Finite Group Databasebeta

← #13080904

Subgroups — #13080904

Order 1408.

386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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×#555C211yesmaximal, characteristic
2D4×Dic22C211yesmaximal, characteristic, complemented
3#10622706C211yesmaximal, characteristic, complemented
4#10622704C211yesmaximal, characteristic, complemented
5#10622655C212yesmaximal, complemented
6#10622653C212yesmaximal, complemented
7#10622632C211yesmaximal, characteristic, complemented
8C4×#4324C211yesmaximal, characteristic, complemented
9#10622625C211yesmaximal, characteristic, complemented
10#10622617C212yesmaximal, complemented
11#10622609C212yesmaximal, complemented
12C22×Dic22C2212yes—
13C11×C4⋊Q8C2211yescharacteristic
14C11×#124—22no—
15C11×#121—21no—
16C11×#121C2212yes—
17C4×D4×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19C11×#117—21no—
20C11×#117C2212yes—
21D4×Dic11—21no—
22C2×#4324C2211yescharacteristic
23C2×#4324C2212yes—
24#66977C2212yes—
25C2×#4318C2212yes—
26#66941—21no—
27#66931—22no—
28#66922C2211yescharacteristic
29C4×Dic22C2211yescharacteristic
30#66896C2211yescharacteristic
31C22⋊(C11⋊C8)C2212yes—
32#66874C2212yes—
33#66874C2212yes—
34#66874C2211yescharacteristic
35#66874C2212yes—
36#66874C2212yes—
37#66872C2211yescharacteristic
38#66871C2212yes—
39C4⋊(C11⋊C8)C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×D4×C11—22no—
43C2×D4×C11D411yescharacteristic
44C2×D4×C11C2311yescharacteristic
45C22×C4×C11—21no—
46C22×C4×C11C2312yes—
47C22×Dic11—22no—
48C2×Dic22—24no—
49C2×Dic22—22no—
50C2×Dic22—42no—
51C2×Dic22C2312yes—
52C2×Dic22C2311yescharacteristic
53C11×C4⋊C4—21no—
54C11×C4⋊C4D411yescharacteristic
55C11×C4⋊C4C2312yes—
56C11×C4⋊C4C2311yescharacteristic
57C11×C22⋊C4—22no—
58C11×C22⋊C4—22no—
59C11×C22⋊C4—21no—
60C11×C22⋊C4D412yes—
61C42×C11—22no—
62C42×C11C2311yescharacteristic
63C22⋊Dic11—22no—
64#4324—22no—
65#4324—42no—
66C4⋊Dic11—21no—
67C4⋊Dic11—21no—
68C4⋊Dic11C2311yescharacteristic
69Dic11⋊C4—21no—
70Dic11⋊C4—22no—
71C4×Dic11—21no—
72#4318—42no—
73C2×C11⋊C8C2311yescharacteristic
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2312yes—
76#3329—111nomaximal, Sylow
77C23×C11—21no—
78C23×C11C2×D412yes—
79Q8×C11—81no—
80D4×C11—22no—
81D4×C11—21no—
82D4×C11—21no—
83D4×C11—82no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—42no—
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11C2×D412yes—
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2411yescharacteristic
93C2×Dic11—21no—
94C2×Dic11—21no—
95C2×Dic11—22no—
96C2×Dic11—44no—
97Dic22—21no—
98Dic22—22no—
99Dic22—22no—
100Dic22—44no—
101Dic22#4112yes—
102C11⋊C8—21no—
103C11⋊C8—21no—
104C11⋊C8—22no—
105#555D1111yescharacteristic
106D4×Q8—111no—
107#487—111no—
108#485—112no—
109#477—111no—
110#468—112no—
111#461—111no—
112#448—112no—
113C4×SD16—111no—
114#436—111no—
115#419—112no—
116C22×C11—22no—
117C22×C11—22no—
118C22×C11—22no—
119C22×C11—41no—
120C22×C11—41no—
121C22×C11—41no—
122C22×C11C22×D411yescharacteristic
123C4×C11—22no—
124C4×C11—21no—
125C4×C11—41no—
126C4×C11—42no—
127C4×C11#13712yes—
128C4×C11C2×#4111yescharacteristic
129C4×C11H(5,𝔽2)11yescharacteristic
130Dic11—22no—
131Dic11—42no—
132Dic11—41no—
133C22×Q8—112no—
134C2×SD16—111no—
135C2×SD16—112no—
136C2×M16—112no—
137C4⋊Q8—111no—
138C4⋊Q8—221no—
139C4⋊Q8C2×D1111yescharacteristic
140#124—22no—
141C22⋊Q8—112no—
142C22⋊Q8—222no—
143#121—21no—
144#121C2×D1112yes—
145C4×Q8—111no—
146C4×D4—221no—
147C4×D4C2×D1111yescharacteristic
148C4×D4C2×D1111yescharacteristic
149#117—21no—
150#117C2×D1112yes—
151#107—112no—
152#106—111no—
153C4⋊C8—111no—
154#103—111no—
155#103—112no—
156#103—112no—
157#103—112no—
158#103—112no—
159#102—111no—
160C22⋊C8—112no—
161C4×C8—111no—
162C2×C11—42no—
163C2×C11—81no—
164C2×C11#54611yescharacteristic
165C2×C11C2×#13711yescharacteristic
166C2×C11#57711yescharacteristic
167C2×Q8—21no—
168C2×Q8—111no—
169C2×Q8—112no—
170C2×Q8—224no—
171C2×Q8—222no—
172C2×Q8—442no—
173C2×D4—22no—
174C2×D4C22⋊D1111yescharacteristic
175C2×D4C22×D1111yescharacteristic
176C22×C4—21no—
177C22×C4—222no—
178C22×C4C22×D1112yes—
179SD16—222no—
180SD16—442no—
181M16—442no—
182C2×C8—111no—
183C2×C8—111no—
184C2×C8—112no—
185C4⋊C4—21no—
186C4⋊C4—111no—
187C4⋊C4—221no—
188C4⋊C4—221no—
189C4⋊C4—222no—
190C4⋊C4—221no—
191C4⋊C4C22⋊D1111yescharacteristic
192C4⋊C4C22×D1111yescharacteristic
193C4⋊C4C22×D1112yes—
194C22⋊C4—22no—
195C22⋊C4—22no—
196C22⋊C4—21no—
197C22⋊C4—222no—
198C22⋊C4C22⋊D1112yes—
199C42—22no—
200C42—221no—
201C42C22×D1111yescharacteristic
202C11#332911yescharacteristic, complemented, Sylow
203C23—21no—
204C23C2×C22⋊D1112yes—
205Q8—81no—
206Q8—112no—
207Q8—221no—
208Q8—222no—
209Q8—222no—
210Q8—444no—
211D4—22no—
212D4—21no—
213D4—21no—
214D4—82no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—42no—
220C2×C4—221no—
221C2×C4—221no—
222C2×C4—222no—
223C2×C4—444no—
224C2×C4C2×C22⋊D1112yes—
225C2×C4C2×C22⋊D1111yescharacteristic
226C2×C4C2×C22⋊D1111yescharacteristic
227C2×C4C23×D1111yescharacteristic
228C8—221no—
229C8—221no—
230C8—222no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—41no—
235C22—41no—
236C22—41no—
237C22C22×C22⋊D1111yescharacteristic
238C4—22no—
239C4—21no—
240C4—41no—
241C4—42no—
242C4—222no—
243C4—442no—
244C4—441no—
245C4#6700412yes—
246C4#41×D1111yescharacteristic
247C4#6704211yescharacteristic
248C2—42no—
249C2—81no—
250C2C2×#6700411yescharacteristic
251C2#1062336011yescharacteristic
252C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#555C2
socleC22×C11C22×D4
hypercenter#555D11
hypocenterC11#3329
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
2. D4×Dic22C2semidirect
3. #10622706C2semidirect
4. #10622704C2semidirect
5. #10622655C2semidirect
6. #10622653C2semidirect
7. #10622632C2semidirect
8. C4×#4324C2semidirect
9. #10622625C2semidirect
10. #10622617C2semidirect
11. #10622609C2semidirect
202. C11#3329semidirect

Maximal subgroups

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

subgroupindex
C11×#5552
D4×Dic222
#106227062
#106227042
#106226552
#106226532
#106226322
C4×#43242
#106226252
#106226172
#106226092
#332911