Finite Group Databasebeta

← #13080778

Subgroups — #13080778

Order 1408.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623147C211yesmaximal, characteristic, complemented
2#10623143C211yesmaximal, characteristic, complemented
3C11×#466C211yesmaximal, characteristic, complemented
4#10622769C211yesmaximal, characteristic, complemented
5#10622766C211yesmaximal, characteristic, complemented
6#10622726C211yesmaximal, characteristic, complemented
7#10622724C211yesmaximal, characteristic, complemented
8#10622650C211yesmaximal, characteristic, complemented
9#10622648C211yesmaximal, characteristic, complemented
10#10622503C211yesmaximal, characteristic, complemented
11#10622501C211yesmaximal, characteristic, complemented
12#10622398C211yesmaximal, characteristic, complemented
13#10622393C211yesmaximal, characteristic, complemented
14#10622383C211yesmaximal, characteristic, complemented
15#10622378C211yesmaximal, characteristic, complemented
16C2×D4×D11C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C2×C11×D8C2211yescharacteristic
19C22×C8×C11C2211yescharacteristic, complemented
20C11×#121C2211yescharacteristic
21C11×#121C2211yescharacteristic, complemented
22#66992—21no—
23#66991—21no—
24#66991C2211yescharacteristic
25#66990—21no—
26#66989—21no—
27#66989C2211yescharacteristic
28D4×Dic11C2211yescharacteristic, complemented
29C2×#4324C2211yescharacteristic, complemented
30C2×#4323C2211yescharacteristic
31C4×C22⋊D11C2211yescharacteristic
32#66979C2211yescharacteristic, complemented
33C2×#4313C2211yescharacteristic
34#66950C2211yescharacteristic
35#66946C2211yescharacteristic
36#66945C2211yescharacteristic
37#66941C2211yescharacteristic, complemented
38#66938—21no—
39#66936—21no—
40C22⋊C4×D11—21no—
41#66930—21no—
42C11×#107C2211yescharacteristic, complemented
43C11×#102C2211yescharacteristic
44C11×#102C2211yescharacteristic, complemented
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47C22⋊(C11⋊C8)C2211yescharacteristic, complemented
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66880C2211yescharacteristic, complemented
52#66880C2211yescharacteristic, complemented
53#66879C2211yescharacteristic, complemented
54Dic11⋊C8C2211yescharacteristic, complemented
55#66874C2211yescharacteristic, complemented
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11D411yescharacteristic
69C22×Dic11—21no—
70D4×D11—22no—
71D4×D11—41no—
72#4339—22no—
73#4339—41no—
74C2×D44C2311yescharacteristic
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11C2311yescharacteristic
78C2×Dic22—21no—
79C2×Dic22C2311yescharacteristic
80C11×D8—41no—
81C2×C8×C11—41no—
82C2×C8×C11C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92C22⋊Dic11—21no—
93C22⋊Dic11D411yescharacteristic
94#4324—41no—
95#4323—22no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4D411yescharacteristic
100C4⋊Dic11—21no—
101C4⋊Dic11C2311yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103Dic11⋊C4—21no—
104Dic11⋊C4D411yescharacteristic
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4313—41no—
111#3319—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11C2×D411yescharacteristic
115C22×D11—21no—
116C22×D11—42no—
117C22×D11—42no—
118C22×D11—81no—
119C22×D11C2×D411yescharacteristic
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—81no—
125D4×C11—81no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2411yescharacteristic
132C22⋊D11—41no—
133C22⋊D11—42no—
134C22⋊D11—42no—
135C22⋊D11—81no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—42no—
140C2×Dic11C2×D411yescharacteristic
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143D44—21no—
144D44#4112yes—
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—42no—
148C4×D11—81no—
149Dic22—21no—
150Dic22—21no—
151Dic22—81no—
152C8×C11—21no—
153C8×C11—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156#555—111no—
157#546—111no—
158#489—111no—
159#485—111no—
160#482—111no—
161#474—111no—
162#468—111no—
163#466D1111yescharacteristic, complemented
164#463—111no—
165#449—111no—
166#447—111no—
167#442—111no—
168#435—111no—
169#418—111no—
170#416—111no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11C22×D411yescharacteristic
181C2×D11—22no—
182C2×D11—21no—
183C2×D11—21no—
184C2×D11—21no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—84no—
188C4×C11—21no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11C2×#4111yescharacteristic
192C4×C11H(5,𝔽2)11yescharacteristic
193Dic11—21no—
194Dic11—21no—
195Dic11—21no—
196Dic11—41no—
197Dic11—41no—
198Dic11—41no—
199C2×#41—111no—
200C22×D4—111no—
201C2×SD16—111no—
202C2×D8—111no—
203C2×D8C2×D1111yescharacteristic
204C2×M16—111no—
205C22×C8C2×D1111yescharacteristic, complemented
206C4⋊Q8—111no—
207#124—111no—
208#124—221no—
209#124—221no—
210#123—221no—
211C22⋊Q8—111no—
212#121—111no—
213#121—221no—
214#121—221no—
215#121C2×D1111yescharacteristic
216#121C2×D1111yescharacteristic, complemented
217#120—221no—
218C4×D4—111no—
219C4×D4—111no—
220C4×D4—111no—
221#117—111no—
222#117—111no—
223#117—221no—
224C2×C22⋊C4—221no—
225#107—111no—
226#107C2×D1111yescharacteristic, complemented
227#106—111no—
228C4⋊C8—111no—
229#103—111no—
230#103—111no—
231#103—111no—
232#102—111no—
233#102—111no—
234#102—111no—
235#102—111no—
236#102—111no—
237#102C2×D1111yescharacteristic
238#102C2×D1111yescharacteristic, complemented
239C22⋊C8—111no—
240C22⋊C8—111no—
241#97—111no—
242C2×C11—41no—
243C2×C11—81no—
244C2×C11—81no—
245C2×C11#54611yescharacteristic
246C2×C11#57511yescharacteristic
247C2×C11#57611yescharacteristic
248D11—41no—
249D11—42no—
250C24—221no—
251#41—222no—
252#41—441no—
253C2×Q8—111no—
254C2×Q8—221no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—111no—
258C2×D4—111no—
259C2×D4—221no—
260C2×D4—222no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4—441no—
264C2×D4C22×D1111yescharacteristic
265C2×D4C22×D1111yescharacteristic
266C22×C4—111no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4C22×D1111yescharacteristic
271SD16—441no—
272D8—41no—
273D8—222no—
274M16—441no—
275C2×C8—41no—
276C2×C8—111no—
277C2×C8—111no—
278C2×C8C22×D1111yescharacteristic
279C2×C8C22×D1111yescharacteristic
280C4⋊C4—111no—
281C4⋊C4—111no—
282C4⋊C4—111no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4C22×D1111yescharacteristic
286C4⋊C4C22×D1111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—111no—
290C22⋊C4—111no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C42—111no—
300C42—221no—
301C42—221no—
302C11#331911yescharacteristic, complemented, Sylow
303C23—21no—
304C23—21no—
305C23—111no—
306C23—221no—
307C23—442no—
308C23—442no—
309C23—881no—
310C23D4×D1111yescharacteristic
311Q8—221no—
312Q8—221no—
313Q8—881no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—81no—
319D4—81no—
320D4—112no—
321D4—221no—
322D4—441no—
323D4—442no—
324D4—442no—
325D4—881no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—111no—
331C2×C4—111no—
332C2×C4—111no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4—881no—
341C2×C4D4×D1111yescharacteristic
342C2×C4C23×D1111yescharacteristic
343C8—21no—
344C8—21no—
345C8—221no—
346C8—221no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—221no—
357C22—221no—
358C22—221no—
359C22—222no—
360C22—441no—
361C22—441no—
362C22—884no—
363C22C2×D4×D1111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—221no—
368C4—221no—
369C4—221no—
370C4—441no—
371C4—441no—
372C4—441no—
373C4#6703711yescharacteristic
374C4#41×D1111yescharacteristic
375C2—41no—
376C2—81no—
377C2—81no—
378C2—441no—
379C2—442no—
380C2#1062314111yescharacteristic
381C2#1062328811yescharacteristic
382C2#1062329911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#466C2
socleC22×C11C22×D4
hypercenter#466D11
hypocenterC11#3319
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #10623147C2semidirect
2. #10623143C2semidirect
3. C11×#466C2semidirect
4. #10622769C2semidirect
5. #10622766C2semidirect
6. #10622726C2semidirect
7. #10622724C2semidirect
8. #10622650C2semidirect
9. #10622648C2semidirect
10. #10622503C2semidirect
11. #10622501C2semidirect
12. #10622398C2semidirect
13. #10622393C2semidirect
14. #10622383C2semidirect
15. #10622378C2semidirect
19. C22×C8×C11C22semidirect
21. C11×#121C22semidirect
28. D4×Dic11C22semidirect
29. C2×#4324C22semidirect
32. #66979C22semidirect
37. #66941C22semidirect
42. C11×#107C22semidirect
44. C11×#102C22semidirect
47. C22⋊(C11⋊C8)C22semidirect
51. #66880C22semidirect
52. #66880C22semidirect
53. #66879C22semidirect
54. Dic11⋊C8C22semidirect
55. #66874C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
163. #466D11semidirect
205. C22×C8C2×D11semidirect
216. #121C2×D11semidirect
226. #107C2×D11semidirect
238. #102C2×D11semidirect
302. C11#3319semidirect

Maximal subgroups

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

subgroupindex
#106231472
#106231432
C11×#4662
#106227692
#106227662
#106227262
#106227242
#106226502
#106226482
#106225032
#106225012
#106223982
#106223932
#106223832
#106223782
#331911