Finite Group Databasebeta

← #14646786

Subgroups — #14646786

Order 2816.

320 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 119 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#13067379C211yesmaximal, characteristic
2#13067379C211yesmaximal, characteristic
3#13067254C212yesmaximal
4#13066527C212yesmaximal
5C11×#2960C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C11×#446—21no—
8C11×#446—21no—
9C8×Q8×C11—21no—
10C8×Q8×C11—21no—
11C11×#424C412yes—
12C11×#423C2211yescharacteristic
13C11×#405C412yes—
14C2×C4×C8×C11C2211yescharacteristic
15#10622539C2212yes—
16#10622539C2212yes—
17#10622181—24no—
18#10622096—21no—
19#10622096—21no—
20#10622095—21no—
21#10622095—21no—
22C2×C11×M16C2×C412yes—
23C22×C8×C11C2×C411yescharacteristic
24C22×C8×C11C2×C411yescharacteristic
25C11×C4⋊Q8Q811yescharacteristic
26C11×C4⋊Q8Q811yescharacteristic
27C11×#125D412yes—
28C11×C22⋊Q8—21no—
29C11×C22⋊Q8—21no—
30C4×Q8×C11—21no—
31C4×Q8×C11—21no—
32C11×#117C2×C412yes—
33C2×C42×C11C2311yescharacteristic
34C11×C4⋊C8—22no—
35C11×C4⋊C8—22no—
36C11×C4⋊C8—21no—
37C11×C4⋊C8—21no—
38C11×#97—22no—
39C4×C8×C11—22no—
40C4×C8×C11D411yescharacteristic
41C4×C8×C11D411yescharacteristic
42C4×C8×C11D411yescharacteristic
43C4×C8×C11D411yescharacteristic
44C22⋊(C11⋊C8)—22no—
45C22⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)—22no—
48#66867—22no—
49#66867—22no—
50#8635—111nomaximal, Sylow
51C2×Q8×C11—21no—
52C2×Q8×C11—21no—
53C22×C4×C11C22×C411yescharacteristic
54C22×C4×C11#4111yescharacteristic
55C22×C4×C11#4111yescharacteristic
56C11×M16—42no—
57C2×C8×C11—22no—
58C2×C8×C11—22no—
59C2×C8×C11—41no—
60C2×C8×C11C22⋊C411yescharacteristic
61C2×C8×C11C22⋊C411yescharacteristic
62C2×C8×C11C22⋊C411yescharacteristic
63C2×C8×C11C22⋊C411yescharacteristic
64C11×C4⋊C4—22no—
65C11×C4⋊C4—22no—
66C11×C4⋊C4—21no—
67C11×C4⋊C4—21no—
68C11×C4⋊C4C4⋊C412yes—
69C11×C4⋊C4C4⋊C412yes—
70C11×C22⋊C4—22no—
71C42×C11—22no—
72C42×C11C2×D411yescharacteristic
73C42×C11C2×D411yescharacteristic
74C42×C11C2×D411yescharacteristic
75C42×C11C2×Q811yescharacteristic
76C2×C11⋊C8—42no—
77C2×C11⋊C8—42no—
78#2960D1111yescharacteristic
79#1568—111no—
80#1568—111no—
81#1537—112no—
82#1307—112no—
83C23×C11#11711yescharacteristic
84Q8×C11—42no—
85Q8×C11—42no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—41no—
91C2×C4×C11—41no—
92C2×C4×C11C2×C22⋊C411yescharacteristic
93C2×C4×C11C2×C4⋊C411yescharacteristic
94C2×C4×C11#12111yescharacteristic
95C2×C4×C11#12111yescharacteristic
96C2×C4×C11C22⋊Q811yescharacteristic
97C2×C4×C11C22⋊Q811yescharacteristic
98C8×C11—21no—
99C8×C11—21no—
100C8×C11—21no—
101C8×C11—42no—
102C8×C11#10112yes—
103C11⋊C8—82no—
104C11⋊C8—82no—
105#533C2×D1111yescharacteristic
106#446—21no—
107#446—21no—
108C8×Q8—21no—
109C8×Q8—21no—
110#432—112no—
111#432—112no—
112#424Dic1112yes—
113#423C2×D1111yescharacteristic
114#405Dic1112yes—
115C2×C4×C8C2×D1111yescharacteristic
116#335—221no—
117#335—221no—
118#334—221no—
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×C11—42no—
131C4×C11—42no—
132C4×C11C2×#10111yescharacteristic
133C4×C11#41311yescharacteristic
134C2×M16C2×Dic1112yes—
135C22×C8C2×Dic1111yescharacteristic
136C22×C8C2×Dic1111yescharacteristic
137C4⋊Q8Dic2211yescharacteristic
138C4⋊Q8Dic2211yescharacteristic
139#125D4412yes—
140C22⋊Q8—21no—
141C22⋊Q8—21no—
142C4×Q8—21no—
143C4×Q8—21no—
144#117C2×Dic1112yes—
145C2×C42C22×D1111yescharacteristic
146C4⋊C8—22no—
147C4⋊C8—22no—
148C4⋊C8—21no—
149C4⋊C8—21no—
150C4⋊C8—222no—
151C4⋊C8—222no—
152C22⋊C8—222no—
153C22⋊C8—222no—
154#97—22no—
155#97—222no—
156#97—222no—
157C4×C8—22no—
158C4×C8C22⋊D1111yescharacteristic
159C4×C8C22⋊D1111yescharacteristic
160C4×C8C22⋊D1111yescharacteristic
161C4×C8C22⋊D1111yescharacteristic
162C2×C11—41no—
163C2×C11#180111yescharacteristic
164C2×C11#181411yescharacteristic
165C2×C11#181411yescharacteristic
166C2×Q8—21no—
167C2×Q8—21no—
168C22×C4#433911yescharacteristic
169C22×C4#433911yescharacteristic
170C22×C4C22×Dic1111yescharacteristic
171M16—42no—
172C2×C8—22no—
173C2×C8—22no—
174C2×C8—41no—
175C2×C8—442no—
176C2×C8—442no—
177C2×C8C22⋊Dic1111yescharacteristic
178C2×C8C22⋊Dic1111yescharacteristic
179C2×C8C22⋊Dic1111yescharacteristic
180C2×C8C22⋊Dic1111yescharacteristic
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4C4⋊Dic1112yes—
186C4⋊C4C4⋊Dic1112yes—
187C22⋊C4—22no—
188C42—22no—
189C42C2×Dic2211yescharacteristic
190C42C2×D4411yescharacteristic
191C42C2×C22⋊D1111yescharacteristic
192C42C2×C22⋊D1111yescharacteristic
193C11#863511yescharacteristic, complemented, Sylow
194C23#6697911yescharacteristic
195Q8—42no—
196Q8—42no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4#6697711yescharacteristic
204C2×C4#6697711yescharacteristic
205C2×C4C2×C4⋊Dic1111yescharacteristic
206C2×C4#6698311yescharacteristic
207C2×C4#6698311yescharacteristic
208C2×C4C2×C22⋊Dic1111yescharacteristic
209C8—21no—
210C8—21no—
211C8—21no—
212C8—42no—
213C8—882no—
214C8—882no—
215C8#6690012yes—
216C22—21no—
217C22—21no—
218C22—21no—
219C22#1062282511yescharacteristic
220C4—21no—
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—42no—
226C4—42no—
227C4C2×#6690011yescharacteristic
228C4#1062285011yescharacteristic
229C2—41no—
230C2#1306861211yescharacteristic
231C2#1306867011yescharacteristic
232C2#1306867011yescharacteristic
subgroupG/H
centerC22#10622825
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2960C2
socleC22×C11#380
prime radicalC23×C11#117
cosocleC2×C42×C11C23
hypercenter#2960D11
hypocenterC11#8635
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2960

Complements

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

NH ≅ G/Ntype
193. C11#8635semidirect

Maximal subgroups

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

subgroupindex
#130673792
#130672542
#130665272
C11×#29602
#863511