Finite Group Databasebeta

← #14911450

Subgroups — #14911450

Order 2816.

528 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 165 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
1Q8×Dic44C211yesmaximal, characteristic, complemented
2#13070839C213yesmaximal, complemented
3#13070763C213yesmaximal, complemented
4#13070653C213yesmaximal, complemented
5Q8×C11⋊C16C211yesmaximal, characteristic, complemented
6C4×#66891C213yesmaximal, complemented
7C11×#3391C211yesmaximal, characteristic
8C11×#550—21no—
9Q8×Dic22—21no—
10C11×#493C2213yes—
11C11×#459—23no—
12C8×Q8×C11C2211yescharacteristic
13C4×C11×D8C2213yes—
14C2×#66891C2213yes—
15#10622463—23no—
16C4×Dic44C2213yes—
17#10622295C2213yes—
18#10622200C2216yes—
19#10622200C2213yes—
20#10622130C2211yescharacteristic
21#10622128C2213yes—
22C4⋊(C11⋊C16)C2213yes—
23C4×C11⋊C16C2213yes—
24C2×C11×#41—41no—
25C2×C11×D8—23no—
26C2×C11×D8C2313yes—
27C11×#127—23no—
28C11×#121—43no—
29C4×Q8×C11D411yescharacteristic
30C4×D4×C11—23no—
31Q8×Dic11—41no—
32C2×Dic44C2311yescharacteristic
33#66941—43no—
34#66922—23no—
35C4×Dic22—23no—
36C11×#107C2311yescharacteristic
37C11×C4⋊C8D413yes—
38C11×#102—23no—
39C4×C8×C11C2313yes—
40#66891—26no—
41#66882—23no—
42#66882C2313yes—
43#66880—23no—
44C2×C11⋊C16C2313yes—
45C2×C11⋊C16C2311yescharacteristic
46#33929—111nomaximal, Sylow
47C11×#41—84no—
48C2×Q8×C11D811yescharacteristic
49C2×D4×C11—23no—
50C2×D4×C11—43no—
51C2×D4×C11—43no—
52C22×C4×C11—43no—
53C2×Dic22—21no—
54C2×Dic22—43no—
55C11×D8—23no—
56C11×D8—23no—
57C11×D8—83no—
58C2×C8×C11C2×D413yes—
59C2×C8×C11C2411yescharacteristic
60C11×C4⋊C4—21no—
61C11×C4⋊C4D813yes—
62C11×C22⋊C4—43no—
63C42×C11C2×D413yes—
64C4⋊Dic11—23no—
65C4⋊Dic11—43no—
66Dic11⋊C4—43no—
67C4×Dic11—43no—
68Dic44—21no—
69Dic44#4112yescomplemented
70C11⋊C16—23no—
71C11⋊C16—21no—
72#3391D1111yescharacteristic
73Q8×Q16—111no—
74#2240—113no—
75#2226—113no—
76#2207—113no—
77Q8×C16—111no—
78C4×SD32—113no—
79C23×C11—43no—
80Q8×C11SD3214yescomplemented
81D4×C11—43no—
82D4×C11—43no—
83D4×C11—86no—
84D4×C11—163no—
85C2×C4×C11—41no—
86C2×C4×C11—86no—
87C2×C4×C11C2×D813yes—
88C2×C4×C11C2×D813yes—
89C2×C4×C11C22×D411yescharacteristic
90C2×Dic11—41no—
91C2×Dic11—43no—
92Dic22—22no—
93Dic22—41no—
94Dic22—163no—
95C8×C11—23no—
96C8×C11C2×#4111yescharacteristic
97C8×C112−1+411yescharacteristic
98Q82—221no—
99#550—21no—
100C2×SD32—113no—
101#500—113no—
102#493C2×D1113yes—
103#477—223no—
104#459—23no—
105C8×Q8C2×D1111yescharacteristic
106C4×Q16—113no—
107C4×D8C2×D1113yes—
108#367—113no—
109C4⋊C16—113no—
110#358—111no—
111#357—113no—
112#357—116no—
113C4×C16—113no—
114C22×C11—83no—
115C22×C11—83no—
116C22×C11—83no—
117C22×C11C22×D811yescharacteristic
118C4×C11—23no—
119C4×C11—81no—
120C4×C11C2×SD3216yes—
121C4×C11#54811yescharacteristic
122C4×C11#57711yescharacteristic
123Dic11—42no—
124Dic11—83no—
125C2×#41—41no—
126C2×Q16—111no—
127C2×D8—23no—
128C2×D8C22×D1113yes—
129C4⋊Q8—223no—
130C4⋊Q8—443no—
131#127—23no—
132#121—43no—
133C4×Q8—223no—
134C4×Q8—441no—
135C4×Q8C22⋊D1111yescharacteristic
136C4×D4—23no—
137SD32—226no—
138C2×C16—111no—
139C2×C16—113no—
140#107—113no—
141#107—223no—
142#107C22×D1111yescharacteristic
143C4⋊C8C22⋊D1113yes—
144#103—223no—
145#102—23no—
146C4×C8C22×D1113yes—
147C2×C11—163no—
148C2×C11#335811yescharacteristic
149C2×C11C22×SD3211yescharacteristic
150C2×C11#341511yescharacteristic
151#41—84no—
152C2×Q8—221no—
153C2×Q8—443no—
154C2×Q8#432311yescharacteristic
155C2×D4—23no—
156C2×D4—43no—
157C2×D4—43no—
158C22×C4—43no—
159Q16—112no—
160Q16—221no—
161D8—23no—
162D8—23no—
163D8—83no—
164C2×C8C2×C22⋊D1113yes—
165C2×C8C23×D1111yescharacteristic
166C4⋊C4—21no—
167C4⋊C4—223no—
168C4⋊C4—443no—
169C4⋊C4—443no—
170C4⋊C4#432313yes—
171C22⋊C4—43no—
172C42—443no—
173C42C2×C22⋊D1113yes—
174C16—223no—
175C16—221no—
176C11#3392911yescharacteristic, complemented, Sylow
177C23—43no—
178Q8—222no—
179Q8—441no—
180Q8—1763no—
181Q8#6689114yescomplemented
182D4—43no—
183D4—43no—
184D4—86no—
185D4—163no—
186C2×C4—41no—
187C2×C4—86no—
188C2×C4—441no—
189C2×C4—443no—
190C2×C4C2×#432313yes—
191C2×C4C2×#432313yes—
192C2×C4C22×C22⋊D1111yescharacteristic
193C8—23no—
194C8#41×D1111yescharacteristic
195C8#6704311yescharacteristic
196C22—83no—
197C22—83no—
198C22—83no—
199C22C22×#432311yescharacteristic
200C4—23no—
201C4—81no—
202C4—442no—
203C4—883no—
204C4C2×#6689116yes—
205C4#1062336211yescharacteristic
206C4#1062336711yescharacteristic
207C2—163no—
208C2#1308124711yescharacteristic
209C2C22×#6689111yescharacteristic
210C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3391C2
socleC22×C11C22×D8
hypercenter#3391D11
hypocenterC11#33929
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3391

Complements

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

NH ≅ G/Ntype
1. Q8×Dic44C2semidirect
2. #13070839C2semidirect
3. #13070763C2semidirect
4. #13070653C2semidirect
5. Q8×C11⋊C16C2semidirect
6. C4×#66891C2semidirect
69. Dic44#41semidirect
80. Q8×C11SD32semidirect
176. C11#33929semidirect
181. Q8#66891semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic442
#130708392
#130707632
#130706532
Q8×C11⋊C162
C4×#668912
C11×#33912
#3392911