Finite Group Databasebeta

← #14663282

Subgroups — #14663282

Order 2816.

262 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 71 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#13077553C211yesmaximal, characteristic
2#13070429C212yesmaximal
3#13066568C212yesmaximal
4#13066567C211yesmaximal, characteristic
5C11×#1327C211yesmaximal, characteristic
6#10623001C411yescharacteristic
7C11×#423C2211yescharacteristic
8#10622735C411yescharacteristic
9#10622735C2211yescharacteristic
10#10622732C411yescharacteristic
11#10622732C2211yescharacteristic
12C2×#66867C411yescharacteristic
13#10622441—22no—
14#10622441—22no—
15C11×#349C2212yes—
16#10622191C2212yes—
17#10622150—22no—
18#10622149—22no—
19C2×C11×M16C2×C411yescharacteristic
20C2×C11×M16C2311yescharacteristic
21C2×C42×C11C2×C411yescharacteristic
22#66979C2×C411yescharacteristic
23#66979C2×C411yescharacteristic
24#66977—22no—
25C22×C11⋊C8C2×C411yescharacteristic
26C22×C11⋊C8C2×C411yescharacteristic
27#66923—21no—
28#66922—21no—
29C4×Dic22—22no—
30C11×M32—22no—
31C11×C4⋊C8—22no—
32#66879—21no—
33#66879D412yes—
34Dic11⋊C8—22no—
35Dic11⋊C8—22no—
36C8×Dic11—21no—
37C8×Dic11D412yes—
38#66876—22no—
39#66867—21no—
40#66867—21no—
41#11540—111nomaximal, Sylow
42C22×C4×C11—21no—
43C22×C4×C11C22×C411yescharacteristic
44C2×Dic22—22no—
45C11×M16—41no—
46C11×M16—41no—
47C2×C8×C11—21no—
48C2×C8×C11C2×D412yes—
49C42×C11—21no—
50C42×C11M1611yescharacteristic
51C42×C11M1611yescharacteristic
52C22⋊Dic11—21no—
53C22⋊Dic11M1612yes—
54C4⋊Dic11—22no—
55C4⋊Dic11—21no—
56C4⋊Dic11—21no—
57Dic11⋊C4—24no—
58C4×Dic11—21no—
59C4×Dic11C22⋊C412yes—
60C2×C11⋊C8—22no—
61C2×C11⋊C8—21no—
62C2×C11⋊C8—41no—
63C2×C11⋊C8C22⋊C411yescharacteristic
64C2×C11⋊C8C22⋊C411yescharacteristic
65C11×C16—42no—
66C11⋊C16—42no—
67#2961—111no—
68#2166—112no—
69#1328—112no—
70#1327—111no—
71#1327D1111yescharacteristic
72C23×C11C2×M1611yescharacteristic
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—81no—
78C2×C4×C11C2×C22⋊C411yescharacteristic
79C2×C4×C11C2×M1611yescharacteristic
80C2×Dic11—22no—
81C2×Dic11—22no—
82Dic22—82no—
83C8×C11—22no—
84C8×C11—41no—
85C11⋊C8—21no—
86C11⋊C8—41no—
87C11⋊C8#10112yes—
88#533—111no—
89#446—222no—
90#446—222no—
91#424—111no—
92#424—111no—
93#423C2×D1111yescharacteristic
94#405—111no—
95#405—111no—
96C2×#97—111no—
97#364—222no—
98#349—112no—
99#349C2×D1112yes—
100#347—222no—
101C22×C11—21no—
102C22×C11—41no—
103C22×C11#40711yescharacteristic
104C4×C11—21no—
105C4×C11—41no—
106C4×C11—41no—
107C4×C11#41011yescharacteristic
108C4×C11C2×#10111yescharacteristic
109Dic11—42no—
110Dic11—42no—
111C2×M16C4×D1111yescharacteristic
112C2×M16C22×D1111yescharacteristic
113C22×C8—111no—
114C22×C8—111no—
115C4⋊Q8—221no—
116#125—221no—
117C22⋊Q8—222no—
118C4×Q8—222no—
119#117—111no—
120#117—111no—
121C2×C42C4×D1111yescharacteristic
122M32—22no—
123M32—222no—
124C4⋊C8—22no—
125C4⋊C8—222no—
126C4⋊C8—222no—
127#97—112no—
128#97—221no—
129#97—221no—
130#97—221no—
131C4×C8—112no—
132C4×C8—221no—
133C2×C11—21no—
134C2×C11—41no—
135C2×C11#146711yescharacteristic
136C2×Q8—222no—
137C22×C4—21no—
138C22×C4C2×C4×D1111yescharacteristic
139M16—41no—
140M16—41no—
141C2×C8—21no—
142C2×C8—111no—
143C2×C8—111no—
144C2×C8—222no—
145C2×C8—221no—
146C2×C8—441no—
147C2×C8D4×D1112yes—
148C4⋊C4—224no—
149C4⋊C4—222no—
150C4⋊C4—221no—
151C4⋊C4—221no—
152C22⋊C4—112no—
153C22⋊C4—221no—
154C42—21no—
155C42—112no—
156C42—221no—
157C42#431311yescharacteristic
158C42#431311yescharacteristic
159C16—42no—
160C16—442no—
161C11#1154011yescharacteristic, complemented, Sylow
162C23M16×D1111yescharacteristic
163Q8—882no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—81no—
169C2×C4—222no—
170C2×C4—222no—
171C2×C4C22⋊C4×D1111yescharacteristic
172C2×C4C2×#431311yescharacteristic
173C8—22no—
174C8—41no—
175C8—112no—
176C8—221no—
177C8—441no—
178C22—21no—
179C22—41no—
180C22#1062233911yescharacteristic
181C4—21no—
182C4—41no—
183C4—41no—
184C4—442no—
185C4—442no—
186C4#1062235311yescharacteristic
187C4D11×#10111yescharacteristic
188C2—21no—
189C2—41no—
190C2#1306695811yescharacteristic
subgroupG/H
centerC4#10622353
commutatorC22×C4×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#1327C2
socleC2×C11#1467
prime radicalC23×C11C2×M16
cosocleC2×C11×M16C23
hypercenter#1327D11
hypocenterC11#11540
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
161. C11#11540semidirect

Maximal subgroups

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

subgroupindex
#130775532
#130704292
#130665682
#130665672
C11×#13272
#1154011