Finite Group Databasebeta

← #14911455

Subgroups — #14911455

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
1#13081591C211yesmaximal, characteristic
2Q8×Dic44C211yesmaximal, characteristic, complemented
3#13070840C213yesmaximal, complemented
4#13070764C213yesmaximal, complemented
5#13070657C213yesmaximal, complemented
6C4×#66864C213yesmaximal, complemented
7Q8×C11×C16C211yesmaximal, characteristic, complemented
8#10623108—21no—
9Q8×Dic22—21no—
10C8×Q8×C11C2211yescharacteristic
11C2×#66864C2213yes—
12#10622463—23no—
13#10622456—23no—
14C4×Dic44C2213yes—
15#10622308C2213yes—
16C4×D88C2213yes—
17#10622295C2213yes—
18C11×C4⋊C16C2213yes—
19C4×C11×C16C2213yes—
20#10622147C2216yes—
21#10622147C2213yes—
22#10622143C2213yes—
23#10622141C2211yescharacteristic
24C2×#4343—41no—
25C4×Q8×C11D411yescharacteristic
26Q8×Dic11—41no—
27C2×Dic44C2311yescharacteristic
28C2×D88—23no—
29C2×D88C2313yes—
30#66948—43no—
31#66941—43no—
32#66927—23no—
33C4×D44—23no—
34#66922—23no—
35C4×Dic22—23no—
36C2×C11×C16C2311yescharacteristic
37C2×C11×C16C2313yes—
38C11×C4⋊C8D413yes—
39C4×C8×C11C2313yes—
40#66885—23no—
41#66882—23no—
42#66882C2313yes—
43#66882C2311yescharacteristic
44#66880—23no—
45#66864—26no—
46#33929—111nomaximal, Sylow
47C2×Q8×C11D811yescharacteristic
48#4343—84no—
49C2×D44—23no—
50C2×D44—43no—
51C2×D44—43no—
52C2×C4×D11—43no—
53C2×Dic22—21no—
54C2×Dic22—43no—
55C2×C8×C11C2×D413yes—
56C2×C8×C11C2411yescharacteristic
57C11×C4⋊C4D813yes—
58C42×C11C2×D413yes—
59(C2×D11)⋊C4—43no—
60C4⋊Dic11—23no—
61C4⋊Dic11—21no—
62C4⋊Dic11—43no—
63Dic11⋊C4—43no—
64C4×Dic11—43no—
65Dic44—21no—
66Dic44#4112yescomplemented
67D88—23no—
68D88—23no—
69D88—83no—
70C11×C16—23no—
71C11×C16—21no—
72#3391—111no—
73Q8×Q16—111no—
74#2240—113no—
75#2226—113no—
76#2207—113no—
77Q8×C16D1111yescharacteristic, complemented
78C4×SD32—113no—
79C22×D11—43no—
80Q8×C11SD3214yescomplemented
81C2×C4×C11C2×D813yes—
82C2×C4×C11C2×D813yes—
83C2×C4×C11C22×D411yescharacteristic
84C2×Dic11—41no—
85C2×Dic11—43no—
86C2×Dic11—41no—
87D44—43no—
88D44—43no—
89D44—86no—
90D44—163no—
91C4×D11—86no—
92Dic22—22no—
93Dic22—41no—
94Dic22—163no—
95C8×C11—23no—
96C8×C11C2×#4111yescharacteristic
97C8×C112−1+411yescharacteristic
98Q82—221no—
99#550—221no—
100C2×SD32—113no—
101#500—113no—
102#493—113no—
103#477—223no—
104#459—223no—
105C8×Q8C2×D1111yescharacteristic
106C4×Q16—113no—
107C4×D8—113no—
108#367—113no—
109C4⋊C16C2×D1113yes—
110#358—111no—
111#357—113no—
112#357—116no—
113C4×C16C2×D1113yes—
114C22×C11C22×D811yescharacteristic
115C2×D11—83no—
116C2×D11—83no—
117C2×D11—83no—
118C4×C11—23no—
119C4×C11C2×SD3216yes—
120C4×C11#54811yescharacteristic
121C4×C11#57711yescharacteristic
122Dic11—42no—
123Dic11—81no—
124Dic11—83no—
125C2×#41—441no—
126C2×Q16—111no—
127C2×D8—113no—
128C2×D8—223no—
129C4⋊Q8—223no—
130C4⋊Q8—443no—
131#127—223no—
132#121—443no—
133C4×Q8—223no—
134C4×Q8—441no—
135C4×Q8D4411yescharacteristic
136C4×D4—223no—
137SD32—226no—
138C2×C16C22×D1111yescharacteristic
139C2×C16C22×D1113yes—
140#107—113no—
141#107—111no—
142#107—223no—
143C4⋊C8D4413yes—
144#103—223no—
145#102—223no—
146C4×C8C22×D1113yes—
147C2×C11#335811yescharacteristic
148C2×C11C22×SD3211yescharacteristic
149C2×C11#341511yescharacteristic
150D11—163no—
151#41—884no—
152C2×Q8—221no—
153C2×Q8—443no—
154C2×Q8D8811yescharacteristic
155C2×D4—223no—
156C2×D4—443no—
157C2×D4—443no—
158C22×C4—443no—
159Q16—112no—
160Q16—221no—
161D8—223no—
162D8—223no—
163D8—883no—
164C2×C8C2×D4413yes—
165C2×C8C23×D1111yescharacteristic
166C4⋊C4—221no—
167C4⋊C4—223no—
168C4⋊C4—443no—
169C4⋊C4—443no—
170C4⋊C4D8813yes—
171C22⋊C4—443no—
172C42—443no—
173C42C2×D4413yes—
174C16—21no—
175C16—23no—
176C11#3392911yescharacteristic, complemented, Sylow
177C23—443no—
178Q8—222no—
179Q8—441no—
180Q8—1763no—
181Q8#6686414yescomplemented
182D4—443no—
183D4—443no—
184D4—886no—
185D4—1763no—
186C2×C4—441no—
187C2×C4—443no—
188C2×C4—441no—
189C2×C4—886no—
190C2×C4C2×D8813yes—
191C2×C4C2×D8813yes—
192C2×C4C22×D4411yescharacteristic
193C8—23no—
194C8#6704011yescharacteristic
195C8#41×D1111yescharacteristic
196C22—883no—
197C22—883no—
198C22—883no—
199C22C22×D8811yescharacteristic
200C4—23no—
201C4—442no—
202C4—881no—
203C4—883no—
204C4C2×#6686416yes—
205C4#1062310711yescharacteristic
206C4#1062328211yescharacteristic
207C2—1763no—
208C2#1308125211yescharacteristic
209C2C22×#6686411yescharacteristic
210C2#1308175711yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingQ8×C11×C16C2
socleC22×C11C22×D8
prime radical#13081591C2
hypercenterQ8×C16D11
hypocenterC11#33929
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ Q8×C16

Complements

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

NH ≅ G/Ntype
2. Q8×Dic44C2semidirect
3. #13070840C2semidirect
4. #13070764C2semidirect
5. #13070657C2semidirect
6. C4×#66864C2semidirect
7. Q8×C11×C16C2semidirect
66. Dic44#41semidirect
77. Q8×C16D11semidirect
80. Q8×C11SD32semidirect
176. C11#33929semidirect
181. Q8#66864semidirect

Maximal subgroups

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

subgroupindex
#130815912
Q8×Dic442
#130708402
#130707642
#130706572
C4×#668642
Q8×C11×C162
#3392911