Finite Group Databasebeta

← #14646770

Subgroups — #14646770

Order 2816.

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

normal subgroups only

This group has 388 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#13077329C211yesmaximal, characteristic
2#13067379C211yesmaximal, characteristic, complemented
3#13067250C212yesmaximal
4#13066526C212yesmaximal, complemented
5C11×#1568C211yesmaximal, characteristic, complemented
6C2×#66954C412yes—
7#10623008C2211yescharacteristic
8C11×#432C2212yes—
9C2×C4×C8×C11C2211yescharacteristic
10#10622723C412yes—
11#10622539C2212yes—
12#10622537C2211yescharacteristic
13#10622301—21no—
14#10622301—21no—
15C8×D44—21no—
16C8×D44—21no—
17C11×#335—21no—
18C11×#334—21no—
19#10622102—24no—
20#10622096—21no—
21#10622095—21no—
22C2×#4339C2×C412yes—
23C22×C8×C11C2×C411yescharacteristic
24C22×C8×C11C2×C411yescharacteristic
25C2×C42×C11C2311yescharacteristic
26#66983—21no—
27#66983—21no—
28C2×#4318C2×C412yes—
29#66954—44no—
30C2×#4313—22no—
31C2×C8×D11—22no—
32#66928D412yes—
33#66927Q811yescharacteristic
34C4×D44—21no—
35C4×D44—21no—
36#66922Q811yescharacteristic
37C11×C4⋊C8—22no—
38C11×C22⋊C8—22no—
39C11×#97—22no—
40C4×C8×C11D411yescharacteristic
41C4×C8×C11D411yescharacteristic
42C4×C8×C11D411yescharacteristic
43C4×C8×C11D411yescharacteristic
44C22⋊(C11⋊C8)—22no—
45(C2×D11)⋊C8—22no—
46(C2×D11)⋊C8—22no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)—22no—
50#66867—22no—
51#8632—111nomaximal, Sylow
52C22×C4×C11C22×C411yescharacteristic
53C22×C4×C11#4111yescharacteristic
54C22×C4×C11#4111yescharacteristic
55C2×C22⋊D11—22no—
56#4339—42no—
57#4339—42no—
58C2×D44—21no—
59C2×D44—21no—
60C2×D44C4⋊C412yes—
61C2×C4×D11—22no—
62C2×Dic22C4⋊C412yes—
63C2×C8×C11—22no—
64C2×C8×C11—41no—
65C2×C8×C11—42no—
66C2×C8×C11C22⋊C411yescharacteristic
67C2×C8×C11C22⋊C411yescharacteristic
68C2×C8×C11C22⋊C411yescharacteristic
69C2×C8×C11C22⋊C411yescharacteristic
70C42×C11C2×D411yescharacteristic
71C42×C11C2×D411yescharacteristic
72C42×C11C2×D411yescharacteristic
73C42×C11C2×Q811yescharacteristic
74(C2×D11)⋊C4—22no—
75(C2×D11)⋊C4—22no—
76C4⋊Dic11—21no—
77C4⋊Dic11—21no—
78#4318—42no—
79C2×C11⋊C8—22no—
80C2×C11⋊C8—42no—
81#4313—44no—
82C8×D11—44no—
83#2931—111no—
84#1568—111no—
85#1568D1111yescharacteristic, complemented
86#1536—112no—
87#1307—112no—
88C23×C11#11711yescharacteristic
89C22×D11—22no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11C2×C22⋊C411yescharacteristic
95C2×C4×C11C2×C4⋊C411yescharacteristic
96C2×C4×C11#12111yescharacteristic
97C2×C4×C11#12111yescharacteristic
98C2×C4×C11C22⋊Q811yescharacteristic
99C2×C4×C11C22⋊Q811yescharacteristic
100C22⋊D11—44no—
101C2×Dic11—22no—
102D44—42no—
103D44—42no—
104D44—42no—
105C4×D11—42no—
106C4×D11—42no—
107Dic22—42no—
108C8×C11—21no—
109C8×C11—21no—
110C8×C11—21no—
111C8×C11—82no—
112C8×C11#10012yes—
113C11⋊C8—42no—
114C11⋊C8—82no—
115C2×#131—112no—
116#532—111no—
117#436—221no—
118#436—221no—
119C8×D4—221no—
120C8×D4—221no—
121#432—112no—
122#432C2×D1112yes—
123#423—111no—
124#408—112no—
125C2×C4×C8C2×D1111yescharacteristic
126#335—21no—
127#335—221no—
128#334—21no—
129#334—221no—
130#329—224no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11—21no—
134C22×C11#38011yescharacteristic
135C2×D11—42no—
136C2×D11—42no—
137C2×D11—42no—
138C4×C11—21no—
139C4×C11—21no—
140C4×C11—21no—
141C4×C11—21no—
142C4×C11—21no—
143C4×C11C2×#10011yescharacteristic
144C4×C11#41311yescharacteristic
145Dic11—42no—
146C2×#41—112no—
147#131—444no—
148C2×M16—112no—
149C2×M16—222no—
150C22×C8—222no—
151C22×C8C4×D1111yescharacteristic
152C22×C8C4×D1111yescharacteristic
153C4⋊Q8—111no—
154#127—111no—
155#124—112no—
156#121—221no—
157#121—221no—
158C4×D4—221no—
159C4×D4—221no—
160C2×C42C22×D1111yescharacteristic
161C4⋊C8—22no—
162C4⋊C8—221no—
163C4⋊C8—222no—
164C4⋊C8—221no—
165C22⋊C8—22no—
166C22⋊C8—222no—
167C22⋊C8—222no—
168C22⋊C8—222no—
169#97—22no—
170#97—222no—
171C4×C8D4411yescharacteristic
172C4×C8D4411yescharacteristic
173C4×C8C22⋊D1111yescharacteristic
174C4×C8C22⋊D1111yescharacteristic
175C2×C11—41no—
176C2×C11#180011yescharacteristic
177C2×C11#181411yescharacteristic
178C2×C11#181411yescharacteristic
179D11—82no—
180#41—442no—
181#41—442no—
182C2×Q8—112no—
183C2×D4—112no—
184C2×D4—222no—
185C2×D4—221no—
186C2×D4—221no—
187C22×C4—222no—
188C22×C4C2×C4×D1111yescharacteristic
189C22×C4#434111yescharacteristic
190C22×C4#434311yescharacteristic
191M16—444no—
192M16—442no—
193C2×C8—22no—
194C2×C8—41no—
195C2×C8—42no—
196C2×C8—222no—
197C2×C8—444no—
198C2×C8—442no—
199C2×C8(C2×D11)⋊C411yescharacteristic
200C2×C8(C2×D11)⋊C411yescharacteristic
201C2×C8(C2×D11)⋊C411yescharacteristic
202C2×C8(C2×D11)⋊C411yescharacteristic
203C4⋊C4—221no—
204C4⋊C4—221no—
205C22⋊C4—222no—
206C22⋊C4—222no—
207C42C2×D4411yescharacteristic
208C42D4×D1111yescharacteristic
209C42Q8×D1111yescharacteristic
210C42C2×C22⋊D1111yescharacteristic
211C11#863211yescharacteristic, complemented, Sylow
212C23—222no—
213C23#6694511yescharacteristic
214Q8—442no—
215D4—442no—
216D4—442no—
217D4—442no—
218D4—444no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—222no—
224C2×C4—442no—
225C2×C4—442no—
226C2×C4C4⋊C4×D1111yescharacteristic
227C2×C4#6694811yescharacteristic
228C2×C4#6695011yescharacteristic
229C2×C4C2×(C2×D11)⋊C411yescharacteristic
230C2×C4#6699111yescharacteristic
231C2×C4#6699911yescharacteristic
232C8—21no—
233C8—21no—
234C8—21no—
235C8—82no—
236C8—442no—
237C8—882no—
238C8#6688712yes—
239C22—21no—
240C22—21no—
241C22—21no—
242C22—442no—
243C22—442no—
244C22—442no—
245C22#1062260011yescharacteristic
246C4—21no—
247C4—21no—
248C4—21no—
249C4—21no—
250C4—21no—
251C4—442no—
252C4C2×#6688711yescharacteristic
253C4#1062274511yescharacteristic
254C2—41no—
255C2—882no—
256C2#1306860511yescharacteristic
257C2#1306866711yescharacteristic
258C2#1306867111yescharacteristic
subgroupG/H
centerC22#10622600
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1568C2
socleC22×C11#380
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1568D11
hypocenterC11#8632
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
2. #13067379C2semidirect
4. #13066526C2semidirect
5. C11×#1568C2semidirect
85. #1568D11semidirect
211. C11#8632semidirect

Maximal subgroups

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

subgroupindex
#130773292
#130673792
#130672502
#130665262
C11×#15682
#863211