Finite Group Databasebeta

← #13074755

Subgroups — #13074755

Order 1408.

534 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×C11×#124C211yesmaximal, characteristic, complemented
2C2×#66929C211yesmaximal, characteristic, complemented
3#10622844C211yesmaximal, characteristic, complemented
4#10622842C211yesmaximal, characteristic, complemented
5#10622836C211yesmaximal, characteristic
6#10622835C211yesmaximal, characteristic, complemented
7#10622574C212yesmaximal, complemented
8#10622570C212yesmaximal, complemented
9#10622561C212yesmaximal, complemented
10#10622558C212yesmaximal, complemented
11C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C22×C22⋊D11C2212yes—
15C11×#124—24no—
16C2×C11×C22⋊C4C2212yes—
17C2×C11×C22⋊C4C2212yes—
18C2×C42×C11C2211yescharacteristic
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2212yes—
22C2×(C2×D11)⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2212yes—
26C2×C4⋊Dic11C2212yes—
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2211yescharacteristic
30C2×Dic11⋊C4C2212yes—
31C2×C4×Dic11C2212yes—
32#66929—24no—
33C11⋊#95C2211yescharacteristic
34C11⋊#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2312yes—
38C23×D11C2311yescharacteristic
39C2×Q8×C11—22no—
40C2×Q8×C11—42no—
41C2×D4×C11—22no—
42C2×D4×C11—42no—
43C22×C4×C11C2312yes—
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C2×C22⋊D11—24no—
48C2×C22⋊D11—42no—
49C2×C22⋊D11—42no—
50C22×Dic11C2312yes—
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2312yes—
55C11×C22⋊C4—24no—
56C11×C22⋊C4—24no—
57C42×C11D414yescomplemented
58C22⋊Dic11—24no—
59C22⋊Dic11—42no—
60C22⋊Dic11—42no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—42no—
65C4⋊Dic11—24no—
66Dic11⋊C4—22no—
67Dic11⋊C4—22no—
68Dic11⋊C4—22no—
69Dic11⋊C4—42no—
70C4×Dic11—42no—
71#2662—111nomaximal, Sylow
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11—22no—
79C23×C11C2411yescharacteristic
80C22×D11—21no—
81C22×D11—22no—
82C22×D11—22no—
83C22×D11—21no—
84C22×D11—21no—
85Q8×C11—44no—
86D4×C11—44no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11C2×D412yes—
95C2×C4×C11C2×D412yes—
96C2×C4×C11C2×D412yes—
97C22⋊D11—48no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—21no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—21no—
109C2×Dic11—21no—
110C2×Dic11#4114yes—
111C2×#126—111no—
112C2×#124D1111yescharacteristic, complemented
113#396—112no—
114#395—111no—
115#394—111no—
116#394—112no—
117#393—111no—
118#392—111no—
119#390—112no—
120#388—112no—
121C4×C4⋊C4—111no—
122C22×C11—42no—
123C22×C11—42no—
124C22×C11—42no—
125C22×C11—42no—
126C22×C11—42no—
127C22×C11—42no—
128C22×C11—42no—
129C22×C11C22×D411yescharacteristic
130C22×C11C2×#4112yes—
131C22×C11H(5,𝔽2)12yes—
132C22×C11H(5,𝔽2)11yescharacteristic
133C22×C112−1+411yescharacteristic
134C2×D11—41no—
135C2×D11—41no—
136C2×D11—41no—
137C2×D11—42no—
138C2×D11—42no—
139C4×C11—22no—
140C4×C11—22no—
141C4×C11—22no—
142C4×C11—42no—
143Dic11—24no—
144Dic11—41no—
145Dic11—41no—
146Dic11—41no—
147Dic11—42no—
148C22×Q8C2×D1111yescharacteristic
149C22×D4—112no—
150C22×D4C2×D1111yescharacteristic
151#126—224no—
152#124—24no—
153C2×C4⋊C4—111no—
154C2×C4⋊C4—111no—
155C2×C4⋊C4—111no—
156C2×C4⋊C4—112no—
157C2×C4⋊C4—112no—
158C2×C22⋊C4—112no—
159C2×C22⋊C4—111no—
160C2×C22⋊C4—111no—
161C2×C22⋊C4—111no—
162C2×C22⋊C4—112no—
163C2×C22⋊C4—112no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4C2×D1112yes—
166C2×C22⋊C4C2×D1112yes—
167C2×C42—112no—
168C2×C42C2×D1111yescharacteristic
169#95—111no—
170#95—111no—
171#95—112no—
172#95—112no—
173C2×C11—82no—
174C2×C11#53211yescharacteristic
175C2×C11#53511yescharacteristic
176C2×C11#53711yescharacteristic
177C2×C11#53812yes—
178C2×C11#54212yes—
179D11—81no—
180C24—111no—
181C24C22×D1112yes—
182C2×Q8—22no—
183C2×Q8—42no—
184C2×D4—22no—
185C2×D4—42no—
186C2×D4—224no—
187C2×D4—442no—
188C2×D4—442no—
189C22×C4—112no—
190C22×C4—112no—
191C22×C4—111no—
192C22×C4—111no—
193C22×C4—111no—
194C22×C4C22×D1112yes—
195C22×C4C22×D1111yescharacteristic
196C22×C4C22×D1111yescharacteristic
197C22×C4C22×D1111yescharacteristic
198C4⋊C4—224no—
199C4⋊C4—222no—
200C4⋊C4—222no—
201C4⋊C4—222no—
202C4⋊C4—442no—
203C22⋊C4—24no—
204C22⋊C4—24no—
205C22⋊C4—224no—
206C22⋊C4—222no—
207C22⋊C4—222no—
208C22⋊C4—222no—
209C22⋊C4—442no—
210C22⋊C4—442no—
211C22⋊C4—442no—
212C42—442no—
213C42C22⋊D1114yescomplemented
214C11#266211yescharacteristic, complemented, Sylow
215C23—22no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—222no—
223C23—222no—
224C23—221no—
225C23—221no—
226C23—221no—
227C23C23×D1111yescharacteristic
228Q8—44no—
229D4—44no—
230D4—448no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—114no—
239C2×C4—222no—
240C2×C4—222no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—222no—
244C2×C4—222no—
245C2×C4—222no—
246C2×C4—221no—
247C2×C4—221no—
248C2×C4—221no—
249C2×C4—221no—
250C2×C4—221no—
251C2×C4C2×C22⋊D1112yes—
252C2×C4C2×C22⋊D1112yes—
253C2×C4C2×C22⋊D1112yes—
254C22—42no—
255C22—42no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—441no—
262C22—441no—
263C22—441no—
264C22—442no—
265C22—442no—
266C22#6703712yes—
267C22#41×D1112yes—
268C22#6704211yescharacteristic
269C22#6704311yescharacteristic
270C22C22×C22⋊D1111yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—42no—
275C4—224no—
276C4—441no—
277C4—441no—
278C4—441no—
279C4—442no—
280C2—82no—
281C2—881no—
282C2#1062320012yes—
283C2#1062320912yes—
284C2#1062333611yescharacteristic
285C2#1062336311yescharacteristic
286C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#124C2
prime radical#10622836C2
hypercenterC2×#124D11
hypocenterC11#2662
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×C11×#124C2semidirect
2. C2×#66929C2semidirect
3. #10622844C2semidirect
4. #10622842C2semidirect
6. #10622835C2semidirect
7. #10622574C2semidirect
8. #10622570C2semidirect
9. #10622561C2semidirect
10. #10622558C2semidirect
11. C4×C4⋊Dic11C2semidirect
57. C42×C11D4semidirect
112. C2×#124D11semidirect
213. C42C22⋊D11semidirect
214. C11#2662semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1242
C2×#669292
#106228442
#106228422
#106228362
#106228352
#106225742
#106225702
#106225612
#106225582
C4×C4⋊Dic112
#266211