Finite Group Databasebeta

← #13080067

Subgroups — #13080067

Order 1408.

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

normal subgroups only

This group has 322 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#10623156C212yesmaximal
2C11×#470C211yesmaximal, characteristic
3#10622795C212yesmaximal, complemented
4#10622750C211yesmaximal, characteristic
5#10622732C211yesmaximal, characteristic
6#10622664C212yesmaximal
7#10622470C212yesmaximal, complemented
8#10622412C212yesmaximal, complemented
9#10622406C212yesmaximal, complemented
10C2×C11×Q16C2211yescharacteristic
11C2×C11×M16C2211yescharacteristic
12C11×C22⋊Q8C2212yes—
13Q8×Dic11C2212yes—
14#66997C2212yes—
15C2×#4326C2212yes—
16#66979C2211yescharacteristic
17#66977C2212yes—
18C22×C11⋊C8C2211yescharacteristic
19C2×Dic44C2211yescharacteristic
20#66943—22no—
21#66943C2212yes—
22#66942—22no—
23#66940C2212yes—
24#66932—22no—
25#66932—22no—
26C11×#106C2211yescharacteristic
27C11×#103C2212yes—
28#66899C2212yes—
29#66881C2211yescharacteristic
30#66880C2212yes—
31Dic11⋊C8C2212yes—
32Dic11⋊C8C2212yes—
33#66874C2212yes—
34#66871C2212yes—
35C2×Q8×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C2×Dic22C2312yes—
38C11×Q16—41no—
39C11×M16—41no—
40C2×C8×C11C2311yescharacteristic
41C2×C8×C11C2311yescharacteristic
42C11×C4⋊C4—22no—
43C11×C4⋊C4C2312yes—
44C11×C22⋊C4—22no—
45C22⋊Dic11—22no—
46C22⋊Dic11D411yescharacteristic
47C22⋊Dic11D411yescharacteristic
48#4326—42no—
49C4⋊Dic11—22no—
50C4⋊Dic11—22no—
51C4⋊Dic11D412yes—
52C4⋊Dic11C2312yes—
53Dic11⋊C4—22no—
54Dic11⋊C4—22no—
55Dic11⋊C4—22no—
56Dic11⋊C4—22no—
57Dic11⋊C4—22no—
58C4×Dic11—22no—
59C4×Dic11—22no—
60C4×Dic11C2312yes—
61C2×C11⋊C8—41no—
62C2×C11⋊C8C2312yes—
63Dic44—41no—
64#3261—111nomaximal, Sylow
65C23×C11C2×D411yescharacteristic
66Q8×C11—22no—
67Q8×C11—22no—
68C2×C4×C11—21no—
69C2×C4×C11—21no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2411yescharacteristic
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11C2×D412yes—
77C2×Dic11C2×D412yes—
78Dic22—22no—
79Dic22—22no—
80C8×C11—21no—
81C8×C11—21no—
82C11⋊C8—22no—
83#541—112no—
84#479—112no—
85#479—112no—
86#470—111no—
87#470D1111yescharacteristic
88#467—112no—
89#462—112no—
90#462—112no—
91#424—111no—
92C22×C11—21no—
93C22×C11—22no—
94C22×C11C22×D411yescharacteristic
95C4×C11—21no—
96C4×C11—42no—
97C4×C11—42no—
98C4×C11H(5,𝔽2)11yescharacteristic
99C4×C112−1+411yescharacteristic
100Dic11—22no—
101Dic11—22no—
102Dic11—42no—
103Dic11—42no—
104C2×Q16—112no—
105C2×Q16—111no—
106C2×Q16C2×D1111yescharacteristic
107C2×M16C2×D1111yescharacteristic
108C22×C8—111no—
109C4⋊Q8—112no—
110#126—222no—
111#126—222no—
112#125—112no—
113#125—222no—
114#125—222no—
115C22⋊Q8—112no—
116C22⋊Q8C2×D1112yes—
117C4×Q8—112no—
118C4×Q8—112no—
119#117—111no—
120#107—112no—
121#106—111no—
122#106C2×D1111yescharacteristic
123C4⋊C8—112no—
124C4⋊C8—112no—
125#103—112no—
126#103—112no—
127#103—112no—
128#103C2×D1112yes—
129C2×C11—41no—
130C2×C11#53711yescharacteristic
131C2×C11#57812yes—
132C2×Q8—112no—
133C2×Q8C22×D1112yes—
134C22×C4C22×D1111yescharacteristic
135Q16—41no—
136Q16—441no—
137Q16—442no—
138M16—41no—
139C2×C8—112no—
140C2×C8—441no—
141C2×C8C22×D1111yescharacteristic
142C2×C8C22×D1111yescharacteristic
143C4⋊C4—22no—
144C4⋊C4—112no—
145C4⋊C4—112no—
146C4⋊C4—222no—
147C4⋊C4—222no—
148C4⋊C4—222no—
149C4⋊C4—222no—
150C4⋊C4—222no—
151C4⋊C4—222no—
152C4⋊C4—222no—
153C4⋊C4C22×D1112yes—
154C22⋊C4—22no—
155C22⋊C4—111no—
156C22⋊C4—111no—
157C22⋊C4—222no—
158C42—112no—
159C42—222no—
160C42—222no—
161C11#326111yescharacteristic, complemented, Sylow
162C23D4×D1111yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—222no—
166Q8—222no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—112no—
172C2×C4—112no—
173C2×C4—222no—
174C2×C4—222no—
175C2×C4D4×D1111yescharacteristic
176C2×C4C23×D1111yescharacteristic
177C8—21no—
178C8—21no—
179C8—222no—
180C22—22no—
181C22—21no—
182C22C2×D4×D1111yescharacteristic
183C4—21no—
184C4—42no—
185C4—42no—
186C4—222no—
187C4—222no—
188C4—442no—
189C4—442no—
190C4#6703711yescharacteristic
191C4#6704311yescharacteristic
192C2—41no—
193C2#1062312811yescharacteristic
194C2#1062331012yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#470C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#470D11
hypocenterC11#3261
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
3. #10622795C2semidirect
7. #10622470C2semidirect
8. #10622412C2semidirect
9. #10622406C2semidirect
161. C11#3261semidirect

Maximal subgroups

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

subgroupindex
#106231562
C11×#4702
#106227952
#106227502
#106227322
#106226642
#106224702
#106224122
#106224062
#326111