Finite Group Databasebeta

← #14663087

Subgroups — #14663087

Order 2816.

364 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 115 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#13070237C212yesmaximal, complemented
2#13066567C212yesmaximal, complemented
3#13066554C212yesmaximal, complemented
4C11×#2932C211yesmaximal, characteristic
5C2×C11×#131C411yescharacteristic
6C2×C11×#131C2211yescharacteristic
7C11×#532C411yescharacteristic
8C11×#435—22no—
9C11×#435—22no—
10C11×#423C2211yescharacteristic
11C11×#408C411yescharacteristic
12C11×#408C2211yescharacteristic
13C2×C11×#97C411yescharacteristic
14C2×#66876—22no—
15#10622191—22no—
16#10622191C2214yes—
17C2×C11×#41C2×C411yescharacteristic
18C2×C11×#41C2×C411yescharacteristic
19C11×#131—42no—
20C11×#131—42no—
21C2×C11×M16—21no—
22C2×C11×M16C2×C411yescharacteristic
23C2×C11×M16D412yes—
24C2×C11×M16C2311yescharacteristic
25C22×C8×C11—21no—
26C22×C8×C11C2×C411yescharacteristic
27C22×C8×C11C2×C411yescharacteristic
28C22×C8×C11D412yes—
29C11×C4⋊Q8C811yescharacteristic
30C11×#127C811yescharacteristic
31C11×#124C811yescharacteristic
32C11×#124C811yescharacteristic
33C11×#121—22no—
34C4×D4×C11—22no—
35C2×C42×C11C2×C411yescharacteristic
36C11×C4⋊C8—22no—
37C11×C22⋊C8—22no—
38C11×C22⋊C8—22no—
39C11×#97—21no—
40C11×#97—21no—
41#66876—24no—
42#66876—42no—
43C2×C11⋊C16—42no—
44#11486—111nomaximal, Sylow
45C11×#41—41no—
46C11×#41—41no—
47C11×#41—41no—
48C11×#41—41no—
49C2×Q8×C11C2×C811yescharacteristic
50C2×Q8×C11C2×C811yescharacteristic
51C2×D4×C11—21no—
52C2×D4×C11—22no—
53C2×D4×C11C2×C811yescharacteristic
54C2×D4×C11C2×C811yescharacteristic
55C2×D4×C11M1612yes—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11C22⋊C412yes—
59C22×C4×C11C22×C411yescharacteristic
60C11×M16—42no—
61C11×M16—41no—
62C11×M16—41no—
63C11×M16—42no—
64C2×C8×C11—22no—
65C2×C8×C11—22no—
66C2×C8×C11—22no—
67C2×C8×C11—21no—
68C2×C8×C11—21no—
69C2×C8×C11—41no—
70C2×C8×C11—42no—
71C2×C8×C11C22⋊C411yescharacteristic
72C2×C8×C11C22⋊C411yescharacteristic
73C2×C8×C11C2×D412yes—
74C11×C4⋊C4—22no—
75C11×C22⋊C4—22no—
76C11×C22⋊C4—22no—
77C42×C11—21no—
78C42×C11C2×C811yescharacteristic
79C42×C11C2×C811yescharacteristic
80C11⋊C16—44no—
81#2932D1111yescharacteristic
82#2115—112no—
83#1327—112no—
84#1321—112no—
85C23×C11—21no—
86C23×C11C22⋊C812yes—
87C23×C11C2×M1611yescharacteristic
88Q8×C11—41no—
89Q8×C11—41no—
90D4×C11—41no—
91D4×C11—42no—
92D4×C11—41no—
93D4×C11—42no—
94D4×C11—82no—
95C2×C4×C11—21no—
96C2×C4×C11—22no—
97C2×C4×C11—21no—
98C2×C4×C11—22no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—41no—
103C2×C4×C11—41no—
104C2×C4×C11—81no—
105C2×C4×C11C22⋊C812yes—
106C2×C4×C11C2×C22⋊C411yescharacteristic
107C2×C4×C11C22×C811yescharacteristic
108C8×C11—22no—
109C8×C11—21no—
110C8×C11—41no—
111C8×C11—41no—
112C8×C11#9912yes—
113C2×#131Dic1111yescharacteristic
114C2×#131C2×D1111yescharacteristic
115#532Dic1111yescharacteristic
116C2×M32—222no—
117#435—22no—
118#435—22no—
119#423C2×D1111yescharacteristic
120#408Dic1111yescharacteristic
121#408C2×D1111yescharacteristic
122C2×#97Dic1111yescharacteristic
123#349—114no—
124#349—222no—
125C22×C11—21no—
126C22×C11—22no—
127C22×C11—41no—
128C22×C11—42no—
129C22×C11—42no—
130C22×C11—41no—
131C22×C11C2×C22⋊C811yescharacteristic
132C4×C11—22no—
133C4×C11—21no—
134C4×C11—41no—
135C4×C11—41no—
136C4×C11—41no—
137C4×C11C2×#9911yescharacteristic
138C4×C11#41311yescharacteristic
139C2×#41C2×Dic1111yescharacteristic
140C2×#41C2×Dic1111yescharacteristic
141#131—42no—
142#131—42no—
143C2×M16—21no—
144C2×M16C2×Dic1111yescharacteristic
145C2×M16C22⋊D1112yes—
146C2×M16C22×D1111yescharacteristic
147C22×C8—21no—
148C22×C8C2×Dic1111yescharacteristic
149C22×C8C2×Dic1111yescharacteristic
150C22×C8C22⋊D1112yes—
151C4⋊Q8C11⋊C811yescharacteristic
152#127C11⋊C811yescharacteristic
153#124C11⋊C811yescharacteristic
154#124C11⋊C811yescharacteristic
155#121—22no—
156C4×D4—22no—
157C2×C42C2×Dic1111yescharacteristic
158M32—224no—
159M32—442no—
160C2×C16—442no—
161C4⋊C8—22no—
162C22⋊C8—22no—
163C22⋊C8—22no—
164#97—21no—
165#97—21no—
166C2×C11—21no—
167C2×C11—41no—
168C2×C11—42no—
169C2×C11—81no—
170C2×C11#145911yescharacteristic
171#41—41no—
172#41—41no—
173#41—41no—
174#41—41no—
175C2×Q8C2×C11⋊C811yescharacteristic
176C2×Q8C2×C11⋊C811yescharacteristic
177C2×D4—21no—
178C2×D4—22no—
179C2×D4C2×C11⋊C811yescharacteristic
180C2×D4C2×C11⋊C811yescharacteristic
181C2×D4#431812yes—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4C22⋊Dic1112yes—
185C22×C4C22×Dic1111yescharacteristic
186M16—41no—
187M16—42no—
188M16—42no—
189M16—41no—
190C2×C8—22no—
191C2×C8—22no—
192C2×C8—22no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8—42no—
196C2×C8—41no—
197C2×C8C22⋊Dic1111yescharacteristic
198C2×C8C22⋊Dic1111yescharacteristic
199C2×C8C2×C22⋊D1112yes—
200C4⋊C4—22no—
201C22⋊C4—22no—
202C22⋊C4—22no—
203C42—21no—
204C42C2×C11⋊C811yescharacteristic
205C42C2×C11⋊C811yescharacteristic
206C16—444no—
207C11#1148611yescharacteristic, complemented, Sylow
208C23—21no—
209C23C22⋊(C11⋊C8)12yes—
210C23C2×#431811yescharacteristic
211Q8—41no—
212Q8—41no—
213D4—41no—
214D4—42no—
215D4—41no—
216D4—42no—
217D4—82no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—81no—
228C2×C4C22⋊(C11⋊C8)12yes—
229C2×C4C22×C11⋊C811yescharacteristic
230C2×C4C2×C22⋊Dic1111yescharacteristic
231C8—22no—
232C8—21no—
233C8—41no—
234C8—41no—
235C8#6689812yes—
236C22—21no—
237C22—22no—
238C22—41no—
239C22—42no—
240C22—42no—
241C22—41no—
242C22C2×C22⋊(C11⋊C8)11yescharacteristic
243C4—22no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—41no—
248C4C2×#6689811yescharacteristic
249C4#1062285011yescharacteristic
250C2—21no—
251C2—41no—
252C2—42no—
253C2—81no—
254C2#1306693411yescharacteristic
subgroupG/H
centerC4C2×#66898
commutatorC2×C4×C11C22×C8
FrattiniC2×M16C22×D11
FittingC11×#2932C2
socleC2×C11#1459
prime radicalC11×#532C4
cosocleC2×C11×M16C23
hypercenter#2932D11
hypocenterC11#11486
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C8 ◁ C2×#131 ◁ #2932

Complements

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

NH ≅ G/Ntype
1. #13070237C2semidirect
2. #13066567C2semidirect
3. #13066554C2semidirect
207. C11#11486semidirect

Maximal subgroups

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

subgroupindex
#130702372
#130665672
#130665542
C11×#29322
#1148611