Finite Group Databasebeta

← #13080997

Subgroups — #13080997

Order 1408.

354 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623096C211yesmaximal, characteristic
2#10623072C211yesmaximal, characteristic, complemented
3C8×D4×C11C211yesmaximal, characteristic, complemented
4#10622727C211yesmaximal, characteristic, complemented
5#10622727C211yesmaximal, characteristic, complemented
6#10622719C211yesmaximal, characteristic, complemented
7C2×#66881C211yesmaximal, characteristic, complemented
8#10622460C211yesmaximal, characteristic, complemented
9#10622442C211yesmaximal, characteristic, complemented
10#10622350C211yesmaximal, characteristic, complemented
11#10622349C211yesmaximal, characteristic, complemented
12#10622336C211yesmaximal, characteristic, complemented
13#10622335C211yesmaximal, characteristic, complemented
14C4×#4314C211yesmaximal, characteristic, complemented
15#10622296C211yesmaximal, characteristic, complemented
16C22×C8×C11C2211yescharacteristic
17C22×C8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#66992—21no—
20#66988—21no—
21#66983C2211yescharacteristic
22#66983C2211yescharacteristic
23#66979C2211yescharacteristic
24#66979C2211yescharacteristic
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27#66977C2211yescharacteristic
28#66977C2211yescharacteristic
29C2×#4314C2211yescharacteristic
30#66951—21no—
31#66942—21no—
32#66936—21no—
33(C22⋊D11)⋊C4—21no—
34#66932—21no—
35#66930—21no—
36C4×D44C2211yescharacteristic
37#66923C2211yescharacteristic
38#66923C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×C22⋊C8C2211yescharacteristic
42C11×C22⋊C8C2211yescharacteristic
43C4×C8×C11C2211yescharacteristic
44#66885C2211yescharacteristic
45#66885C2211yescharacteristic
46#66885C2211yescharacteristic
47#66882C2211yescharacteristic
48#66882C2211yescharacteristic
49#66882C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66881C2211yescharacteristic
53#66881C2211yescharacteristic
54#66881C2211yescharacteristic
55#66881C2211yescharacteristic
56#66880C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59C2×D4×C11D411yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C22×Dic11—21no—
65C22×Dic11—21no—
66C2×D44C2311yescharacteristic
67C2×C4×D11—21no—
68C2×Dic22C2311yescharacteristic
69C2×C8×C11—22no—
70C2×C8×C11—22no—
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C11×C4⋊C4D411yescharacteristic
76C11×C22⋊C4D411yescharacteristic
77C11×C22⋊C4D411yescharacteristic
78C42×C11C2311yescharacteristic
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104#4314—22no—
105#3337—111nomaximal, Sylow
106C23×C11C2×D411yescharacteristic
107C23×C11C2×D411yescharacteristic
108C22×D11—21no—
109D4×C11—22no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2411yescharacteristic
119C22⋊D11—42no—
120C22⋊D11—81no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—42no—
129C2×Dic11—81no—
130D44—21no—
131D44—21no—
132C4×D11—81no—
133Dic22—21no—
134Dic22—21no—
135C8×C11—21no—
136C8×C11—21no—
137C8×C11—21no—
138C8×C11#4112yes—
139#553—111no—
140#552—111no—
141#499—111no—
142#485—111no—
143#484—111no—
144#482—111no—
145#480—111no—
146#479—111no—
147#478—111no—
148#465—111no—
149#465—111no—
150C4×SD16—111no—
151C8×D4D1111yescharacteristic, complemented
152#427—111no—
153C2×#106—111no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11#13512yes—
160C22×C11C22×D411yescharacteristic
161C2×D11—41no—
162C2×D11—41no—
163C2×D11—41no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11C2×#4111yescharacteristic
169C4×C112−1+411yescharacteristic
170Dic11—41no—
171Dic11—41no—
172Dic11—41no—
173Dic11—41no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177C2×SD16—111no—
178C22×C8C2×D1111yescharacteristic
179C22×C8C2×D1111yescharacteristic
180#126—221no—
181#126—221no—
182#125—111no—
183#125—111no—
184#125—221no—
185#123—221no—
186#123—221no—
187C22⋊Q8—111no—
188C22⋊Q8—111no—
189#121—111no—
190#121—111no—
191#121—221no—
192C4×Q8—111no—
193C4×D4—111no—
194C4×D4—221no—
195C4×D4C2×D1111yescharacteristic
196#117—111no—
197#117—111no—
198#117—221no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—111no—
201#107—111no—
202#107—111no—
203#107—111no—
204#107—111no—
205#106—111no—
206#106—111no—
207#106—111no—
208#106—111no—
209#106—111no—
210C4⋊C8C2×D1111yescharacteristic
211#103—111no—
212#103—111no—
213#103—111no—
214#102—111no—
215#102—111no—
216#102—111no—
217C22⋊C8C2×D1111yescharacteristic
218C22⋊C8C2×D1111yescharacteristic
219C4×C8C2×D1111yescharacteristic
220C2×C11—22no—
221C2×C11—41no—
222C2×C11#54711yescharacteristic
223C2×C11C2×#13511yescharacteristic
224C2×C11#57711yescharacteristic
225D11—81no—
226C2×Q8—111no—
227C2×D4—111no—
228C2×D4—221no—
229C2×D4—221no—
230C2×D4D4411yescharacteristic
231C22×C4—221no—
232C22×C4—221no—
233C22×C4—221no—
234C22×C4C22×D1111yescharacteristic
235C22×C4C22×D1111yescharacteristic
236SD16—222no—
237C2×C8—22no—
238C2×C8—22no—
239C2×C8C22×D1111yescharacteristic
240C2×C8C22×D1111yescharacteristic
241C2×C8C22×D1111yescharacteristic
242C2×C8C22×D1111yescharacteristic
243C4⋊C4—111no—
244C4⋊C4—111no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—111no—
248C4⋊C4—111no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4D4411yescharacteristic
259C22⋊C4—221no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4D4411yescharacteristic
267C22⋊C4D4411yescharacteristic
268C42—221no—
269C42—221no—
270C42—221no—
271C42C22×D1111yescharacteristic
272C11#333711yescharacteristic, complemented, Sylow
273C23—221no—
274C23C2×D4411yescharacteristic
275C23C2×D4411yescharacteristic
276Q8—221no—
277Q8—221no—
278D4—22no—
279D4—221no—
280D4—221no—
281D4—442no—
282D4—881no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—442no—
295C2×C4—881no—
296C2×C4—881no—
297C2×C4C2×D4411yescharacteristic
298C2×C4C2×D4411yescharacteristic
299C2×C4C2×D4411yescharacteristic
300C2×C4C2×D4411yescharacteristic
301C2×C4C23×D1111yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8#434112yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—441no—
312C22—441no—
313C22—441no—
314C22#6695712yes—
315C22C22×D4411yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—441no—
321C4—441no—
322C4—441no—
323C4—441no—
324C4—441no—
325C4—441no—
326C4—441no—
327C4C2×#434111yescharacteristic
328C4#6704311yescharacteristic
329C2—22no—
330C2—41no—
331C2—881no—
332C2#1062308611yescharacteristic
333C2C2×#6695711yescharacteristic
334C2#1062328211yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC8×D4×C11C2
socleC22×C11C22×D4
prime radical#10623096C2
hypercenterC8×D4D11
hypocenterC11#3337
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #10623072C2semidirect
3. C8×D4×C11C2semidirect
4. #10622727C2semidirect
5. #10622727C2semidirect
6. #10622719C2semidirect
7. C2×#66881C2semidirect
8. #10622460C2semidirect
9. #10622442C2semidirect
10. #10622350C2semidirect
11. #10622349C2semidirect
12. #10622336C2semidirect
13. #10622335C2semidirect
14. C4×#4314C2semidirect
15. #10622296C2semidirect
151. C8×D4D11semidirect
272. C11#3337semidirect

Maximal subgroups

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

subgroupindex
#106230962
#106230722
C8×D4×C112
#106227272
#106227192
C2×#668812
#106224602
#106224422
#106223502
#106223492
#106223362
#106223352
C4×#43142
#106222962
#333711