Finite Group Databasebeta

← #14667232

Subgroups — #14667232

Order 2816.

384 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 75 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#13070871C211yesmaximal, characteristic, complemented
2#13070666C211yesmaximal, characteristic, complemented
3#13067981C211yesmaximal, characteristic, complemented
4#13066662C211yesmaximal, characteristic, complemented
5#13066580C211yesmaximal, characteristic, complemented
6D4⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
7C11×#3287C211yesmaximal, characteristic
8C2×C11×#135—21no—
9C11×#550—21no—
10C11×#493C2211yescharacteristic
11C11×#466—21no—
12C11×#460—21no—
13C11×#449—22no—
14C4×C11×Q16C2211yescharacteristic
15C8×D4×C11C2211yescharacteristic
16C2×#66893—21no—
17C2×#66891—22no—
18#10622620—21no—
19#10622312C2211yescharacteristic
20#10622130—21no—
21#10622120—21no—
22C4⋊(C11⋊C16)C2211yescharacteristic
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×#41—22no—
26C11×#135—42no—
27C11×#135—42no—
28C2×C11×Q16D411yescharacteristic
29C2×C11×SD16—22no—
30C2×C11×D8—21no—
31C2×C11×D8D412yes—
32C22×C8×C11—21no—
33C11×#127—21no—
34C11×#127—41no—
35C11×#121—22no—
36C11×#121—42no—
37C4×Q8×C11—21no—
38C4×D4×C11—41no—
39C4×D4×C11D411yescharacteristic
40C2×Dic44—21no—
41C2×Dic44—21no—
42#66922—21no—
43C11×#107D411yescharacteristic
44C11×C4⋊C8D411yescharacteristic
45C11×#103—21no—
46C11×#102—22no—
47C11×C22⋊C8—21no—
48C4×C8×C11C2311yescharacteristic
49#66896—41no—
50#66893—42no—
51#66891—44no—
52C2×C11⋊C16—21no—
53C2×C11⋊C16—21no—
54#66871—41no—
55C4⋊(C11⋊C8)—21no—
56#12321—111nomaximal, Sylow
57C11×#41—44no—
58C11×#41—82no—
59C2×Q8×C11—21no—
60C2×D4×C11—22no—
61C2×D4×C11—42no—
62C2×D4×C11—42no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11D811yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11—42no—
68C2×Dic22—41no—
69C11×Q16—21no—
70C11×Q16D812yes—
71C11×SD16—44no—
72C11×D8—41no—
73C11×D8—41no—
74C11×D8—42no—
75C2×C8×C11—21no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11C2×D411yescharacteristic
79C2×C8×C11C2×D411yescharacteristic
80C11×C4⋊C4—21no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4D811yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—42no—
85C42×C11—41no—
86C42×C11C2×D411yescharacteristic
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89C2×C11⋊C8—41no—
90Dic44—42no—
91Dic44—41no—
92Dic44—41no—
93C11⋊C16—22no—
94C11⋊C16—41no—
95#3287D1111yescharacteristic
96#2248—111no—
97#2209—111no—
98#1669—111no—
99#1361—111no—
100#1332—111no—
101D4⋊C16—111no—
102C23×C11—21no—
103C23×C11—42no—
104Q8×C11—22no—
105Q8×C11—41no—
106D4×C11—21no—
107D4×C11—21no—
108D4×C11—42no—
109D4×C11—42no—
110D4×C11—84no—
111D4×C11—81no—
112D4×C11—81no—
113D4×C11—161no—
114D4×C11—162no—
115C2×C4×C11—21no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—84no—
121C2×C4×C11#12011yescharacteristic
122C2×C4×C11C2×D811yescharacteristic
123C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
124C2×Dic11—81no—
125Dic22—81no—
126Dic22—81no—
127C8×C11—21no—
128C8×C11—41no—
129C8×C11C2×D811yescharacteristic
130C8×C11AGL(1,ℤ/8)11yescharacteristic
131C11⋊C8—81no—
132C2×#135—21no—
133#550—21no—
134C2×Q32—221no—
135C2×SD32—222no—
136#494—111no—
137#493C2×D1111yescharacteristic
138#474—221no—
139#466—21no—
140#460—21no—
141#449—22no—
142C4×Q16C2×D1111yescharacteristic
143C8×D4C2×D1111yescharacteristic
144C4⋊C16—111no—
145#358—221no—
146C4×C16—111no—
147#335—111no—
148#332—221no—
149C22×C11—41no—
150C22×C11—41no—
151C22×C11—41no—
152C22×C11—82no—
153C22×C11—82no—
154C22×C11—82no—
155C22×C11#44711yescharacteristic
156C4×C11—21no—
157C4×C11—41no—
158C4×C11—42no—
159C4×C11—81no—
160C4×C11#44711yescharacteristic
161C4×C11#45311yescharacteristic
162C4×C11#50811yescharacteristic
163C4×C11#51011yescharacteristic
164Dic11—161no—
165C2×#41—22no—
166#135—42no—
167#135—42no—
168C2×Q16—221no—
169C2×Q16—221no—
170C2×Q16C22⋊D1111yescharacteristic
171C2×SD16—22no—
172C2×D8—21no—
173C2×D8C22⋊D1112yes—
174C22×C8—21no—
175C4⋊Q8—221no—
176#127—21no—
177#127—41no—
178#121—22no—
179#121—42no—
180C4×Q8—21no—
181C4×D4—41no—
182C4×D4C22⋊D1111yescharacteristic
183Q32—442no—
184SD32—444no—
185C2×C16—221no—
186C2×C16—221no—
187#107—441no—
188#107C22⋊D1111yescharacteristic
189C4⋊C8—221no—
190C4⋊C8C22⋊D1111yescharacteristic
191#103—21no—
192#102—22no—
193#102—441no—
194C22⋊C8—21no—
195C4×C8C22×D1111yescharacteristic
196C2×C11—81no—
197C2×C11—162no—
198C2×C11#161911yescharacteristic
199C2×C11#218911yescharacteristic
200C2×C11#219411yescharacteristic
201#41—44no—
202#41—82no—
203C2×Q8—21no—
204C2×Q8—441no—
205C2×D4—22no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4#432311yescharacteristic
211C22×C4—21no—
212C22×C4—42no—
213Q16—21no—
214Q16—442no—
215Q16—441no—
216Q16—441no—
217Q16#432312yes—
218SD16—44no—
219D8—42no—
220D8—41no—
221D8—41no—
222C2×C8—21no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—441no—
226C2×C8C2×C22⋊D1111yescharacteristic
227C2×C8C2×C22⋊D1111yescharacteristic
228C4⋊C4—21no—
229C4⋊C4—41no—
230C4⋊C4—441no—
231C4⋊C4—441no—
232C4⋊C4#432311yescharacteristic
233C22⋊C4—21no—
234C22⋊C4—42no—
235C42—41no—
236C42C2×C22⋊D1111yescharacteristic
237C16—222no—
238C16—441no—
239C11#1232111yescharacteristic, complemented, Sylow
240C23—21no—
241C23—42no—
242Q8—22no—
243Q8—41no—
244Q8—881no—
245Q8—881no—
246D4—21no—
247D4—21no—
248D4—42no—
249D4—42no—
250D4—84no—
251D4—81no—
252D4—81no—
253D4—161no—
254D4—162no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—84no—
261C2×C4—881no—
262C2×C4C2×#432311yescharacteristic
263C2×C4#6698511yescharacteristic
264C2×C4#6700611yescharacteristic
265C8—21no—
266C8—41no—
267C8—881no—
268C8C2×#432311yescharacteristic
269C8#6698511yescharacteristic
270C22—41no—
271C22—41no—
272C22—41no—
273C22—82no—
274C22—82no—
275C22—82no—
276C22#1062283011yescharacteristic
277C4—21no—
278C4—41no—
279C4—42no—
280C4—81no—
281C4—1761no—
282C4#1062280711yescharacteristic
283C4#1062280811yescharacteristic
284C4#1062283011yescharacteristic
285C4#1062285411yescharacteristic
286C2—81no—
287C2—162no—
288C2#1306767011yescharacteristic
289C2#1307055611yescharacteristic
290C2#1307058711yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
Fitting, prime radicalC11×#3287C2
socleC22×C11#447
hypercenter#3287D11
hypocenterC11#12321
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #3287

Complements

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

NH ≅ G/Ntype
1. #13070871C2semidirect
2. #13070666C2semidirect
3. #13067981C2semidirect
4. #13066662C2semidirect
5. #13066580C2semidirect
6. D4⋊(C11⋊C16)C2semidirect
239. C11#12321semidirect

Maximal subgroups

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

subgroupindex
#130708712
#130706662
#130679812
#130666622
#130665802
D4⋊(C11⋊C16)2
C11×#32872
#1232111