Finite Group Databasebeta

← #13080653

Subgroups — #13080653

Order 1408.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623337C211yesmaximal, characteristic
2#10623064C211yesmaximal, characteristic, complemented
3C11×#418C211yesmaximal, characteristic, complemented
4#10622831C211yesmaximal, characteristic, complemented
5#10622750C211yesmaximal, characteristic, complemented
6#10622740C211yesmaximal, characteristic, complemented
7#10622609C211yesmaximal, characteristic, complemented
8#10622396C211yesmaximal, characteristic, complemented
9#10622392C211yesmaximal, characteristic, complemented
10#10622391C211yesmaximal, characteristic, complemented
11#10622385C211yesmaximal, characteristic, complemented
12#10622380C211yesmaximal, characteristic, complemented
13#10622378C211yesmaximal, characteristic, complemented
14#10622374C211yesmaximal, characteristic, complemented
15#10622370C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×C11×M16C2211yescharacteristic
19C11×#117C2211yescharacteristic
20#67006—21no—
21C2×C22⋊Dic11—21no—
22#66992—21no—
23#66991C2211yescharacteristic
24#66989C2211yescharacteristic
25#66988—21no—
26D4×Dic11C2211yescharacteristic
27C2×#4324C2211yescharacteristic
28C2×#4324C2211yescharacteristic
29C4×C22⋊D11C2211yescharacteristic
30#66977C2211yescharacteristic
31#66977C2211yescharacteristic
32C2×Dic44C2211yescharacteristic, complemented
33C2×C8×D11C2211yescharacteristic, complemented
34#66950C2211yescharacteristic, complemented
35#66945C2211yescharacteristic, complemented
36#66941C2211yescharacteristic, complemented
37#66940C2211yescharacteristic, complemented
38#66938—21no—
39#66932—21no—
40#66929—21no—
41C4×Dic22—21no—
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic, complemented
50#66881C2211yescharacteristic, complemented
51#66880C2211yescharacteristic, complemented
52#66880C2211yescharacteristic, complemented
53#66879C2211yescharacteristic, complemented
54Dic11⋊C8C2211yescharacteristic, complemented
55#66874C2211yescharacteristic, complemented
56#66874C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C24×C11—21no—
60C2×D4×C11—22no—
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C2×D4×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71#4341—22no—
72#4341—41no—
73C2×C4×D11C2311yescharacteristic
74C2×Dic22—21no—
75C2×Dic22C2311yescharacteristic
76C2×Dic22C2311yescharacteristic
77C11×M16—41no—
78C2×C8×C11C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C22⋊C4—21no—
83C42×C11—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11D411yescharacteristic
91#4324—22no—
92#4324—41no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4D411yescharacteristic
96C4⋊Dic11—21no—
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4D411yescharacteristic
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109Dic44—41no—
110C8×D11—41no—
111#3311—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—42no—
115C23×C11—42no—
116C23×C11—81no—
117C23×C11C2×D411yescharacteristic
118C22×D11C2×D411yescharacteristic
119D4×C11—21no—
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—42no—
123D4×C11#4112yes—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2411yescharacteristic
130C22⋊D11—41no—
131C22⋊D11—42no—
132C22⋊D11—81no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—42no—
138C2×Dic11—81no—
139C2×Dic11C2×D411yescharacteristic
140C2×Dic11C2×D411yescharacteristic
141C2×Dic11C2×D411yescharacteristic
142C4×D11—21no—
143C4×D11—21no—
144Dic22—21no—
145Dic22—21no—
146Dic22—21no—
147Dic22—21no—
148Dic22—42no—
149C8×C11—21no—
150C8×C11—21no—
151C11⋊C8—21no—
152C11⋊C8—21no—
153#556—111no—
154#546—111no—
155#489—111no—
156#485—111no—
157#482—111no—
158#476—111no—
159#470—111no—
160#465—111no—
161#464—111no—
162#452—111no—
163#450—111no—
164#440—111no—
165#435—111no—
166#418D1111yescharacteristic, complemented
167#416—111no—
168C22×C11—21no—
169C22×C11—22no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—84no—
178C22×C11C22×D411yescharacteristic
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—21no—
182C4×C11—21no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11C2×#4111yescharacteristic
186C4×C11H(5,𝔽2)11yescharacteristic
187Dic11—21no—
188Dic11—21no—
189Dic11—21no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193Dic11—41no—
194C2×#41—111no—
195C22×D4C2×D1111yescharacteristic
196C2×Q16—111no—
197C2×SD16—111no—
198C2×SD16—111no—
199C2×M16C2×D1111yescharacteristic
200C22×C8—111no—
201C4⋊Q8—111no—
202#126—221no—
203#126—221no—
204#124—111no—
205#124—221no—
206#123—221no—
207C22⋊Q8—111no—
208C22⋊Q8—111no—
209C22⋊Q8—111no—
210#121—111no—
211#121—221no—
212#120—221no—
213C4×Q8—111no—
214C4×Q8—221no—
215C4×D4—111no—
216C4×D4—111no—
217#117—111no—
218#117C2×D1111yescharacteristic
219C2×C22⋊C4—221no—
220#107—111no—
221#106—111no—
222#106—111no—
223C4⋊C8—111no—
224#103—111no—
225#103—111no—
226#103—111no—
227#103—111no—
228#102—111no—
229#102—111no—
230#102C2×D1111yescharacteristic
231#102C2×D1111yescharacteristic
232#102C2×D1111yescharacteristic
233#102C2×D1111yescharacteristic
234C22⋊C8—111no—
235C22⋊C8—111no—
236#97—111no—
237C2×C11—41no—
238C2×C11—42no—
239C2×C11—81no—
240C2×C11#54611yescharacteristic
241C2×C11#57511yescharacteristic
242C2×C11#57711yescharacteristic
243D11—41no—
244C24—21no—
245#41—222no—
246#41—441no—
247C2×Q8—111no—
248C2×Q8—111no—
249C2×Q8—221no—
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—111no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4C22×D1111yescharacteristic
257C2×D4C22×D1111yescharacteristic
258C22×C4—111no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4C22×D1111yescharacteristic
262Q16—441no—
263SD16—222no—
264SD16—441no—
265M16—41no—
266C2×C8—111no—
267C2×C8—111no—
268C2×C8—441no—
269C2×C8C22×D1111yescharacteristic
270C2×C8C22×D1111yescharacteristic
271C4⋊C4—111no—
272C4⋊C4—111no—
273C4⋊C4—111no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4C22×D1111yescharacteristic
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—21no—
293C42—111no—
294C42—221no—
295C42—221no—
296C11#331111yescharacteristic, complemented, Sylow
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—111no—
303C23D4×D1111yescharacteristic
304Q8—221no—
305Q8—221no—
306Q8—221no—
307Q8—221no—
308Q8—442no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—441no—
314D4—442no—
315D4—881no—
316D4#433912yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—111no—
322C2×C4—111no—
323C2×C4—111no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—442no—
331C2×C4—881no—
332C2×C4D4×D1111yescharacteristic
333C2×C4C23×D1111yescharacteristic
334C8—21no—
335C8—21no—
336C8—221no—
337C8—221no—
338C22—21no—
339C22—22no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—84no—
348C22—221no—
349C22—221no—
350C22—221no—
351C22C2×D4×D1111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—221no—
356C4—221no—
357C4—221no—
358C4—441no—
359C4—441no—
360C4—441no—
361C4—441no—
362C4C2×#433911yescharacteristic
363C4#6703711yescharacteristic
364C2—41no—
365C2—42no—
366C2—81no—
367C2—441no—
368C2#1062302111yescharacteristic
369C2#1062330411yescharacteristic
370C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#418C2
socleC22×C11C22×D4
prime radical#10623337C2
hypercenter#418D11
hypocenterC11#3311
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #10623064C2semidirect
3. C11×#418C2semidirect
4. #10622831C2semidirect
5. #10622750C2semidirect
6. #10622740C2semidirect
7. #10622609C2semidirect
8. #10622396C2semidirect
9. #10622392C2semidirect
10. #10622391C2semidirect
11. #10622385C2semidirect
12. #10622380C2semidirect
13. #10622378C2semidirect
14. #10622374C2semidirect
15. #10622370C2semidirect
32. C2×Dic44C22semidirect
33. C2×C8×D11C22semidirect
34. #66950C22semidirect
35. #66945C22semidirect
36. #66941C22semidirect
37. #66940C22semidirect
49. (C2×D11)⋊C8C22semidirect
50. #66881C22semidirect
51. #66880C22semidirect
52. #66880C22semidirect
53. #66879C22semidirect
54. Dic11⋊C8C22semidirect
55. #66874C22semidirect
56. #66874C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
166. #418D11semidirect
296. C11#3311semidirect

Maximal subgroups

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

subgroupindex
#106233372
#106230642
C11×#4182
#106228312
#106227502
#106227402
#106226092
#106223962
#106223922
#106223912
#106223852
#106223802
#106223782
#106223742
#106223702
#331111