Finite Group Databasebeta

← #13080068

Subgroups — #13080068

Order 1408.

322 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623262C211yesmaximal, characteristic
2#10623114C211yesmaximal, characteristic
3C11×#462C211yesmaximal, characteristic, complemented
4#10622802C211yesmaximal, characteristic
5#10622801C211yesmaximal, characteristic
6#10622795C211yesmaximal, characteristic, complemented
7#10622795C211yesmaximal, characteristic, complemented
8#10622703C211yesmaximal, characteristic, complemented
9#10622635C211yesmaximal, characteristic, complemented
10#10622452C211yesmaximal, characteristic
11#10622442C211yesmaximal, characteristic, complemented
12#10622429C211yesmaximal, characteristic
13#10622426C211yesmaximal, characteristic
14#10622412C211yesmaximal, characteristic, complemented
15#10622409C211yesmaximal, characteristic, complemented
16C2×C11×Q16C2211yescharacteristic
17C2×C11×Q16C2211yescharacteristic
18C11×C4⋊Q8C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20#66999C2211yescharacteristic
21#66999C2211yescharacteristic
22#66999C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24Q8×Dic11C2211yescharacteristic
25#66997C2211yescharacteristic
26C2×#4326C2211yescharacteristic
27C2×#4326C2211yescharacteristic
28C2×#4313C2211yescharacteristic
29C2×C8×D11C2211yescharacteristic
30#66951—21no—
31#66951—21no—
32#66951—21no—
33#66950C2211yescharacteristic
34#66943C2211yescharacteristic
35#66942—21no—
36#66942—21no—
37#66942—21no—
38#66929—21no—
39#66925C2211yescharacteristic
40#66923—21no—
41#66923C2211yescharacteristic
42C4×Dic22C2211yescharacteristic
43C11×C4⋊C8C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#103C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66899C2211yescharacteristic
49#66899C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×C4×D11C2311yescharacteristic
63C2×Dic22C2311yescharacteristic
64C11×Q16—41no—
65C11×Q16—41no—
66C2×C8×C11C2311yescharacteristic
67C2×C8×C11C2311yescharacteristic
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4C2311yescharacteristic
72C42×C11—21no—
73C42×C11C2311yescharacteristic
74#4326—41no—
75#4326—41no—
76(C2×D11)⋊C4—21no—
77(C2×D11)⋊C4—21no—
78(C2×D11)⋊C4—21no—
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4D411yescharacteristic
81(C2×D11)⋊C4D411yescharacteristic
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11C2311yescharacteristic
87C4⋊Dic11C2311yescharacteristic
88C4⋊Dic11C2311yescharacteristic
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4D411yescharacteristic
99Dic11⋊C4D411yescharacteristic
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#4313—41no—
107C8×D11—41no—
108#3261—111nomaximal, Sylow
109C22×D11C2×D411yescharacteristic
110Q8×C11—21no—
111Q8×C11—21no—
112Q8×C11—21no—
113Q8×C11—21no—
114Q8×C11—21no—
115Q8×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2411yescharacteristic
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130C4×D11—21no—
131C4×D11—21no—
132Dic22—21no—
133Dic22—21no—
134C8×C11—21no—
135C8×C11—21no—
136C11⋊C8—21no—
137C11⋊C8—21no—
138#541—111no—
139#541—111no—
140#479—111no—
141#479—111no—
142#479—111no—
143#479—111no—
144#470—111no—
145#470—111no—
146#467—111no—
147#467—111no—
148#462—111no—
149#462—111no—
150#462—111no—
151#462D1111yescharacteristic, complemented
152#424—111no—
153C22×C11C22×D411yescharacteristic
154C2×D11—21no—
155C2×D11—21no—
156C2×D11—21no—
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11H(5,𝔽2)11yescharacteristic
164C4×C112−1+411yescharacteristic
165Dic11—21no—
166Dic11—21no—
167Dic11—21no—
168Dic11—41no—
169Dic11—41no—
170Dic11—41no—
171Dic11—41no—
172C2×Q16—111no—
173C2×Q16—111no—
174C2×Q16C2×D1111yescharacteristic
175C2×Q16C2×D1111yescharacteristic
176C2×M16—111no—
177C22×C8—111no—
178C4⋊Q8—111no—
179C4⋊Q8C2×D1111yescharacteristic
180#126—221no—
181#126—221no—
182#126—221no—
183#126—221no—
184#125—111no—
185#125—111no—
186#125—221no—
187#125—221no—
188#125—221no—
189#125—221no—
190C22⋊Q8—111no—
191C22⋊Q8—111no—
192C22⋊Q8—111no—
193C22⋊Q8—111no—
194C4×Q8—111no—
195C4×Q8—111no—
196C4×Q8—111no—
197C4×Q8C2×D1111yescharacteristic
198#117—111no—
199#107—111no—
200#107—111no—
201#106—111no—
202#106—111no—
203C4⋊C8—111no—
204C4⋊C8—111no—
205C4⋊C8—111no—
206C4⋊C8C2×D1111yescharacteristic
207#103—111no—
208#103—111no—
209#103—111no—
210#103—111no—
211#103—111no—
212#103—111no—
213#103C2×D1111yescharacteristic
214#103C2×D1111yescharacteristic
215C2×C11#53711yescharacteristic
216C2×C11#57811yescharacteristic
217C2×C11#57811yescharacteristic
218D11—41no—
219C2×Q8—111no—
220C2×Q8C22×D1111yescharacteristic
221C2×Q8C22×D1111yescharacteristic
222C2×Q8C22×D1111yescharacteristic
223C22×C4—111no—
224Q16—41no—
225Q16—41no—
226Q16—441no—
227Q16—441no—
228M16—441no—
229C2×C8—111no—
230C2×C8—111no—
231C2×C8—441no—
232C2×C8C22×D1111yescharacteristic
233C2×C8C22×D1111yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—111no—
238C4⋊C4—111no—
239C4⋊C4—111no—
240C4⋊C4—111no—
241C4⋊C4—111no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4C22×D1111yescharacteristic
256C22⋊C4—111no—
257C22⋊C4—111no—
258C22⋊C4—221no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C42—21no—
263C42—111no—
264C42—221no—
265C42—221no—
266C42—221no—
267C42C22×D1111yescharacteristic
268C11#326111yescharacteristic, complemented, Sylow
269C23—111no—
270Q8—21no—
271Q8—21no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—221no—
277Q8—221no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—111no—
283C2×C4—111no—
284C2×C4—111no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4D4×D1111yescharacteristic
292C2×C4D4×D1111yescharacteristic
293C2×C4C23×D1111yescharacteristic
294C8—21no—
295C8—21no—
296C8—221no—
297C8—221no—
298C22—221no—
299C22—221no—
300C22—221no—
301C22C2×D4×D1111yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—221no—
309C4—221no—
310C4—221no—
311C4—441no—
312C4—441no—
313C4—441no—
314C4—441no—
315C4#6703711yescharacteristic
316C4#6704311yescharacteristic
317C2—441no—
318C2#1062313911yescharacteristic
319C2#1062329711yescharacteristic
320C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#462C2
socleC22×C11C22×D4
prime radicalC22×D11C2×D4
hypercenter#462D11
hypocenterC11#3261
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. C11×#462C2semidirect
6. #10622795C2semidirect
7. #10622795C2semidirect
8. #10622703C2semidirect
9. #10622635C2semidirect
11. #10622442C2semidirect
14. #10622412C2semidirect
15. #10622409C2semidirect
151. #462D11semidirect
268. C11#3261semidirect

Maximal subgroups

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

subgroupindex
#106232622
#106231142
C11×#4622
#106228022
#106228012
#106227952
#106227032
#106226352
#106224522
#106224422
#106224292
#106224262
#106224122
#106224092
#326111