Finite Group Databasebeta

← #14653881

Subgroups — #14653881

Order 2816.

424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 123 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#13076979C211yesmaximal, characteristic
2#13068365C211yesmaximal, characteristic
3#13066498C214yesmaximal
4C11×#1767C211yesmaximal, characteristic
5C2×#66923C412yes—
6C2×C11×C4⋊C8—21no—
7C2×C11×#97C2212yes—
8C43×C11C2211yescharacteristic
9#10622549C2212yes—
10#10622548C411yescharacteristic
11#10622548C411yescharacteristic
12#10622541—21no—
13#10622541—21no—
14#10622541—21no—
15#10622541—21no—
16C2×#66867C2212yes—
17C11×#336—21no—
18#10622162—21no—
19#10622162—21no—
20C22×C8×C11—22no—
21C2×C42×C11C2×C411yescharacteristic
22C2×C42×C11C2×C411yescharacteristic
23C2×C42×C11D411yescharacteristic
24C2×C42×C11D411yescharacteristic
25C2×C42×C11D411yescharacteristic
26C2×C42×C11D411yescharacteristic
27C2×C42×C11C2311yescharacteristic
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11C2×C412yes—
33C2×C4⋊Dic11C2×C412yes—
34C2×Dic11⋊C4—22no—
35C2×Dic11⋊C4—22no—
36C22×C11⋊C8—22no—
37#66923—44no—
38C11×C4⋊C8—24no—
39C11×#97—24no—
40C11⋊#95—22no—
41C11⋊#95—22no—
42#66867—22no—
43#66867Q814yes—
44#9894—111nomaximal, Sylow
45C22×C4×C11C22⋊C411yescharacteristic
46C22×C4×C11C22⋊C411yescharacteristic
47C22×C4×C11C22⋊C411yescharacteristic
48C22×C4×C11C22⋊C411yescharacteristic
49C22×C4×C11C22×C411yescharacteristic
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11C2×D411yescharacteristic
52C22×Dic11—22no—
53C22×Dic11—22no—
54C2×C8×C11—24no—
55C2×C8×C11—42no—
56C2×C8×C11—42no—
57C42×C11—22no—
58C42×C11—22no—
59C42×C11—22no—
60C42×C11—41no—
61C42×C11—41no—
62C42×C11—41no—
63C42×C11C2×Q812yes—
64C42×C11#4112yes—
65C4⋊Dic11—42no—
66C4⋊Dic11—42no—
67C4⋊Dic11—42no—
68C4⋊Dic11—42no—
69C4⋊Dic11—42no—
70C4⋊Dic11—42no—
71Dic11⋊C4—44no—
72Dic11⋊C4—44no—
73C2×C11⋊C8—24no—
74C2×C11⋊C8—42no—
75C2×C11⋊C8—42no—
76#2859—111no—
77#1767D1111yescharacteristic
78#1745—111no—
79#1295—114no—
80C23×C11C2×C22⋊C411yescharacteristic
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11#10012yes—
97C2×C4×C11#10112yes—
98C2×C4×C11#10412yes—
99C2×C4×C11C4×Q812yes—
100C2×C4×C11C22⋊Q812yes—
101C2×C4×C11#12411yescharacteristic
102C2×C4×C11C4⋊Q811yescharacteristic
103C2×Dic11—42no—
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C8×C11—44no—
110C11⋊C8—44no—
111C2×#125—112no—
112C2×C4⋊C8—21no—
113C2×#97—112no—
114C2×#97C2×D1112yes—
115#389—221no—
116#389—221no—
117#389—221no—
118#389—221no—
119#384—111no—
120#384—111no—
121#382—112no—
122C43C2×D1111yescharacteristic
123#336—21no—
124#336—221no—
125#336—221no—
126C22×C11#39111yescharacteristic
127C22×C11C2×#10011yescharacteristic
128C22×C11C2×#10111yescharacteristic
129C22×C11C2×#10411yescharacteristic
130C22×C11#42111yescharacteristic
131C22×C11#42111yescharacteristic
132C22×C11#42111yescharacteristic
133C4×C11—21no—
134C4×C11—21no—
135C4×C11—22no—
136C4×C11—22no—
137C4×C11—22no—
138C4×C11—22no—
139C4×C11—22no—
140C4×C11—41no—
141Dic11—82no—
142Dic11—82no—
143C22×C8—22no—
144C22×C8—222no—
145#125—444no—
146C2×C4⋊C4—112no—
147C2×C4⋊C4—112no—
148C2×C4⋊C4—222no—
149C2×C4⋊C4—222no—
150C2×C4⋊C4—221no—
151C2×C4⋊C4—221no—
152C2×C4⋊C4—221no—
153C2×C4⋊C4—221no—
154C2×C42C4×D1111yescharacteristic
155C2×C42C4×D1111yescharacteristic
156C2×C42D4411yescharacteristic
157C2×C42D4411yescharacteristic
158C2×C42C22⋊D1111yescharacteristic
159C2×C42C22⋊D1111yescharacteristic
160C2×C42C22×D1111yescharacteristic
161C4⋊C8—24no—
162#97—24no—
163#97—114no—
164#97—222no—
165#95—222no—
166#95—222no—
167C2×C11#152811yescharacteristic
168C2×C11#153011yescharacteristic
169C2×C11#153411yescharacteristic
170C2×C11#153611yescharacteristic
171C2×C11#198611yescharacteristic
172C2×C11#199511yescharacteristic
173C2×C11#199711yescharacteristic
174C22×C4—222no—
175C22×C4—222no—
176C22×C4(C2×D11)⋊C411yescharacteristic
177C22×C4(C2×D11)⋊C411yescharacteristic
178C22×C4(C2×D11)⋊C411yescharacteristic
179C22×C4(C2×D11)⋊C411yescharacteristic
180C22×C4C2×C4×D1111yescharacteristic
181C22×C4C2×D4411yescharacteristic
182C22×C4C2×C22⋊D1111yescharacteristic
183C2×C8—24no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—224no—
187C2×C8—442no—
188C2×C8—442no—
189C4⋊C4—442no—
190C4⋊C4—442no—
191C4⋊C4—444no—
192C4⋊C4—442no—
193C4⋊C4—442no—
194C4⋊C4—442no—
195C4⋊C4—442no—
196C4⋊C4—444no—
197C42—22no—
198C42—22no—
199C42—22no—
200C42—41no—
201C42—41no—
202C42—41no—
203C42#434112yes—
204C42Q8×D1112yes—
205C11#989411yescharacteristic, complemented, Sylow
206C23C2×(C2×D11)⋊C411yescharacteristic
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—442no—
223C2×C4—442no—
224C2×C4—442no—
225C2×C4—442no—
226C2×C4—442no—
227C2×C4—442no—
228C2×C4#6686912yes—
229C2×C4#6688712yes—
230C2×C4#6688812yes—
231C2×C4#6694012yes—
232C2×C4#6695012yes—
233C2×C4#6698911yescharacteristic
234C2×C4#6699711yescharacteristic
235C8—44no—
236C8—444no—
237C22C2×#6686911yescharacteristic
238C22#1062258711yescharacteristic
239C22#1062261811yescharacteristic
240C22C2×#6688711yescharacteristic
241C22C2×#6688811yescharacteristic
242C22#1062275211yescharacteristic
243C22#1062275211yescharacteristic
244C4—22no—
245C4—22no—
246C4—22no—
247C4—22no—
248C4—22no—
249C4—21no—
250C4—21no—
251C4—41no—
252C4—882no—
253C4—882no—
254C2#1306721711yescharacteristic
255C2#1306722611yescharacteristic
256C2#1306724211yescharacteristic
257C2#1306725011yescharacteristic
258C2#1306955911yescharacteristic
259C2#1306959611yescharacteristic
260C2#1306960411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1767C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1767D11
hypocenterC11#9894
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
205. C11#9894semidirect

Maximal subgroups

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

subgroupindex
#130769792
#130683652
#130664982
C11×#17672
#989411