Finite Group Databasebeta

← #14667331

Subgroups — #14667331

Order 2816.

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

normal subgroups only

This group has 312 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#13081606C211yesmaximal, characteristic
2#13070868C211yesmaximal, characteristic, complemented
3#13070662C211yesmaximal, characteristic
4#13067987C211yesmaximal, characteristic, complemented
5#13066594C211yesmaximal, characteristic, complemented
6#13066576C211yesmaximal, characteristic
7C11×#1362C211yesmaximal, characteristic, complemented
8#10623263—21no—
9C11×#494C2211yescharacteristic
10#10622804—21no—
11#10622798—22no—
12Q16×Dic11—21no—
13C2×#66893—22no—
14#10622696—21no—
15C2×#66864—21no—
16#10622464—21no—
17#10622312C2211yescharacteristic
18C4×D88C2211yescharacteristic
19C8×Dic22C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C11×#335C2211yescharacteristic
22#10622141—21no—
23#10622124—21no—
24C4×C11⋊C16C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16D412yes—
27C11×C4⋊Q8—21no—
28#67000—22no—
29Q8×Dic11—22no—
30C2×#4325—22no—
31C2×Dic44—21no—
32C2×Dic44—21no—
33C2×D88D411yescharacteristic
34#66951—42no—
35#66950—41no—
36#66945—41no—
37C4×D44—21no—
38#66922—21no—
39C4×Dic22D411yescharacteristic
40C2×C11×C16—21no—
41C11×C4⋊C8—21no—
42C4×C8×C11C2311yescharacteristic
43#66899—22no—
44#66893—44no—
45#66885—21no—
46#66882D411yescharacteristic
47#66881—41no—
48#66880—41no—
49Dic11⋊C8—21no—
50C8×Dic11—21no—
51C2×C11⋊C16—21no—
52C4⋊(C11⋊C8)D411yescharacteristic
53#66864—42no—
54#12335—111nomaximal, Sylow
55C2×Q8×C11—22no—
56C2×D44—21no—
57C2×C4×D11—41no—
58C2×Dic22—41no—
59C2×Dic22D811yescharacteristic
60C11×Q16—41no—
61C11×Q16—41no—
62C11×Q16—42no—
63C2×C8×C11—41no—
64C2×C8×C11C2×D411yescharacteristic
65C2×C8×C11C2×D411yescharacteristic
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C42×C11C2×D411yescharacteristic
69#4325—82no—
70(C2×D11)⋊C4—42no—
71(C2×D11)⋊C4—42no—
72(C2×D11)⋊C4—41no—
73C4⋊Dic11—21no—
74C4⋊Dic11—42no—
75C4⋊Dic11—41no—
76C4⋊Dic11—41no—
77C4⋊Dic11D811yescharacteristic
78Dic11⋊C4—21no—
79C4×Dic11—21no—
80C4×Dic11—42no—
81C2×C11⋊C8—21no—
82Dic44—42no—
83Dic44—41no—
84Dic44—41no—
85D88—21no—
86D88—21no—
87C11×C16—41no—
88C11⋊C16—22no—
89#3393—111no—
90#2247—111no—
91#2208—111no—
92#1670—111no—
93#1362D1111yescharacteristic, complemented
94Q8⋊C16—111no—
95#1331—111no—
96C22×D11—41no—
97Q8×C11—42no—
98Q8×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11#12011yescharacteristic
101C2×C4×C11C2×D811yescharacteristic
102C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
103C2×Dic11—21no—
104C2×Dic11—21no—
105C2×Dic11—41no—
106C2×Dic11—81no—
107D44—41no—
108D44—41no—
109C4×D11—81no—
110C4×D11—81no—
111Dic22—21no—
112Dic22—21no—
113Dic22—81no—
114Dic22—81no—
115C8×C11—21no—
116C8×C11—81no—
117C8×C11#13511yescharacteristic
118C8×C11AGL(1,ℤ/8)11yescharacteristic
119C11⋊C8—41no—
120#556—221no—
121C2×Q32—222no—
122C2×SD32—221no—
123#495—221no—
124#494—111no—
125#494C2×D1111yescharacteristic
126#475—221no—
127#464—222no—
128#461—221no—
129C8×Q8—111no—
130C4×Q16—221no—
131C4×D8—111no—
132C4⋊C16C2×D1111yescharacteristic
133#358—221no—
134C4×C16—111no—
135#335C2×D1111yescharacteristic
136#332—221no—
137C22×C11#44711yescharacteristic
138C2×D11—81no—
139C2×D11—81no—
140C2×D11—81no—
141C4×C11—21no—
142C4×C11—82no—
143C4×C11#44911yescharacteristic
144C4×C11#45311yescharacteristic
145C4×C11#50811yescharacteristic
146C4×C11#51011yescharacteristic
147Dic11—41no—
148Dic11—41no—
149Dic11—81no—
150Dic11—161no—
151C2×Q16—21no—
152C2×Q16—221no—
153C2×Q16—221no—
154C2×Q16D4412yes—
155C2×SD16—222no—
156C2×D8—111no—
157C4⋊Q8—21no—
158C4⋊Q8—221no—
159#126—442no—
160#124—222no—
161C22⋊Q8—441no—
162C4×Q8—111no—
163C4×Q8—222no—
164C4×D4—221no—
165#117—441no—
166Q32—444no—
167SD32—442no—
168C2×C16—21no—
169C2×C16—221no—
170#107—111no—
171#106—441no—
172C4⋊C8—21no—
173C4⋊C8—111no—
174C4⋊C8—221no—
175#103—222no—
176#103—441no—
177#102—221no—
178C4×C8—221no—
179C4×C8C22×D1111yescharacteristic
180C2×C11#162111yescharacteristic
181C2×C11#218911yescharacteristic
182C2×C11#219511yescharacteristic
183D11—161no—
184C2×Q8—22no—
185C2×Q8—111no—
186C2×Q8—441no—
187C2×D4—221no—
188C22×C4—441no—
189Q16—42no—
190Q16—41no—
191Q16—41no—
192Q16—442no—
193Q16—441no—
194Q16—441no—
195SD16—882no—
196D8—221no—
197D8—221no—
198C2×C8—41no—
199C2×C8—221no—
200C2×C8C2×D4411yescharacteristic
201C2×C8D4×D1111yescharacteristic
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—111no—
205C4⋊C4—221no—
206C4⋊C4—221no—
207C4⋊C4—442no—
208C4⋊C4—441no—
209C4⋊C4—441no—
210C22⋊C4—442no—
211C22⋊C4—442no—
212C22⋊C4—441no—
213C42—221no—
214C42—442no—
215C42D4×D1111yescharacteristic
216C16—41no—
217C16—222no—
218C11#1233511yescharacteristic, complemented, Sylow
219C23—441no—
220Q8—42no—
221Q8—42no—
222Q8—221no—
223Q8—221no—
224Q8—881no—
225Q8—881no—
226D4—441no—
227D4—441no—
228C2×C4—42no—
229C2×C4—221no—
230C2×C4—221no—
231C2×C4—441no—
232C2×C4—881no—
233C2×C4—881no—
234C2×C4—881no—
235C2×C4#6693511yescharacteristic
236C2×C4D8×D1111yescharacteristic
237C2×C4#6696711yescharacteristic
238C8—21no—
239C8—81no—
240C8—441no—
241C8#6696411yescharacteristic
242C8#6696911yescharacteristic
243C22—881no—
244C22—881no—
245C22—881no—
246C22#1062238611yescharacteristic
247C4—21no—
248C4—82no—
249C4—441no—
250C4—441no—
251C4—881no—
252C4—1761no—
253C4#1062236011yescharacteristic
254C4#1062239411yescharacteristic
255C4#1062252911yescharacteristic
256C4#1062253111yescharacteristic
257C2—1761no—
258C2#1306768211yescharacteristic
259C2#1307055911yescharacteristic
260C2#1307059711yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1362C2
socleC22×C11#447
prime radicalC2×D88D4
hypercenter#1362D11
hypocenterC11#12335
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
2. #13070868C2semidirect
4. #13067987C2semidirect
5. #13066594C2semidirect
7. C11×#1362C2semidirect
93. #1362D11semidirect
218. C11#12335semidirect

Maximal subgroups

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

subgroupindex
#130816062
#130708682
#130706622
#130679872
#130665942
#130665762
C11×#13622
#1233511