Finite Group Databasebeta

← #13078912

Subgroups — #13078912

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#10623156C211yesmaximal, characteristic
2#10623047C211yesmaximal, characteristic
3C11×#485C211yesmaximal, characteristic
4#10622663C211yesmaximal, characteristic
5#10622609C211yesmaximal, characteristic
6#10622490C211yesmaximal, characteristic, complemented
7#10622486C211yesmaximal, characteristic, complemented
8#10622470C211yesmaximal, characteristic, complemented
9#10622466C211yesmaximal, characteristic, complemented
10#10622406C211yesmaximal, characteristic, complemented
11#10622406C211yesmaximal, characteristic, complemented
12#10622403C211yesmaximal, characteristic, complemented
13#10622402C211yesmaximal, characteristic, complemented
14#10622352C211yesmaximal, characteristic
15#10622333C211yesmaximal, characteristic
16C22×Dic22C2211yescharacteristic
17C11×C22⋊Q8C2211yescharacteristic
18C11×#117C2211yescharacteristic
19Q8×Dic11C2211yescharacteristic
20#66997C2211yescharacteristic
21C2×#4326C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23#66979C2211yescharacteristic
24#66977C2211yescharacteristic
25C2×Dic44C2211yescharacteristic
26C2×Dic44C2211yescharacteristic
27#66943—21no—
28#66943C2211yescharacteristic
29#66942—21no—
30#66940C2211yescharacteristic
31#66940C2211yescharacteristic
32#66940C2211yescharacteristic
33#66940C2211yescharacteristic
34#66940C2211yescharacteristic
35#66932—21no—
36#66932—21no—
37#66930—21no—
38#66930—21no—
39C4×Dic22—21no—
40C4×Dic22—21no—
41C11×#107C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×C22⋊C8C2211yescharacteristic
46C22⋊(C11⋊C8)C2211yescharacteristic
47#66880C2211yescharacteristic
48#66880C2211yescharacteristic
49#66879C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52C8×Dic11C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66874C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×Dic11—21no—
62C2×Dic22—22no—
63C2×Dic22—22no—
64C2×Dic22—21no—
65C2×Dic22C2311yescharacteristic
66C2×Dic22C2311yescharacteristic
67C2×Dic22C2311yescharacteristic
68C2×C8×C11C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C11×C4⋊C4—21no—
71C11×C4⋊C4C2311yescharacteristic
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C22⋊C4—21no—
75C11×C22⋊C4—21no—
76C42×C11—21no—
77C22⋊Dic11—21no—
78C22⋊Dic11D411yescharacteristic
79C22⋊Dic11D411yescharacteristic
80#4326—22no—
81#4326—22no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11D411yescharacteristic
85C4⋊Dic11D411yescharacteristic
86C4⋊Dic11C2311yescharacteristic
87Dic11⋊C4—21no—
88Dic11⋊C4—21no—
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11C2311yescharacteristic
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106Dic44—22no—
107Dic44—22no—
108#3127—111nomaximal, Sylow
109C23×C11C2×D411yescharacteristic
110Q8×C11—21no—
111Q8×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C2×Dic11—24no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129Dic22—24no—
130Dic22—21no—
131Dic22—21no—
132Dic22—21no—
133Dic22—21no—
134Dic22#4112yes—
135Dic22#4112yes—
136C8×C11—21no—
137C8×C11—21no—
138C11⋊C8—21no—
139C11⋊C8—21no—
140#541—111no—
141#519—111no—
142#485—111no—
143#485D1111yescharacteristic
144#479—111no—
145#479—111no—
146#462—111no—
147#462—111no—
148#451—111no—
149#451—111no—
150#441—111no—
151#441—111no—
152C4×Q16—111no—
153C4×Q16—111no—
154#433—111no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11C22×D411yescharacteristic
159C4×C11—21no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11C2×#4111yescharacteristic
165C4×C11C2×#4111yescharacteristic
166Dic11—22no—
167Dic11—22no—
168Dic11—21no—
169Dic11—21no—
170Dic11—21no—
171Dic11—21no—
172Dic11—41no—
173Dic11—41no—
174C22×Q8—111no—
175C2×Q16—111no—
176C2×Q16—111no—
177C2×Q16—111no—
178C2×Q16—111no—
179C4⋊Q8—111no—
180#126—221no—
181#126—221no—
182#125—111no—
183#125—221no—
184#125—221no—
185C22⋊Q8—111no—
186C22⋊Q8C2×D1111yescharacteristic
187C4×Q8—111no—
188C4×Q8—111no—
189C4×Q8—111no—
190C4×Q8—111no—
191C4×Q8—111no—
192C4×Q8—111no—
193C4×Q8—221no—
194C4×Q8—221no—
195#117—111no—
196#117—221no—
197#117—221no—
198#117C2×D1111yescharacteristic
199#107—111no—
200#107C2×D1111yescharacteristic
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⋊C8C2×D1111yescharacteristic
215#97—111no—
216C4×C8—111no—
217C2×C11—41no—
218C2×C11#52511yescharacteristic
219C2×C11#57811yescharacteristic
220C2×C11#57811yescharacteristic
221C2×Q8—111no—
222C2×Q8—111no—
223C2×Q8—111no—
224C2×Q8—222no—
225C2×Q8—222no—
226C2×Q8—221no—
227C2×Q8C22×D1111yescharacteristic
228C22×C4—221no—
229C22×C4C22×D1111yescharacteristic
230Q16—222no—
231Q16—222no—
232Q16—222no—
233Q16—222no—
234C2×C8—111no—
235C2×C8—111no—
236C2×C8C22×D1111yescharacteristic
237C2×C8C22×D1111yescharacteristic
238C4⋊C4—21no—
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⋊C4C22×D1111yescharacteristic
254C4⋊C4C22×D1111yescharacteristic
255C4⋊C4C22×D1111yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—111no—
259C22⋊C4—111no—
260C22⋊C4—221no—
261C42—21no—
262C42—111no—
263C42—111no—
264C42—221no—
265C42—221no—
266C42—221no—
267C42—221no—
268C42—221no—
269C42—221no—
270C11#312711yescharacteristic, complemented, Sylow
271C23D4×D1111yescharacteristic
272Q8—21no—
273Q8—21no—
274Q8—112no—
275Q8—112no—
276Q8—224no—
277Q8—221no—
278Q8—221no—
279Q8—221no—
280Q8—221no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—111no—
288C2×C4—111no—
289C2×C4—111no—
290C2×C4—111no—
291C2×C4—224no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4D4×D1111yescharacteristic
297C2×C4C23×D1111yescharacteristic
298C8—21no—
299C8—21no—
300C8—221no—
301C8—221no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22C2×D4×D1111yescharacteristic
306C4—21no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—221no—
312C4—221no—
313C4—221no—
314C4—221no—
315C4—222no—
316C4—222no—
317C4—441no—
318C4—441no—
319C4#41×D1111yescharacteristic
320C4#41×D1111yescharacteristic
321C2—41no—
322C2#1062318711yescharacteristic
323C2#1062330211yescharacteristic
324C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#485C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#485D11
hypocenterC11#3127
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
6. #10622490C2semidirect
7. #10622486C2semidirect
8. #10622470C2semidirect
9. #10622466C2semidirect
10. #10622406C2semidirect
11. #10622406C2semidirect
12. #10622403C2semidirect
13. #10622402C2semidirect
270. C11#3127semidirect

Maximal subgroups

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

subgroupindex
#106231562
#106230472
C11×#4852
#106226632
#106226092
#106224902
#106224862
#106224702
#106224662
#106224062
#106224032
#106224022
#106223522
#106223332
#312711