Finite Group Databasebeta

← #13070262

Subgroups — #13070262

Order 1408.

280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C11×#534C211yesmaximal, characteristic
2C2×#66898C211yesmaximal, characteristic, complemented
3C2×#66897C211yesmaximal, characteristic, complemented
4#10622177C212yesmaximal, complemented
5#10622174C212yesmaximal, complemented
6C22×D4×C11C411yescharacteristic, complemented
7C22×D4×C11C2211yescharacteristic
8C11×#123—21no—
9C11×#123C411yescharacteristic, complemented
10C11×#123C2211yescharacteristic
11C11×#121—21no—
12C11×#121—21no—
13C11×#120—21no—
14C11×#120C411yescharacteristic, complemented
15C11×#120C2211yescharacteristic
16C2×C11×C22⋊C4C411yescharacteristic, complemented
17C2×C22⋊Dic11—21no—
18C2×#4318—21no—
19#66898—21no—
20#66898C2212yes—
21#66897—21no—
22#66897C2212yes—
23C24×C11C2×C411yescharacteristic
24C24×C11C2×C411yescharacteristic, complemented
25C24×C11D411yescharacteristic
26C2×D4×C11—21no—
27C2×D4×C11—21no—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D4×C11—41no—
31C2×D4×C11—41no—
32C2×D4×C11—41no—
33C2×D4×C11—41no—
34C2×D4×C11C2×C411yescharacteristic
35C2×D4×C11D411yescharacteristic
36C2×D4×C11D411yescharacteristic
37C2×D4×C11C2311yescharacteristic
38C22×C4×C11—21no—
39C22×C4×C11C2×C411yescharacteristic, complemented
40C22×C4×C11D411yescharacteristic
41C22×Dic11—41no—
42C11×C4⋊C4—21no—
43C11×C4⋊C4—21no—
44C11×C22⋊C4—21no—
45C11×C22⋊C4—21no—
46C11×C22⋊C4—21no—
47C11×C22⋊C4—21no—
48C11×C22⋊C4—21no—
49C11×C22⋊C4C2×C411yescharacteristic, complemented
50C11×C22⋊C4C2×C411yescharacteristic, complemented
51C22⋊Dic11—22no—
52C22⋊Dic11—41no—
53#4318—22no—
54#4318—41no—
55C2×C11⋊C8—41no—
56#2121—111nomaximal, Sylow
57C23×C11—21no—
58C23×C11—21no—
59C23×C11—21no—
60C23×C11—21no—
61C23×C11—21no—
62C23×C11—41no—
63C23×C11—81no—
64C23×C11—81no—
65C23×C11—81no—
66C23×C11C22⋊C411yescharacteristic
67C23×C11C22⋊C411yescharacteristic
68C23×C11C22⋊C411yescharacteristic
69C23×C11C22×C411yescharacteristic
70C23×C11C2×D411yescharacteristic
71D4×C11—41no—
72D4×C11—41no—
73D4×C11—41no—
74D4×C11—41no—
75D4×C11—42no—
76D4×C11—41no—
77D4×C11—41no—
78D4×C11—81no—
79D4×C11—81no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—41no—
86C2×C4×C11—81no—
87C2×C4×C11C22⋊C411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×Dic11—42no—
90C2×Dic11—82no—
91C11⋊C8—42no—
92#534D1111yescharacteristic
93C2×#100—111no—
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—41no—
108C22×C11—41no—
109C22×C11—41no—
110C22×C11—81no—
111C22×C11—81no—
112C22×C11—81no—
113C22×C11—82no—
114C22×C11#9911yescharacteristic
115C22×C11#9911yescharacteristic
116C22×C11C2×C22⋊C411yescharacteristic
117C4×C11—21no—
118C4×C11—21no—
119C4×C11—41no—
120C4×C11—41no—
121C4×C11—41no—
122Dic11—82no—
123C22×D4Dic1111yescharacteristic, complemented
124C22×D4C2×D1111yescharacteristic
125C2×M16—221no—
126#123—21no—
127#123Dic1111yescharacteristic, complemented
128#123C2×D1111yescharacteristic
129#121—21no—
130#121—21no—
131#120—21no—
132#120Dic1111yescharacteristic, complemented
133#120C2×D1111yescharacteristic
134C2×C22⋊C4—221no—
135C2×C22⋊C4Dic1111yescharacteristic, complemented
136#100—112no—
137#100—221no—
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×C11—81no—
148C2×C11C2×#9911yescharacteristic
149C24C2×Dic1111yescharacteristic
150C24C2×Dic1111yescharacteristic, complemented
151C24C22⋊D1111yescharacteristic
152C2×D4—21no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—21no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4C2×Dic1111yescharacteristic
161C2×D4C22⋊D1111yescharacteristic
162C2×D4C22⋊D1111yescharacteristic
163C2×D4C22×D1111yescharacteristic
164C22×C4—21no—
165C22×C4—441no—
166C22×C4C2×Dic1111yescharacteristic, complemented
167C22×C4C22⋊D1111yescharacteristic
168M16—222no—
169M16—441no—
170C2×C8—441no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C22⋊C4—21no—
174C22⋊C4—21no—
175C22⋊C4—21no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—222no—
179C22⋊C4—441no—
180C22⋊C4C2×Dic1111yescharacteristic, complemented
181C22⋊C4C2×Dic1111yescharacteristic, complemented
182C11#212111yescharacteristic, complemented, Sylow
183C23—21no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—21no—
188C23—41no—
189C23—81no—
190C23—81no—
191C23—81no—
192C23C22⋊Dic1111yescharacteristic
193C23C22⋊Dic1111yescharacteristic
194C23C22⋊Dic1111yescharacteristic
195C23C22×Dic1111yescharacteristic
196C23C2×C22⋊D1111yescharacteristic
197D4—41no—
198D4—41no—
199D4—41no—
200D4—41no—
201D4—42no—
202D4—41no—
203D4—41no—
204D4—81no—
205D4—81no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—81no—
213C2×C4—442no—
214C2×C4—882no—
215C2×C4C22⋊Dic1111yescharacteristic
216C2×C4C2×C22⋊D1111yescharacteristic
217C8—442no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—42no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—81no—
232C22—81no—
233C22—81no—
234C22—82no—
235C22#6689811yescharacteristic
236C22#6689811yescharacteristic
237C22C2×C22⋊Dic1111yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—41no—
243C4—882no—
244C2—21no—
245C2—21no—
246C2—21no—
247C2—41no—
248C2—41no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2C2×#6689811yescharacteristic
subgroupG/H
centerC2C2×#66898
commutatorC23×C11C22×C4
FrattiniC2×D4C22×D11
Fitting, prime radicalC11×#534C2
socleC2×C11C2×#99
cosocleC2×D4×C11C23
hypercenter#534D11
hypocenterC11#2121
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ #534

Complements

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

NH ≅ G/Ntype
2. C2×#66898C2semidirect
3. C2×#66897C2semidirect
4. #10622177C2semidirect
5. #10622174C2semidirect
6. C22×D4×C11C4semidirect
9. C11×#123C4semidirect
14. C11×#120C4semidirect
16. C2×C11×C22⋊C4C4semidirect
24. C24×C11C2×C4semidirect
39. C22×C4×C11C2×C4semidirect
49. C11×C22⋊C4C2×C4semidirect
50. C11×C22⋊C4C2×C4semidirect
123. C22×D4Dic11semidirect
127. #123Dic11semidirect
132. #120Dic11semidirect
135. C2×C22⋊C4Dic11semidirect
150. C24C2×Dic11semidirect
166. C22×C4C2×Dic11semidirect
180. C22⋊C4C2×Dic11semidirect
181. C22⋊C4C2×Dic11semidirect
182. C11#2121semidirect

Maximal subgroups

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

subgroupindex
C11×#5342
C2×#668982
C2×#668972
#106221772
#106221742
#212111