Finite Group Databasebeta

← #13081078

Subgroups — #13081078

Order 1408.

344 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623225C211yesmaximal, characteristic
2#10623110C211yesmaximal, characteristic
3C11×#479C211yesmaximal, characteristic, complemented
4#10622678C211yesmaximal, characteristic, complemented
5#10622643C211yesmaximal, characteristic, complemented
6#10622497C211yesmaximal, characteristic, complemented
7#10622494C211yesmaximal, characteristic, complemented
8#10622475C211yesmaximal, characteristic, complemented
9D11×#106C211yesmaximal, characteristic, complemented
10#10622464C211yesmaximal, characteristic, complemented
11#10622449C211yesmaximal, characteristic
12#10622429C211yesmaximal, characteristic, complemented
13#10622428C211yesmaximal, characteristic, complemented
14#10622426C211yesmaximal, characteristic, complemented
15#10622418C211yesmaximal, characteristic, complemented
16C11×#125C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18#66999C2211yescharacteristic
19#66999C2211yescharacteristic
20C2×#4326C2211yescharacteristic
21C2×#4313C2211yescharacteristic
22C2×C8×D11C2211yescharacteristic
23#66951—21no—
24#66950C2211yescharacteristic
25#66950C2211yescharacteristic
26#66949—21no—
27#66949—21no—
28#66947—21no—
29#66945—21no—
30#66945C2211yescharacteristic
31C4⋊C4×D11C2211yescharacteristic
32C4⋊C4×D11C2211yescharacteristic
33C4⋊C4×D11C2211yescharacteristic
34#66943—21no—
35C4×D44—21no—
36C4×D44C2211yescharacteristic
37#66923—21no—
38#66922C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×C4⋊C8C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45#66899C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48#66881C2211yescharacteristic
49#66881C2211yescharacteristic
50#66880C2211yescharacteristic
51#66880C2211yescharacteristic
52#66874C2211yescharacteristic
53#66872C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D44D411yescharacteristic
61C2×C4×D11—21no—
62C2×C4×D11—21no—
63C2×C4×D11—21no—
64C2×C4×D11C2311yescharacteristic
65C2×C4×D11C2311yescharacteristic
66C2×Dic22—21no—
67C2×Dic22C2311yescharacteristic
68C2×C8×C11C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C42×C11—21no—
77C42×C11C2311yescharacteristic
78#4326—22no—
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4D411yescharacteristic
85(C2×D11)⋊C4D411yescharacteristic
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11D411yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103#4313—22no—
104C8×D11—22no—
105#3344—111nomaximal, Sylow
106C22×D11C2×D411yescharacteristic
107C22×D11C2×D411yescharacteristic
108Q8×C11—21no—
109Q8×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2411yescharacteristic
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11C2×D411yescharacteristic
122C2×Dic11C2×D411yescharacteristic
123D44—22no—
124C4×D11—21no—
125C4×D11—21no—
126C4×D11—21no—
127C4×D11—21no—
128C4×D11—42no—
129C4×D11—81no—
130C4×D11—81no—
131Dic22—21no—
132Dic22—21no—
133Dic22—81no—
134C8×C11—21no—
135C8×C11—21no—
136C11⋊C8—21no—
137C11⋊C8#4112yes—
138#554—111no—
139#552—111no—
140#501—111no—
141#485—111no—
142#484—111no—
143#483—111no—
144#483—111no—
145#479D1111yescharacteristic, complemented
146#475—111no—
147#470—111no—
148#467—111no—
149#441—111no—
150#435—111no—
151#428—111no—
152C2×#106—111no—
153C22×C11C22×D411yescharacteristic
154C2×D11—21no—
155C2×D11—21no—
156C2×D11—21no—
157C2×D11—21no—
158C2×D11—21no—
159C2×D11#13712yes—
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11C2×#4111yescharacteristic
167C4×C112−1+411yescharacteristic
168Dic11—21no—
169Dic11—21no—
170Dic11—41no—
171Dic11—41no—
172Dic11—41no—
173Dic11—41no—
174C2×Q16—111no—
175C2×M16—111no—
176C22×C8—111no—
177C4⋊Q8—111no—
178#126—221no—
179#125—221no—
180#125—221no—
181#125C2×D1111yescharacteristic
182#123—221no—
183C22⋊Q8—111no—
184C22⋊Q8—111no—
185C22⋊Q8—111no—
186C22⋊Q8—111no—
187C22⋊Q8—221no—
188C22⋊Q8—221no—
189C4×Q8—111no—
190C4×Q8C2×D1111yescharacteristic
191C4×D4—111no—
192C4×D4—221no—
193#117—111no—
194#117—221no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198#107—111no—
199#107—111no—
200#107C2×D1111yescharacteristic
201#106—111no—
202#106—111no—
203#106—111no—
204#106—111no—
205#106—111no—
206#106C2×D1111yescharacteristic
207C4⋊C8C2×D1111yescharacteristic
208#103—111no—
209#103—111no—
210#103—111no—
211#103—111no—
212#103C2×D1111yescharacteristic
213#103C2×D1111yescharacteristic
214C22⋊C8—111no—
215C22⋊C8—111no—
216#97—111no—
217C2×C11#54711yescharacteristic
218C2×C11C2×#13711yescharacteristic
219C2×C11#57711yescharacteristic
220D11—22no—
221D11—41no—
222C2×Q8—111no—
223C2×Q8—221no—
224C2×Q8C22×D1111yescharacteristic
225C2×D4—111no—
226C22×C4—111no—
227C22×C4—111no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4—221no—
231Q16—222no—
232M16—222no—
233C2×C8—111no—
234C2×C8—111no—
235C2×C8—222no—
236C2×C8C22×D1111yescharacteristic
237C2×C8C22×D1111yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—111no—
242C4⋊C4—111no—
243C4⋊C4—111no—
244C4⋊C4—111no—
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⋊C4—221no—
254C4⋊C4C22×D1111yescharacteristic
255C4⋊C4C22×D1111yescharacteristic
256C4⋊C4C22×D1111yescharacteristic
257C22⋊C4—111no—
258C22⋊C4—111no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C42—21no—
265C42—221no—
266C42—221no—
267C42C22×D1111yescharacteristic
268C11#334411yescharacteristic, complemented, Sylow
269C23—111no—
270C23—111no—
271Q8—21no—
272Q8—21no—
273Q8—221no—
274Q8—221no—
275Q8—881no—
276D4—222no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—111no—
282C2×C4—111no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—442no—
292C2×C4—881no—
293C2×C4—881no—
294C2×C4D4×D1111yescharacteristic
295C2×C4D4×D1111yescharacteristic
296C2×C4C23×D1111yescharacteristic
297C8—21no—
298C8—21no—
299C8—112no—
300C8—221no—
301C22—112no—
302C22—221no—
303C22—221no—
304C22—221no—
305C22—221no—
306C22—221no—
307C22C2×D4×D1111yescharacteristic
308C4—21no—
309C4—21no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—221no—
315C4—221no—
316C4—441no—
317C4—441no—
318C4—441no—
319C4—441no—
320C4#6704011yescharacteristic
321C4#41×D1111yescharacteristic
322C2—222no—
323C2—441no—
324C2#1062316211yescharacteristic
325C2#1062330111yescharacteristic
326C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#479C2
socleC22×C11C22×D4
prime radicalC2×D44D4
hypercenter#479D11
hypocenterC11#3344
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
3. C11×#479C2semidirect
4. #10622678C2semidirect
5. #10622643C2semidirect
6. #10622497C2semidirect
7. #10622494C2semidirect
8. #10622475C2semidirect
9. D11×#106C2semidirect
10. #10622464C2semidirect
12. #10622429C2semidirect
13. #10622428C2semidirect
14. #10622426C2semidirect
15. #10622418C2semidirect
145. #479D11semidirect
268. C11#3344semidirect

Maximal subgroups

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

subgroupindex
#106232252
#106231102
C11×#4792
#106226782
#106226432
#106224972
#106224942
#106224752
D11×#1062
#106224642
#106224492
#106224292
#106224282
#106224262
#106224182
#334411