Finite Group Databasebeta

← #13080983

Subgroups — #13080983

Order 1408.

342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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#10623225C212yesmaximal
2C11×#499C211yesmaximal, characteristic, complemented
3#10622676C212yesmaximal, complemented
4#10622500C211yesmaximal, characteristic, complemented
5#10622500C211yesmaximal, characteristic, complemented
6#10622493C211yesmaximal, characteristic, complemented
7D11×#107C211yesmaximal, characteristic, complemented
8#10622480C212yesmaximal, complemented
9#10622475C212yesmaximal, complemented
10C4×Dic44C211yesmaximal, characteristic, complemented
11C8×D44C211yesmaximal, characteristic
12C11×#125C2212yes—
13C2×Dic44C2211yescharacteristic
14C2×C8×D11C2211yescharacteristic
15C2×C8×D11C2211yescharacteristic
16#66951—22no—
17#66950C2212yes—
18#66950C2212yes—
19#66947—22no—
20#66945—22no—
21#66945C2212yes—
22C4⋊C4×D11C2212yes—
23#66943—22no—
24C4×D44C2211yescharacteristic
25C4×Dic22C2212yes—
26C11×#107C2211yescharacteristic
27C11×#107C2211yescharacteristic
28C11×#106C2212yes—
29C4×C8×C11C2211yescharacteristic
30(C2×D11)⋊C8C2211yescharacteristic
31(C2×D11)⋊C8C2211yescharacteristic
32#66882C2211yescharacteristic
33#66880C2212yes—
34#66874C2212yes—
35#66874C2212yes—
36#66872C2212yes—
37#66871C2212yes—
38C4⋊(C11⋊C8)C2211yescharacteristic
39C2×D44D411yescharacteristic
40C2×C4×D11—22no—
41C2×C4×D11C2311yescharacteristic
42C2×C4×D11C2311yescharacteristic
43C2×Dic22C2312yes—
44C2×C8×C11C2311yescharacteristic
45C2×C8×C11C2311yescharacteristic
46C11×C4⋊C4—22no—
47C11×C4⋊C4—22no—
48C11×C4⋊C4C2312yes—
49C11×C4⋊C4C2312yes—
50C42×C11C2311yescharacteristic
51(C2×D11)⋊C4—22no—
52(C2×D11)⋊C4—22no—
53(C2×D11)⋊C4—22no—
54(C2×D11)⋊C4D411yescharacteristic
55(C2×D11)⋊C4D411yescharacteristic
56C4⋊Dic11—22no—
57C4⋊Dic11—22no—
58C4⋊Dic11D411yescharacteristic
59C4⋊Dic11C2312yes—
60Dic11⋊C4—22no—
61Dic11⋊C4—22no—
62C4×Dic11—22no—
63C4×Dic11—22no—
64C2×C11⋊C8C2311yescharacteristic
65C2×C11⋊C8C2311yescharacteristic
66Dic44—22no—
67C8×D11—22no—
68C8×D11—22no—
69#3336—111nomaximal, Sylow
70C22×D11C2×D411yescharacteristic
71C22×D11C2×D411yescharacteristic
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2411yescharacteristic
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11C2×D411yescharacteristic
80C2×Dic11C2×D411yescharacteristic
81D44—22no—
82C4×D11—21no—
83C4×D11—21no—
84C4×D11—21no—
85C4×D11—21no—
86C4×D11—44no—
87Dic22—22no—
88Dic22—22no—
89C8×C11—21no—
90C8×C11#4112yes—
91C11⋊C8—21no—
92C11⋊C8—21no—
93#552—112no—
94#499D1111yescharacteristic, complemented
95#485—112no—
96#483—112no—
97#479—112no—
98#467—111no—
99#467—111no—
100C4×Q16—111no—
101C8×D4—111no—
102#427—111no—
103C2×#107—111no—
104C22×C11C22×D411yescharacteristic
105C2×D11—21no—
106C2×D11—21no—
107C2×D11—21no—
108C2×D11—21no—
109C2×D11—21no—
110C2×D11#13512yes—
111C4×C11—21no—
112C4×C11—21no—
113C4×C11—42no—
114C4×C11—42no—
115C4×C11C2×#4111yescharacteristic
116C4×C112−1+411yescharacteristic
117Dic11—21no—
118Dic11—21no—
119Dic11—42no—
120Dic11—42no—
121C2×Q16—111no—
122C22×C8—111no—
123C22×C8—111no—
124#126—222no—
125#125—222no—
126#125C2×D1112yes—
127#123—222no—
128C22⋊Q8—112no—
129C22⋊Q8—112no—
130C4×Q8—112no—
131C4×D4—111no—
132#117—112no—
133#117—222no—
134C2×C4⋊C4—112no—
135#107—111no—
136#107—112no—
137#107C2×D1111yescharacteristic
138#107C2×D1111yescharacteristic
139#106—112no—
140#106C2×D1112yes—
141C4⋊C8—111no—
142#103—112no—
143#103—112no—
144#103—112no—
145C22⋊C8—111no—
146C22⋊C8—111no—
147C4×C8C2×D1111yescharacteristic
148C2×C11#54711yescharacteristic
149C2×C11C2×#13511yescharacteristic
150C2×C11#57811yescharacteristic
151D11—22no—
152D11—41no—
153C2×Q8—112no—
154C2×D4—111no—
155C22×C4—111no—
156C22×C4—111no—
157C22×C4—222no—
158Q16—222no—
159C2×C8—111no—
160C2×C8—111no—
161C2×C8—222no—
162C2×C8—222no—
163C2×C8C22×D1111yescharacteristic
164C2×C8C22×D1111yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—22no—
167C4⋊C4—111no—
168C4⋊C4—112no—
169C4⋊C4—222no—
170C4⋊C4—222no—
171C4⋊C4—222no—
172C4⋊C4—222no—
173C4⋊C4C22×D1112yes—
174C4⋊C4C22×D1112yes—
175C22⋊C4—111no—
176C22⋊C4—111no—
177C22⋊C4—222no—
178C22⋊C4—222no—
179C22⋊C4—222no—
180C42—222no—
181C42—222no—
182C42C22×D1111yescharacteristic
183C11#333611yescharacteristic, complemented, Sylow
184C23—111no—
185C23—111no—
186Q8—222no—
187Q8—222no—
188D4—222no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—111no—
192C2×C4—111no—
193C2×C4—221no—
194C2×C4—221no—
195C2×C4—221no—
196C2×C4—221no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4—444no—
200C2×C4D4×D1111yescharacteristic
201C2×C4D4×D1111yescharacteristic
202C2×C4C23×D1111yescharacteristic
203C8—21no—
204C8—221no—
205C8—221no—
206C8#434312yes—
207C22—112no—
208C22—221no—
209C22—221no—
210C22—221no—
211C22—221no—
212C22—221no—
213C22C2×D4×D1111yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—42no—
218C4—221no—
219C4—221no—
220C4—442no—
221C4—442no—
222C4C2×#434311yescharacteristic
223C4#6704011yescharacteristic
224C2—222no—
225C2—441no—
226C2#1062325711yescharacteristic
227C2D11×#13511yescharacteristic
228C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#499C2
socleC22×C11C22×D4
prime radicalC2×D44D4
hypercenter#499D11
hypocenterC11#3336
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
2. C11×#499C2semidirect
3. #10622676C2semidirect
4. #10622500C2semidirect
5. #10622500C2semidirect
6. #10622493C2semidirect
7. D11×#107C2semidirect
8. #10622480C2semidirect
9. #10622475C2semidirect
10. C4×Dic44C2semidirect
94. #499D11semidirect
183. C11#3336semidirect

Maximal subgroups

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

subgroupindex
#106232252
C11×#4992
#106226762
#106225002
#106224932
D11×#1072
#106224802
#106224752
C4×Dic442
C8×D442
#333611