Finite Group Databasebeta

← #13081192

Subgroups — #13081192

Order 1408.

336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 336 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#10623112C212yesmaximal
2C4×C11×Q16C211yesmaximal, characteristic, complemented
3#10622802C212yesmaximal, complemented
4#10622635C212yesmaximal, complemented
5#10622494C212yesmaximal, complemented
6#10622427C212yesmaximal, complemented
7#10622422C212yesmaximal, complemented
8#10622301C211yesmaximal, characteristic
9#10622296C211yesmaximal, characteristic, complemented
10C2×C11×Q16C2211yescharacteristic
11C4×Q8×C11C2212yes—
12#66999C2212yes—
13#66999C2212yes—
14C2×#4313C2212yes—
15#66947—22no—
16#66945C2212yes—
17C4⋊C4×D11C2212yes—
18#66942—22no—
19#66929—22no—
20C4×D44C2211yescharacteristic
21#66925—22no—
22#66923C2212yes—
23C11×#107C2211yescharacteristic
24C11×#103C2212yes—
25C4×C8×C11C2211yescharacteristic
26#66899C2212yes—
27#66899C2212yes—
28(C2×D11)⋊C8C2212yes—
29#66882C2211yescharacteristic
30#66882C2211yescharacteristic
31#66881C2212yes—
32#66872C2212yes—
33#66871C2212yes—
34C4⋊(C11⋊C8)C2211yescharacteristic
35C2×Q8×C11C2312yes—
36C2×D44D411yescharacteristic
37C2×C4×D11—22no—
38C2×C4×D11C2312yes—
39C11×Q16—22no—
40C2×C8×C11C2311yescharacteristic
41C2×C8×C11C2311yescharacteristic
42C11×C4⋊C4—22no—
43C11×C4⋊C4C2312yes—
44C42×C11—22no—
45C42×C11C2311yescharacteristic
46(C2×D11)⋊C4—22no—
47(C2×D11)⋊C4—22no—
48(C2×D11)⋊C4—22no—
49(C2×D11)⋊C4D412yes—
50C4⋊Dic11D411yescharacteristic
51C4⋊Dic11C2312yes—
52C4⋊Dic11C2312yes—
53Dic11⋊C4—22no—
54Dic11⋊C4—22no—
55Dic11⋊C4—22no—
56Dic11⋊C4—22no—
57Dic11⋊C4—22no—
58C4×Dic11—22no—
59C2×C11⋊C8C2312yes—
60#4313—24no—
61#3352—111nomaximal, Sylow
62C22×D11C2×D412yes—
63Q8×C11—22no—
64Q8×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11C2×D411yescharacteristic
68C2×C4×C11C2×D411yescharacteristic
69C2×C4×C11C2411yescharacteristic
70C2×Dic11—22no—
71C2×Dic11—22no—
72C2×Dic11C2×D412yes—
73D44—41no—
74C4×D11—22no—
75C4×D11—22no—
76C4×D11—44no—
77C8×C11—21no—
78C8×C11#4112yes—
79C11⋊C8—22no—
80#552—112no—
81#499—111no—
82#485—112no—
83#484—112no—
84#479—112no—
85#470—112no—
86C4×Q16D1111yescharacteristic, complemented
87#436—111no—
88#428—112no—
89C22×C11C22×D411yescharacteristic
90C2×D11—22no—
91C2×D11—22no—
92C2×D11—22no—
93C4×C11—21no—
94C4×C11—21no—
95C4×C11—42no—
96C4×C11—42no—
97C4×C11C2×#4111yescharacteristic
98C4×C112−1+411yescharacteristic
99Dic11—22no—
100Dic11—42no—
101Dic11—42no—
102C2×Q16C2×D1111yescharacteristic
103C2×M16—112no—
104#126—222no—
105#125—112no—
106#125—222no—
107#123—222no—
108C22⋊Q8—112no—
109C22⋊Q8—112no—
110C4×Q8C2×D1112yes—
111C4×D4—111no—
112#117—112no—
113#117—222no—
114C2×C4⋊C4—112no—
115#107—111no—
116#107—111no—
117#107—112no—
118#107C2×D1111yescharacteristic
119#106—112no—
120#106—112no—
121C4⋊C8—111no—
122#103—112no—
123#103—112no—
124#103C2×D1112yes—
125C22⋊C8—112no—
126C4×C8C2×D1111yescharacteristic
127C2×C11#54711yescharacteristic
128C2×C11#57511yescharacteristic
129C2×C11#57811yescharacteristic
130D11—42no—
131C2×Q8C22×D1112yes—
132C2×D4—111no—
133C22×C4—112no—
134C22×C4—222no—
135Q16—22no—
136M16—224no—
137C2×C8—112no—
138C2×C8C22×D1111yescharacteristic
139C2×C8C22×D1111yescharacteristic
140C4⋊C4—22no—
141C4⋊C4—111no—
142C4⋊C4—112no—
143C4⋊C4—112no—
144C4⋊C4—222no—
145C4⋊C4—222no—
146C4⋊C4—222no—
147C4⋊C4—222no—
148C4⋊C4—222no—
149C4⋊C4C22×D1112yes—
150C22⋊C4—112no—
151C22⋊C4—222no—
152C22⋊C4—222no—
153C22⋊C4—222no—
154C42—22no—
155C42—222no—
156C42C22×D1111yescharacteristic
157C11#335211yescharacteristic, complemented, Sylow
158C23—112no—
159Q8—22no—
160Q8—22no—
161D4—441no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—112no—
165C2×C4—222no—
166C2×C4—222no—
167C2×C4—222no—
168C2×C4—222no—
169C2×C4—444no—
170C2×C4D4×D1111yescharacteristic
171C2×C4D4×D1111yescharacteristic
172C2×C4C23×D1111yescharacteristic
173C8—21no—
174C8—222no—
175C8#433912yes—
176C22—222no—
177C22—222no—
178C22—222no—
179C22C2×D4×D1111yescharacteristic
180C4—21no—
181C4—21no—
182C4—42no—
183C4—42no—
184C4—222no—
185C4—442no—
186C4—442no—
187C4C2×#433911yescharacteristic
188C4#6704311yescharacteristic
189C2—442no—
190C2#1062308211yescharacteristic
191C2#1062329711yescharacteristic
192C2#1062329911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×Q16C2
socleC22×C11C22×D4
prime radicalC2×D44D4
hypercenterC4×Q16D11
hypocenterC11#3352
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. C4×C11×Q16C2semidirect
3. #10622802C2semidirect
4. #10622635C2semidirect
5. #10622494C2semidirect
6. #10622427C2semidirect
7. #10622422C2semidirect
9. #10622296C2semidirect
86. C4×Q16D11semidirect
157. C11#3352semidirect

Maximal subgroups

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

subgroupindex
#106231122
C4×C11×Q162
#106228022
#106226352
#106224942
#106224272
#106224222
#106223012
#106222962
#335211