Finite Group Databasebeta

← #13080063

Subgroups — #13080063

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
1#10623066C211yesmaximal, characteristic
2#10623049C211yesmaximal, characteristic, complemented
3C11×#424C211yesmaximal, characteristic, complemented
4#10622747C212yesmaximal, complemented
5#10622727C212yesmaximal, complemented
6#10622461C212yesmaximal, complemented
7#10622460C212yesmaximal, complemented
8#10622454C212yesmaximal, complemented
9#10622442C212yesmaximal, complemented
10C2×C11×M16C2211yescharacteristic
11C22×C8×C11C2211yescharacteristic
12C11×#117C2211yescharacteristic
13#66983C2212yes—
14#66977C2212yes—
15C2×#4314C2212yes—
16C2×#4314C2212yes—
17#66947—22no—
18#66942—22no—
19#66937—22no—
20#66932—22no—
21#66927C2211yescharacteristic
22C4×D44C2212yes—
23#66923C2211yescharacteristic
24#66923C2211yescharacteristic
25#66922C2211yescharacteristic
26C4×Dic22C2212yes—
27C11×C4⋊C8C2212yes—
28C11×C4⋊C8C2212yes—
29#66885C2212yes—
30#66885C2212yes—
31#66882C2212yes—
32#66881C2212yes—
33#66880C2212yes—
34#66880C2212yes—
35C22×C4×C11C2311yescharacteristic
36C2×C22⋊D11—22no—
37C2×D44—22no—
38C2×D44C2312yes—
39C2×C4×D11—22no—
40C2×Dic22C2312yes—
41C11×M16—41no—
42C2×C8×C11—41no—
43C2×C8×C11C2312yes—
44C2×C8×C11C2312yes—
45C11×C4⋊C4D412yes—
46C11×C22⋊C4D412yes—
47C42×C11C2311yescharacteristic
48C42×C11C2311yescharacteristic
49C22⋊Dic11—22no—
50(C2×D11)⋊C4—22no—
51(C2×D11)⋊C4—22no—
52C4⋊Dic11—22no—
53C4⋊Dic11C2312yes—
54C4⋊Dic11C2312yes—
55Dic11⋊C4—22no—
56Dic11⋊C4—22no—
57Dic11⋊C4—22no—
58Dic11⋊C4—22no—
59C4×Dic11—22no—
60#4314—42no—
61#4314—42no—
62#3260—111nomaximal, Sylow
63C23×C11C2×D411yescharacteristic
64C22×D11—22no—
65C2×C4×C11—21no—
66C2×C4×C11—21no—
67C2×C4×C11C2×D412yes—
68C2×C4×C11C2×D411yescharacteristic
69C2×C4×C11C2×D412yes—
70C2×C4×C11C2411yescharacteristic
71C22⋊D11—82no—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75D44—22no—
76D44—22no—
77D44—82no—
78C4×D11—82no—
79Dic22—22no—
80Dic22—22no—
81C8×C11—22no—
82C8×C11—22no—
83#541—111no—
84#540—111no—
85#479—112no—
86#478—112no—
87#468—112no—
88#465—112no—
89#461—112no—
90#460—112no—
91#424D1111yescharacteristic, complemented
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×C11H(5,𝔽2)11yescharacteristic
102C4×C112−1+411yescharacteristic
103Dic11—42no—
104Dic11—42no—
105Dic11—42no—
106C2×SD16—112no—
107C2×SD16—112no—
108C2×M16C2×D1111yescharacteristic
109C22×C8C2×D1111yescharacteristic
110C4⋊Q8—111no—
111#127—111no—
112#126—222no—
113#125—111no—
114#125—111no—
115#125—222no—
116#123—222no—
117C22⋊Q8—112no—
118#121—112no—
119#121—222no—
120C4×Q8—112no—
121C4×D4—112no—
122#117C2×D1111yescharacteristic
123#107—112no—
124#106—112no—
125C4⋊C8C2×D1112yes—
126C4⋊C8C2×D1112yes—
127#103—112no—
128#103—112no—
129#102—112no—
130#102—112no—
131C2×C11—41no—
132C2×C11#53711yescharacteristic
133C2×C11#57712yes—
134D11—82no—
135C2×Q8—112no—
136C2×D4—112no—
137C2×D4—222no—
138C2×D4—222no—
139C22×C4—222no—
140C22×C4C22×D1111yescharacteristic
141SD16—442no—
142SD16—442no—
143M16—41no—
144C2×C8—41no—
145C2×C8C22×D1112yes—
146C2×C8C22×D1112yes—
147C4⋊C4—112no—
148C4⋊C4—112no—
149C4⋊C4—222no—
150C4⋊C4—222no—
151C4⋊C4—222no—
152C4⋊C4—222no—
153C4⋊C4—222no—
154C4⋊C4D4412yes—
155C22⋊C4—222no—
156C22⋊C4—222no—
157C22⋊C4—222no—
158C22⋊C4D4412yes—
159C42—222no—
160C42C22×D1111yescharacteristic
161C42C22×D1111yescharacteristic
162C11#326011yescharacteristic, complemented, Sylow
163C23—222no—
164C23C2×D4411yescharacteristic
165Q8—222no—
166Q8—222no—
167D4—222no—
168D4—222no—
169D4—882no—
170D4—882no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—222no—
174C2×C4—222no—
175C2×C4—222no—
176C2×C4—882no—
177C2×C4C2×D4412yes—
178C2×C4C2×D4412yes—
179C2×C4C2×D4411yescharacteristic
180C2×C4C23×D1111yescharacteristic
181C8—22no—
182C8—22no—
183C22—22no—
184C22—21no—
185C22—442no—
186C22—442no—
187C22—442no—
188C22C22×D4411yescharacteristic
189C4—22no—
190C4—22no—
191C4—21no—
192C4—442no—
193C4—442no—
194C4—442no—
195C4#6703711yescharacteristic
196C4#6704011yescharacteristic
197C2—41no—
198C2—882no—
199C2#1062304111yescharacteristic
200C2#1062328212yes—
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#424C2
socleC22×C11C22×D4
prime radical#10623066C2
hypercenter#424D11
hypocenterC11#3260
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #10623049C2semidirect
3. C11×#424C2semidirect
4. #10622747C2semidirect
5. #10622727C2semidirect
6. #10622461C2semidirect
7. #10622460C2semidirect
8. #10622454C2semidirect
9. #10622442C2semidirect
91. #424D11semidirect
162. C11#3260semidirect

Maximal subgroups

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

subgroupindex
#106230662
#106230492
C11×#4242
#106227472
#106227272
#106224612
#106224602
#106224542
#106224422
#326011