Finite Group Databasebeta

← #14656846

Subgroups — #14656846

Order 2816.

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

normal subgroups only

This group has 400 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#13076888C211yesmaximal, characteristic
2#13069590C212yesmaximal
3#13066498C212yesmaximal
4#13066497C211yesmaximal, characteristic
5C11×#1960C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C11×#103—21no—
8C2×C11×#103—21no—
9C2×C11×#97C2211yescharacteristic
10C11×#382C2211yescharacteristic
11#10622599—21no—
12#10622592—21no—
13#10622549C2212yes—
14C2×#66867C2212yes—
15#10622273—22no—
16#10622269—22no—
17#10622167—22no—
18#10622167—22no—
19C22×Q8×C11—21no—
20C22×Dic22—21no—
21C22×C8×C11—21no—
22C11×C4⋊Q8—22no—
23C11×C4⋊Q8—21no—
24C11×C4⋊Q8Q812yescomplemented
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11D412yes—
31C2×C4⋊Dic11D412yes—
32C2×Dic11⋊C4—22no—
33C22×C11⋊C8—22no—
34C11×#103—42no—
35C11×#103—42no—
36C11×#97—22no—
37C11×#95—22no—
38C11⋊#95—22no—
39C11⋊#95—21no—
40C11⋊#95—21no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43#66867—22no—
44#66867—22no—
45#10359—111nomaximal, Sylow
46C2×Q8×C11—22no—
47C2×Q8×C11—41no—
48C2×Q8×C11—41no—
49C2×Q8×C11—41no—
50C2×Q8×C11—41no—
51C2×Q8×C11—41no—
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—41no—
55C22×C4×C11C2×D412yes—
56C22×C4×C11C2×D411yescharacteristic
57C22×Dic11—22no—
58C22×Dic11—22no—
59C2×Dic22—81no—
60C2×Dic22—82no—
61C2×C8×C11—22no—
62C2×C8×C11—41no—
63C2×C8×C11—41no—
64C11×C4⋊C4—24no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—42no—
68C42×C11C2×Q811yescharacteristic
69C42×C11#4111yescharacteristic
70C42×C11#4112yes—
71C4⋊Dic11—42no—
72C4⋊Dic11—42no—
73C4⋊Dic11—81no—
74Dic11⋊C4—82no—
75C2×C11⋊C8—24no—
76C2×C11⋊C8—42no—
77C2×C11⋊C8—42no—
78#2844—111no—
79#1993—112no—
80#1960D1111yescharacteristic
81#1295—112no—
82#1295—111no—
83C23×C11#12011yescharacteristic
84Q8×C11—42no—
85Q8×C11—42no—
86Q8×C11—81no—
87Q8×C11—81no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—42no—
93C2×C4×C11—41no—
94C2×C4×C11—41no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—81no—
98C2×C4×C11—81no—
99C2×C4×C11C22⋊Q812yes—
100C2×C4×C11C22⋊Q811yescharacteristic
101C2×C4×C11#12412yes—
102C2×C4×C11#12411yescharacteristic
103C2×Dic11—42no—
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109Dic22—84no—
110C8×C11—42no—
111C11⋊C8—44no—
112C2×C4⋊Q8C2×D1111yescharacteristic
113C2×#103—21no—
114C2×#103—21no—
115C2×#97—112no—
116C2×#97C2×D1111yescharacteristic
117#400—222no—
118#400—221no—
119#395—222no—
120#395—221no—
121#382—112no—
122#382C2×D1111yescharacteristic
123#340—222no—
124#340—222no—
125C22×C11#39311yescharacteristic
126C22×C11#45311yescharacteristic
127C22×C11#45411yescharacteristic
128C22×C11#45512yes—
129C22×C11#45612yes—
130C4×C11—21no—
131C4×C11—21no—
132C4×C11—22no—
133C4×C11—22no—
134C4×C11—81no—
135C4×C11—81no—
136C4×C11—82no—
137Dic11—82no—
138Dic11—82no—
139C22×Q8—21no—
140C22×Q8—221no—
141C22×C8—21no—
142C22×C8—222no—
143C4⋊Q8—21no—
144C4⋊Q8—22no—
145C4⋊Q8Dic2212yescomplemented
146C2×C4⋊C4—22no—
147C2×C4⋊C4—112no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4—222no—
150C2×C4⋊C4—221no—
151C2×C4⋊C4C22⋊D1111yescharacteristic
152C2×C4⋊C4C22⋊D1111yescharacteristic
153C2×C42C22×D1111yescharacteristic
154#103—42no—
155#103—42no—
156#97—22no—
157#97—222no—
158#97—222no—
159#95—22no—
160#95—222no—
161#95—221no—
162#95—221no—
163#95—222no—
164#95—222no—
165C2×C11#165911yescharacteristic
166C2×C11#166011yescharacteristic
167C2×C11#166412yes—
168C2×C11#202711yescharacteristic
169C2×C11#202812yes—
170C2×Q8—22no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—882no—
177C2×Q8—881no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—222no—
182C22×C4—222no—
183C22×C4D4×D1112yes—
184C22×C4C2×C22⋊D1111yescharacteristic
185C2×C8—22no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—224no—
189C2×C8—442no—
190C2×C8—442no—
191C4⋊C4—24no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—442no—
196C4⋊C4—442no—
197C4⋊C4—882no—
198C4⋊C4—881no—
199C42C2×Dic2211yescharacteristic
200C42#433911yescharacteristic
201C42#434112yes—
202C11#1035911yescharacteristic, complemented, Sylow
203C23#6699011yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—81no—
207Q8—81no—
208Q8—884no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—442no—
221C2×C4—442no—
222C2×C4—442no—
223C2×C4—442no—
224C2×C4—442no—
225C2×C4—442no—
226C2×C4#6693112yes—
227C2×C4#6693812yes—
228C2×C4#6697711yescharacteristic
229C2×C4#6698911yescharacteristic
230C8—42no—
231C8—444no—
232C22#1062256011yescharacteristic
233C22#1062267511yescharacteristic
234C22#1062269011yescharacteristic
235C22#1062281512yes—
236C22#1062281812yes—
237C4—21no—
238C4—21no—
239C4—22no—
240C4—22no—
241C4—81no—
242C4—81no—
243C4—82no—
244C4—882no—
245C4—882no—
246C2#1306792011yescharacteristic
247C2#1306792511yescharacteristic
248C2#1306794712yes—
249C2#1306977211yescharacteristic
250C2#1306977512yes—
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1960C2
socle, prime radicalC23×C11#120
hypercenter#1960D11
hypocenterC11#10359
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
24. C11×C4⋊Q8Q8semidirect
145. C4⋊Q8Dic22semidirect
202. C11#10359semidirect

Maximal subgroups

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

subgroupindex
#130768882
#130695902
#130664982
#130664972
C11×#19602
#1035911