Finite Group Databasebeta

← #13079506

Subgroups — #13079506

Order 1408.

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

normal subgroups only

This group has 378 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#10623159C212yesmaximal
2C11×#467C211yesmaximal, characteristic, complemented
3#10622799C212yesmaximal, complemented
4#10622729C211yesmaximal, characteristic, complemented
5#10622723C211yesmaximal, characteristic
6#10622665C212yesmaximal, complemented
7#10622501C212yesmaximal, complemented
8#10622427C212yesmaximal, complemented
9#10622421C212yesmaximal, complemented
10C2×Q8×D11C2212yes—
11C2×#4339C2211yescharacteristic
12C2×C11×Q16C2211yescharacteristic
13C22×C8×C11C2211yescharacteristic
14C11×C22⋊Q8C2212yes—
15#66999C2212yes—
16C2×#4326C2212yes—
17#66977C2212yes—
18C2×#4318C2211yescharacteristic
19C2×Dic44C2211yescharacteristic
20#66950C2212yes—
21#66947—22no—
22#66945C2212yes—
23#66941—22no—
24#66938—22no—
25#66936—22no—
26C11×#107C2211yescharacteristic
27C11×#103C2212yes—
28#66899C2212yes—
29(C2×D11)⋊C8C2212yes—
30(C2×D11)⋊C8C2212yes—
31#66882C2211yescharacteristic
32#66880C2212yes—
33#66874C2212yes—
34#66872C2212yes—
35C2×Q8×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C2×C22⋊D11D412yes—
38Q8×D11—42no—
39Q8×D11—42no—
40#4339—41no—
41#4339—41no—
42C2×D44D411yescharacteristic
43C2×C4×D11—22no—
44C2×C4×D11C2312yes—
45C2×Dic22—22no—
46C2×Dic22D411yescharacteristic
47C2×Dic22C2312yes—
48C11×Q16—41no—
49C2×C8×C11—41no—
50C2×C8×C11C2311yescharacteristic
51C2×C8×C11C2311yescharacteristic
52C11×C4⋊C4—22no—
53C11×C4⋊C4C2312yes—
54C11×C22⋊C4—22no—
55C22⋊Dic11—22no—
56#4326—42no—
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—22no—
60C4⋊Dic11—22no—
61C4⋊Dic11C2312yes—
62Dic11⋊C4—22no—
63Dic11⋊C4—22no—
64C4×Dic11—22no—
65#4318—41no—
66C2×C11⋊C8C2312yes—
67Dic44—41no—
68#3202—111nomaximal, Sylow
69C23×C11C2×D411yescharacteristic
70C22×D11C2×D412yes—
71Q8×C11—22no—
72Q8×C11—22no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2411yescharacteristic
79C22⋊D11—42no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11C2×D412yes—
83D44—41no—
84C4×D11—22no—
85C4×D11—22no—
86C4×D11—44no—
87Dic22—22no—
88Dic22—22no—
89Dic22—41no—
90Dic22—44no—
91C8×C11—21no—
92C8×C11—21no—
93C11⋊C8—22no—
94#536—112no—
95#485—112no—
96#485—112no—
97#470—112no—
98#467—111no—
99#467D1111yescharacteristic, complemented
100#451—112no—
101#451—112no—
102#408—111no—
103C22×C11—21no—
104C22×C11—21no—
105C22×C11—21no—
106C22×C11C22×D411yescharacteristic
107C2×D11—22no—
108C2×D11—22no—
109C2×D11—22no—
110C4×C11—21no—
111C4×C11—42no—
112C4×C11—42no—
113C4×C11H(5,𝔽2)11yescharacteristic
114C4×C11H(5,𝔽2)11yescharacteristic
115Dic11—22no—
116Dic11—42no—
117Dic11—42no—
118C2×#41—111no—
119C22×Q8—112no—
120C2×Q16—112no—
121C2×Q16—111no—
122C2×Q16C2×D1111yescharacteristic
123C2×M16—111no—
124C22×C8C2×D1111yescharacteristic
125C4⋊Q8—222no—
126#124—222no—
127#123—222no—
128#123—222no—
129C22⋊Q8—112no—
130C22⋊Q8—112no—
131C22⋊Q8—112no—
132C22⋊Q8C2×D1112yes—
133#117—112no—
134#107—111no—
135#107C2×D1111yescharacteristic
136#106—112no—
137#103—112no—
138#103—112no—
139#103—112no—
140#103C2×D1112yes—
141C22⋊C8—112no—
142C22⋊C8—112no—
143C2×C11—41no—
144C2×C11#53411yescharacteristic
145C2×C11#57811yescharacteristic
146C2×C11#57811yescharacteristic
147D11—42no—
148#41—441no—
149#41—441no—
150C2×Q8—111no—
151C2×Q8—112no—
152C2×Q8—222no—
153C2×Q8—442no—
154C2×Q8—442no—
155C2×Q8C22×D1112yes—
156C2×D4—112no—
157C2×D4—111no—
158C22×C4—112no—
159C22×C4—222no—
160C22×C4C22×D1111yescharacteristic
161Q16—41no—
162Q16—441no—
163Q16—442no—
164M16—441no—
165C2×C8—41no—
166C2×C8—112no—
167C2×C8C22×D1111yescharacteristic
168C2×C8C22×D1111yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—112no—
171C4⋊C4—222no—
172C4⋊C4—222no—
173C4⋊C4—222no—
174C4⋊C4C22×D1112yes—
175C22⋊C4—22no—
176C22⋊C4—222no—
177C22⋊C4—222no—
178C22⋊C4—222no—
179C22⋊C4—222no—
180C42—222no—
181C11#320211yescharacteristic, complemented, Sylow
182C23—112no—
183C23D4×D1111yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—222no—
187Q8—222no—
188Q8—441no—
189Q8—444no—
190D4—441no—
191D4—442no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—112no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—444no—
202C2×C4D4×D1111yescharacteristic
203C2×C4C23×D1111yescharacteristic
204C8—21no—
205C8—21no—
206C8—222no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—222no—
211C22—222no—
212C22—222no—
213C22C2×D4×D1111yescharacteristic
214C4—21no—
215C4—42no—
216C4—42no—
217C4—222no—
218C4—442no—
219C4—442no—
220C4#6703711yescharacteristic
221C4#6704211yescharacteristic
222C2—41no—
223C2—442no—
224C2#1062313611yescharacteristic
225C2#1062329711yescharacteristic
226C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#467C2
socleC22×C11C22×D4
prime radicalC2×#4339C22
hypercenter#467D11
hypocenterC11#3202
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. C11×#467C2semidirect
3. #10622799C2semidirect
4. #10622729C2semidirect
6. #10622665C2semidirect
7. #10622501C2semidirect
8. #10622427C2semidirect
9. #10622421C2semidirect
99. #467D11semidirect
181. C11#3202semidirect

Maximal subgroups

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

subgroupindex
#106231592
C11×#4672
#106227992
#106227292
#106227232
#106226652
#106225012
#106224272
#106224212
#320211