Finite Group Databasebeta

← #14667442

Subgroups — #14667442

Order 2816.

286 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 67 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#13070863C211yesmaximal, characteristic, complemented
2#13070666C211yesmaximal, characteristic, complemented
3#13068105C211yesmaximal, characteristic
4#13066668C211yesmaximal, characteristic, complemented
5#13066586C211yesmaximal, characteristic, complemented
6#13066574C211yesmaximal, characteristic
7C11×#3352C211yesmaximal, characteristic
8C11×#552—21no—
9C11×#499C2211yescharacteristic
10C11×#485—21no—
11C11×#484—21no—
12C11×#479—21no—
13C11×#470—21no—
14C4×C11×Q16C2211yescharacteristic
15C11×#436C2211yescharacteristic
16C11×#428—21no—
17C2×#66893—21no—
18#10622620—21no—
19#10622312C2211yescharacteristic
20#10622130—21no—
21#10622130—21no—
22#10622130—21no—
23#10622120—21no—
24C4⋊(C11⋊C16)C2211yescharacteristic
25#10622099C2211yescharacteristic
26#10622095C2211yescharacteristic
27C2×C11×Q16D411yescharacteristic
28C2×C11×M16—21no—
29C11×#126—41no—
30C11×#125—21no—
31C11×#125—41no—
32C11×#123—41no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C4×Q8×C11—21no—
36C4×D4×C11D411yescharacteristic
37C11×#117—21no—
38C11×#117—41no—
39C2×C11×C4⋊C4—21no—
40C2×Dic44—21no—
41C2×Dic44—21no—
42#66922—21no—
43C11×#107—21no—
44C11×#107D411yescharacteristic
45C11×#107D411yescharacteristic
46C11×#107D411yescharacteristic
47C11×#106—21no—
48C11×#106—21no—
49C11×C4⋊C8D411yescharacteristic
50C11×#103—21no—
51C11×#103—21no—
52C11×#103—21no—
53C11×C22⋊C8—21no—
54C4×C8×C11C2311yescharacteristic
55#66896—41no—
56#66893—42no—
57C2×C11⋊C16—21no—
58C2×C11⋊C16—21no—
59#66871—41no—
60C4⋊(C11⋊C8)—21no—
61#12351—111nomaximal, Sylow
62C2×Q8×C11—21no—
63C2×D4×C11D811yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—41no—
66C2×Dic22—41no—
67C11×Q16—21no—
68C11×Q16—21no—
69C11×M16—41no—
70C11×M16—41no—
71C2×C8×C11—21no—
72C2×C8×C11C2×D411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4D811yescharacteristic
84C11×C22⋊C4—21no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C42×C11—41no—
89C42×C11—41no—
90C42×C11C2×D411yescharacteristic
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C2×C11⋊C8—41no—
94Dic44—42no—
95Dic44—41no—
96Dic44—41no—
97C11⋊C16—41no—
98C11⋊C16—41no—
99#3352D1111yescharacteristic
100#2245—111no—
101#2209—111no—
102#1689—111no—
103#1363—111no—
104#1334—111no—
105#1330—111no—
106C23×C11—21no—
107Q8×C11—41no—
108Q8×C11—41no—
109D4×C11—41no—
110C2×C4×C11—21no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—82no—
118C2×C4×C11#12011yescharacteristic
119C2×C4×C11C2×D811yescharacteristic
120C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
121C2×Dic11—81no—
122Dic22—81no—
123Dic22—81no—
124C8×C11—21no—
125C8×C11—41no—
126C8×C11#13511yescharacteristic
127C8×C11AGL(1,ℤ/8)11yescharacteristic
128C11⋊C8—81no—
129#552—21no—
130C2×Q32—221no—
131#499C2×D1111yescharacteristic
132#494—111no—
133#485—21no—
134#484—21no—
135#479—21no—
136#474—221no—
137#470—21no—
138C4×Q16C2×D1111yescharacteristic
139#436C2×D1111yescharacteristic
140#428—21no—
141C4⋊C16—111no—
142#358—221no—
143#358—221no—
144#358—221no—
145#346—111no—
146#334—111no—
147#332—221no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11—41no—
151C22×C11#44711yescharacteristic
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—41no—
155C4×C11—81no—
156C4×C11—81no—
157C4×C11—81no—
158C4×C11—81no—
159C4×C11#44911yescharacteristic
160C4×C11#45411yescharacteristic
161Dic11—161no—
162C2×Q16—221no—
163C2×Q16—221no—
164C2×Q16C22⋊D1111yescharacteristic
165C2×M16—21no—
166C4⋊Q8—221no—
167#126—41no—
168#125—21no—
169#125—41no—
170#123—41no—
171C22⋊Q8—21no—
172C22⋊Q8—21no—
173C4×Q8—21no—
174C4×D4C22⋊D1111yescharacteristic
175#117—21no—
176#117—41no—
177C2×C4⋊C4—21no—
178Q32—442no—
179C2×C16—221no—
180C2×C16—221no—
181#107—21no—
182#107—441no—
183#107C22⋊D1111yescharacteristic
184#107C22⋊D1111yescharacteristic
185#107C22⋊D1111yescharacteristic
186#106—21no—
187#106—21no—
188C4⋊C8—221no—
189C4⋊C8C22⋊D1111yescharacteristic
190#103—21no—
191#103—21no—
192#103—21no—
193#102—441no—
194C22⋊C8—21no—
195C4×C8C22×D1111yescharacteristic
196C2×C11—81no—
197C2×C11#162511yescharacteristic
198C2×C11#219111yescharacteristic
199C2×C11#219511yescharacteristic
200C2×Q8—21no—
201C2×Q8—441no—
202C2×D4#432311yescharacteristic
203C22×C4—21no—
204C22×C4—41no—
205Q16—21no—
206Q16—21no—
207Q16—442no—
208Q16—441no—
209Q16—441no—
210M16—41no—
211M16—41no—
212C2×C8—21no—
213C2×C8—441no—
214C2×C8C2×C22⋊D1111yescharacteristic
215C2×C8C2×C22⋊D1111yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—441no—
226C4⋊C4—441no—
227C4⋊C4#432311yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—41no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C42—41no—
233C42—41no—
234C42C2×C22⋊D1111yescharacteristic
235C16—441no—
236C16—441no—
237C11#1235111yescharacteristic, complemented, Sylow
238C23—21no—
239Q8—41no—
240Q8—41no—
241Q8—881no—
242Q8—881no—
243D4—41no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—82no—
252C2×C4—881no—
253C2×C4C2×#432311yescharacteristic
254C2×C4#6698511yescharacteristic
255C2×C4#6700611yescharacteristic
256C8—21no—
257C8—41no—
258C8—881no—
259C8#6700211yescharacteristic
260C8#6700311yescharacteristic
261C22—41no—
262C22—41no—
263C22—41no—
264C22#1062283011yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—81no—
269C4—81no—
270C4—81no—
271C4—81no—
272C4—1761no—
273C4#1062285111yescharacteristic
274C4#1062285811yescharacteristic
275C2—81no—
276C2#1306770511yescharacteristic
277C2#1307056711yescharacteristic
278C2#1307059411yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#3352C2
socleC22×C11#447
prime radicalC2×D4×C11D8
hypercenter#3352D11
hypocenterC11#12351
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #436 ◁ #3352

Complements

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

NH ≅ G/Ntype
1. #13070863C2semidirect
2. #13070666C2semidirect
4. #13066668C2semidirect
5. #13066586C2semidirect
237. C11#12351semidirect

Maximal subgroups

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

subgroupindex
#130708632
#130706662
#130681052
#130666682
#130665862
#130665742
C11×#33522
#1235111