Finite Group Databasebeta

← #13080625

Subgroups — #13080625

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
1#10623130C211yesmaximal, characteristic, complemented
2#10623045C211yesmaximal, characteristic, complemented
3C11×#480C211yesmaximal, characteristic, complemented
4#10622652C211yesmaximal, characteristic, complemented
5#10622579C211yesmaximal, characteristic, complemented
6#10622502C211yesmaximal, characteristic, complemented
7#10622498C211yesmaximal, characteristic, complemented
8#10622496C211yesmaximal, characteristic, complemented
9#10622490C211yesmaximal, characteristic, complemented
10#10622399C211yesmaximal, characteristic, complemented
11#10622394C211yesmaximal, characteristic, complemented
12#10622385C211yesmaximal, characteristic, complemented
13#10622377C211yesmaximal, characteristic, complemented
14#10622347C211yesmaximal, characteristic, complemented
15#10622341C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C11×#121C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20#66993—21no—
21#66993C2211yescharacteristic
22#66992—21no—
23C2×#4323C2211yescharacteristic
24#66983—21no—
25#66983C2211yescharacteristic
26C4×C22⋊D11—21no—
27C4×C22⋊D11C2211yescharacteristic
28C2×#4318C2211yescharacteristic
29C2×D88C2211yescharacteristic
30C2×#4314C2211yescharacteristic
31C2×C8×D11C2211yescharacteristic
32#66951—21no—
33#66948C2211yescharacteristic
34#66948C2211yescharacteristic
35#66947—21no—
36#66946C2211yescharacteristic
37#66945C2211yescharacteristic
38#66943C2211yescharacteristic
39#66940C2211yescharacteristic
40#66937—21no—
41(C22⋊D11)⋊C4—21no—
42C11×#107C2211yescharacteristic
43C11×#107C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46C11×C22⋊C8C2211yescharacteristic
47#66896C2211yescharacteristic
48#66885C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66880C2211yescharacteristic
51#66879C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66873C2211yescharacteristic
58#66872C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11D411yescharacteristic
69C22×Dic11—21no—
70#4341—22no—
71#4341—41no—
72#4339—22no—
73#4339—41no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44C2311yescharacteristic
77C2×D44C2311yescharacteristic
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11C2311yescharacteristic
81C2×Dic22C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C11×C4⋊C4—21no—
85C11×C4⋊C4C2311yescharacteristic
86C11×C4⋊C4C2311yescharacteristic
87C11×C4⋊C4C2311yescharacteristic
88C11×C22⋊C4—21no—
89C22⋊Dic11D411yescharacteristic
90#4323—41no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4D411yescharacteristic
97C4⋊Dic11—21no—
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4D411yescharacteristic
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11C2311yescharacteristic
105#4318—41no—
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108D88—41no—
109#4314—22no—
110C8×D11—41no—
111#3309—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11C2×D411yescharacteristic
114C22×D11—21no—
115C22×D11—21no—
116C22×D11C2×D411yescharacteristic
117D4×C11—21no—
118D4×C11—21no—
119D4×C11—81no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—81no—
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C22⋊D11—41no—
129C22⋊D11—42no—
130C22⋊D11—42no—
131C22⋊D11—42no—
132C22⋊D11—42no—
133C22⋊D11—81no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—42no—
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140D44—21no—
141D44—21no—
142D44—21no—
143D44—21no—
144D44—81no—
145D44—81no—
146C4×D11—21no—
147C4×D11—21no—
148C4×D11—42no—
149C4×D11—81no—
150Dic22—21no—
151Dic22#4112yes—
152C8×C11—21no—
153C8×C11—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156#553—111no—
157#550—111no—
158#490—111no—
159#482—111no—
160#480D1111yescharacteristic, complemented
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—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11C22×D411yescharacteristic
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—41no—
182C2×D11—41no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C4×C11—21no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11C2×#4111yescharacteristic
192C4×C11H(5,𝔽2)11yescharacteristic
193Dic11—22no—
194Dic11—21no—
195Dic11—21no—
196Dic11—21no—
197Dic11—41no—
198C2×#41—111no—
199C2×#41—111no—
200C2×SD16—111no—
201C2×D8—111no—
202C2×D8—111no—
203C2×M16—111no—
204C22×C8—111no—
205#127—111no—
206#127—221no—
207#126—221no—
208#125—111no—
209#123—221no—
210#121—111no—
211#121—111no—
212#121—111no—
213#121—221no—
214#121—221no—
215#121—221no—
216#121C2×D1111yescharacteristic
217C4×Q8—111no—
218C4×D4—111no—
219C4×D4—111no—
220C4×D4—221no—
221C4×D4—221no—
222#117—111no—
223C2×C4⋊C4C2×D1111yescharacteristic
224#107C2×D1111yescharacteristic
225#107C2×D1111yescharacteristic
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#102C2×D1111yescharacteristic
237#102C2×D1111yescharacteristic
238C22⋊C8—111no—
239C22⋊C8C2×D1111yescharacteristic
240#97—111no—
241C2×C11—41no—
242C2×C11—81no—
243C2×C11#54611yescharacteristic
244C2×C11#57511yescharacteristic
245C2×C11#57611yescharacteristic
246D11—41no—
247D11—81no—
248D11—81no—
249#41—222no—
250#41—222no—
251#41—441no—
252#41—441no—
253C2×Q8—111no—
254C2×D4—21no—
255C2×D4—111no—
256C2×D4—111no—
257C2×D4—111no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4—221no—
264C2×D4—221no—
265C2×D4C22×D1111yescharacteristic
266C22×C4—21no—
267C22×C4—111no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4C22×D1111yescharacteristic
272SD16—222no—
273D8—441no—
274D8—441no—
275M16—441no—
276C2×C8—111no—
277C2×C8—111no—
278C2×C8—441no—
279C2×C8C22×D1111yescharacteristic
280C2×C8C22×D1111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—111no—
283C4⋊C4—111no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4C22×D1111yescharacteristic
288C4⋊C4C22×D1111yescharacteristic
289C4⋊C4C22×D1111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—111no—
292C22⋊C4—111no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C42—111no—
299C42—221no—
300C42—221no—
301C11#330911yescharacteristic, complemented, Sylow
302C23—21no—
303C23—111no—
304C23—221no—
305C23—221no—
306C23D4×D1111yescharacteristic
307Q8—112no—
308Q8—221no—
309D4—21no—
310D4—21no—
311D4—81no—
312D4—221no—
313D4—221no—
314D4—221no—
315D4—221no—
316D4—441no—
317D4—442no—
318D4—442no—
319D4—442no—
320D4—442no—
321D4—881no—
322D4—881no—
323D4—881no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—81no—
330C2×C4—111no—
331C2×C4—111no—
332C2×C4—111no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—442no—
338C2×C4—442no—
339C2×C4—881no—
340C2×C4D4×D1111yescharacteristic
341C2×C4C23×D1111yescharacteristic
342C8—21no—
343C8—21no—
344C8—221no—
345C8—221no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—221no—
353C22—221no—
354C22—221no—
355C22—441no—
356C22—441no—
357C22—441no—
358C22—441no—
359C22—441no—
360C22—441no—
361C22C2×D4×D1111yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—221no—
367C4—221no—
368C4—221no—
369C4—222no—
370C4—441no—
371C4#41×D1111yescharacteristic
372C4#6704211yescharacteristic
373C2—41no—
374C2—81no—
375C2—441no—
376C2—881no—
377C2—881no—
378C2#1062318511yescharacteristic
379C2#1062328811yescharacteristic
380C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#480C2
socleC22×C11C22×D4
hypercenter#480D11
hypocenterC11#3309
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #10623130C2semidirect
2. #10623045C2semidirect
3. C11×#480C2semidirect
4. #10622652C2semidirect
5. #10622579C2semidirect
6. #10622502C2semidirect
7. #10622498C2semidirect
8. #10622496C2semidirect
9. #10622490C2semidirect
10. #10622399C2semidirect
11. #10622394C2semidirect
12. #10622385C2semidirect
13. #10622377C2semidirect
14. #10622347C2semidirect
15. #10622341C2semidirect
160. #480D11semidirect
301. C11#3309semidirect

Maximal subgroups

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

subgroupindex
#106231302
#106230452
C11×#4802
#106226522
#106225792
#106225022
#106224982
#106224962
#106224902
#106223992
#106223942
#106223852
#106223772
#106223472
#106223412
#330911