Finite Group Databasebeta

← #13080622

Subgroups — #13080622

Order 1408.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#550C211yesmaximal, characteristic, complemented
2#10623096C211yesmaximal, characteristic, complemented
3#10622851C211yesmaximal, characteristic, complemented
4#10622851C211yesmaximal, characteristic, complemented
5#10622846C211yesmaximal, characteristic, complemented
6#10622845C211yesmaximal, characteristic, complemented
7#10622685C211yesmaximal, characteristic, complemented
8#10622684C211yesmaximal, characteristic, complemented
9#10622652C211yesmaximal, characteristic, complemented
10#10622651C211yesmaximal, characteristic, complemented
11#10622648C211yesmaximal, characteristic, complemented
12#10622646C211yesmaximal, characteristic, complemented
13#10622639C211yesmaximal, characteristic, complemented
14#10622635C211yesmaximal, characteristic, complemented
15#10622624C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×C11×#41C2211yescharacteristic
18C11×#127—21no—
19C11×#127C2211yescharacteristic
20C11×#121—21no—
21C11×#121—21no—
22C11×#121C2211yescharacteristic
23C11×#121C2211yescharacteristic
24C4×Q8×C11C2211yescharacteristic
25C4×D4×C11—21no—
26C4×D4×C11C2211yescharacteristic
27C2×#4325C2211yescharacteristic
28#66992—21no—
29C2×#4323C2211yescharacteristic
30C2×#4323C2211yescharacteristic
31#66983C2211yescharacteristic
32#66983C2211yescharacteristic
33#66979C2211yescharacteristic
34C2×C4⋊Dic11C2211yescharacteristic
35C2×#4318C2211yescharacteristic
36C22×C11⋊C8C2211yescharacteristic
37#66951—21no—
38#66936—21no—
39(C22⋊D11)⋊C4—21no—
40C4×D44C2211yescharacteristic
41#66923C2211yescharacteristic
42#66899C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50#66896C2211yescharacteristic
51C22⋊(C11⋊C8)C2211yescharacteristic
52C22⋊(C11⋊C8)C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58#66867C2211yescharacteristic
59C11×#41—22no—
60C11×#41—22no—
61C11×#41—41no—
62C11×#41—41no—
63C2×Q8×C11C2311yescharacteristic
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11D411yescharacteristic
71C2×D4×C11C2311yescharacteristic
72C2×D4×C11C2311yescharacteristic
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C2×C22⋊D11—21no—
78C2×C22⋊D11—21no—
79C22×Dic11—21no—
80C2×D44C2311yescharacteristic
81C2×C4×D11—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4D411yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C11×C22⋊C4—21no—
87C11×C22⋊C4D411yescharacteristic
88C11×C22⋊C4D411yescharacteristic
89C42×C11—21no—
90C42×C11C2311yescharacteristic
91C22⋊Dic11—21no—
92#4325—22no—
93#4323—41no—
94#4323—41no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104C4×Dic11—21no—
105#4318—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111#3309—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11C2×D411yescharacteristic
115C23×C11C2×D411yescharacteristic
116C22×D11—21no—
117Q8×C11—21no—
118Q8×C11#4112yes—
119D4×C11—21no—
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—41no—
124D4×C11—42no—
125D4×C11—42no—
126D4×C11—42no—
127D4×C11—81no—
128D4×C11—81no—
129D4×C11—81no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11C2×D411yescharacteristic
139C2×C4×C11C2×D411yescharacteristic
140C2×C4×C11C2×D411yescharacteristic
141C2×C4×C11C2×D411yescharacteristic
142C2×C4×C11C2411yescharacteristic
143C22⋊D11—42no—
144C22⋊D11—81no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—81no—
149D44—21no—
150D44—21no—
151C4×D11—81no—
152C11⋊C8—21no—
153C11⋊C8—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156#553—111no—
157#550D1111yescharacteristic, complemented
158#490—111no—
159#482—111no—
160#480—111no—
161#479—111no—
162#469—111no—
163#466—111no—
164#459—111no—
165#449—111no—
166#449—111no—
167#440—111no—
168#435—111no—
169#417—111no—
170#416—111no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11C22×D411yescharacteristic
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—22no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—41no—
193C4×C11C2×#4111yescharacteristic
194C4×C11H(5,𝔽2)11yescharacteristic
195Dic11—41no—
196Dic11—41no—
197Dic11—41no—
198C2×#41C2×D1111yescharacteristic
199C2×#41C2×D1111yescharacteristic
200C2×SD16—111no—
201C2×D8—111no—
202C2×D8—111no—
203C2×M16—111no—
204C22×C8—111no—
205#127—21no—
206#127C2×D1111yescharacteristic
207#126—221no—
208#125—111no—
209#123—221no—
210#121—21no—
211#121—21no—
212#121—111no—
213#121—111no—
214#121—221no—
215#121C2×D1111yescharacteristic
216#121C2×D1111yescharacteristic
217C4×Q8C2×D1111yescharacteristic
218C4×D4—21no—
219C4×D4—111no—
220C4×D4—221no—
221C4×D4C2×D1111yescharacteristic
222#117—111no—
223C2×C4⋊C4—111no—
224#107—111no—
225#107—111no—
226#106—111no—
227C4⋊C8—111no—
228#103—111no—
229#103—111no—
230#103—111no—
231#102—111no—
232#102—111no—
233#102—111no—
234#102—111no—
235#102—111no—
236#102—111no—
237#102—111no—
238C22⋊C8—111no—
239C22⋊C8—111no—
240#97—111no—
241C2×C11—41no—
242C2×C11—41no—
243C2×C11—81no—
244C2×C11—81no—
245C2×C11#54611yescharacteristic
246C2×C11#57511yescharacteristic
247C2×C11#57611yescharacteristic
248D11—81no—
249#41—22no—
250#41—22no—
251#41—41no—
252#41—41no—
253C2×Q8C22×D1111yescharacteristic
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—111no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4C22⋊D1111yescharacteristic
264C2×D4C22×D1111yescharacteristic
265C2×D4C22×D1111yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4C22×D1111yescharacteristic
271C22×C4C22×D1111yescharacteristic
272SD16—222no—
273D8—441no—
274D8—441no—
275M16—441no—
276C2×C8—111no—
277C2×C8—111no—
278C2×C8—111no—
279C2×C8—111no—
280C2×C8—441no—
281C4⋊C4—21no—
282C4⋊C4—111no—
283C4⋊C4—111no—
284C4⋊C4—111no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4C22⋊D1111yescharacteristic
289C4⋊C4C22×D1111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4C22⋊D1111yescharacteristic
297C22⋊C4C22⋊D1111yescharacteristic
298C42—21no—
299C42—221no—
300C42C22×D1111yescharacteristic
301C11#330911yescharacteristic, complemented, Sylow
302C23—21no—
303C23—21no—
304C23—221no—
305C23C2×C22⋊D1111yescharacteristic
306C23C2×C22⋊D1111yescharacteristic
307Q8—21no—
308Q8#434112yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4—81no—
319D4—81no—
320D4—221no—
321D4—221no—
322D4—442no—
323D4—881no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—881no—
336C2×C4—881no—
337C2×C4C2×C22⋊D1111yescharacteristic
338C2×C4C2×C22⋊D1111yescharacteristic
339C2×C4C2×C22⋊D1111yescharacteristic
340C2×C4C2×C22⋊D1111yescharacteristic
341C2×C4C23×D1111yescharacteristic
342C8—221no—
343C8—221no—
344C8—221no—
345C8—221no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—441no—
359C22—441no—
360C22—441no—
361C22C22×C22⋊D1111yescharacteristic
362C4—21no—
363C4—21no—
364C4—22no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—441no—
369C4—441no—
370C4—441no—
371C4C2×#434111yescharacteristic
372C4#6703711yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—81no—
377C2—881no—
378C2#1062333711yescharacteristic
379C2#1062335311yescharacteristic
380C2#1062336611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#550C2
socleC22×C11C22×D4
hypercenter#550D11
hypocenterC11#3309
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C11×#550C2semidirect
2. #10623096C2semidirect
3. #10622851C2semidirect
4. #10622851C2semidirect
5. #10622846C2semidirect
6. #10622845C2semidirect
7. #10622685C2semidirect
8. #10622684C2semidirect
9. #10622652C2semidirect
10. #10622651C2semidirect
11. #10622648C2semidirect
12. #10622646C2semidirect
13. #10622639C2semidirect
14. #10622635C2semidirect
15. #10622624C2semidirect
157. #550D11semidirect
301. C11#3309semidirect

Maximal subgroups

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

subgroupindex
C11×#5502
#106230962
#106228512
#106228462
#106228452
#106226852
#106226842
#106226522
#106226512
#106226482
#106226462
#106226392
#106226352
#106226242
#330911