Finite Group Databasebeta

← #13074762

Subgroups — #13074762

Order 1408.

534 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 129 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×#67000C211yesmaximal, characteristic, complemented
2C2×#66932C211yesmaximal, characteristic, complemented
3C11×#393C211yesmaximal, characteristic, complemented
4#10622842C211yesmaximal, characteristic, complemented
5#10622573C211yesmaximal, characteristic
6#10622572C212yesmaximal, complemented
7#10622570C212yesmaximal, complemented
8#10622289C212yesmaximal, complemented
9#10622285C211yesmaximal, characteristic, complemented
10#10622283C212yesmaximal, complemented
11#10622262C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×C22⋊D11C2212yes—
14C22×D44C2211yescharacteristic
15C2×C11×C22⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4C2212yes—
17C2×C22⋊Dic11C2211yescharacteristic
18C2×C22⋊Dic11C2211yescharacteristic
19#67000—24no—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×C4⋊Dic11C2211yescharacteristic
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2212yes—
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2212yes—
31C2×C4×Dic11C2211yescharacteristic
32#66932—24no—
33C11×#95C2211yescharacteristic
34C11×#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C23×D11C2312yes—
39C2×Q8×C11—22no—
40C2×Q8×C11—42no—
41C22×C4×C11C2312yes—
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C2×C22⋊D11—24no—
46C2×C22⋊D11—42no—
47C2×C22⋊D11—42no—
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2311yescharacteristic
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2312yes—
53C2×D44—22no—
54C2×D44—42no—
55C11×C22⋊C4—22no—
56C11×C22⋊C4—42no—
57C22⋊Dic11—22no—
58C22⋊Dic11—22no—
59(C2×D11)⋊C4—24no—
60(C2×D11)⋊C4—24no—
61(C2×D11)⋊C4—24no—
62(C2×D11)⋊C4—42no—
63(C2×D11)⋊C4—42no—
64C4⋊Dic11—22no—
65Dic11⋊C4—22no—
66Dic11⋊C4—24no—
67Dic11⋊C4—22no—
68Dic11⋊C4—42no—
69C4×Dic11—42no—
70C4×Dic11D414yescomplemented
71#2662—111nomaximal, Sylow
72C23×C11—21no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—21no—
76C23×C11—21no—
77C23×C11C2411yescharacteristic
78C22×D11—22no—
79C22×D11—22no—
80C22×D11—22no—
81C22×D11—22no—
82C22×D11—22no—
83C22×D11—22no—
84C22×D11—22no—
85Q8×C11—44no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11C2×D412yes—
96C22⋊D11—48no—
97C2×Dic11—22no—
98C2×Dic11—21no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—21no—
102C2×Dic11—21no—
103C2×Dic11—21no—
104C2×Dic11—22no—
105C2×Dic11—21no—
106C2×Dic11—21no—
107C2×Dic11C2×D412yes—
108C2×Dic11C2×D412yes—
109C2×Dic11#4114yes—
110D44—44no—
111C2×#126—111no—
112C2×#124—111no—
113#396—112no—
114#395—111no—
115#394—112no—
116#394—111no—
117#393D1111yescharacteristic, complemented
118#392—111no—
119#390—112no—
120#388—112no—
121C4×C4⋊C4—111no—
122C22×C11—41no—
123C22×C11—41no—
124C22×C11—41no—
125C22×C11—42no—
126C22×C11—42no—
127C22×C11C22×D411yescharacteristic
128C22×C11C2×#4112yes—
129C22×C11H(5,𝔽2)12yes—
130C22×C11H(5,𝔽2)11yescharacteristic
131C22×C112−1+411yescharacteristic
132C2×D11—42no—
133C2×D11—42no—
134C2×D11—42no—
135C2×D11—42no—
136C2×D11—42no—
137C2×D11—42no—
138C2×D11—42no—
139C4×C11—22no—
140C4×C11—41no—
141C4×C11—42no—
142C4×C11—42no—
143Dic11—22no—
144Dic11—22no—
145Dic11—24no—
146Dic11—41no—
147Dic11—41no—
148C22×Q8C2×D1111yescharacteristic
149C22×D4—112no—
150C22×D4—111no—
151#126—224no—
152#124—224no—
153C2×C4⋊C4—111no—
154C2×C4⋊C4—111no—
155C2×C4⋊C4—111no—
156C2×C4⋊C4—112no—
157C2×C4⋊C4—112no—
158C2×C22⋊C4—111no—
159C2×C22⋊C4—111no—
160C2×C22⋊C4—112no—
161C2×C22⋊C4—112no—
162C2×C22⋊C4—112no—
163C2×C22⋊C4—112no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4C2×D1111yescharacteristic
166C2×C22⋊C4C2×D1112yes—
167C2×C42—111no—
168C2×C42—112no—
169#95—111no—
170#95—112no—
171#95C2×D1111yescharacteristic
172#95C2×D1112yes—
173C2×C11—81no—
174C2×C11#53211yescharacteristic
175C2×C11#53511yescharacteristic
176C2×C11#53711yescharacteristic
177C2×C11#53812yes—
178C2×C11#54212yes—
179D11—82no—
180C24—112no—
181C24C22×D1111yescharacteristic
182C2×Q8—22no—
183C2×Q8—42no—
184C2×D4—224no—
185C2×D4—222no—
186C2×D4—442no—
187C2×D4—442no—
188C2×D4—442no—
189C22×C4—112no—
190C22×C4—111no—
191C22×C4—111no—
192C22×C4—111no—
193C22×C4—111no—
194C22×C4C22×D1112yes—
195C22×C4C22×D1112yes—
196C22×C4C22×D1111yescharacteristic
197C22×C4C22×D1111yescharacteristic
198C4⋊C4—222no—
199C4⋊C4—222no—
200C4⋊C4—224no—
201C4⋊C4—222no—
202C4⋊C4—442no—
203C22⋊C4—22no—
204C22⋊C4—42no—
205C22⋊C4—224no—
206C22⋊C4—224no—
207C22⋊C4—224no—
208C22⋊C4—222no—
209C22⋊C4—222no—
210C22⋊C4—442no—
211C22⋊C4—442no—
212C42—114no—
213C42—442no—
214C11#266211yescharacteristic, complemented, Sylow
215C23—21no—
216C23—22no—
217C23—21no—
218C23—22no—
219C23—21no—
220C23—222no—
221C23—222no—
222C23—222no—
223C23—222no—
224C23—222no—
225C23—222no—
226C23—222no—
227C23C23×D1111yescharacteristic
228Q8—44no—
229D4—444no—
230D4—448no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—112no—
241C2×C4—112no—
242C2×C4—114no—
243C2×C4—222no—
244C2×C4—221no—
245C2×C4—222no—
246C2×C4—221no—
247C2×C4—222no—
248C2×C4—221no—
249C2×C4—221no—
250C2×C4—222no—
251C2×C4—221no—
252C2×C4—221no—
253C2×C4D4×D1112yes—
254C22—41no—
255C22—41no—
256C22—42no—
257C22—41no—
258C22—42no—
259C22—442no—
260C22—442no—
261C22—442no—
262C22—442no—
263C22—442no—
264C22—442no—
265C22—442no—
266C22C2×D4×D1111yescharacteristic
267C22#6703712yes—
268C22#6704011yescharacteristic
269C22#41×D1112yes—
270C22#6704211yescharacteristic
271C4—22no—
272C4—42no—
273C4—41no—
274C4—42no—
275C4—222no—
276C4—222no—
277C4—224no—
278C4—441no—
279C4—441no—
280C2—81no—
281C2—882no—
282C2#1062312311yescharacteristic
283C2#1062316011yescharacteristic
284C2#1062317112yes—
285C2#1062319911yescharacteristic
286C2#1062320912yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#393C2
prime radical#10622573C2
hypercenter#393D11
hypocenterC11#2662
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#67000C2semidirect
2. C2×#66932C2semidirect
3. C11×#393C2semidirect
4. #10622842C2semidirect
6. #10622572C2semidirect
7. #10622570C2semidirect
8. #10622289C2semidirect
9. #10622285C2semidirect
10. #10622283C2semidirect
11. #10622262C2semidirect
70. C4×Dic11D4semidirect
117. #393D11semidirect
214. C11#2662semidirect

Maximal subgroups

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

subgroupindex
C2×#670002
C2×#669322
C11×#3932
#106228422
#106225732
#106225722
#106225702
#106222892
#106222852
#106222832
#106222622
#266211