Finite Group Databasebeta

← #14673431

Subgroups — #14673431

Order 2816.

318 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 99 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#13070390C212yesmaximal
3#13066717C212yesmaximal
4#13066696C211yesmaximal, characteristic
5C11×#1946C211yesmaximal, characteristic
6#10623001—21no—
7C2×C11×#108C2211yescharacteristic
8C11×#427C2211yescharacteristic
9C11×#424—21no—
10C2×C11×#97C2211yescharacteristic
11#10622719—21no—
12#10622719C2212yes—
13C2×#66876C2212yes—
14#10622315—24no—
15C11×#339—21no—
16#10622132—24no—
17C2×C11×M16—21no—
18C22×C8×C11D411yescharacteristic
19C22×C8×C11C2311yescharacteristic
20C11×#117—21no—
21C2×C42×C11D411yescharacteristic
22#66979—22no—
23#66977—42no—
24#66923—22no—
25#66922—22no—
26C4×Dic22—42no—
27C11×#108—22no—
28C11×#107—21no—
29C11×#106Q812yescomplemented
30C11×C4⋊C8—42no—
31C11×#97—22no—
32#66882—22no—
33#66882—22no—
34#66881—22no—
35#66881D414yes—
36#66876—22no—
37#66876—22no—
38C2×C11⋊C16Q814yescomplemented
39#13459—111nomaximal, Sylow
40C22×C4×C11—21no—
41C22×C4×C11C2×D411yescharacteristic
42C2×Dic22—42no—
43C11×M16—41no—
44C11×M16—41no—
45C2×C8×C11—21no—
46C2×C8×C11—21no—
47C2×C8×C11—41no—
48C2×C8×C11SD1612yes—
49C2×C8×C11C2×D412yes—
50C2×C8×C11C2×Q811yescharacteristic
51C2×C8×C11C2×Q812yes—
52C2×C8×C11#4111yescharacteristic
53C11×C4⋊C4—22no—
54C11×C22⋊C4—41no—
55C42×C11—21no—
56C42×C11—41no—
57C42×C11SD1612yes—
58C22⋊Dic11—42no—
59C4⋊Dic11—24no—
60C4⋊Dic11—42no—
61Dic11⋊C4—44no—
62C4×Dic11—42no—
63C11⋊C16—24no—
64#3162—111no—
65#2155—112no—
66#1946D1111yescharacteristic
67#1384—112no—
68#1375—111no—
69C23×C11AGL(1,ℤ/8)11yescharacteristic
70C2×C4×C11—22no—
71C2×C4×C11—42no—
72C2×C4×C11—81no—
73C2×C4×C11#12011yescharacteristic
74C2×C4×C11C22⋊Q811yescharacteristic
75C2×C4×C11C4⋊Q811yescharacteristic
76C2×C4×C11C2×SD1611yescharacteristic
77C2×C4×C11C2×SD1611yescharacteristic
78C2×C4×C11#13711yescharacteristic
79C2×Dic11—44no—
80Dic22—84no—
81C8×C11—22no—
82C8×C11—81no—
83C8×C11C22⋊Q812yes—
84C8×C11C4⋊Q812yes—
85#533—221no—
86C2×M32—112no—
87#501—224no—
88C2×#108C2×D1111yescharacteristic
89#427—112no—
90#427—221no—
91#427C2×D1111yescharacteristic
92#424—21no—
93C2×#97C2×D1111yescharacteristic
94#365—224no—
95#339—21no—
96C22×C11—41no—
97C22×C11#45011yescharacteristic
98C22×C11#47611yescharacteristic
99C22×C11#50111yescharacteristic
100C4×C11—42no—
101C4×C11—82no—
102C4×C11#39511yescharacteristic
103C4×C11#44811yescharacteristic
104C4×C11#47511yescharacteristic
105C4×C11#49811yescharacteristic
106Dic11—84no—
107C2×M16—21no—
108C22×C8C22⋊D1111yescharacteristic
109C22×C8C22×D1111yescharacteristic
110C4⋊Q8—222no—
111#125—222no—
112C22⋊Q8—442no—
113C4×Q8—442no—
114#117—21no—
115#117—222no—
116C2×C42C22⋊D1111yescharacteristic
117M32—222no—
118M32—222no—
119C2×C16—114no—
120#108—22no—
121#107—21no—
122#107—222no—
123#107—222no—
124#106—114no—
125#106—222no—
126#106Dic2212yescomplemented
127C4⋊C8—42no—
128#97—22no—
129C2×C11—21no—
130C2×C11—21no—
131C2×C11—21no—
132C2×C11#205811yescharacteristic
133C2×Q8—442no—
134C22×C4—21no—
135C22×C4C2×C22⋊D1111yescharacteristic
136M16—41no—
137M16—41no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—41no—
141C2×C8#432412yes—
142C2×C8C2×Dic2211yescharacteristic
143C2×C8#433911yescharacteristic
144C2×C8D4×D1112yes—
145C2×C8Q8×D1112yes—
146C4⋊C4—22no—
147C4⋊C4—224no—
148C4⋊C4—444no—
149C4⋊C4—442no—
150C22⋊C4—41no—
151C22⋊C4—442no—
152C42—21no—
153C42—41no—
154C42—442no—
155C42#432512yes—
156C16—224no—
157C11#1345911yescharacteristic, complemented, Sylow
158C23#6700211yescharacteristic
159Q8—884no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—81no—
163C2×C4—444no—
164C2×C4#6697711yescharacteristic
165C2×C4C2×#432411yescharacteristic
166C2×C4#6699011yescharacteristic
167C2×C4C2×#432511yescharacteristic
168C2×C4#6699711yescharacteristic
169C2×C4#6700411yescharacteristic
170C8—22no—
171C8—81no—
172C8#6694112yes—
173C8#6694912yes—
174C22—41no—
175C22#1062262111yescharacteristic
176C22#1062265911yescharacteristic
177C22#1062267811yescharacteristic
178C4—42no—
179C4—82no—
180C4—884no—
181C4#1062259211yescharacteristic
182C4#1062263311yescharacteristic
183C4#1062265311yescharacteristic
184C4#1062269211yescharacteristic
185C2—21no—
186C2—21no—
187C2—21no—
188C2#1306994911yescharacteristic
subgroupG/H
centerC4#10622692
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1946C2
socleC2×C11#2058
prime radicalC23×C11AGL(1,ℤ/8)
hypercenter#1946D11
hypocenterC11#13459
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#97 ◁ #1946

Complements

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

NH ≅ G/Ntype
29. C11×#106Q8semidirect
38. C2×C11⋊C16Q8semidirect
126. #106Dic22semidirect
157. C11#13459semidirect

Maximal subgroups

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

subgroupindex
#130791402
#130703902
#130667172
#130666962
C11×#19462
#1345911