Finite Group Databasebeta

← #13078914

Subgroups — #13078914

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#10623262C211yesmaximal, characteristic
2#10623103C211yesmaximal, characteristic
3C11×#462C211yesmaximal, characteristic, complemented
4#10622799C211yesmaximal, characteristic
5#10622799C211yesmaximal, characteristic
6#10622797C211yesmaximal, characteristic, complemented
7Q16×Dic11C211yesmaximal, characteristic, complemented
8#10622703C211yesmaximal, characteristic, complemented
9#10622635C211yesmaximal, characteristic, complemented
10#10622453C211yesmaximal, characteristic
11#10622442C211yesmaximal, characteristic, complemented
12#10622428C211yesmaximal, characteristic
13#10622427C211yesmaximal, characteristic
14#10622403C211yesmaximal, characteristic, complemented
15#10622402C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×C11×Q16C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic
19C11×C4⋊Q8C2211yescharacteristic
20C4×Q8×C11C2211yescharacteristic
21#66999C2211yescharacteristic
22#66999C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24Q8×Dic11C2211yescharacteristic
25Q8×Dic11C2211yescharacteristic
26C2×#4326C2211yescharacteristic
27C2×#4326C2211yescharacteristic
28#66951—21no—
29#66951—21no—
30#66945—21no—
31#66945C2211yescharacteristic
32#66942—21no—
33#66942—21no—
34#66940—21no—
35#66940C2211yescharacteristic
36#66925—21no—
37#66925C2211yescharacteristic
38#66923C2211yescharacteristic
39C4×Dic22—21no—
40C4×Dic22C2211yescharacteristic
41C11×C4⋊C8C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54#66879C2211yescharacteristic
55C8×Dic11C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62Q8×D11—22no—
63Q8×D11—22no—
64C2×C4×D11—21no—
65C2×C4×D11C2311yescharacteristic
66C2×Dic22—21no—
67C2×Dic22C2311yescharacteristic
68C11×Q16—22no—
69C11×Q16—22no—
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4C2311yescharacteristic
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
90C4⋊Dic11C2311yescharacteristic
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×Dic11—21no—
105C4×Dic11C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#3127—111nomaximal, Sylow
109C22×D11C2×D411yescharacteristic
110Q8×C11—21no—
111Q8×C11—21no—
112Q8×C11—21no—
113Q8×C11—21no—
114Q8×C11—21no—
115Q8×C11#4112yes—
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—24no—
131C4×D11—21no—
132C4×D11—21no—
133Dic22—24no—
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#462D1111yescharacteristic, complemented
148#451—111no—
149#451—111no—
150#441—111no—
151#441—111no—
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×Q16C2×D1111yescharacteristic
178C2×Q16C2×D1111yescharacteristic
179C4⋊Q8C2×D1111yescharacteristic
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—111no—
192C4×Q8—221no—
193C4×Q8—221no—
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#106—111no—
203C4⋊C8—111no—
204C4⋊C8C2×D1111yescharacteristic
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#97—111no—
216C4×C8—111no—
217C2×C11#52511yescharacteristic
218C2×C11#57811yescharacteristic
219C2×C11#57811yescharacteristic
220D11—41no—
221C2×Q8—111no—
222C2×Q8—221no—
223C2×Q8—222no—
224C2×Q8—222no—
225C2×Q8C22×D1111yescharacteristic
226C2×Q8C22×D1111yescharacteristic
227C2×Q8C22×D1111yescharacteristic
228C22×C4—111no—
229C22×C4—221no—
230Q16—22no—
231Q16—22no—
232Q16—222no—
233Q16—222no—
234C2×C8—111no—
235C2×C8—111no—
236C2×C8C22×D1111yescharacteristic
237C2×C8C22×D1111yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—111no—
242C4⋊C4—111no—
243C4⋊C4—111no—
244C4⋊C4—111no—
245C4⋊C4—111no—
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—
261C42—21no—
262C42—111no—
263C42—221no—
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—21no—
276Q8—21no—
277Q8—112no—
278Q8—224no—
279Q8—221no—
280Q8#434112yes—
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×#434111yescharacteristic
320C4#41×D1111yescharacteristic
321C2—441no—
322C2#1062313711yescharacteristic
323C2#1062329711yescharacteristic
324C2#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#3127
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. #10622797C2semidirect
7. Q16×Dic11C2semidirect
8. #10622703C2semidirect
9. #10622635C2semidirect
11. #10622442C2semidirect
14. #10622403C2semidirect
15. #10622402C2semidirect
147. #462D11semidirect
270. C11#3127semidirect

Maximal subgroups

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

subgroupindex
#106232622
#106231032
C11×#4622
#106227992
#106227972
Q16×Dic112
#106227032
#106226352
#106224532
#106224422
#106224282
#106224272
#106224032
#106224022
#312711