Finite Group Databasebeta

← #13079519

Subgroups — #13079519

Order 1408.

402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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#10623160C212yesmaximal, complemented
2C11×#467C211yesmaximal, characteristic, complemented
3#10622800C212yesmaximal, complemented
4#10622728C211yesmaximal, characteristic, complemented
5#10622723C211yesmaximal, characteristic, complemented
6#10622662C212yesmaximal, complemented
7#10622495C212yesmaximal, complemented
8#10622424C212yesmaximal, complemented
9#10622422C212yesmaximal, complemented
10C2×#4343C2212yes—
11C2×#4339C2211yescharacteristic
12C2×C11×Q16C2211yescharacteristic
13C22×C8×C11C2211yescharacteristic
14C11×C22⋊Q8C2212yes—
15#66999C2212yes—
16C2×#4325C2212yes—
17#66983C2212yes—
18C2×#4318C2211yescharacteristic
19C2×D88C2211yescharacteristic
20#66949—22no—
21#66948—22no—
22#66948C2212yes—
23C4⋊C4×D11C2212yes—
24#66937—22no—
25#66937—22no—
26C11×#107C2211yescharacteristic
27C11×#103C2212yes—
28#66899C2212yes—
29#66885C2212yes—
30(C2×D11)⋊C8C2212yes—
31(C2×D11)⋊C8C2212yes—
32#66882C2211yescharacteristic
33#66873C2212yes—
34#66871C2212yes—
35C2×Q8×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C2×C22⋊D11—22no—
38C2×C22⋊D11D412yes—
39#4343—42no—
40#4343—42no—
41#4339—41no—
42#4339—41no—
43C2×D44—22no—
44C2×D44—22no—
45C2×D44D411yescharacteristic
46C2×D44C2312yes—
47C2×C4×D11—22no—
48C2×C4×D11—22no—
49C2×C4×D11C2312yes—
50C2×Dic22D411yescharacteristic
51C11×Q16—41no—
52C2×C8×C11—41no—
53C2×C8×C11C2311yescharacteristic
54C2×C8×C11C2311yescharacteristic
55C11×C4⋊C4—22no—
56C11×C4⋊C4C2312yes—
57C11×C22⋊C4—22no—
58#4325—42no—
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—22no—
62C4⋊Dic11C2312yes—
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65#4318—41no—
66C2×C11⋊C8C2312yes—
67D88—41no—
68#3203—111nomaximal, Sylow
69C23×C11C2×D411yescharacteristic
70C22×D11—22no—
71C22×D11C2×D412yes—
72Q8×C11—22no—
73Q8×C11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2411yescharacteristic
80C22⋊D11—42no—
81C22⋊D11—82no—
82C2×Dic11—22no—
83C2×Dic11C2×D412yes—
84D44—22no—
85D44—22no—
86D44—41no—
87D44—44no—
88D44—82no—
89C4×D11—22no—
90C4×D11—22no—
91C4×D11—44no—
92C4×D11—82no—
93Dic22—41no—
94C8×C11—21no—
95C8×C11—21no—
96C11⋊C8—22no—
97#537—112no—
98#484—112no—
99#480—112no—
100#468—112no—
101#467D1111yescharacteristic, complemented
102#466—111no—
103#452—112no—
104#449—112no—
105#408—111no—
106C22×C11—21no—
107C22×C11—21no—
108C22×C11—21no—
109C22×C11C22×D411yescharacteristic
110C2×D11—22no—
111C2×D11—22no—
112C2×D11—22no—
113C2×D11—42no—
114C2×D11—42no—
115C2×D11—42no—
116C4×C11—21no—
117C4×C11—42no—
118C4×C11—42no—
119C4×C11H(5,𝔽2)11yescharacteristic
120C4×C11H(5,𝔽2)11yescharacteristic
121Dic11—22no—
122Dic11—42no—
123C2×#41—111no—
124C2×#41—112no—
125C2×Q16C2×D1111yescharacteristic
126C2×SD16—112no—
127C2×D8—111no—
128C2×M16—111no—
129C22×C8C2×D1111yescharacteristic
130C22⋊Q8—112no—
131C22⋊Q8—222no—
132C22⋊Q8C2×D1112yes—
133#121—112no—
134#121—112no—
135#121—222no—
136#121—222no—
137#121—222no—
138C2×C4⋊C4—112no—
139#107—111no—
140#107—112no—
141#107C2×D1111yescharacteristic
142#103—112no—
143#103C2×D1112yes—
144#102—112no—
145#102—112no—
146C22⋊C8—112no—
147C22⋊C8—112no—
148C2×C11—41no—
149C2×C11#53411yescharacteristic
150C2×C11#57611yescharacteristic
151C2×C11#57811yescharacteristic
152D11—42no—
153D11—82no—
154#41—441no—
155#41—441no—
156#41—442no—
157#41—442no—
158C2×Q8—111no—
159C2×Q8C22×D1112yes—
160C2×D4—112no—
161C2×D4—111no—
162C2×D4—112no—
163C2×D4—222no—
164C2×D4—222no—
165C2×D4—222no—
166C22×C4—112no—
167C22×C4—222no—
168C22×C4—222no—
169C22×C4C22×D1111yescharacteristic
170Q16—41no—
171SD16—442no—
172D8—441no—
173M16—441no—
174C2×C8—41no—
175C2×C8—112no—
176C2×C8C22×D1111yescharacteristic
177C2×C8C22×D1111yescharacteristic
178C4⋊C4—22no—
179C4⋊C4—112no—
180C4⋊C4—222no—
181C4⋊C4—222no—
182C4⋊C4C22×D1112yes—
183C22⋊C4—22no—
184C22⋊C4—222no—
185C22⋊C4—222no—
186C22⋊C4—222no—
187C11#320311yescharacteristic, complemented, Sylow
188C23—112no—
189C23—222no—
190C23D4×D1111yescharacteristic
191Q8—22no—
192Q8—22no—
193Q8—441no—
194D4—222no—
195D4—222no—
196D4—441no—
197D4—444no—
198D4—442no—
199D4—882no—
200D4—882no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—112no—
206C2×C4—222no—
207C2×C4—222no—
208C2×C4—222no—
209C2×C4—444no—
210C2×C4—882no—
211C2×C4D4×D1111yescharacteristic
212C2×C4C23×D1111yescharacteristic
213C8—21no—
214C8—21no—
215C8—222no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—222no—
220C22—222no—
221C22—222no—
222C22—442no—
223C22—442no—
224C22—442no—
225C22C2×D4×D1111yescharacteristic
226C4—21no—
227C4—42no—
228C4—42no—
229C4—222no—
230C4—442no—
231C4#6703711yescharacteristic
232C4#6704211yescharacteristic
233C2—41no—
234C2—442no—
235C2—882no—
236C2#1062313611yescharacteristic
237C2#1062329711yescharacteristic
238C2#1062330011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#467C2
socleC22×C11C22×D4
hypercenter#467D11
hypocenterC11#3203
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #10623160C2semidirect
2. C11×#467C2semidirect
3. #10622800C2semidirect
4. #10622728C2semidirect
5. #10622723C2semidirect
6. #10622662C2semidirect
7. #10622495C2semidirect
8. #10622424C2semidirect
9. #10622422C2semidirect
101. #467D11semidirect
187. C11#3203semidirect

Maximal subgroups

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

subgroupindex
#106231602
C11×#4672
#106228002
#106227282
#106227232
#106226622
#106224952
#106224242
#106224222
#320311