×C4—222no—
197C22×C4(C2×D11)⋊C411yescharacteristic
198C22×C4(C2×D11)⋊C411yescharacteristic
199C22×C4(C2×D11)⋊C411yescharacteristic
200C22×C4(C2×D11)⋊C411yescharacteristic
201C22×C4C2×C4×D1111yescharacteristic
202C22×C4C2×D4411yescharacteristic
203C2×C8—442no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—442no—
207C4⋊C4—442no—
208C4⋊C4—441no—
209C4⋊C4—441no—
210C4⋊C4—882no—
211C22⋊C4—41no—
212C22⋊C4—41no—
213C22⋊C4—42no—
214C22⋊C4—42no—
215C22⋊C4—882no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—21no—
220C11#1181211yescharacteristic, complemented, Sylow
221C23—21no—
222C23—21no—
223C23—41no—
224C23—41no—
225C23C2×(C2×D11)⋊C411yescharacteristic
226C23#6700412yes—
227Q8—884no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—82no—
244C2×C4—82no—
245C2×C4—82no—
246C2×C4—442no—
247C2×C4—442no—
248C2×C4—442no—
249C2×C4—442no—
250C2×C4—442no—
251C2×C4—442no—
252C2×C4#6687011yescharacteristic
253C2×C4#6687011yescharacteristic
254C8—882no—
255C22—21no—
256C22—21no—
257C22—22no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—81no—
262C22C2×#6687011yescharacteristic
263C22#1062261711yescharacteristic
264C22#1062261811yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—162no—
273C4—882no—
274C4—882no—
275C2—21no—
276C2—21no—
277C2—42no—
278C2#1306714811yescharacteristic
279C2#1307026511yescharacteristic
280C2#1307029011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1820C2
socleC22×C11C2×#99
prime radicalC24×C11C2×D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1820D11
hypocenterC11#11812
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1820

Complements

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

NH ≅ G/Ntype
6. C2×#66922C4semidirect
10. #10622592C4semidirect
13. #10622549C4semidirect
220. C11#11812semidirect

Maximal subgroups

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

subgroupindex
#130744372
#130669502
#130666362
C11×#18202
#1181211