Finite Group Databasebeta

← #13081136

Subgroups — #13081136

Order 1408.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623112C211yesmaximal, characteristic, complemented
2#10623094C211yesmaximal, characteristic
3C11×#440C211yesmaximal, characteristic, complemented
4#10622787C211yesmaximal, characteristic, complemented
5#10622784C211yesmaximal, characteristic, complemented
6#10622633C211yesmaximal, characteristic, complemented
7#10622622C211yesmaximal, characteristic, complemented
8#10622494C211yesmaximal, characteristic, complemented
9#10622493C211yesmaximal, characteristic, complemented
10#10622428C211yesmaximal, characteristic, complemented
11#10622427C211yesmaximal, characteristic, complemented
12#10622397C211yesmaximal, characteristic, complemented
13#10622390C211yesmaximal, characteristic, complemented
14#10622319C211yesmaximal, characteristic, complemented
15#10622315C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#66999C2211yescharacteristic
20#66999C2211yescharacteristic
21#66991C2211yescharacteristic
22#66991C2211yescharacteristic
23#66983—21no—
24#66979—21no—
25C2×#4313C2211yescharacteristic
26C2×C8×D11C2211yescharacteristic
27#66947—21no—
28#66945C2211yescharacteristic
29#66945C2211yescharacteristic
30#66945C2211yescharacteristic
31C4⋊C4×D11C2211yescharacteristic
32#66942—21no—
33#66938—21no—
34#66938—21no—
35#66929—21no—
36C4×D44C2211yescharacteristic
37#66925—21no—
38#66923C2211yescharacteristic
39#66922C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#97C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66882C2211yescharacteristic
51#66882C2211yescharacteristic
52#66881C2211yescharacteristic
53#66881C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C2×D44D411yescharacteristic
65C2×C4×D11—21no—
66C2×C4×D11C2311yescharacteristic
67C2×C4×D11C2311yescharacteristic
68C2×Dic22—21no—
69C11×SD16—22no—
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C22⋊C4—21no—
76C42×C11—21no—
77C42×C11C2311yescharacteristic
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4D411yescharacteristic
86(C2×D11)⋊C4D411yescharacteristic
87C4⋊Dic11—21no—
88C4⋊Dic11D411yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103#4313—22no—
104C8×D11—22no—
105#3348—111nomaximal, Sylow
106C23×C11—21no—
107C22×D11C2×D411yescharacteristic
108C22×D11C2×D411yescharacteristic
109Q8×C11—21no—
110Q8×C11—21no—
111D4×C11—21no—
112D4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—42no—
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C22⋊D11—81no—
121C22⋊D11—81no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128D44—41no—
129C4×D11—21no—
130C4×D11—21no—
131C4×D11—21no—
132C4×D11—21no—
133C4×D11—42no—
134Dic22—81no—
135C8×C11—21no—
136C8×C11#4112yes—
137C11⋊C8—21no—
138C11⋊C8—21no—
139#555—111no—
140#552—111no—
141#501—111no—
142#485—111no—
143#485—111no—
144#482—111no—
145#481—111no—
146#478—111no—
147#475—111no—
148#468—111no—
149#465—111no—
150#440D1111yescharacteristic, complemented
151#435—111no—
152#428—111no—
153#427—111no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11C22×D411yescharacteristic
158C2×D11—21no—
159C2×D11—21no—
160C2×D11—21no—
161C2×D11—21no—
162C2×D11—21no—
163C2×D11—21no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11C2×#4111yescharacteristic
170C4×C112−1+411yescharacteristic
171Dic11—21no—
172Dic11—21no—
173Dic11—41no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177C2×SD16C2×D1111yescharacteristic
178C2×M16—111no—
179C22×C8—111no—
180C4⋊Q8—111no—
181#126—221no—
182#125—111no—
183#125—221no—
184#124—221no—
185#124—221no—
186#123—221no—
187C22⋊Q8—111no—
188C22⋊Q8—111no—
189#121—111no—
190#121—111no—
191#121—221no—
192C4×Q8C2×D1111yescharacteristic
193C4×D4—111no—
194C4×D4C2×D1111yescharacteristic
195#117—111no—
196#117—111no—
197#117—111no—
198#117—221no—
199#117—221no—
200C2×C4⋊C4—111no—
201#107—111no—
202#107—111no—
203#107—111no—
204#107C2×D1111yescharacteristic
205#106—111no—
206#106—111no—
207#106—111no—
208#106—111no—
209#106—111no—
210C4⋊C8—111no—
211#103—111no—
212#103—111no—
213#103C2×D1111yescharacteristic
214#102—111no—
215#102—111no—
216#102C2×D1111yescharacteristic
217C22⋊C8—111no—
218C22⋊C8—111no—
219#97C2×D1111yescharacteristic
220C2×C11—81no—
221C2×C11#54711yescharacteristic
222C2×C11#57511yescharacteristic
223C2×C11#57711yescharacteristic
224D11—41no—
225D11—41no—
226C2×Q8—221no—
227C2×Q8C22×D1111yescharacteristic
228C2×D4—111no—
229C2×D4—221no—
230C2×D4—221no—
231C2×D4C22×D1111yescharacteristic
232C22×C4—21no—
233C22×C4—111no—
234C22×C4—111no—
235C22×C4—221no—
236SD16—22no—
237M16—222no—
238C2×C8—111no—
239C2×C8—111no—
240C2×C8—222no—
241C2×C8C22×D1111yescharacteristic
242C2×C8C22×D1111yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—111no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—111no—
248C4⋊C4—111no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4C22×D1111yescharacteristic
256C4⋊C4C22×D1111yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—111no—
259C22⋊C4—111no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C42—21no—
268C42—221no—
269C42—221no—
270C42—221no—
271C42C22×D1111yescharacteristic
272C11#334811yescharacteristic, complemented, Sylow
273C23—21no—
274C23—111no—
275C23—111no—
276Q8—21no—
277Q8—21no—
278Q8—881no—
279D4—21no—
280D4—21no—
281D4—441no—
282D4—881no—
283D4—881no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—42no—
288C2×C4—111no—
289C2×C4—111no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—442no—
299C2×C4D4×D1111yescharacteristic
300C2×C4D4×D1111yescharacteristic
301C2×C4C23×D1111yescharacteristic
302C8—21no—
303C8—221no—
304C8—221no—
305C8#433912yes—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—221no—
310C22—221no—
311C22—221no—
312C22—221no—
313C22—221no—
314C22—221no—
315C22C2×D4×D1111yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—221no—
322C4—221no—
323C4—441no—
324C4—441no—
325C4—441no—
326C4—441no—
327C4C2×#433911yescharacteristic
328C4#6704311yescharacteristic
329C2—81no—
330C2—441no—
331C2—441no—
332C2#1062308211yescharacteristic
333C2#1062330411yescharacteristic
334C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radical#10623094C2
hypercenter#440D11
hypocenterC11#3348
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #10623112C2semidirect
3. C11×#440C2semidirect
4. #10622787C2semidirect
5. #10622784C2semidirect
6. #10622633C2semidirect
7. #10622622C2semidirect
8. #10622494C2semidirect
9. #10622493C2semidirect
10. #10622428C2semidirect
11. #10622427C2semidirect
12. #10622397C2semidirect
13. #10622390C2semidirect
14. #10622319C2semidirect
15. #10622315C2semidirect
150. #440D11semidirect
272. C11#3348semidirect

Maximal subgroups

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

subgroupindex
#106231122
#106230942
C11×#4402
#106227872
#106227842
#106226332
#106226222
#106224942
#106224932
#106224282
#106224272
#106223972
#106223902
#106223192
#106223152
#334811