Finite Group Databasebeta

← #14668203

Subgroups — #14668203

Order 2816.

218 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 63 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#13070843C211yesmaximal, characteristic, complemented
2#13070435C211yesmaximal, characteristic
3#13068016C211yesmaximal, characteristic
4#13067978C211yesmaximal, characteristic
5#13066687C211yesmaximal, characteristic, complemented
6#13066673C211yesmaximal, characteristic, complemented
7C11×#1362C211yesmaximal, characteristic, complemented
8C11×#494C2211yescharacteristic
9#10622700—21no—
10C2×C16×D11—21no—
11#10622455—21no—
12C8×D44C2211yescharacteristic
13#10622295C2211yescharacteristic
14C11×C4⋊C16C2211yescharacteristic
15C11×#335C2211yescharacteristic
16#10622202—21no—
17#10622202—21no—
18#10622185—21no—
19(C2×D11)⋊C16—21no—
20#10622119—21no—
21C4×C11⋊C16C2211yescharacteristic
22#10622096C2211yescharacteristic
23C2×C11×Q16—21no—
24C2×C11×Q16—21no—
25C11×C4⋊Q8—21no—
26C2×C8×D11—21no—
27C4×D44D411yescharacteristic
28#66922—21no—
29C2×C11×C16—21no—
30C11×C4⋊C8—21no—
31C4×C8×C11C2311yescharacteristic
32#66885—41no—
33(C2×D11)⋊C8—21no—
34#66882—21no—
35#66882—21no—
36#66881—41no—
37C2×C11⋊C16D411yescharacteristic
38C2×C11⋊C16D411yescharacteristic
39#66873—41no—
40#66871—41no—
41C4⋊(C11⋊C8)—21no—
42C4⋊(C11⋊C8)D411yescharacteristic
43C16×D11—42no—
44#12469—111nomaximal, Sylow
45C2×Q8×C11—41no—
46C2×D44D811yescharacteristic
47C2×C4×D11—21no—
48C2×Dic22—41no—
49C11×Q16—41no—
50C11×Q16—41no—
51C11×Q16—81no—
52C2×C8×C11—41no—
53C2×C8×C11C2×D411yescharacteristic
54C2×C8×C11#4111yescharacteristic
55C11×C4⋊C4—41no—
56C11×C4⋊C4—41no—
57C42×C11C2×D411yescharacteristic
58(C2×D11)⋊C4—21no—
59C4⋊Dic11—41no—
60C4⋊Dic11—41no—
61C4⋊Dic11D811yescharacteristic
62C2×C11⋊C8—21no—
63C2×C11⋊C8—41no—
64C8×D11—41no—
65C8×D11—41no—
66C11×C16—41no—
67C11⋊C16—21no—
68C11⋊C16—21no—
69#2241—111no—
70D4×C16—111no—
71#1675—111no—
72#1669—111no—
73#1371—111no—
74#1365—111no—
75#1362D1111yescharacteristic, complemented
76C22×D11—21no—
77Q8×C11—81no—
78Q8×C11—81no—
79C2×C4×C11—81no—
80C2×C4×C11#12111yescharacteristic
81C2×C4×C11C2×D811yescharacteristic
82C2×C4×C11#13511yescharacteristic
83C2×Dic11—21no—
84C2×Dic11—81no—
85D44—21no—
86D44Q3212yes—
87C4×D11—41no—
88C4×D11—41no—
89Dic22—161no—
90C8×C11—21no—
91C8×C11—81no—
92C8×C11#13511yescharacteristic
93C8×C11AGL(1,ℤ/8)11yescharacteristic
94C11⋊C8—41no—
95C11⋊C8—81no—
96C22×C16—221no—
97#500—111no—
98#494C2×D1111yescharacteristic
99#476—221no—
100#474—221no—
101C8×D4—111no—
102C4⋊C16C2×D1111yescharacteristic
103#358—221no—
104#358—221no—
105C22⋊C16—221no—
106C4×C16—111no—
107#335—111no—
108#335C2×D1111yescharacteristic
109#333—221no—
110#332—221no—
111C22×C11#46611yescharacteristic
112C2×D11—22no—
113C2×D11—41no—
114C2×D11—41no—
115C4×C11—21no—
116C4×C11—161no—
117C4×C11#46311yescharacteristic
118C4×C11#47111yescharacteristic
119C4×C11C2×Q3211yescharacteristic
120C4×C11#50811yescharacteristic
121Dic11—41no—
122Dic11—161no—
123C2×Q16—21no—
124C2×Q16—21no—
125C22×C8—221no—
126C4⋊Q8—21no—
127C4⋊Q8—221no—
128C4×D4—111no—
129C2×C16—21no—
130C2×C16—111no—
131C2×C16—111no—
132C2×C16—442no—
133#107—221no—
134#107—221no—
135#107—441no—
136#106—441no—
137C4⋊C8—21no—
138C4⋊C8—111no—
139C4⋊C8—221no—
140#102—441no—
141#102—441no—
142C22⋊C8—221no—
143C4×C8C22×D1111yescharacteristic
144C2×C11#168111yescharacteristic
145C2×C11#221611yescharacteristic
146C2×C11#222311yescharacteristic
147D11—42no—
148C2×Q8—41no—
149C2×Q8—441no—
150C2×D4—111no—
151C22×C4—221no—
152Q16—41no—
153Q16—41no—
154Q16—81no—
155C2×C8—41no—
156C2×C8—221no—
157C2×C8—441no—
158C2×C8—441no—
159C2×C8—441no—
160C2×C8#433911yescharacteristic
161C2×C8D4×D1111yescharacteristic
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—111no—
165C4⋊C4—441no—
166C4⋊C4—441no—
167C22⋊C4—221no—
168C42D4×D1111yescharacteristic
169C16—41no—
170C16—221no—
171C16—221no—
172C11#1246911yescharacteristic, complemented, Sylow
173C23—221no—
174Q8—81no—
175Q8—81no—
176Q8—1761no—
177D4—112no—
178D4—221no—
179C2×C4—81no—
180C2×C4—221no—
181C2×C4—441no—
182C2×C4—441no—
183C2×C4—881no—
184C2×C4#6693711yescharacteristic
185C2×C4D8×D1111yescharacteristic
186C2×C4#6696911yescharacteristic
187C8—21no—
188C8—81no—
189C8—441no—
190C8—881no—
191C8#6696411yescharacteristic
192C8#6696911yescharacteristic
193C22—222no—
194C22—441no—
195C22—441no—
196C22#1062238811yescharacteristic
197C4—21no—
198C4—161no—
199C4—441no—
200C4—1761no—
201C4#1062236111yescharacteristic
202C4#1062240011yescharacteristic
203C4#1062252911yescharacteristic
204C4D11×Q3211yescharacteristic
205C2—442no—
206C2#1306805211yescharacteristic
207C2#1307070611yescharacteristic
208C2#1307074911yescharacteristic
subgroupG/H
centerC22#10622388
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1362C2
socleC22×C11#466
prime radicalC2×D44D8
hypercenter#1362D11
hypocenterC11#12469
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
1. #13070843C2semidirect
5. #13066687C2semidirect
6. #13066673C2semidirect
7. C11×#1362C2semidirect
75. #1362D11semidirect
172. C11#12469semidirect

Maximal subgroups

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

subgroupindex
#130708432
#130704352
#130680162
#130679782
#130666872
#130666732
C11×#13622
#1246911