Finite Group Databasebeta

← #13079868

Subgroups — #13079868

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#10623093C211yesmaximal, characteristic
3C11×#476C211yesmaximal, characteristic, complemented
4#10622700C211yesmaximal, characteristic, complemented
5#10622622C211yesmaximal, characteristic, complemented
6#10622479C211yesmaximal, characteristic, complemented
7#10622476C211yesmaximal, characteristic, complemented
8#10622471C211yesmaximal, characteristic, complemented
9#10622469C211yesmaximal, characteristic, complemented
10#10622460C211yesmaximal, characteristic, complemented
11#10622453C211yesmaximal, characteristic, complemented
12#10622392C211yesmaximal, characteristic, complemented
13#10622387C211yesmaximal, characteristic, complemented
14#10622377C211yesmaximal, characteristic, complemented
15#10622373C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C4×D4×C11C2211yescharacteristic
18#66999—21no—
19#66997—21no—
20#66993C2211yescharacteristic
21#66991C2211yescharacteristic
22#66983—21no—
23#66982—21no—
24#66949—21no—
25#66948C2211yescharacteristic
26#66945C2211yescharacteristic
27C4⋊C4×D11C2211yescharacteristic
28#66943C2211yescharacteristic
29#66943C2211yescharacteristic
30#66942—21no—
31#66941C2211yescharacteristic
32#66937—21no—
33#66936—21no—
34C4×D44C2211yescharacteristic
35#66925C2211yescharacteristic
36#66923C2211yescharacteristic
37C11×#106C2211yescharacteristic
38C11×#106C2211yescharacteristic
39C11×C4⋊C8C2211yescharacteristic
40C11×#102C2211yescharacteristic
41C11×#102C2211yescharacteristic
42#66896C2211yescharacteristic
43#66896C2211yescharacteristic
44#66885C2211yescharacteristic
45#66885C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48#66882C2211yescharacteristic
49#66881C2211yescharacteristic
50#66879C2211yescharacteristic
51C8×Dic11C2211yescharacteristic
52#66873C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×D44—21no—
66C2×D44C2311yescharacteristic
67C2×C4×D11—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
76C11×C4⋊C4C2311yescharacteristic
77C11×C22⋊C4—21no—
78C42×C11C2311yescharacteristic
79C22⋊Dic11—21no—
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⋊Dic11C2311yescharacteristic
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
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—
104C22×D11—21no—
105C22×D11C2×D411yescharacteristic
106Q8×C11—81no—
107D4×C11—21no—
108D4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—81no—
113C2×C4×C11C2×D411yescharacteristic
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2411yescharacteristic
116C22⋊D11—81no—
117C22⋊D11—81no—
118C22⋊D11—81no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124C2×Dic11C2×D411yescharacteristic
125D44—21no—
126D44—21no—
127D44—81no—
128C4×D11—21no—
129C4×D11—21no—
130C4×D11—81no—
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#486—111no—
143#482—111no—
144#482—111no—
145#481—111no—
146#480—111no—
147#478—111no—
148#478—111no—
149#476D1111yescharacteristic, complemented
150#474—111no—
151#433—111no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11C22×D411yescharacteristic
156C2×D11—21no—
157C2×D11—21no—
158C2×D11—21no—
159C2×D11—41no—
160C2×D11—41no—
161C2×D11—41no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C112−1+411yescharacteristic
168C4×C112−1+411yescharacteristic
169Dic11—21no—
170Dic11—21no—
171Dic11—21no—
172Dic11—41no—
173Dic11—41no—
174Dic11—41no—
175C4⋊Q8—111no—
176C4⋊Q8—221no—
177C4⋊Q8C2×D1111yescharacteristic
178#127—111no—
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×D4C2×D1111yescharacteristic
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#106C2×D1111yescharacteristic
203#106C2×D1111yescharacteristic
204C4⋊C8—111no—
205C4⋊C8C2×D1111yescharacteristic
206#102—111no—
207#102—111no—
208#102—111no—
209#102—111no—
210#102—111no—
211#102—111no—
212#102C2×D1111yescharacteristic
213#102C2×D1111yescharacteristic
214C22⋊C8—111no—
215C22⋊C8—111no—
216#97—111no—
217C4×C8—111no—
218C2×C11—81no—
219C2×C11#53611yescharacteristic
220C2×C11#57611yescharacteristic
221C2×C11#57711yescharacteristic
222D11—41no—
223D11—81no—
224C2×Q8—21no—
225C2×Q8—221no—
226C2×D4—111no—
227C2×D4—221no—
228C2×D4—221no—
229C2×D4—221no—
230C2×D4—221no—
231C2×D4C22×D1111yescharacteristic
232C22×C4—21no—
233C22×C4—111no—
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—221no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4C22×D1111yescharacteristic
255C4⋊C4C22×D1111yescharacteristic
256C4⋊C4C22×D1111yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—111no—
259C22⋊C4—111no—
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—111no—
270C23—221no—
271Q8—81no—
272Q8—881no—
273D4—21no—
274D4—21no—
275D4—221no—
276D4—221no—
277D4—881no—
278D4—881no—
279D4—881no—
280D4—881no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—111no—
286C2×C4—111no—
287C2×C4—111no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
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—221no—
306C22—221no—
307C22—221no—
308C22—441no—
309C22—441no—
310C22—441no—
311C22C2×D4×D1111yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—221no—
318C4—221no—
319C4—221no—
320C4—441no—
321C4—441no—
322C4—441no—
323C4#6704011yescharacteristic
324C4#6704311yescharacteristic
325C2—81no—
326C2—441no—
327C2—881no—
328C2#1062315911yescharacteristic
329C2#1062329311yescharacteristic
330C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#476C2
socleC22×C11C22×D4
prime radical#10623093C2
hypercenter#476D11
hypocenterC11#3241
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #10623260C2semidirect
3. C11×#476C2semidirect
4. #10622700C2semidirect
5. #10622622C2semidirect
6. #10622479C2semidirect
7. #10622476C2semidirect
8. #10622471C2semidirect
9. #10622469C2semidirect
10. #10622460C2semidirect
11. #10622453C2semidirect
12. #10622392C2semidirect
13. #10622387C2semidirect
14. #10622377C2semidirect
15. #10622373C2semidirect
149. #476D11semidirect
267. C11#3241semidirect

Maximal subgroups

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

subgroupindex
#106232602
#106230932
C11×#4762
#106227002
#106226222
#106224792
#106224762
#106224712
#106224692
#106224602
#106224532
#106223922
#106223872
#106223772
#106223732
#324111