Finite Group Databasebeta

← #13068968

Subgroups — #13068968

Order 1408.

374 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#4324C211yesmaximal, characteristic
2C2×#66940C211yesmaximal, characteristic, complemented
3C2×C11×#102C211yesmaximal, characteristic
4#10622834C211yesmaximal, characteristic
5C2×#66880C211yesmaximal, characteristic, complemented
6#10622188C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C22×Dic22C2211yescharacteristic
10C22×C8×C11C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C22⋊Dic11—21no—
13C2×C22⋊Dic11—21no—
14C2×#4324—22no—
15C2×#4324—22no—
16C2×#4324C414yescomplemented
17C2×C4⋊Dic11C2211yescharacteristic
18C2×Dic11⋊C4—21no—
19C2×C4×Dic11—21no—
20C2×C4×Dic11C2211yescharacteristic
21C22×C11⋊C8C2211yescharacteristic
22#66940—22no—
23#66940—22no—
24C11×#102—22no—
25#66880—22no—
26C24×C11—21no—
27C2×D4×C11—21no—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D4×C11—21no—
31C2×D4×C11—21no—
32C2×D4×C11C2×C412yes—
33C22×C4×C11—21no—
34C22×C4×C11C2311yescharacteristic
35C22×Dic11—21no—
36C22×Dic11—21no—
37C22×Dic11D411yescharacteristic
38C22×Dic11D411yescharacteristic
39C2×Dic22—21no—
40C2×Dic22—21no—
41C2×Dic22—21no—
42C2×Dic22C2×C412yes—
43C2×Dic22D412yes—
44C2×Dic22D412yes—
45C2×C8×C11—21no—
46C2×C8×C11—21no—
47C2×C8×C11—21no—
48C11×C4⋊C4—21no—
49C11×C4⋊C4D412yes—
50C22⋊Dic11—42no—
51C22⋊Dic11—42no—
52#4324—28no—
53C4⋊Dic11—21no—
54C4⋊Dic11—21no—
55Dic11⋊C4—24no—
56C4×Dic11—24no—
57C4×Dic11—21no—
58C4×Dic11—21no—
59C2×C11⋊C8—21no—
60C2×C11⋊C8—21no—
61C2×C11⋊C8C2×C412yes—
62#1880—111nomaximal, Sylow
63C23×C11—22no—
64C23×C11—41no—
65C23×C11—41no—
66C23×C11—41no—
67C23×C11—41no—
68C23×C11—41no—
69C23×C11—41no—
70C23×C11C2×D411yescharacteristic
71D4×C11—22no—
72D4×C11—22no—
73D4×C11—41no—
74D4×C11—41no—
75C2×C4×C11—22no—
76C2×C4×C11—41no—
77C2×C4×C11—41no—
78C2×C4×C11C22×C411yescharacteristic
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11#4111yescharacteristic
83C2×C4×C11#4111yescharacteristic
84C2×Dic11—22no—
85C2×Dic11—21no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11—21no—
91C2×Dic11—21no—
92C2×Dic11—41no—
93C2×Dic11—41no—
94C2×Dic11—41no—
95C2×Dic11SD1612yescomplemented
96Dic22—22no—
97Dic22—22no—
98Dic22—22no—
99Dic22C22⋊C414yescomplemented
100C8×C11—41no—
101C11⋊C8—22no—
102C22×SD16—111no—
103C2×C4×Q8—111no—
104C2×#103—111no—
105C2×#102D1111yescharacteristic
106#390—111no—
107#340—111no—
108#336—111no—
109C22×C11—42no—
110C22×C11—42no—
111C22×C11—42no—
112C22×C11—81no—
113C22×C11—81no—
114C22×C11—81no—
115C22×C11—81no—
116C22×C11C4×D411yescharacteristic
117C22×C11#12011yescharacteristic
118C22×C11#12111yescharacteristic
119C22×C11C2×SD1611yescharacteristic
120C22×C11#13511yescharacteristic
121C22×C11AGL(1,ℤ/8)11yescharacteristic
122C22×C11#13711yescharacteristic
123C4×C11—42no—
124C4×C11C2×C22⋊C411yescharacteristic
125C4×C11C4×D411yescharacteristic
126C4×C11#12111yescharacteristic
127C4×C11#12311yescharacteristic
128Dic11—24no—
129Dic11—22no—
130Dic11—41no—
131Dic11—81no—
132C22×Q8—111no—
133C22×D4C2×D1111yescharacteristic
134C2×SD16—114no—
135C2×SD16—222no—
136C2×SD16—222no—
137C22×C8—111no—
138C22×C8C2×D1111yescharacteristic
139C4×Q8—222no—
140C4×Q8—222no—
141C2×C4⋊C4—111no—
142C2×C4⋊C4—221no—
143C2×C4⋊C4C2×D1111yescharacteristic
144C2×C22⋊C4—221no—
145C2×C22⋊C4—221no—
146C2×C42—111no—
147C2×C42—221no—
148#103—222no—
149#102—22no—
150C2×C11—82no—
151C2×C11#38611yescharacteristic
152C2×C11C4×SD1611yescharacteristic
153C2×C11#44011yescharacteristic
154C2×C11#44811yescharacteristic
155C2×C11#44911yescharacteristic
156C2×C11#46011yescharacteristic
157C2×C11#46411yescharacteristic
158C24—21no—
159C2×Q8—112no—
160C2×Q8—112no—
161C2×Q8—112no—
162C2×Q8—221no—
163C2×Q8—221no—
164C2×Q8—221no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4C4×D1112yes—
171C22×C4—21no—
172C22×C4—111no—
173C22×C4—111no—
174C22×C4—221no—
175C22×C4—221no—
176C22×C4C22×D1111yescharacteristic
177SD16—228no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—112no—
182C2×C8—221no—
183C2×C8—221no—
184C4⋊C4—21no—
185C4⋊C4—224no—
186C4⋊C4—221no—
187C4⋊C4—221no—
188C4⋊C4C22⋊D1112yes—
189C22⋊C4—442no—
190C22⋊C4—442no—
191C42—224no—
192C42—221no—
193C42—221no—
194C11#188011yescharacteristic, complemented, Sylow
195C23—22no—
196C23—41no—
197C23—41no—
198C23—41no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23D4×D1111yescharacteristic
203Q8—114no—
204Q8—222no—
205Q8—222no—
206Q8—222no—
207D4—22no—
208D4—22no—
209D4—41no—
210D4—41no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—112no—
215C2×C4—222no—
216C2×C4—222no—
217C2×C4—221no—
218C2×C4—221no—
219C2×C4—222no—
220C2×C4—221no—
221C2×C4—221no—
222C2×C4—221no—
223C2×C4—441no—
224C2×C4—441no—
225C2×C4—441no—
226C2×C4C2×C4×D1111yescharacteristic
227C2×C4#433911yescharacteristic
228C2×C4D4×D1111yescharacteristic
229C2×C4D4×D1111yescharacteristic
230C2×C4#434111yescharacteristic
231C2×C4C2×C22⋊D1111yescharacteristic
232C8—41no—
233C8—222no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22—81no—
241C22(C22⋊D11)⋊C411yescharacteristic
242C22#6693711yescharacteristic
243C22#6696411yescharacteristic
244C22#6696511yescharacteristic
245C22SD16×D1111yescharacteristic
246C22#6696811yescharacteristic
247C22#6699011yescharacteristic
248C4—42no—
249C4—222no—
250C4—224no—
251C4—441no—
252C4—881no—
253C4C22⋊C4×D1111yescharacteristic
254C4#6693611yescharacteristic
255C4C4×C22⋊D1111yescharacteristic
256C4#6699111yescharacteristic
257C2—82no—
258C2#1062237011yescharacteristic
259C2#1062237111yescharacteristic
260C2#1062237511yescharacteristic
261C2#1062238011yescharacteristic
262C2#1062256911yescharacteristic
263C2#1062277111yescharacteristic
264C2#1062278311yescharacteristic
subgroupG/H
centerC23D4×D11
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC2×C11×#102C2
socleC23×C11C2×D4
prime radicalC22×D4×C11C22
cosocleC22×C4×C11C23
hypercenterC2×#102D11
hypocenterC11#1880
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#66940C2semidirect
5. C2×#66880C2semidirect
6. #10622188C2semidirect
7. #10622167C2semidirect
16. C2×#4324C4semidirect
95. C2×Dic11SD16semidirect
99. Dic22C22⋊C4semidirect
194. C11#1880semidirect

Maximal subgroups

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

subgroupindex
C22×#43242
C2×#669402
C2×C11×#1022
#106228342
C2×#668802
#106221882
#106221672
#188011