Finite Group Databasebeta

← #14667515

Subgroups — #14667515

Order 2816.

294 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 65 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#13081581C211yesmaximal, characteristic, complemented
2#13070858C211yesmaximal, characteristic
3#13070656C211yesmaximal, characteristic
4#13068101C211yesmaximal, characteristic
5#13066669C211yesmaximal, characteristic, complemented
6#13066599C211yesmaximal, characteristic, complemented
7C11×#1334C211yesmaximal, characteristic, complemented
8#10623100—21no—
9C4×C11×Q16C2211yescharacteristic
10#10622797—21no—
11C2×#66892—21no—
12#10622635—21no—
13#10622489—21no—
14#10622461—21no—
15#10622409—21no—
16#10622407—21no—
17#10622308C2211yescharacteristic
18#10622296C2211yescharacteristic
19#10622292C2211yescharacteristic
20C11×#346C2211yescharacteristic
21C11×#334C2211yescharacteristic
22#10622147—21no—
23#10622147—21no—
24#10622129—21no—
25#10622123—21no—
26C4⋊(C11⋊C16)C2211yescharacteristic
27C2×C11×Q16D411yescharacteristic
28C4×Q8×C11—21no—
29Q8×Dic11—21no—
30Q8×Dic11—21no—
31C2×D88—21no—
32C2×D88—21no—
33C2×#4314—41no—
34#66943—21no—
35#66943—41no—
36#66941—21no—
37#66941—41no—
38#66927—21no—
39#66923—21no—
40#66923—41no—
41C4×Dic22—41no—
42C4×Dic22D411yescharacteristic
43C2×C11×C16—21no—
44C11×#107D411yescharacteristic
45C11×C4⋊C8—21no—
46C11×#103—21no—
47C4×C8×C11C2311yescharacteristic
48#66899—21no—
49#66899—21no—
50#66892—42no—
51#66885—41no—
52#66882D411yescharacteristic
53#66882D411yescharacteristic
54#66881—21no—
55#66879—21no—
56Dic11⋊C8—21no—
57C2×C11⋊C16—21no—
58#66872—21no—
59#66871—21no—
60C4⋊(C11⋊C8)D411yescharacteristic
61#12361—111nomaximal, Sylow
62C2×Q8×C11—21no—
63C2×D44—41no—
64C2×D44—41no—
65C2×D44—41no—
66C2×Dic22—41no—
67C2×Dic22D811yescharacteristic
68C11×Q16—21no—
69C11×Q16SD1612yescomplemented
70C2×C8×C11—41no—
71C2×C8×C11C2×D411yescharacteristic
72C2×C8×C11C2×D411yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4—41no—
75C42×C11—41no—
76C42×C11C2×D411yescharacteristic
77C4⋊Dic11—21no—
78C4⋊Dic11—21no—
79C4⋊Dic11—41no—
80C4⋊Dic11—41no—
81C4⋊Dic11—41no—
82C4⋊Dic11D811yescharacteristic
83Dic11⋊C4—21no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88C4×Dic11—21no—
89C4×Dic11—41no—
90C4×Dic11—41no—
91C2×C11⋊C8—21no—
92D88—42no—
93D88—41no—
94D88—41no—
95#4314—82no—
96C11×C16—41no—
97C11⋊C16—41no—
98#3390—111no—
99#2244—111no—
100#2207—111no—
101#1688—111no—
102#1363—111no—
103#1338—111no—
104#1334D1111yescharacteristic, complemented
105C22×D11—81no—
106Q8×C11—22no—
107Q8×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11#12011yescharacteristic
111C2×C4×C11C2×D811yescharacteristic
112C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—41no—
116C2×Dic11—41no—
117D44—81no—
118D44—81no—
119D44—81no—
120D44—81no—
121D44—161no—
122Dic22—41no—
123Dic22—82no—
124C8×C11—21no—
125C8×C11—81no—
126C8×C11C2×SD1611yescharacteristic
127C8×C11#13711yescharacteristic
128C11⋊C8—41no—
129#557—221no—
130C2×SD32—221no—
131#501—221no—
132#499—111no—
133#493—111no—
134#479—221no—
135#479—221no—
136#477—221no—
137#460—221no—
138#446—111no—
139#441—221no—
140C4×Q16C2×D1111yescharacteristic
141C4⋊C16—111no—
142#357—221no—
143#357—221no—
144#357—221no—
145#346C2×D1111yescharacteristic
146#334C2×D1111yescharacteristic
147#331—221no—
148C22×C11#44711yescharacteristic
149C2×D11—161no—
150C2×D11—161no—
151C2×D11—161no—
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—42no—
155C4×C11—81no—
156C4×C11#44811yescharacteristic
157C4×C11#45411yescharacteristic
158Dic11—41no—
159Dic11—41no—
160Dic11—81no—
161Dic11—81no—
162C2×Q16D4411yescharacteristic
163C2×SD16—441no—
164C2×D8—221no—
165C2×D8—221no—
166C4⋊Q8—221no—
167C4⋊Q8—441no—
168#127—221no—
169#125—221no—
170#125—221no—
171#125—441no—
172#125—441no—
173C4×Q8—21no—
174C4×Q8—111no—
175C4×Q8—221no—
176C4×Q8—221no—
177C4×Q8—441no—
178SD32—442no—
179C2×C16—21no—
180C2×C16—221no—
181#107—111no—
182#107—111no—
183#107—221no—
184#107D4411yescharacteristic
185#106—221no—
186#106—221no—
187C4⋊C8—21no—
188C4⋊C8—111no—
189C4⋊C8—221no—
190#103—21no—
191#103—221no—
192#103—221no—
193#102—441no—
194#97—221no—
195C4×C8C22×D1111yescharacteristic
196C2×C11#162711yescharacteristic
197C2×C11#219011yescharacteristic
198C2×C11#219311yescharacteristic
199D11—321no—
200C2×Q8—21no—
201C2×Q8—111no—
202C2×Q8—441no—
203C2×D4—441no—
204C2×D4—441no—
205C2×D4—441no—
206Q16—21no—
207Q16#431412yescomplemented
208SD16—882no—
209D8—442no—
210D8—441no—
211D8—441no—
212C2×C8—41no—
213C2×C8—221no—
214C2×C8C2×D4411yescharacteristic
215C2×C8D4×D1111yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—41no—
218C4⋊C4—111no—
219C4⋊C4—221no—
220C4⋊C4—221no—
221C4⋊C4—221no—
222C4⋊C4—441no—
223C4⋊C4—441no—
224C4⋊C4—441no—
225C4⋊C4—441no—
226C4⋊C4—441no—
227C4⋊C4—441no—
228C4⋊C4—441no—
229C42—41no—
230C42—221no—
231C42—441no—
232C42—441no—
233C42D4×D1111yescharacteristic
234C16—41no—
235C16—441no—
236C11#1236111yescharacteristic, complemented, Sylow
237C23—881no—
238Q8—22no—
239Q8—41no—
240Q8—441no—
241Q8—882no—
242D4—881no—
243D4—881no—
244D4—881no—
245D4—881no—
246D4—1761no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—221no—
250C2×C4—221no—
251C2×C4—441no—
252C2×C4—441no—
253C2×C4#6693511yescharacteristic
254C2×C4D8×D1111yescharacteristic
255C2×C4#6696711yescharacteristic
256C8—21no—
257C8—81no—
258C8—441no—
259C8C2×#431411yescharacteristic
260C8#6696211yescharacteristic
261C22—1761no—
262C22—1761no—
263C22—1761no—
264C22#1062238611yescharacteristic
265C4—21no—
266C4—21no—
267C4—42no—
268C4—81no—
269C4—441no—
270C4—441no—
271C4—881no—
272C4—881no—
273C4#1062235111yescharacteristic
274C4#1062244011yescharacteristic
275C2—3521no—
276C2#1306772211yescharacteristic
277C2#1307056311yescharacteristic
278C2#1307058311yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1334C2
socleC22×C11#447
prime radical#10622308C22
hypercenter#1334D11
hypocenterC11#12361
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1334

Complements

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

NH ≅ G/Ntype
1. #13081581C2semidirect
5. #13066669C2semidirect
6. #13066599C2semidirect
7. C11×#1334C2semidirect
69. C11×Q16SD16semidirect
104. #1334D11semidirect
207. Q16#4314semidirect
236. C11#12361semidirect

Maximal subgroups

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

subgroupindex
#130815812
#130708582
#130706562
#130681012
#130666692
#130665992
C11×#13342
#1236111