Finite Group Databasebeta

← #13078713

Subgroups — #13078713

Order 1408.

444 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623109C211yesmaximal, characteristic, complemented
2C4×D4×D11C211yesmaximal, characteristic
3C11×#440C211yesmaximal, characteristic, complemented
4#10622782C211yesmaximal, characteristic
5#10622775C211yesmaximal, characteristic, complemented
6#10622639C211yesmaximal, characteristic, complemented
7#10622631C211yesmaximal, characteristic, complemented
8#10622503C211yesmaximal, characteristic, complemented
9#10622497C211yesmaximal, characteristic, complemented
10#10622431C211yesmaximal, characteristic, complemented
11#10622422C211yesmaximal, characteristic, complemented
12#10622389C211yesmaximal, characteristic
13#10622372C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622318C211yesmaximal, characteristic, complemented
16C2×D4×D11C2211yescharacteristic
17C22×C4×D11—21no—
18C2×C11×SD16C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic, complemented
20C4×D4×C11C2211yescharacteristic
21#66999C2211yescharacteristic
22#66997C2211yescharacteristic, complemented
23C2×#4325C2211yescharacteristic
24D4×Dic11C2211yescharacteristic
25C2×#4324C2211yescharacteristic
26C4×C22⋊D11—21no—
27C2×#4314C2211yescharacteristic
28#66950C2211yescharacteristic
29#66949—21no—
30#66946C2211yescharacteristic
31C4⋊C4×D11C2211yescharacteristic
32#66942—21no—
33#66941C2211yescharacteristic, complemented
34(C22⋊D11)⋊C4—21no—
35C22⋊C4×D11—21no—
36C4×D44C2211yescharacteristic
37#66925—21no—
38C42×D11C2211yescharacteristic
39C4×Dic22—21no—
40C4×Dic22C2211yescharacteristic, complemented
41C11×#107C2211yescharacteristic, complemented
42C11×#103C2211yescharacteristic, complemented
43C11×#102C2211yescharacteristic
44C11×#97C2211yescharacteristic, complemented
45#66899C2211yescharacteristic, complemented
46#66896C2211yescharacteristic
47#66885C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66882C2211yescharacteristic, complemented
51#66880C2211yescharacteristic, complemented
52Dic11⋊C8C2211yescharacteristic, complemented
53Dic11⋊C8C2211yescharacteristic, complemented
54#66874C2211yescharacteristic, complemented
55#66873C2211yescharacteristic
56#66871C2211yescharacteristic, complemented
57#66871C2211yescharacteristic, complemented
58#66867C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C2×C22⋊D11—21no—
64C22×Dic11—21no—
65D4×D11—22no—
66D4×D11—22no—
67C2×D44C2311yescharacteristic
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11—44no—
72C2×C4×D11D411yescharacteristic
73C2×C4×D11D411yescharacteristic
74C2×C4×D11C2311yescharacteristic
75C2×Dic22—21no—
76C2×Dic22C2311yescharacteristic
77C11×SD16—22no—
78C2×C8×C11C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C11×C4⋊C4—21no—
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C42×C11—21no—
85C42×C11C2311yescharacteristic
86C22⋊Dic11—21no—
87#4325—22no—
88#4324—22no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102C4×Dic11—21no—
103C4×Dic11D411yescharacteristic
104C4×Dic11D411yescharacteristic
105C4×Dic11C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#4314—22no—
109#3110—111nomaximal, Sylow
110C23×C11—21no—
111C22×D11—24no—
112C22×D11—21no—
113C22×D11—42no—
114C22×D11—42no—
115C22×D11C2×D411yescharacteristic
116Q8×C11—21no—
117Q8×C11—21no—
118D4×C11—21no—
119D4×C11#4112yes—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—42no—
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2411yescharacteristic
127C22⋊D11—24no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—42no—
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134C2×Dic11C2×D411yescharacteristic
135D44—21no—
136D44#4112yes—
137C4×D11—22no—
138C4×D11—21no—
139C4×D11—21no—
140C4×D11—22no—
141C4×D11—42no—
142C4×D11—42no—
143C4×D11—42no—
144Dic22—21no—
145Dic22—21no—
146Dic22—42no—
147C8×C11—21no—
148C8×C11—21no—
149C11⋊C8—21no—
150C11⋊C8—21no—
151#533—111no—
152C2×C4×D4—111no—
153#484—111no—
154#484—111no—
155#474—111no—
156#474—111no—
157#461—111no—
158#461—111no—
159#450—111no—
160#450—111no—
161#440—111no—
162#440—111no—
163#440—111no—
164#440D1111yescharacteristic, complemented
165#432—111no—
166C22×C11—22no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11C22×D411yescharacteristic
170C2×D11—21no—
171C2×D11—21no—
172C2×D11—22no—
173C2×D11—48no—
174C2×D11—41no—
175C2×D11—41no—
176C2×D11#13712yes—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11C2×#4111yescharacteristic
183C4×C11C2×#4111yescharacteristic
184Dic11—21no—
185Dic11—21no—
186Dic11—41no—
187Dic11—41no—
188Dic11—41no—
189Dic11AGL(1,ℤ/8)12yes—
190C22×D4—111no—
191C23×C4—221no—
192C2×SD16—111no—
193C2×SD16—111no—
194C2×SD16—111no—
195C2×SD16C2×D1111yescharacteristic
196C4⋊Q8—111no—
197C4⋊Q8—111no—
198#125—221no—
199C22⋊Q8—111no—
200C22⋊Q8—111no—
201C22⋊Q8—221no—
202C4×Q8—111no—
203C4×Q8—221no—
204C4×Q8C2×D1111yescharacteristic, complemented
205C4×D4—111no—
206C4×D4—111no—
207C4×D4—111no—
208C4×D4—221no—
209C4×D4—221no—
210C4×D4C2×D1111yescharacteristic
211#117—221no—
212C2×C4⋊C4—111no—
213C2×C22⋊C4—221no—
214C2×C42—111no—
215#107—111no—
216#107—111no—
217#107—111no—
218#107C2×D1111yescharacteristic, complemented
219C4⋊C8—111no—
220C4⋊C8—111no—
221#103—111no—
222#103—111no—
223#103—111no—
224#103C2×D1111yescharacteristic, complemented
225#102—111no—
226#102—111no—
227#102—111no—
228#102C2×D1111yescharacteristic
229C22⋊C8—111no—
230C22⋊C8—111no—
231#97—111no—
232#97C2×D1111yescharacteristic, complemented
233C2×C11—42no—
234C2×C11#52511yescharacteristic
235C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
236C2×C11C2×#13711yescharacteristic
237D11—22no—
238D11—42no—
239C24—221no—
240C2×Q8—111no—
241C2×Q8—221no—
242C2×Q8C22×D1111yescharacteristic
243C2×D4—111no—
244C2×D4—221no—
245C2×D4—222no—
246C2×D4—222no—
247C2×D4C22×D1111yescharacteristic
248C22×C4—21no—
249C22×C4—111no—
250C22×C4—111no—
251C22×C4—111no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—444no—
257SD16—22no—
258SD16—222no—
259SD16—222no—
260SD16—222no—
261C2×C8—111no—
262C2×C8—111no—
263C2×C8C22×D1111yescharacteristic
264C2×C8C22×D1111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—111no—
267C4⋊C4—111no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4C22×D1111yescharacteristic
276C4⋊C4C22×D1111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C42—21no—
284C42—111no—
285C42—111no—
286C42—111no—
287C42—221no—
288C42C22×D1111yescharacteristic
289C11#311011yescharacteristic, complemented, Sylow
290C23—21no—
291C23—111no—
292C23—224no—
293C23—221no—
294C23—442no—
295C23—442no—
296Q8—21no—
297Q8—21no—
298Q8—221no—
299Q8—221no—
300Q8—442no—
301D4—21no—
302D4—112no—
303D4—224no—
304D4—221no—
305D4#433912yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—111no—
311C2×C4—111no—
312C2×C4—111no—
313C2×C4—222no—
314C2×C4—222no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4D4×D1111yescharacteristic
325C2×C4D4×D1111yescharacteristic
326C2×C4C23×D1111yescharacteristic
327C8—21no—
328C8—21no—
329C8—221no—
330C8—221no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—112no—
335C22—221no—
336C22—221no—
337C22—222no—
338C22—448no—
339C22—441no—
340C22—441no—
341C22C2×D4×D1111yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—112no—
348C4—221no—
349C4—221no—
350C4—441no—
351C4—441no—
352C4—441no—
353C4C2×#433911yescharacteristic
354C4#41×D1111yescharacteristic
355C2—42no—
356C2—222no—
357C2—442no—
358C2#1062307811yescharacteristic
359C2D11×AGL(1,ℤ/8)11yescharacteristic
360C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radicalC2×D4×D11C22
hypercenter#440D11
hypocenterC11#3110
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. #10623109C2semidirect
3. C11×#440C2semidirect
5. #10622775C2semidirect
6. #10622639C2semidirect
7. #10622631C2semidirect
8. #10622503C2semidirect
9. #10622497C2semidirect
10. #10622431C2semidirect
11. #10622422C2semidirect
13. #10622372C2semidirect
14. #10622323C2semidirect
15. #10622318C2semidirect
19. C4×Q8×C11C22semidirect
22. #66997C22semidirect
33. #66941C22semidirect
40. C4×Dic22C22semidirect
41. C11×#107C22semidirect
42. C11×#103C22semidirect
44. C11×#97C22semidirect
45. #66899C22semidirect
50. #66882C22semidirect
51. #66880C22semidirect
52. Dic11⋊C8C22semidirect
53. Dic11⋊C8C22semidirect
54. #66874C22semidirect
56. #66871C22semidirect
57. #66871C22semidirect
58. #66867C22semidirect
164. #440D11semidirect
204. C4×Q8C2×D11semidirect
218. #107C2×D11semidirect
224. #103C2×D11semidirect
232. #97C2×D11semidirect
289. C11#3110semidirect

Maximal subgroups

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

subgroupindex
#106231092
C4×D4×D112
C11×#4402
#106227822
#106227752
#106226392
#106226312
#106225032
#106224972
#106224312
#106224222
#106223892
#106223722
#106223232
#106223182
#311011