Finite Group Databasebeta

← #13078915

Subgroups — #13078915

Order 1408.

358 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623114C211yesmaximal, characteristic
2#10623103C211yesmaximal, characteristic
3C11×#441C211yesmaximal, characteristic, complemented
4#10622799C211yesmaximal, characteristic
5#10622795C211yesmaximal, characteristic, complemented
6C4×#4326C211yesmaximal, characteristic, complemented
7C4×#4326C211yesmaximal, characteristic, complemented
8#10622480C211yesmaximal, characteristic
9#10622470C211yesmaximal, characteristic, complemented
10#10622428C211yesmaximal, characteristic
11#10622421C211yesmaximal, characteristic
12#10622412C211yesmaximal, characteristic, complemented
13#10622406C211yesmaximal, characteristic, complemented
14#10622329C211yesmaximal, characteristic, complemented
15#10622322C211yesmaximal, characteristic
16C2×Q8×D11C2211yescharacteristic
17C2×C11×Q16C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20#66999C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22#66997C2211yescharacteristic
23C2×#4326C2211yescharacteristic
24C2×#4326C2211yescharacteristic
25C2×Dic44C2211yescharacteristic
26#66951—21no—
27#66950C2211yescharacteristic
28#66945—21no—
29#66945C2211yescharacteristic
30#66943C2211yescharacteristic
31#66942—21no—
32#66940—21no—
33#66940C2211yescharacteristic
34#66929—21no—
35#66925—21no—
36#66925C2211yescharacteristic
37#66923—21no—
38C4×Dic22—21no—
39C4×Dic22C2211yescharacteristic
40C4×Dic22C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#97C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66881C2211yescharacteristic
50#66880C2211yescharacteristic
51#66880C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61Q8×D11—22no—
62Q8×D11—22no—
63C2×C4×D11—21no—
64C2×C4×D11C2311yescharacteristic
65C2×Dic22—21no—
66C2×Dic22C2311yescharacteristic
67C2×Dic22C2311yescharacteristic
68C11×Q16—22no—
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C42×C11—21no—
76C42×C11—21no—
77C42×C11C2311yescharacteristic
78#4326—22no—
79#4326—22no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4D411yescharacteristic
84(C2×D11)⋊C4D411yescharacteristic
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4D411yescharacteristic
98Dic11⋊C4D411yescharacteristic
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107Dic44—22no—
108#3127—111nomaximal, Sylow
109C22×D11C2×D411yescharacteristic
110Q8×C11—21no—
111Q8×C11—21no—
112Q8×C11—21no—
113Q8×C11#4112yes—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2411yescharacteristic
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128C4×D11—24no—
129C4×D11—21no—
130C4×D11—21no—
131Dic22—24no—
132Dic22—21no—
133Dic22—21no—
134Dic22—21no—
135Dic22#4112yes—
136C8×C11—21no—
137C8×C11—21no—
138C11⋊C8—21no—
139C11⋊C8—21no—
140#541—111no—
141#519—111no—
142#485—111no—
143#485—111no—
144#479—111no—
145#479—111no—
146#462—111no—
147#462—111no—
148#451—111no—
149#451—111no—
150#441—111no—
151#441D1111yescharacteristic, complemented
152C4×Q16—111no—
153C4×Q16—111no—
154#433—111no—
155C22×C11C22×D411yescharacteristic
156C2×D11—21no—
157C2×D11—21no—
158C2×D11—21no—
159C4×C11—22no—
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11C2×#4111yescharacteristic
166C4×C11C2×#4111yescharacteristic
167Dic11—21no—
168Dic11—22no—
169Dic11—21no—
170Dic11—21no—
171Dic11—41no—
172Dic11—41no—
173Dic11—41no—
174C22×Q8—111no—
175C2×Q16—111no—
176C2×Q16—111no—
177C2×Q16—111no—
178C2×Q16C2×D1111yescharacteristic
179C4⋊Q8—111no—
180#126—221no—
181#126—221no—
182#125—111no—
183#125—221no—
184#125—221no—
185C22⋊Q8—111no—
186C22⋊Q8—111no—
187C4×Q8—111no—
188C4×Q8—111no—
189C4×Q8—111no—
190C4×Q8—111no—
191C4×Q8—221no—
192C4×Q8—221no—
193C4×Q8C2×D1111yescharacteristic
194C4×Q8C2×D1111yescharacteristic
195#117—111no—
196#117—111no—
197#117—221no—
198#117—221no—
199#107—111no—
200#107—111no—
201#106—111no—
202#106C2×D1111yescharacteristic
203C4⋊C8—111no—
204C4⋊C8—111no—
205#103—111no—
206#103—111no—
207#103—111no—
208#103—111no—
209#103—111no—
210#103—111no—
211#103C2×D1111yescharacteristic
212#103C2×D1111yescharacteristic
213C22⋊C8—111no—
214C22⋊C8—111no—
215#97C2×D1111yescharacteristic
216C4×C8—111no—
217C2×C11#52511yescharacteristic
218C2×C11#57811yescharacteristic
219C2×C11#57811yescharacteristic
220D11—41no—
221C2×Q8—111no—
222C2×Q8—111no—
223C2×Q8—221no—
224C2×Q8—222no—
225C2×Q8—222no—
226C2×Q8C22×D1111yescharacteristic
227C2×Q8C22×D1111yescharacteristic
228C22×C4—111no—
229C22×C4—221no—
230Q16—22no—
231Q16—222no—
232Q16—222no—
233Q16—222no—
234C2×C8—111no—
235C2×C8—111no—
236C2×C8C22×D1111yescharacteristic
237C2×C8C22×D1111yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—111no—
241C4⋊C4—111no—
242C4⋊C4—111no—
243C4⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
255C4⋊C4C22×D1111yescharacteristic
256C22⋊C4—111no—
257C22⋊C4—111no—
258C22⋊C4—221no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C42—21no—
262C42—21no—
263C42—111no—
264C42—221no—
265C42—221no—
266C42—221no—
267C42—221no—
268C42—221no—
269C42C22×D1111yescharacteristic
270C11#312711yescharacteristic, complemented, Sylow
271C23—111no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—112no—
276Q8—224no—
277Q8—221no—
278Q8—221no—
279Q8—221no—
280Q8#433912yes—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—111no—
286C2×C4—111no—
287C2×C4—111no—
288C2×C4—224no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4D4×D1111yescharacteristic
296C2×C4D4×D1111yescharacteristic
297C2×C4C23×D1111yescharacteristic
298C8—21no—
299C8—21no—
300C8—221no—
301C8—221no—
302C22—221no—
303C22—221no—
304C22—221no—
305C22C2×D4×D1111yescharacteristic
306C4—21no—
307C4—21no—
308C4—22no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—221no—
313C4—221no—
314C4—221no—
315C4—222no—
316C4—441no—
317C4—441no—
318C4—441no—
319C4C2×#433911yescharacteristic
320C4#41×D1111yescharacteristic
321C2—441no—
322C2#1062307811yescharacteristic
323C2#1062331011yescharacteristic
324C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#441C2
socleC22×C11C22×D4
prime radicalC22×D11C2×D4
hypercenter#441D11
hypocenterC11#3127
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. C11×#441C2semidirect
5. #10622795C2semidirect
6. C4×#4326C2semidirect
7. C4×#4326C2semidirect
9. #10622470C2semidirect
12. #10622412C2semidirect
13. #10622406C2semidirect
14. #10622329C2semidirect
151. #441D11semidirect
270. C11#3127semidirect

Maximal subgroups

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

subgroupindex
#106231142
#106231032
C11×#4412
#106227992
#106227952
C4×#43262
#106224802
#106224702
#106224282
#106224212
#106224122
#106224062
#106223292
#106223222
#312711