Finite Group Databasebeta

← #13081017

Subgroups — #13081017

Order 1408.

366 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 115 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#10623226C212yesmaximal, complemented
2C11×#499C211yesmaximal, characteristic, complemented
3#10622679C212yesmaximal, complemented
4#10622496C211yesmaximal, characteristic, complemented
5#10622496C211yesmaximal, characteristic, complemented
6#10622493C211yesmaximal, characteristic, complemented
7D11×#107C211yesmaximal, characteristic, complemented
8#10622479C212yesmaximal, complemented
9#10622476C212yesmaximal, complemented
10C4×D88C211yesmaximal, characteristic, complemented
11C8×D44C211yesmaximal, characteristic, complemented
12C11×#125C2212yes—
13C2×D88C2211yescharacteristic
14C2×C8×D11C2211yescharacteristic
15C2×C8×D11C2211yescharacteristic
16#66951—22no—
17#66948—22no—
18#66948C2212yes—
19#66948C2212yes—
20#66947—22no—
21#66946—22no—
22#66945C2212yes—
23C4⋊C4×D11C2212yes—
24C4×D44C2211yescharacteristic
25C4×D44C2212yes—
26C11×#107C2211yescharacteristic
27C11×#107C2211yescharacteristic
28C11×#106C2212yes—
29C4×C8×C11C2211yescharacteristic
30#66885C2212yes—
31(C2×D11)⋊C8C2211yescharacteristic
32(C2×D11)⋊C8C2211yescharacteristic
33#66882C2211yescharacteristic
34#66873C2212yes—
35#66873C2212yes—
36#66872C2212yes—
37#66871C2212yes—
38C4⋊(C11⋊C8)C2211yescharacteristic
39C2×D44—22no—
40C2×D44—22no—
41C2×D44D411yescharacteristic
42C2×D44C2312yes—
43C2×C4×D11—22no—
44C2×C4×D11—22no—
45C2×C4×D11C2311yescharacteristic
46C2×C4×D11C2311yescharacteristic
47C2×C8×C11C2311yescharacteristic
48C2×C8×C11C2311yescharacteristic
49C11×C4⋊C4—22no—
50C11×C4⋊C4—22no—
51C11×C4⋊C4C2312yes—
52C11×C4⋊C4C2312yes—
53C42×C11C2311yescharacteristic
54(C2×D11)⋊C4—22no—
55(C2×D11)⋊C4—22no—
56(C2×D11)⋊C4—22no—
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4D411yescharacteristic
59(C2×D11)⋊C4D411yescharacteristic
60C4⋊Dic11D411yescharacteristic
61C4⋊Dic11C2312yes—
62Dic11⋊C4—22no—
63C4×Dic11—22no—
64C2×C11⋊C8C2311yescharacteristic
65C2×C11⋊C8C2311yescharacteristic
66D88—22no—
67C8×D11—22no—
68C8×D11—22no—
69#3339—111nomaximal, Sylow
70C22×D11—22no—
71C22×D11C2×D411yescharacteristic
72C22×D11C2×D411yescharacteristic
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2411yescharacteristic
78C2×Dic11—22no—
79C2×Dic11C2×D411yescharacteristic
80C2×Dic11C2×D411yescharacteristic
81D44—22no—
82D44—22no—
83D44—22no—
84D44—44no—
85D44—82no—
86C4×D11—21no—
87C4×D11—21no—
88C4×D11—21no—
89C4×D11—21no—
90C4×D11—82no—
91C4×D11—82no—
92C8×C11—21no—
93C8×C11#4112yes—
94C11⋊C8—21no—
95C11⋊C8—21no—
96#553—112no—
97#499D1111yescharacteristic, complemented
98#482—112no—
99#481—112no—
100#478—112no—
101#466—111no—
102#466—111no—
103C4×D8—111no—
104C8×D4—111no—
105#427—111no—
106C2×#107—111no—
107C22×C11C22×D411yescharacteristic
108C2×D11—21no—
109C2×D11—21no—
110C2×D11—21no—
111C2×D11—21no—
112C2×D11—21no—
113C2×D11—42no—
114C2×D11—42no—
115C2×D11—42no—
116C2×D11#13512yes—
117C4×C11—21no—
118C4×C11—21no—
119C4×C11—42no—
120C4×C11—42no—
121C4×C11C2×#4111yescharacteristic
122C4×C112−1+411yescharacteristic
123Dic11—21no—
124Dic11—21no—
125Dic11—42no—
126C2×D8—111no—
127C22×C8—111no—
128C22×C8—111no—
129#126—222no—
130#125C2×D1112yes—
131#123—222no—
132#121—112no—
133#121—112no—
134#121—222no—
135C4×D4—111no—
136C4×D4—112no—
137C4×D4—222no—
138#117—112no—
139C2×C4⋊C4—112no—
140#107—111no—
141#107—112no—
142#107C2×D1111yescharacteristic
143#107C2×D1111yescharacteristic
144#106—112no—
145#106C2×D1112yes—
146C4⋊C8—111no—
147#102—112no—
148#102—112no—
149#102—112no—
150C22⋊C8—111no—
151C22⋊C8—111no—
152C4×C8C2×D1111yescharacteristic
153C2×C11#54711yescharacteristic
154C2×C11C2×#13511yescharacteristic
155C2×C11#57611yescharacteristic
156D11—22no—
157D11—41no—
158D11—82no—
159C2×D4—111no—
160C2×D4—112no—
161C2×D4—222no—
162C2×D4—222no—
163C22×C4—111no—
164C22×C4—111no—
165C22×C4—222no—
166C22×C4—222no—
167D8—222no—
168C2×C8—111no—
169C2×C8—111no—
170C2×C8—222no—
171C2×C8—222no—
172C2×C8C22×D1111yescharacteristic
173C2×C8C22×D1111yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—111no—
177C4⋊C4—112no—
178C4⋊C4—222no—
179C4⋊C4C22×D1112yes—
180C4⋊C4C22×D1112yes—
181C22⋊C4—111no—
182C22⋊C4—111no—
183C22⋊C4—222no—
184C22⋊C4—222no—
185C22⋊C4—222no—
186C22⋊C4—222no—
187C42—222no—
188C42C22×D1111yescharacteristic
189C11#333911yescharacteristic, complemented, Sylow
190C23—111no—
191C23—111no—
192C23—222no—
193D4—222no—
194D4—222no—
195D4—222no—
196D4—444no—
197D4—882no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—111no—
201C2×C4—111no—
202C2×C4—221no—
203C2×C4—221no—
204C2×C4—221no—
205C2×C4—221no—
206C2×C4—222no—
207C2×C4—882no—
208C2×C4—882no—
209C2×C4D4×D1111yescharacteristic
210C2×C4D4×D1111yescharacteristic
211C2×C4C23×D1111yescharacteristic
212C8—21no—
213C8—221no—
214C8—221no—
215C8#434312yes—
216C22—112no—
217C22—221no—
218C22—221no—
219C22—221no—
220C22—221no—
221C22—221no—
222C22—442no—
223C22—442no—
224C22—442no—
225C22C2×D4×D1111yescharacteristic
226C4—21no—
227C4—21no—
228C4—42no—
229C4—42no—
230C4—221no—
231C4—221no—
232C4—442no—
233C4C2×#434311yescharacteristic
234C4#6704011yescharacteristic
235C2—222no—
236C2—441no—
237C2—882no—
238C2#1062325711yescharacteristic
239C2D11×#13511yescharacteristic
240C2#1062330011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#499C2
socleC22×C11C22×D4
hypercenter#499D11
hypocenterC11#3339
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #10623226C2semidirect
2. C11×#499C2semidirect
3. #10622679C2semidirect
4. #10622496C2semidirect
5. #10622496C2semidirect
6. #10622493C2semidirect
7. D11×#107C2semidirect
8. #10622479C2semidirect
9. #10622476C2semidirect
10. C4×D88C2semidirect
11. C8×D44C2semidirect
97. #499D11semidirect
189. C11#3339semidirect

Maximal subgroups

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

subgroupindex
#106232262
C11×#4992
#106226792
#106224962
#106224932
D11×#1072
#106224792
#106224762
C4×D882
C8×D442
#333911