Finite Group Databasebeta

← #14667330

Subgroups — #14667330

Order 2816.

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

normal subgroups only

This group has 312 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#13070868C211yesmaximal, characteristic, complemented
2#13070661C211yesmaximal, characteristic
3#13067986C211yesmaximal, characteristic, complemented
4#13066665C211yesmaximal, characteristic, complemented
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066577C211yesmaximal, characteristic
7C11×#3393C211yesmaximal, characteristic
8C11×#556—21no—
9C11×#495—21no—
10C11×#494C2211yescharacteristic
11C11×#464—22no—
12C11×#461—21no—
13C8×Q8×C11C2211yescharacteristic
14C4×C11×Q16—21no—
15C4×C11×D8C2211yescharacteristic
16C2×#66893—22no—
17C2×#66891—21no—
18#10622633—21no—
19#10622312C2211yescharacteristic
20#10622130—21no—
21#10622120—21no—
22C4⋊(C11⋊C16)C2211yescharacteristic
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16D412yes—
27C2×C11×SD16—22no—
28C2×C11×D8D411yescharacteristic
29C11×C4⋊Q8—21no—
30C11×#126—42no—
31C11×#124—22no—
32C11×C22⋊Q8—41no—
33C4×Q8×C11—22no—
34C4×Q8×C11D411yescharacteristic
35C4×D4×C11—21no—
36C11×#117—41no—
37C2×Dic44—21no—
38C2×Dic44—21no—
39#66922—21no—
40C11×#107D411yescharacteristic
41C11×C4⋊C8—21no—
42C11×C4⋊C8D411yescharacteristic
43C11×#103—22no—
44C11×#102—21no—
45C4×C8×C11—21no—
46C4×C8×C11C2311yescharacteristic
47#66899—41no—
48#66893—44no—
49#66891—42no—
50C2×C11⋊C16—21no—
51C2×C11⋊C16—21no—
52#66872—41no—
53C4⋊(C11⋊C8)—21no—
54#12335—111nomaximal, Sylow
55C2×Q8×C11—22no—
56C2×Q8×C11D811yescharacteristic
57C2×D4×C11—21no—
58C22×C4×C11—41no—
59C2×Dic22—41no—
60C11×Q16—41no—
61C11×Q16—41no—
62C11×Q16—42no—
63C11×SD16—82no—
64C11×D8—21no—
65C11×D8—21no—
66C2×C8×C11—21no—
67C2×C8×C11C2×D411yescharacteristic
68C2×C8×C11C2×D411yescharacteristic
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4D811yescharacteristic
75C11×C22⋊C4—42no—
76C11×C22⋊C4—42no—
77C11×C22⋊C4—41no—
78C42×C11—21no—
79C42×C11—42no—
80C42×C11C2×D411yescharacteristic
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83C2×C11⋊C8—41no—
84Dic44—42no—
85Dic44—41no—
86Dic44—41no—
87C11⋊C16—22no—
88C11⋊C16—41no—
89#3393D1111yescharacteristic
90#2247—111no—
91#2208—111no—
92#1670—111no—
93#1362—111no—
94Q8⋊C16—111no—
95#1331—111no—
96C23×C11—41no—
97Q8×C11—21no—
98Q8×C11—21no—
99Q8×C11—42no—
100Q8×C11—42no—
101D4×C11—41no—
102D4×C11—41no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11—81no—
108C2×C4×C11—81no—
109C2×C4×C11#12011yescharacteristic
110C2×C4×C11C2×D811yescharacteristic
111C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
112C2×Dic11—81no—
113Dic22—81no—
114Dic22—81no—
115C8×C11—21no—
116C8×C11—41no—
117C8×C11#13511yescharacteristic
118C8×C11AGL(1,ℤ/8)11yescharacteristic
119C11⋊C8—81no—
120#556—21no—
121C2×Q32—222no—
122C2×SD32—221no—
123#495—21no—
124#494—111no—
125#494C2×D1111yescharacteristic
126#475—221no—
127#464—22no—
128#461—21no—
129C8×Q8C2×D1111yescharacteristic
130C4×Q16—21no—
131C4×D8C2×D1111yescharacteristic
132C4⋊C16—111no—
133#358—221no—
134C4×C16—111no—
135#335—111no—
136#332—221no—
137C22×C11—81no—
138C22×C11—81no—
139C22×C11—81no—
140C22×C11#44711yescharacteristic
141C4×C11—21no—
142C4×C11—41no—
143C4×C11—41no—
144C4×C11—82no—
145C4×C11—81no—
146C4×C11#44911yescharacteristic
147C4×C11#45311yescharacteristic
148C4×C11#50811yescharacteristic
149C4×C11#51011yescharacteristic
150Dic11—161no—
151C2×Q16—21no—
152C2×Q16—221no—
153C2×Q16—221no—
154C2×Q16C22⋊D1112yes—
155C2×SD16—22no—
156C2×D8C22⋊D1111yescharacteristic
157C4⋊Q8—21no—
158C4⋊Q8—221no—
159#126—42no—
160#124—22no—
161C22⋊Q8—41no—
162C4×Q8—22no—
163C4×Q8C22⋊D1111yescharacteristic
164C4×D4—21no—
165#117—41no—
166Q32—444no—
167SD32—442no—
168C2×C16—221no—
169C2×C16—221no—
170#107C22⋊D1111yescharacteristic
171#106—441no—
172C4⋊C8—21no—
173C4⋊C8—221no—
174C4⋊C8C22⋊D1111yescharacteristic
175#103—22no—
176#103—441no—
177#102—21no—
178C4×C8—21no—
179C4×C8C22×D1111yescharacteristic
180C2×C11—161no—
181C2×C11#162111yescharacteristic
182C2×C11#218911yescharacteristic
183C2×C11#219511yescharacteristic
184C2×Q8—22no—
185C2×Q8—441no—
186C2×Q8#432311yescharacteristic
187C2×D4—21no—
188C22×C4—41no—
189Q16—42no—
190Q16—41no—
191Q16—41no—
192Q16—442no—
193Q16—441no—
194Q16—441no—
195SD16—82no—
196D8—21no—
197D8—21no—
198C2×C8—21no—
199C2×C8—441no—
200C2×C8C2×C22⋊D1111yescharacteristic
201C2×C8C2×C22⋊D1111yescharacteristic
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—42no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—441no—
208C4⋊C4—441no—
209C4⋊C4#432311yescharacteristic
210C22⋊C4—42no—
211C22⋊C4—42no—
212C22⋊C4—41no—
213C42—21no—
214C42—42no—
215C42C2×C22⋊D1111yescharacteristic
216C16—222no—
217C16—441no—
218C11#1233511yescharacteristic, complemented, Sylow
219C23—41no—
220Q8—21no—
221Q8—21no—
222Q8—42no—
223Q8—42no—
224Q8—881no—
225Q8—881no—
226D4—41no—
227D4—41no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—881no—
235C2×C4C2×#432311yescharacteristic
236C2×C4#6698511yescharacteristic
237C2×C4#6700611yescharacteristic
238C8—21no—
239C8—41no—
240C8—881no—
241C8#6700211yescharacteristic
242C8#6700311yescharacteristic
243C22—81no—
244C22—81no—
245C22—81no—
246C22#1062283011yescharacteristic
247C4—21no—
248C4—41no—
249C4—41no—
250C4—82no—
251C4—81no—
252C4—1761no—
253C4#1062280711yescharacteristic
254C4#1062280811yescharacteristic
255C4#1062285111yescharacteristic
256C4#1062285411yescharacteristic
257C2—161no—
258C2#1306768111yescharacteristic
259C2#1307055611yescharacteristic
260C2#1307059411yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#3393C2
socleC22×C11#447
prime radicalC2×C11×D8D4
hypercenter#3393D11
hypocenterC11#12335
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3393

Complements

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

NH ≅ G/Ntype
1. #13070868C2semidirect
3. #13067986C2semidirect
4. #13066665C2semidirect
5. Q8⋊(C11⋊C16)C2semidirect
218. C11#12335semidirect

Maximal subgroups

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

subgroupindex
#130708682
#130706612
#130679862
#130666652
Q8⋊(C11⋊C16)2
#130665772
C11×#33932
#1233511