Finite Group Databasebeta

← #14911414

Subgroups — #14911414

Order 2816.

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

normal subgroups only

This group has 562 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×D88C211yesmaximal, characteristic, complemented
2#13070839C213yesmaximal, complemented
3#13070753C213yesmaximal, complemented
4#13070648C213yesmaximal, complemented
5Q8×C11⋊C16C211yesmaximal, characteristic, complemented
6C4×#66890C213yesmaximal, complemented
7C11×#3391C211yesmaximal, characteristic, complemented
8C11×#550—21no—
9Q8×D44—21no—
10C11×#493C2213yes—
11C11×#459—23no—
12C8×Q8×C11C2211yescharacteristic
13C4×C11×D8C2213yes—
14C2×#66890C2213yes—
15#10622459—23no—
16C4×D88C2213yes—
17#10622295C2213yes—
18#10622200C2216yes—
19#10622200C2213yes—
20#10622129C2211yescharacteristic
21#10622127C2213yes—
22C4⋊(C11⋊C16)C2213yes—
23C4×C11⋊C16C2213yes—
24C2×C11×#41—41no—
25C2×Q8×D11—41no—
26C2×C11×D8—23no—
27C2×C11×D8C2313yes—
28C11×#127—23no—
29C11×#121—43no—
30C4×Q8×C11D411yescharacteristic
31C4×D4×C11—23no—
32C2×D88C2311yescharacteristic
33#66950—43no—
34C4×D44—23no—
35#66922—23no—
36C11×#107C2311yescharacteristic
37C11×C4⋊C8D413yes—
38C11×#102—23no—
39C4×C8×C11C2313yes—
40#66890—26no—
41#66885—23no—
42#66882—23no—
43#66882C2313yes—
44C2×C11⋊C16C2313yes—
45C2×C11⋊C16C2311yescharacteristic
46#33925—111nomaximal, Sylow
47C11×#41—84no—
48C2×Q8×C11D811yescharacteristic
49C2×D4×C11—23no—
50C2×D4×C11—43no—
51C2×D4×C11—43no—
52C22×C4×C11—43no—
53Q8×D11—84no—
54C2×D44—21no—
55C2×C4×D11—43no—
56C2×Dic22—43no—
57C11×D8—23no—
58C11×D8—23no—
59C11×D8—83no—
60C2×C8×C11C2×D413yes—
61C2×C8×C11C2411yescharacteristic
62C11×C4⋊C4—21no—
63C11×C4⋊C4D813yes—
64C11×C22⋊C4—43no—
65C42×C11C2×D413yes—
66(C2×D11)⋊C4—43no—
67C4⋊Dic11—23no—
68C4⋊Dic11—43no—
69D88—21no—
70D88#4112yescomplemented
71C11⋊C16—23no—
72C11⋊C16—21no—
73#3391D1111yescharacteristic, complemented
74Q8×D8—111no—
75#2240—113no—
76#2224—113no—
77#2206—113no—
78Q8×C16—111no—
79C4×D16—113no—
80C23×C11—43no—
81C22×D11—41no—
82Q8×C11D1614yescomplemented
83D4×C11—43no—
84D4×C11—43no—
85D4×C11—86no—
86D4×C11—163no—
87C2×C4×C11—41no—
88C2×C4×C11—86no—
89C2×C4×C11C2×D813yes—
90C2×C4×C11C2×D813yes—
91C2×C4×C11C22×D411yescharacteristic
92C2×Dic11—43no—
93D44—22no—
94D44—41no—
95C4×D11—86no—
96Dic22—86no—
97C8×C11—23no—
98C8×C11C2×#4111yescharacteristic
99C8×C112−1+411yescharacteristic
100#550—21no—
101D4×Q8—221no—
102C2×D16—113no—
103#500—113no—
104#493C2×D1113yes—
105#474—223no—
106#459—23no—
107C8×Q8C2×D1111yescharacteristic
108C4×D8—113no—
109C4×D8C2×D1113yes—
110#366—113no—
111C4⋊C16—113no—
112#357—113no—
113#357—116no—
114#357—111no—
115C4×C16—113no—
116C22×C11—83no—
117C22×C11—83no—
118C22×C11—83no—
119C22×C11C22×D811yescharacteristic
120C2×D11—42no—
121C2×D11—81no—
122C2×D11—81no—
123C4×C11—23no—
124C4×C11—81no—
125C4×C11C2×D1616yes—
126C4×C11#54811yescharacteristic
127C4×C11#57711yescharacteristic
128Dic11—83no—
129C2×#41—41no—
130C22×Q8—441no—
131C2×D8—23no—
132C2×D8—111no—
133C2×D8C22×D1113yes—
134C4⋊Q8—223no—
135#127—23no—
136C22⋊Q8—443no—
137#121—43no—
138C4×Q8C22⋊D1111yescharacteristic
139C4×D4—23no—
140C4×D4—223no—
141D16—226no—
142C2×C16—111no—
143C2×C16—113no—
144#107—113no—
145#107—223no—
146#107C22×D1111yescharacteristic
147C4⋊C8C22⋊D1113yes—
148#102—23no—
149#102—223no—
150C4×C8C22×D1113yes—
151C2×C11—163no—
152C2×C11#335811yescharacteristic
153C2×C11C22×D1611yescharacteristic
154C2×C11#341611yescharacteristic
155D11—82no—
156#41—84no—
157C2×Q8—443no—
158C2×Q8—884no—
159C2×Q8#432311yescharacteristic
160C2×D4—23no—
161C2×D4—43no—
162C2×D4—43no—
163C2×D4—221no—
164C22×C4—43no—
165C22×C4—443no—
166D8—23no—
167D8—23no—
168D8—83no—
169D8—112no—
170D8—221no—
171C2×C8C2×C22⋊D1113yes—
172C2×C8C23×D1111yescharacteristic
173C4⋊C4—21no—
174C4⋊C4—223no—
175C4⋊C4—443no—
176C4⋊C4#432313yes—
177C22⋊C4—43no—
178C22⋊C4—443no—
179C42C2×C22⋊D1113yes—
180C16—223no—
181C16—221no—
182C11#3392511yescharacteristic, complemented, Sylow
183C23—43no—
184C23—441no—
185Q8—886no—
186Q8#6689014yescomplemented
187D4—43no—
188D4—43no—
189D4—86no—
190D4—163no—
191D4—222no—
192D4—441no—
193C2×C4—41no—
194C2×C4—86no—
195C2×C4—443no—
196C2×C4—886no—
197C2×C4C2×#432313yes—
198C2×C4C2×#432313yes—
199C2×C4C22×C22⋊D1111yescharacteristic
200C8—23no—
201C8#41×D1111yescharacteristic
202C8#6704311yescharacteristic
203C22—83no—
204C22—83no—
205C22—83no—
206C22—442no—
207C22—881no—
208C22—881no—
209C22C22×#432311yescharacteristic
210C4—23no—
211C4—81no—
212C4—883no—
213C4C2×#6689016yes—
214C4#1062336211yescharacteristic
215C4#1062336711yescharacteristic
216C2—163no—
217C2—882no—
218C2#1308124711yescharacteristic
219C2C22×#6689011yescharacteristic
220C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3391C2
socleC22×C11C22×D8
hypercenter#3391D11
hypocenterC11#33925
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×D88C2semidirect
2. #13070839C2semidirect
3. #13070753C2semidirect
4. #13070648C2semidirect
5. Q8×C11⋊C16C2semidirect
6. C4×#66890C2semidirect
7. C11×#3391C2semidirect
70. D88#41semidirect
73. #3391D11semidirect
82. Q8×C11D16semidirect
182. C11#33925semidirect
186. Q8#66890semidirect

Maximal subgroups

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

subgroupindex
Q8×D882
#130708392
#130707532
#130706482
Q8×C11⋊C162
C4×#668902
C11×#33912
#3392511