Finite Group Databasebeta

← #13078862

Subgroups — #13078862

Order 1408.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623329C211yesmaximal, characteristic
2#10623156C211yesmaximal, characteristic, complemented
3C11×#450C211yesmaximal, characteristic
4#10622831C211yesmaximal, characteristic
5#10622777C211yesmaximal, characteristic, complemented
6#10622775C211yesmaximal, characteristic, complemented
7#10622775C211yesmaximal, characteristic, complemented
8SD16×Dic11C211yesmaximal, characteristic, complemented
9#10622658C211yesmaximal, characteristic, complemented
10#10622379C211yesmaximal, characteristic, complemented
11#10622376C211yesmaximal, characteristic, complemented
12#10622371C211yesmaximal, characteristic, complemented
13#10622370C211yesmaximal, characteristic, complemented
14#10622336C211yesmaximal, characteristic, complemented
15#10622333C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C11×C22⋊Q8C2211yescharacteristic
20C2×C22⋊Dic11—21no—
21C2×C22⋊Dic11—21no—
22Q8×Dic11C2211yescharacteristic, complemented
23#66997C2211yescharacteristic, complemented
24D4×Dic11—21no—
25D4×Dic11—21no—
26D4×Dic11C2211yescharacteristic
27D4×Dic11C2211yescharacteristic
28D4×Dic11C2211yescharacteristic
29D4×Dic11C2211yescharacteristic
30C2×#4324C2211yescharacteristic
31C2×#4324C2211yescharacteristic
32#66979C2211yescharacteristic
33#66979C2211yescharacteristic
34#66977C2211yescharacteristic
35#66943—21no—
36#66943C2211yescharacteristic, complemented
37#66942—21no—
38#66940C2211yescharacteristic, complemented
39#66932—21no—
40#66932—21no—
41C11×#102C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×C22⋊C8C2211yescharacteristic
44#66899C2211yescharacteristic, complemented
45#66899C2211yescharacteristic, complemented
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49#66882C2211yescharacteristic, complemented
50#66881C2211yescharacteristic, complemented
51#66880C2211yescharacteristic, complemented
52#66880C2211yescharacteristic, complemented
53#66879C2211yescharacteristic, complemented
54Dic11⋊C8C2211yescharacteristic, complemented
55Dic11⋊C8C2211yescharacteristic, complemented
56C8×Dic11C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C24×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—21no—
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C2×Dic22C2311yescharacteristic
72C11×SD16—22no—
73C11×SD16—22no—
74C2×C8×C11C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C11×C4⋊C4—21no—
77C11×C4⋊C4C2311yescharacteristic
78C11×C22⋊C4—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11D411yescharacteristic
86C22⋊Dic11D411yescharacteristic
87#4324—22no—
88#4324—22no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11D411yescharacteristic
92C4⋊Dic11D411yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11C2311yescharacteristic
105C4×Dic11C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#3123—111nomaximal, Sylow
109C23×C11—24no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—81no—
113C23×C11—81no—
114C23×C11C2×D411yescharacteristic
115Q8×C11—21no—
116Q8×C11—21no—
117D4×C11—24no—
118D4×C11—21no—
119D4×C11—21no—
120D4×C11#4112yes—
121D4×C11#4112yes—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—81no—
133C2×Dic11—81no—
134C2×Dic11—81no—
135C2×Dic11—81no—
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140Dic22—21no—
141Dic22—21no—
142C8×C11—21no—
143C8×C11—21no—
144C11⋊C8—21no—
145C11⋊C8—21no—
146#541—111no—
147#518—111no—
148#485—111no—
149#485—111no—
150#478—111no—
151#478—111no—
152#461—111no—
153#461—111no—
154#450—111no—
155#450D1111yescharacteristic
156#440—111no—
157#440—111no—
158C4×SD16—111no—
159C4×SD16—111no—
160#433—111no—
161C22×C11—21no—
162C22×C11—22no—
163C22×C11—22no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—84no—
171C22×C11C22×D411yescharacteristic
172C4×C11—21no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11C2×#4111yescharacteristic
176C4×C11C2×#4111yescharacteristic
177Dic11—21no—
178Dic11—21no—
179Dic11—21no—
180Dic11—21no—
181Dic11—41no—
182Dic11—41no—
183Dic11—41no—
184Dic11—41no—
185C22×D4C2×D1111yescharacteristic
186C2×SD16—111no—
187C2×SD16—111no—
188C2×SD16C2×D1111yescharacteristic
189C2×SD16C2×D1111yescharacteristic
190C4⋊Q8—111no—
191#126—221no—
192#126—221no—
193#125—111no—
194#125—221no—
195#125—221no—
196C22⋊Q8—111no—
197C22⋊Q8C2×D1111yescharacteristic
198C4×Q8—111no—
199C4×Q8—111no—
200C4×D4—111no—
201C4×D4—111no—
202C4×D4—111no—
203C4×D4—111no—
204C4×D4—221no—
205C4×D4—221no—
206#117—111no—
207#117—111no—
208C2×C22⋊C4—221no—
209C2×C22⋊C4—221no—
210#107—111no—
211#107—111no—
212#106—111no—
213#106—111no—
214C4⋊C8—111no—
215C4⋊C8—111no—
216#103—111no—
217#103—111no—
218#103—111no—
219#103—111no—
220#102—111no—
221#102—111no—
222#102C2×D1111yescharacteristic
223#102C2×D1111yescharacteristic
224C22⋊C8—111no—
225C22⋊C8C2×D1111yescharacteristic
226#97—111no—
227C4×C8—111no—
228C2×C11—41no—
229C2×C11—42no—
230C2×C11—42no—
231C2×C11#52511yescharacteristic
232C2×C11#57711yescharacteristic
233C2×C11#57711yescharacteristic
234C24—21no—
235C2×Q8—111no—
236C2×Q8C22×D1111yescharacteristic
237C2×D4—22no—
238C2×D4—22no—
239C2×D4—21no—
240C2×D4C22×D1111yescharacteristic
241C2×D4C22×D1111yescharacteristic
242C22×C4—221no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4C22×D1111yescharacteristic
247SD16—22no—
248SD16—22no—
249SD16—222no—
250SD16—222no—
251C2×C8—111no—
252C2×C8—111no—
253C2×C8C22×D1111yescharacteristic
254C2×C8C22×D1111yescharacteristic
255C4⋊C4—21no—
256C4⋊C4—111no—
257C4⋊C4—111no—
258C4⋊C4—111no—
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4C22×D1111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—111no—
271C22⋊C4—111no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C42—111no—
279C42—111no—
280C42—221no—
281C42—221no—
282C42—221no—
283C11#312311yescharacteristic, complemented, Sylow
284C23—24no—
285C23—21no—
286C23—21no—
287C23—81no—
288C23—81no—
289C23D4×D1111yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—221no—
293Q8—221no—
294D4—24no—
295D4—21no—
296D4—21no—
297D4#434112yes—
298D4#434112yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—111no—
306C2×C4—111no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—881no—
312C2×C4—881no—
313C2×C4—881no—
314C2×C4—881no—
315C2×C4D4×D1111yescharacteristic
316C2×C4C23×D1111yescharacteristic
317C8—21no—
318C8—21no—
319C8—221no—
320C8—221no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—84no—
331C22C2×D4×D1111yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—221no—
336C4—221no—
337C4—221no—
338C4—221no—
339C4—441no—
340C4—441no—
341C4—441no—
342C4—441no—
343C4C2×#434111yescharacteristic
344C4C2×#434111yescharacteristic
345C2—41no—
346C2—42no—
347C2—42no—
348C2#1062311711yescharacteristic
349C2#1062329311yescharacteristic
350C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#450C2
socleC22×C11C22×D4
prime radicalC22×D4×C11C22
hypercenter#450D11
hypocenterC11#3123
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. #10623156C2semidirect
5. #10622777C2semidirect
6. #10622775C2semidirect
7. #10622775C2semidirect
8. SD16×Dic11C2semidirect
9. #10622658C2semidirect
10. #10622379C2semidirect
11. #10622376C2semidirect
12. #10622371C2semidirect
13. #10622370C2semidirect
14. #10622336C2semidirect
15. #10622333C2semidirect
22. Q8×Dic11C22semidirect
23. #66997C22semidirect
36. #66943C22semidirect
38. #66940C22semidirect
44. #66899C22semidirect
45. #66899C22semidirect
49. #66882C22semidirect
50. #66881C22semidirect
51. #66880C22semidirect
52. #66880C22semidirect
53. #66879C22semidirect
54. Dic11⋊C8C22semidirect
55. Dic11⋊C8C22semidirect
56. C8×Dic11C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
283. C11#3123semidirect

Maximal subgroups

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

subgroupindex
#106233292
#106231562
C11×#4502
#106228312
#106227772
#106227752
SD16×Dic112
#106226582
#106223792
#106223762
#106223712
#106223702
#106223362
#106223332
#312311