Finite Group Databasebeta

← #13079151

Subgroups — #13079151

Order 1408.

340 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623260C211yesmaximal, characteristic
2#10623220C211yesmaximal, characteristic
3C11×#501C211yesmaximal, characteristic, complemented
4#10622691C211yesmaximal, characteristic, complemented
5#10622677C211yesmaximal, characteristic, complemented
6#10622494C211yesmaximal, characteristic
7D11×#107C211yesmaximal, characteristic
8#10622489C211yesmaximal, characteristic, complemented
9#10622487C211yesmaximal, characteristic, complemented
10#10622474C211yesmaximal, characteristic
11#10622473C211yesmaximal, characteristic
12#10622471C211yesmaximal, characteristic, complemented
13#10622469C211yesmaximal, characteristic, complemented
14#10622321C211yesmaximal, characteristic
15#10622315C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#125C2211yescharacteristic
18#66999—21no—
19#66997—21no—
20C2×#4313C2211yescharacteristic
21C2×C8×D11C2211yescharacteristic
22#66950—21no—
23#66949—21no—
24#66949—21no—
25#66945C2211yescharacteristic
26#66945C2211yescharacteristic
27C4⋊C4×D11C2211yescharacteristic
28C4⋊C4×D11C2211yescharacteristic
29#66943C2211yescharacteristic
30#66943C2211yescharacteristic
31#66942—21no—
32#66942—21no—
33#66941—21no—
34#66941C2211yescharacteristic
35#66941C2211yescharacteristic
36#66925C2211yescharacteristic
37#66923C2211yescharacteristic
38#66922C2211yescharacteristic
39C11×#107C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×#97C2211yescharacteristic
44#66882C2211yescharacteristic
45#66882C2211yescharacteristic
46#66881C2211yescharacteristic
47#66881C2211yescharacteristic
48#66879C2211yescharacteristic
49C8×Dic11C2211yescharacteristic
50#66872C2211yescharacteristic
51#66872C2211yescharacteristic
52#66871C2211yescharacteristic
53#66871C2211yescharacteristic
54#66871C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×C4×D11—21no—
61C2×C4×D11—21no—
62C2×C4×D11C2311yescharacteristic
63C2×Dic22—21no—
64C2×Dic22—21no—
65C2×Dic22—21no—
66C2×C8×C11C2311yescharacteristic
67C2×C8×C11C2311yescharacteristic
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4C2311yescharacteristic
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C42×C11C2311yescharacteristic
76(C2×D11)⋊C4—21no—
77(C2×D11)⋊C4—21no—
78(C2×D11)⋊C4D411yescharacteristic
79(C2×D11)⋊C4D411yescharacteristic
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11C2311yescharacteristic
84C4⋊Dic11C2311yescharacteristic
85C4⋊Dic11C2311yescharacteristic
86C4⋊Dic11C2311yescharacteristic
87Dic11⋊C4—21no—
88Dic11⋊C4—21no—
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4D411yescharacteristic
96Dic11⋊C4D411yescharacteristic
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102#4313Q814yescomplemented
103C8×D11Q814yescomplemented
104#3164—111nomaximal, Sylow
105C22×D11C2×D411yescharacteristic
106Q8×C11—81no—
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×Dic11—21no—
118C2×Dic11C2×D411yescharacteristic
119C2×Dic11C2×D411yescharacteristic
120C2×Dic11C2×D411yescharacteristic
121C4×D11—81no—
122C4×D11—81no—
123C4×D11C2×Q812yes—
124C4×D11C2×Q812yes—
125Dic22—81no—
126Dic22—81no—
127Dic22—81no—
128C8×C11C2×Q812yes—
129C8×C11C2×Q812yes—
130C11⋊C8C2×Q812yes—
131C11⋊C8C2×Q812yes—
132#544—111no—
133#544—111no—
134#501—111no—
135#501—111no—
136#501—111no—
137#501D1111yescharacteristic, complemented
138#500—111no—
139#500—111no—
140#499—111no—
141#499—111no—
142#428—111no—
143#428—111no—
144#427—111no—
145C2×#107—111no—
146#405—111no—
147C22×C11C22×D411yescharacteristic
148C2×D11—21no—
149C2×D11—21no—
150C2×D11C4⋊Q812yes—
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—41no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C11—41no—
157C4×C11C22×Q811yescharacteristic
158C4×C11C22×Q811yescharacteristic
159Dic11—21no—
160Dic11—21no—
161Dic11—41no—
162Dic11—41no—
163Dic11—41no—
164Dic11—41no—
165Dic11C4⋊Q812yes—
166C2×M16—111no—
167C22×C8—111no—
168C4⋊Q8—111no—
169C4⋊Q8—111no—
170C4⋊Q8—111no—
171C4⋊Q8—221no—
172C4⋊Q8—221no—
173C4⋊Q8C2×D1111yescharacteristic
174#125—111no—
175#125—111no—
176#125—111no—
177#125—221no—
178#125—221no—
179#125C2×D1111yescharacteristic
180C22⋊Q8—221no—
181C22⋊Q8—221no—
182C22⋊Q8—221no—
183C22⋊Q8—221no—
184#117—111no—
185#117—111no—
186#117—111no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—111no—
189#107—111no—
190#107—111no—
191#107—111no—
192#107—111no—
193#107—111no—
194#107—111no—
195#107—111no—
196#107—111no—
197#107C2×D1111yescharacteristic
198#107C2×D1111yescharacteristic
199#106—111no—
200#106—111no—
201#106—111no—
202#106—111no—
203#106C2×D1111yescharacteristic
204#106C2×D1111yescharacteristic
205#97—111no—
206#97C2×D1111yescharacteristic
207C4×C8—111no—
208C4×C8—111no—
209C2×C11C2×C4⋊Q811yescharacteristic
210C2×C11#57611yescharacteristic
211C2×C11#57811yescharacteristic
212D11—22no—
213C2×Q8—21no—
214C2×Q8—221no—
215C2×Q8—221no—
216C2×Q8—221no—
217C22×C4—111no—
218C22×C4—221no—
219C22×C4—221no—
220M16—114no—
221C2×C8—111no—
222C2×C8—111no—
223C2×C8—114no—
224C2×C8C22×D1111yescharacteristic
225C2×C8C22×D1111yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—111no—
230C4⋊C4—111no—
231C4⋊C4—111no—
232C4⋊C4—111no—
233C4⋊C4—111no—
234C4⋊C4—111no—
235C4⋊C4—221no—
236C4⋊C4—221no—
237C4⋊C4—221no—
238C4⋊C4—221no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4C22×D1111yescharacteristic
247C4⋊C4C22×D1111yescharacteristic
248C4⋊C4C22×D1111yescharacteristic
249C4⋊C4C22×D1111yescharacteristic
250C22⋊C4—111no—
251C22⋊C4—111no—
252C22⋊C4—221no—
253C22⋊C4—221no—
254C42—111no—
255C42—221no—
256C42—221no—
257C42C22×D1111yescharacteristic
258C11#316411yescharacteristic, complemented, Sylow
259C23—111no—
260Q8—81no—
261Q8—881no—
262Q8—881no—
263Q8—881no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—111no—
269C2×C4—112no—
270C2×C4—112no—
271C2×C4—111no—
272C2×C4—111no—
273C2×C4—221no—
274C2×C4—221no—
275C2×C4—221no—
276C2×C4—221no—
277C2×C4—881no—
278C2×C4—881no—
279C2×C4D4×D1111yescharacteristic
280C2×C4D4×D1111yescharacteristic
281C2×C4C23×D1111yescharacteristic
282C8—112no—
283C8—112no—
284C8Q8×D1112yes—
285C8Q8×D1112yes—
286C22—112no—
287C22—221no—
288C22—221no—
289C22C2×D4×D1111yescharacteristic
290C4—21no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—112no—
297C4—221no—
298C4—221no—
299C4—441no—
300C4—441no—
301C4—441no—
302C4—441no—
303C4C2×Q8×D1111yescharacteristic
304C4C2×Q8×D1111yescharacteristic
305C2—222no—
306C2D11×C4⋊Q811yescharacteristic
307C2#1062330511yescharacteristic
308C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#501C2
socleC22×C11C22×D4
prime radicalC22×D11C2×D4
hypercenter#501D11
hypocenterC11#3164
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. C11×#501C2semidirect
4. #10622691C2semidirect
5. #10622677C2semidirect
8. #10622489C2semidirect
9. #10622487C2semidirect
12. #10622471C2semidirect
13. #10622469C2semidirect
15. #10622315C2semidirect
102. #4313Q8semidirect
103. C8×D11Q8semidirect
137. #501D11semidirect
258. C11#3164semidirect

Maximal subgroups

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

subgroupindex
#106232602
#106232202
C11×#5012
#106226912
#106226772
#106224942
D11×#1072
#106224892
#106224872
#106224742
#106224732
#106224712
#106224692
#106223212
#106223152
#316411