Finite Group Databasebeta

← #13081447

Subgroups — #13081447

Order 1408.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623202C211yesmaximal, characteristic, complemented
2#10623070C211yesmaximal, characteristic, complemented
3C11×#463C211yesmaximal, characteristic
4#10622777C211yesmaximal, characteristic, complemented
5#10622775C211yesmaximal, characteristic, complemented
6#10622766C211yesmaximal, characteristic
7#10622765C211yesmaximal, characteristic
8#10622669C211yesmaximal, characteristic, complemented
9C4×#4324C211yesmaximal, characteristic, complemented
10#10622444C211yesmaximal, characteristic, complemented
11#10622442C211yesmaximal, characteristic, complemented
12#10622410C211yesmaximal, characteristic, complemented
13#10622404C211yesmaximal, characteristic, complemented
14#10622379C211yesmaximal, characteristic, complemented
15#10622378C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C2×C11×D8C2211yescharacteristic
18C11×#124C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20Q8×Dic11C2211yescharacteristic
21#66997C2211yescharacteristic
22#66989C2211yescharacteristic
23D4×Dic11C2211yescharacteristic
24D4×Dic11C2211yescharacteristic
25D4×Dic11C2211yescharacteristic
26C2×#4324C2211yescharacteristic
27#66977—21no—
28C2×Dic11⋊C4—21no—
29#66943C2211yescharacteristic
30#66941C2211yescharacteristic
31#66932—21no—
32#66932—21no—
33#66931—21no—
34#66931—21no—
35#66931—21no—
36#66930—21no—
37#66923C2211yescharacteristic
38C4×Dic22C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#102C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66882C2211yescharacteristic
49#66881C2211yescharacteristic
50#66880C2211yescharacteristic
51#66880C2211yescharacteristic
52#66879C2211yescharacteristic
53#66879C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56#66874C2211yescharacteristic
57#66872C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C22×Dic11—21no—
64C22×Dic11—21no—
65C22×Dic11—21no—
66C2×Dic22—21no—
67C2×Dic22D411yescharacteristic
68C2×Dic22C2311yescharacteristic
69C11×SD16—22no—
70C11×D8—22no—
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C22⋊C4—21no—
75C11×C22⋊C4—21no—
76C11×C22⋊C4—21no—
77C42×C11C2311yescharacteristic
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83#4324—22no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11D411yescharacteristic
87C4⋊Dic11C2311yescharacteristic
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×Dic11C2311yescharacteristic
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3376—111nomaximal, Sylow
106C23×C11—21no—
107C23×C11—21no—
108Q8×C11—21no—
109Q8×C11—21no—
110D4×C11—21no—
111D4×C11—21no—
112D4×C11—21no—
113D4×C11#4112yes—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—81no—
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C2×Dic11—81no—
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131Dic22—21no—
132Dic22—21no—
133Dic22—41no—
134Dic22—81no—
135C8×C11—21no—
136C8×C11—21no—
137C11⋊C8—21no—
138C11⋊C8—21no—
139#556—111no—
140#554—111no—
141#491—111no—
142#489—111no—
143#488—111no—
144#479—111no—
145#478—111no—
146#475—111no—
147#463—111no—
148#463D1111yescharacteristic
149#461—111no—
150#446—111no—
151#442—111no—
152#440—111no—
153C4×SD16—111no—
154C22×C11—22no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11C22×D411yescharacteristic
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11C2×#4111yescharacteristic
166C4×C112−1+411yescharacteristic
167Dic11—21no—
168Dic11—21no—
169Dic11—21no—
170Dic11—21no—
171Dic11—41no—
172Dic11—41no—
173Dic11—41no—
174Dic11—41no—
175C2×SD16—111no—
176C2×SD16C2×D1111yescharacteristic
177C2×D8C2×D1111yescharacteristic
178C4⋊Q8—111no—
179C4⋊Q8—111no—
180#126—221no—
181#126—221no—
182#125—111no—
183#125—111no—
184#124—111no—
185#124C2×D1111yescharacteristic
186C22⋊Q8—221no—
187C22⋊Q8—221no—
188C22⋊Q8—221no—
189C22⋊Q8—221no—
190C4×Q8—111no—
191C4×Q8—111no—
192C4×Q8—111no—
193C4×D4—111no—
194C4×D4—111no—
195C4×D4—111no—
196C4×D4C2×D1111yescharacteristic
197#117—221no—
198C2×C4⋊C4—221no—
199#107—111no—
200#106—111no—
201#106—111no—
202C4⋊C8—111no—
203C4⋊C8—111no—
204C4⋊C8C2×D1111yescharacteristic
205#103—111no—
206#103—111no—
207#103—111no—
208#103—111no—
209#103—111no—
210#103C2×D1111yescharacteristic
211#102—111no—
212#102—111no—
213#102—111no—
214#102C2×D1111yescharacteristic
215#97—111no—
216#97—111no—
217C4×C8—111no—
218C2×C11—42no—
219C2×C11—81no—
220C2×C11#54811yescharacteristic
221C2×C11#57511yescharacteristic
222C2×C11#57711yescharacteristic
223C2×Q8—111no—
224C2×Q8—111no—
225C2×Q8—221no—
226C2×Q8C22×D1111yescharacteristic
227C2×D4C22×D1111yescharacteristic
228C2×D4C22×D1111yescharacteristic
229C22×C4—21no—
230C22×C4—221no—
231C22×C4—221no—
232C22×C4—221no—
233SD16—22no—
234SD16—222no—
235D8—22no—
236C2×C8—111no—
237C2×C8—111no—
238C2×C8C22×D1111yescharacteristic
239C2×C8C22×D1111yescharacteristic
240C4⋊C4—111no—
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—21no—
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C42—111no—
265C42—111no—
266C42—221no—
267C42—221no—
268C42C22×D1111yescharacteristic
269C11#337611yescharacteristic, complemented, Sylow
270C23—21no—
271C23—21no—
272Q8—21no—
273Q8—21no—
274Q8—221no—
275Q8—221no—
276Q8—441no—
277Q8—881no—
278D4—21no—
279D4—21no—
280D4—21no—
281D4#434112yes—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—111no—
286C2×C4—111no—
287C2×C4—111no—
288C2×C4—111no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—442no—
294C2×C4—442no—
295C2×C4—881no—
296C2×C4D4×D1111yescharacteristic
297C2×C4D4×D1111yescharacteristic
298C2×C4C23×D1111yescharacteristic
299C8—21no—
300C8—21no—
301C8—221no—
302C8—221no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C2×D4×D1111yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—221no—
315C4—221no—
316C4—221no—
317C4—221no—
318C4—441no—
319C4—441no—
320C4—441no—
321C4—441no—
322C4C2×#434111yescharacteristic
323C4#6704311yescharacteristic
324C2—42no—
325C2—81no—
326C2#1062312911yescharacteristic
327C2#1062329911yescharacteristic
328C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#463C2
socleC22×C11C22×D4
prime radicalC2×C11×D8C22
hypercenter#463D11
hypocenterC11#3376
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #10623202C2semidirect
2. #10623070C2semidirect
4. #10622777C2semidirect
5. #10622775C2semidirect
8. #10622669C2semidirect
9. C4×#4324C2semidirect
10. #10622444C2semidirect
11. #10622442C2semidirect
12. #10622410C2semidirect
13. #10622404C2semidirect
14. #10622379C2semidirect
15. #10622378C2semidirect
269. C11#3376semidirect

Maximal subgroups

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

subgroupindex
#106232022
#106230702
C11×#4632
#106227772
#106227752
#106227662
#106227652
#106226692
C4×#43242
#106224442
#106224422
#106224102
#106224042
#106223792
#106223782
#337611