Finite Group Databasebeta

← #14664091

Subgroups — #14664091

Order 2816.

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

normal subgroups only

This group has 432 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#13074437C211yesmaximal, characteristic
2#13066930C211yesmaximal, characteristic
3#13066645C214yesmaximal, complemented
4C11×#1742C211yesmaximal, characteristic
5C22×C11×M16—21no—
6C2×C11×#117C2211yescharacteristic
7C2×#66922C411yescharacteristic
8#10622825—21no—
9#10622599—21no—
10#10622592C2212yes—
11#10622562—21no—
12#10622560C412yes—
13#10622549C411yescharacteristic
14#10622541—21no—
15#10622538—21no—
16C11×#343—21no—
17C11×#343C2212yes—
18#10622166C2212yes—
19#10622163—21no—
20C23×C4×C11D411yescharacteristic
21C22×Dic22C2×C412yes—
22C2×C11×M16—24no—
23C2×C11×M16—22no—
24C2×C11×M16—41no—
25C2×C11×M16—42no—
26C22×C8×C11—41no—
27C11×#117—41no—
28C11×#117—41no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C11×C22⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—22no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×Dic11⋊C4—22no—
40#66922—41no—
41#66922—41no—
42C11⋊#95—22no—
43C11⋊#95—21no—
44C11⋊#95—22no—
45C11⋊#95C2×C412yes—
46C22⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)—41no—
48C4×C11⋊C8—41no—
49#11724—111nomaximal, Sylow
50C24×C11C22⋊C411yescharacteristic
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11SD1612yes—
58C22×C4×C11Q1612yes—
59C22×C4×C11C22×C411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×Dic11—22no—
63C22×Dic11—22no—
64C2×Dic22—42no—
65C2×Dic22—82no—
66C11×M16—24no—
67C11×M16—44no—
68C11×M16—42no—
69C2×C8×C11—42no—
70C2×C8×C11—44no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C11×C22⋊C4—41no—
74C11×C22⋊C4—41no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—21no—
79C22⋊Dic11—82no—
80C4⋊Dic11—42no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83C4⋊Dic11—42no—
84Dic11⋊C4—82no—
85C2×C11⋊C8—42no—
86#2628—111no—
87#1742D1111yescharacteristic
88#1458—111no—
89#1354—114no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—41no—
93C23×C11—41no—
94C23×C11#10312yes—
95C23×C11C2×C22⋊C411yescharacteristic
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11#9911yescharacteristic
111C2×C4×C11#9911yescharacteristic
112C2×C4×C11#10312yes—
113C2×C4×C11#10412yes—
114C2×C4×C11C2×SD1611yescharacteristic
115C2×C4×C11C2×Q1611yescharacteristic
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11—42no—
122Dic22—84no—
123C8×C11—44no—
124C11⋊C8—82no—
125C22×M16—21no—
126C2×C4⋊Q8—111no—
127C2×#117C2×D1111yescharacteristic
128#431—221no—
129#400—221no—
130#399—221no—
131#395—112no—
132#393—112no—
133#389—221no—
134#382—111no—
135#380—221no—
136#343—21no—
137#343C2×D1112yes—
138#324—112no—
139#323—221no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—22no—
143C22×C11—42no—
144C22×C11—41no—
145C22×C11—41no—
146C22×C11—81no—
147C22×C11C2×#9911yescharacteristic
148C22×C11C2×#10311yescharacteristic
149C22×C11C2×#10411yescharacteristic
150C4×C11—21no—
151C4×C11—21no—
152C4×C11—41no—
153C4×C11—41no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C11#32812yes—
157C4×C11#32812yes—
158Dic11—82no—
159Dic11—82no—
160C22×Q8—112no—
161C23×C4C22⋊D1111yescharacteristic
162C2×M16—24no—
163C2×M16—22no—
164C2×M16—41no—
165C2×M16—42no—
166C22×C8—41no—
167C4⋊Q8—441no—
168C4⋊Q8—441no—
169#117—41no—
170#117—41no—
171C2×C4⋊C4—221no—
172C2×C4⋊C4—221no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4—222no—
175C2×C4⋊C4C22⋊D1111yescharacteristic
176C2×C4⋊C4C22×D1111yescharacteristic
177C2×C22⋊C4—222no—
178C2×C22⋊C4C4×D1111yescharacteristic
179C2×C22⋊C4D4411yescharacteristic
180C2×C42C4×D1111yescharacteristic
181C2×C42D4411yescharacteristic
182C4⋊C8—441no—
183C22⋊C8—222no—
184C4×C8—441no—
185#95—112no—
186#95—221no—
187#95—222no—
188#95—222no—
189C2×C11—21no—
190C2×C11—21no—
191C2×C11—42no—
192C2×C11C2×#32811yescharacteristic
193C2×C11#212211yescharacteristic
194C2×C11#213511yescharacteristic
195C24(C2×D11)⋊C411yescharacteristic
196C2×Q8—442no—
197C2×Q8—882no—
198C22×C4—22no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—222no—
202C22×C4—222no—
203C22×C4(C2×D11)⋊C411yescharacteristic
204C22×C4(C2×D11)⋊C411yescharacteristic
205C22×C4(C2×D11)⋊C411yescharacteristic
206C22×C4#432412yes—
207C22×C4#432612yes—
208C22×C4C2×C4×D1111yescharacteristic
209C22×C4C2×D4411yescharacteristic
210C22×C4C2×C22⋊D1111yescharacteristic
211M16—24no—
212M16—44no—
213M16—42no—
214C2×C8—42no—
215C2×C8—44no—
216C2×C8—442no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—442no—
220C4⋊C4—442no—
221C4⋊C4—441no—
222C4⋊C4—441no—
223C4⋊C4—882no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C22⋊C4—882no—
227C42—21no—
228C42—21no—
229C42—21no—
230C42—21no—
231C11#1172411yescharacteristic, complemented, Sylow
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23#6687412yes—
237C23C2×(C2×D11)⋊C411yescharacteristic
238Q8—884no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—442no—
254C2×C4—442no—
255C2×C4—442no—
256C2×C4—442no—
257C2×C4—442no—
258C2×C4—442no—
259C2×C4#6686912yes—
260C2×C4#6687011yescharacteristic
261C2×C4#6687011yescharacteristic
262C2×C4#6687412yes—
263C2×C4C2×#432411yescharacteristic
264C2×C4C2×#432611yescharacteristic
265C8—44no—
266C8—882no—
267C22—21no—
268C22—21no—
269C22—22no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—81no—
274C22C2×#6686911yescharacteristic
275C22C2×#6687011yescharacteristic
276C22C2×#6687411yescharacteristic
277C4—21no—
278C4—21no—
279C4—41no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—882no—
284C4—882no—
285C4#1062209012yes—
286C4#1062209012yes—
287C2—21no—
288C2—21no—
289C2—42no—
290C2C2×#1062209011yescharacteristic
291C2#1307026711yescharacteristic
292C2#1307031011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1742C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1742D11
hypocenterC11#11724
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1742

Complements

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

NH ≅ G/Ntype
3. #13066645C2semidirect
231. C11#11724semidirect

Maximal subgroups

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

subgroupindex
#130744372
#130669302
#130666452
C11×#17422
#1172411