Finite Group Databasebeta

← #14656852

Subgroups — #14656852

Order 2816.

476 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 89 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#13076891C211yesmaximal, characteristic, complemented
2#13069440C212yesmaximal
3#13069439C211yesmaximal, characteristic
4#13066498C212yesmaximal, complemented
5C11×#1295C211yesmaximal, characteristic, complemented
6C2×#66927C2211yescharacteristic
7C2×C11×#97C2212yes—
8C11×#382C2211yescharacteristic
9C2×#66885—22no—
10C2×#66885—22no—
11#10622597—22no—
12C2×#66873—22no—
13#10622549C2212yes—
14C2×#66867C2211yescharacteristic
15#10622274—22no—
16#10622270—22no—
17C22×D44—22no—
18C22×D44—21no—
19C22×C8×C11—22no—
20C2×C11×C4⋊C4D412yes—
21C2×C42×C11C2311yescharacteristic
22C2×C4⋊Dic11—22no—
23C2×C4⋊Dic11D412yes—
24C2×C4⋊Dic11D412yes—
25C2×Dic11⋊C4—22no—
26C2×Dic11⋊C4—22no—
27C22×C11⋊C8—21no—
28#66927—22no—
29#66927—21no—
30#66927Q812yes—
31C11×#97—22no—
32C11×#97—22no—
33C11×#95—22no—
34C11⋊#95—22no—
35C11⋊#95—22no—
36C11⋊#95—22no—
37#66885—44no—
38#66885—44no—
39#66873—44no—
40#66867—22no—
41#10360—111nomaximal, Sylow
42C23×D11—41no—
43C22×C4×C11—22no—
44C22×C4×C11C2×D411yescharacteristic
45C22×C4×C11C2×D412yes—
46C22×Dic11—22no—
47C22×Dic11—22no—
48C2×D44—24no—
49C2×D44—22no—
50C2×D44—42no—
51C2×D44—42no—
52C2×D44—42no—
53C2×D44—42no—
54C2×D44—42no—
55C2×D44—42no—
56C2×D44—41no—
57C2×D44—42no—
58C2×C8×C11—24no—
59C2×C8×C11—42no—
60C2×C8×C11—42no—
61C11×C4⋊C4—42no—
62C42×C11C2×Q811yescharacteristic
63C42×C11#4112yes—
64C42×C11#4111yescharacteristic
65C4⋊Dic11—42no—
66C4⋊Dic11—42no—
67C4⋊Dic11—82no—
68Dic11⋊C4—82no—
69Dic11⋊C4—82no—
70C2×C11⋊C8—22no—
71C2×C11⋊C8—41no—
72C2×C11⋊C8—41no—
73#2845—111no—
74#1961—112no—
75#1961—111no—
76#1295—112no—
77#1295D1111yescharacteristic, complemented
78C23×C11#12011yescharacteristic
79C22×D11—42no—
80C22×D11—81no—
81C22×D11—82no—
82C22×D11—81no—
83C22×D11—82no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—42no—
89C2×C4×C11—42no—
90C2×C4×C11—42no—
91C2×C4×C11C22⋊Q812yes—
92C2×C4×C11C22⋊Q811yescharacteristic
93C2×C4×C11#12411yescharacteristic
94C2×C4×C11#12412yes—
95C2×Dic11—42no—
96C2×Dic11—42no—
97C2×Dic11—42no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101D44—44no—
102D44—44no—
103D44—44no—
104D44—82no—
105D44—82no—
106D44—82no—
107C8×C11—44no—
108C11⋊C8—42no—
109C2×#127—111no—
110C2×#102—222no—
111C2×#102—222no—
112C2×#102—222no—
113C2×#97—111no—
114C2×#97C2×D1112yes—
115#398—222no—
116#398—222no—
117#398—222no—
118#382—112no—
119#382C2×D1111yescharacteristic
120C22×C11#39311yescharacteristic
121C22×C11#45311yescharacteristic
122C22×C11#45312yes—
123C22×C11#45411yescharacteristic
124C22×C11#45412yes—
125C2×D11—84no—
126C2×D11—82no—
127C2×D11—162no—
128C2×D11—161no—
129C2×D11—161no—
130C4×C11—22no—
131C4×C11—21no—
132C4×C11—21no—
133C4×C11—22no—
134C4×C11—82no—
135Dic11—82no—
136Dic11—82no—
137C22×D4—221no—
138C22×D4—222no—
139C22×C8—22no—
140C22×C8—221no—
141#127—112no—
142#127—222no—
143#127—221no—
144C2×C4⋊C4—112no—
145C2×C4⋊C4—112no—
146C2×C4⋊C4—222no—
147C2×C4⋊C4—222no—
148C2×C4⋊C4—222no—
149C2×C4⋊C4D4412yes—
150C2×C42C22×D1111yescharacteristic
151#102—444no—
152#102—444no—
153#102—444no—
154#97—22no—
155#97—22no—
156#97—222no—
157#95—22no—
158#95—222no—
159#95—222no—
160#95—222no—
161C2×C11#165612yes—
162C2×C11#165611yescharacteristic
163C2×C11#165811yescharacteristic
164C2×C11#202712yes—
165C2×C11#202711yescharacteristic
166D11—162no—
167C24—441no—
168C2×D4—224no—
169C2×D4—222no—
170C2×D4—442no—
171C2×D4—442no—
172C2×D4—442no—
173C2×D4—442no—
174C2×D4—442no—
175C2×D4—442no—
176C2×D4—441no—
177C2×D4—442no—
178C22×C4—22no—
179C22×C4—222no—
180C22×C4—222no—
181C22×C4C2×D4411yescharacteristic
182C22×C4D4×D1112yes—
183C2×C8—24no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—222no—
187C2×C8—441no—
188C2×C8—441no—
189C4⋊C4—42no—
190C4⋊C4—442no—
191C4⋊C4—442no—
192C4⋊C4—882no—
193C4⋊C4—882no—
194C4⋊C4—882no—
195C42#433912yes—
196C42#434111yescharacteristic
197C42Q8×D1111yescharacteristic
198C11#1036011yescharacteristic, complemented, Sylow
199C23—442no—
200C23—881no—
201C23—881no—
202C23—882no—
203C23—882no—
204C23#6693511yescharacteristic
205D4—444no—
206D4—444no—
207D4—444no—
208D4—882no—
209D4—882no—
210D4—882no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—442no—
219C2×C4—442no—
220C2×C4—442no—
221C2×C4—442no—
222C2×C4—442no—
223C2×C4—442no—
224C2×C4#6692811yescharacteristic
225C2×C4#6693812yes—
226C2×C4#6694912yes—
227C2×C4#6695011yescharacteristic
228C8—44no—
229C8—442no—
230C22—884no—
231C22—882no—
232C22—1762no—
233C22—1761no—
234C22—1761no—
235C22#1062228611yescharacteristic
236C22#1062236011yescharacteristic
237C22#1062236611yescharacteristic
238C22#1062243512yes—
239C22#1062244012yes—
240C4—22no—
241C4—22no—
242C4—21no—
243C4—21no—
244C4—82no—
245C4—882no—
246C4—882no—
247C2—1762no—
248C2#1306791012yes—
249C2#1306791111yescharacteristic
250C2#1306791911yescharacteristic
251C2#1306977112yes—
252C2#1306977311yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socleC23×C11#120
prime radicalC2×#66927C22
hypercenter#1295D11
hypocenterC11#10360
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
1. #13076891C2semidirect
4. #13066498C2semidirect
5. C11×#1295C2semidirect
77. #1295D11semidirect
198. C11#10360semidirect

Maximal subgroups

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

subgroupindex
#130768912
#130694402
#130694392
#130664982
C11×#12952
#1036011