Finite Group Databasebeta

← #13078856

Subgroups — #13078856

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#10623093C211yesmaximal, characteristic, complemented
2#10623076C211yesmaximal, characteristic, complemented
3C4×C11×D8C211yesmaximal, characteristic, complemented
4#10622769C211yesmaximal, characteristic, complemented
5#10622763C211yesmaximal, characteristic, complemented
6#10622627C211yesmaximal, characteristic, complemented
7#10622627C211yesmaximal, characteristic, complemented
8#10622504C211yesmaximal, characteristic, complemented
9#10622498C211yesmaximal, characteristic, complemented
10#10622399C211yesmaximal, characteristic, complemented
11#10622397C211yesmaximal, characteristic, complemented
12#10622386C211yesmaximal, characteristic, complemented
13#10622379C211yesmaximal, characteristic, complemented
14C4×D88C211yesmaximal, characteristic, complemented
15#10622303C211yesmaximal, characteristic, complemented
16C2×D4×D11C2211yescharacteristic
17C2×C11×D8C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic, complemented
20#66993C2211yescharacteristic, complemented
21#66991C2211yescharacteristic
22D4×Dic11C2211yescharacteristic
23C2×#4323C2211yescharacteristic
24C2×#4323C2211yescharacteristic
25#66983—21no—
26#66982—21no—
27C4×C22⋊D11—21no—
28C2×(C2×D11)⋊C4—21no—
29C2×D88C2211yescharacteristic
30#66948C2211yescharacteristic
31#66946C2211yescharacteristic
32#66945C2211yescharacteristic
33#66943C2211yescharacteristic, complemented
34#66937—21no—
35#66936—21no—
36(C22⋊D11)⋊C4—21no—
37C22⋊C4×D11—21no—
38C4×D44C2211yescharacteristic
39C4×D44C2211yescharacteristic, complemented
40#66925C2211yescharacteristic
41C11×#107C2211yescharacteristic, complemented
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic, complemented
44C4×C8×C11C2211yescharacteristic, complemented
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic, complemented
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic, complemented
49(C2×D11)⋊C8C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66882C2211yescharacteristic, complemented
52Dic11⋊C8C2211yescharacteristic, complemented
53Dic11⋊C8C2211yescharacteristic, complemented
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic, complemented
56#66872C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66867C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×D4×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C22×Dic11—21no—
69D4×D11—22no—
70D4×D11—22no—
71C2×D44—21no—
72C2×D44C2311yescharacteristic
73C2×D44C2311yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11C2311yescharacteristic
78C11×D8—22no—
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C42×C11C2311yescharacteristic
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88#4323—22no—
89#4323—22no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4D411yescharacteristic
96(C2×D11)⋊C4D411yescharacteristic
97C4⋊Dic11—21no—
98C4⋊Dic11C2311yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100Dic11⋊C4—21no—
101Dic11⋊C4D411yescharacteristic
102Dic11⋊C4D411yescharacteristic
103C4×Dic11—21no—
104C4×Dic11C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107D88—22no—
108#3122—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11—21no—
111C22×D11—21no—
112C22×D11—24no—
113C22×D11—21no—
114C22×D11—81no—
115C22×D11—81no—
116C22×D11C2×D411yescharacteristic
117D4×C11—21no—
118D4×C11—21no—
119D4×C11—21no—
120D4×C11#4112yes—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C22⋊D11—24no—
129C22⋊D11—81no—
130C22⋊D11—81no—
131C22⋊D11—81no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—81no—
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138D44—21no—
139D44—21no—
140D44—21no—
141D44—81no—
142D44#4112yes—
143C4×D11—21no—
144C4×D11—21no—
145C4×D11—81no—
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#459—111no—
160#447—111no—
161#447—111no—
162#442—111no—
163#442—111no—
164C4×D8—111no—
165C4×D8D1111yescharacteristic, complemented
166#433—111no—
167C22×C11—22no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11C22×D411yescharacteristic
174C2×D11—21no—
175C2×D11—22no—
176C2×D11—21no—
177C2×D11—21no—
178C2×D11—41no—
179C2×D11—41no—
180C2×D11—41no—
181C2×D11—41no—
182C2×D11—41no—
183C2×D11—84no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11C2×#4111yescharacteristic
189C4×C11C2×#4111yescharacteristic
190Dic11—21no—
191Dic11—21no—
192Dic11—21no—
193Dic11—41no—
194Dic11—41no—
195C22×D4—111no—
196C2×D8—111no—
197C2×D8—111no—
198C2×D8—111no—
199C2×D8C2×D1111yescharacteristic
200#127—111no—
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—221no—
213C4×D4—221no—
214C4×D4C2×D1111yescharacteristic
215C4×D4C2×D1111yescharacteristic, complemented
216#117—111no—
217#117—111no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4—221no—
220#107—111no—
221#107C2×D1111yescharacteristic, complemented
222#106—111no—
223#106—111no—
224C4⋊C8—111no—
225C4⋊C8—111no—
226#102—111no—
227#102—111no—
228#102—111no—
229#102—111no—
230#102—111no—
231#102—111no—
232#102C2×D1111yescharacteristic
233#102C2×D1111yescharacteristic, complemented
234C22⋊C8—111no—
235C22⋊C8—111no—
236#97—111no—
237C4×C8C2×D1111yescharacteristic, complemented
238C2×C11—42no—
239C2×C11—81no—
240C2×C11#52511yescharacteristic
241C2×C11#57611yescharacteristic
242C2×C11#57611yescharacteristic
243D11—41no—
244D11—42no—
245D11—81no—
246C24—221no—
247C2×D4—111no—
248C2×D4—111no—
249C2×D4—221no—
250C2×D4—221no—
251C2×D4—221no—
252C2×D4—221no—
253C2×D4—222no—
254C2×D4—222no—
255C2×D4—221no—
256C2×D4C22×D1111yescharacteristic
257C2×D4C22×D1111yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—111no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265D8—22no—
266D8—222no—
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—221no—
278C4⋊C4—221no—
279C4⋊C4C22×D1111yescharacteristic
280C4⋊C4C22×D1111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—111no—
284C22⋊C4—111no—
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—111no—
299C23—224no—
300C23—221no—
301C23—221no—
302C23—881no—
303C23—881no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—112no—
308D4—224no—
309D4—221no—
310D4—221no—
311D4—221no—
312D4—881no—
313D4—881no—
314D4—881no—
315D4—881no—
316D4#433912yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—111no—
322C2×C4—111no—
323C2×C4—111no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
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—221no—
346C22—221no—
347C22—221no—
348C22—222no—
349C22—441no—
350C22—441no—
351C22—441no—
352C22—441no—
353C22—441no—
354C22—884no—
355C22C2×D4×D1111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—221no—
361C4—221no—
362C4—221no—
363C4—441no—
364C4—441no—
365C4C2×#433911yescharacteristic
366C4#41×D1111yescharacteristic
367C2—42no—
368C2—81no—
369C2—441no—
370C2—442no—
371C2—881no—
372C2#1062307811yescharacteristic
373C2#1062328811yescharacteristic
374C2#1062330011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×D8C2
socleC22×C11C22×D4
hypercenterC4×D8D11
hypocenterC11#3122
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #10623093C2semidirect
2. #10623076C2semidirect
3. C4×C11×D8C2semidirect
4. #10622769C2semidirect
5. #10622763C2semidirect
6. #10622627C2semidirect
7. #10622627C2semidirect
8. #10622504C2semidirect
9. #10622498C2semidirect
10. #10622399C2semidirect
11. #10622397C2semidirect
12. #10622386C2semidirect
13. #10622379C2semidirect
14. C4×D88C2semidirect
15. #10622303C2semidirect
19. C4×D4×C11C22semidirect
20. #66993C22semidirect
33. #66943C22semidirect
39. C4×D44C22semidirect
41. C11×#107C22semidirect
43. C11×#102C22semidirect
44. C4×C8×C11C22semidirect
46. #66896C22semidirect
48. #66885C22semidirect
51. #66882C22semidirect
52. Dic11⋊C8C22semidirect
53. Dic11⋊C8C22semidirect
55. #66873C22semidirect
56. #66872C22semidirect
57. #66872C22semidirect
58. #66867C22semidirect
165. C4×D8D11semidirect
215. C4×D4C2×D11semidirect
221. #107C2×D11semidirect
233. #102C2×D11semidirect
237. C4×C8C2×D11semidirect
295. C11#3122semidirect

Maximal subgroups

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

subgroupindex
#106230932
#106230762
C4×C11×D82
#106227692
#106227632
#106226272
#106225042
#106224982
#106223992
#106223972
#106223862
#106223792
C4×D882
#106223032
#312211