Finite Group Databasebeta

← #13078445

Subgroups — #13078445

Order 1408.

398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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#10623052C211yesmaximal, characteristic
2#10623031C211yesmaximal, characteristic, complemented
3C11×#428C211yesmaximal, characteristic, complemented
4#10622744C211yesmaximal, characteristic
5#10622732C211yesmaximal, characteristic, complemented
6#10622611C211yesmaximal, characteristic, complemented
7C2×#66873C211yesmaximal, characteristic
8#10622504C212yesmaximal, complemented
9#10622503C212yesmaximal, complemented
10#10622484C212yesmaximal, complemented
11#10622483C212yesmaximal, complemented
12C22×D44C2211yescharacteristic
13C2×C11×M16C2211yescharacteristic
14C11×#117C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16#66979C2211yescharacteristic
17#66979C2211yescharacteristic
18#66977—22no—
19C22×C11⋊C8C2211yescharacteristic
20#66946C2212yes—
21#66946C2212yes—
22#66943—21no—
23#66943C2212yescomplemented
24#66941—21no—
25#66941C2212yescomplemented
26C22⋊C4×D11—22no—
27C4×D44—21no—
28C4×D44—21no—
29C11×#107C2212yescomplemented
30C11×#106C2212yescomplemented
31#66885C2212yes—
32#66885C2212yes—
33Dic11⋊C8C2212yescomplemented
34Dic11⋊C8C2212yescomplemented
35#66873C2212yes—
36#66873C2212yes—
37#66872C2211yescharacteristic, complemented
38#66872C2211yescharacteristic, complemented
39#66871C2211yescharacteristic, complemented
40#66871C2211yescharacteristic, complemented
41C23×D11—21no—
42C22×C4×C11—21no—
43C22×C4×C11C2311yescharacteristic
44C2×D44—21no—
45C2×D44—22no—
46C2×D44Q814yescomplemented
47C2×D44C2312yes—
48C2×C4×D11—22no—
49C2×C4×D11—22no—
50C2×Dic22—22no—
51C11×M16—22no—
52C2×C8×C11C2312yes—
53C11×C4⋊C4—21no—
54C11×C4⋊C4C2311yescharacteristic
55C11×C4⋊C4C2311yescharacteristic
56C11×C4⋊C4C2312yes—
57C11×C22⋊C4—21no—
58C42×C11—21no—
59C22⋊Dic11—21no—
60C22⋊Dic11D412yes—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4—22no—
63C4⋊Dic11—22no—
64C4⋊Dic11D411yescharacteristic
65C4⋊Dic11D411yescharacteristic
66C4⋊Dic11C2311yescharacteristic
67C4⋊Dic11C2311yescharacteristic
68Dic11⋊C4—22no—
69Dic11⋊C4—22no—
70C4×Dic11—21no—
71C4×Dic11C2312yes—
72C2×C11⋊C8—22no—
73C2×C11⋊C8C2311yescharacteristic
74C2×C11⋊C8C2311yescharacteristic
75#3081—111nomaximal, Sylow
76C23×C11C2×D411yescharacteristic
77C22×D11—22no—
78C22×D11—24no—
79C22×D11—81no—
80C22×D11—81no—
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—81no—
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×Q812yes—
87C2×C4×C11#4112yes—
88C2×C4×C11C2411yescharacteristic
89C2×Dic11—21no—
90C2×Dic11—21no—
91C2×Dic11C2×D412yes—
92C2×Dic11C2×D412yes—
93D44—24no—
94D44—22no—
95D44C2×Q814yes—
96C4×D11—82no—
97C4×D11—82no—
98Dic22—82no—
99C8×C11—22no—
100C11⋊C8—21no—
101C11⋊C8—21no—
102#544—111no—
103#518—111no—
104#478—112no—
105#478—112no—
106#476—112no—
107#474—112no—
108#428D1111yescharacteristic, complemented
109#427—111no—
110#424—111no—
111#418—111no—
112C2×#102—111no—
113C22×C11—21no—
114C22×C11—21no—
115C22×C11C22⋊Q812yes—
116C22×C11C22×D411yescharacteristic
117C2×D11—24no—
118C2×D11—42no—
119C2×D11—42no—
120C2×D11—84no—
121C4×C11—42no—
122C4×C11—41no—
123C4×C11—41no—
124C4×C11C22⋊Q812yes—
125C4×C11C22×Q811yescharacteristic
126C4×C11C2×#4111yescharacteristic
127Dic11—22no—
128Dic11—22no—
129Dic11—41no—
130Dic11—41no—
131C22×D4—111no—
132C2×M16C2×D1111yescharacteristic
133C22×C8—111no—
134C4⋊Q8—112no—
135C4⋊Q8—221no—
136#125—112no—
137#125—221no—
138C22⋊Q8—222no—
139C4×D4—112no—
140C4×D4—112no—
141C4×D4—221no—
142C4×D4—221no—
143#117—111no—
144#117—111no—
145#117C2×D1111yescharacteristic
146C2×C4⋊C4C2×D1111yescharacteristic
147C2×C22⋊C4—222no—
148#107—111no—
149#107—111no—
150#107C2×D1112yescomplemented
151#106—111no—
152#106—111no—
153#106C2×D1112yescomplemented
154C4⋊C8—112no—
155C4⋊C8—112no—
156#102—112no—
157#102—112no—
158#102—112no—
159#102—112no—
160C2×C11—22no—
161C2×C11C2×C22⋊Q811yescharacteristic
162C2×C11#57611yescharacteristic
163C2×C11#57711yescharacteristic
164D11—44no—
165C24—221no—
166C2×Q8—222no—
167C2×D4—114no—
168C2×D4—112no—
169C2×D4—222no—
170C2×D4—221no—
171C22×C4—21no—
172C22×C4—222no—
173C22×C4—222no—
174C22×C4C22×D1111yescharacteristic
175M16—22no—
176C2×C8—111no—
177C2×C8—111no—
178C2×C8—222no—
179C2×C8C22×D1112yes—
180C4⋊C4—21no—
181C4⋊C4—111no—
182C4⋊C4—111no—
183C4⋊C4—111no—
184C4⋊C4—111no—
185C4⋊C4—222no—
186C4⋊C4—222no—
187C4⋊C4—222no—
188C4⋊C4C22×D1112yes—
189C4⋊C4C22×D1111yescharacteristic
190C4⋊C4C22×D1111yescharacteristic
191C22⋊C4—21no—
192C22⋊C4—112no—
193C22⋊C4—222no—
194C22⋊C4—222no—
195C22⋊C4—221no—
196C42—21no—
197C42—112no—
198C42—221no—
199C11#308111yescharacteristic, complemented, Sylow
200C23—222no—
201C23—224no—
202C23—881no—
203C23—881no—
204C23D4×D1111yescharacteristic
205Q8—882no—
206D4—114no—
207D4—224no—
208D4—222no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—81no—
213C2×C4—112no—
214C2×C4—112no—
215C2×C4—221no—
216C2×C4—221no—
217C2×C4—882no—
218C2×C4—882no—
219C2×C4#433912yes—
220C2×C4D4×D1111yescharacteristic
221C2×C4Q8×D1112yes—
222C2×C4C23×D1111yescharacteristic
223C8—22no—
224C8—221no—
225C8—221no—
226C22—21no—
227C22—21no—
228C22—224no—
229C22—442no—
230C22—442no—
231C22—884no—
232C22#6694912yes—
233C22C2×D4×D1111yescharacteristic
234C4—42no—
235C4—41no—
236C4—41no—
237C4—222no—
238C4—222no—
239C4—441no—
240C4—441no—
241C4#6694912yes—
242C4C2×#433911yescharacteristic
243C4C2×Q8×D1111yescharacteristic
244C2—22no—
245C2—444no—
246C2C2×#6694911yescharacteristic
247C2#1062330511yescharacteristic
248C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#428C2
socleC22×C11C22×D4
prime radicalC22×D44C22
hypercenter#428D11
hypocenterC11#3081
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #10623031C2semidirect
3. C11×#428C2semidirect
5. #10622732C2semidirect
6. #10622611C2semidirect
8. #10622504C2semidirect
9. #10622503C2semidirect
10. #10622484C2semidirect
11. #10622483C2semidirect
23. #66943C22semidirect
25. #66941C22semidirect
29. C11×#107C22semidirect
30. C11×#106C22semidirect
33. Dic11⋊C8C22semidirect
34. Dic11⋊C8C22semidirect
37. #66872C22semidirect
38. #66872C22semidirect
39. #66871C22semidirect
40. #66871C22semidirect
46. C2×D44Q8semidirect
108. #428D11semidirect
150. #107C2×D11semidirect
153. #106C2×D11semidirect
199. C11#3081semidirect

Maximal subgroups

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

subgroupindex
#106230522
#106230312
C11×#4282
#106227442
#106227322
#106226112
C2×#668732
#106225042
#106225032
#106224842
#106224832
#308111