Finite Group Databasebeta

← #13080533

Subgroups — #13080533

Order 1408.

386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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×#547C211yesmaximal, characteristic
2#10623073C211yesmaximal, characteristic, complemented
3#10622852C212yesmaximal, complemented
4#10622846C212yesmaximal, complemented
5#10622703C211yesmaximal, characteristic, complemented
6#10622694C211yesmaximal, characteristic, complemented
7#10622664C212yesmaximal, complemented
8#10622658C212yesmaximal, complemented
9C4×#4324C211yesmaximal, characteristic, complemented
10D4×C11⋊C8C211yesmaximal, characteristic, complemented
11#10622620C211yesmaximal, characteristic, complemented
12C2×C11×#41C2212yes—
13C11×C4⋊Q8C2211yescharacteristic
14C11×#123—22no—
15C11×C22⋊Q8C2212yes—
16C11×#121—21no—
17C4×D4×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19C2×C11×C4⋊C4—21no—
20C2×#4326C2212yes—
21#66989—21no—
22C2×#4324C2211yescharacteristic
23#66979C2212yes—
24#66977C2212yes—
25C22×C11⋊C8C2212yes—
26#66940—21no—
27#66932—22no—
28#66922C2211yescharacteristic
29C4×Dic22C2211yescharacteristic
30#66899C2212yes—
31#66899C2212yes—
32#66899C2212yes—
33#66896C2211yescharacteristic
34#66896C2212yes—
35C22⋊(C11⋊C8)C2212yes—
36#66874C2211yescharacteristic
37#66872C2211yescharacteristic
38#66871C2212yes—
39C4⋊(C11⋊C8)C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C11×#41—24no—
42C11×#41—42no—
43C2×Q8×C11C2312yes—
44C2×D4×C11—22no—
45C2×D4×C11D411yescharacteristic
46C2×D4×C11C2311yescharacteristic
47C22×C4×C11—21no—
48C22×C4×C11—22no—
49C22×C4×C11C2312yes—
50C2×Dic22—21no—
51C2×Dic22C2311yescharacteristic
52C11×C4⋊C4—21no—
53C11×C4⋊C4—22no—
54C11×C4⋊C4—21no—
55C11×C4⋊C4D411yescharacteristic
56C11×C4⋊C4C2311yescharacteristic
57C11×C22⋊C4—22no—
58C11×C22⋊C4—21no—
59C11×C22⋊C4D412yes—
60C42×C11C2311yescharacteristic
61C22⋊Dic11—22no—
62C22⋊Dic11—22no—
63#4326—42no—
64#4324—22no—
65C4⋊Dic11—21no—
66C4⋊Dic11C2312yes—
67C4⋊Dic11C2311yescharacteristic
68Dic11⋊C4—21no—
69Dic11⋊C4—22no—
70C4×Dic11—21no—
71C4×Dic11—22no—
72C2×C11⋊C8—42no—
73C2×C11⋊C8C2311yescharacteristic
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2312yes—
76#3302—111nomaximal, Sylow
77C23×C11—21no—
78C23×C11C2×D412yes—
79Q8×C11—22no—
80Q8×C11—22no—
81D4×C11—22no—
82D4×C11—21no—
83D4×C11—44no—
84D4×C11#4112yes—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—44no—
90C2×C4×C11—42no—
91C2×C4×C11C2×D412yes—
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2411yescharacteristic
95C2×Dic11—21no—
96C2×Dic11—21no—
97C2×Dic11—22no—
98Dic22—21no—
99Dic22—21no—
100Dic22—42no—
101C11⋊C8—21no—
102C11⋊C8—21no—
103C11⋊C8—22no—
104#556—111no—
105#547D1111yescharacteristic
106#487—111no—
107#485—112no—
108#474—111no—
109#467—112no—
110#462—111no—
111#452—112no—
112C4×SD16—111no—
113C8×D4—111no—
114#416—112no—
115C22×C11—22no—
116C22×C11—22no—
117C22×C11—22no—
118C22×C11—22no—
119C22×C11—41no—
120C22×C11—41no—
121C22×C11C22×D411yescharacteristic
122C4×C11—22no—
123C4×C11—21no—
124C4×C11—42no—
125C4×C11—41no—
126C4×C11#13512yes—
127C4×C11C2×#4111yescharacteristic
128C4×C11H(5,𝔽2)11yescharacteristic
129Dic11—41no—
130Dic11—42no—
131Dic11—41no—
132C2×#41C2×D1112yes—
133C2×Q16—112no—
134C2×SD16—111no—
135C22×C8—112no—
136C4⋊Q8—111no—
137C4⋊Q8C2×D1111yescharacteristic
138#126—222no—
139#124—221no—
140#123—22no—
141C22⋊Q8—112no—
142C22⋊Q8C2×D1112yes—
143#121—21no—
144C4×Q8—111no—
145C4×Q8—221no—
146C4×D4C2×D1111yescharacteristic
147C4×D4C2×D1111yescharacteristic
148#117—112no—
149C2×C4⋊C4—21no—
150#107—112no—
151#106—111no—
152C4⋊C8—111no—
153#103—112no—
154#103—112no—
155#103—112no—
156#103—111no—
157#102—111no—
158#102—112no—
159C22⋊C8—112no—
160C4×C8—111no—
161C2×C11—42no—
162C2×C11—42no—
163C2×C11#54611yescharacteristic
164C2×C11C2×#13511yescharacteristic
165C2×C11#57811yescharacteristic
166#41—24no—
167#41—42no—
168C2×Q8—111no—
169C2×Q8—221no—
170C2×Q8C22×D1112yes—
171C2×D4—22no—
172C2×D4C22⋊D1111yescharacteristic
173C2×D4C22×D1111yescharacteristic
174C22×C4—21no—
175C22×C4—22no—
176C22×C4C22×D1112yes—
177Q16—442no—
178SD16—222no—
179C2×C8—111no—
180C2×C8—111no—
181C2×C8—112no—
182C2×C8—442no—
183C4⋊C4—21no—
184C4⋊C4—22no—
185C4⋊C4—21no—
186C4⋊C4—111no—
187C4⋊C4—112no—
188C4⋊C4—221no—
189C4⋊C4—222no—
190C4⋊C4—221no—
191C4⋊C4C22⋊D1111yescharacteristic
192C4⋊C4C22×D1111yescharacteristic
193C22⋊C4—22no—
194C22⋊C4—21no—
195C22⋊C4—222no—
196C22⋊C4—222no—
197C22⋊C4C22⋊D1112yes—
198C42—222no—
199C42—221no—
200C42C22×D1111yescharacteristic
201C11#330211yescharacteristic, complemented, Sylow
202C23—21no—
203C23C2×C22⋊D1112yes—
204Q8—22no—
205Q8—22no—
206Q8—221no—
207Q8—221no—
208Q8—442no—
209D4—22no—
210D4—21no—
211D4—44no—
212D4#434112yes—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—44no—
218C2×C4—42no—
219C2×C4—221no—
220C2×C4—222no—
221C2×C4—221no—
222C2×C4C2×C22⋊D1112yes—
223C2×C4C2×C22⋊D1111yescharacteristic
224C2×C4C2×C22⋊D1111yescharacteristic
225C2×C4C23×D1111yescharacteristic
226C8—221no—
227C8—221no—
228C8—222no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—41no—
234C22—41no—
235C22C22×C22⋊D1111yescharacteristic
236C4—22no—
237C4—21no—
238C4—42no—
239C4—41no—
240C4—441no—
241C4—442no—
242C4—441no—
243C4#6700312yes—
244C4C2×#434111yescharacteristic
245C4#6703711yescharacteristic
246C2—42no—
247C2—42no—
248C2#1062333711yescharacteristic
249C2C2×#6700311yescharacteristic
250C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#547C2
socleC22×C11C22×D4
hypercenter#547D11
hypocenterC11#3302
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
2. #10623073C2semidirect
3. #10622852C2semidirect
4. #10622846C2semidirect
5. #10622703C2semidirect
6. #10622694C2semidirect
7. #10622664C2semidirect
8. #10622658C2semidirect
9. C4×#4324C2semidirect
10. D4×C11⋊C8C2semidirect
11. #10622620C2semidirect
201. C11#3302semidirect

Maximal subgroups

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

subgroupindex
C11×#5472
#106230732
#106228522
#106228462
#106227032
#106226942
#106226642
#106226582
C4×#43242
D4×C11⋊C82
#106226202
#330211