Finite Group Databasebeta

← #14656787

Subgroups — #14656787

Order 2816.

504 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 129 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#13073645C211yesmaximal, characteristic
2#13069563C212yesmaximal
3#13069417C211yesmaximal, characteristic
4#13066455C212yesmaximal
5C11×#1296C211yesmaximal, characteristic
6C2×#66941—22no—
7C2×#66922C2211yescharacteristic
8C2×C11×C4⋊C8C2212yes—
9C11×#384C2211yescharacteristic
10#10622592—22no—
11#10622586—22no—
12C2×#66874—22no—
13C4×C4⋊Dic11C2212yes—
14C2×C4×C11⋊C8C2211yescharacteristic
15#10622189—22no—
16#10622189—22no—
17C22×Dic22—21no—
18C22×Dic22—22no—
19C22×C8×C11—22no—
20C2×C11×C4⋊C4—22no—
21C2×C11×C4⋊C4D412yes—
22C2×C42×C11C2311yescharacteristic
23C2×C4⋊Dic11—22no—
24C2×C4⋊Dic11D412yes—
25C2×C4⋊Dic11D412yes—
26C2×Dic11⋊C4—24no—
27C2×C4×Dic11—22no—
28C22×C11⋊C8—21no—
29#66941—44no—
30#66941—44no—
31#66922—22no—
32#66922—21no—
33#66922Q812yescomplemented
34C11×C4⋊C8—22no—
35C11×C4⋊C8—22no—
36C11⋊#95—22no—
37C11⋊#95—22no—
38#66874—44no—
39C4×C11⋊C8—22no—
40#10349—111nomaximal, Sylow
41C22×C4×C11—22no—
42C22×C4×C11C2×D411yescharacteristic
43C22×C4×C11C2×D412yes—
44C22×Dic11—22no—
45C22×Dic11—22no—
46C22×Dic11—41no—
47C2×Dic22—22no—
48C2×Dic22—42no—
49C2×Dic22—42no—
50C2×Dic22—48no—
51C2×Dic22—41no—
52C2×Dic22—82no—
53C2×C8×C11—42no—
54C2×C8×C11—42no—
55C2×C8×C11—42no—
56C11×C4⋊C4—42no—
57C11×C4⋊C4—42no—
58C11×C4⋊C4—42no—
59C42×C11C2×Q811yescharacteristic
60C42×C11#4112yes—
61C42×C11#4111yescharacteristic
62C4⋊Dic11—24no—
63C4⋊Dic11—22no—
64C4⋊Dic11—22no—
65C4⋊Dic11—42no—
66C4⋊Dic11SD1614yes—
67C4⋊Dic11Q1614yes—
68Dic11⋊C4—48no—
69C4×Dic11—42no—
70C4×Dic11—42no—
71C2×C11⋊C8—22no—
72C2×C11⋊C8—41no—
73C2×C11⋊C8—41no—
74#2551—111no—
75#1987—112no—
76#1956—111no—
77#1296D1111yescharacteristic
78#1279—112no—
79C23×C11#12011yescharacteristic
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—44no—
83C2×C4×C11—42no—
84C2×C4×C11C22⋊Q812yes—
85C2×C4×C11C22⋊Q811yescharacteristic
86C2×C4×C11#12411yescharacteristic
87C2×C4×C11#12412yes—
88C2×C4×C11C2×SD1612yes—
89C2×C4×C11C2×Q1612yes—
90C2×C4×C11AGL(1,ℤ/8)12yes—
91C2×C4×C11#13712yes—
92C2×Dic11—24no—
93C2×Dic11—24no—
94C2×Dic11—42no—
95C2×Dic11—42no—
96C2×Dic11—42no—
97C2×Dic11—42no—
98C2×Dic11—42no—
99C2×Dic11—81no—
100C2×Dic11—81no—
101Dic22—44no—
102Dic22—88no—
103Dic22—82no—
104C8×C11—82no—
105C11⋊C8—42no—
106C2×C4⋊Q8—111no—
107C2×C4⋊Q8—222no—
108C2×C4⋊C8C2×D1112yes—
109C2×#103—222no—
110C2×C4×C8—111no—
111#395—222no—
112#389—222no—
113#384C2×D1111yescharacteristic
114C4×C4⋊C4—112no—
115#340—222no—
116#340—222no—
117C22×C11#39311yescharacteristic
118C22×C11#45012yes—
119C22×C11#45112yes—
120C22×C11#45311yescharacteristic
121C22×C11#45411yescharacteristic
122C4×C11—21no—
123C4×C11—21no—
124C4×C11—82no—
125C4×C11#47512yes—
126C4×C11#47712yes—
127C4×C11#48712yes—
128C4×C11#48912yes—
129Dic11—44no—
130Dic11—44no—
131Dic11—82no—
132C22×Q8—222no—
133C22×Q8—221no—
134C22×C8—22no—
135C22×C8—221no—
136C4⋊Q8—112no—
137C4⋊Q8—222no—
138C4⋊Q8—221no—
139C4⋊Q8—444no—
140C4⋊Q8—444no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—112no—
143C2×C4⋊C4—112no—
144C2×C4⋊C4—222no—
145C2×C4⋊C4—224no—
146C2×C4⋊C4D4412yes—
147C2×C42—222no—
148C2×C42C22×D1111yescharacteristic
149C4⋊C8—22no—
150C4⋊C8—22no—
151#103—444no—
152C4×C8—222no—
153#95—222no—
154#95—222no—
155C2×C11#162911yescharacteristic
156C2×C11#163311yescharacteristic
157C2×C11#163712yes—
158C2×C11#202412yes—
159C2×C11#202711yescharacteristic
160C2×Q8—222no—
161C2×Q8—442no—
162C2×Q8—442no—
163C2×Q8—448no—
164C2×Q8—441no—
165C2×Q8—882no—
166C22×C4—22no—
167C22×C4—222no—
168C22×C4—222no—
169C22×C4—441no—
170C22×C4C2×D4411yescharacteristic
171C22×C4D4×D1112yes—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—222no—
176C2×C8—441no—
177C2×C8—441no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—114no—
182C4⋊C4—114no—
183C4⋊C4—222no—
184C4⋊C4—222no—
185C4⋊C4—224no—
186C4⋊C4—448no—
187C4⋊C4—442no—
188C42—442no—
189C42—442no—
190C42#433912yes—
191C42#434111yescharacteristic
192C42Q8×D1111yescharacteristic
193C11#1034911yescharacteristic, complemented, Sylow
194C23#6693511yescharacteristic
195Q8—444no—
196Q8—882no—
197Q8—888no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—42no—
201C2×C4—44no—
202C2×C4—224no—
203C2×C4—224no—
204C2×C4—442no—
205C2×C4—442no—
206C2×C4—442no—
207C2×C4—442no—
208C2×C4—442no—
209C2×C4—881no—
210C2×C4—881no—
211C2×C4#6692811yescharacteristic
212C2×C4#6693812yes—
213C2×C4#6694912yes—
214C2×C4#6695011yescharacteristic
215C2×C4#6696412yes—
216C2×C4SD16×D1112yes—
217C2×C4#6696812yes—
218C2×C4Q16×D1112yes—
219C8—82no—
220C8—442no—
221C22#1062228611yescharacteristic
222C22#1062236011yescharacteristic
223C22#1062236611yescharacteristic
224C22#1062238912yes—
225C22#1062242112yes—
226C4—21no—
227C4—21no—
228C4—82no—
229C4—444no—
230C4—444no—
231C4—882no—
232C4#1062237812yes—
233C4#1062240512yes—
234C4#1062246712yes—
235C4#1062248812yes—
236C2#1306773311yescharacteristic
237C2#1306775711yescharacteristic
238C2#1306778212yes—
239C2#1306975612yes—
240C2#1306977311yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socle, prime radicalC23×C11#120
hypercenter#1296D11
hypocenterC11#10349
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
33. #66922Q8semidirect
193. C11#10349semidirect

Maximal subgroups

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

subgroupindex
#130736452
#130695632
#130694172
#130664552
C11×#12962
#1034911