Finite Group Databasebeta

← #13081032

Subgroups — #13081032

Order 1408.

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

normal subgroups only

This group has 352 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#10623265C211yesmaximal, characteristic
2#10623115C211yesmaximal, characteristic, complemented
3C11×#477C211yesmaximal, characteristic, complemented
4#10622692C211yesmaximal, characteristic, complemented
5C4×#4325C211yesmaximal, characteristic, complemented
6#10622498C212yesmaximal, complemented
7#10622493C212yesmaximal, complemented
8#10622459C211yesmaximal, characteristic, complemented
9#10622447C211yesmaximal, characteristic, complemented
10#10622427C212yesmaximal, complemented
11#10622420C212yesmaximal, complemented
12C11×C4⋊Q8C2211yescharacteristic
13C4×Q8×C11C2211yescharacteristic
14#67000—22no—
15#66999C2212yes—
16C2×#4325C2211yescharacteristic
17C2×C8×D11C2212yes—
18#66951—22no—
19#66948—21no—
20#66948C2212yes—
21#66945—21no—
22#66945C2212yes—
23#66945C2212yes—
24#66928—21no—
25C4×D44C2211yescharacteristic
26C4×D44C2211yescharacteristic
27#66922C2211yescharacteristic
28C4×Dic22—21no—
29C11×#107C2212yes—
30C11×C4⋊C8C2211yescharacteristic
31C11×#103C2212yes—
32#66899C2211yescharacteristic
33#66885C2212yes—
34(C2×D11)⋊C8C2212yes—
35#66882C2212yes—
36#66873C2211yescharacteristic
37#66872C2211yescharacteristic
38#66872C2212yes—
39#66872C2212yes—
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×Q8×C11C2311yescharacteristic
43C2×D44—22no—
44C2×D44D411yescharacteristic
45C2×D44C2311yescharacteristic
46C2×C4×D11—21no—
47C2×C4×D11C2312yes—
48C2×Dic22—21no—
49C2×C8×C11C2312yes—
50C11×C4⋊C4—21no—
51C11×C4⋊C4—21no—
52C11×C4⋊C4C2312yes—
53C11×C4⋊C4C2311yescharacteristic
54C42×C11—21no—
55C42×C11C2311yescharacteristic
56#4325—22no—
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—21no—
62(C2×D11)⋊C4D412yes—
63C4⋊Dic11—21no—
64C4⋊Dic11D411yescharacteristic
65C4⋊Dic11C2312yes—
66C4⋊Dic11C2311yescharacteristic
67Dic11⋊C4—22no—
68C4×Dic11—22no—
69C4×Dic11—22no—
70C2×C11⋊C8C2311yescharacteristic
71C2×C11⋊C8C2311yescharacteristic
72C8×D11—24no—
73#3340—111nomaximal, Sylow
74C22×D11—21no—
75C22×D11C2×D412yes—
76Q8×C11—21no—
77Q8×C11—21no—
78Q8×C11—81no—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11—21no—
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2411yescharacteristic
85C2×Dic11—21no—
86C2×Dic11—22no—
87C2×Dic11C2×D412yes—
88D44—22no—
89D44—21no—
90D44—21no—
91D44—82no—
92C4×D11—22no—
93C4×D11—22no—
94C4×D11—42no—
95Dic22—42no—
96C8×C11—22no—
97C11⋊C8—21no—
98C11⋊C8#4112yes—
99#556—111no—
100#555—111no—
101#498—111no—
102#485—112no—
103#482—112no—
104#477D1111yescharacteristic, complemented
105#474—111no—
106#465—112no—
107C4×SD16—111no—
108C8×D4—111no—
109#427—112no—
110C22×C11C22×D411yescharacteristic
111C2×D11—22no—
112C2×D11—22no—
113C2×D11—22no—
114C2×D11—41no—
115C2×D11—41no—
116C2×D11—41no—
117C4×C11—21no—
118C4×C11—41no—
119C4×C11—41no—
120C4×C11—42no—
121C4×C11#13512yes—
122C4×C11C2×#4111yescharacteristic
123C4×C112−1+411yescharacteristic
124Dic11—22no—
125Dic11—42no—
126Dic11—41no—
127C2×SD16—111no—
128C22×C8—112no—
129C4⋊Q8—111no—
130C4⋊Q8C2×D1111yescharacteristic
131#126—222no—
132#124—221no—
133#124—222no—
134C22⋊Q8—112no—
135#121—112no—
136#121—221no—
137C4×Q8—221no—
138C4×Q8C2×D1111yescharacteristic
139C4×D4—111no—
140C4×D4—111no—
141#117—112no—
142#117—112no—
143#117—221no—
144#107—112no—
145#107C2×D1112yes—
146#106—111no—
147#106—112no—
148#106—112no—
149C4⋊C8C2×D1111yescharacteristic
150#103—111no—
151#103C2×D1112yes—
152#102—112no—
153#102—111no—
154C22⋊C8—112no—
155C4×C8—111no—
156C2×C11#54711yescharacteristic
157C2×C11C2×#13511yescharacteristic
158C2×C11#57711yescharacteristic
159D11—42no—
160D11—81no—
161C2×Q8—21no—
162C2×Q8—221no—
163C2×Q8C22×D1111yescharacteristic
164C2×D4—111no—
165C2×D4—111no—
166C2×D4—222no—
167C22×C4—112no—
168C22×C4—221no—
169SD16—222no—
170C2×C8—111no—
171C2×C8—111no—
172C2×C8—224no—
173C2×C8C22×D1112yes—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—111no—
177C4⋊C4—112no—
178C4⋊C4—111no—
179C4⋊C4—222no—
180C4⋊C4—221no—
181C4⋊C4C22×D1111yescharacteristic
182C4⋊C4C22×D1112yes—
183C22⋊C4—112no—
184C22⋊C4—222no—
185C22⋊C4—222no—
186C22⋊C4—222no—
187C22⋊C4—222no—
188C22⋊C4—221no—
189C42—21no—
190C42—222no—
191C42—222no—
192C42C22×D1111yescharacteristic
193C11#334011yescharacteristic, complemented, Sylow
194C23—112no—
195C23—221no—
196Q8—21no—
197Q8—21no—
198Q8—81no—
199Q8—442no—
200D4—222no—
201D4—221no—
202D4—221no—
203D4—882no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—112no—
208C2×C4—222no—
209C2×C4—222no—
210C2×C4—221no—
211C2×C4—222no—
212C2×C4—442no—
213C2×C4D4×D1111yescharacteristic
214C2×C4D4×D1111yescharacteristic
215C2×C4C23×D1111yescharacteristic
216C8—22no—
217C8—112no—
218C8—221no—
219C22—222no—
220C22—222no—
221C22—222no—
222C22—441no—
223C22—441no—
224C22—441no—
225C22C2×D4×D1111yescharacteristic
226C4—21no—
227C4—42no—
228C4—41no—
229C4—41no—
230C4—222no—
231C4—441no—
232C4—442no—
233C4#6697212yes—
234C4#6704011yescharacteristic
235C4#41×D1111yescharacteristic
236C2—442no—
237C2—881no—
238C2#1062316211yescharacteristic
239C2C2×#6697211yescharacteristic
240C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#477C2
socleC22×C11C22×D4
prime radical#10623265C2
hypercenter#477D11
hypocenterC11#3340
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #10623115C2semidirect
3. C11×#477C2semidirect
4. #10622692C2semidirect
5. C4×#4325C2semidirect
6. #10622498C2semidirect
7. #10622493C2semidirect
8. #10622459C2semidirect
9. #10622447C2semidirect
10. #10622427C2semidirect
11. #10622420C2semidirect
104. #477D11semidirect
193. C11#3340semidirect

Maximal subgroups

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

subgroupindex
#106232652
#106231152
C11×#4772
#106226922
C4×#43252
#106224982
#106224932
#106224592
#106224472
#106224272
#106224202
#334011