Finite Group Databasebeta

← #13069785

Subgroups — #13069785

Order 1408.

244 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 67 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×#533C211yesmaximal, characteristic, complemented
2#10622619C211yesmaximal, characteristic
3#10622618C211yesmaximal, characteristic
4C2×#66869C211yesmaximal, characteristic
5#10622171C211yesmaximal, characteristic, complemented
6#10622169C211yesmaximal, characteristic, complemented
7#10622161C211yesmaximal, characteristic, complemented
8C2×#4339C2211yescharacteristic
9C11×C4⋊Q8—21no—
10C11×#125—21no—
11C11×C22⋊Q8—22no—
12C4×Q8×C11—22no—
13C11×#117C2211yescharacteristic
14C11×#117C2211yescharacteristic
15C2×C42×C11C2211yescharacteristic
16#66979C2211yescharacteristic
17C2×#4318C2211yescharacteristic
18C2×#4318C2211yescharacteristic
19#66870—22no—
20#66869—21no—
21#66869—21no—
22#66869—22no—
23C2×Q8×C11—22no—
24C22×C4×C11—21no—
25C22×C4×C11C2311yescharacteristic
26C2×C22⋊D11—21no—
27#4339—21no—
28#4339—21no—
29#4339—21no—
30#4339—21no—
31C2×D44Q811yescharacteristic, complemented
32C2×C4×D11—21no—
33C2×Dic22Q811yescharacteristic, complemented
34C11×C4⋊C4—24no—
35C11×C4⋊C4—22no—
36C11×C4⋊C4—21no—
37C11×C4⋊C4—21no—
38C11×C22⋊C4—21no—
39C11×C22⋊C4D412yes—
40C42×C11—21no—
41C42×C11—21no—
42C42×C11D411yescharacteristic
43C42×C11D411yescharacteristic
44C42×C11D412yes—
45C22⋊Dic11—21no—
46C4⋊Dic11—21no—
47C4×Dic11—21no—
48#4318—21no—
49#4318—21no—
50#4318—21no—
51#4318—21no—
52C2×C11⋊C8—21no—
53C2×C11⋊C8—21no—
54#2031—111nomaximal, Sylow
55C23×C11C2×D411yescharacteristic
56C22×D11—21no—
57Q8×C11—44no—
58C2×C4×C11—21no—
59C2×C4×C11—21no—
60C2×C4×C11—22no—
61C2×C4×C11—22no—
62C2×C4×C11—42no—
63C2×C4×C11C2×D411yescharacteristic
64C2×C4×C11C2×D411yescharacteristic
65C2×C4×C11C2×Q811yescharacteristic
66C2×C4×C11#4111yescharacteristic
67C2×C4×C11#4111yescharacteristic
68C2×C4×C11#4111yescharacteristic
69C22⋊D11—41no—
70C22⋊D11—41no—
71C2×Dic11—21no—
72C2×Dic11—41no—
73D44—21no—
74D44—21no—
75C4×D11—41no—
76C4×D11—41no—
77Dic22—21no—
78Dic22—21no—
79C11⋊C8—41no—
80C11⋊C8—41no—
81#533D1111yescharacteristic, complemented
82#421—111no—
83C2×#104—111no—
84#410—111no—
85#344—111no—
86#339—111no—
87H(3,ℤ/4)—111no—
88C22×C11—41no—
89C22×C11#12011yescharacteristic
90C22×C11C22⋊Q811yescharacteristic
91C22×C11#12411yescharacteristic
92C2×D11—41no—
93C2×D11—81no—
94C4×C11—22no—
95C4×C11—41no—
96C4×C11—42no—
97C4×C11—42no—
98C4×C11C22⋊Q811yescharacteristic
99C4×C11C22⋊Q811yescharacteristic
100C4×C11#12411yescharacteristic
101C4×C11#12411yescharacteristic
102Dic11—41no—
103Dic11—81no—
104C2×#41—111no—
105C2×M16—111no—
106C2×M16—111no—
107C4⋊Q8—21no—
108#125—21no—
109C22⋊Q8—22no—
110C4×Q8—22no—
111#117—111no—
112#117C2×D1111yescharacteristic
113#117C2×D1111yescharacteristic
114C2×C42C2×D1111yescharacteristic
115#104—221no—
116#104—221no—
117#104—222no—
118#99—222no—
119C2×C11—21no—
120C2×C11—21no—
121C2×C11—21no—
122C2×C11#39311yescharacteristic
123D11—81no—
124#41—221no—
125#41—221no—
126#41—221no—
127#41—221no—
128C2×Q8—22no—
129C2×Q8—111no—
130C2×D4—111no—
131C2×D4—221no—
132C22×C4—21no—
133C22×C4—221no—
134C22×C4C22×D1111yescharacteristic
135M16—221no—
136M16—221no—
137M16—221no—
138M16—221no—
139C2×C8—221no—
140C2×C8—221no—
141C4⋊C4—24no—
142C4⋊C4—22no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—221no—
146C22⋊C4—21no—
147C22⋊C4—221no—
148C22⋊C4C22⋊D1112yes—
149C42—21no—
150C42—21no—
151C42—221no—
152C42C22⋊D1111yescharacteristic
153C42C22⋊D1111yescharacteristic
154C42C22⋊D1112yes—
155C11#203111yescharacteristic, complemented, Sylow
156C23—221no—
157C23C2×C22⋊D1111yescharacteristic
158Q8—44no—
159Q8—221no—
160Q8—221no—
161D4—221no—
162D4—221no—
163D4—441no—
164D4—441no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—221no—
171C2×C4—441no—
172C2×C4—441no—
173C2×C4—441no—
174C2×C4Q8×D1111yescharacteristic
175C2×C4#434311yescharacteristic
176C2×C4#434311yescharacteristic
177C2×C4#434311yescharacteristic
178C2×C4C2×C22⋊D1111yescharacteristic
179C2×C4C2×C22⋊D1111yescharacteristic
180C8—441no—
181C8—441no—
182C22—41no—
183C22—441no—
184C22—881no—
185C22#6699911yescharacteristic
186C22#6700011yescharacteristic
187C22#6700611yescharacteristic
188C4—22no—
189C4—41no—
190C4—42no—
191C4—42no—
192C4—441no—
193C4—881no—
194C4#6699911yescharacteristic
195C4#6699911yescharacteristic
196C4#6700011yescharacteristic
197C4#6700011yescharacteristic
198C2—21no—
199C2—21no—
200C2—21no—
201C2—881no—
202C2#1062284411yescharacteristic
subgroupG/H
centerC4#67000
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#533C2
socleC2×C11#393
prime radicalC2×#4339C22
hypercenter#533D11
hypocenterC11#2031
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C11×#533C2semidirect
5. #10622171C2semidirect
6. #10622169C2semidirect
7. #10622161C2semidirect
31. C2×D44Q8semidirect
33. C2×Dic22Q8semidirect
81. #533D11semidirect
155. C11#2031semidirect

Maximal subgroups

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

subgroupindex
C11×#5332
#106226192
#106226182
C2×#668692
#106221712
#106221692
#106221612
#203111