Finite Group Databasebeta

← #14646766

Subgroups — #14646766

Order 2816.

320 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 103 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#13077550C211yesmaximal, characteristic
2#13067379C211yesmaximal, characteristic
3#13067253C212yesmaximal
4#13066526C212yesmaximal
5C11×#1568C211yesmaximal, characteristic
6#10623001C2211yescharacteristic
7C11×#432C2212yes—
8C2×C4×C8×C11C2211yescharacteristic
9#10622715C412yes—
10#10622714C412yes—
11#10622539C2212yes—
12#10622537C2211yescharacteristic
13#10622292—21no—
14#10622292—21no—
15C8×Dic22—21no—
16C8×Dic22—21no—
17C11×#335—21no—
18C11×#334—21no—
19#10622103—24no—
20#10622096—21no—
21#10622095—21no—
22C22×C8×C11C2×C411yescharacteristic
23C22×C8×C11C2×C411yescharacteristic
24C2×C42×C11C2311yescharacteristic
25#66979C2×C412yes—
26#66977—21no—
27#66977—21no—
28C2×#4318C2×C412yes—
29#66923D412yes—
30#66922Q811yescharacteristic
31#66922Q811yescharacteristic
32C4×Dic22—21no—
33C4×Dic22—21no—
34C11×C4⋊C8—22no—
35C11×C22⋊C8—22no—
36C11×#97—22no—
37C4×C8×C11D411yescharacteristic
38C4×C8×C11D411yescharacteristic
39C4×C8×C11D411yescharacteristic
40C4×C8×C11D411yescharacteristic
41C22⋊(C11⋊C8)—22no—
42#66879—22no—
43Dic11⋊C8—22no—
44Dic11⋊C8—22no—
45C8×Dic11—22no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—22no—
49#66867—22no—
50#8631—111nomaximal, Sylow
51C22×C4×C11C22×C411yescharacteristic
52C22×C4×C11#4111yescharacteristic
53C22×C4×C11#4111yescharacteristic
54C2×Dic22—21no—
55C2×Dic22—21no—
56C2×C8×C11—22no—
57C2×C8×C11—41no—
58C2×C8×C11—42no—
59C2×C8×C11C22⋊C411yescharacteristic
60C2×C8×C11C22⋊C411yescharacteristic
61C2×C8×C11C22⋊C411yescharacteristic
62C2×C8×C11C22⋊C411yescharacteristic
63C42×C11C2×D411yescharacteristic
64C42×C11C2×D411yescharacteristic
65C42×C11C2×D411yescharacteristic
66C42×C11C2×Q811yescharacteristic
67C22⋊Dic11—22no—
68C4⋊Dic11—21no—
69C4⋊Dic11—21no—
70C4⋊Dic11C4⋊C412yes—
71C4⋊Dic11C4⋊C412yes—
72Dic11⋊C4—22no—
73Dic11⋊C4—22no—
74C4×Dic11—22no—
75#4318—42no—
76C2×C11⋊C8—22no—
77C2×C11⋊C8—42no—
78#2960—111no—
79#1568—111no—
80#1568D1111yescharacteristic
81#1537—112no—
82#1307—112no—
83C23×C11#11711yescharacteristic
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11C2×C22⋊C411yescharacteristic
89C2×C4×C11C2×C4⋊C411yescharacteristic
90C2×C4×C11#12111yescharacteristic
91C2×C4×C11#12111yescharacteristic
92C2×C4×C11C22⋊Q811yescharacteristic
93C2×C4×C11C22⋊Q811yescharacteristic
94C2×Dic11—22no—
95C2×Dic11—22no—
96Dic22—42no—
97Dic22—42no—
98C8×C11—21no—
99C8×C11—21no—
100C8×C11—21no—
101C8×C11—82no—
102C8×C11#10112yes—
103C11⋊C8—42no—
104C11⋊C8—82no—
105#533—111no—
106#446—221no—
107#446—221no—
108C8×Q8—221no—
109C8×Q8—221no—
110#432—112no—
111#432C2×D1112yes—
112#424—112no—
113#423—111no—
114#405—112no—
115C2×C4×C8C2×D1111yescharacteristic
116#335—21no—
117#335—221no—
118#334—21no—
119#334—221no—
120#330—224no—
121C22×C11—21no—
122C22×C11—21no—
123C22×C11—21no—
124C22×C11#38011yescharacteristic
125C4×C11—21no—
126C4×C11—21no—
127C4×C11—21no—
128C4×C11—21no—
129C4×C11—21no—
130C4×C11C2×#10111yescharacteristic
131C4×C11#41311yescharacteristic
132Dic11—42no—
133Dic11—42no—
134C2×M16—112no—
135C22×C8C4×D1111yescharacteristic
136C22×C8C4×D1111yescharacteristic
137C4⋊Q8—111no—
138C4⋊Q8—111no—
139#125—112no—
140C22⋊Q8—221no—
141C22⋊Q8—221no—
142C4×Q8—221no—
143C4×Q8—221no—
144#117—112no—
145C2×C42C22×D1111yescharacteristic
146C4⋊C8—22no—
147C4⋊C8—222no—
148C4⋊C8—222no—
149C4⋊C8—221no—
150C4⋊C8—222no—
151C4⋊C8—221no—
152C22⋊C8—22no—
153C22⋊C8—222no—
154#97—22no—
155#97—222no—
156#97—222no—
157C4×C8—222no—
158C4×C8D4411yescharacteristic
159C4×C8D4411yescharacteristic
160C4×C8C22⋊D1111yescharacteristic
161C4×C8C22⋊D1111yescharacteristic
162C2×C11—41no—
163C2×C11#180111yescharacteristic
164C2×C11#181411yescharacteristic
165C2×C11#181411yescharacteristic
166C2×Q8—221no—
167C2×Q8—221no—
168C22×C4C2×C4×D1111yescharacteristic
169C22×C4#434111yescharacteristic
170C22×C4#434311yescharacteristic
171M16—442no—
172C2×C8—22no—
173C2×C8—41no—
174C2×C8—42no—
175C2×C8—222no—
176C2×C8—442no—
177C2×C8(C2×D11)⋊C411yescharacteristic
178C2×C8(C2×D11)⋊C411yescharacteristic
179C2×C8(C2×D11)⋊C411yescharacteristic
180C2×C8(C2×D11)⋊C411yescharacteristic
181C4⋊C4—112no—
182C4⋊C4—112no—
183C4⋊C4—222no—
184C4⋊C4—221no—
185C4⋊C4—222no—
186C4⋊C4—221no—
187C22⋊C4—222no—
188C42—222no—
189C42C2×D4411yescharacteristic
190C42D4×D1111yescharacteristic
191C42Q8×D1111yescharacteristic
192C42C2×C22⋊D1111yescharacteristic
193C11#863111yescharacteristic, complemented, Sylow
194C23#6694511yescharacteristic
195Q8—442no—
196Q8—442no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4C4⋊C4×D1111yescharacteristic
204C2×C4#6694811yescharacteristic
205C2×C4#6695011yescharacteristic
206C2×C4C2×(C2×D11)⋊C411yescharacteristic
207C2×C4#6699111yescharacteristic
208C2×C4#6699911yescharacteristic
209C8—21no—
210C8—21no—
211C8—21no—
212C8—82no—
213C8—442no—
214C8—882no—
215C8#6688812yes—
216C22—21no—
217C22—21no—
218C22—21no—
219C22#1062260011yescharacteristic
220C4—21no—
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—442no—
226C4—442no—
227C4#1062274511yescharacteristic
228C4C2×#6688811yescharacteristic
229C2—41no—
230C2#1306860911yescharacteristic
231C2#1306866711yescharacteristic
232C2#1306867111yescharacteristic
subgroupG/H
centerC22#10622600
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1568C2
socleC22×C11#380
prime radicalC23×C11#117
cosocleC2×C42×C11C23
hypercenter#1568D11
hypocenterC11#8631
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
193. C11#8631semidirect

Maximal subgroups

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

subgroupindex
#130775502
#130673792
#130672532
#130665262
C11×#15682
#863111