Finite Group Databasebeta

← #14667328

Subgroups — #14667328

Order 2816.

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

normal subgroups only

This group has 312 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#13081605C211yesmaximal, characteristic
2#13070868C211yesmaximal, characteristic, complemented
3#13070658C211yesmaximal, characteristic
4#13066664C211yesmaximal, characteristic, complemented
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066576C211yesmaximal, characteristic
7C11×#1670C211yesmaximal, characteristic, complemented
8#10623115—21no—
9C11×#494C2211yescharacteristic
10C11×#475—21no—
11C8×Q8×C11C2211yescharacteristic
12C2×#66893—22no—
13C2×#66892—21no—
14#10622458—22no—
15#10622454—21no—
16#10622312C2211yescharacteristic
17C4×Dic44—21no—
18#10622309—21no—
19C4×D88C2211yescharacteristic
20C11×#335C2211yescharacteristic
21C11×#332—21no—
22#10622202—21no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24C4×C11⋊C16C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16—21no—
27C11×C4⋊Q8—21no—
28C4×Q8×C11D411yescharacteristic
29#66999—41no—
30C2×Dic44—21no—
31C2×Dic44D412yes—
32C2×D88D411yescharacteristic
33C2×#4314—22no—
34#66951—42no—
35#66945—41no—
36#66928—22no—
37C4×D44—21no—
38#66922—21no—
39C4×Dic22—22no—
40C11×#106—41no—
41C11×C4⋊C8—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8D411yescharacteristic
44C11×#103—41no—
45C4×C8×C11—21no—
46C4×C8×C11C2311yescharacteristic
47#66893—44no—
48#66892—42no—
49#66885—21no—
50#66882D411yescharacteristic
51#66880—22no—
52C2×C11⋊C16—21no—
53C2×C11⋊C16—21no—
54#12335—111nomaximal, Sylow
55C2×Q8×C11—41no—
56C2×Q8×C11D811yescharacteristic
57C2×D44—21no—
58C2×C4×D11—41no—
59C2×Dic22—22no—
60C11×Q16—42no—
61C11×Q16—41no—
62C11×Q16—41no—
63C2×C8×C11—21no—
64C2×C8×C11—41no—
65C2×C8×C11C2×D411yescharacteristic
66C2×C8×C11C2×D411yescharacteristic
67C11×C4⋊C4—21no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4D811yescharacteristic
71C42×C11—21no—
72C42×C11C2×D411yescharacteristic
73(C2×D11)⋊C4—42no—
74(C2×D11)⋊C4—42no—
75(C2×D11)⋊C4—41no—
76C4⋊Dic11—21no—
77C4⋊Dic11—41no—
78C4⋊Dic11—41no—
79Dic11⋊C4—42no—
80C4×Dic11—42no—
81Dic44—42no—
82Dic44—41no—
83Dic44—41no—
84D88—21no—
85D88—21no—
86#4314—82no—
87C11⋊C16—22no—
88C11⋊C16—41no—
89#3393—111no—
90#2247—111no—
91#2208—111no—
92#1670D1111yescharacteristic, complemented
93#1362—111no—
94Q8⋊C16—111no—
95#1331—111no—
96C22×D11—41no—
97Q8×C11—21no—
98Q8×C11—21no—
99Q8×C11—81no—
100Q8×C11—81no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—81no—
104C2×C4×C11#12011yescharacteristic
105C2×C4×C11C2×D811yescharacteristic
106C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
107C2×Dic11—41no—
108C2×Dic11—42no—
109D44—41no—
110D44—41no—
111C4×D11—81no—
112C4×D11—81no—
113Dic22—42no—
114Dic22—42no—
115C8×C11—21no—
116C8×C11—41no—
117C8×C11—81no—
118C8×C11#13511yescharacteristic
119C8×C11AGL(1,ℤ/8)11yescharacteristic
120#556—221no—
121C2×Q32—222no—
122C2×SD32—221no—
123#495—221no—
124#494—111no—
125#494C2×D1111yescharacteristic
126#475—21no—
127#464—222no—
128#461—221no—
129C8×Q8C2×D1111yescharacteristic
130C4×Q16—221no—
131C4×D8—111no—
132C4⋊C16—111no—
133#358—221no—
134C4×C16—111no—
135#335C2×D1111yescharacteristic
136#332—21no—
137C22×C11#44711yescharacteristic
138C2×D11—81no—
139C2×D11—81no—
140C2×D11—81no—
141C4×C11—21no—
142C4×C11—41no—
143C4×C11—41no—
144C4×C11—161no—
145C4×C11#44911yescharacteristic
146C4×C11#45311yescharacteristic
147C4×C11#50811yescharacteristic
148C4×C11#51011yescharacteristic
149Dic11—82no—
150Dic11—81no—
151C2×Q16—21no—
152C2×Q16—21no—
153C2×Q16—112no—
154C2×Q16—221no—
155C2×SD16—222no—
156C2×D8—111no—
157C4⋊Q8—21no—
158C4⋊Q8—221no—
159#126—442no—
160#124—222no—
161C22⋊Q8—441no—
162C4×Q8—222no—
163C4×Q8C22⋊D1111yescharacteristic
164C4×D4—221no—
165#117—441no—
166Q32—444no—
167SD32—442no—
168C2×C16—221no—
169C2×C16—221no—
170#107—111no—
171#106—41no—
172C4⋊C8—21no—
173C4⋊C8—21no—
174C4⋊C8C22⋊D1111yescharacteristic
175#103—41no—
176#103—222no—
177#102—221no—
178C4×C8—21no—
179C4×C8C22×D1111yescharacteristic
180C2×C11#162111yescharacteristic
181C2×C11#218911yescharacteristic
182C2×C11#219511yescharacteristic
183D11—161no—
184C2×Q8—41no—
185C2×Q8—222no—
186C2×Q8#432311yescharacteristic
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—21no—
199C2×C8—41no—
200C2×C8D4×D1111yescharacteristic
201C2×C8D4×D1111yescharacteristic
202C4⋊C4—21no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—221no—
206C4⋊C4—442no—
207C4⋊C4—441no—
208C4⋊C4—441no—
209C4⋊C4#432311yescharacteristic
210C22⋊C4—442no—
211C22⋊C4—442no—
212C22⋊C4—441no—
213C42—21no—
214C42—442no—
215C42C2×C22⋊D1111yescharacteristic
216C16—222no—
217C16—441no—
218C11#1233511yescharacteristic, complemented, Sylow
219C23—441no—
220Q8—21no—
221Q8—21no—
222Q8—81no—
223Q8—81no—
224Q8—442no—
225Q8—442no—
226D4—441no—
227D4—441no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—81no—
231C2×C4—441no—
232C2×C4—442no—
233C2×C4—881no—
234C2×C4—881no—
235C2×C4C2×#432311yescharacteristic
236C2×C4#6699011yescharacteristic
237C2×C4#6700211yescharacteristic
238C8—21no—
239C8—41no—
240C8—81no—
241C8#6696711yescharacteristic
242C8#6696911yescharacteristic
243C22—881no—
244C22—881no—
245C22—881no—
246C22#1062264911yescharacteristic
247C4—21no—
248C4—41no—
249C4—41no—
250C4—161no—
251C4—882no—
252C4—881no—
253C4#1062278511yescharacteristic
254C4#1062279211yescharacteristic
255C4#1062280711yescharacteristic
256C4#1062281111yescharacteristic
257C2—1761no—
258C2#1306767911yescharacteristic
259C2#1307055411yescharacteristic
260C2#1307059211yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1670C2
socleC22×C11#447
prime radicalC2×D88D4
hypercenter#1670D11
hypocenterC11#12335
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1670

Complements

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

NH ≅ G/Ntype
2. #13070868C2semidirect
4. #13066664C2semidirect
5. Q8⋊(C11⋊C16)C2semidirect
7. C11×#1670C2semidirect
92. #1670D11semidirect
218. C11#12335semidirect

Maximal subgroups

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

subgroupindex
#130816052
#130708682
#130706582
#130666642
Q8⋊(C11⋊C16)2
#130665762
C11×#16702
#1233511