Finite Group Databasebeta

← #13078984

Subgroups — #13078984

Order 1408.

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

normal subgroups only

This group has 372 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
1#10623356C211yesmaximal, characteristic
2#10623031C211yesmaximal, characteristic, complemented
3C11×#417C211yesmaximal, characteristic
4#10622846C211yesmaximal, characteristic
5#10622735C211yesmaximal, characteristic, complemented
6#10622733C211yesmaximal, characteristic, complemented
7C2×#66874C211yesmaximal, characteristic, complemented
8#10622410C212yesmaximal, complemented
9#10622405C212yesmaximal, complemented
10#10622381C212yesmaximal, complemented
11#10622378C212yesmaximal, complemented
12C2×C11×#41C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C2×C11×M16C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16#66997C2212yes—
17#66989C2212yes—
18#66988—22no—
19#66979C2211yescharacteristic
20#66979C2211yescharacteristic
21#66977—22no—
22#66977—21no—
23#66977—21no—
24C22×C11⋊C8C2211yescharacteristic
25#66943—21no—
26#66943C2212yes—
27#66941—21no—
28#66941C2212yes—
29C11×#103C2212yes—
30C11×#102C2212yes—
31#66899C2211yescharacteristic
32#66899C2211yescharacteristic
33#66896C2211yescharacteristic
34#66896C2211yescharacteristic
35#66880C2212yes—
36#66880C2212yes—
37#66879C2212yes—
38C8×Dic11C2212yes—
39#66874C2212yes—
40#66874C2212yes—
41C11×#41—22no—
42C11×#41—22no—
43C2×Q8×C11C2311yescharacteristic
44C2×D4×C11—21no—
45C2×D4×C11C2311yescharacteristic
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11C2311yescharacteristic
49C22×Dic11—21no—
50C2×Dic22—22no—
51C2×Dic22—21no—
52C2×Dic22—22no—
53C2×Dic22—22no—
54C2×Dic22C2312yes—
55C11×M16—22no—
56C2×C8×C11C2312yes—
57C11×C4⋊C4—21no—
58C11×C4⋊C4C2312yes—
59C22⋊Dic11—22no—
60C22⋊Dic11—22no—
61C22⋊Dic11—21no—
62C22⋊Dic11D412yes—
63C4⋊Dic11—22no—
64C4⋊Dic11D411yescharacteristic
65C4⋊Dic11D411yescharacteristic
66C4⋊Dic11C2311yescharacteristic
67C4⋊Dic11C2311yescharacteristic
68Dic11⋊C4—22no—
69Dic11⋊C4—22no—
70Dic11⋊C4—22no—
71Dic11⋊C4—22no—
72C4×Dic11—21no—
73C4×Dic11C2312yes—
74C2×C11⋊C8—22no—
75C2×C11⋊C8C2311yescharacteristic
76C2×C11⋊C8C2311yescharacteristic
77#3137—111nomaximal, Sylow
78C23×C11—21no—
79C23×C11C2×D411yescharacteristic
80Q8×C11—21no—
81Q8×C11—21no—
82D4×C11—21no—
83D4×C11—21no—
84D4×C11—42no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11—42no—
88C2×C4×C11—81no—
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11#4112yes—
91C2×C4×C11#4112yes—
92C2×C4×C11C2411yescharacteristic
93C2×Dic11—21no—
94C2×Dic11—21no—
95C2×Dic11—22no—
96C2×Dic11—42no—
97C2×Dic11C2×D412yes—
98C2×Dic11C2×D412yes—
99Dic22—22no—
100Dic22—22no—
101Dic22—42no—
102Dic22—82no—
103C8×C11—22no—
104C11⋊C8—21no—
105C11⋊C8—21no—
106#544—111no—
107#536—111no—
108#491—112no—
109#489—112no—
110#488—112no—
111#487—112no—
112#419—111no—
113#417D1111yescharacteristic
114#416—111no—
115C2×#103—111no—
116#405—111no—
117C22×C11—21no—
118C22×C11—21no—
119C22×C11—41no—
120C22×C11—41no—
121C22×C11—41no—
122C22×C11#12412yes—
123C22×C11C22×D411yescharacteristic
124C4×C11—41no—
125C4×C11—42no—
126C4×C11#12412yes—
127C4×C11C2×#4111yescharacteristic
128C4×C11C2×#4111yescharacteristic
129Dic11—22no—
130Dic11—22no—
131Dic11—42no—
132Dic11—41no—
133Dic11—41no—
134C2×#41C2×D1111yescharacteristic
135C22×Q8—111no—
136C2×M16C2×D1111yescharacteristic
137C22×C8—111no—
138C4⋊Q8—112no—
139C4⋊Q8—112no—
140C4⋊Q8—221no—
141#125—112no—
142#125—221no—
143#124—112no—
144#123—222no—
145C22⋊Q8—222no—
146C22⋊Q8—221no—
147C22⋊Q8—221no—
148#117—111no—
149#117—111no—
150C2×C4⋊C4C2×D1111yescharacteristic
151#103—111no—
152#103—111no—
153#103—112no—
154#103—112no—
155#103—112no—
156#103—112no—
157#103C2×D1112yes—
158#102—111no—
159#102—111no—
160#102C2×D1112yes—
161#97—112no—
162C4×C8—112no—
163C2×C11—22no—
164C2×C11—81no—
165C2×C11C2×#12411yescharacteristic
166C2×C11#57711yescharacteristic
167C2×C11#57811yescharacteristic
168#41—22no—
169#41—22no—
170C2×Q8—112no—
171C2×Q8—222no—
172C2×Q8—221no—
173C2×Q8—222no—
174C2×Q8—222no—
175C2×Q8C22×D1111yescharacteristic
176C2×D4—21no—
177C2×D4C22×D1111yescharacteristic
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—221no—
181C22×C4C22×D1111yescharacteristic
182M16—22no—
183C2×C8—111no—
184C2×C8—111no—
185C2×C8—222no—
186C2×C8C22×D1112yes—
187C4⋊C4—21no—
188C4⋊C4—111no—
189C4⋊C4—111no—
190C4⋊C4—111no—
191C4⋊C4—111no—
192C4⋊C4—222no—
193C4⋊C4—222no—
194C4⋊C4—222no—
195C4⋊C4—222no—
196C4⋊C4—222no—
197C4⋊C4C22×D1112yes—
198C22⋊C4—112no—
199C22⋊C4—222no—
200C22⋊C4—222no—
201C22⋊C4—221no—
202C42—112no—
203C42—221no—
204C11#313711yescharacteristic, complemented, Sylow
205C23—21no—
206C23D4×D1111yescharacteristic
207Q8—21no—
208Q8—21no—
209Q8—222no—
210Q8—222no—
211Q8—442no—
212Q8—882no—
213D4—21no—
214D4—21no—
215D4—42no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—81no—
220C2×C4—112no—
221C2×C4—112no—
222C2×C4—221no—
223C2×C4—221no—
224C2×C4—222no—
225C2×C4—442no—
226C2×C4#433912yes—
227C2×C4D4×D1111yescharacteristic
228C2×C4#434112yes—
229C2×C4C23×D1111yescharacteristic
230C8—22no—
231C8—221no—
232C8—221no—
233C22—21no—
234C22—21no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22#6693812yes—
239C22C2×D4×D1111yescharacteristic
240C4—41no—
241C4—42no—
242C4—222no—
243C4—222no—
244C4—442no—
245C4—441no—
246C4—441no—
247C4#6693812yes—
248C4C2×#433911yescharacteristic
249C4C2×#434111yescharacteristic
250C2—22no—
251C2—81no—
252C2C2×#6693811yescharacteristic
253C2#1062330611yescharacteristic
254C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#417C2
socleC22×C11C22×D4
prime radicalC2×C11×#41C22
hypercenter#417D11
hypocenterC11#3137
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. #10623031C2semidirect
5. #10622735C2semidirect
6. #10622733C2semidirect
7. C2×#66874C2semidirect
8. #10622410C2semidirect
9. #10622405C2semidirect
10. #10622381C2semidirect
11. #10622378C2semidirect
204. C11#3137semidirect

Maximal subgroups

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

subgroupindex
#106233562
#106230312
C11×#4172
#106228462
#106227352
#106227332
C2×#668742
#106224102
#106224052
#106223812
#106223782
#313711