Finite Group Databasebeta

← #14664936

Subgroups — #14664936

Order 2816.

372 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 107 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#13068612C211yesmaximal, characteristic
2#13066940C211yesmaximal, characteristic
3#13066643C214yesmaximal
4C11×#2568C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C11×#400C412yes—
8C11×#400C2212yes—
9C11×#391—21no—
10C11×#391—21no—
11C11×#391—21no—
12C11×#382—21no—
13C4×C11×C4⋊C4C411yescharacteristic
14C2×#66900—21no—
15#10622538—21no—
16#10622537—21no—
17#10622168C2212yes—
18#10622166—21no—
19#10622166C2212yes—
20C22×Q8×C11—21no—
21C22×Q8×C11D411yescharacteristic
22C11×C4⋊Q8—41no—
23C11×C4⋊Q8—41no—
24C4×Q8×C11—41no—
25C4×Q8×C11—41no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4C2×C412yes—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C42×C11—21no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×#4318—22no—
37C11×#95—22no—
38C11×#95—22no—
39C11×#95—22no—
40C11×#95—22no—
41C11×#95C2×C412yes—
42#66900—42no—
43C22⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)—41no—
45C4⋊(C11⋊C8)—41no—
46C4⋊(C11⋊C8)—41no—
47C4×C11⋊C8—41no—
48#11907—111nomaximal, Sylow
49C2×Q8×C11—41no—
50C2×Q8×C11—41no—
51C2×Q8×C11—44no—
52C2×Q8×C11—41no—
53C2×Q8×C11—41no—
54C2×Q8×C11SD1612yes—
55C2×Q8×C11Q1612yes—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C11×C4⋊C4—41no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C42×C11—21no—
72C42×C11—21no—
73C42×C11—21no—
74C42×C11—21no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—42no—
78#4318—42no—
79#4318—42no—
80C2×C11⋊C8—42no—
81C2×C11⋊C8—42no—
82#2568D1111yescharacteristic
83#1801—111no—
84#1461—111no—
85#1353—114no—
86C23×C11C2×C22⋊C411yescharacteristic
87Q8×C11—42no—
88Q8×C11—42no—
89Q8×C11—82no—
90Q8×C11—82no—
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—22no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—41no—
102C2×C4×C11—41no—
103C2×C4×C11—41no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—44no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11#9911yescharacteristic
110C2×C4×C11#9911yescharacteristic
111C2×C4×C11#10312yes—
112C2×C4×C11#10312yes—
113C2×C4×C11C2×SD1611yescharacteristic
114C2×C4×C11C2×Q1611yescharacteristic
115C11⋊C8—82no—
116C11⋊C8—82no—
117C2×C4⋊Q8Dic1111yescharacteristic
118C2×C4×Q8C2×D1111yescharacteristic
119#431—221no—
120#423—221no—
121C2×#101—221no—
122#400Dic1112yes—
123#400C2×D1112yes—
124#391—21no—
125#391—21no—
126#391—21no—
127#382—21no—
128C4×C4⋊C4Dic1111yescharacteristic
129#343—112no—
130#324—112no—
131#324—221no—
132C22×C11—21no—
133C22×C11—21no—
134C22×C11C2×#9911yescharacteristic
135C22×C11C2×#10311yescharacteristic
136C22×C11#42111yescharacteristic
137C4×C11—21no—
138C4×C11—22no—
139C4×C11—22no—
140C4×C11—21no—
141C4×C11—21no—
142C4×C11—41no—
143C4×C11—41no—
144C4×C11—41no—
145C4×C11—82no—
146C4×C11—82no—
147C4×C11#35512yes—
148C22×Q8—21no—
149C22×Q8C22⋊D1111yescharacteristic
150C2×M16—222no—
151C4⋊Q8—41no—
152C4⋊Q8—41no—
153C4×Q8—41no—
154C4×Q8—41no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C2×Dic1112yes—
158C2×C4⋊C4C2×Dic1111yescharacteristic
159C2×C4⋊C4C22⋊D1111yescharacteristic
160C2×C4⋊C4C22×D1111yescharacteristic
161C2×C42—21no—
162C2×C42C2×Dic1111yescharacteristic
163C2×C42C22⋊D1111yescharacteristic
164C2×C42C22⋊D1111yescharacteristic
165C4⋊C8—441no—
166C4⋊C8—441no—
167C4⋊C8—441no—
168#101—442no—
169C22⋊C8—222no—
170C4×C8—441no—
171#95—22no—
172#95—22no—
173#95—22no—
174#95—22no—
175#95C2×Dic1112yes—
176C2×C11—21no—
177C2×C11—21no—
178C2×C11#152011yescharacteristic
179C2×C11#212311yescharacteristic
180C2×C11C2×#35511yescharacteristic
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8—44no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8#432512yes—
187C2×Q8#432612yes—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4C22⋊Dic1111yescharacteristic
191C22×C4C22⋊Dic1111yescharacteristic
192C22×C4C22⋊Dic1111yescharacteristic
193C22×C4C22⋊Dic1111yescharacteristic
194C22×C4C22×Dic1111yescharacteristic
195C22×C4C2×C22⋊D1111yescharacteristic
196C22×C4C2×C22⋊D1111yescharacteristic
197M16—442no—
198M16—442no—
199C2×C8—442no—
200C2×C8—442no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—42no—
214C11#1190711yescharacteristic, complemented, Sylow
215C23C2×C22⋊Dic1111yescharacteristic
216Q8—42no—
217Q8—42no—
218Q8—82no—
219Q8—82no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—44no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4#6689811yescharacteristic
239C2×C4#6689811yescharacteristic
240C2×C4#6689912yes—
241C2×C4#6689912yes—
242C2×C4C2×#432511yescharacteristic
243C2×C4C2×#432611yescharacteristic
244C8—882no—
245C8—882no—
246C22—21no—
247C22—21no—
248C22C2×#6689811yescharacteristic
249C22C2×#6689911yescharacteristic
250C22#1062284911yescharacteristic
251C4—21no—
252C4—22no—
253C4—22no—
254C4—21no—
255C4—21no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—82no—
260C4—82no—
261C4#1062218012yes—
262C2—21no—
263C2—21no—
264C2#1306718811yescharacteristic
265C2#1307027011yescharacteristic
266C2C2×#1062218011yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2568C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2568D11
hypocenterC11#11907
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2568

Complements

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

NH ≅ G/Ntype
214. C11#11907semidirect

Maximal subgroups

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

subgroupindex
#130686122
#130669402
#130666432
C11×#25682
#1190711