Finite Group Databasebeta

← #13081575

Subgroups — #13081575

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#10623074C211yesmaximal, characteristic, complemented
2#10623070C211yesmaximal, characteristic, complemented
3C11×#442C211yesmaximal, characteristic
4#10622765C211yesmaximal, characteristic
5D8×Dic11C211yesmaximal, characteristic
6#10622622C211yesmaximal, characteristic, complemented
7#10622620C211yesmaximal, characteristic, complemented
8#10622471C211yesmaximal, characteristic, complemented
9#10622469C211yesmaximal, characteristic, complemented
10#10622379C211yesmaximal, characteristic, complemented
11#10622376C211yesmaximal, characteristic, complemented
12#10622376C211yesmaximal, characteristic, complemented
13#10622372C211yesmaximal, characteristic, complemented
14#10622315C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C2×C11×D8C2211yescharacteristic
17C4×D4×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19D4×Dic11C2211yescharacteristic
20D4×Dic11C2211yescharacteristic
21D4×Dic11C2211yescharacteristic
22D4×Dic11C2211yescharacteristic
23C2×C4⋊Dic11—21no—
24#66977—21no—
25#66977—21no—
26C2×Dic11⋊C4—21no—
27#66943C2211yescharacteristic
28#66943C2211yescharacteristic
29#66943C2211yescharacteristic
30#66941C2211yescharacteristic
31#66931—21no—
32#66931—21no—
33#66931—21no—
34#66931—21no—
35#66923C2211yescharacteristic
36#66922C2211yescharacteristic
37C4×Dic22C2211yescharacteristic
38C11×#106C2211yescharacteristic
39C11×#102C2211yescharacteristic
40C11×#102C2211yescharacteristic
41C11×#97C2211yescharacteristic
42#66896C2211yescharacteristic
43#66896C2211yescharacteristic
44#66896C2211yescharacteristic
45#66896C2211yescharacteristic
46#66882C2211yescharacteristic
47#66882C2211yescharacteristic
48#66881C2211yescharacteristic
49#66881C2211yescharacteristic
50#66879C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×D4×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×Dic11—21no—
64C22×Dic11—21no—
65C22×Dic11—21no—
66C22×Dic11—21no—
67C2×Dic22—21no—
68C2×Dic22—21no—
69C2×Dic22D411yescharacteristic
70C11×D8Q814yescomplemented
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C22⋊C4—21no—
76C11×C22⋊C4—21no—
77C42×C11C2311yescharacteristic
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11D411yescharacteristic
87C4⋊Dic11C2311yescharacteristic
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—
105C23×C11—21no—
106D4×C11—21no—
107D4×C11—21no—
108D4×C11C2×Q812yes—
109D4×C11C2×Q812yes—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—42no—
113C2×C4×C11—81no—
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2411yescharacteristic
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—42no—
122C2×Dic11—81no—
123C2×Dic11—81no—
124C2×Dic11—81no—
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129Dic22—41no—
130Dic22—81no—
131Dic22—81no—
132C8×C11—21no—
133C8×C11C2×Q812yes—
134C11⋊C8—21no—
135C11⋊C8—21no—
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#478—111no—
145#474—111no—
146#474—111no—
147#446—111no—
148#442—111no—
149#442D1111yescharacteristic
150C4×D8—111no—
151C22×C11—22no—
152C22×C11—22no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11C22×D411yescharacteristic
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11C22×Q811yescharacteristic
163C4×C112−1+411yescharacteristic
164Dic11—21no—
165Dic11—21no—
166Dic11—21no—
167Dic11—21no—
168Dic11—41no—
169Dic11—41no—
170Dic11—41no—
171Dic11—41no—
172C2×D8C2×D1111yescharacteristic
173C4⋊Q8—111no—
174C4⋊Q8—111no—
175#125—111no—
176#125—111no—
177#125—111no—
178#125—111no—
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×D4C2×D1111yescharacteristic
191C4×D4C2×D1111yescharacteristic
192C2×C4⋊C4—221no—
193C2×C4⋊C4—221no—
194#107—111no—
195#107—111no—
196#107—111no—
197#107—111no—
198#107—111no—
199#106—111no—
200#106—111no—
201#106—111no—
202#106C2×D1111yescharacteristic
203C4⋊C8—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#97—111no—
213#97C2×D1111yescharacteristic
214C4×C8—111no—
215C2×C11—42no—
216C2×C11—42no—
217C2×C11D4×Q811yescharacteristic
218C2×C11#57511yescharacteristic
219C2×C11#57611yescharacteristic
220C2×Q8—111no—
221C2×Q8—221no—
222C2×Q8—221no—
223C2×D4C22×D1111yescharacteristic
224C2×D4C22×D1111yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4—221no—
231D8Dic2214yescomplemented
232C2×C8—111no—
233C2×C8—111no—
234C2×C8C22×D1111yescharacteristic
235C2×C8C22×D1111yescharacteristic
236C4⋊C4—111no—
237C4⋊C4—111no—
238C4⋊C4—111no—
239C4⋊C4—111no—
240C4⋊C4—111no—
241C4⋊C4—111no—
242C4⋊C4—111no—
243C4⋊C4—221no—
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⋊C4—221no—
253C4⋊C4C22×D1111yescharacteristic
254C4⋊C4C22×D1111yescharacteristic
255C22⋊C4—21no—
256C22⋊C4—21no—
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—21no—
267Q8—441no—
268Q8—881no—
269Q8—881no—
270D4—21no—
271D4—21no—
272D4C2×Dic2212yes—
273D4C2×Dic2212yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—42no—
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—221no—
286C2×C4—442no—
287C2×C4—881no—
288C2×C4—881no—
289C2×C4—881no—
290C2×C4D4×D1111yescharacteristic
291C2×C4D4×D1111yescharacteristic
292C2×C4C23×D1111yescharacteristic
293C8—21no—
294C8—221no—
295C8—221no—
296C8C2×Dic2212yes—
297C22—22no—
298C22—22no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—41no—
303C22C2×D4×D1111yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—221no—
309C4—221no—
310C4—221no—
311C4—221no—
312C4—441no—
313C4—441no—
314C4—441no—
315C4—441no—
316C4C22×Dic2211yescharacteristic
317C4#6704311yescharacteristic
318C2—42no—
319C2—42no—
320C2D4×Dic2211yescharacteristic
321C2#1062330411yescharacteristic
322C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#442C2
socleC22×C11C22×D4
prime radicalC2×C11×D8C22
hypercenter#442D11
hypocenterC11#3389
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #10623074C2semidirect
2. #10623070C2semidirect
6. #10622622C2semidirect
7. #10622620C2semidirect
8. #10622471C2semidirect
9. #10622469C2semidirect
10. #10622379C2semidirect
11. #10622376C2semidirect
12. #10622376C2semidirect
13. #10622372C2semidirect
14. #10622315C2semidirect
15. #10622314C2semidirect
70. C11×D8Q8semidirect
231. D8Dic22semidirect
264. C11#3389semidirect

Maximal subgroups

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

subgroupindex
#106230742
#106230702
C11×#4422
#106227652
D8×Dic112
#106226222
#106226202
#106224712
#106224692
#106223792
#106223762
#106223722
#106223152
#106223142
#338911