Finite Group Databasebeta

← #13081006

Subgroups — #13081006

Order 1408.

356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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#10623042C212yesmaximal
2C2×C11×#107C211yesmaximal, characteristic, complemented
3#10622729C211yesmaximal, characteristic, complemented
4C8×C22⋊D11C211yesmaximal, characteristic
5#10622583C212yesmaximal, complemented
6#10622500C211yesmaximal, characteristic, complemented
7#10622497C212yesmaximal, complemented
8D11×#107C211yesmaximal, characteristic, complemented
9#10622488C212yesmaximal, complemented
10#10622487C211yesmaximal, characteristic, complemented
11#10622486C211yesmaximal, characteristic, complemented
12C22×C8×C11C2211yescharacteristic
13C2×C11×C4⋊C4C2212yes—
14C4×C22⋊D11—22no—
15C4×C22⋊D11C2211yescharacteristic
16#66977—22no—
17#66977C2212yes—
18C2×Dic44C2211yescharacteristic
19C2×C8×D11C2211yescharacteristic
20#66950C2212yes—
21#66949—22no—
22C4⋊C4×D11C2212yes—
23#66942—22no—
24#66941C2212yes—
25#66940C2212yes—
26C11×#107C2211yescharacteristic
27C11×#107C2211yescharacteristic
28C11×#107C2212yes—
29C22⋊(C11⋊C8)C2211yescharacteristic
30(C2×D11)⋊C8C2211yescharacteristic
31#66882C2211yescharacteristic
32#66880C2212yes—
33Dic11⋊C8C2211yescharacteristic
34C8×Dic11C2211yescharacteristic
35#66874C2212yes—
36#66874C2212yes—
37#66871C2212yes—
38#66871C2212yes—
39C22×C4×C11—22no—
40C22×C4×C11C2311yescharacteristic
41C2×C22⋊D11D411yescharacteristic
42C2×C4×D11—22no—
43C2×C4×D11C2311yescharacteristic
44C2×Dic22—22no—
45C2×Dic22C2312yes—
46C2×C8×C11—22no—
47C2×C8×C11C2311yescharacteristic
48C2×C8×C11C2311yescharacteristic
49C11×C4⋊C4—22no—
50C11×C4⋊C4C2312yes—
51C11×C4⋊C4C2312yes—
52C22⋊Dic11—22no—
53C22⋊Dic11D411yescharacteristic
54(C2×D11)⋊C4—22no—
55(C2×D11)⋊C4D411yescharacteristic
56C4⋊Dic11—22no—
57C4⋊Dic11C2312yes—
58Dic11⋊C4—22no—
59Dic11⋊C4—22no—
60Dic11⋊C4—22no—
61Dic11⋊C4—22no—
62Dic11⋊C4D411yescharacteristic
63C4×Dic11—22no—
64C4×Dic11C2311yescharacteristic
65C2×C11⋊C8C2311yescharacteristic
66C2×C11⋊C8C2311yescharacteristic
67Dic44—22no—
68C8×D11—22no—
69#3338—111nomaximal, Sylow
70C23×C11C2×D411yescharacteristic
71C22×D11C2×D411yescharacteristic
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—82no—
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2411yescharacteristic
79C22⋊D11Q1614yescomplemented
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11C2×D411yescharacteristic
83C2×Dic11C2×D411yescharacteristic
84C2×Dic11C2×D411yescharacteristic
85C4×D11—21no—
86C4×D11—21no—
87C4×D11—82no—
88Dic22—22no—
89Dic22—22no—
90Dic22—82no—
91C8×C11—21no—
92C8×C11#4112yes—
93C11⋊C8—21no—
94C11⋊C8—21no—
95#554—112no—
96#500—111no—
97#484—112no—
98#484—112no—
99#477—112no—
100#467—111no—
101#467—111no—
102C4×Q16—111no—
103C8×D4—111no—
104C2×#107—111no—
105C2×#107D1111yescharacteristic, complemented
106C22×C11—21no—
107C22×C11—21no—
108C22×C11C2×Q1612yes—
109C22×C11C22×D411yescharacteristic
110C2×D11—21no—
111C2×D11—21no—
112C2×D11C2×Q1612yes—
113C4×C11—21no—
114C4×C11—42no—
115C4×C11—42no—
116C4×C11C2×#4111yescharacteristic
117C4×C112−1+411yescharacteristic
118Dic11—21no—
119Dic11—21no—
120Dic11—42no—
121Dic11—42no—
122Dic11C2×Q1612yes—
123C2×Q16—111no—
124C22×C8—111no—
125C22×C8C2×D1111yescharacteristic
126C4⋊Q8—112no—
127#125—222no—
128C22⋊Q8—112no—
129C22⋊Q8—112no—
130C22⋊Q8—222no—
131C22⋊Q8—222no—
132C4×Q8—112no—
133C4×D4—111no—
134C4×D4—222no—
135C2×C4⋊C4—112no—
136C2×C4⋊C4C2×D1112yes—
137#107—111no—
138#107—112no—
139#107—112no—
140#107C2×D1111yescharacteristic
141#107C2×D1111yescharacteristic
142#107C2×D1112yes—
143C4⋊C8—111no—
144#103—112no—
145#103—112no—
146#103—112no—
147C22⋊C8—111no—
148C22⋊C8—111no—
149C4×C8—111no—
150C2×C11—22no—
151C2×C11#54711yescharacteristic
152C2×C11C22×Q1611yescharacteristic
153C2×C11#57611yescharacteristic
154D11—22no—
155C2×Q8—112no—
156C2×Q8—222no—
157C2×D4—111no—
158C22×C4—22no—
159C22×C4—111no—
160C22×C4—222no—
161C22×C4C22×D1111yescharacteristic
162Q16—222no—
163C2×C8—22no—
164C2×C8—111no—
165C2×C8—111no—
166C2×C8—222no—
167C2×C8C22×D1111yescharacteristic
168C2×C8C22×D1111yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—111no—
171C4⋊C4—112no—
172C4⋊C4—222no—
173C4⋊C4—222no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4C22×D1112yes—
178C4⋊C4C22×D1112yes—
179C22⋊C4—111no—
180C22⋊C4—111no—
181C22⋊C4—222no—
182C22⋊C4—222no—
183C42—111no—
184C42—222no—
185C11#333811yescharacteristic, complemented, Sylow
186C23—111no—
187C23D4×D1111yescharacteristic
188Q8—222no—
189Q8—222no—
190Q8—882no—
191D4—114no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—82no—
197C2×C4—111no—
198C2×C4—111no—
199C2×C4—111no—
200C2×C4—221no—
201C2×C4—221no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—882no—
205C2×C4D4×D1111yescharacteristic
206C2×C4C23×D1111yescharacteristic
207C8—21no—
208C8—221no—
209C8—221no—
210C8#433912yes—
211C22—21no—
212C22—21no—
213C22—112no—
214C22—221no—
215C22—221no—
216C22Q16×D1112yes—
217C22C2×D4×D1111yescharacteristic
218C4—21no—
219C4—42no—
220C4—42no—
221C4—112no—
222C4—221no—
223C4—221no—
224C4—442no—
225C4—442no—
226C4C2×#433911yescharacteristic
227C4#6704011yescharacteristic
228C2—22no—
229C2—222no—
230C2#1062303811yescharacteristic
231C2#1062328811yescharacteristic
232C2C2×Q16×D1111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#107C2
socleC22×C11C22×D4
prime radicalC2×C22⋊D11D4
hypercenterC2×#107D11
hypocenterC11#3338
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×C11×#107C2semidirect
3. #10622729C2semidirect
5. #10622583C2semidirect
6. #10622500C2semidirect
7. #10622497C2semidirect
8. D11×#107C2semidirect
9. #10622488C2semidirect
10. #10622487C2semidirect
11. #10622486C2semidirect
79. C22⋊D11Q16semidirect
105. C2×#107D11semidirect
185. C11#3338semidirect

Maximal subgroups

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

subgroupindex
#106230422
C2×C11×#1072
#106227292
C8×C22⋊D112
#106225832
#106225002
#106224972
D11×#1072
#106224882
#106224872
#106224862
#333811