Finite Group Databasebeta

← #13079962

Subgroups — #13079962

Order 1408.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#10623131C212yesmaximal, complemented
2C11×#466C211yesmaximal, characteristic
3#10622766C212yesmaximal, complemented
4#10622729C211yesmaximal, characteristic, complemented
5C2×Dic11⋊C8C211yesmaximal, characteristic, complemented
6#10622654C212yesmaximal, complemented
7#10622490C212yesmaximal, complemented
8#10622380C212yesmaximal, complemented
9#10622379C212yesmaximal, complemented
10C2×C11×D8C2211yescharacteristic
11C22×C8×C11C2211yescharacteristic
12C11×#121C2212yes—
13#66989C2212yes—
14#66988—22no—
15D4×Dic11—22no—
16D4×Dic11C2212yes—
17C2×#4324C2212yes—
18#66977C2212yes—
19C2×C4×Dic11C2211yescharacteristic
20C22×C11⋊C8C2211yescharacteristic
21C2×Dic44C2211yescharacteristic
22#66943C2212yes—
23#66940C2212yes—
24#66932—22no—
25#66930—22no—
26C11×#107C2211yescharacteristic
27C11×#102C2212yes—
28#66896C2212yes—
29#66882C2211yescharacteristic
30#66880C2212yes—
31Dic11⋊C8C2212yes—
32Dic11⋊C8C2212yes—
33#66874C2212yes—
34#66872C2212yes—
35C2×D4×C11—22no—
36C2×D4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C22×Dic11—22no—
39C22×Dic11D411yescharacteristic
40C22×Dic11D411yescharacteristic
41C2×Dic22C2312yes—
42C11×D8—41no—
43C2×C8×C11—41no—
44C2×C8×C11C2311yescharacteristic
45C2×C8×C11C2311yescharacteristic
46C11×C4⋊C4C2312yes—
47C11×C22⋊C4—22no—
48C22⋊Dic11—22no—
49C22⋊Dic11—22no—
50C22⋊Dic11—22no—
51C22⋊Dic11—22no—
52#4324—42no—
53C4⋊Dic11—22no—
54C4⋊Dic11C2312yes—
55Dic11⋊C4—22no—
56Dic11⋊C4—22no—
57Dic11⋊C4—22no—
58C4×Dic11—22no—
59C4×Dic11D412yes—
60C4×Dic11C2312yes—
61C2×C11⋊C8—41no—
62C2×C11⋊C8C2312yes—
63Dic44—41no—
64#3250—111nomaximal, Sylow
65C23×C11—22no—
66C23×C11C2×D411yescharacteristic
67D4×C11—22no—
68D4×C11—22no—
69D4×C11—44no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—22no—
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2411yescharacteristic
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—41no—
79C2×Dic11—44no—
80C2×Dic11C2×D412yes—
81C2×Dic11C2×D412yes—
82Dic22—22no—
83Dic22—22no—
84C8×C11—21no—
85C8×C11—21no—
86C11⋊C8—22no—
87#529—112no—
88#479—112no—
89#478—112no—
90#467—111no—
91#466D1111yescharacteristic
92#465—112no—
93#464—112no—
94#463—112no—
95C2×C4⋊C8—111no—
96C22×C11—21no—
97C22×C11—21no—
98C22×C11—42no—
99C22×C11—42no—
100C22×C11—42no—
101C22×C11#13512yes—
102C22×C11C22×D411yescharacteristic
103C4×C11—21no—
104C4×C11—42no—
105C4×C11H(5,𝔽2)11yescharacteristic
106C4×C112−1+411yescharacteristic
107Dic11—22no—
108Dic11—22no—
109Dic11—42no—
110Dic11—42no—
111C2×Q16—111no—
112C2×SD16—112no—
113C2×D8C2×D1111yescharacteristic
114C22×C8—111no—
115C22×C8C2×D1111yescharacteristic
116#126—222no—
117#125—112no—
118#124—112no—
119#123—222no—
120C22⋊Q8—112no—
121#121C2×D1112yes—
122C4×Q8—112no—
123C4×D4—112no—
124C4×D4—222no—
125#117—222no—
126C2×C42—111no—
127#107—111no—
128#107C2×D1111yescharacteristic
129#106—112no—
130C4⋊C8—112no—
131C4⋊C8—112no—
132#103—112no—
133#103—112no—
134#102—112no—
135#102C2×D1112yes—
136C2×C11—22no—
137C2×C11—82no—
138C2×C11#53711yescharacteristic
139C2×C11C2×#13511yescharacteristic
140C2×C11#57511yescharacteristic
141C2×Q8—112no—
142C2×D4—22no—
143C2×D4C22×D1112yes—
144C22×C4—111no—
145C22×C4—111no—
146C22×C4—222no—
147C22×C4C22×D1111yescharacteristic
148Q16—441no—
149SD16—442no—
150D8—41no—
151C2×C8—41no—
152C2×C8—112no—
153C2×C8—441no—
154C2×C8C22×D1111yescharacteristic
155C2×C8C22×D1111yescharacteristic
156C4⋊C4—112no—
157C4⋊C4—222no—
158C4⋊C4—222no—
159C4⋊C4—222no—
160C4⋊C4—222no—
161C4⋊C4C22×D1112yes—
162C22⋊C4—22no—
163C22⋊C4—222no—
164C22⋊C4—222no—
165C22⋊C4—222no—
166C22⋊C4—222no—
167C42—112no—
168C42—112no—
169C42—222no—
170C11#325011yescharacteristic, complemented, Sylow
171C23—22no—
172C23D4×D1111yescharacteristic
173Q8—222no—
174Q8—222no—
175D4—22no—
176D4—22no—
177D4—44no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—112no—
182C2×C4—112no—
183C2×C4—222no—
184C2×C4—222no—
185C2×C4—222no—
186C2×C4—441no—
187C2×C4—444no—
188C2×C4D4×D1111yescharacteristic
189C2×C4C23×D1111yescharacteristic
190C8—21no—
191C8—21no—
192C8—222no—
193C22—21no—
194C22—21no—
195C22—42no—
196C22—42no—
197C22—42no—
198C22#6696512yes—
199C22C2×D4×D1111yescharacteristic
200C4—21no—
201C4—42no—
202C4—222no—
203C4—222no—
204C4—442no—
205C4—442no—
206C4#6703711yescharacteristic
207C4#6704311yescharacteristic
208C2—22no—
209C2—82no—
210C2#1062312811yescharacteristic
211C2C2×#6696511yescharacteristic
212C2#1062329911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#466C2
socleC22×C11C22×D4
hypercenter#466D11
hypocenterC11#3250
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #10623131C2semidirect
3. #10622766C2semidirect
4. #10622729C2semidirect
5. C2×Dic11⋊C8C2semidirect
6. #10622654C2semidirect
7. #10622490C2semidirect
8. #10622380C2semidirect
9. #10622379C2semidirect
170. C11#3250semidirect

Maximal subgroups

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

subgroupindex
#106231312
C11×#4662
#106227662
#106227292
C2×Dic11⋊C82
#106226542
#106224902
#106223802
#106223792
#325011