Finite Group Databasebeta

← #13081574

Subgroups — #13081574

Order 1408.

348 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623221C211yesmaximal, characteristic, complemented
2#10623070C211yesmaximal, characteristic, complemented
3C11×#478C211yesmaximal, characteristic, complemented
4#10622677C211yesmaximal, characteristic, complemented
5C4×#4323C211yesmaximal, characteristic
6#10622503C211yesmaximal, characteristic, complemented
7#10622489C211yesmaximal, characteristic, complemented
8#10622484C211yesmaximal, characteristic, complemented
9#10622469C211yesmaximal, characteristic, complemented
10#10622460C211yesmaximal, characteristic, complemented
11#10622444C211yesmaximal, characteristic, complemented
12#10622398C211yesmaximal, characteristic
13#10622398C211yesmaximal, characteristic
14#10622376C211yesmaximal, characteristic, complemented
15#10622372C211yesmaximal, characteristic, complemented
16C11×#125C2211yescharacteristic
17C4×D4×C11C2211yescharacteristic
18D4×Dic11C2211yescharacteristic
19D4×Dic11C2211yescharacteristic
20C2×#4323C2211yescharacteristic
21#66977—21no—
22C2×Dic11⋊C4—21no—
23#66950—21no—
24#66949—21no—
25#66949—21no—
26#66946C2211yescharacteristic
27#66946C2211yescharacteristic
28C4⋊C4×D11—21no—
29#66943C2211yescharacteristic
30#66943C2211yescharacteristic
31#66941C2211yescharacteristic
32#66941C2211yescharacteristic
33#66931—21no—
34#66931—21no—
35C4×D44C2211yescharacteristic
36#66923C2211yescharacteristic
37C4×Dic22C2211yescharacteristic
38C11×#107C2211yescharacteristic
39C11×#106C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×#102C2211yescharacteristic
42C11×#102C2211yescharacteristic
43#66896C2211yescharacteristic
44#66885C2211yescharacteristic
45#66885C2211yescharacteristic
46#66882C2211yescharacteristic
47#66881C2211yescharacteristic
48#66879C2211yescharacteristic
49#66879C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52#66873C2211yescharacteristic
53#66872C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×D4×C11C2311yescharacteristic
60C22×C4×C11—21no—
61C22×Dic11—21no—
62C22×Dic11—21no—
63C2×D44C2311yescharacteristic
64C2×C4×D11—21no—
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×Dic22—21no—
68C2×Dic22—21no—
69C2×Dic22D411yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C22⋊C4—21no—
78C42×C11C2311yescharacteristic
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81#4323Q814yescomplemented
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11D411yescharacteristic
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×Dic11C2311yescharacteristic
100C4×Dic11C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103#3389—111nomaximal, Sylow
104C23×C11—21no—
105C22×D11—21no—
106D4×C11—21no—
107D4×C11C2×Q812yes—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—81no—
112C2×C4×C11C2×D411yescharacteristic
113C2×C4×C11C2×D411yescharacteristic
114C2×C4×C11C2411yescharacteristic
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—42no—
119C2×Dic11—81no—
120C2×Dic11C2×D411yescharacteristic
121C2×Dic11C2×D411yescharacteristic
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124D44—21no—
125D44C2×Q812yes—
126C4×D11—42no—
127C4×D11—81no—
128C4×D11—81no—
129Dic22—41no—
130Dic22—81no—
131Dic22—81no—
132C8×C11—21no—
133C8×C11—21no—
134C11⋊C8—21no—
135C11⋊C8C2×Q812yes—
136#554—111no—
137#554—111no—
138#501—111no—
139#501—111no—
140#499—111no—
141#478—111no—
142#478—111no—
143#478—111no—
144#478D1111yescharacteristic, complemented
145#474—111no—
146#474—111no—
147#446—111no—
148#442—111no—
149#442—111no—
150C4×D8—111no—
151C22×C11—22no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11C22×D411yescharacteristic
155C2×D11—22no—
156C2×D11—41no—
157C2×D11—41no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11C22×Q811yescharacteristic
164C4×C112−1+411yescharacteristic
165Dic11—21no—
166Dic11—21no—
167Dic11—21no—
168Dic11—21no—
169Dic11—41no—
170Dic11—41no—
171Dic11—41no—
172C2×D8—111no—
173C4⋊Q8—111no—
174C4⋊Q8—111no—
175#125—111no—
176#125—111no—
177#125—111no—
178#125C2×D1111yescharacteristic
179C22⋊Q8—221no—
180C22⋊Q8—221no—
181C22⋊Q8—221no—
182C22⋊Q8—221no—
183C22⋊Q8—221no—
184C22⋊Q8—221no—
185C4×Q8—111no—
186C4×D4—111no—
187C4×D4—111no—
188C4×D4—111no—
189C4×D4—111no—
190C4×D4—111no—
191C4×D4C2×D1111yescharacteristic
192C2×C4⋊C4—221no—
193C2×C4⋊C4—221no—
194#107—111no—
195#107—111no—
196#107—111no—
197#107—111no—
198#107C2×D1111yescharacteristic
199#106—111no—
200#106—111no—
201#106—111no—
202#106C2×D1111yescharacteristic
203C4⋊C8—111no—
204C4⋊C8—111no—
205C4⋊C8C2×D1111yescharacteristic
206#102—111no—
207#102—111no—
208#102—111no—
209#102—111no—
210#102C2×D1111yescharacteristic
211#102C2×D1111yescharacteristic
212#97—111no—
213#97—111no—
214C4×C8—111no—
215C2×C11—42no—
216C2×C11D4×Q811yescharacteristic
217C2×C11#57511yescharacteristic
218C2×C11#57611yescharacteristic
219D11—42no—
220C2×Q8—111no—
221C2×Q8—221no—
222C2×Q8—221no—
223C2×D4—111no—
224C2×D4C22×D1111yescharacteristic
225C22×C4—21no—
226C22×C4—221no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4—221no—
231D8—114no—
232C2×C8—111no—
233C2×C8—111no—
234C2×C8C22×D1111yescharacteristic
235C2×C8C22×D1111yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—111no—
239C4⋊C4—111no—
240C4⋊C4—111no—
241C4⋊C4—111no—
242C4⋊C4—111no—
243C4⋊C4—111no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4C22×D1111yescharacteristic
253C4⋊C4C22×D1111yescharacteristic
254C4⋊C4C22×D1111yescharacteristic
255C22⋊C4—21no—
256C22⋊C4—221no—
257C22⋊C4—221no—
258C22⋊C4—221no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C42—111no—
262C42—111no—
263C42C22×D1111yescharacteristic
264C11#338911yescharacteristic, complemented, Sylow
265C23—21no—
266C23—221no—
267Q8—441no—
268Q8—881no—
269Q8—881no—
270D4—21no—
271D4—112no—
272D4—221no—
273D4Q8×D1112yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—81no—
278C2×C4—111no—
279C2×C4—111no—
280C2×C4—111no—
281C2×C4—111no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4—881no—
288C2×C4—881no—
289C2×C4—881no—
290C2×C4D4×D1111yescharacteristic
291C2×C4D4×D1111yescharacteristic
292C2×C4C23×D1111yescharacteristic
293C8—21no—
294C8—21no—
295C8—112no—
296C8—221no—
297C22—22no—
298C22—41no—
299C22—41no—
300C22—222no—
301C22—441no—
302C22—441no—
303C22C2×D4×D1111yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—221no—
310C4—221no—
311C4—221no—
312C4—221no—
313C4—441no—
314C4—441no—
315C4—441no—
316C4C2×Q8×D1111yescharacteristic
317C4#6704311yescharacteristic
318C2—42no—
319C2—442no—
320C2#1062316311yescharacteristic
321C2#1062329911yescharacteristic
322C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#478C2
socleC22×C11C22×D4
prime radicalC2×#4323C22
hypercenter#478D11
hypocenterC11#3389
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #10623221C2semidirect
2. #10623070C2semidirect
3. C11×#478C2semidirect
4. #10622677C2semidirect
6. #10622503C2semidirect
7. #10622489C2semidirect
8. #10622484C2semidirect
9. #10622469C2semidirect
10. #10622460C2semidirect
11. #10622444C2semidirect
14. #10622376C2semidirect
15. #10622372C2semidirect
81. #4323Q8semidirect
144. #478D11semidirect
264. C11#3389semidirect

Maximal subgroups

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

subgroupindex
#106232212
#106230702
C11×#4782
#106226772
C4×#43232
#106225032
#106224892
#106224842
#106224692
#106224602
#106224442
#106223982
#106223762
#106223722
#338911