Finite Group Databasebeta

← #14667395

Subgroups — #14667395

Order 2816.

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

normal subgroups only

This group has 330 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#13080964C211yesmaximal, characteristic
2#13070844C211yesmaximal, characteristic, complemented
3#13070662C211yesmaximal, characteristic, complemented
4#13067981C211yesmaximal, characteristic, complemented
5#13066670C211yesmaximal, characteristic, complemented
6#13066578C211yesmaximal, characteristic, complemented
7C11×D4⋊C16C211yesmaximal, characteristic, complemented
8#10623086—21no—
9C8×D4×C11C2211yescharacteristic
10#10622728—21no—
11C2×#66882—21no—
12#10622620—21no—
13C2×#66864—21no—
14#10622459—21no—
15#10622349—22no—
16#10622312C2211yescharacteristic
17C4×D88C2211yescharacteristic
18#10622295C2211yescharacteristic
19C11×C4⋊C16C2211yescharacteristic
20C4×C11×C16C2211yescharacteristic
21#10622141—21no—
22#10622141—22no—
23#10622120—21no—
24#10622096C2211yescharacteristic
25C2×#4341—41no—
26C22×C8×C11—21no—
27C4×D4×C11D411yescharacteristic
28#66983—22no—
29C2×C4⋊Dic11—22no—
30C2×Dic44—21no—
31C2×Dic44—21no—
32C2×D88D411yescharacteristic
33#66950—41no—
34#66939—42no—
35C4×D44—21no—
36#66922—21no—
37#66922—21no—
38C2×C11×C16—21no—
39C2×C11×C16—21no—
40C11×C4⋊C8D411yescharacteristic
41C11×C22⋊C8—21no—
42C4×C8×C11C2311yescharacteristic
43#66896—41no—
44#66885—22no—
45#66885—21no—
46#66882—22no—
47#66882—21no—
48#66882D412yes—
49#66882D411yescharacteristic
50#66871—41no—
51C4⋊(C11⋊C8)—21no—
52#66864—42no—
53#12344—111nomaximal, Sylow
54C2×D4×C11D811yescharacteristic
55C22×C4×C11—21no—
56C2×C22⋊D11—42no—
57C22×Dic11—42no—
58#4341—82no—
59#4341—82no—
60C2×D44—21no—
61C2×C4×D11—41no—
62C2×Dic22—41no—
63C2×Dic22—41no—
64C2×C8×C11—21no—
65C2×C8×C11—41no—
66C2×C8×C11—41no—
67C2×C8×C11C2×D411yescharacteristic
68C2×C8×C11C2×D411yescharacteristic
69C11×C4⋊C4D811yescharacteristic
70C11×C22⋊C4—21no—
71C42×C11C2×D411yescharacteristic
72(C2×D11)⋊C4—42no—
73(C2×D11)⋊C4—41no—
74C4⋊Dic11—22no—
75C4⋊Dic11—21no—
76C4⋊Dic11—42no—
77C4⋊Dic11—41no—
78C4⋊Dic11—41no—
79C4⋊Dic11—41no—
80C2×C11⋊C8—41no—
81Dic44—42no—
82Dic44—41no—
83Dic44—41no—
84D88—21no—
85D88—21no—
86C11×C16—41no—
87C11×C16—41no—
88#3334—111no—
89#2241—111no—
90#2208—111no—
91#1669—111no—
92#1364—111no—
93#1331—111no—
94D4⋊C16D1111yescharacteristic, complemented
95C23×C11—21no—
96C22×D11—41no—
97D4×C11—21no—
98D4×C11SD3212yescomplemented
99C2×C4×C11—21no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11#12011yescharacteristic
103C2×C4×C11C2×D811yescharacteristic
104C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
105C22⋊D11—84no—
106C2×Dic11—42no—
107C2×Dic11—41no—
108C2×Dic11—84no—
109C2×Dic11—81no—
110D44—41no—
111D44—41no—
112C4×D11—81no—
113C4×D11—81no—
114Dic22—81no—
115Dic22—81no—
116Dic22—81no—
117Dic22—81no—
118C8×C11—21no—
119C8×C11—41no—
120C8×C11#13511yescharacteristic
121C8×C11AGL(1,ℤ/8)11yescharacteristic
122C11⋊C8—81no—
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×D8—111no—
132C8×D4C2×D1111yescharacteristic
133C2×#107—221no—
134C4⋊C16C2×D1111yescharacteristic
135#358—221no—
136#358—222no—
137C4×C16C2×D1111yescharacteristic
138#335—111no—
139#332—221no—
140C22×C11—22no—
141C22×C11—41no—
142C22×C11—41no—
143C22×C11#44711yescharacteristic
144C2×D11—81no—
145C2×D11—81no—
146C2×D11—81no—
147C4×C11—21no—
148C4×C11—41no—
149C4×C11#44911yescharacteristic
150C4×C11#45411yescharacteristic
151C4×C11C2×SD3211yescharacteristic
152C4×C11#50911yescharacteristic
153Dic11—82no—
154Dic11—81no—
155Dic11—161no—
156C2×#41—441no—
157C2×Q16—221no—
158C2×Q16—221no—
159C2×D8—111no—
160C22×C8—21no—
161C4⋊Q8—221no—
162C4⋊Q8—221no—
163#123—442no—
164C22⋊Q8—441no—
165#121—222no—
166C4×D4—221no—
167C4×D4D4411yescharacteristic
168C2×C4⋊C4—222no—
169SD32—442no—
170C2×C16—21no—
171C2×C16—21no—
172#107—111no—
173#107—112no—
174#107—222no—
175#107—221no—
176#107—441no—
177C4⋊C8—221no—
178C4⋊C8D4411yescharacteristic
179#102—222no—
180#102—221no—
181#102—441no—
182C22⋊C8—21no—
183C4×C8C22×D1111yescharacteristic
184C2×C11—42no—
185C2×C11#162511yescharacteristic
186C2×C11#218711yescharacteristic
187C2×C11#219511yescharacteristic
188D11—161no—
189#41—882no—
190#41—882no—
191C2×Q8—441no—
192C2×Q8—441no—
193C2×D4—221no—
194C2×D4—442no—
195C2×D4D8811yescharacteristic
196C22×C4—21no—
197C22×C4—442no—
198C22×C4—441no—
199Q16—442no—
200Q16—441no—
201Q16—441no—
202D8—221no—
203D8—221no—
204C2×C8—21no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—441no—
208C2×C8D4×D1111yescharacteristic
209C2×C8D4×D1111yescharacteristic
210C4⋊C4—221no—
211C4⋊C4—222no—
212C4⋊C4—442no—
213C4⋊C4—441no—
214C4⋊C4—441no—
215C4⋊C4—441no—
216C4⋊C4D8811yescharacteristic
217C22⋊C4—21no—
218C22⋊C4—442no—
219C22⋊C4—441no—
220C42C2×D4411yescharacteristic
221C16—41no—
222C16—41no—
223C11#1234411yescharacteristic, complemented, Sylow
224C23—21no—
225C23—441no—
226Q8—881no—
227Q8—881no—
228Q8—881no—
229Q8—881no—
230D4—21no—
231D4—441no—
232D4—441no—
233D4—884no—
234D4#6686412yescomplemented
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—441no—
239C2×C4—442no—
240C2×C4—884no—
241C2×C4—881no—
242C2×C4—881no—
243C2×C4—881no—
244C2×C4#6693511yescharacteristic
245C2×C4C2×D8811yescharacteristic
246C2×C4#6696111yescharacteristic
247C8—21no—
248C8—41no—
249C8—881no—
250C8#6696411yescharacteristic
251C8#6696911yescharacteristic
252C22—22no—
253C22—41no—
254C22—41no—
255C22—881no—
256C22—881no—
257C22—881no—
258C22#1062234511yescharacteristic
259C4—21no—
260C4—41no—
261C4—881no—
262C4—882no—
263C4—1761no—
264C4#1062239411yescharacteristic
265C4#1062244011yescharacteristic
266C4C2×#6686411yescharacteristic
267C4#1062252111yescharacteristic
268C2—42no—
269C2—1761no—
270C2#1306770711yescharacteristic
271C2#1307054711yescharacteristic
272C2#1307059611yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×D4⋊C16C2
socleC22×C11#447
prime radical#13080964C2
hypercenterD4⋊C16D11
hypocenterC11#12344
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ D4⋊C16

Complements

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

NH ≅ G/Ntype
2. #13070844C2semidirect
3. #13070662C2semidirect
4. #13067981C2semidirect
5. #13066670C2semidirect
6. #13066578C2semidirect
7. C11×D4⋊C16C2semidirect
94. D4⋊C16D11semidirect
98. D4×C11SD32semidirect
223. C11#12344semidirect
234. D4#66864semidirect

Maximal subgroups

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

subgroupindex
#130809642
#130708442
#130706622
#130679812
#130666702
#130665782
C11×D4⋊C162
#1234411