Finite Group Databasebeta

← #13078907

Subgroups — #13078907

Order 1408.

382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 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×#519C211yesmaximal, characteristic, complemented
2#10623066C211yesmaximal, characteristic
3#10622840C212yesmaximal, complemented
4#10622640C212yesmaximal, complemented
5#10622639C212yesmaximal, complemented
6C4×#4325C212yesmaximal, complemented
7#10622635C212yesmaximal, complemented
8#10622616C212yesmaximal, complemented
9#10622613C211yesmaximal, characteristic, complemented
10C22×Q8×C11C2211yescharacteristic
11C4×Q8×C11—22no—
12C4×Q8×C11C2212yes—
13C4×Q8×C11C2212yes—
14C11×#117—22no—
15C11×#117C2211yescharacteristic
16C11×#117C2211yescharacteristic
17C2×#4325C2212yes—
18C2×#4325C2212yes—
19#66983C2212yes—
20#66947—22no—
21#66937—22no—
22#66927C2211yescharacteristic
23C4×D44C2212yes—
24#66923C2211yescharacteristic
25#66899C2212yes—
26#66899C2212yes—
27C22⋊(C11⋊C8)C2212yes—
28#66873C2212yes—
29#66873C2212yes—
30#66872C2212yes—
31#66871C2212yes—
32C4⋊(C11⋊C8)C2212yes—
33#66867C2211yescharacteristic
34C4×C11⋊C8C2211yescharacteristic
35C2×Q8×C11—24no—
36C2×Q8×C11—21no—
37C2×Q8×C11C2312yes—
38C22×C4×C11—21no—
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—22no—
41C2×D44—22no—
42C2×D44C2312yes—
43C2×C4×D11—22no—
44C11×C4⋊C4—22no—
45C11×C4⋊C4—22no—
46C11×C4⋊C4D412yes—
47C11×C4⋊C4C2312yes—
48C11×C22⋊C4—21no—
49C11×C22⋊C4D412yes—
50C42×C11—22no—
51C42×C11—22no—
52C42×C11—21no—
53C42×C11C2311yescharacteristic
54C42×C11C2311yescharacteristic
55#4325—24no—
56#4325—24no—
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4—22no—
59C4⋊Dic11C2312yes—
60Dic11⋊C4—22no—
61C2×C11⋊C8C2312yes—
62C2×C11⋊C8C2312yes—
63#3126—111nomaximal, Sylow
64C23×C11C2×D411yescharacteristic
65C22×D11—22no—
66Q8×C11—24no—
67Q8×C11—22no—
68Q8×C11#4114yes—
69C2×C4×C11—24no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11C2×D412yes—
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2×D412yes—
76C2×C4×C11C2411yescharacteristic
77C22⋊D11—82no—
78C2×Dic11—22no—
79D44—22no—
80D44—22no—
81D44—82no—
82C4×D11—82no—
83C11⋊C8—22no—
84C11⋊C8—22no—
85#540—111no—
86#519D1111yescharacteristic, complemented
87#482—112no—
88#479—112no—
89#460—112no—
90#448—112no—
91#440—112no—
92C4×SD16—112no—
93#433—111no—
94C22×C11—21no—
95C22×C11—22no—
96C22×C11C22×D411yescharacteristic
97C2×D11—42no—
98C2×D11—42no—
99C2×D11—42no—
100C4×C11—24no—
101C4×C11—21no—
102C4×C11—22no—
103C4×C11—22no—
104C4×C11—42no—
105C4×C11C2×#4112yes—
106Dic11—42no—
107C22×Q8C2×D1111yescharacteristic
108C2×SD16—112no—
109C2×SD16—112no—
110#127—111no—
111#125—111no—
112#123—222no—
113#121—112no—
114#121—222no—
115C4×Q8—22no—
116C4×Q8C2×D1112yes—
117C4×Q8C2×D1112yes—
118C4×D4—112no—
119#117—22no—
120#117C2×D1111yescharacteristic
121#117C2×D1111yescharacteristic
122#107—112no—
123#106—112no—
124C4⋊C8—112no—
125#103—112no—
126#103—112no—
127#102—112no—
128#102—112no—
129C22⋊C8—112no—
130#97—111no—
131C4×C8—111no—
132C2×C11—41no—
133C2×C11#52511yescharacteristic
134C2×C11#57712yes—
135D11—82no—
136C2×Q8—24no—
137C2×Q8—21no—
138C2×Q8C22×D1112yes—
139C2×D4—112no—
140C2×D4—222no—
141C2×D4—222no—
142C22×C4—21no—
143C22×C4—222no—
144C22×C4C22×D1111yescharacteristic
145SD16—224no—
146SD16—224no—
147C2×C8—112no—
148C2×C8—112no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—112no—
152C4⋊C4—222no—
153C4⋊C4C22⋊D1112yes—
154C4⋊C4C22×D1112yes—
155C22⋊C4—21no—
156C22⋊C4—222no—
157C22⋊C4—222no—
158C22⋊C4C22⋊D1112yes—
159C42—22no—
160C42—22no—
161C42—21no—
162C42C22×D1111yescharacteristic
163C42C22×D1111yescharacteristic
164C11#312611yescharacteristic, complemented, Sylow
165C23—222no—
166C23C2×C22⋊D1111yescharacteristic
167Q8—24no—
168Q8—22no—
169Q8#433914yes—
170D4—222no—
171D4—222no—
172D4—882no—
173D4—882no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—222no—
179C2×C4—882no—
180C2×C4C2×C22⋊D1112yes—
181C2×C4C2×C22⋊D1112yes—
182C2×C4C2×C22⋊D1111yescharacteristic
183C2×C4C23×D1111yescharacteristic
184C8—222no—
185C8—222no—
186C22—21no—
187C22—22no—
188C22—442no—
189C22—442no—
190C22—442no—
191C22C22×C22⋊D1111yescharacteristic
192C4—24no—
193C4—21no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—442no—
198C4C2×#433912yes—
199C2—41no—
200C2—882no—
201C2#1062332211yescharacteristic
202C2#1062336812yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#519C2
socleC22×C11C22×D4
prime radical#10623066C2
hypercenter#519D11
hypocenterC11#3126
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
1. C11×#519C2semidirect
3. #10622840C2semidirect
4. #10622640C2semidirect
5. #10622639C2semidirect
6. C4×#4325C2semidirect
7. #10622635C2semidirect
8. #10622616C2semidirect
9. #10622613C2semidirect
86. #519D11semidirect
164. C11#3126semidirect

Maximal subgroups

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

subgroupindex
C11×#5192
#106230662
#106228402
#106226402
#106226392
C4×#43252
#106226352
#106226162
#106226132
#312611