Finite Group Databasebeta

← #13080909

Subgroups — #13080909

Order 1408.

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

normal subgroups only

This group has 386 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#10623258C211yesmaximal, characteristic, complemented
3C11×#487C211yesmaximal, characteristic, complemented
4#10622704C211yesmaximal, characteristic, complemented
5#10622696C211yesmaximal, characteristic, complemented
6#10622428C212yesmaximal, complemented
7#10622425C212yesmaximal, complemented
8#10622419C212yesmaximal, complemented
9#10622415C212yesmaximal, complemented
10C4×#4314C211yesmaximal, characteristic, complemented
11#10622301C211yesmaximal, characteristic, complemented
12C2×Q8×D11C2212yes—
13C11×C4⋊Q8C2211yescharacteristic
14C11×C4⋊Q8C2211yescharacteristic
15#67000—22no—
16#66999C2212yes—
17C2×#4325C2212yes—
18C2×#4314C2211yescharacteristic
19C2×#4313C2212yes—
20#66949—22no—
21#66948—21no—
22#66948C2212yes—
23#66946—21no—
24#66945—21no—
25#66945C2212yes—
26#66941—21no—
27C4×D44C2211yescharacteristic
28C4×D44C2211yescharacteristic
29C4×Dic22C2211yescharacteristic
30C11×#103C2212yes—
31C11×#103C2212yes—
32C4×C8×C11C2211yescharacteristic
33#66899C2212yes—
34#66885C2211yescharacteristic
35(C2×D11)⋊C8C2212yes—
36#66881C2211yescharacteristic
37#66880C2211yescharacteristic
38#66874C2212yes—
39#66871C2212yes—
40C4⋊(C11⋊C8)C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×Q8×C11C2312yes—
43Q8×D11—24no—
44Q8×D11—42no—
45C2×D44—22no—
46C2×D44D411yescharacteristic
47C2×D44C2311yescharacteristic
48C2×C4×D11—22no—
49C2×C4×D11—21no—
50C2×C4×D11C2312yes—
51C2×Dic22—22no—
52C2×Dic22C2311yescharacteristic
53C2×C8×C11C2311yescharacteristic
54C2×C8×C11C2311yescharacteristic
55C11×C4⋊C4—21no—
56C11×C4⋊C4—21no—
57C11×C4⋊C4—21no—
58C11×C4⋊C4C2312yes—
59C42×C11C2311yescharacteristic
60#4325—42no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—21no—
65(C2×D11)⋊C4D412yes—
66C4⋊Dic11D411yescharacteristic
67C4⋊Dic11C2311yescharacteristic
68C4⋊Dic11C2311yescharacteristic
69Dic11⋊C4—22no—
70Dic11⋊C4—21no—
71C4×Dic11—22no—
72C4×Dic11—21no—
73C2×C11⋊C8C2312yes—
74#4314—22no—
75#4313—42no—
76#3329—111nomaximal, Sylow
77C22×D11—21no—
78C22×D11C2×D412yes—
79Q8×C11—22no—
80Q8×C11—22no—
81Q8×C11—81no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2411yescharacteristic
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11C2×D412yes—
91D44—22no—
92D44—21no—
93D44—21no—
94D44—82no—
95C4×D11—22no—
96C4×D11—22no—
97C4×D11—44no—
98C4×D11—42no—
99Dic22—21no—
100Dic22—44no—
101Dic22#4112yes—
102C8×C11—21no—
103C8×C11—21no—
104C11⋊C8—22no—
105#555—111no—
106D4×Q8—111no—
107#487D1111yescharacteristic, complemented
108#485—112no—
109#477—111no—
110#468—112no—
111#461—111no—
112#448—112no—
113C4×SD16—111no—
114#436—111no—
115#419—112no—
116C22×C11C22×D411yescharacteristic
117C2×D11—22no—
118C2×D11—22no—
119C2×D11—22no—
120C2×D11—41no—
121C2×D11—41no—
122C2×D11—41no—
123C4×C11—21no—
124C4×C11—42no—
125C4×C11—42no—
126C4×C11#13712yes—
127C4×C11C2×#4111yescharacteristic
128C4×C11H(5,𝔽2)11yescharacteristic
129Dic11—22no—
130Dic11—22no—
131Dic11—41no—
132Dic11—41no—
133C22×Q8—112no—
134C2×SD16—112no—
135C2×SD16—111no—
136C2×M16—112no—
137C4⋊Q8—221no—
138C4⋊Q8C2×D1111yescharacteristic
139C4⋊Q8C2×D1111yescharacteristic
140#124—222no—
141C22⋊Q8—112no—
142C22⋊Q8—222no—
143#121—112no—
144#121—221no—
145C4×Q8—111no—
146C4×D4—111no—
147C4×D4—111no—
148C4×D4—221no—
149#117—112no—
150#117—221no—
151#107—112no—
152#106—111no—
153C4⋊C8—111no—
154#103—112no—
155#103—111no—
156#103—112no—
157#103C2×D1112yes—
158#103C2×D1112yes—
159#102—111no—
160C22⋊C8—112no—
161C4×C8C2×D1111yescharacteristic
162C2×C11#54611yescharacteristic
163C2×C11C2×#13711yescharacteristic
164C2×C11#57711yescharacteristic
165D11—42no—
166D11—81no—
167C2×Q8—21no—
168C2×Q8—111no—
169C2×Q8—222no—
170C2×Q8—224no—
171C2×Q8—442no—
172C2×Q8C22×D1112yes—
173C2×D4—111no—
174C2×D4—111no—
175C2×D4—222no—
176C22×C4—112no—
177C22×C4—222no—
178C22×C4—221no—
179SD16—222no—
180SD16—442no—
181M16—442no—
182C2×C8—112no—
183C2×C8C22×D1111yescharacteristic
184C2×C8C22×D1111yescharacteristic
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—111no—
189C4⋊C4—111no—
190C4⋊C4—111no—
191C4⋊C4—222no—
192C4⋊C4—221no—
193C4⋊C4C22×D1112yes—
194C22⋊C4—112no—
195C22⋊C4—222no—
196C22⋊C4—222no—
197C22⋊C4—222no—
198C22⋊C4—221no—
199C42—222no—
200C42—221no—
201C42C22×D1111yescharacteristic
202C11#332911yescharacteristic, complemented, Sylow
203C23—112no—
204C23—221no—
205Q8—22no—
206Q8—22no—
207Q8—81no—
208Q8—112no—
209Q8—221no—
210Q8—444no—
211D4—222no—
212D4—221no—
213D4—221no—
214D4—882no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—112no—
218C2×C4—221no—
219C2×C4—222no—
220C2×C4—222no—
221C2×C4—221no—
222C2×C4—221no—
223C2×C4—444no—
224C2×C4—442no—
225C2×C4D4×D1111yescharacteristic
226C2×C4D4×D1111yescharacteristic
227C2×C4C23×D1111yescharacteristic
228C8—21no—
229C8—21no—
230C8—222no—
231C22—222no—
232C22—222no—
233C22—222no—
234C22—441no—
235C22—441no—
236C22—441no—
237C22C2×D4×D1111yescharacteristic
238C4—21no—
239C4—42no—
240C4—42no—
241C4—222no—
242C4—222no—
243C4—441no—
244C4—441no—
245C4#6697112yes—
246C4#41×D1111yescharacteristic
247C4#6704211yescharacteristic
248C2—442no—
249C2—881no—
250C2#1062320711yescharacteristic
251C2#1062329311yescharacteristic
252C2C2×#6697111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#487C2
socleC22×C11C22×D4
prime radical#10623265C2
hypercenter#487D11
hypocenterC11#3329
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #10623258C2semidirect
3. C11×#487C2semidirect
4. #10622704C2semidirect
5. #10622696C2semidirect
6. #10622428C2semidirect
7. #10622425C2semidirect
8. #10622419C2semidirect
9. #10622415C2semidirect
10. C4×#4314C2semidirect
11. #10622301C2semidirect
107. #487D11semidirect
202. C11#3329semidirect

Maximal subgroups

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

subgroupindex
#106232652
#106232582
C11×#4872
#106227042
#106226962
#106224282
#106224252
#106224192
#106224152
C4×#43142
#106223012
#332911