Finite Group Databasebeta

← #13079527

Subgroups — #13079527

Order 1408.

402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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#10623139C212yesmaximal, complemented
2C11×#469C211yesmaximal, characteristic, complemented
3#10622771C212yesmaximal, complemented
4#10622750C211yesmaximal, characteristic, complemented
5#10622742C211yesmaximal, characteristic, complemented
6#10622654C212yesmaximal, complemented
7#10622475C212yesmaximal, complemented
8#10622396C212yesmaximal, complemented
9#10622390C212yesmaximal, complemented
10C2×#4341C2212yes—
11C2×#4339C2211yescharacteristic
12C2×C11×D8C2211yescharacteristic
13C2×C11×M16C2211yescharacteristic
14C11×#121C2212yes—
15#66992—22no—
16#66991—22no—
17#66991C2212yes—
18C2×#4324C2212yes—
19#66977C2212yes—
20C22×C11⋊C8C2211yescharacteristic
21C2×Dic44C2211yescharacteristic
22#66950C2212yes—
23C4⋊C4×D11C2212yes—
24#66937—22no—
25#66931—22no—
26C11×#106C2211yescharacteristic
27C11×#102C2212yes—
28#66896C2212yes—
29(C2×D11)⋊C8C2212yes—
30(C2×D11)⋊C8C2212yes—
31#66881C2211yescharacteristic
32#66880C2212yes—
33#66874C2212yes—
34#66872C2212yes—
35C2×D4×C11—22no—
36C2×D4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C2×C22⋊D11—22no—
39C2×C22⋊D11—22no—
40C2×C22⋊D11D412yes—
41C22×Dic11—22no—
42#4341—42no—
43#4341—42no—
44#4339—41no—
45#4339—41no—
46C2×D44D411yescharacteristic
47C2×C4×D11—22no—
48C2×C4×D11C2312yes—
49C2×Dic22D411yescharacteristic
50C2×Dic22C2312yes—
51C11×D8—41no—
52C11×M16—41no—
53C2×C8×C11C2311yescharacteristic
54C2×C8×C11C2311yescharacteristic
55C11×C4⋊C4C2312yes—
56C11×C22⋊C4—22no—
57C22⋊Dic11—22no—
58C22⋊Dic11—22no—
59#4324—42no—
60(C2×D11)⋊C4—22no—
61C4⋊Dic11—22no—
62C4⋊Dic11C2312yes—
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65C2×C11⋊C8—41no—
66C2×C11⋊C8C2312yes—
67Dic44—41no—
68#3204—111nomaximal, Sylow
69C23×C11—22no—
70C23×C11C2×D411yescharacteristic
71C22×D11C2×D412yes—
72D4×C11—22no—
73D4×C11—22no—
74D4×C11—82no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2411yescharacteristic
80C22⋊D11—42no—
81C22⋊D11—44no—
82C22⋊D11—82no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—44no—
86C2×Dic11C2×D412yes—
87D44—41no—
88C4×D11—22no—
89C4×D11—22no—
90C4×D11—82no—
91Dic22—22no—
92Dic22—22no—
93Dic22—41no—
94C8×C11—21no—
95C8×C11—21no—
96C11⋊C8—22no—
97#537—112no—
98#483—112no—
99#481—112no—
100#470—111no—
101#469D1111yescharacteristic, complemented
102#465—112no—
103#452—112no—
104#449—112no—
105#408—111no—
106C22×C11—21no—
107C22×C11—22no—
108C22×C11—42no—
109C22×C11—42no—
110C22×C11—42no—
111C22×C11C22×D411yescharacteristic
112C2×D11—22no—
113C2×D11—22no—
114C2×D11—22no—
115C4×C11—21no—
116C4×C11—42no—
117C4×C11H(5,𝔽2)11yescharacteristic
118C4×C11H(5,𝔽2)11yescharacteristic
119Dic11—22no—
120Dic11—42no—
121Dic11—42no—
122C2×#41—111no—
123C2×#41—112no—
124C2×Q16—111no—
125C2×SD16—112no—
126C2×D8C2×D1111yescharacteristic
127C2×M16C2×D1111yescharacteristic
128C22×C8—111no—
129C22⋊Q8—112no—
130C22⋊Q8—112no—
131C22⋊Q8—222no—
132#121—112no—
133#121—222no—
134#121—222no—
135#121—222no—
136#121C2×D1112yes—
137C2×C4⋊C4—112no—
138#106—111no—
139#106—112no—
140#106C2×D1111yescharacteristic
141#103—112no—
142#103—112no—
143#102—112no—
144#102C2×D1112yes—
145C22⋊C8—112no—
146C22⋊C8—112no—
147C2×C11—41no—
148C2×C11—82no—
149C2×C11#53411yescharacteristic
150C2×C11#57712yes—
151D11—42no—
152#41—441no—
153#41—441no—
154#41—442no—
155#41—442no—
156C2×Q8—111no—
157C2×Q8—112no—
158C2×D4—22no—
159C2×D4—112no—
160C2×D4—111no—
161C2×D4—222no—
162C2×D4—222no—
163C2×D4C22×D1112yes—
164C22×C4—112no—
165C22×C4—222no—
166C22×C4—222no—
167C22×C4C22×D1111yescharacteristic
168Q16—441no—
169SD16—442no—
170D8—41no—
171M16—41no—
172C2×C8—112no—
173C2×C8—441no—
174C2×C8C22×D1111yescharacteristic
175C2×C8C22×D1111yescharacteristic
176C4⋊C4—112no—
177C4⋊C4—222no—
178C4⋊C4—222no—
179C4⋊C4—222no—
180C4⋊C4C22×D1112yes—
181C22⋊C4—22no—
182C22⋊C4—222no—
183C22⋊C4—222no—
184C22⋊C4—222no—
185C11#320411yescharacteristic, complemented, Sylow
186C23—22no—
187C23—112no—
188C23D4×D1111yescharacteristic
189Q8—222no—
190Q8—222no—
191Q8—441no—
192D4—22no—
193D4—22no—
194D4—82no—
195D4—441no—
196D4—442no—
197D4—444no—
198D4—882no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—112no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—222no—
207C2×C4—444no—
208C2×C4—882no—
209C2×C4D4×D1111yescharacteristic
210C2×C4C23×D1111yescharacteristic
211C8—21no—
212C8—21no—
213C8—222no—
214C22—22no—
215C22—21no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22—222no—
220C22—222no—
221C22—222no—
222C22C2×D4×D1111yescharacteristic
223C4—21no—
224C4—42no—
225C4—222no—
226C4—442no—
227C4—442no—
228C4#6703711yescharacteristic
229C4#6704211yescharacteristic
230C2—41no—
231C2—82no—
232C2—442no—
233C2#1062313611yescharacteristic
234C2#1062330612yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#469C2
socleC22×C11C22×D4
hypercenter#469D11
hypocenterC11#3204
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #10623139C2semidirect
2. C11×#469C2semidirect
3. #10622771C2semidirect
4. #10622750C2semidirect
5. #10622742C2semidirect
6. #10622654C2semidirect
7. #10622475C2semidirect
8. #10622396C2semidirect
9. #10622390C2semidirect
101. #469D11semidirect
185. C11#3204semidirect

Maximal subgroups

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

subgroupindex
#106231392
C11×#4692
#106227712
#106227502
#106227422
#106226542
#106224752
#106223962
#106223902
#320411