Finite Group Databasebeta

← #13081640

Subgroups — #13081640

Order 1408.

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

normal subgroups only

This group has 406 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#10623249C211yesmaximal, characteristic, complemented
2#10623073C211yesmaximal, characteristic, complemented
3C11×#459C211yesmaximal, characteristic, complemented
4#10622767C212yesmaximal, complemented
5#10622766C212yesmaximal, complemented
6#10622689C211yesmaximal, characteristic, complemented
7C4×#4323C211yesmaximal, characteristic, complemented
8#10622454C211yesmaximal, characteristic, complemented
9#10622444C211yesmaximal, characteristic, complemented
10#10622375C212yesmaximal, complemented
11#10622370C212yesmaximal, complemented
12C2×#4341—21no—
13C2×C11×D8C2212yes—
14C11×#127C2211yescharacteristic
15C4×D4×C11C2211yescharacteristic
16#66993C2212yes—
17#66992—22no—
18#66991—21no—
19#66989C2212yes—
20D4×Dic11C2212yes—
21C2×#4324C2212yes—
22C2×#4324C2212yes—
23C2×#4323C2211yescharacteristic
24#66979—21no—
25#66977—21no—
26C2×#4314C2212yes—
27#66940C2212yes—
28#66932—22no—
29C4×D44C2211yescharacteristic
30#66922C2211yescharacteristic
31C4×Dic22C2211yescharacteristic
32C11×C4⋊C8C2211yescharacteristic
33C11×#102C2212yes—
34#66896C2211yescharacteristic
35#66880C2212yes—
36#66879C2212yes—
37Dic11⋊C8C2212yes—
38#66873C2211yescharacteristic
39#66871C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×D4×C11—21no—
42C2×D4×C11—21no—
43C2×D4×C11C2311yescharacteristic
44C2×D4×C11C2312yes—
45C22×C4×C11—21no—
46C2×C22⋊D11—22no—
47C2×C22⋊D11—22no—
48C22×Dic11—22no—
49#4341—44no—
50C2×D44C2311yescharacteristic
51C2×C4×D11—21no—
52C2×Dic22D411yescharacteristic
53C2×Dic22C2312yes—
54C11×D8—42no—
55C2×C8×C11C2312yes—
56C11×C4⋊C4C2311yescharacteristic
57C11×C22⋊C4—21no—
58C42×C11C2311yescharacteristic
59C22⋊Dic11—22no—
60C22⋊Dic11—22no—
61C22⋊Dic11—22no—
62#4324—24no—
63#4324—42no—
64#4323—22no—
65(C2×D11)⋊C4—21no—
66C4⋊Dic11—21no—
67C4⋊Dic11—21no—
68C4⋊Dic11D411yescharacteristic
69C4⋊Dic11C2311yescharacteristic
70Dic11⋊C4—22no—
71Dic11⋊C4D412yes—
72C4×Dic11—22no—
73C4×Dic11C2312yes—
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2311yescharacteristic
76#4314—42no—
77#3397—111nomaximal, Sylow
78C23×C11—21no—
79C23×C11—22no—
80C22×D11—21no—
81D4×C11—21no—
82D4×C11—22no—
83D4×C11—22no—
84D4×C11—21no—
85D4×C11—42no—
86D4×C11—81no—
87C2×C4×C11—21no—
88C2×C4×C11—42no—
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2411yescharacteristic
92C22⋊D11—44no—
93C22⋊D11—82no—
94C2×Dic11—22no—
95C2×Dic11—21no—
96C2×Dic11—44no—
97C2×Dic11C2×D412yes—
98C2×Dic11C2×D412yes—
99D44—21no—
100D44—21no—
101C4×D11—42no—
102Dic22—22no—
103Dic22—22no—
104Dic22—22no—
105C8×C11—22no—
106C11⋊C8—21no—
107C11⋊C8#4112yescomplemented
108#556—111no—
109#550—111no—
110#496—112no—
111#492—111no—
112#463—112no—
113#461—111no—
114#460—112no—
115#459D1111yescharacteristic, complemented
116#446—111no—
117#440—112no—
118C4×D8—111no—
119C22×C11—41no—
120C22×C11—42no—
121C22×C11—41no—
122C22×C11—42no—
123C22×C11—42no—
124C22×C11—41no—
125C22×C11C22×D411yescharacteristic
126C2×D11—41no—
127C2×D11—41no—
128C2×D11—41no—
129C4×C11—21no—
130C4×C11—41no—
131C4×C11AGL(1,ℤ/8)12yes—
132C4×C11C2×#4111yescharacteristic
133C4×C11H(5,𝔽2)11yescharacteristic
134Dic11—22no—
135Dic11—22no—
136Dic11—42no—
137Dic11—41no—
138C2×#41—221no—
139C2×SD16—112no—
140C2×SD16—112no—
141C2×SD16—112no—
142C2×D8—111no—
143C2×D8C2×D1112yes—
144C4⋊Q8—111no—
145#127—112no—
146#127C2×D1111yescharacteristic
147#126—222no—
148#124—112no—
149C22⋊Q8—221no—
150#121—221no—
151#121—222no—
152C4×Q8—111no—
153C4×Q8—112no—
154C4×D4—112no—
155C4×D4—111no—
156C4×D4C2×D1111yescharacteristic
157#117—221no—
158#107—111no—
159C4⋊C8—112no—
160C4⋊C8C2×D1111yescharacteristic
161#103—112no—
162#102—111no—
163#102—111no—
164#102C2×D1112yes—
165#97—112no—
166C4×C8—111no—
167C2×C11—81no—
168C2×C11—82no—
169C2×C11#55011yescharacteristic
170C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C11#57711yescharacteristic
172D11—81no—
173#41—444no—
174C2×Q8—111no—
175C2×Q8—112no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—111no—
179C2×D4—222no—
180C2×D4—222no—
181C2×D4C22×D1111yescharacteristic
182C2×D4C22×D1112yes—
183C22×C4—21no—
184C22×C4—222no—
185C22×C4—221no—
186SD16—224no—
187SD16—442no—
188SD16—442no—
189D8—42no—
190D8—222no—
191C2×C8—111no—
192C2×C8—111no—
193C2×C8C22×D1112yes—
194C4⋊C4—111no—
195C4⋊C4—112no—
196C4⋊C4—111no—
197C4⋊C4—222no—
198C4⋊C4—221no—
199C4⋊C4—221no—
200C4⋊C4C22×D1111yescharacteristic
201C22⋊C4—21no—
202C22⋊C4—222no—
203C22⋊C4—222no—
204C22⋊C4—222no—
205C22⋊C4—221no—
206C42—112no—
207C42—222no—
208C42C22×D1111yescharacteristic
209C11#339711yescharacteristic, complemented, Sylow
210C23—21no—
211C23—22no—
212C23—221no—
213Q8—222no—
214Q8—222no—
215Q8—222no—
216D4—21no—
217D4—22no—
218D4—21no—
219D4—22no—
220D4—42no—
221D4—81no—
222D4—221no—
223D4—221no—
224D4—444no—
225D4—882no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—112no—
229C2×C4—112no—
230C2×C4—222no—
231C2×C4—221no—
232C2×C4—444no—
233C2×C4—442no—
234C2×C4D4×D1111yescharacteristic
235C2×C4D4×D1111yescharacteristic
236C2×C4C23×D1111yescharacteristic
237C8—22no—
238C8—112no—
239C8—221no—
240C22—41no—
241C22—42no—
242C22—42no—
243C22—41no—
244C22—41no—
245C22—42no—
246C22—441no—
247C22—441no—
248C22—441no—
249C22C2×D4×D1111yescharacteristic
250C4—21no—
251C4—41no—
252C4—222no—
253C4—222no—
254C4—441no—
255C4—442no—
256C4#6696412yes—
257C4#6703711yescharacteristic
258C4#41×D1111yescharacteristic
259C2—81no—
260C2—82no—
261C2—881no—
262C2#1062313011yescharacteristic
263C2C2×#6696411yescharacteristic
264C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#459C2
socleC22×C11C22×D4
hypercenter#459D11
hypocenterC11#3397
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #10623249C2semidirect
2. #10623073C2semidirect
3. C11×#459C2semidirect
4. #10622767C2semidirect
5. #10622766C2semidirect
6. #10622689C2semidirect
7. C4×#4323C2semidirect
8. #10622454C2semidirect
9. #10622444C2semidirect
10. #10622375C2semidirect
11. #10622370C2semidirect
107. C11⋊C8#41semidirect
115. #459D11semidirect
209. C11#3397semidirect

Maximal subgroups

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

subgroupindex
#106232492
#106230732
C11×#4592
#106227672
#106227662
#106226892
C4×#43232
#106224542
#106224442
#106223752
#106223702
#339711