Finite Group Databasebeta

← #14666367

Subgroups — #14666367

Order 2816.

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

normal subgroups only

This group has 372 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#13067585C212yesmaximal
3#13066645C212yesmaximal, complemented
4#13066560C211yesmaximal, characteristic, complemented
5C11×#2040C211yesmaximal, characteristic
6C11×#537C2211yescharacteristic
7C2×C11×#104—21no—
8C11×#417—21no—
9C11×#382C2211yescharacteristic
10#10622653—22no—
11#10622599—21no—
12#10622592C2212yes—
13#10622549—21no—
14#10622273—22no—
15#10622269—22no—
16C11×#343C2211yescharacteristic
17#10622175—22no—
18#10622166C2212yes—
19C2×C11×#41—21no—
20C22×Dic22D412yes—
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×#4324—42no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×Dic11⋊C4—22no—
33C11×#104—42no—
34C11×#103—41no—
35C11×#102—41no—
36C11×#95—22no—
37C11⋊#95—22no—
38C11⋊#95—22no—
39C11⋊#95—21no—
40C11⋊#95—22no—
41C11⋊#95D412yes—
42C22⋊(C11⋊C8)—22no—
43#66874—42no—
44#12184—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—42no—
61C2×Dic22—82no—
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×C11SD1612yescomplemented
71#4324—84no—
72C4⋊Dic11—81no—
73C4⋊Dic11—81no—
74C4⋊Dic11—81no—
75Dic11⋊C4—82no—
76C2×C11⋊C8—42no—
77#2844—111no—
78#2040D1111yescharacteristic
79#1604—112no—
80#1354—112no—
81#1324—111no—
82C23×C11—41no—
83C23×C11#12011yescharacteristic
84Q8×C11—41no—
85Q8×C11—41no—
86D4×C11—41no—
87D4×C11—41no—
88D4×C11—82no—
89D4×C11—81no—
90D4×C11—81no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—41no—
96C2×C4×C11—41no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11—81no—
102C2×C4×C11—81no—
103C2×C4×C11C2×SD1611yescharacteristic
104C2×C4×C11#13711yescharacteristic
105C2×Dic11—42no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C2×Dic11—42no—
111Dic22—44no—
112Dic22—82no—
113C8×C11—81no—
114C11⋊C8—82no—
115#537C2×D1111yescharacteristic
116#448—222no—
117C2×#104—21no—
118#417—21no—
119#400—222no—
120#400—221no—
121#395—112no—
122#395—222no—
123#382—221no—
124#382C2×D1111yescharacteristic
125#343C2×D1111yescharacteristic
126#327—222no—
127#324—112no—
128C22×C11—21no—
129C22×C11—21no—
130C22×C11—81no—
131C22×C11—81no—
132C22×C11—81no—
133C22×C11#44811yescharacteristic
134C22×C11#45411yescharacteristic
135C22×C11B(4,𝔽2)11yescharacteristic
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—42no—
139C4×C11—42no—
140C4×C11—81no—
141C4×C11—81no—
142Dic11—82no—
143Dic11—82no—
144C2×#41—21no—
145C22×Q8—112no—
146C2×SD16—442no—
147C2×M16—21no—
148C22⋊Q8—41no—
149#121—22no—
150#121—41no—
151C2×C4⋊C4—221no—
152C2×C4⋊C4—221no—
153C2×C4⋊C4—221no—
154C2×C4⋊C4—222no—
155C2×C4⋊C4C22⋊D1111yescharacteristic
156C2×C4⋊C4C22×D1111yescharacteristic
157C2×C42C22⋊D1111yescharacteristic
158#104—42no—
159#103—41no—
160#103—442no—
161#102—41no—
162C22⋊C8—222no—
163#95—22no—
164#95—112no—
165#95—222no—
166#95—222no—
167#95—221no—
168#95—222no—
169C2×C11—21no—
170C2×C11—21no—
171C2×C11—161no—
172C2×C11#159911yescharacteristic
173C2×C11#219911yescharacteristic
174C2×C11#220311yescharacteristic
175#41—41no—
176#41—41no—
177#41—41no—
178#41—41no—
179C2×Q8—21no—
180C2×Q8—442no—
181C2×Q8—882no—
182C2×D4—21no—
183C2×D4—22no—
184C2×D4—41no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—41no—
188C22×C4—222no—
189C22×C4—222no—
190C22×C4D4×D1112yes—
191C22×C4C2×C22⋊D1111yescharacteristic
192SD16—884no—
193M16—41no—
194M16—41no—
195C2×C8—41no—
196C2×C8—442no—
197C4⋊C4—22no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—882no—
201C4⋊C4—881no—
202C4⋊C4—881no—
203C4⋊C4—881no—
204C22⋊C4—42no—
205C42—21no—
206C42#432412yescomplemented
207C11#1218411yescharacteristic, complemented, Sylow
208C23—41no—
209C23#6699011yescharacteristic
210Q8—41no—
211Q8—41no—
212Q8—444no—
213Q8—882no—
214D4—41no—
215D4—41no—
216D4—82no—
217D4—81no—
218D4—81no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4—442no—
232C2×C4—442no—
233C2×C4—442no—
234C2×C4—442no—
235C2×C4—442no—
236C2×C4—442no—
237C2×C4C2×#432411yescharacteristic
238C2×C4#6700411yescharacteristic
239C8—81no—
240C8—882no—
241C22—21no—
242C22—21no—
243C22—81no—
244C22—81no—
245C22—81no—
246C22#1062264511yescharacteristic
247C22#1062265311yescharacteristic
248C22#1062267511yescharacteristic
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—81no—
254C4—81no—
255C4—882no—
256C4—882no—
257C2—21no—
258C2—21no—
259C2—161no—
260C2#1306755511yescharacteristic
261C2#1307061611yescharacteristic
262C2#1307063611yescharacteristic
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#12184
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. #13066645C2semidirect
4. #13066560C2semidirect
70. C42×C11SD16semidirect
206. C42#4324semidirect
207. C11#12184semidirect

Maximal subgroups

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

subgroupindex
#130768882
#130675852
#130666452
#130665602
C11×#20402
#1218411