Finite Group Databasebeta

← #14667469

Subgroups — #14667469

Order 2816.

312 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 69 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#13081481C211yesmaximal, characteristic, complemented
2#13070839C211yesmaximal, characteristic, complemented
3#13067973C211yesmaximal, characteristic, complemented
4#13066673C211yesmaximal, characteristic, complemented
5#13066594C211yesmaximal, characteristic, complemented
6#13066577C211yesmaximal, characteristic, complemented
7C11×#2206C211yesmaximal, characteristic
8#10623074—21no—
9C2×C11×D16—21no—
10C11×#493C2211yescharacteristic
11C4×C11×D8C2211yescharacteristic
12D8×Dic11—21no—
13#10622688—21no—
14#10622621—21no—
15#10622491—21no—
16#10622379—22no—
17#10622295C2211yescharacteristic
18C8×Dic22C2211yescharacteristic
19C11×C4⋊C16C2211yescharacteristic
20C11×#357—21no—
21#10622200—22no—
22#10622182—21no—
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×D8—21no—
26C2×C11×D8—21no—
27C2×C11×D8D411yescharacteristic
28C11×#127—21no—
29C4×D4×C11—21no—
30D4×Dic11—22no—
31C2×#4324—41no—
32C2×C4⋊Dic11—41no—
33#66977—41no—
34#66943—22no—
35#66931—42no—
36#66922—21no—
37C4×Dic22D411yescharacteristic
38C11×D16—42no—
39C2×C11×C16—21no—
40C11×#107D411yescharacteristic
41C11×#102—21no—
42C4×C8×C11C2311yescharacteristic
43#66896—22no—
44#66896—41no—
45#66882—21no—
46#66882D412yes—
47Dic11⋊C8—21no—
48C8×Dic11—21no—
49C2×C11⋊C16—21no—
50#66872—22no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)D411yescharacteristic
53#12355—111nomaximal, Sylow
54C2×D4×C11—21no—
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C22×C4×C11—41no—
59C22×Dic11—42no—
60C2×Dic22—41no—
61C2×Dic22D811yescharacteristic
62C11×D8—21no—
63C11×D8—42no—
64C11×D8—41no—
65C11×D8—41no—
66C11×D8SD1612yescomplemented
67C2×C8×C11C2×D411yescharacteristic
68C2×C8×C11C2×D411yescharacteristic
69C11×C4⋊C4—21no—
70C11×C22⋊C4—41no—
71C42×C11C2×D411yescharacteristic
72C22⋊Dic11—42no—
73#4324—82no—
74C4⋊Dic11—22no—
75C4⋊Dic11—42no—
76C4⋊Dic11—41no—
77C4⋊Dic11D811yescharacteristic
78Dic11⋊C4—21no—
79Dic11⋊C4—42no—
80C4×Dic11—21no—
81C2×C11⋊C8—21no—
82C2×C11⋊C8—41no—
83C11×C16—41no—
84C11⋊C16—41no—
85#3380—111no—
86#2240—111no—
87#2206D1111yescharacteristic
88#1668—111no—
89#1365—111no—
90Q8⋊C16—111no—
91#1331—111no—
92C23×C11—41no—
93C23×C11—81no—
94D4×C11—22no—
95D4×C11—41no—
96D4×C11—81no—
97D4×C11—81no—
98D4×C11—81no—
99D4×C11—81no—
100D4×C11—161no—
101C2×C4×C11—41no—
102C2×C4×C11—81no—
103C2×C4×C11—81no—
104C2×C4×C11#12011yescharacteristic
105C2×C4×C11C2×D811yescharacteristic
106C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
107C2×Dic11—21no—
108C2×Dic11—21no—
109C2×Dic11—42no—
110C2×Dic11—162no—
111Dic22—21no—
112Dic22—21no—
113Dic22—161no—
114C8×C11—21no—
115C8×C11C2×SD1611yescharacteristic
116C8×C11#13711yescharacteristic
117C11⋊C8—41no—
118C11⋊C8—81no—
119#554—221no—
120C2×D16—21no—
121#500—111no—
122#499—221no—
123#493C2×D1111yescharacteristic
124#478—222no—
125#476—221no—
126#460—221no—
127C8×Q8—111no—
128C4×D8—221no—
129C4×D8C2×D1111yescharacteristic
130C4⋊C16C2×D1111yescharacteristic
131#357—21no—
132#357—222no—
133C4×C16—111no—
134#335—111no—
135#331—221no—
136C22×C11—42no—
137C22×C11—81no—
138C22×C11—81no—
139C22×C11—161no—
140C22×C11—161no—
141C22×C11—161no—
142C22×C11#44711yescharacteristic
143C4×C11—21no—
144C4×C11—81no—
145C4×C11#44811yescharacteristic
146C4×C11#45411yescharacteristic
147C4×C11#50811yescharacteristic
148C4×C11#50911yescharacteristic
149Dic11—41no—
150Dic11—41no—
151Dic11—82no—
152C2×SD16—441no—
153C2×D8—21no—
154C2×D8—21no—
155C2×D8C22⋊D1111yescharacteristic
156C4⋊Q8—221no—
157#127—21no—
158#125—222no—
159C22⋊Q8—442no—
160C22⋊Q8—441no—
161C4×Q8—111no—
162C4×D4—21no—
163C4×D4—222no—
164C2×C4⋊C4—441no—
165D16—42no—
166C2×C16—21no—
167C2×C16—221no—
168#107—112no—
169#107—221no—
170#107C22⋊D1111yescharacteristic
171#106—222no—
172C4⋊C8—111no—
173C4⋊C8—221no—
174C4⋊C8—221no—
175#102—21no—
176#102—222no—
177#102—441no—
178C4×C8—221no—
179C4×C8C22×D1111yescharacteristic
180C2×C11—82no—
181C2×C11—321no—
182C2×C11#162711yescharacteristic
183C2×C11#218611yescharacteristic
184C2×C11#219211yescharacteristic
185C2×Q8—111no—
186C2×Q8—441no—
187C2×D4—21no—
188C2×D4—41no—
189C2×D4—41no—
190C2×D4—41no—
191C22×C4—41no—
192C22×C4—442no—
193SD16—882no—
194D8—21no—
195D8—42no—
196D8—41no—
197D8—41no—
198D8#432412yescomplemented
199C2×C8—221no—
200C2×C8—441no—
201C2×C8D4×D1111yescharacteristic
202C2×C8C2×C22⋊D1111yescharacteristic
203C4⋊C4—21no—
204C4⋊C4—111no—
205C4⋊C4—221no—
206C4⋊C4—222no—
207C4⋊C4—442no—
208C4⋊C4—442no—
209C4⋊C4—441no—
210C22⋊C4—41no—
211C22⋊C4—442no—
212C42—221no—
213C42D4×D1111yescharacteristic
214C16—41no—
215C16—441no—
216C11#1235511yescharacteristic, complemented, Sylow
217C23—41no—
218C23—81no—
219Q8—221no—
220Q8—221no—
221Q8—1761no—
222D4—22no—
223D4—41no—
224D4—81no—
225D4—81no—
226D4—81no—
227D4—81no—
228D4—161no—
229C2×C4—41no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—221no—
233C2×C4—221no—
234C2×C4—442no—
235C2×C4—1762no—
236C2×C4D8×D1111yescharacteristic
237C2×C4#6696411yescharacteristic
238C2×C4#6699011yescharacteristic
239C8—21no—
240C8—441no—
241C8—881no—
242C8C2×#432411yescharacteristic
243C8#6700411yescharacteristic
244C22—42no—
245C22—81no—
246C22—81no—
247C22—161no—
248C22—161no—
249C22—161no—
250C22#1062276911yescharacteristic
251C4—21no—
252C4—81no—
253C4—441no—
254C4—441no—
255C4—882no—
256C4#1062252411yescharacteristic
257C4#1062252511yescharacteristic
258C4#1062265311yescharacteristic
259C4#1062281411yescharacteristic
260C2—82no—
261C2—321no—
262C2#1306771811yescharacteristic
263C2#1307053611yescharacteristic
264C2#1307057011yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
Fitting, prime radicalC11×#2206C2
socleC22×C11#447
hypercenter#2206D11
hypocenterC11#12355
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #13081481C2semidirect
2. #13070839C2semidirect
3. #13067973C2semidirect
4. #13066673C2semidirect
5. #13066594C2semidirect
6. #13066577C2semidirect
66. C11×D8SD16semidirect
198. D8#4324semidirect
216. C11#12355semidirect

Maximal subgroups

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

subgroupindex
#130814812
#130708392
#130679732
#130666732
#130665942
#130665772
C11×#22062
#1235511