Finite Group Databasebeta

← #14667396

Subgroups — #14667396

Order 2816.

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

normal subgroups only

This group has 330 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#13080965C211yesmaximal, characteristic
2#13070844C211yesmaximal, characteristic, complemented
3#13070661C211yesmaximal, characteristic, complemented
4#13067982C211yesmaximal, characteristic, complemented
5#13066672C211yesmaximal, characteristic, complemented
6#13066572C211yesmaximal, characteristic, complemented
7C11×#1331C211yesmaximal, characteristic, complemented
8#10623082—21no—
9C4×C11×D8C2211yescharacteristic
10#10622770—21no—
11C2×#66891—21no—
12#10622620—21no—
13D11×#107—21no—
14#10622459—21no—
15#10622387—22no—
16#10622312C2211yescharacteristic
17C8×D44C2211yescharacteristic
18#10622295C2211yescharacteristic
19C4×C11×C16C2211yescharacteristic
20C11×#335C2211yescharacteristic
21#10622141—22no—
22#10622130—21no—
23#10622124—21no—
24C4⋊(C11⋊C16)C2211yescharacteristic
25C2×#4339—41no—
26C2×C11×D8D411yescharacteristic
27C4×D4×C11—21no—
28#66991—22no—
29#66977—41no—
30C2×Dic44—21no—
31C2×Dic44—21no—
32C2×C8×D11—21no—
33C4⋊C4×D11—22no—
34#66936—42no—
35C4×D44D411yescharacteristic
36#66922—21no—
37#66922—21no—
38C2×C11×C16—21no—
39C11×#107D411yescharacteristic
40C11×C4⋊C8—21no—
41C11×#102—21no—
42C4×C8×C11C2311yescharacteristic
43#66896—22no—
44#66891—42no—
45#66885—41no—
46(C2×D11)⋊C8—21no—
47#66882—21no—
48#66882—41no—
49#66882D412yes—
50C2×C11⋊C16—21no—
51#66871—22no—
52C4⋊(C11⋊C8)D411yescharacteristic
53#12344—111nomaximal, Sylow
54C2×D4×C11—21no—
55C22×C4×C11—41no—
56C2×C22⋊D11—42no—
57#4339—82no—
58#4339—82no—
59C2×D44D811yescharacteristic
60C2×C4×D11—21no—
61C2×C4×D11—42no—
62C2×Dic22—41no—
63C2×Dic22—41no—
64C11×D8—21no—
65C11×D8—21no—
66C2×C8×C11—41no—
67C2×C8×C11C2×D411yescharacteristic
68C2×C8×C11C2×D411yescharacteristic
69C11×C4⋊C4—21no—
70C11×C22⋊C4—41no—
71C42×C11C2×D411yescharacteristic
72C22⋊Dic11—42no—
73(C2×D11)⋊C4—21no—
74C4⋊Dic11—22no—
75C4⋊Dic11—41no—
76C4⋊Dic11—41no—
77C4⋊Dic11—41no—
78C4⋊Dic11D811yescharacteristic
79Dic11⋊C4—42no—
80C2×C11⋊C8—21no—
81Dic44—42no—
82Dic44—41no—
83Dic44—41no—
84C8×D11—41no—
85C8×D11—41no—
86C11×C16—41no—
87C11⋊C16—41no—
88#3334—111no—
89#2241—111no—
90#2208—111no—
91#1669—111no—
92#1364—111no—
93#1331D1111yescharacteristic, complemented
94D4⋊C16—111no—
95C23×C11—41no—
96C22×D11—21no—
97D4×C11—41no—
98D4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—81no—
101C2×C4×C11—81no—
102C2×C4×C11#12011yescharacteristic
103C2×C4×C11C2×D811yescharacteristic
104C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
105C22⋊D11—84no—
106C2×Dic11—21no—
107C2×Dic11—42no—
108C2×Dic11—81no—
109D44—21no—
110D44SD3212yescomplemented
111C4×D11—41no—
112C4×D11—41no—
113C4×D11—84no—
114Dic22—81no—
115Dic22—81no—
116Dic22—81no—
117Dic22—81no—
118C8×C11—21no—
119C8×C11—81no—
120C8×C11#13511yescharacteristic
121C8×C11AGL(1,ℤ/8)11yescharacteristic
122C11⋊C8—41no—
123#547—221no—
124C2×SD32—221no—
125#500—111no—
126#494—111no—
127#480—222no—
128#474—221no—
129#474—221no—
130#466—221no—
131C4×D8C2×D1111yescharacteristic
132C8×D4—111no—
133C2×#107—221no—
134C4⋊C16—111no—
135#358—222no—
136#358—221no—
137C4×C16C2×D1111yescharacteristic
138#335C2×D1111yescharacteristic
139#332—221no—
140C22×C11—81no—
141C22×C11—81no—
142C22×C11—81no—
143C22×C11#44711yescharacteristic
144C2×D11—22no—
145C2×D11—41no—
146C2×D11—41no—
147C4×C11—21no—
148C4×C11—81no—
149C4×C11#44911yescharacteristic
150C4×C11#45411yescharacteristic
151C4×C11C2×SD3211yescharacteristic
152C4×C11#50911yescharacteristic
153Dic11—41no—
154Dic11—82no—
155Dic11—161no—
156C2×#41—441no—
157C2×Q16—221no—
158C2×Q16—221no—
159C2×D8D4411yescharacteristic
160C22×C8—221no—
161C4⋊Q8—221no—
162C4⋊Q8—221no—
163#123—442no—
164C22⋊Q8—441no—
165#121—222no—
166C4×D4—21no—
167C4×D4—111no—
168C2×C4⋊C4—222no—
169SD32—442no—
170C2×C16—21no—
171C2×C16—221no—
172#107—112no—
173#107—222no—
174#107—221no—
175#107—441no—
176#107D4411yescharacteristic
177C4⋊C8—21no—
178C4⋊C8—111no—
179#102—21no—
180#102—222no—
181#102—441no—
182C22⋊C8—221no—
183C4×C8C22×D1111yescharacteristic
184C2×C11—161no—
185C2×C11#162511yescharacteristic
186C2×C11#218711yescharacteristic
187C2×C11#219511yescharacteristic
188D11—42no—
189#41—882no—
190#41—882no—
191C2×Q8—441no—
192C2×Q8—441no—
193C2×D4—21no—
194C2×D4—111no—
195C2×D4—442no—
196C22×C4—41no—
197C22×C4—221no—
198C22×C4—442no—
199Q16—442no—
200Q16—441no—
201Q16—441no—
202D8—21no—
203D8—21no—
204C2×C8—41no—
205C2×C8—221no—
206C2×C8—441no—
207C2×C8—441no—
208C2×C8C2×D4411yescharacteristic
209C2×C8D4×D1111yescharacteristic
210C4⋊C4—21no—
211C4⋊C4—111no—
212C4⋊C4—222no—
213C4⋊C4—442no—
214C4⋊C4—441no—
215C4⋊C4—441no—
216C4⋊C4—441no—
217C22⋊C4—41no—
218C22⋊C4—221no—
219C22⋊C4—442no—
220C42D4×D1111yescharacteristic
221C16—41no—
222C16—441no—
223C11#1234411yescharacteristic, complemented, Sylow
224C23—41no—
225C23—221no—
226Q8—881no—
227Q8—881no—
228Q8—881no—
229Q8—881no—
230D4—41no—
231D4—41no—
232D4—112no—
233D4—221no—
234D4—884no—
235C2×C4—41no—
236C2×C4—81no—
237C2×C4—81no—
238C2×C4—221no—
239C2×C4—441no—
240C2×C4—441no—
241C2×C4—442no—
242C2×C4—884no—
243C2×C4—881no—
244C2×C4#6693511yescharacteristic
245C2×C4D8×D1111yescharacteristic
246C2×C4#6696711yescharacteristic
247C8—21no—
248C8—81no—
249C8—441no—
250C8#6695711yescharacteristic
251C8#6696111yescharacteristic
252C22—81no—
253C22—81no—
254C22—81no—
255C22—222no—
256C22—441no—
257C22—441no—
258C22#1062238611yescharacteristic
259C4—21no—
260C4—81no—
261C4—441no—
262C4—882no—
263C4—1761no—
264C4#1062234711yescharacteristic
265C4#1062244011yescharacteristic
266C4#1062252411yescharacteristic
267C4D11×SD3211yescharacteristic
268C2—161no—
269C2—442no—
270C2#1306770811yescharacteristic
271C2#1307054611yescharacteristic
272C2#1307059511yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1331C2
socleC22×C11#447
prime radical#13080965C2
hypercenter#1331D11
hypocenterC11#12344
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
2. #13070844C2semidirect
3. #13070661C2semidirect
4. #13067982C2semidirect
5. #13066672C2semidirect
6. #13066572C2semidirect
7. C11×#1331C2semidirect
93. #1331D11semidirect
110. D44SD32semidirect
223. C11#12344semidirect

Maximal subgroups

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

subgroupindex
#130809652
#130708442
#130706612
#130679822
#130666722
#130665722
C11×#13312
#1234411