Finite Group Databasebeta

← #14667293

Subgroups — #14667293

Order 2816.

322 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 71 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#13081622C211yesmaximal, characteristic, complemented
2#13070871C211yesmaximal, characteristic
3#13070653C211yesmaximal, characteristic
4#13066664C211yesmaximal, characteristic, complemented
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066579C211yesmaximal, characteristic, complemented
7C11×#1668C211yesmaximal, characteristic
8#10623101—21no—
9C11×#493C2211yescharacteristic
10C11×#460—21no—
11C8×Q8×C11C2211yescharacteristic
12C2×#66891—22no—
13C2×#66891—21no—
14#10622462—22no—
15#10622462—21no—
16#10622312—21no—
17#10622312C2211yescharacteristic
18C4×Dic44—21no—
19C4×Dic44C2211yescharacteristic
20C11×#335C2211yescharacteristic
21C11×#331—21no—
22#10622200—21no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24C4×C11⋊C16C2211yescharacteristic
25C2×C11×SD16—41no—
26C2×C11×D8—21no—
27C2×C11×D8—21no—
28C11×#127—21no—
29C4×Q8×C11D411yescharacteristic
30Q8×Dic11—41no—
31C2×Dic44—21no—
32C2×Dic44—22no—
33C2×Dic44D411yescharacteristic
34C2×Dic44D412yes—
35#66943—42no—
36#66943—41no—
37#66922—22no—
38#66922—21no—
39C4×Dic22—22no—
40C4×Dic22—21no—
41C11×C4⋊C8—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8D411yescharacteristic
44C11×#102—41no—
45C4×C8×C11—21no—
46C4×C8×C11C2311yescharacteristic
47#66891—44no—
48#66891—42no—
49#66882D411yescharacteristic
50#66880—22no—
51#66880—21no—
52C2×C11⋊C16—21no—
53C2×C11⋊C16—21no—
54#12330—111nomaximal, Sylow
55C2×Q8×C11D811yescharacteristic
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C2×Dic22—21no—
60C2×Dic22—22no—
61C11×SD16—82no—
62C11×D8—42no—
63C11×D8—41no—
64C11×D8—41no—
65C2×C8×C11—21no—
66C2×C8×C11—41no—
67C2×C8×C11C2×D411yescharacteristic
68C2×C8×C11C2×D411yescharacteristic
69C11×C4⋊C4—21no—
70C11×C4⋊C4D811yescharacteristic
71C42×C11—21no—
72C42×C11C2×D411yescharacteristic
73C4⋊Dic11—21no—
74C4⋊Dic11—42no—
75C4⋊Dic11—42no—
76C4⋊Dic11—41no—
77C4⋊Dic11—41no—
78Dic11⋊C4—42no—
79Dic11⋊C4—41no—
80C4×Dic11—42no—
81C4×Dic11—41no—
82Dic44—21no—
83Dic44—21no—
84Dic44—42no—
85Dic44—41no—
86Dic44—41no—
87Dic44—82no—
88C11⋊C16—22no—
89C11⋊C16—41no—
90#3395—111no—
91#2248—111no—
92#2207—111no—
93#1668D1111yescharacteristic
94#1362—111no—
95Q8⋊C16—111no—
96#1332—111no—
97C23×C11—81no—
98Q8×C11—21no—
99Q8×C11SD3212yescomplemented
100D4×C11—81no—
101D4×C11—81no—
102D4×C11—81no—
103D4×C11—81no—
104D4×C11—161no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11#12011yescharacteristic
108C2×C4×C11C2×D811yescharacteristic
109C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
110C2×Dic11—41no—
111C2×Dic11—42no—
112C2×Dic11—41no—
113Dic22—41no—
114Dic22—42no—
115Dic22—42no—
116Dic22—41no—
117C8×C11—21no—
118C8×C11—41no—
119C8×C11—81no—
120C8×C11#13511yescharacteristic
121C8×C11AGL(1,ℤ/8)11yescharacteristic
122#557—221no—
123C2×SD32—221no—
124C2×SD32—222no—
125#494—111no—
126#494—221no—
127#493C2×D1111yescharacteristic
128#462—222no—
129#462—221no—
130#460—21no—
131C8×Q8C2×D1111yescharacteristic
132C4×Q16—111no—
133C4×Q16—221no—
134C4⋊C16—111no—
135#357—221no—
136C4×C16—111no—
137#335C2×D1111yescharacteristic
138#331—21no—
139C22×C11—161no—
140C22×C11—161no—
141C22×C11—161no—
142C22×C11#44711yescharacteristic
143C4×C11—22no—
144C4×C11—21no—
145C4×C11—41no—
146C4×C11#44911yescharacteristic
147C4×C11#45311yescharacteristic
148C4×C11C2×SD3211yescharacteristic
149C4×C11#51011yescharacteristic
150Dic11—81no—
151Dic11—82no—
152Dic11—81no—
153C2×Q16—111no—
154C2×Q16—112no—
155C2×Q16—222no—
156C2×Q16—221no—
157C2×SD16—41no—
158C2×D8—21no—
159C2×D8—21no—
160C4⋊Q8—222no—
161C4⋊Q8—221no—
162#127—21no—
163#125—442no—
164#125—441no—
165C4×Q8—222no—
166C4×Q8—221no—
167C4×Q8—441no—
168C4×Q8C22⋊D1111yescharacteristic
169SD32—444no—
170SD32—442no—
171C2×C16—221no—
172C2×C16—221no—
173#107—111no—
174C4⋊C8—21no—
175C4⋊C8—21no—
176C4⋊C8C22⋊D1111yescharacteristic
177#103—222no—
178#103—221no—
179#102—41no—
180C4×C8—21no—
181C4×C8C22×D1111yescharacteristic
182C2×C11—321no—
183C2×C11#162111yescharacteristic
184C2×C11#218511yescharacteristic
185C2×C11#219311yescharacteristic
186C2×Q8—221no—
187C2×Q8—222no—
188C2×Q8#432311yescharacteristic
189C2×D4—41no—
190C2×D4—41no—
191C2×D4—41no—
192Q16—221no—
193Q16—221no—
194Q16—442no—
195Q16—441no—
196Q16—441no—
197Q16—882no—
198SD16—82no—
199D8—42no—
200D8—41no—
201D8—41no—
202C2×C8—21no—
203C2×C8—41no—
204C2×C8D4×D1111yescharacteristic
205C2×C8D4×D1111yescharacteristic
206C4⋊C4—21no—
207C4⋊C4—221no—
208C4⋊C4—442no—
209C4⋊C4—442no—
210C4⋊C4—442no—
211C4⋊C4—441no—
212C4⋊C4—441no—
213C4⋊C4—441no—
214C4⋊C4#432311yescharacteristic
215C42—21no—
216C42—442no—
217C42—441no—
218C42C2×C22⋊D1111yescharacteristic
219C16—222no—
220C16—441no—
221C11#1233011yescharacteristic, complemented, Sylow
222C23—81no—
223Q8—21no—
224Q8—441no—
225Q8—442no—
226Q8—442no—
227Q8—441no—
228Q8#6689112yescomplemented
229D4—81no—
230D4—81no—
231D4—81no—
232D4—81no—
233D4—161no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—441no—
237C2×C4—442no—
238C2×C4—441no—
239C2×C4C2×#432311yescharacteristic
240C2×C4#6699011yescharacteristic
241C2×C4#6700211yescharacteristic
242C8—21no—
243C8—41no—
244C8—81no—
245C8#6696711yescharacteristic
246C8#6696911yescharacteristic
247C22—161no—
248C22—161no—
249C22—161no—
250C22#1062264911yescharacteristic
251C4—22no—
252C4—21no—
253C4—41no—
254C4—881no—
255C4—882no—
256C4—881no—
257C4C2×#6689111yescharacteristic
258C4#1062278511yescharacteristic
259C4#1062280811yescharacteristic
260C4#1062281111yescharacteristic
261C2—321no—
262C2#1306767911yescharacteristic
263C2#1307053211yescharacteristic
264C2#1307057811yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1668C2
socleC22×C11#447
prime radicalC11×#493C22
hypercenter#1668D11
hypocenterC11#12330
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1668

Complements

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

NH ≅ G/Ntype
1. #13081622C2semidirect
4. #13066664C2semidirect
5. Q8⋊(C11⋊C16)C2semidirect
6. #13066579C2semidirect
99. Q8×C11SD32semidirect
221. C11#12330semidirect
228. Q8#66891semidirect

Maximal subgroups

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

subgroupindex
#130816222
#130708712
#130706532
#130666642
Q8⋊(C11⋊C16)2
#130665792
C11×#16682
#1233011