Finite Group Databasebeta

← #13079528

Subgroups — #13079528

Order 1408.

402 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 117 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#10623364C212yesmaximal, complemented
2C11×#408C211yesmaximal, characteristic, complemented
3#10622750C211yesmaximal, characteristic, complemented
4#10622748C211yesmaximal, characteristic, complemented
5#10622727C212yesmaximal, complemented
6#10622348C212yesmaximal, complemented
7#10622347C212yesmaximal, complemented
8#10622346C212yesmaximal, complemented
9#10622334C212yesmaximal, complemented
10C2×C11×#41C2211yescharacteristic
11C2×#4339C2212yes—
12C2×C11×M16C2211yescharacteristic
13C22×C8×C11C2211yescharacteristic
14#66999—22no—
15#66992—22no—
16#66992—22no—
17#66991—22no—
18#66983C2212yes—
19#66983C2212yes—
20C2×C4⋊Dic11C2212yes—
21#66977C2212yes—
22#66977C2212yes—
23C2×Dic44C2211yescharacteristic
24C2×D88C2211yescharacteristic
25C2×#4314C2212yes—
26C11×C22⋊C8C2212yes—
27C11×C22⋊C8C2212yes—
28#66885C2212yes—
29#66885C2212yes—
30#66881C2212yes—
31#66881C2211yescharacteristic
32#66881C2211yescharacteristic
33#66880C2212yes—
34#66880C2212yes—
35C11×#41—41no—
36C11×#41—41no—
37C2×Q8×C11D411yescharacteristic
38C2×D4×C11D412yes—
39C2×D4×C11D411yescharacteristic
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C2×C22⋊D11—22no—
43C2×C22⋊D11—22no—
44C2×C22⋊D11—22no—
45C22×Dic11—22no—
46#4339—42no—
47#4339—42no—
48C2×D44C2312yes—
49C2×C4×D11—22no—
50C2×Dic22C2312yes—
51C11×M16—41no—
52C2×C8×C11—41no—
53C2×C8×C11C2311yescharacteristic
54C2×C8×C11C2312yes—
55C2×C8×C11C2311yescharacteristic
56C22⋊Dic11—22no—
57C22⋊Dic11—22no—
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—22no—
60C4⋊Dic11—22no—
61C4⋊Dic11C2312yes—
62C4⋊Dic11C2312yes—
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65Dic44—41no—
66D88—41no—
67#4314—42no—
68#3204—111nomaximal, Sylow
69C23×C11C2×D411yescharacteristic
70C23×C11C2×D412yes—
71C22×D11—22no—
72Q8×C11—41no—
73D4×C11—41no—
74D4×C11—42no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2×D412yes—
81C2×C4×C11C2411yescharacteristic
82C22⋊D11—44no—
83C22⋊D11—82no—
84C22⋊D11—82no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—82no—
89D44—22no—
90D44—22no—
91C4×D11—44no—
92Dic22—22no—
93Dic22—22no—
94C8×C11—22no—
95C8×C11—21no—
96C8×C11—21no—
97#537—112no—
98#483—112no—
99#481—112no—
100#470—111no—
101#469—111no—
102#465—112no—
103#452—112no—
104#449—112no—
105#408D1111yescharacteristic, complemented
106C22×C11—21no—
107C22×C11—22no—
108C22×C11—22no—
109C22×C11—22no—
110C22×C11—22no—
111C22×C11C22×D411yescharacteristic
112C2×D11—42no—
113C2×D11—42no—
114C2×D11—42no—
115C4×C11—21no—
116C4×C11—22no—
117C4×C11H(5,𝔽2)11yescharacteristic
118C4×C11H(5,𝔽2)11yescharacteristic
119Dic11—42no—
120Dic11—42no—
121Dic11—42no—
122C2×#41—112no—
123C2×#41C2×D1111yescharacteristic
124C2×Q16—111no—
125C2×SD16—112no—
126C2×D8—111no—
127C2×M16C2×D1111yescharacteristic
128C22×C8C2×D1111yescharacteristic
129C22⋊Q8—112no—
130C22⋊Q8—112no—
131C22⋊Q8—222no—
132#121—112no—
133#121—112no—
134#121—222no—
135#121—222no—
136#121—222no—
137C2×C4⋊C4—112no—
138#106—112no—
139#106—111no—
140#106—111no—
141#103—112no—
142#103—112no—
143#102—112no—
144#102—112no—
145C22⋊C8C2×D1112yes—
146C22⋊C8C2×D1112yes—
147C2×C11—41no—
148C2×C11—42no—
149C2×C11#53411yescharacteristic
150C2×C11#57712yes—
151D11—82no—
152#41—41no—
153#41—41no—
154#41—442no—
155#41—442no—
156C2×Q8—112no—
157C2×Q8D4411yescharacteristic
158C2×D4—112no—
159C2×D4—222no—
160C2×D4—222no—
161C2×D4—222no—
162C2×D4D4411yescharacteristic
163C2×D4D4412yes—
164C22×C4—222no—
165C22×C4—222no—
166C22×C4C22×D1112yes—
167C22×C4C22×D1111yescharacteristic
168Q16—441no—
169SD16—442no—
170D8—441no—
171M16—41no—
172C2×C8—41no—
173C2×C8C22×D1111yescharacteristic
174C2×C8C22×D1112yes—
175C2×C8C22×D1111yescharacteristic
176C4⋊C4—112no—
177C4⋊C4—112no—
178C4⋊C4—222no—
179C4⋊C4—222no—
180C4⋊C4—222no—
181C22⋊C4—222no—
182C22⋊C4—222no—
183C22⋊C4—222no—
184C22⋊C4—222no—
185C11#320411yescharacteristic, complemented, Sylow
186C23—222no—
187C23C2×D4411yescharacteristic
188C23C2×D4412yes—
189Q8—41no—
190Q8—222no—
191Q8—222no—
192D4—42no—
193D4—41no—
194D4—222no—
195D4—222no—
196D4—444no—
197D4—882no—
198D4—882no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—444no—
207C2×C4—882no—
208C2×C4C2×D4411yescharacteristic
209C2×C4C2×D4412yes—
210C2×C4C23×D1111yescharacteristic
211C8—22no—
212C8—21no—
213C8—21no—
214C22—22no—
215C22—21no—
216C22—22no—
217C22—22no—
218C22—22no—
219C22—442no—
220C22—442no—
221C22—442no—
222C22C22×D4411yescharacteristic
223C4—22no—
224C4—21no—
225C4—442no—
226C4—442no—
227C4—442no—
228C4#6703711yescharacteristic
229C4#6703711yescharacteristic
230C2—42no—
231C2—41no—
232C2—882no—
233C2#1062302411yescharacteristic
234C2#1062328212yes—
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#408C2
socleC22×C11C22×D4
hypercenter#408D11
hypocenterC11#3204
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #10623364C2semidirect
2. C11×#408C2semidirect
3. #10622750C2semidirect
4. #10622748C2semidirect
5. #10622727C2semidirect
6. #10622348C2semidirect
7. #10622347C2semidirect
8. #10622346C2semidirect
9. #10622334C2semidirect
105. #408D11semidirect
185. C11#3204semidirect

Maximal subgroups

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

subgroupindex
#106233642
C11×#4082
#106227502
#106227482
#106227272
#106223482
#106223472
#106223462
#106223342
#320411