Finite Group Databasebeta

← #13078588

Subgroups — #13078588

Order 1408.

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

normal subgroups only

This group has 386 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#10623057C211yesmaximal, characteristic
2#10623054C211yesmaximal, characteristic
3C11×#427C211yesmaximal, characteristic, complemented
4#10622723C211yesmaximal, characteristic
5C2×#66880C211yesmaximal, characteristic, complemented
6#10622617C211yesmaximal, characteristic, complemented
7#10622608C211yesmaximal, characteristic, complemented
8#10622501C212yesmaximal, complemented
9#10622497C212yesmaximal, complemented
10#10622480C212yesmaximal, complemented
11#10622475C212yesmaximal, complemented
12C2×#4339C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C22×C8×C11C2211yescharacteristic
15C11×#117C2211yescharacteristic
16C11×#117C2211yescharacteristic
17C2×C4⋊Dic11C2211yescharacteristic
18C2×#4318C2211yescharacteristic
19#66950C2212yes—
20#66950C2212yes—
21#66945C2212yes—
22C4⋊C4×D11C2212yes—
23#66939—22no—
24(C22⋊D11)⋊C4—22no—
25#66928—21no—
26C4×D44—21no—
27#66922—21no—
28C4×Dic22—21no—
29C11×#107C2211yescharacteristic
30C11×#107C2211yescharacteristic
31C11×#106C2211yescharacteristic
32C11×#106C2211yescharacteristic
33(C2×D11)⋊C8C2212yes—
34(C2×D11)⋊C8C2212yes—
35#66880C2212yes—
36#66880C2212yes—
37#66874C2212yes—
38#66874C2212yes—
39#66872C2212yes—
40#66871C2212yes—
41C22×C4×C11C2311yescharacteristic
42C2×C22⋊D11D412yes—
43C22×Dic11—21no—
44C22×Dic11—21no—
45#4339—22no—
46#4339—22no—
47C2×D44D411yescharacteristic
48C2×C4×D11—22no—
49C2×C4×D11C2312yes—
50C2×Dic22—21no—
51C2×Dic22—22no—
52C2×Dic22—22no—
53C2×Dic22D411yescharacteristic
54C2×Dic22C2312yes—
55C2×C8×C11—22no—
56C2×C8×C11C2311yescharacteristic
57C2×C8×C11C2311yescharacteristic
58C11×C4⋊C4C2311yescharacteristic
59C11×C4⋊C4C2311yescharacteristic
60C11×C4⋊C4C2311yescharacteristic
61C11×C4⋊C4C2311yescharacteristic
62C11×C22⋊C4—21no—
63C11×C22⋊C4—21no—
64C42×C11—21no—
65C42×C11—21no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—22no—
69C4⋊Dic11—22no—
70C4⋊Dic11—22no—
71C4⋊Dic11—21no—
72C4⋊Dic11C2312yes—
73Dic11⋊C4—22no—
74C4×Dic11—22no—
75#4318—22no—
76C2×C11⋊C8C2312yes—
77#3097—111nomaximal, Sylow
78C23×C11C2×D411yescharacteristic
79C22×D11C2×D412yes—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11#4112yes—
86C2×C4×C11#4112yes—
87C2×C4×C11C2411yescharacteristic
88C22⋊D11—24no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—42no—
92C2×Dic11—81no—
93C2×Dic11C2×D412yes—
94D44—22no—
95C4×D11—22no—
96C4×D11—22no—
97C4×D11—82no—
98Dic22—22no—
99Dic22—22no—
100Dic22—22no—
101Dic22—42no—
102C8×C11—21no—
103C8×C11—21no—
104C11⋊C8—22no—
105#536—111no—
106#520—111no—
107#485—112no—
108#485—112no—
109#484—112no—
110#483—112no—
111#428—111no—
112#427D1111yescharacteristic, complemented
113#419—111no—
114C2×#103—111no—
115#408—111no—
116C22×C11—21no—
117C22×C11—21no—
118C22×C11#12312yes—
119C22×C11C22×D411yescharacteristic
120C2×D11—22no—
121C2×D11—22no—
122C2×D11—22no—
123C4×C11—41no—
124C4×C11—41no—
125C4×C11—41no—
126C4×C11—41no—
127C4×C11#12312yes—
128C4×C11C2×#4111yescharacteristic
129C4×C11C2×#4111yescharacteristic
130Dic11—22no—
131Dic11—42no—
132Dic11—42no—
133C2×#41—111no—
134C22×Q8—111no—
135C2×M16—111no—
136C22×C8C2×D1111yescharacteristic
137C4⋊Q8—221no—
138#124—221no—
139#123—222no—
140C22⋊Q8—112no—
141C22⋊Q8—112no—
142C4×Q8—221no—
143C4×D4—221no—
144C4×D4—222no—
145#117—112no—
146#117C2×D1111yescharacteristic
147#117C2×D1111yescharacteristic
148C2×C4⋊C4—111no—
149C2×C4⋊C4—112no—
150#107—112no—
151#107C2×D1111yescharacteristic
152#107C2×D1111yescharacteristic
153#106—112no—
154#106C2×D1111yescharacteristic
155#106C2×D1111yescharacteristic
156#103—112no—
157#103—112no—
158#103—112no—
159#103—112no—
160C22⋊C8—112no—
161C22⋊C8—112no—
162C2×C11—22no—
163C2×C11C2×#12311yescharacteristic
164C2×C11#57711yescharacteristic
165C2×C11#57811yescharacteristic
166D11—42no—
167#41—222no—
168#41—222no—
169C2×Q8—111no—
170C2×Q8—112no—
171C2×Q8—221no—
172C2×Q8—222no—
173C2×Q8—222no—
174C2×D4—112no—
175C2×D4—111no—
176C22×C4—112no—
177C22×C4—222no—
178C22×C4—221no—
179C22×C4—221no—
180C22×C4C22×D1111yescharacteristic
181M16—222no—
182C2×C8—22no—
183C2×C8—112no—
184C2×C8C22×D1111yescharacteristic
185C2×C8C22×D1111yescharacteristic
186C4⋊C4—112no—
187C4⋊C4—222no—
188C4⋊C4—222no—
189C4⋊C4—222no—
190C4⋊C4—221no—
191C4⋊C4C22×D1111yescharacteristic
192C4⋊C4C22×D1111yescharacteristic
193C4⋊C4C22×D1111yescharacteristic
194C4⋊C4C22×D1111yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—21no—
197C22⋊C4—222no—
198C22⋊C4—222no—
199C22⋊C4—222no—
200C42—21no—
201C42—21no—
202C42—222no—
203C11#309711yescharacteristic, complemented, Sylow
204C23—112no—
205C23D4×D1111yescharacteristic
206Q8—222no—
207Q8—222no—
208Q8—222no—
209Q8—442no—
210D4—224no—
211D4—222no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—112no—
217C2×C4—222no—
218C2×C4—222no—
219C2×C4—222no—
220C2×C4—222no—
221C2×C4—442no—
222C2×C4—882no—
223C2×C4—881no—
224C2×C4#433912yes—
225C2×C4D4×D1111yescharacteristic
226C2×C4#434312yes—
227C2×C4C23×D1111yescharacteristic
228C8—21no—
229C8—21no—
230C8—222no—
231C22—21no—
232C22—21no—
233C22—222no—
234C22—222no—
235C22—222no—
236C22#6694712yes—
237C22C2×D4×D1111yescharacteristic
238C4—41no—
239C4—41no—
240C4—41no—
241C4—41no—
242C4—222no—
243C4—442no—
244C4—442no—
245C4#6694712yes—
246C4C2×#433911yescharacteristic
247C4C2×#434311yescharacteristic
248C2—22no—
249C2—442no—
250C2C2×#6694711yescharacteristic
251C2#1062330111yescharacteristic
252C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#427C2
socleC22×C11C22×D4
prime radicalC2×#4339C22
hypercenter#427D11
hypocenterC11#3097
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
3. C11×#427C2semidirect
5. C2×#66880C2semidirect
6. #10622617C2semidirect
7. #10622608C2semidirect
8. #10622501C2semidirect
9. #10622497C2semidirect
10. #10622480C2semidirect
11. #10622475C2semidirect
112. #427D11semidirect
203. C11#3097semidirect

Maximal subgroups

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

subgroupindex
#106230572
#106230542
C11×#4272
#106227232
C2×#668802
#106226172
#106226082
#106225012
#106224972
#106224802
#106224752
#309711