Finite Group Databasebeta

← #14673432

Subgroups — #14673432

Order 2816.

318 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079140C211yesmaximal, characteristic
2#13070389C212yesmaximal
3#13069369C211yesmaximal, characteristic
4#13066718C212yesmaximal
5C11×#1375C211yesmaximal, characteristic
6#10623001—21no—
7C2×C11×M32C2212yes—
8C2×C11×#97C2211yescharacteristic
9C2×#66883C2211yescharacteristic
10#10622719—21no—
11#10622719C2212yes—
12#10622719C2211yescharacteristic
13#10622715—21no—
14#10622315—24no—
15#10622161—21no—
16#10622151—24no—
17C22×C8×C11D411yescharacteristic
18C22×C8×C11C2311yescharacteristic
19C2×C42×C11D411yescharacteristic
20#66979—22no—
21#66979—21no—
22#66977—42no—
23C2×#4318—21no—
24#66923—22no—
25#66922—22no—
26C4×Dic22—42no—
27C11×M32—22no—
28C11×M32—22no—
29C2×C11×C16Q814yescomplemented
30C11×#97—22no—
31#66883—22no—
32#66882—22no—
33#66882—22no—
34#66882—21no—
35#66881—22no—
36#66881D414yes—
37#66881Q812yescomplemented
38Dic11⋊C8—42no—
39#13459—111nomaximal, Sylow
40C22×C4×C11—21no—
41C22×C4×C11C2×D411yescharacteristic
42C2×Dic22—42no—
43C2×C8×C11—21no—
44C2×C8×C11—21no—
45C2×C8×C11SD1612yes—
46C2×C8×C11C2×D412yes—
47C2×C8×C11C2×Q811yescharacteristic
48C2×C8×C11C2×Q812yes—
49C2×C8×C11#4111yescharacteristic
50C42×C11—21no—
51C42×C11SD1612yes—
52C22⋊Dic11—42no—
53C22⋊Dic11—41no—
54C4⋊Dic11—24no—
55C4⋊Dic11—22no—
56C4⋊Dic11—42no—
57Dic11⋊C4—44no—
58C4×Dic11—41no—
59C4×Dic11—42no—
60#4318—41no—
61#4318—41no—
62C2×C11⋊C8—41no—
63C11×C16—24no—
64#3162—111no—
65#2155—112no—
66#1946—111no—
67#1384—112no—
68#1375D1111yescharacteristic
69C23×C11AGL(1,ℤ/8)11yescharacteristic
70C2×C4×C11—22no—
71C2×C4×C11—81no—
72C2×C4×C11#12011yescharacteristic
73C2×C4×C11C22⋊Q811yescharacteristic
74C2×C4×C11C4⋊Q811yescharacteristic
75C2×C4×C11C2×SD1611yescharacteristic
76C2×C4×C11C2×SD1611yescharacteristic
77C2×C4×C11#13711yescharacteristic
78C2×Dic11—44no—
79C2×Dic11—42no—
80Dic22—84no—
81C8×C11—22no—
82C8×C11C22⋊Q812yes—
83C8×C11C4⋊Q812yes—
84C11⋊C8—81no—
85#533—221no—
86C2×M32C2×D1112yes—
87#501—224no—
88C2×#108—111no—
89#427—112no—
90#427—111no—
91#427—221no—
92#424—221no—
93C2×#97C2×D1111yescharacteristic
94#365—224no—
95#339—221no—
96C22×C11—41no—
97C22×C11#45011yescharacteristic
98C22×C11#47611yescharacteristic
99C22×C11#50111yescharacteristic
100C4×C11—42no—
101C4×C11#39511yescharacteristic
102C4×C11#44811yescharacteristic
103C4×C11#47511yescharacteristic
104C4×C11#49811yescharacteristic
105Dic11—84no—
106Dic11—82no—
107C2×M16—221no—
108C22×C8D4411yescharacteristic
109C22×C8C22×D1111yescharacteristic
110C4⋊Q8—222no—
111#125—222no—
112C22⋊Q8—442no—
113C4×Q8—442no—
114#117—222no—
115#117—221no—
116C2×C42D4411yescharacteristic
117M32—22no—
118M32—22no—
119C2×C16Dic2214yescomplemented
120#108—222no—
121#107—222no—
122#107—222no—
123#107—221no—
124#106—114no—
125#106—112no—
126#106—222no—
127C4⋊C8—442no—
128#97—22no—
129C2×C11—21no—
130C2×C11—21no—
131C2×C11—21no—
132C2×C11#205811yescharacteristic
133C2×Q8—442no—
134C22×C4—21no—
135C22×C4C2×D4411yescharacteristic
136M16—441no—
137M16—441no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—441no—
141C2×C8#431412yes—
142C2×C8C2×Dic2212yes—
143C2×C8D4×D1112yes—
144C2×C8#434111yescharacteristic
145C2×C8Q8×D1111yescharacteristic
146C4⋊C4—224no—
147C4⋊C4—222no—
148C4⋊C4—444no—
149C4⋊C4—442no—
150C22⋊C4—442no—
151C22⋊C4—441no—
152C42—21no—
153C42—441no—
154C42—442no—
155C42#431412yes—
156C16—24no—
157C11#1345911yescharacteristic, complemented, Sylow
158C23#6696111yescharacteristic
159Q8—884no—
160C2×C4—22no—
161C2×C4—81no—
162C2×C4—444no—
163C2×C4—442no—
164C2×C4#6692211yescharacteristic
165C2×C4#6693511yescharacteristic
166C2×C4#6695011yescharacteristic
167C2×C4C2×#431411yescharacteristic
168C2×C4C2×#431411yescharacteristic
169C2×C4#6696211yescharacteristic
170C8—22no—
171C8—881no—
172C8#6693112yes—
173C8#6694112yes—
174C22—41no—
175C22#1062231511yescharacteristic
176C22#1062234411yescharacteristic
177C22#1062245511yescharacteristic
178C4—42no—
179C4—884no—
180C4—882no—
181C4#1062226911yescharacteristic
182C4#1062229311yescharacteristic
183C4#1062235111yescharacteristic
184C4#1062246411yescharacteristic
185C2—21no—
186C2—21no—
187C2—21no—
188C2#1306995011yescharacteristic
subgroupG/H
centerC4#10622293
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1375C2
socleC2×C11#2058
prime radicalC23×C11AGL(1,ℤ/8)
hypercenter#1375D11
hypocenterC11#13459
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#97 ◁ #1375

Complements

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

NH ≅ G/Ntype
29. C2×C11×C16Q8semidirect
37. #66881Q8semidirect
119. C2×C16Dic22semidirect
157. C11#13459semidirect

Maximal subgroups

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

subgroupindex
#130791402
#130703892
#130693692
#130667182
C11×#13752
#1345911