Finite Group Databasebeta

← #13067634

Subgroups — #13067634

Order 1408.

288 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 51 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#10623136C211yesmaximal, characteristic
2C11×#481C211yesmaximal, characteristic, complemented
3#10622605C211yesmaximal, characteristic, complemented
4#10622581C211yesmaximal, characteristic, complemented
5#10622175C211yesmaximal, characteristic, complemented
6#10622108C211yesmaximal, characteristic, complemented
7#10622106C211yesmaximal, characteristic, complemented
8C2×D4×D11—21no—
9C11×#121C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic, complemented
11#66992—21no—
12#66990—21no—
13#66983C2211yescharacteristic
14C2×(C2×D11)⋊C4—21no—
15C2×(C2×D11)⋊C4C2211yescharacteristic
16C2×Dic11⋊C4—21no—
17#66947—21no—
18#66936—21no—
19#66935—21no—
20C11×#106—21no—
21C11×#102—21no—
22C11×C22⋊C8C2211yescharacteristic, complemented
23C11⋊#95C2211yescharacteristic, complemented
24C22⋊(C11⋊C8)C2211yescharacteristic, complemented
25#66873—21no—
26#66872—21no—
27C23×D11—21no—
28C23×D11D411yescharacteristic
29C2×D4×C11—21no—
30C2×D4×C11D411yescharacteristic
31C22×C4×C11—21no—
32C22×C4×C11C2311yescharacteristic
33C2×C22⋊D11—21no—
34C2×C22⋊D11—21no—
35C2×C22⋊D11—21no—
36C22×Dic11—21no—
37C22×Dic11D411yescharacteristic
38D4×D11—42no—
39D4×D11—42no—
40C2×D44—21no—
41C2×D44D411yescharacteristic
42C2×C4×D11—21no—
43C2×C8×C11—21no—
44C11×C4⋊C4—21no—
45C11×C4⋊C4—21no—
46C11×C4⋊C4D411yescharacteristic
47C11×C22⋊C4—21no—
48C22⋊Dic11—21no—
49(C2×D11)⋊C4—21no—
50(C2×D11)⋊C4—21no—
51(C2×D11)⋊C4—21no—
52(C2×D11)⋊C4—21no—
53(C2×D11)⋊C4—42no—
54C4⋊Dic11D411yescharacteristic
55Dic11⋊C4—21no—
56Dic11⋊C4—42no—
57C2×C11⋊C8—21no—
58#1613—111nomaximal, Sylow
59C23×C11—21no—
60C23×C11C2×D411yescharacteristic
61C22×D11—21no—
62C22×D11—21no—
63C22×D11—21no—
64C22×D11—42no—
65C22×D11—41no—
66C22×D11—41no—
67C22×D11—81no—
68C22×D11—81no—
69C22×D11SD1612yes—
70D4×C11—41no—
71D4×C11—41no—
72D4×C11—41no—
73C2×C4×C11—21no—
74C2×C4×C11—41no—
75C2×C4×C11—41no—
76C2×C4×C11—41no—
77C2×C4×C11—41no—
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2×D411yescharacteristic
80C22⋊D11—42no—
81C22⋊D11—41no—
82C22⋊D11—41no—
83C22⋊D11—81no—
84C2×Dic11—22no—
85C2×Dic11—21no—
86C2×Dic11—21no—
87C2×Dic11—41no—
88C2×Dic11—41no—
89C2×Dic11—41no—
90D44—41no—
91D44—42no—
92C4×D11—42no—
93C8×C11—41no—
94C11⋊C8—41no—
95#534—111no—
96#481—111no—
97#481D1111yescharacteristic, complemented
98#399—111no—
99#327—111no—
100#327—111no—
101#323—111no—
102C22×C11—21no—
103C22×C11—21no—
104C22×C11—41no—
105C22×C11—41no—
106C22×C11—41no—
107C22×C11#12011yescharacteristic
108C22×C11C2×SD1611yescharacteristic
109C22×C11AGL(1,ℤ/8)11yescharacteristic
110C2×D11—22no—
111C2×D11—41no—
112C2×D11—41no—
113C2×D11—42no—
114C2×D11—41no—
115C2×D11—41no—
116C2×D11—41no—
117C2×D11—81no—
118C2×D11—84no—
119C4×C11—21no—
120C4×C11—21no—
121C4×C11—41no—
122C4×C11—81no—
123Dic11—42no—
124Dic11—41no—
125Dic11—41no—
126C22×D4—221no—
127#123—221no—
128#123—221no—
129#121—111no—
130#121—221no—
131#121C2×D1111yescharacteristic
132#120—221no—
133#120—221no—
134C2×C4⋊C4—221no—
135C2×C4⋊C4C2×D1111yescharacteristic, complemented
136C2×C22⋊C4—111no—
137C2×C22⋊C4—221no—
138#106—21no—
139#106—221no—
140#102—21no—
141#102—221no—
142C22⋊C8—111no—
143C22⋊C8C2×D1111yescharacteristic, complemented
144#95—111no—
145C2×C11—21no—
146C2×C11—21no—
147C2×C11—81no—
148C2×C11#45011yescharacteristic
149C2×C11#45311yescharacteristic
150C2×C11#45811yescharacteristic
151D11—42no—
152D11—81no—
153C24—111no—
154C24—221no—
155C2×D4—21no—
156C2×D4—111no—
157C2×D4—221no—
158C2×D4—221no—
159C2×D4—221no—
160C2×D4—221no—
161C2×D4—442no—
162C2×D4—442no—
163C2×D4C22⋊D1111yescharacteristic
164C22×C4—21no—
165C22×C4—111no—
166C22×C4—221no—
167C22×C4—221no—
168C22×C4C22×D1111yescharacteristic
169C2×C8—21no—
170C2×C8—221no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—111no—
174C4⋊C4—221no—
175C4⋊C4—442no—
176C4⋊C4C22⋊D1111yescharacteristic
177C22⋊C4—21no—
178C22⋊C4—221no—
179C22⋊C4—221no—
180C22⋊C4—221no—
181C22⋊C4—221no—
182C22⋊C4—221no—
183C22⋊C4—442no—
184C11#161311yescharacteristic, complemented, Sylow
185C23—21no—
186C23—112no—
187C23—221no—
188C23—221no—
189C23—221no—
190C23—441no—
191C23—441no—
192C23—442no—
193C23—881no—
194C23—881no—
195C23D4×D1111yescharacteristic
196D4—41no—
197D4—41no—
198D4—41no—
199D4—441no—
200D4—442no—
201D4—442no—
202D4—441no—
203D4—441no—
204D4—881no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—222no—
211C2×C4—221no—
212C2×C4—221no—
213C2×C4—442no—
214C2×C4—441no—
215C2×C4—441no—
216C2×C4—441no—
217C2×C4D4×D1111yescharacteristic
218C2×C4C2×C22⋊D1111yescharacteristic
219C8—41no—
220C8—441no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—222no—
227C22—442no—
228C22—441no—
229C22—441no—
230C22—441no—
231C22—441no—
232C22—441no—
233C22—881no—
234C22—884no—
235C22SD16×D1111yescharacteristic
236C22#6696711yescharacteristic
237C22#6699011yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—442no—
243C4—441no—
244C4—441no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—442no—
249C2—881no—
250C2#1062266611yescharacteristic
251C2#1062278211yescharacteristic
252C2#1062281111yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#481C2
socleC22×C11#120
prime radical#10623136C2
hypercenter#481D11
hypocenterC11#1613
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C11×#481C2semidirect
3. #10622605C2semidirect
4. #10622581C2semidirect
5. #10622175C2semidirect
6. #10622108C2semidirect
7. #10622106C2semidirect
10. C2×C11×C4⋊C4C22semidirect
22. C11×C22⋊C8C22semidirect
23. C11⋊#95C22semidirect
24. C22⋊(C11⋊C8)C22semidirect
97. #481D11semidirect
135. C2×C4⋊C4C2×D11semidirect
143. C22⋊C8C2×D11semidirect
184. C11#1613semidirect

Maximal subgroups

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

subgroupindex
#106231362
C11×#4812
#106226052
#106225812
#106221752
#106221082
#106221062
#161311