Finite Group Databasebeta

← #13079862

Subgroups — #13079862

Order 1408.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623260C211yesmaximal, characteristic, complemented
2#10623250C211yesmaximal, characteristic
3C11×#486C211yesmaximal, characteristic, complemented
4#10622693C211yesmaximal, characteristic, complemented
5#10622684C211yesmaximal, characteristic, complemented
6#10622397C211yesmaximal, characteristic, complemented
7#10622392C211yesmaximal, characteristic, complemented
8#10622390C211yesmaximal, characteristic, complemented
9#10622387C211yesmaximal, characteristic, complemented
10#10622379C211yesmaximal, characteristic, complemented
11#10622376C211yesmaximal, characteristic, complemented
12#10622374C211yesmaximal, characteristic, complemented
13#10622372C211yesmaximal, characteristic, complemented
14#10622303C211yesmaximal, characteristic, complemented
15#10622296C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#127C2211yescharacteristic
18#66999—21no—
19#66997—21no—
20#66992—21no—
21#66992—21no—
22#66991C2211yescharacteristic
23#66991C2211yescharacteristic
24#66988—21no—
25#66988—21no—
26D4×Dic11C2211yescharacteristic
27D4×Dic11C2211yescharacteristic
28#66949—21no—
29#66945C2211yescharacteristic
30C4⋊C4×D11C2211yescharacteristic
31#66943C2211yescharacteristic
32#66942—21no—
33#66941C2211yescharacteristic
34#66925C2211yescharacteristic
35#66923C2211yescharacteristic
36#66923C2211yescharacteristic
37C11×#102C2211yescharacteristic
38C11×#102C2211yescharacteristic
39C11×#102C2211yescharacteristic
40C11×#102C2211yescharacteristic
41C4×C8×C11C2211yescharacteristic
42#66896C2211yescharacteristic
43#66896C2211yescharacteristic
44#66896C2211yescharacteristic
45#66896C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48#66882C2211yescharacteristic
49#66882C2211yescharacteristic
50#66881C2211yescharacteristic
51#66881C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C22×Dic11—21no—
67C22×Dic11—21no—
68C2×C4×D11—21no—
69C2×C4×D11C2311yescharacteristic
70C2×Dic22—21no—
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C42×C11C2311yescharacteristic
77C22⋊Dic11—21no—
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4D411yescharacteristic
83(C2×D11)⋊C4D411yescharacteristic
84C4⋊Dic11—21no—
85C4⋊Dic11C2311yescharacteristic
86C4⋊Dic11C2311yescharacteristic
87C4⋊Dic11C2311yescharacteristic
88C4⋊Dic11C2311yescharacteristic
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4D411yescharacteristic
97Dic11⋊C4D411yescharacteristic
98C4×Dic11—21no—
99C4×Dic11C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102#3241—111nomaximal, Sylow
103C23×C11—21no—
104C23×C11—21no—
105C22×D11C2×D411yescharacteristic
106Q8×C11—81no—
107D4×C11—21no—
108D4×C11—21no—
109D4×C11—21no—
110D4×C11—21no—
111D4×C11—81no—
112D4×C11—81no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2411yescharacteristic
118C22⋊D11—81no—
119C22⋊D11—81no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—81no—
125C2×Dic11—81no—
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129C4×D11—21no—
130C4×D11—21no—
131C4×D11—81no—
132Dic22—81no—
133C8×C11—21no—
134C8×C11—21no—
135C11⋊C8—21no—
136C11⋊C8—21no—
137#544—111no—
138#540—111no—
139#501—111no—
140#499—111no—
141#490—111no—
142#486D1111yescharacteristic, complemented
143#482—111no—
144#482—111no—
145#481—111no—
146#480—111no—
147#478—111no—
148#478—111no—
149#476—111no—
150#474—111no—
151#433—111no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11C22×D411yescharacteristic
159C2×D11—21no—
160C2×D11—21no—
161C2×D11—21no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C112−1+411yescharacteristic
167C4×C112−1+411yescharacteristic
168Dic11—21no—
169Dic11—21no—
170Dic11—21no—
171Dic11—41no—
172Dic11—41no—
173Dic11—41no—
174Dic11—41no—
175C4⋊Q8—111no—
176C4⋊Q8—221no—
177C4⋊Q8C2×D1111yescharacteristic
178#127C2×D1111yescharacteristic
179#125—111no—
180#125—111no—
181#125—111no—
182#125—221no—
183#123—221no—
184#123—221no—
185C22⋊Q8—221no—
186C22⋊Q8—221no—
187#121—111no—
188#121—111no—
189#121—221no—
190#121—221no—
191C4×D4—111no—
192C4×D4—111no—
193#117—111no—
194#117—111no—
195C2×C4⋊C4—111no—
196#107—111no—
197#107—111no—
198#107—111no—
199#107—111no—
200#106—111no—
201#106—111no—
202#106—111no—
203#106—111no—
204C4⋊C8—111no—
205C4⋊C8—111no—
206#102—111no—
207#102—111no—
208#102—111no—
209#102—111no—
210#102C2×D1111yescharacteristic
211#102C2×D1111yescharacteristic
212#102C2×D1111yescharacteristic
213#102C2×D1111yescharacteristic
214C22⋊C8—111no—
215C22⋊C8—111no—
216#97—111no—
217C4×C8C2×D1111yescharacteristic
218C2×C11—81no—
219C2×C11—81no—
220C2×C11#53611yescharacteristic
221C2×C11#57611yescharacteristic
222C2×C11#57711yescharacteristic
223D11—41no—
224C2×Q8—21no—
225C2×Q8—221no—
226C2×D4—21no—
227C2×D4—21no—
228C2×D4—221no—
229C2×D4—221no—
230C2×D4C22×D1111yescharacteristic
231C2×D4C22×D1111yescharacteristic
232C22×C4—111no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4—221no—
236C2×C8—111no—
237C2×C8—111no—
238C2×C8C22×D1111yescharacteristic
239C2×C8C22×D1111yescharacteristic
240C4⋊C4—21no—
241C4⋊C4—111no—
242C4⋊C4—111no—
243C4⋊C4—111no—
244C4⋊C4—111no—
245C4⋊C4—111no—
246C4⋊C4—111no—
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
256C4⋊C4C22×D1111yescharacteristic
257C22⋊C4—111no—
258C22⋊C4—111no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C42—111no—
265C42—221no—
266C42C22×D1111yescharacteristic
267C11#324111yescharacteristic, complemented, Sylow
268C23—21no—
269C23—21no—
270C23—111no—
271Q8—81no—
272Q8—881no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—881no—
280D4—881no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—111no—
284C2×C4—111no—
285C2×C4—111no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—881no—
293C2×C4—881no—
294C2×C4—881no—
295C2×C4D4×D1111yescharacteristic
296C2×C4D4×D1111yescharacteristic
297C2×C4C23×D1111yescharacteristic
298C8—21no—
299C8—21no—
300C8—221no—
301C8—221no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—221no—
309C22—221no—
310C22—221no—
311C22C2×D4×D1111yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—221no—
317C4—221no—
318C4—221no—
319C4—441no—
320C4—441no—
321C4—441no—
322C4—441no—
323C4#6704311yescharacteristic
324C4#6704311yescharacteristic
325C2—81no—
326C2—81no—
327C2—441no—
328C2#1062320611yescharacteristic
329C2#1062328811yescharacteristic
330C2#1062329311yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#486C2
socleC22×C11C22×D4
prime radical#10623250C2
hypercenter#486D11
hypocenterC11#3241
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #10623260C2semidirect
3. C11×#486C2semidirect
4. #10622693C2semidirect
5. #10622684C2semidirect
6. #10622397C2semidirect
7. #10622392C2semidirect
8. #10622390C2semidirect
9. #10622387C2semidirect
10. #10622379C2semidirect
11. #10622376C2semidirect
12. #10622374C2semidirect
13. #10622372C2semidirect
14. #10622303C2semidirect
15. #10622296C2semidirect
142. #486D11semidirect
267. C11#3241semidirect

Maximal subgroups

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

subgroupindex
#106232602
#106232502
C11×#4862
#106226932
#106226842
#106223972
#106223922
#106223902
#106223872
#106223792
#106223762
#106223742
#106223722
#106223032
#106222962
#324111