Finite Group Databasebeta

← #13080491

Subgroups — #13080491

Order 1408.

388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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#10623261C211yesmaximal, characteristic
2#10623258C211yesmaximal, characteristic
3C11×#487C211yesmaximal, characteristic, complemented
4#10622704C211yesmaximal, characteristic, complemented
5#10622703C211yesmaximal, characteristic, complemented
6#10622426C212yesmaximal, complemented
7#10622422C212yesmaximal, complemented
8#10622421C212yesmaximal, complemented
9D11×#103C212yesmaximal, complemented
10C4×Dic44C211yesmaximal, characteristic, complemented
11C8×D44C211yesmaximal, characteristic
12C2×Q8×D11C2212yes—
13C11×C4⋊Q8C2211yescharacteristic
14C11×C4⋊Q8C2211yescharacteristic
15#66999—22no—
16#66999C2212yes—
17C2×#4326C2212yes—
18C2×Dic44C2211yescharacteristic
19C2×C8×D11C2212yes—
20#66950C2212yes—
21#66949—22no—
22#66946—21no—
23#66946—21no—
24C4⋊C4×D11C2212yes—
25#66943—21no—
26#66941—21no—
27C4×D44C2211yescharacteristic
28C4×Dic22C2211yescharacteristic
29C4×Dic22C2211yescharacteristic
30C11×#103C2212yes—
31C11×#103C2212yes—
32C4×C8×C11C2211yescharacteristic
33#66899C2212yes—
34(C2×D11)⋊C8C2212yes—
35#66882C2211yescharacteristic
36#66880C2211yescharacteristic
37#66880C2211yescharacteristic
38#66874C2212yes—
39#66871C2212yes—
40C4⋊(C11⋊C8)C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×Q8×C11C2312yes—
43Q8×D11—24no—
44Q8×D11—42no—
45C2×D44D411yescharacteristic
46C2×C4×D11—22no—
47C2×C4×D11—22no—
48C2×C4×D11C2312yes—
49C2×Dic22—22no—
50C2×Dic22C2311yescharacteristic
51C2×Dic22C2311yescharacteristic
52C2×C8×C11C2311yescharacteristic
53C2×C8×C11C2311yescharacteristic
54C11×C4⋊C4—21no—
55C11×C4⋊C4—21no—
56C11×C4⋊C4—21no—
57C11×C4⋊C4C2312yes—
58C42×C11C2311yescharacteristic
59#4326—42no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4D412yes—
63C4⋊Dic11—22no—
64C4⋊Dic11D411yescharacteristic
65C4⋊Dic11C2311yescharacteristic
66C4⋊Dic11C2311yescharacteristic
67Dic11⋊C4—22no—
68Dic11⋊C4—22no—
69Dic11⋊C4—21no—
70Dic11⋊C4—21no—
71C4×Dic11—21no—
72C4×Dic11—21no—
73C2×C11⋊C8C2312yes—
74Dic44—22no—
75C8×D11—42no—
76#3299—111nomaximal, Sylow
77C22×D11C2×D412yes—
78Q8×C11—22no—
79Q8×C11—22no—
80Q8×C11—81no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2411yescharacteristic
86C2×Dic11—21no—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11C2×D412yes—
91D44Q1614yescomplemented
92C4×D11—22no—
93C4×D11—22no—
94C4×D11—44no—
95C4×D11—82no—
96Dic22—21no—
97Dic22—21no—
98Dic22—21no—
99Dic22—44no—
100Dic22#4112yes—
101C8×C11—21no—
102C8×C11—21no—
103C11⋊C8—22no—
104#554—111no—
105D4×Q8—111no—
106#487D1111yescharacteristic, complemented
107#484—112no—
108#477—111no—
109#467—112no—
110#462—111no—
111#451—112no—
112C4×Q16—111no—
113C8×D4—111no—
114C2×#103—112no—
115C22×C11C22×D411yescharacteristic
116C2×D11—22no—
117C2×D11—22no—
118C2×D11C2×Q1614yes—
119C4×C11—21no—
120C4×C11—42no—
121C4×C11—42no—
122C4×C11C2×Q1612yes—
123C4×C11C2×#4111yescharacteristic
124C4×C11H(5,𝔽2)11yescharacteristic
125Dic11—22no—
126Dic11—22no—
127Dic11—41no—
128Dic11—41no—
129Dic11—41no—
130C22×Q8—112no—
131C2×Q16—112no—
132C2×Q16—111no—
133C22×C8—112no—
134C4⋊Q8—221no—
135C4⋊Q8C2×D1111yescharacteristic
136C4⋊Q8C2×D1111yescharacteristic
137#125—221no—
138C22⋊Q8—112no—
139C22⋊Q8—112no—
140C22⋊Q8—222no—
141C22⋊Q8—222no—
142C4×Q8—111no—
143C4×Q8—111no—
144C4×D4—111no—
145C4×D4—221no—
146C4×D4—221no—
147C2×C4⋊C4—112no—
148#107—111no—
149#107—112no—
150C4⋊C8—111no—
151#103—112no—
152#103—111no—
153#103—111no—
154#103—112no—
155#103C2×D1112yes—
156#103C2×D1112yes—
157C22⋊C8—112no—
158C4×C8C2×D1111yescharacteristic
159C2×C11#54611yescharacteristic
160C2×C11C22×Q1611yescharacteristic
161C2×C11#57711yescharacteristic
162D11—24no—
163C2×Q8—21no—
164C2×Q8—111no—
165C2×Q8—111no—
166C2×Q8—222no—
167C2×Q8—224no—
168C2×Q8—442no—
169C2×Q8C22×D1112yes—
170C2×D4—111no—
171C22×C4—112no—
172C22×C4—222no—
173C22×C4—222no—
174Q16—222no—
175Q16—442no—
176C2×C8—112no—
177C2×C8—442no—
178C2×C8C22×D1111yescharacteristic
179C2×C8C22×D1111yescharacteristic
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—111no—
184C4⋊C4—111no—
185C4⋊C4—111no—
186C4⋊C4—222no—
187C4⋊C4—222no—
188C4⋊C4—222no—
189C4⋊C4—221no—
190C4⋊C4—221no—
191C4⋊C4C22×D1112yes—
192C22⋊C4—112no—
193C22⋊C4—222no—
194C22⋊C4—222no—
195C42—221no—
196C42—221no—
197C42C22×D1111yescharacteristic
198C11#329911yescharacteristic, complemented, Sylow
199C23—112no—
200Q8—22no—
201Q8—22no—
202Q8—81no—
203Q8—112no—
204Q8—221no—
205Q8—221no—
206Q8—221no—
207Q8—444no—
208D4—114no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—112no—
212C2×C4—221no—
213C2×C4—222no—
214C2×C4—222no—
215C2×C4—221no—
216C2×C4—221no—
217C2×C4—221no—
218C2×C4—444no—
219C2×C4—882no—
220C2×C4D4×D1111yescharacteristic
221C2×C4D4×D1111yescharacteristic
222C2×C4C23×D1111yescharacteristic
223C8—21no—
224C8—21no—
225C8—222no—
226C22—114no—
227C22—222no—
228C22—222no—
229C22C2×D4×D1111yescharacteristic
230C4—21no—
231C4—42no—
232C4—42no—
233C4—222no—
234C4—222no—
235C4—441no—
236C4—441no—
237C4—441no—
238C4Q16×D1112yes—
239C4#41×D1111yescharacteristic
240C4#6704211yescharacteristic
241C2—224no—
242C2#1062320711yescharacteristic
243C2#1062329311yescharacteristic
244C2C2×Q16×D1111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#487C2
socleC22×C11C22×D4
prime radicalC2×D44D4
hypercenter#487D11
hypocenterC11#3299
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. C11×#487C2semidirect
4. #10622704C2semidirect
5. #10622703C2semidirect
6. #10622426C2semidirect
7. #10622422C2semidirect
8. #10622421C2semidirect
9. D11×#103C2semidirect
10. C4×Dic44C2semidirect
91. D44Q16semidirect
106. #487D11semidirect
198. C11#3299semidirect

Maximal subgroups

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

subgroupindex
#106232612
#106232582
C11×#4872
#106227042
#106227032
#106224262
#106224222
#106224212
D11×#1032
C4×Dic442
C8×D442
#329911