Finite Group Databasebeta

← #13070263

Subgroups — #13070263

Order 1408.

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

normal subgroups only

This group has 280 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#10623335C211yesmaximal, characteristic
2C2×C11×#100C211yesmaximal, characteristic, complemented
3C2×#66898C211yesmaximal, characteristic, complemented
4#10622114C212yesmaximal, complemented
5#10622113C212yesmaximal, complemented
6C22×D4×C11C2211yescharacteristic
7C22×C22⋊D11C411yescharacteristic, complemented
8C2×C11×M16—21no—
9#67006—21no—
10C2×C22⋊Dic11—21no—
11C2×C22⋊Dic11C411yescharacteristic, complemented
12#66992—21no—
13#66992—21no—
14#66990C411yescharacteristic, complemented
15#66990C2211yescharacteristic
16#66988C411yescharacteristic, complemented
17#66988C2211yescharacteristic
18#66982—21no—
19C11×#100—21no—
20C11×#100C2212yes—
21#66898—21no—
22#66898C2212yes—
23C24×C11C2×C411yescharacteristic
24C24×C11D411yescharacteristic
25C23×D11C2×C411yescharacteristic, complemented
26C2×D4×C11—41no—
27C2×D4×C11—41no—
28C2×D4×C11C2×C411yescharacteristic
29C2×D4×C11D411yescharacteristic
30C2×D4×C11D411yescharacteristic
31C2×D4×C11C2311yescharacteristic
32C22×C4×C11D411yescharacteristic
33C2×C22⋊D11—21no—
34C2×C22⋊D11—21no—
35C2×C22⋊D11—21no—
36C2×C22⋊D11—21no—
37C2×C22⋊D11—41no—
38C2×C22⋊D11—41no—
39C22×Dic11—21no—
40C22×Dic11—41no—
41C22×Dic11C2×C411yescharacteristic, complemented
42C11×M16—22no—
43C11×M16—41no—
44C2×C8×C11—41no—
45C22⋊Dic11—21no—
46C22⋊Dic11—21no—
47C22⋊Dic11—21no—
48C22⋊Dic11—22no—
49C22⋊Dic11—41no—
50C22⋊Dic11C2×C411yescharacteristic, complemented
51C22⋊Dic11C2×C411yescharacteristic, complemented
52(C2×D11)⋊C4—21no—
53(C2×D11)⋊C4—21no—
54Dic11⋊C4—21no—
55Dic11⋊C4—21no—
56#2121—111nomaximal, Sylow
57C23×C11—21no—
58C23×C11—21no—
59C23×C11—21no—
60C23×C11—21no—
61C23×C11—81no—
62C23×C11—81no—
63C23×C11C22⋊C411yescharacteristic
64C23×C11C22⋊C411yescharacteristic
65C23×C11C22⋊C411yescharacteristic
66C23×C11C22×C411yescharacteristic
67C23×C11C2×D411yescharacteristic
68C22×D11—21no—
69C22×D11—41no—
70C22×D11—81no—
71D4×C11—41no—
72D4×C11—41no—
73D4×C11—41no—
74D4×C11—41no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11C22⋊C411yescharacteristic
78C2×C4×C11C2×D411yescharacteristic
79C22⋊D11—42no—
80C22⋊D11—41no—
81C22⋊D11—41no—
82C22⋊D11—81no—
83C22⋊D11—81no—
84C2×Dic11—21no—
85C2×Dic11—21no—
86C2×Dic11—21no—
87C2×Dic11—41no—
88C2×Dic11—42no—
89C2×Dic11—81no—
90C2×Dic11—82no—
91C8×C11—42no—
92#534—111no—
93C2×#100D1111yescharacteristic, complemented
94C2×#99—111no—
95#352—112no—
96AΣL(1,𝔽16)—112no—
97C22×C11—21no—
98C22×C11—21no—
99C22×C11—21no—
100C22×C11—21no—
101C22×C11—41no—
102C22×C11—41no—
103C22×C11—41no—
104C22×C11—41no—
105C22×C11—41no—
106C22×C11—42no—
107C22×C11—81no—
108C22×C11—81no—
109C22×C11—81no—
110C22×C11#9911yescharacteristic
111C22×C11#9911yescharacteristic
112C22×C11C2×C22⋊C411yescharacteristic
113C2×D11—41no—
114C2×D11—41no—
115C2×D11—41no—
116C2×D11—82no—
117C4×C11—21no—
118C4×C11—21no—
119Dic11—41no—
120Dic11—41no—
121Dic11—41no—
122Dic11—82no—
123C22×D4—111no—
124C22×D4C2×D1111yescharacteristic
125C2×M16—21no—
126#123—111no—
127#123—111no—
128#123—221no—
129#121—221no—
130#121—221no—
131#120—111no—
132#120—111no—
133#120—221no—
134C2×C22⋊C4—111no—
135C2×C22⋊C4—221no—
136#100—21no—
137#100C2×D1112yes—
138#99—112no—
139#99—221no—
140C2×C11—21no—
141C2×C11—21no—
142C2×C11—21no—
143C2×C11—41no—
144C2×C11—41no—
145C2×C11—41no—
146C2×C11—41no—
147C2×C11C2×#9911yescharacteristic
148D11—81no—
149C24—111no—
150C24C4×D1111yescharacteristic
151C24D4411yescharacteristic
152C2×D4—41no—
153C2×D4—41no—
154C2×D4—221no—
155C2×D4—221no—
156C2×D4—221no—
157C2×D4—221no—
158C2×D4—441no—
159C2×D4—441no—
160C2×D4C4×D1111yescharacteristic
161C2×D4D4411yescharacteristic
162C2×D4C22⋊D1111yescharacteristic
163C2×D4C22×D1111yescharacteristic
164C22×C4—111no—
165C22×C4—221no—
166C22×C4—441no—
167C22×C4C22⋊D1111yescharacteristic
168M16—22no—
169M16—41no—
170C2×C8—41no—
171C4⋊C4—221no—
172C4⋊C4—221no—
173C22⋊C4—111no—
174C22⋊C4—111no—
175C22⋊C4—221no—
176C22⋊C4—221no—
177C22⋊C4—221no—
178C22⋊C4—221no—
179C22⋊C4—221no—
180C22⋊C4—222no—
181C22⋊C4—441no—
182C11#212111yescharacteristic, complemented, Sylow
183C23—21no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—81no—
188C23—81no—
189C23—221no—
190C23—441no—
191C23—881no—
192C23(C2×D11)⋊C411yescharacteristic
193C23(C2×D11)⋊C411yescharacteristic
194C23(C2×D11)⋊C411yescharacteristic
195C23C2×C4×D1111yescharacteristic
196C23C2×D4411yescharacteristic
197D4—41no—
198D4—41no—
199D4—41no—
200D4—41no—
201D4—442no—
202D4—441no—
203D4—441no—
204D4—881no—
205D4—881no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—221no—
209C2×C4—221no—
210C2×C4—221no—
211C2×C4—441no—
212C2×C4—442no—
213C2×C4—881no—
214C2×C4—882no—
215C2×C4(C2×D11)⋊C411yescharacteristic
216C2×C4C2×C22⋊D1111yescharacteristic
217C8—42no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—42no—
228C22—81no—
229C22—81no—
230C22—81no—
231C22—441no—
232C22—441no—
233C22—441no—
234C22—882no—
235C22#6687011yescharacteristic
236C22#6687011yescharacteristic
237C22C2×(C2×D11)⋊C411yescharacteristic
238C4—21no—
239C4—21no—
240C4—441no—
241C4—441no—
242C4—441no—
243C4—882no—
244C2—21no—
245C2—21no—
246C2—21no—
247C2—41no—
248C2—41no—
249C2—41no—
250C2—41no—
251C2—881no—
252C2C2×#6687011yescharacteristic
subgroupG/H
centerC2C2×#66870
commutatorC23×C11C22×C4
FrattiniC2×D4C22×D11
FittingC2×C11×#100C2
socleC2×C11C2×#99
prime radical#10623335C2
cosocleC2×D4×C11C23
hypercenterC2×#100D11
hypocenterC11#2121
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. C2×C11×#100C2semidirect
3. C2×#66898C2semidirect
4. #10622114C2semidirect
5. #10622113C2semidirect
7. C22×C22⋊D11C4semidirect
11. C2×C22⋊Dic11C4semidirect
14. #66990C4semidirect
16. #66988C4semidirect
25. C23×D11C2×C4semidirect
41. C22×Dic11C2×C4semidirect
50. C22⋊Dic11C2×C4semidirect
51. C22⋊Dic11C2×C4semidirect
93. C2×#100D11semidirect
182. C11#2121semidirect

Maximal subgroups

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

subgroupindex
#106233352
C2×C11×#1002
C2×#668982
#106221142
#106221132
#212111