Finite Group Databasebeta

← #13081220

Subgroups — #13081220

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#10623226C212yesmaximal, complemented
2C11×#499C211yesmaximal, characteristic, complemented
3#10622679C212yesmaximal, complemented
4#10622498C212yesmaximal, complemented
5#10622495C212yesmaximal, complemented
6#10622478C212yesmaximal, complemented
7#10622474C212yesmaximal, complemented
8C4×D88C211yesmaximal, characteristic, complemented
9#10622301C211yesmaximal, characteristic, complemented
10C11×#125C2212yes—
11C2×D88C2211yescharacteristic
12C2×#4313C2212yes—
13#66951—22no—
14#66948—22no—
15#66948C2212yes—
16#66948C2212yes—
17#66947—22no—
18#66946—22no—
19#66945C2212yes—
20C4⋊C4×D11C2212yes—
21C4×D44C2211yescharacteristic
22C4×D44C2212yes—
23C11×#107C2211yescharacteristic
24C11×#107C2211yescharacteristic
25C11×#106C2212yes—
26C4×C8×C11C2211yescharacteristic
27#66885C2212yes—
28(C2×D11)⋊C8C2212yes—
29#66882C2211yescharacteristic
30#66873C2212yes—
31#66873C2212yes—
32#66872C2212yes—
33#66871C2212yes—
34C4⋊(C11⋊C8)C2211yescharacteristic
35C2×D44—22no—
36C2×D44—22no—
37C2×D44D411yescharacteristic
38C2×D44C2312yes—
39C2×C4×D11—22no—
40C2×C4×D11—22no—
41C2×C4×D11C2312yes—
42C2×C8×C11C2311yescharacteristic
43C2×C8×C11C2311yescharacteristic
44C11×C4⋊C4—22no—
45C11×C4⋊C4—22no—
46C11×C4⋊C4C2312yes—
47C11×C4⋊C4C2312yes—
48C42×C11C2311yescharacteristic
49(C2×D11)⋊C4—22no—
50(C2×D11)⋊C4—22no—
51(C2×D11)⋊C4—22no—
52(C2×D11)⋊C4—22no—
53(C2×D11)⋊C4D412yes—
54C4⋊Dic11D411yescharacteristic
55C4⋊Dic11C2312yes—
56Dic11⋊C4—22no—
57C4×Dic11—22no—
58C2×C11⋊C8C2312yes—
59D88—22no—
60#4313—24no—
61#3355—111nomaximal, Sylow
62C22×D11—22no—
63C22×D11C2×D412yes—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11C2×D411yescharacteristic
67C2×C4×C11C2×D411yescharacteristic
68C2×C4×C11C2411yescharacteristic
69C2×Dic11—22no—
70C2×Dic11C2×D412yes—
71D44—22no—
72D44—22no—
73D44—41no—
74D44—44no—
75D44—82no—
76C4×D11—22no—
77C4×D11—22no—
78C4×D11—82no—
79C4×D11—82no—
80C8×C11—21no—
81C8×C11#4112yes—
82C11⋊C8—22no—
83#553—112no—
84#499D1111yescharacteristic, complemented
85#482—112no—
86#480—112no—
87#478—112no—
88#469—112no—
89C4×D8—111no—
90#436—111no—
91#428—112no—
92C22×C11C22×D411yescharacteristic
93C2×D11—22no—
94C2×D11—22no—
95C2×D11—22no—
96C2×D11—42no—
97C2×D11—42no—
98C2×D11—42no—
99C4×C11—21no—
100C4×C11—21no—
101C4×C11—42no—
102C4×C11—42no—
103C4×C11C2×#4111yescharacteristic
104C4×C112−1+411yescharacteristic
105Dic11—22no—
106Dic11—42no—
107C2×D8—111no—
108C2×M16—112no—
109#126—222no—
110#125C2×D1112yes—
111#123—222no—
112#121—112no—
113#121—112no—
114#121—222no—
115C4×D4—111no—
116C4×D4—112no—
117C4×D4—222no—
118#117—112no—
119C2×C4⋊C4—112no—
120#107—111no—
121#107—112no—
122#107C2×D1111yescharacteristic
123#107C2×D1111yescharacteristic
124#106—112no—
125#106C2×D1112yes—
126C4⋊C8—111no—
127#102—112no—
128#102—112no—
129#102—112no—
130C22⋊C8—112no—
131C4×C8C2×D1111yescharacteristic
132C2×C11#54711yescharacteristic
133C2×C11#57511yescharacteristic
134C2×C11#57611yescharacteristic
135D11—42no—
136D11—82no—
137C2×D4—111no—
138C2×D4—112no—
139C2×D4—222no—
140C2×D4—222no—
141C22×C4—112no—
142C22×C4—222no—
143C22×C4—222no—
144D8—222no—
145M16—224no—
146C2×C8—112no—
147C2×C8C22×D1111yescharacteristic
148C2×C8C22×D1111yescharacteristic
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—111no—
152C4⋊C4—112no—
153C4⋊C4—222no—
154C4⋊C4C22×D1112yes—
155C4⋊C4C22×D1112yes—
156C22⋊C4—112no—
157C22⋊C4—222no—
158C22⋊C4—222no—
159C22⋊C4—222no—
160C22⋊C4—222no—
161C42—222no—
162C42C22×D1111yescharacteristic
163C11#335511yescharacteristic, complemented, Sylow
164C23—112no—
165C23—222no—
166D4—222no—
167D4—222no—
168D4—441no—
169D4—444no—
170D4—882no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—112no—
174C2×C4—222no—
175C2×C4—222no—
176C2×C4—222no—
177C2×C4—882no—
178C2×C4—882no—
179C2×C4D4×D1111yescharacteristic
180C2×C4D4×D1111yescharacteristic
181C2×C4C23×D1111yescharacteristic
182C8—21no—
183C8—222no—
184C8#434312yes—
185C22—222no—
186C22—222no—
187C22—222no—
188C22—442no—
189C22—442no—
190C22—442no—
191C22C2×D4×D1111yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—42no—
196C4—222no—
197C4—442no—
198C4C2×#434311yescharacteristic
199C4#6704011yescharacteristic
200C2—442no—
201C2—882no—
202C2#1062325711yescharacteristic
203C2#1062329911yescharacteristic
204C2#1062330011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#499C2
socleC22×C11C22×D4
hypercenter#499D11
hypocenterC11#3355
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #10623226C2semidirect
2. C11×#499C2semidirect
3. #10622679C2semidirect
4. #10622498C2semidirect
5. #10622495C2semidirect
6. #10622478C2semidirect
7. #10622474C2semidirect
8. C4×D88C2semidirect
9. #10622301C2semidirect
84. #499D11semidirect
163. C11#3355semidirect

Maximal subgroups

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

subgroupindex
#106232262
C11×#4992
#106226792
#106224982
#106224952
#106224782
#106224742
C4×D882
#106223012
#335511