Finite Group Databasebeta

← #14666372

Subgroups — #14666372

Order 2816.

360 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 59 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, complemented
2#13067653C212yesmaximal
3#13066642C212yesmaximal, complemented
4#13066560C211yesmaximal, characteristic, complemented
5C11×#2040C211yesmaximal, characteristic
6C11×#537C2211yescharacteristic
7C2×C11×#104—21no—
8C11×#417—21no—
9C11×#382C2211yescharacteristic
10#10622647—22no—
11#10622599C2212yes—
12#10622592—21no—
13#10622549—21no—
14#10622273—22no—
15#10622269—22no—
16C11×#343C2211yescharacteristic
17#10622175—22no—
18#10622166C2212yes—
19C2×C11×#41—21no—
20C22×Dic22—21no—
21C2×C11×M16—21no—
22C11×C22⋊Q8—41no—
23C11×#121—22no—
24C11×#121—41no—
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C11×C4⋊C4C2311yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11D412yes—
31C2×Dic11⋊C4—22no—
32C11×#104—42no—
33C11×#103—41no—
34C11×#102—41no—
35C11×#95—22no—
36#66896—42no—
37C11⋊#95—22no—
38C11⋊#95—21no—
39C11⋊#95—22no—
40C11⋊#95—22no—
41C11⋊#95D412yes—
42C22⋊(C11⋊C8)—22no—
43#66872—42no—
44#12185—111nomaximal, Sylow
45C11×#41—41no—
46C11×#41—41no—
47C11×#41—41no—
48C11×#41—41no—
49C2×Q8×C11—21no—
50C2×D4×C11—21no—
51C2×D4×C11—22no—
52C2×D4×C11—41no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—41no—
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11C2×D412yes—
58C22×Dic11—22no—
59C22×Dic11—22no—
60C2×Dic22—82no—
61C2×Dic22—81no—
62C11×M16—41no—
63C11×M16—41no—
64C2×C8×C11—41no—
65C11×C4⋊C4—22no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C11×C22⋊C4—42no—
69C42×C11—21no—
70C42×C11SD1612yes—
71C4⋊Dic11—42no—
72C4⋊Dic11—81no—
73C4⋊Dic11—81no—
74Dic11⋊C4—82no—
75C2×C11⋊C8—42no—
76#2844—111no—
77#2040D1111yescharacteristic
78#1616—112no—
79#1353—112no—
80#1324—111no—
81C23×C11—41no—
82C23×C11#12011yescharacteristic
83Q8×C11—41no—
84Q8×C11—41no—
85D4×C11—41no—
86D4×C11—41no—
87D4×C11—82no—
88D4×C11—81no—
89D4×C11—81no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—81no—
101C2×C4×C11—81no—
102C2×C4×C11C2×SD1611yescharacteristic
103C2×C4×C11#13711yescharacteristic
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110Dic22—84no—
111C8×C11—81no—
112C11⋊C8—82no—
113#537C2×D1111yescharacteristic
114#481—222no—
115C2×#104—21no—
116#417—21no—
117#400—112no—
118#400—222no—
119#395—222no—
120#395—221no—
121#382—221no—
122#382C2×D1111yescharacteristic
123#343C2×D1111yescharacteristic
124#327—222no—
125#324—112no—
126C22×C11—21no—
127C22×C11—21no—
128C22×C11—81no—
129C22×C11—81no—
130C22×C11—81no—
131C22×C11#44811yescharacteristic
132C22×C11#45411yescharacteristic
133C22×C11B(4,𝔽2)11yescharacteristic
134C4×C11—21no—
135C4×C11—21no—
136C4×C11—42no—
137C4×C11—42no—
138C4×C11—81no—
139C4×C11—81no—
140Dic11—82no—
141Dic11—82no—
142C2×#41—21no—
143C22×Q8—221no—
144C2×M16—21no—
145C22⋊Q8—41no—
146#121—22no—
147#121—41no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4—221no—
150C2×C4⋊C4—221no—
151C2×C4⋊C4—222no—
152C2×C4⋊C4C22⋊D1111yescharacteristic
153C2×C4⋊C4C22×D1111yescharacteristic
154C2×C42C22⋊D1111yescharacteristic
155#106—442no—
156#104—42no—
157#103—41no—
158#102—41no—
159#102—442no—
160C22⋊C8—222no—
161#95—22no—
162#95—112no—
163#95—222no—
164#95—221no—
165#95—222no—
166#95—222no—
167C2×C11—21no—
168C2×C11—21no—
169C2×C11—161no—
170C2×C11#159911yescharacteristic
171C2×C11#220111yescharacteristic
172C2×C11#220211yescharacteristic
173#41—41no—
174#41—41no—
175#41—41no—
176#41—41no—
177C2×Q8—21no—
178C2×Q8—882no—
179C2×Q8—881no—
180C2×D4—21no—
181C2×D4—22no—
182C2×D4—41no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—41no—
186C22×C4—222no—
187C22×C4—222no—
188C22×C4D4×D1112yes—
189C22×C4C2×C22⋊D1111yescharacteristic
190M16—41no—
191M16—41no—
192C2×C8—41no—
193C2×C8—442no—
194C4⋊C4—22no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—442no—
198C4⋊C4—882no—
199C4⋊C4—881no—
200C4⋊C4—881no—
201C22⋊C4—42no—
202C42—21no—
203C42#432412yes—
204C11#1218511yescharacteristic, complemented, Sylow
205C23—41no—
206C23#6699011yescharacteristic
207Q8—41no—
208Q8—41no—
209Q8—884no—
210D4—41no—
211D4—41no—
212D4—82no—
213D4—81no—
214D4—81no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4—442no—
228C2×C4—442no—
229C2×C4—442no—
230C2×C4—442no—
231C2×C4—442no—
232C2×C4—442no—
233C2×C4C2×#432411yescharacteristic
234C2×C4#6700411yescharacteristic
235C8—81no—
236C8—882no—
237C22—21no—
238C22—21no—
239C22—81no—
240C22—81no—
241C22—81no—
242C22#1062264511yescharacteristic
243C22#1062265311yescharacteristic
244C22#1062267511yescharacteristic
245C4—21no—
246C4—21no—
247C4—42no—
248C4—42no—
249C4—81no—
250C4—81no—
251C4—882no—
252C4—882no—
253C2—21no—
254C2—21no—
255C2—161no—
256C2#1306755511yescharacteristic
257C2#1307062811yescharacteristic
258C2#1307063211yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2040C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#537C22
hypercenter#2040D11
hypocenterC11#12185
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2040

Complements

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

NH ≅ G/Ntype
1. #13076888C2semidirect
3. #13066642C2semidirect
4. #13066560C2semidirect
204. C11#12185semidirect

Maximal subgroups

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

subgroupindex
#130768882
#130676532
#130666422
#130665602
C11×#20402
#1218511