Finite Group Databasebeta

← #13081529

Subgroups — #13081529

Order 1408.

340 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623221C211yesmaximal, characteristic
2Q8×Dic22C211yesmaximal, characteristic, complemented
3C11×#479C211yesmaximal, characteristic, complemented
4#10622678C211yesmaximal, characteristic, complemented
5#10622639C211yesmaximal, characteristic
6#10622503C211yesmaximal, characteristic
7#10622487C211yesmaximal, characteristic, complemented
8#10622483C211yesmaximal, characteristic
9#10622469C211yesmaximal, characteristic, complemented
10#10622459C211yesmaximal, characteristic
11#10622441C211yesmaximal, characteristic, complemented
12#10622430C211yesmaximal, characteristic
13#10622409C211yesmaximal, characteristic, complemented
14#10622407C211yesmaximal, characteristic, complemented
15#10622401C211yesmaximal, characteristic
16C11×#125C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18Q8×Dic11C2211yescharacteristic
19Q8×Dic11C2211yescharacteristic
20C2×#4325C2211yescharacteristic
21#66950—21no—
22#66949—21no—
23#66949—21no—
24#66946C2211yescharacteristic
25#66946C2211yescharacteristic
26C4⋊C4×D11—21no—
27#66943C2211yescharacteristic
28#66941—21no—
29#66941—21no—
30#66941C2211yescharacteristic
31#66941C2211yescharacteristic
32#66941C2211yescharacteristic
33C4×D44C2211yescharacteristic
34#66922—21no—
35#66922C2211yescharacteristic
36C4×Dic22—21no—
37C4×Dic22C2211yescharacteristic
38C11×#107C2211yescharacteristic
39C11×#106C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#103C2211yescharacteristic
43#66899C2211yescharacteristic
44#66885C2211yescharacteristic
45#66885C2211yescharacteristic
46#66882C2211yescharacteristic
47#66882C2211yescharacteristic
48#66879C2211yescharacteristic
49Dic11⋊C8C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51C8×Dic11C2211yescharacteristic
52#66873C2211yescharacteristic
53#66872C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D44C2311yescharacteristic
61C2×C4×D11—21no—
62C2×C4×D11—21no—
63C2×C4×D11—21no—
64C2×Dic22—21no—
65C2×Dic22—21no—
66C2×Dic22—21no—
67C2×Dic22—21no—
68C2×Dic22D411yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C42×C11—21no—
78C42×C11C2311yescharacteristic
79#4325Q814yescomplemented
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—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⋊C4D411yescharacteristic
96Dic11⋊C4D411yescharacteristic
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11C2311yescharacteristic
100C4×Dic11C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103#3385—111nomaximal, Sylow
104C22×D11—21no—
105Q8×C11—21no—
106Q8×C11C2×Q812yes—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11C2×D411yescharacteristic
112C2×C4×C11C2×D411yescharacteristic
113C2×C4×C11C2411yescharacteristic
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11C2×D411yescharacteristic
118C2×Dic11C2×D411yescharacteristic
119C2×Dic11C2×D411yescharacteristic
120C2×Dic11C2×D411yescharacteristic
121D44—21no—
122D44C2×Q812yes—
123C4×D11—42no—
124C4×D11—81no—
125C4×D11—81no—
126Dic22—22no—
127Dic22—81no—
128Dic22—81no—
129Dic22—81no—
130Dic22—81no—
131C8×C11—21no—
132C8×C11—21no—
133C11⋊C8—21no—
134C11⋊C8C2×Q812yes—
135Q82—111no—
136#554—111no—
137#501—111no—
138#501—111no—
139#500—111no—
140#479—111no—
141#479D1111yescharacteristic, complemented
142#477—111no—
143#476—111no—
144#474—111no—
145#474—111no—
146#446—111no—
147#440—111no—
148#440—111no—
149C4×SD16—111no—
150C22×C11C22×D411yescharacteristic
151C2×D11—22no—
152C2×D11—41no—
153C2×D11—41no—
154C4×C11—22no—
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11C22×Q811yescharacteristic
161C4×C112−1+411yescharacteristic
162Dic11—21no—
163Dic11—21no—
164Dic11—21no—
165Dic11—41no—
166Dic11—41no—
167Dic11—41no—
168Dic11#13712yes—
169C2×SD16—111no—
170C4⋊Q8—111no—
171C4⋊Q8—111no—
172C4⋊Q8—111no—
173C4⋊Q8—111no—
174C4⋊Q8—221no—
175C4⋊Q8—221no—
176C4⋊Q8—221no—
177#125—111no—
178#125C2×D1111yescharacteristic
179C22⋊Q8—221no—
180C22⋊Q8—221no—
181C22⋊Q8—221no—
182C4×Q8—111no—
183C4×Q8—111no—
184C4×Q8—111no—
185C4×Q8—221no—
186C4×Q8C2×D1111yescharacteristic
187C4×D4—111no—
188C4×D4—111no—
189C4×D4—111no—
190C2×C4⋊C4—221no—
191#107—111no—
192#107—111no—
193#107—111no—
194#107—111no—
195#107—111no—
196#107C2×D1111yescharacteristic
197#106—111no—
198#106—111no—
199#106C2×D1111yescharacteristic
200C4⋊C8—111no—
201C4⋊C8—111no—
202C4⋊C8C2×D1111yescharacteristic
203#103—111no—
204#103C2×D1111yescharacteristic
205#103C2×D1111yescharacteristic
206#102—111no—
207#102—111no—
208#102—111no—
209#97—111no—
210#97—111no—
211C4×C8—111no—
212C2×C11D4×Q811yescharacteristic
213C2×C11C2×#13711yescharacteristic
214C2×C11#57611yescharacteristic
215D11—42no—
216C2×Q8—111no—
217C2×Q8—221no—
218C2×Q8—221no—
219C2×Q8—221no—
220C2×Q8—221no—
221C2×Q8C22×D1111yescharacteristic
222C2×D4—111no—
223C22×C4—221no—
224C22×C4—221no—
225C22×C4—221no—
226SD16—114no—
227C2×C8—111no—
228C2×C8—111no—
229C2×C8C22×D1111yescharacteristic
230C2×C8C22×D1111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—111no—
235C4⋊C4—111no—
236C4⋊C4—111no—
237C4⋊C4—111no—
238C4⋊C4—111no—
239C4⋊C4—111no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4—221no—
248C4⋊C4C22×D1111yescharacteristic
249C4⋊C4C22×D1111yescharacteristic
250C4⋊C4C22×D1111yescharacteristic
251C22⋊C4—221no—
252C22⋊C4—221no—
253C22⋊C4—221no—
254C42—21no—
255C42—111no—
256C42—111no—
257C42—221no—
258C42—221no—
259C42C22×D1111yescharacteristic
260C11#338511yescharacteristic, complemented, Sylow
261C23—221no—
262Q8—21no—
263Q8—222no—
264Q8—881no—
265Q8—881no—
266Q8—881no—
267Q8—881no—
268Q8Q8×D1112yes—
269D4—112no—
270D4—221no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—111no—
276C2×C4—111no—
277C2×C4—111no—
278C2×C4—111no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—221no—
282C2×C4—442no—
283C2×C4—881no—
284C2×C4—881no—
285C2×C4D4×D1111yescharacteristic
286C2×C4D4×D1111yescharacteristic
287C2×C4C23×D1111yescharacteristic
288C8—21no—
289C8—21no—
290C8—112no—
291C8—221no—
292C22—222no—
293C22—441no—
294C22—441no—
295C22C2×D4×D1111yescharacteristic
296C4—21no—
297C4—21no—
298C4—22no—
299C4—41no—
300C4—41no—
301C4—41no—
302C4—112no—
303C4—221no—
304C4—221no—
305C4—221no—
306C4—441no—
307C4—441no—
308C4—441no—
309C4C2×Q8×D1111yescharacteristic
310C4#6704311yescharacteristic
311C2—442no—
312C2#1062316311yescharacteristic
313C2#1062330011yescharacteristic
314C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#479C2
socleC22×C11C22×D4
prime radicalC2×D44C23
hypercenter#479D11
hypocenterC11#3385
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. Q8×Dic22C2semidirect
3. C11×#479C2semidirect
4. #10622678C2semidirect
7. #10622487C2semidirect
9. #10622469C2semidirect
11. #10622441C2semidirect
13. #10622409C2semidirect
14. #10622407C2semidirect
79. #4325Q8semidirect
141. #479D11semidirect
260. C11#3385semidirect

Maximal subgroups

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

subgroupindex
#106232212
Q8×Dic222
C11×#4792
#106226782
#106226392
#106225032
#106224872
#106224832
#106224692
#106224592
#106224412
#106224302
#106224092
#106224072
#106224012
#338511