Finite Group Databasebeta

← #13080820

Subgroups — #13080820

Order 1408.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623143C211yesmaximal, characteristic, complemented
2#10623045C211yesmaximal, characteristic, complemented
3C11×#480C211yesmaximal, characteristic, complemented
4#10622652C211yesmaximal, characteristic, complemented
5#10622579C211yesmaximal, characteristic, complemented
6#10622504C211yesmaximal, characteristic, complemented
7#10622501C211yesmaximal, characteristic, complemented
8#10622499C211yesmaximal, characteristic, complemented
9#10622485C211yesmaximal, characteristic, complemented
10#10622400C211yesmaximal, characteristic, complemented
11#10622386C211yesmaximal, characteristic, complemented
12#10622383C211yesmaximal, characteristic, complemented
13#10622381C211yesmaximal, characteristic, complemented
14#10622347C211yesmaximal, characteristic, complemented
15#10622342C211yesmaximal, characteristic, complemented
16C2×D4×D11C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C11×#121C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic, complemented
20#66991—21no—
21#66990—21no—
22#66989C2211yescharacteristic
23C2×#4323C2211yescharacteristic
24#66983—21no—
25#66983C2211yescharacteristic, complemented
26C4×C22⋊D11—21no—
27C4×C22⋊D11C2211yescharacteristic
28C2×#4318C2211yescharacteristic, complemented
29C2×D88C2211yescharacteristic
30C2×#4314C2211yescharacteristic, complemented
31C2×#4313C2211yescharacteristic
32#66951—21no—
33#66950C2211yescharacteristic
34#66948C2211yescharacteristic
35#66947—21no—
36#66946C2211yescharacteristic
37#66946C2211yescharacteristic, complemented
38#66945C2211yescharacteristic
39#66943C2211yescharacteristic, complemented
40#66936—21no—
41C22⋊C4×D11—21no—
42C11×#107C2211yescharacteristic, complemented
43C11×#107C2211yescharacteristic, complemented
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46C11×C22⋊C8C2211yescharacteristic, complemented
47#66896C2211yescharacteristic
48#66885C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66880C2211yescharacteristic, complemented
51Dic11⋊C8C2211yescharacteristic, complemented
52C8×Dic11C2211yescharacteristic, complemented
53#66874C2211yescharacteristic, complemented
54#66874C2211yescharacteristic, complemented
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66873C2211yescharacteristic, complemented
58#66872C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C22×C4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11D411yescharacteristic
68D4×D11—22no—
69D4×D11—41no—
70#4339—22no—
71#4339—41no—
72C2×D44—21no—
73C2×D44C2311yescharacteristic
74C2×D44C2311yescharacteristic
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×Dic22C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4—21no—
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C22⋊C4—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11—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)⋊C4—21no—
97(C2×D11)⋊C4D411yescharacteristic
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11C2311yescharacteristic
101Dic11⋊C4—21no—
102Dic11⋊C4D411yescharacteristic
103C4×Dic11—21no—
104C4×Dic11C2311yescharacteristic
105#4318—41no—
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108D88—22no—
109#4314—41no—
110#4313—41no—
111#3322—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11C2×D411yescharacteristic
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—42no—
117C22×D11—42no—
118C22×D11—81no—
119C22×D11C2×D411yescharacteristic
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—81no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—81no—
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C22⋊D11—41no—
132C22⋊D11—42no—
133C22⋊D11—42no—
134C22⋊D11—42no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140D44—21no—
141D44—21no—
142D44—21no—
143D44—81no—
144D44#4112yes—
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—42no—
148C4×D11—81no—
149C4×D11—81no—
150Dic22—21no—
151Dic22—21no—
152C8×C11—21no—
153C8×C11—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156#553—111no—
157#546—111no—
158#488—111no—
159#485—111no—
160#480D1111yescharacteristic, complemented
161#478—111no—
162#469—111no—
163#468—111no—
164#463—111no—
165#449—111no—
166#447—111no—
167C4×D8—111no—
168#436—111no—
169#418—111no—
170#417—111no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11C22×D411yescharacteristic
178C2×D11—22no—
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—21no—
182C2×D11—41no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—84no—
188C4×C11—21no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11C2×#4111yescharacteristic
193C4×C11H(5,𝔽2)11yescharacteristic
194Dic11—21no—
195Dic11—21no—
196Dic11—21no—
197Dic11—41no—
198Dic11—41no—
199C2×#41—111no—
200C22×D4—111no—
201C2×SD16—111no—
202C2×D8—111no—
203C2×D8—111no—
204C2×M16—111no—
205C2×M16—111no—
206#126—221no—
207#125—111no—
208#124—111no—
209#123—221no—
210#123—221no—
211C22⋊Q8—111no—
212#121—111no—
213#121—111no—
214#121—221no—
215#121—221no—
216#121C2×D1111yescharacteristic
217#120—221no—
218C4×D4—111no—
219C4×D4—111no—
220C4×D4—111no—
221C4×D4—221no—
222#117—111no—
223C2×C4⋊C4C2×D1111yescharacteristic, complemented
224C2×C22⋊C4—221no—
225#107C2×D1111yescharacteristic, complemented
226#107C2×D1111yescharacteristic, complemented
227#106—111no—
228C4⋊C8—111no—
229#103—111no—
230#103—111no—
231#103—111no—
232#102—111no—
233#102—111no—
234#102—111no—
235#102—111no—
236#102—111no—
237#102C2×D1111yescharacteristic
238#102C2×D1111yescharacteristic
239C22⋊C8—111no—
240C22⋊C8C2×D1111yescharacteristic, complemented
241C4×C8—111no—
242C2×C11—41no—
243C2×C11—81no—
244C2×C11#54611yescharacteristic
245C2×C11#57511yescharacteristic
246C2×C11#57611yescharacteristic
247D11—41no—
248D11—42no—
249D11—81no—
250C24—221no—
251#41—222no—
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—222no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4—441no—
264C2×D4C22×D1111yescharacteristic
265C22×C4—21no—
266C22×C4—111no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4C22×D1111yescharacteristic
271SD16—441no—
272D8—222no—
273D8—441no—
274M16—441no—
275M16—441no—
276C2×C8—111no—
277C2×C8—111no—
278C2×C8C22×D1111yescharacteristic
279C2×C8C22×D1111yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—111no—
282C4⋊C4—111no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4C22×D1111yescharacteristic
287C4⋊C4C22×D1111yescharacteristic
288C4⋊C4C22×D1111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—111no—
291C22⋊C4—111no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C42—111no—
301C42—221no—
302C11#332211yescharacteristic, complemented, Sylow
303C23—21no—
304C23—111no—
305C23—221no—
306C23—221no—
307C23—442no—
308C23—442no—
309C23—881no—
310C23D4×D1111yescharacteristic
311Q8—221no—
312Q8—221no—
313D4—21no—
314D4—21no—
315D4—81no—
316D4—112no—
317D4—221no—
318D4—221no—
319D4—221no—
320D4—441no—
321D4—442no—
322D4—442no—
323D4—442no—
324D4—881no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—81no—
331C2×C4—111no—
332C2×C4—111no—
333C2×C4—111no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—442no—
339C2×C4—881no—
340C2×C4—881no—
341C2×C4D4×D1111yescharacteristic
342C2×C4C23×D1111yescharacteristic
343C8—21no—
344C8—21no—
345C8—221no—
346C8—221no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—221no—
354C22—221no—
355C22—221no—
356C22—222no—
357C22—441no—
358C22—441no—
359C22—441no—
360C22—441no—
361C22—441no—
362C22—884no—
363C22C2×D4×D1111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—221no—
369C4—221no—
370C4—221no—
371C4—441no—
372C4—441no—
373C4#41×D1111yescharacteristic
374C4#6704211yescharacteristic
375C2—41no—
376C2—81no—
377C2—441no—
378C2—442no—
379C2—881no—
380C2#1062318511yescharacteristic
381C2#1062328811yescharacteristic
382C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#480C2
socleC22×C11C22×D4
hypercenter#480D11
hypocenterC11#3322
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. #10623143C2semidirect
2. #10623045C2semidirect
3. C11×#480C2semidirect
4. #10622652C2semidirect
5. #10622579C2semidirect
6. #10622504C2semidirect
7. #10622501C2semidirect
8. #10622499C2semidirect
9. #10622485C2semidirect
10. #10622400C2semidirect
11. #10622386C2semidirect
12. #10622383C2semidirect
13. #10622381C2semidirect
14. #10622347C2semidirect
15. #10622342C2semidirect
19. C2×C11×C4⋊C4C22semidirect
25. #66983C22semidirect
28. C2×#4318C22semidirect
30. C2×#4314C22semidirect
37. #66946C22semidirect
39. #66943C22semidirect
42. C11×#107C22semidirect
43. C11×#107C22semidirect
46. C11×C22⋊C8C22semidirect
50. #66880C22semidirect
51. Dic11⋊C8C22semidirect
52. C8×Dic11C22semidirect
53. #66874C22semidirect
54. #66874C22semidirect
57. #66873C22semidirect
58. #66872C22semidirect
160. #480D11semidirect
223. C2×C4⋊C4C2×D11semidirect
225. #107C2×D11semidirect
226. #107C2×D11semidirect
240. C22⋊C8C2×D11semidirect
302. C11#3322semidirect

Maximal subgroups

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

subgroupindex
#106231432
#106230452
C11×#4802
#106226522
#106225792
#106225042
#106225012
#106224992
#106224852
#106224002
#106223862
#106223832
#106223812
#106223472
#106223422
#332211