Finite Group Databasebeta

← #13078857

Subgroups — #13078857

Order 1408.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623250C211yesmaximal, characteristic, complemented
2#10623076C211yesmaximal, characteristic, complemented
3C11×#459C211yesmaximal, characteristic, complemented
4#10622769C211yesmaximal, characteristic, complemented
5#10622769C211yesmaximal, characteristic, complemented
6#10622765C211yesmaximal, characteristic, complemented
7D8×Dic11C211yesmaximal, characteristic, complemented
8#10622685C211yesmaximal, characteristic, complemented
9#10622622C211yesmaximal, characteristic, complemented
10#10622460C211yesmaximal, characteristic, complemented
11#10622453C211yesmaximal, characteristic, complemented
12#10622398C211yesmaximal, characteristic, complemented
13#10622397C211yesmaximal, characteristic, complemented
14#10622392C211yesmaximal, characteristic, complemented
15#10622369C211yesmaximal, characteristic, complemented
16C2×D4×D11C2211yescharacteristic
17C2×C11×D8C2211yescharacteristic
18C2×C11×D8C2211yescharacteristic
19C11×#127C2211yescharacteristic, complemented
20C4×D4×C11C2211yescharacteristic
21#66992—21no—
22#66992—21no—
23#66991C2211yescharacteristic
24#66991C2211yescharacteristic
25#66988—21no—
26#66988—21no—
27D4×Dic11C2211yescharacteristic
28D4×Dic11C2211yescharacteristic, complemented
29D4×Dic11C2211yescharacteristic, complemented
30C2×#4323C2211yescharacteristic
31C2×#4323C2211yescharacteristic
32C4×C22⋊D11—21no—
33C2×(C2×D11)⋊C4—21no—
34#66946C2211yescharacteristic
35#66945C2211yescharacteristic
36(C22⋊D11)⋊C4—21no—
37C22⋊C4×D11—21no—
38C4×D44C2211yescharacteristic
39#66925C2211yescharacteristic
40#66923C2211yescharacteristic, complemented
41C11×C4⋊C8C2211yescharacteristic, complemented
42C11×#102C2211yescharacteristic, complemented
43C11×#102C2211yescharacteristic, complemented
44#66896C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic, complemented
47#66896C2211yescharacteristic, complemented
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52#66882C2211yescharacteristic, complemented
53#66881C2211yescharacteristic, complemented
54#66879C2211yescharacteristic, complemented
55C8×Dic11C2211yescharacteristic, complemented
56#66872C2211yescharacteristic, complemented
57#66871C2211yescharacteristic, complemented
58C4⋊(C11⋊C8)C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72D4×D11—22no—
73D4×D11—22no—
74C2×D44C2311yescharacteristic
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11C2311yescharacteristic
78C11×D8—22no—
79C11×D8—22no—
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C42×C11C2311yescharacteristic
85C22⋊Dic11—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90#4323—22no—
91#4323—22no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4D411yescharacteristic
96(C2×D11)⋊C4D411yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4D411yescharacteristic
103Dic11⋊C4D411yescharacteristic
104C4×Dic11—21no—
105C4×Dic11C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#3122—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C22×D11—21no—
113C22×D11—24no—
114C22×D11—81no—
115C22×D11—81no—
116C22×D11C2×D411yescharacteristic
117D4×C11—21no—
118D4×C11—21no—
119D4×C11—21no—
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—81no—
123D4×C11—81no—
124D4×C11#4112yes—
125C2×C4×C11—21no—
126C2×C4×C11—81no—
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2411yescharacteristic
130C22⋊D11—24no—
131C22⋊D11—81no—
132C22⋊D11—81no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—81no—
137C2×Dic11—81no—
138C2×Dic11—81no—
139C2×Dic11C2×D411yescharacteristic
140C2×Dic11C2×D411yescharacteristic
141C2×Dic11C2×D411yescharacteristic
142D44—21no—
143D44#4112yes—
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—81no—
147C4×D11—81no—
148C8×C11—21no—
149C8×C11—21no—
150C11⋊C8—21no—
151C11⋊C8—21no—
152#540—111no—
153#518—111no—
154#482—111no—
155#482—111no—
156#478—111no—
157#478—111no—
158#459—111no—
159#459D1111yescharacteristic, complemented
160#447—111no—
161#447—111no—
162#442—111no—
163#442—111no—
164C4×D8—111no—
165C4×D8—111no—
166#433—111no—
167C22×C11—22no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11C22×D411yescharacteristic
177C2×D11—21no—
178C2×D11—22no—
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—41no—
182C2×D11—41no—
183C2×D11—84no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—41no—
187C4×C11C2×#4111yescharacteristic
188C4×C11C2×#4111yescharacteristic
189Dic11—21no—
190Dic11—21no—
191Dic11—21no—
192Dic11—41no—
193Dic11—41no—
194Dic11—41no—
195C22×D4—111no—
196C2×D8—111no—
197C2×D8—111no—
198C2×D8C2×D1111yescharacteristic
199C2×D8C2×D1111yescharacteristic
200#127C2×D1111yescharacteristic, complemented
201#125—111no—
202#123—221no—
203#123—221no—
204#121—111no—
205#121—111no—
206#121—221no—
207#121—221no—
208C4×D4—111no—
209C4×D4—111no—
210C4×D4—111no—
211C4×D4—111no—
212C4×D4—111no—
213C4×D4—221no—
214C4×D4—221no—
215C4×D4C2×D1111yescharacteristic
216#117—111no—
217#117—111no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4—221no—
220#107—111no—
221#107—111no—
222#106—111no—
223#106—111no—
224C4⋊C8—111no—
225C4⋊C8C2×D1111yescharacteristic, complemented
226#102—111no—
227#102—111no—
228#102—111no—
229#102—111no—
230#102—111no—
231#102—111no—
232#102C2×D1111yescharacteristic, complemented
233#102C2×D1111yescharacteristic, complemented
234C22⋊C8—111no—
235C22⋊C8—111no—
236#97—111no—
237C4×C8—111no—
238C2×C11—42no—
239C2×C11—81no—
240C2×C11—81no—
241C2×C11#52511yescharacteristic
242C2×C11#57611yescharacteristic
243C2×C11#57611yescharacteristic
244D11—41no—
245D11—42no—
246C24—221no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—111no—
250C2×D4—221no—
251C2×D4—222no—
252C2×D4—222no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4C22×D1111yescharacteristic
256C2×D4C22×D1111yescharacteristic
257C2×D4C22×D1111yescharacteristic
258C22×C4—21no—
259C22×C4—111no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265D8—22no—
266D8—22no—
267D8—222no—
268D8—222no—
269C2×C8—111no—
270C2×C8—111no—
271C2×C8C22×D1111yescharacteristic
272C2×C8C22×D1111yescharacteristic
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—111no—
276C4⋊C4—111no—
277C4⋊C4—111no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4C22×D1111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—111no—
283C22⋊C4—111no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C42—111no—
293C42—221no—
294C42C22×D1111yescharacteristic
295C11#312211yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—21no—
299C23—111no—
300C23—224no—
301C23—221no—
302C23—881no—
303C23—881no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—81no—
311D4—112no—
312D4—224no—
313D4—221no—
314D4—881no—
315D4—881no—
316D4#434112yes—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—111no—
320C2×C4—111no—
321C2×C4—111no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—881no—
328C2×C4—881no—
329C2×C4—881no—
330C2×C4—881no—
331C2×C4—881no—
332C2×C4D4×D1111yescharacteristic
333C2×C4D4×D1111yescharacteristic
334C2×C4C23×D1111yescharacteristic
335C8—21no—
336C8—21no—
337C8—221no—
338C8—221no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—221no—
349C22—221no—
350C22—221no—
351C22—222no—
352C22—441no—
353C22—441no—
354C22—884no—
355C22C2×D4×D1111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—221no—
360C4—221no—
361C4—221no—
362C4—441no—
363C4—441no—
364C4—441no—
365C4C2×#434111yescharacteristic
366C4#41×D1111yescharacteristic
367C2—42no—
368C2—81no—
369C2—81no—
370C2—441no—
371C2—442no—
372C2#1062313711yescharacteristic
373C2#1062328811yescharacteristic
374C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#459C2
socleC22×C11C22×D4
hypercenter#459D11
hypocenterC11#3122
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #10623250C2semidirect
2. #10623076C2semidirect
3. C11×#459C2semidirect
4. #10622769C2semidirect
5. #10622769C2semidirect
6. #10622765C2semidirect
7. D8×Dic11C2semidirect
8. #10622685C2semidirect
9. #10622622C2semidirect
10. #10622460C2semidirect
11. #10622453C2semidirect
12. #10622398C2semidirect
13. #10622397C2semidirect
14. #10622392C2semidirect
15. #10622369C2semidirect
19. C11×#127C22semidirect
28. D4×Dic11C22semidirect
29. D4×Dic11C22semidirect
40. #66923C22semidirect
41. C11×C4⋊C8C22semidirect
42. C11×#102C22semidirect
43. C11×#102C22semidirect
46. #66896C22semidirect
47. #66896C22semidirect
52. #66882C22semidirect
53. #66881C22semidirect
54. #66879C22semidirect
55. C8×Dic11C22semidirect
56. #66872C22semidirect
57. #66871C22semidirect
58. C4⋊(C11⋊C8)C22semidirect
159. #459D11semidirect
200. #127C2×D11semidirect
225. C4⋊C8C2×D11semidirect
232. #102C2×D11semidirect
233. #102C2×D11semidirect
295. C11#3122semidirect

Maximal subgroups

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

subgroupindex
#106232502
#106230762
C11×#4592
#106227692
#106227652
D8×Dic112
#106226852
#106226222
#106224602
#106224532
#106223982
#106223972
#106223922
#106223692
#312211