Finite Group Databasebeta

← #13080607

Subgroups — #13080607

Order 1408.

420 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
1C11×#548C211yesmaximal, characteristic, complemented
2#10623086C211yesmaximal, characteristic, complemented
3#10622851C211yesmaximal, characteristic, complemented
4#10622845C211yesmaximal, characteristic, complemented
5#10622840C211yesmaximal, characteristic, complemented
6C2×#66899C211yesmaximal, characteristic, complemented
7#10622670C211yesmaximal, characteristic, complemented
8#10622668C211yesmaximal, characteristic, complemented
9#10622662C211yesmaximal, characteristic, complemented
10#10622657C211yesmaximal, characteristic, complemented
11#10622651C211yesmaximal, characteristic, complemented
12#10622646C211yesmaximal, characteristic, complemented
13#10622639C211yesmaximal, characteristic, complemented
14#10622634C211yesmaximal, characteristic, complemented
15#10622624C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic
18C2×#4341—21no—
19C11×#124—21no—
20C11×#124C2211yescharacteristic
21C11×C22⋊Q8—21no—
22C11×C22⋊Q8C2211yescharacteristic
23C11×#121—21no—
24C11×#121C2211yescharacteristic
25C4×Q8×C11C2211yescharacteristic
26C4×D4×C11—21no—
27C4×D4×C11C2211yescharacteristic
28C2×#4325C2211yescharacteristic
29C2×#4325C2211yescharacteristic
30C2×#4323C2211yescharacteristic
31#66983C2211yescharacteristic
32#66983C2211yescharacteristic
33C2×C4⋊Dic11C2211yescharacteristic
34C2×C4⋊Dic11C2211yescharacteristic
35C2×#4318C2211yescharacteristic
36C22×C11⋊C8C2211yescharacteristic
37#66950—21no—
38#66939—21no—
39#66939—21no—
40C4×D44C2211yescharacteristic
41#66922C2211yescharacteristic
42#66899C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50#66896C2211yescharacteristic
51C22⋊(C11⋊C8)C2211yescharacteristic
52C22⋊(C11⋊C8)C2211yescharacteristic
53#66873C2211yescharacteristic
54#66871C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58#66867C2211yescharacteristic
59C11×#41—22no—
60C11×#41—41no—
61C2×Q8×C11—21no—
62C2×Q8×C11—22no—
63C2×Q8×C11—41no—
64C2×Q8×C11C2311yescharacteristic
65C2×Q8×C11C2311yescharacteristic
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11D411yescharacteristic
69C2×D4×C11C2311yescharacteristic
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C2×C22⋊D11—21no—
75C2×C22⋊D11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78#4341—44no—
79C2×D44C2311yescharacteristic
80C2×C4×D11—21no—
81C2×Dic22—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4D411yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C11×C22⋊C4—21no—
89C11×C22⋊C4—21no—
90C11×C22⋊C4D411yescharacteristic
91C11×C22⋊C4D411yescharacteristic
92C42×C11—21no—
93C42×C11C2311yescharacteristic
94#4325—22no—
95#4325—41no—
96#4323—41no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11C2311yescharacteristic
104C4⋊Dic11C2311yescharacteristic
105C4⋊Dic11C2311yescharacteristic
106#4318—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112#3308—111nomaximal, Sylow
113C23×C11—21no—
114C23×C11C2×D411yescharacteristic
115C23×C11C2×D411yescharacteristic
116C22×D11—21no—
117Q8×C11—21no—
118Q8×C11—21no—
119Q8×C11—21no—
120Q8×C11—42no—
121Q8×C11#4112yescomplemented
122D4×C11—22no—
123D4×C11—21no—
124D4×C11—21no—
125D4×C11—42no—
126D4×C11—42no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11C2×D411yescharacteristic
137C2×C4×C11C2×D411yescharacteristic
138C2×C4×C11C2×D411yescharacteristic
139C2×C4×C11C2×D411yescharacteristic
140C2×C4×C11C2411yescharacteristic
141C22⋊D11—42no—
142C22⋊D11—42no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148D44—21no—
149D44—21no—
150C4×D11—42no—
151Dic22—42no—
152C11⋊C8—21no—
153C11⋊C8—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156#548D1111yescharacteristic, complemented
157#547—111no—
158#489—111no—
159#484—111no—
160#480—111no—
161#477—111no—
162#468—111no—
163#466—111no—
164#463—111no—
165#449—111no—
166#448—111no—
167#440—111no—
168#435—111no—
169#417—111no—
170C2×#103—111no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11AGL(1,ℤ/8)12yes—
180C22×C11C22×D411yescharacteristic
181C2×D11—41no—
182C2×D11—41no—
183C2×D11—41no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—22no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11C2×#4111yescharacteristic
192C4×C11H(5,𝔽2)11yescharacteristic
193Dic11—41no—
194Dic11—41no—
195Dic11—41no—
196C2×#41—221no—
197C2×#41C2×D1111yescharacteristic
198C22×Q8C2×D1111yescharacteristic
199C2×SD16—111no—
200C2×SD16—111no—
201C2×D8—111no—
202C2×M16—111no—
203C22×C8—111no—
204C4⋊Q8—111no—
205#124—21no—
206#124C2×D1111yescharacteristic
207#123—221no—
208#123—221no—
209C22⋊Q8—21no—
210C22⋊Q8—221no—
211C22⋊Q8C2×D1111yescharacteristic
212#121—21no—
213#121—111no—
214#121—111no—
215#121C2×D1111yescharacteristic
216C4×Q8C2×D1111yescharacteristic
217C4×D4—21no—
218C4×D4—111no—
219C4×D4C2×D1111yescharacteristic
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222#107—111no—
223#107—111no—
224#107—111no—
225C4⋊C8—111no—
226#103—111no—
227#103—111no—
228#103—111no—
229#103—111no—
230#103—111no—
231#103—111no—
232#102—111no—
233#102—111no—
234#102—111no—
235#102—111no—
236C22⋊C8—111no—
237C22⋊C8—111no—
238#97—111no—
239C2×C11—22no—
240C2×C11—41no—
241C2×C11—81no—
242C2×C11#54611yescharacteristic
243C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
244C2×C11#57811yescharacteristic
245D11—81no—
246#41—22no—
247#41—41no—
248#41—444no—
249C2×Q8—21no—
250C2×Q8—22no—
251C2×Q8—41no—
252C2×Q8—221no—
253C2×Q8C22×D1111yescharacteristic
254C2×Q8C22×D1111yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—111no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4C22⋊D1111yescharacteristic
261C2×D4C22×D1111yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4C22×D1111yescharacteristic
268C22×C4C22×D1111yescharacteristic
269SD16—222no—
270SD16—441no—
271D8—441no—
272M16—441no—
273C2×C8—111no—
274C2×C8—111no—
275C2×C8—111no—
276C2×C8—111no—
277C2×C8—441no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—111no—
281C4⋊C4—111no—
282C4⋊C4—111no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4C22⋊D1111yescharacteristic
287C4⋊C4C22×D1111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4C22⋊D1111yescharacteristic
296C22⋊C4C22⋊D1111yescharacteristic
297C42—21no—
298C42C22×D1111yescharacteristic
299C11#330811yescharacteristic, complemented, Sylow
300C23—21no—
301C23—221no—
302C23C2×C22⋊D1111yescharacteristic
303C23C2×C22⋊D1111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—442no—
309Q8#434112yescomplemented
310D4—22no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—42no—
315D4—221no—
316D4—221no—
317D4—442no—
318D4—442no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—442no—
334C2×C4C2×C22⋊D1111yescharacteristic
335C2×C4C2×C22⋊D1111yescharacteristic
336C2×C4C2×C22⋊D1111yescharacteristic
337C2×C4C2×C22⋊D1111yescharacteristic
338C2×C4C23×D1111yescharacteristic
339C8—221no—
340C8—221no—
341C8—221no—
342C8—221no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—441no—
352C22—441no—
353C22—441no—
354C22#6700212yes—
355C22C22×C22⋊D1111yescharacteristic
356C4—21no—
357C4—21no—
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—441no—
364C4—441no—
365C4—441no—
366C4C2×#434111yescharacteristic
367C4#6703711yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—881no—
372C2#1062333711yescharacteristic
373C2C2×#6700211yescharacteristic
374C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#548C2
socleC22×C11C22×D4
hypercenter#548D11
hypocenterC11#3308
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C11×#548C2semidirect
2. #10623086C2semidirect
3. #10622851C2semidirect
4. #10622845C2semidirect
5. #10622840C2semidirect
6. C2×#66899C2semidirect
7. #10622670C2semidirect
8. #10622668C2semidirect
9. #10622662C2semidirect
10. #10622657C2semidirect
11. #10622651C2semidirect
12. #10622646C2semidirect
13. #10622639C2semidirect
14. #10622634C2semidirect
15. #10622624C2semidirect
121. Q8×C11#41semidirect
156. #548D11semidirect
299. C11#3308semidirect
309. Q8#4341semidirect

Maximal subgroups

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

subgroupindex
C11×#5482
#106230862
#106228512
#106228452
#106228402
C2×#668992
#106226702
#106226682
#106226622
#106226572
#106226512
#106226462
#106226392
#106226342
#106226242
#330811