Finite Group Databasebeta

← #13080062

Subgroups — #13080062

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×#540C211yesmaximal, characteristic
2#10623049C211yesmaximal, characteristic, complemented
3#10622688C212yesmaximal, complemented
4#10622676C212yesmaximal, complemented
5#10622655C212yesmaximal, complemented
6#10622654C212yesmaximal, complemented
7#10622632C212yesmaximal, complemented
8#10622622C212yesmaximal, complemented
9#10622612C211yesmaximal, characteristic, complemented
10C11×#127C2211yescharacteristic
11C11×#125C2211yescharacteristic
12C11×#123—22no—
13C11×#121—22no—
14C11×#121C2212yes—
15C4×D4×C11C2212yes—
16C11×#117C2211yescharacteristic
17C2×#4324C2212yes—
18C2×#4324C2212yes—
19#66977C2212yes—
20C2×#4318C2211yescharacteristic
21C22×C11⋊C8C2211yescharacteristic
22#66942—22no—
23#66932—22no—
24#66923C2211yescharacteristic
25#66922C2211yescharacteristic
26C4×Dic22C2212yes—
27#66896C2212yes—
28#66896C2212yes—
29#66874C2212yes—
30#66874C2212yes—
31#66872C2212yes—
32#66871C2212yes—
33C4⋊(C11⋊C8)C2212yes—
34C4⋊(C11⋊C8)C2212yes—
35C2×D4×C11—22no—
36C2×D4×C11—22no—
37C2×D4×C11C2312yes—
38C22×C4×C11—22no—
39C22×C4×C11C2311yescharacteristic
40C2×Dic22C2312yes—
41C11×C4⋊C4—22no—
42C11×C4⋊C4D412yes—
43C11×C4⋊C4C2312yes—
44C11×C22⋊C4—22no—
45C11×C22⋊C4—22no—
46C11×C22⋊C4D412yes—
47C42×C11C2311yescharacteristic
48C42×C11C2311yescharacteristic
49C22⋊Dic11—22no—
50#4324—42no—
51#4324—42no—
52C4⋊Dic11—22no—
53C4⋊Dic11C2312yes—
54Dic11⋊C4—22no—
55Dic11⋊C4—22no—
56Dic11⋊C4—22no—
57C4×Dic11—22no—
58#4318—41no—
59C2×C11⋊C8—41no—
60C2×C11⋊C8C2312yes—
61C2×C11⋊C8C2312yes—
62#3260—111nomaximal, Sylow
63C23×C11—22no—
64C23×C11C2×D411yescharacteristic
65D4×C11—22no—
66D4×C11—22no—
67D4×C11—82no—
68D4×C11—82no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—22no—
72C2×C4×C11—82no—
73C2×C4×C11C2×D412yes—
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2×D412yes—
76C2×C4×C11C2411yescharacteristic
77C2×Dic11—22no—
78C2×Dic11—22no—
79Dic22—22no—
80Dic22—22no—
81C11⋊C8—22no—
82C11⋊C8—22no—
83#541—111no—
84#540D1111yescharacteristic
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×C11—42no—
95C22×C11—42no—
96C22×C11—42no—
97C22×C11C22×D411yescharacteristic
98C4×C11—21no—
99C4×C11—22no—
100C4×C11—22no—
101C4×C11—42no—
102C4×C11H(5,𝔽2)11yescharacteristic
103C4×C112−1+411yescharacteristic
104Dic11—42no—
105Dic11—42no—
106C2×SD16—112no—
107C2×SD16—112no—
108C2×M16—111no—
109C22×C8—111no—
110C4⋊Q8—111no—
111#127C2×D1111yescharacteristic
112#126—222no—
113#125—111no—
114#125—222no—
115#125C2×D1111yescharacteristic
116#123—22no—
117C22⋊Q8—112no—
118#121—22no—
119#121C2×D1112yes—
120C4×Q8—112no—
121C4×D4C2×D1112yes—
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—82no—
133C2×C11#53711yescharacteristic
134C2×C11#57712yes—
135C2×Q8—112no—
136C2×D4—22no—
137C2×D4—22no—
138C2×D4C22×D1112yes—
139C22×C4—22no—
140C22×C4C22×D1111yescharacteristic
141SD16—442no—
142SD16—442no—
143M16—441no—
144C2×C8—112no—
145C2×C8—112no—
146C2×C8—441no—
147C4⋊C4—22no—
148C4⋊C4—112no—
149C4⋊C4—222no—
150C4⋊C4—222no—
151C4⋊C4—222no—
152C4⋊C4—222no—
153C4⋊C4C22⋊D1112yes—
154C4⋊C4C22×D1112yes—
155C22⋊C4—22no—
156C22⋊C4—22no—
157C22⋊C4—222no—
158C22⋊C4C22⋊D1112yes—
159C42—222no—
160C42C22×D1111yescharacteristic
161C42C22×D1111yescharacteristic
162C11#326011yescharacteristic, complemented, Sylow
163C23—22no—
164C23C2×C22⋊D1111yescharacteristic
165Q8—222no—
166Q8—222no—
167D4—22no—
168D4—22no—
169D4—82no—
170D4—82no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—82no—
175C2×C4—222no—
176C2×C4—222no—
177C2×C4C2×C22⋊D1112yes—
178C2×C4C2×C22⋊D1112yes—
179C2×C4C2×C22⋊D1111yescharacteristic
180C2×C4C23×D1111yescharacteristic
181C8—222no—
182C8—222no—
183C22—21no—
184C22—22no—
185C22—42no—
186C22—42no—
187C22—42no—
188C22C22×C22⋊D1111yescharacteristic
189C4—21no—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—442no—
194C4—442no—
195C4#6704211yescharacteristic
196C4#6704311yescharacteristic
197C2—41no—
198C2—82no—
199C2#1062336411yescharacteristic
200C2#1062336712yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#540C2
socleC22×C11C22×D4
hypercenter#540D11
hypocenterC11#3260
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
2. #10623049C2semidirect
3. #10622688C2semidirect
4. #10622676C2semidirect
5. #10622655C2semidirect
6. #10622654C2semidirect
7. #10622632C2semidirect
8. #10622622C2semidirect
9. #10622612C2semidirect
162. C11#3260semidirect

Maximal subgroups

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

subgroupindex
C11×#5402
#106230492
#106226882
#106226762
#106226552
#106226542
#106226322
#106226222
#106226122
#326011