Finite Group Databasebeta

← #13080652

Subgroups — #13080652

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
1C11×#546C211yesmaximal, characteristic
2#10623073C211yesmaximal, characteristic, complemented
3#10622852C211yesmaximal, characteristic, complemented
4#10622846C211yesmaximal, characteristic, complemented
5#10622831C211yesmaximal, characteristic, complemented
6#10622828C211yesmaximal, characteristic, complemented
7#10622668C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622665C211yesmaximal, characteristic, complemented
10#10622658C211yesmaximal, characteristic, complemented
11#10622654C211yesmaximal, characteristic, complemented
12#10622648C211yesmaximal, characteristic, complemented
13#10622631C211yesmaximal, characteristic, complemented
14#10622624C211yesmaximal, characteristic, complemented
15#10622621C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C11×#124C2211yescharacteristic
19C11×#123—21no—
20C11×C22⋊Q8C2211yescharacteristic
21C11×#121—21no—
22C11×#121C2211yescharacteristic
23C11×#120—21no—
24C4×D4×C11C2211yescharacteristic
25C4×D4×C11C2211yescharacteristic
26C2×C11×C22⋊C4—21no—
27C2×#4326C2211yescharacteristic, complemented
28#66989—21no—
29C2×#4324C2211yescharacteristic
30C2×#4324C2211yescharacteristic
31#66979C2211yescharacteristic
32#66979C2211yescharacteristic, complemented
33#66977C2211yescharacteristic
34#66977C2211yescharacteristic, complemented
35C2×#4318C2211yescharacteristic
36C22×C11⋊C8C2211yescharacteristic, complemented
37#66940—21no—
38#66932—21no—
39#66932—21no—
40#66922C2211yescharacteristic, complemented
41C4×Dic22C2211yescharacteristic, complemented
42#66899C2211yescharacteristic, complemented
43#66899C2211yescharacteristic, complemented
44#66899C2211yescharacteristic, complemented
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50#66896C2211yescharacteristic
51C22⋊(C11⋊C8)C2211yescharacteristic
52C22⋊(C11⋊C8)C2211yescharacteristic, complemented
53#66874C2211yescharacteristic, complemented
54#66872C2211yescharacteristic, complemented
55#66872C2211yescharacteristic, complemented
56#66871C2211yescharacteristic, complemented
57C4⋊(C11⋊C8)C2211yescharacteristic, complemented
58#66867C2211yescharacteristic, complemented
59C24×C11—21no—
60C11×#41—22no—
61C11×#41—41no—
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—22no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—41no—
68C2×D4×C11D411yescharacteristic
69C2×D4×C11C2311yescharacteristic
70C2×D4×C11C2311yescharacteristic
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C2×Dic22—21no—
76C2×Dic22C2311yescharacteristic
77C11×C4⋊C4—21no—
78C11×C4⋊C4D411yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C22⋊C4—21no—
81C11×C22⋊C4—21no—
82C11×C22⋊C4—21no—
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C11×C22⋊C4D411yescharacteristic
86C11×C22⋊C4D411yescharacteristic
87C42×C11C2311yescharacteristic
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92#4326—41no—
93#4324—22no—
94#4324—41no—
95C4⋊Dic11—21no—
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105#4318—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111#3311—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—42no—
115C23×C11—42no—
116C23×C11—81no—
117C23×C11C2×D411yescharacteristic
118C23×C11C2×D411yescharacteristic
119Q8×C11—21no—
120Q8×C11—21no—
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—41no—
125D4×C11—42no—
126D4×C11—42no—
127D4×C11—81no—
128D4×C11#4112yes—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—42no—
136C2×C4×C11—81no—
137C2×C4×C11C2×D411yescharacteristic
138C2×C4×C11C2×D411yescharacteristic
139C2×C4×C11C2×D411yescharacteristic
140C2×C4×C11C2×D411yescharacteristic
141C2×C4×C11C2411yescharacteristic
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146Dic22—21no—
147Dic22—21no—
148Dic22—42no—
149C11⋊C8—21no—
150C11⋊C8—21no—
151C11⋊C8—21no—
152C11⋊C8—21no—
153#556—111no—
154#546D1111yescharacteristic
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#418—111no—
167#416—111no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—22no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—84no—
181C22×C11C22×D411yescharacteristic
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11C2×#4111yescharacteristic
189C4×C11H(5,𝔽2)11yescharacteristic
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193Dic11—41no—
194C2×#41C2×D1111yescharacteristic
195C22×D4C2×D1111yescharacteristic
196C2×Q16—111no—
197C2×SD16—111no—
198C2×SD16—111no—
199C2×M16—111no—
200C22×C8—111no—
201C4⋊Q8—111no—
202#126—221no—
203#126—221no—
204#124—221no—
205#124C2×D1111yescharacteristic
206#123—21no—
207C22⋊Q8—111no—
208C22⋊Q8—111no—
209C22⋊Q8C2×D1111yescharacteristic
210#121—21no—
211#121C2×D1111yescharacteristic
212#120—21no—
213C4×Q8—111no—
214C4×Q8—221no—
215C4×D4C2×D1111yescharacteristic
216C4×D4C2×D1111yescharacteristic
217#117—111no—
218#117—111no—
219C2×C22⋊C4—21no—
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#102—111no—
231#102—111no—
232#102—111no—
233#102—111no—
234C22⋊C8—111no—
235C22⋊C8—111no—
236#97—111no—
237C2×C11—41no—
238C2×C11—41no—
239C2×C11—42no—
240C2×C11—81no—
241C2×C11#54611yescharacteristic
242C2×C11#57511yescharacteristic
243C2×C11#57711yescharacteristic
244C24—21no—
245#41—22no—
246#41—41no—
247C2×Q8—111no—
248C2×Q8—221no—
249C2×Q8C22×D1111yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4C22⋊D1111yescharacteristic
256C2×D4C22×D1111yescharacteristic
257C2×D4C22×D1111yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4C22×D1111yescharacteristic
261C22×C4C22×D1111yescharacteristic
262Q16—441no—
263SD16—222no—
264SD16—441no—
265M16—441no—
266C2×C8—111no—
267C2×C8—111no—
268C2×C8—111no—
269C2×C8—111no—
270C2×C8—441no—
271C4⋊C4—21no—
272C4⋊C4—111no—
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4C22⋊D1111yescharacteristic
280C4⋊C4C22×D1111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4C22⋊D1111yescharacteristic
291C22⋊C4C22⋊D1111yescharacteristic
292C42—221no—
293C42—221no—
294C42—221no—
295C42C22×D1111yescharacteristic
296C11#331111yescharacteristic, complemented, Sylow
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D1111yescharacteristic
303C23C2×C22⋊D1111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—221no—
307Q8—221no—
308Q8—442no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—42no—
314D4—42no—
315D4—81no—
316D4#434112yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4C2×C22⋊D1111yescharacteristic
330C2×C4C2×C22⋊D1111yescharacteristic
331C2×C4C2×C22⋊D1111yescharacteristic
332C2×C4C2×C22⋊D1111yescharacteristic
333C2×C4C23×D1111yescharacteristic
334C8—221no—
335C8—221no—
336C8—221no—
337C8—221no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—84no—
351C22C22×C22⋊D1111yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—441no—
359C4—441no—
360C4—441no—
361C4—441no—
362C4C2×#434111yescharacteristic
363C4#6703711yescharacteristic
364C2—41no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#1062333711yescharacteristic
369C2#1062335311yescharacteristic
370C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#546C2
socleC22×C11C22×D4
hypercenter#546D11
hypocenterC11#3311
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
2. #10623073C2semidirect
3. #10622852C2semidirect
4. #10622846C2semidirect
5. #10622831C2semidirect
6. #10622828C2semidirect
7. #10622668C2semidirect
8. #10622667C2semidirect
9. #10622665C2semidirect
10. #10622658C2semidirect
11. #10622654C2semidirect
12. #10622648C2semidirect
13. #10622631C2semidirect
14. #10622624C2semidirect
15. #10622621C2semidirect
27. C2×#4326C22semidirect
32. #66979C22semidirect
34. #66977C22semidirect
36. C22×C11⋊C8C22semidirect
40. #66922C22semidirect
41. C4×Dic22C22semidirect
42. #66899C22semidirect
43. #66899C22semidirect
44. #66899C22semidirect
52. C22⋊(C11⋊C8)C22semidirect
53. #66874C22semidirect
54. #66872C22semidirect
55. #66872C22semidirect
56. #66871C22semidirect
57. C4⋊(C11⋊C8)C22semidirect
58. #66867C22semidirect
296. C11#3311semidirect

Maximal subgroups

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

subgroupindex
C11×#5462
#106230732
#106228522
#106228462
#106228312
#106228282
#106226682
#106226672
#106226652
#106226582
#106226542
#106226482
#106226312
#106226242
#106226212
#331111