Finite Group Databasebeta

← #13080057

Subgroups — #13080057

Order 1408.

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

normal subgroups only

This group has 346 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
1C11×#541C211yesmaximal, characteristic, complemented
2#10623066C211yesmaximal, characteristic
3#10622696C212yesmaximal, complemented
4#10622679C212yesmaximal, complemented
5#10622662C212yesmaximal, complemented
6#10622661C212yesmaximal, complemented
7#10622640C212yesmaximal, complemented
8#10622635C212yesmaximal, complemented
9#10622612C211yesmaximal, characteristic, complemented
10C11×C4⋊Q8C2211yescharacteristic
11C11×#126—22no—
12C11×#125—22no—
13C11×#125C2211yescharacteristic
14C11×C22⋊Q8C2212yes—
15C4×Q8×C11C2212yes—
16C11×#117C2211yescharacteristic
17C2×#4325C2212yes—
18C2×#4325C2212yes—
19#66983C2212yes—
20C2×#4318C2211yescharacteristic
21C22×C11⋊C8C2211yescharacteristic
22#66947—22no—
23#66937—22no—
24#66927C2211yescharacteristic
25C4×D44C2212yes—
26#66923C2211yescharacteristic
27#66899C2212yes—
28#66899C2212yes—
29#66873C2212yes—
30#66873C2212yes—
31#66872C2212yes—
32#66871C2212yes—
33C4⋊(C11⋊C8)C2212yes—
34C4⋊(C11⋊C8)C2212yes—
35C2×Q8×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C2×C22⋊D11—22no—
38C2×D44—22no—
39C2×D44C2312yes—
40C2×C4×D11—22no—
41C11×C4⋊C4—22no—
42C11×C4⋊C4—22no—
43C11×C4⋊C4—22no—
44C11×C4⋊C4—22no—
45C11×C4⋊C4D412yes—
46C11×C4⋊C4C2312yes—
47C11×C22⋊C4—22no—
48C11×C22⋊C4D412yes—
49C42×C11—22no—
50C42×C11C2311yescharacteristic
51C42×C11C2311yescharacteristic
52#4325—42no—
53#4325—42no—
54(C2×D11)⋊C4—22no—
55(C2×D11)⋊C4—22no—
56C4⋊Dic11C2312yes—
57Dic11⋊C4—22no—
58#4318—41no—
59C2×C11⋊C8—41no—
60C2×C11⋊C8C2312yes—
61C2×C11⋊C8C2312yes—
62#3260—111nomaximal, Sylow
63C23×C11C2×D411yescharacteristic
64C22×D11—22no—
65Q8×C11—22no—
66Q8×C11—22no—
67C2×C4×C11—21no—
68C2×C4×C11—21no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11C2×D412yes—
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2×D412yes—
74C2×C4×C11C2411yescharacteristic
75C22⋊D11—82no—
76C2×Dic11—22no—
77D44—22no—
78D44—22no—
79D44—82no—
80C4×D11—82no—
81C11⋊C8—22no—
82C11⋊C8—22no—
83#541D1111yescharacteristic, complemented
84#540—111no—
85#479—112no—
86#478—112no—
87#468—112no—
88#465—112no—
89#461—112no—
90#460—112no—
91#424—111no—
92C22×C11—21no—
93C22×C11—22no—
94C22×C11C22×D411yescharacteristic
95C2×D11—42no—
96C2×D11—42no—
97C2×D11—42no—
98C4×C11—21no—
99C4×C11—22no—
100C4×C11—22no—
101C4×C11—42no—
102C4×C11—42no—
103C4×C11H(5,𝔽2)11yescharacteristic
104C4×C112−1+411yescharacteristic
105Dic11—42no—
106C2×SD16—112no—
107C2×SD16—112no—
108C2×M16—111no—
109C22×C8—111no—
110C4⋊Q8C2×D1111yescharacteristic
111#127—111no—
112#126—22no—
113#125—22no—
114#125—111no—
115#125C2×D1111yescharacteristic
116#123—222no—
117C22⋊Q8C2×D1112yes—
118#121—112no—
119#121—222no—
120C4×Q8C2×D1112yes—
121C4×D4—112no—
122#117C2×D1111yescharacteristic
123#107—112no—
124#106—112no—
125C4⋊C8—112no—
126C4⋊C8—112no—
127#103—112no—
128#103—112no—
129#102—112no—
130#102—112no—
131C2×C11—41no—
132C2×C11#53711yescharacteristic
133C2×C11#57712yes—
134D11—82no—
135C2×Q8C22×D1112yes—
136C2×D4—112no—
137C2×D4—222no—
138C2×D4—222no—
139C22×C4—222no—
140C22×C4C22×D1111yescharacteristic
141SD16—442no—
142SD16—442no—
143M16—441no—
144C2×C8—112no—
145C2×C8—112no—
146C2×C8—441no—
147C4⋊C4—22no—
148C4⋊C4—22no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—112no—
152C4⋊C4—222no—
153C4⋊C4C22⋊D1112yes—
154C4⋊C4C22×D1112yes—
155C22⋊C4—22no—
156C22⋊C4—222no—
157C22⋊C4—222no—
158C22⋊C4C22⋊D1112yes—
159C42—22no—
160C42C22×D1111yescharacteristic
161C42C22×D1111yescharacteristic
162C11#326011yescharacteristic, complemented, Sylow
163C23—222no—
164C23C2×C22⋊D1111yescharacteristic
165Q8—22no—
166Q8—22no—
167D4—222no—
168D4—222no—
169D4—882no—
170D4—882no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—222no—
176C2×C4—882no—
177C2×C4C2×C22⋊D1112yes—
178C2×C4C2×C22⋊D1112yes—
179C2×C4C2×C22⋊D1111yescharacteristic
180C2×C4C23×D1111yescharacteristic
181C8—222no—
182C8—222no—
183C22—21no—
184C22—22no—
185C22—442no—
186C22—442no—
187C22—442no—
188C22C22×C22⋊D1111yescharacteristic
189C4—21no—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—42no—
194C4—442no—
195C4#6704211yescharacteristic
196C4#6704311yescharacteristic
197C2—41no—
198C2—882no—
199C2#1062336411yescharacteristic
200C2#1062336812yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#541C2
socleC22×C11C22×D4
prime radical#10623066C2
hypercenter#541D11
hypocenterC11#3260
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
1. C11×#541C2semidirect
3. #10622696C2semidirect
4. #10622679C2semidirect
5. #10622662C2semidirect
6. #10622661C2semidirect
7. #10622640C2semidirect
8. #10622635C2semidirect
9. #10622612C2semidirect
83. #541D11semidirect
162. C11#3260semidirect

Maximal subgroups

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

subgroupindex
C11×#5412
#106230662
#106226962
#106226792
#106226622
#106226612
#106226402
#106226352
#106226122
#326011