Finite Group Databasebeta

← #14656851

Subgroups — #14656851

Order 2816.

476 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 91 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#13069441C212yesmaximal
3#13066498C212yesmaximal, complemented
4#13066497C211yesmaximal, characteristic, complemented
5C11×#1961C211yesmaximal, characteristic
6C2×C11×#127C2211yescharacteristic
7C2×C11×#102—22no—
8C2×C11×#97C2211yescharacteristic
9C11×#382C2211yescharacteristic
10C2×#66896—22no—
11C2×#66896—22no—
12#10622597—22no—
13#10622549C2212yes—
14C2×#66867C2212yes—
15#10622274—22no—
16#10622270—22no—
17C22×D4×C11—22no—
18C22×D4×C11—21no—
19C22×C8×C11—21no—
20C11×#127—21no—
21C11×#127—22no—
22C11×#127Q812yes—
23C2×C11×C4⋊C4D412yes—
24C2×C42×C11C2311yescharacteristic
25C2×C4⋊Dic11—22no—
26C2×C4⋊Dic11D412yes—
27C2×C4⋊Dic11D412yes—
28C2×Dic11⋊C4—22no—
29C2×Dic11⋊C4—22no—
30C22×C11⋊C8—22no—
31C11×#102—44no—
32C11×#97—22no—
33C11×#95—22no—
34#66896—44no—
35#66896—44no—
36C11⋊#95—22no—
37C11⋊#95—22no—
38C11⋊#95—22no—
39#66867—22no—
40#66867—22no—
41#10360—111nomaximal, Sylow
42C24×C11—41no—
43C2×D4×C11—24no—
44C2×D4×C11—22no—
45C2×D4×C11—42no—
46C2×D4×C11—42no—
47C2×D4×C11—42no—
48C2×D4×C11—42no—
49C2×D4×C11—42no—
50C2×D4×C11—42no—
51C2×D4×C11—42no—
52C2×D4×C11—41no—
53C22×C4×C11—22no—
54C22×C4×C11C2×D412yes—
55C22×C4×C11C2×D411yescharacteristic
56C22×Dic11—22no—
57C22×Dic11—22no—
58C2×C8×C11—22no—
59C2×C8×C11—41no—
60C2×C8×C11—41no—
61C11×C4⋊C4—42no—
62C42×C11C2×Q811yescharacteristic
63C42×C11#4111yescharacteristic
64C42×C11#4112yes—
65C4⋊Dic11—42no—
66C4⋊Dic11—42no—
67C4⋊Dic11—82no—
68Dic11⋊C4—82no—
69Dic11⋊C4—82no—
70C2×C11⋊C8—24no—
71C2×C11⋊C8—42no—
72C2×C11⋊C8—42no—
73#2845—111no—
74#1961—112no—
75#1961D1111yescharacteristic
76#1295—112no—
77#1295—111no—
78C23×C11—42no—
79C23×C11—82no—
80C23×C11—81no—
81C23×C11—82no—
82C23×C11—81no—
83C23×C11#12011yescharacteristic
84D4×C11—44no—
85D4×C11—44no—
86D4×C11—44no—
87D4×C11—82no—
88D4×C11—82no—
89D4×C11—82no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—42no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11C22⋊Q812yes—
98C2×C4×C11C22⋊Q811yescharacteristic
99C2×C4×C11#12412yes—
100C2×C4×C11#12411yescharacteristic
101C2×Dic11—42no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107C8×C11—42no—
108C11⋊C8—44no—
109C2×#127C2×D1111yescharacteristic
110C2×#102—22no—
111C2×#102—222no—
112C2×#102—222no—
113C2×#97—112no—
114C2×#97C2×D1111yescharacteristic
115#398—222no—
116#398—222no—
117#398—222no—
118#382—112no—
119#382C2×D1111yescharacteristic
120C22×C11—84no—
121C22×C11—82no—
122C22×C11—162no—
123C22×C11—161no—
124C22×C11—161no—
125C22×C11#39311yescharacteristic
126C22×C11#45312yes—
127C22×C11#45311yescharacteristic
128C22×C11#45412yes—
129C22×C11#45411yescharacteristic
130C4×C11—22no—
131C4×C11—21no—
132C4×C11—22no—
133C4×C11—21no—
134C4×C11—82no—
135Dic11—82no—
136Dic11—82no—
137C22×D4—22no—
138C22×D4—21no—
139C22×C8—21no—
140C22×C8—222no—
141#127—21no—
142#127—22no—
143#127Dic2212yes—
144C2×C4⋊C4—112no—
145C2×C4⋊C4—112no—
146C2×C4⋊C4—222no—
147C2×C4⋊C4—222no—
148C2×C4⋊C4—222no—
149C2×C4⋊C4C22⋊D1112yes—
150C2×C42C22×D1111yescharacteristic
151#102—44no—
152#102—444no—
153#102—444no—
154#97—22no—
155#97—222no—
156#97—222no—
157#95—22no—
158#95—222no—
159#95—222no—
160#95—222no—
161C2×C11—162no—
162C2×C11#165612yes—
163C2×C11#165611yescharacteristic
164C2×C11#165811yescharacteristic
165C2×C11#202712yes—
166C2×C11#202711yescharacteristic
167C24—41no—
168C2×D4—24no—
169C2×D4—22no—
170C2×D4—42no—
171C2×D4—42no—
172C2×D4—42no—
173C2×D4—42no—
174C2×D4—42no—
175C2×D4—42no—
176C2×D4—42no—
177C2×D4—41no—
178C22×C4—22no—
179C22×C4—222no—
180C22×C4—222no—
181C22×C4D4×D1112yes—
182C22×C4C2×C22⋊D1111yescharacteristic
183C2×C8—22no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—224no—
187C2×C8—442no—
188C2×C8—442no—
189C4⋊C4—42no—
190C4⋊C4—442no—
191C4⋊C4—442no—
192C4⋊C4—882no—
193C4⋊C4—882no—
194C4⋊C4—882no—
195C42C2×Dic2211yescharacteristic
196C42#433911yescharacteristic
197C42#434112yes—
198C11#1036011yescharacteristic, complemented, Sylow
199C23—42no—
200C23—82no—
201C23—82no—
202C23—81no—
203C23—81no—
204C23#6699011yescharacteristic
205D4—44no—
206D4—44no—
207D4—44no—
208D4—82no—
209D4—82no—
210D4—82no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
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#6693112yes—
225C2×C4#6693812yes—
226C2×C4#6697711yescharacteristic
227C2×C4#6698911yescharacteristic
228C8—42no—
229C8—444no—
230C22—84no—
231C22—82no—
232C22—162no—
233C22—161no—
234C22—161no—
235C22#1062256011yescharacteristic
236C22#1062267511yescharacteristic
237C22#1062269011yescharacteristic
238C22#1062281112yes—
239C22#1062281412yes—
240C4—22no—
241C4—22no—
242C4—21no—
243C4—21no—
244C4—82no—
245C4—882no—
246C4—882no—
247C2—162no—
248C2#1306790712yes—
249C2#1306790811yescharacteristic
250C2#1306791711yescharacteristic
251C2#1306977012yes—
252C2#1306977211yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1961C2
socleC23×C11#120
prime radicalC2×C11×#127C22
hypercenter#1961D11
hypocenterC11#10360
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
1. #13076891C2semidirect
3. #13066498C2semidirect
4. #13066497C2semidirect
198. C11#10360semidirect

Maximal subgroups

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

subgroupindex
#130768912
#130694412
#130664982
#130664972
C11×#19612
#1036011