Finite Group Databasebeta

← #13076629

Subgroups — #13076629

Order 1408.

478 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 133 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×#123C211yesmaximal, characteristic
2C2×#66977C211yesmaximal, characteristic, complemented
3#10622835C212yesmaximal
4#10622825C211yesmaximal, characteristic, complemented
5#10622597C212yesmaximal, complemented
6#10622596C211yesmaximal, characteristic, complemented
7#10622592C211yesmaximal, characteristic, complemented
8#10622566C211yesmaximal, characteristic, complemented
9#10622565C212yesmaximal, complemented
10#10622561C212yesmaximal, complemented
11#10622560C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C22×Dic22C2211yescharacteristic
15C11×#123—24no—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C22⋊Dic11C2212yes—
22C2×C22⋊Dic11C2212yes—
23C2×C22⋊Dic11C2212yes—
24C2×C22⋊Dic11C2212yes—
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2212yes—
27#66977—24no—
28C2×Dic11⋊C4C2212yes—
29C2×Dic11⋊C4C2212yes—
30C2×Dic11⋊C4C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2211yescharacteristic
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C24×C11C2311yescharacteristic
39C2×D4×C11—22no—
40C2×D4×C11—42no—
41C22×C4×C11—42no—
42C22×C4×C11D414yes—
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C22×Dic11C2312yes—
49C22×Dic11C2312yes—
50C22×Dic11C2312yes—
51C22×Dic11C2312yes—
52C2×Dic22—22no—
53C2×Dic22—42no—
54C11×C4⋊C4—22no—
55C11×C4⋊C4—22no—
56C11×C22⋊C4—22no—
57C11×C22⋊C4—22no—
58C11×C22⋊C4—22no—
59C22⋊Dic11—24no—
60C22⋊Dic11—42no—
61C22⋊Dic11—42no—
62C22⋊Dic11—42no—
63C4⋊Dic11—22no—
64C4⋊Dic11—42no—
65Dic11⋊C4—24no—
66Dic11⋊C4—42no—
67Dic11⋊C4—42no—
68#2814—111nomaximal, Sylow
69C23×C11—21no—
70C23×C11—22no—
71C23×C11—22no—
72C23×C11—21no—
73C23×C11—21no—
74C23×C11—21no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—21no—
78C23×C11C2×D412yes—
79C23×C11C2411yescharacteristic
80D4×C11—44no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—44no—
91C2×C4×C11C2×D412yes—
92C2×C4×C11C2×D412yes—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105Dic22—44no—
106C2×#123D1111yescharacteristic
107C2×C22⋊Q8—111no—
108#398—111no—
109#398—112no—
110#397—112no—
111#397—111no—
112#396—112no—
113#395—111no—
114#394—112no—
115#393—111no—
116#380—111no—
117C22×C11—22no—
118C22×C11—22no—
119C22×C11—22no—
120C22×C11—42no—
121C22×C11—42no—
122C22×C11—41no—
123C22×C11—41no—
124C22×C11—41no—
125C22×C11—42no—
126C22×C11—42no—
127C22×C11C22×D411yescharacteristic
128C22×C11H(5,𝔽2)12yes—
129C22×C11H(5,𝔽2)11yescharacteristic
130C22×C112−1+412yes—
131C22×C112−1+411yescharacteristic
132C4×C11—22no—
133C4×C11—22no—
134C4×C11—41no—
135C4×C11—41no—
136C4×C11—41no—
137Dic11—42no—
138Dic11—42no—
139Dic11—42no—
140Dic11—42no—
141C22×Q8—111no—
142C22×D4C2×D1111yescharacteristic
143C23×C4C2×D1111yescharacteristic
144#123—24no—
145C22⋊Q8—224no—
146C2×C4⋊C4—112no—
147C2×C4⋊C4—111no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4—112no—
150C2×C4⋊C4—112no—
151C2×C4⋊C4C2×D1111yescharacteristic
152C2×C4⋊C4C2×D1111yescharacteristic
153C2×C22⋊C4—112no—
154C2×C22⋊C4—112no—
155C2×C22⋊C4—112no—
156C2×C22⋊C4—112no—
157C2×C22⋊C4C2×D1111yescharacteristic
158C2×C22⋊C4C2×D1111yescharacteristic
159C2×C22⋊C4C2×D1111yescharacteristic
160#95—111no—
161#95—111no—
162#95—112no—
163#95—112no—
164#95—112no—
165#95—112no—
166C2×C11—42no—
167C2×C11—81no—
168C2×C11#53411yescharacteristic
169C2×C11#53611yescharacteristic
170C2×C11#53711yescharacteristic
171C2×C11#56212yes—
172C2×C11#56312yes—
173C24C22×D1111yescharacteristic
174C24C22×D1111yescharacteristic
175C2×Q8—222no—
176C2×Q8—442no—
177C2×D4—22no—
178C2×D4—42no—
179C22×C4—42no—
180C22×C4—112no—
181C22×C4—112no—
182C22×C4—112no—
183C22×C4—112no—
184C22×C4C22⋊D1114yes—
185C22×C4C22×D1111yescharacteristic
186C22×C4C22×D1111yescharacteristic
187C22×C4C22×D1111yescharacteristic
188C22×C4C22×D1111yescharacteristic
189C22×C4C22×D1111yescharacteristic
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—224no—
193C4⋊C4—222no—
194C4⋊C4—442no—
195C4⋊C4—442no—
196C4⋊C4—442no—
197C22⋊C4—22no—
198C22⋊C4—22no—
199C22⋊C4—22no—
200C22⋊C4—224no—
201C22⋊C4—442no—
202C22⋊C4—442no—
203C22⋊C4—442no—
204C11#281411yescharacteristic, complemented, Sylow
205C23—22no—
206C23—21no—
207C23—22no—
208C23—21no—
209C23—22no—
210C23—21no—
211C23—22no—
212C23—21no—
213C23—21no—
214C23C2×C22⋊D1112yes—
215C23C23×D1111yescharacteristic
216Q8—444no—
217D4—44no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—44no—
228C2×C4—222no—
229C2×C4—222no—
230C2×C4—222no—
231C2×C4—222no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—222no—
235C2×C4—222no—
236C2×C4—222no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4—222no—
240C2×C4C2×C22⋊D1112yes—
241C2×C4C2×C22⋊D1112yes—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—42no—
251C22—42no—
252C22#6703712yes—
253C22#6704211yescharacteristic
254C22#6704312yes—
255C22#6704311yescharacteristic
256C22C22×C22⋊D1111yescharacteristic
257C4—22no—
258C4—22no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4—442no—
263C4—442no—
264C4—442no—
265C4—442no—
266C2—42no—
267C2—81no—
268C2#1062318212yes—
269C2#1062319812yes—
270C2#1062333511yescharacteristic
271C2#1062335611yescharacteristic
272C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#123C2
prime radicalC22×D4×C11C22
hypercenterC2×#123D11
hypocenterC11#2814
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×#66977C2semidirect
4. #10622825C2semidirect
5. #10622597C2semidirect
6. #10622596C2semidirect
7. #10622592C2semidirect
8. #10622566C2semidirect
9. #10622565C2semidirect
10. #10622561C2semidirect
11. #10622560C2semidirect
204. C11#2814semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1232
C2×#669772
#106228352
#106228252
#106225972
#106225962
#106225922
#106225662
#106225652
#106225612
#106225602
#281411