Finite Group Databasebeta

← #13080813

Subgroups — #13080813

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#10623337C211yesmaximal, characteristic, complemented
2#10623061C211yesmaximal, characteristic, complemented
3C11×#418C211yesmaximal, characteristic, complemented
4#10622830C211yesmaximal, characteristic, complemented
5#10622747C211yesmaximal, characteristic, complemented
6#10622741C211yesmaximal, characteristic, complemented
7#10622609C211yesmaximal, characteristic, complemented
8#10622400C211yesmaximal, characteristic, complemented
9#10622395C211yesmaximal, characteristic, complemented
10#10622394C211yesmaximal, characteristic, complemented
11#10622387C211yesmaximal, characteristic, complemented
12#10622384C211yesmaximal, characteristic, complemented
13#10622381C211yesmaximal, characteristic, complemented
14#10622379C211yesmaximal, characteristic, complemented
15#10622369C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×C11×M16C2211yescharacteristic
19C11×#117C2211yescharacteristic
20#67006—21no—
21C2×C22⋊Dic11—21no—
22#66992—21no—
23#66991C2211yescharacteristic
24#66989C2211yescharacteristic
25#66988—21no—
26D4×Dic11C2211yescharacteristic
27C2×#4323C2211yescharacteristic
28C2×#4323C2211yescharacteristic
29#66983C2211yescharacteristic
30C4×C22⋊D11C2211yescharacteristic
31#66977C2211yescharacteristic
32C2×#4314C2211yescharacteristic, complemented
33C2×#4313C2211yescharacteristic, complemented
34#66948C2211yescharacteristic, complemented
35#66946C2211yescharacteristic, complemented
36C4⋊C4×D11C2211yescharacteristic, complemented
37#66943C2211yescharacteristic, complemented
38#66937—21no—
39#66936—21no—
40#66929—21no—
41C4×D44—21no—
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49#66885C2211yescharacteristic, complemented
50(C2×D11)⋊C8C2211yescharacteristic, complemented
51#66882C2211yescharacteristic, complemented
52#66880C2211yescharacteristic, complemented
53Dic11⋊C8C2211yescharacteristic, complemented
54C8×Dic11C2211yescharacteristic, complemented
55#66874C2211yescharacteristic, complemented
56#66874C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C24×C11—21no—
60C2×D4×C11—22no—
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C2×D4×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72#4341—22no—
73#4341—41no—
74C2×D44—21no—
75C2×D44C2311yescharacteristic
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×Dic22C2311yescharacteristic
80C11×M16—41no—
81C2×C8×C11C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C42×C11—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92C22⋊Dic11D411yescharacteristic
93#4323—22no—
94#4323—41no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4D411yescharacteristic
99C4⋊Dic11—21no—
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4D411yescharacteristic
106C4×Dic11C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109#4314—41no—
110#4313—41no—
111#3322—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—42no—
115C23×C11—42no—
116C23×C11—81no—
117C23×C11C2×D411yescharacteristic
118C22×D11—21no—
119C22×D11C2×D411yescharacteristic
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—42no—
124D4×C11#4112yes—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C22⋊D11—41no—
132C22⋊D11—42no—
133C22⋊D11—81no—
134C22⋊D11—81no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—42no—
139C2×Dic11—81no—
140C2×Dic11C2×D411yescharacteristic
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143D44—21no—
144D44—21no—
145D44—42no—
146C4×D11—21no—
147C4×D11—21no—
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#480—111no—
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#418D1111yescharacteristic, complemented
170#417—111no—
171C22×C11—21no—
172C22×C11—22no—
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
182C2×D11—21no—
183C2×D11—21no—
184C2×D11—21no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—41no—
188C4×C11—21no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11C2×#4111yescharacteristic
192C4×C11H(5,𝔽2)11yescharacteristic
193Dic11—21no—
194Dic11—21no—
195Dic11—21no—
196Dic11—41no—
197Dic11—41no—
198Dic11—41no—
199C2×#41—111no—
200C22×D4C2×D1111yescharacteristic
201C2×SD16—111no—
202C2×D8—111no—
203C2×D8—111no—
204C2×M16—111no—
205C2×M16C2×D1111yescharacteristic
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—111no—
215#121—221no—
216#121—221no—
217#120—221no—
218C4×D4—111no—
219C4×D4—111no—
220C4×D4—111no—
221C4×D4—221no—
222#117C2×D1111yescharacteristic
223C2×C4⋊C4—111no—
224C2×C22⋊C4—221no—
225#107—111no—
226#107—111no—
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#102C2×D1111yescharacteristic
236#102C2×D1111yescharacteristic
237#102C2×D1111yescharacteristic
238#102C2×D1111yescharacteristic
239C22⋊C8—111no—
240C22⋊C8—111no—
241C4×C8—111no—
242C2×C11—41no—
243C2×C11—42no—
244C2×C11—81no—
245C2×C11#54611yescharacteristic
246C2×C11#57511yescharacteristic
247C2×C11#57611yescharacteristic
248D11—41no—
249D11—81no—
250C24—21no—
251#41—222no—
252#41—441no—
253C2×Q8—111no—
254C2×D4—22no—
255C2×D4—21no—
256C2×D4—41no—
257C2×D4—111no—
258C2×D4—111no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4C22×D1111yescharacteristic
264C2×D4C22×D1111yescharacteristic
265C22×C4—111no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4C22×D1111yescharacteristic
271SD16—441no—
272D8—222no—
273D8—441no—
274M16—41no—
275M16—441no—
276C2×C8—111no—
277C2×C8—111no—
278C2×C8C22×D1111yescharacteristic
279C2×C8C22×D1111yescharacteristic
280C4⋊C4—111no—
281C4⋊C4—111no—
282C4⋊C4—111no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
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—21no—
301C42—111no—
302C11#332211yescharacteristic, complemented, Sylow
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—111no—
309C23—221no—
310C23D4×D1111yescharacteristic
311Q8—221no—
312Q8—221no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—221no—
318D4—221no—
319D4—442no—
320D4—441no—
321D4—442no—
322D4—881no—
323D4—881no—
324D4#433912yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—111no—
330C2×C4—111no—
331C2×C4—111no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—442no—
338C2×C4—881no—
339C2×C4—881no—
340C2×C4—881no—
341C2×C4D4×D1111yescharacteristic
342C2×C4C23×D1111yescharacteristic
343C8—21no—
344C8—21no—
345C8—221no—
346C8—221no—
347C22—21no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—84no—
357C22—221no—
358C22—221no—
359C22—221no—
360C22—441no—
361C22—441no—
362C22—441no—
363C22C2×D4×D1111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—221no—
368C4—221no—
369C4—221no—
370C4—441no—
371C4—441no—
372C4—441no—
373C4C2×#433911yescharacteristic
374C4#6703711yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—441no—
379C2—881no—
380C2#1062302111yescharacteristic
381C2#1062330411yescharacteristic
382C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#418C2
socleC22×C11C22×D4
hypercenter#418D11
hypocenterC11#3322
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #10623337C2semidirect
2. #10623061C2semidirect
3. C11×#418C2semidirect
4. #10622830C2semidirect
5. #10622747C2semidirect
6. #10622741C2semidirect
7. #10622609C2semidirect
8. #10622400C2semidirect
9. #10622395C2semidirect
10. #10622394C2semidirect
11. #10622387C2semidirect
12. #10622384C2semidirect
13. #10622381C2semidirect
14. #10622379C2semidirect
15. #10622369C2semidirect
32. C2×#4314C22semidirect
33. C2×#4313C22semidirect
34. #66948C22semidirect
35. #66946C22semidirect
36. C4⋊C4×D11C22semidirect
37. #66943C22semidirect
49. #66885C22semidirect
50. (C2×D11)⋊C8C22semidirect
51. #66882C22semidirect
52. #66880C22semidirect
53. Dic11⋊C8C22semidirect
54. C8×Dic11C22semidirect
55. #66874C22semidirect
56. #66874C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
169. #418D11semidirect
302. C11#3322semidirect

Maximal subgroups

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

subgroupindex
#106233372
#106230612
C11×#4182
#106228302
#106227472
#106227412
#106226092
#106224002
#106223952
#106223942
#106223872
#106223842
#106223812
#106223792
#106223692
#332211