Finite Group Databasebeta

← #13080465

Subgroups — #13080465

Order 1408.

420 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#10623226C211yesmaximal, characteristic, complemented
2#10623207C211yesmaximal, characteristic, complemented
3C11×#488C211yesmaximal, characteristic, complemented
4#10622679C211yesmaximal, characteristic, complemented
5#10622670C211yesmaximal, characteristic, complemented
6#10622424C211yesmaximal, characteristic, complemented
7#10622422C211yesmaximal, characteristic, complemented
8#10622420C211yesmaximal, characteristic, complemented
9#10622417C211yesmaximal, characteristic, complemented
10#10622397C211yesmaximal, characteristic, complemented
11#10622388C211yesmaximal, characteristic, complemented
12#10622386C211yesmaximal, characteristic, complemented
13D11×#102C211yesmaximal, characteristic, complemented
14C4×D88C211yesmaximal, characteristic, complemented
15C8×D44C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C11×#125C2211yescharacteristic, complemented
19C11×#124C2211yescharacteristic
20#66999C2211yescharacteristic
21C2×#4325C2211yescharacteristic, complemented
22#66991C2211yescharacteristic
23C2×#4323C2211yescharacteristic
24C2×D88C2211yescharacteristic
25C2×C8×D11C2211yescharacteristic
26C2×C8×D11C2211yescharacteristic, complemented
27#66951—21no—
28#66948—21no—
29#66948C2211yescharacteristic
30#66948C2211yescharacteristic, complemented
31#66947—21no—
32#66946—21no—
33#66945C2211yescharacteristic, complemented
34C4⋊C4×D11C2211yescharacteristic
35#66937—21no—
36#66936—21no—
37#66935—21no—
38C22⋊C4×D11—21no—
39C4×D44C2211yescharacteristic
40C4×D44C2211yescharacteristic
41C4×D44C2211yescharacteristic, complemented
42C11×#103C2211yescharacteristic, complemented
43C11×#103C2211yescharacteristic, complemented
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46C4×C8×C11C2211yescharacteristic, complemented
47#66899C2211yescharacteristic, complemented
48#66896C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic, complemented
51(C2×D11)⋊C8C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic, complemented
53#66882C2211yescharacteristic, complemented
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic, complemented
57#66871C2211yescharacteristic, complemented
58C4⋊(C11⋊C8)C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64#4343—22no—
65#4343—41no—
66D4×D11—22no—
67D4×D11—41no—
68C2×D44—21no—
69C2×D44—21no—
70C2×D44—21no—
71C2×D44D411yescharacteristic
72C2×D44C2311yescharacteristic
73C2×D44C2311yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×C4×D11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C42×C11C2311yescharacteristic
89C22⋊Dic11—21no—
90#4325—41no—
91#4323—41no—
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)⋊C4—21no—
98(C2×D11)⋊C4D411yescharacteristic
99(C2×D11)⋊C4D411yescharacteristic
100C4⋊Dic11D411yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105C4×Dic11—21no—
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108D88—22no—
109C8×D11—41no—
110C8×D11—41no—
111#3297—111nomaximal, Sylow
112C23×C11—21no—
113C22×D11—21no—
114C22×D11—21no—
115C22×D11—42no—
116C22×D11—42no—
117C22×D11—81no—
118C22×D11C2×D411yescharacteristic
119C22×D11C2×D411yescharacteristic
120Q8×C11—21no—
121Q8×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2411yescharacteristic
130C22⋊D11—42no—
131C22⋊D11—81no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136D44—22no—
137D44—21no—
138D44—21no—
139D44—21no—
140D44—42no—
141D44—42no—
142D44—81no—
143D44#4112yes—
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—21no—
148C4×D11—42no—
149C4×D11—81no—
150C4×D11—81no—
151C4×D11—81no—
152C8×C11—21no—
153C8×C11—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156#553—111no—
157#546—111no—
158#488D1111yescharacteristic, complemented
159#484—111no—
160#482—111no—
161#478—111no—
162#466—111no—
163#465—111no—
164#463—111no—
165#449—111no—
166#447—111no—
167C4×D8—111no—
168C8×D4—111no—
169#416—111no—
170C2×#102—111no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11C22×D411yescharacteristic
175C2×D11—21no—
176C2×D11—21no—
177C2×D11—22no—
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—84no—
187C2×D11#13512yes—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11C2×#4111yescharacteristic
194C4×C11H(5,𝔽2)11yescharacteristic
195Dic11—21no—
196Dic11—21no—
197Dic11—41no—
198Dic11—41no—
199C2×#41—111no—
200C22×D4—111no—
201C2×SD16—111no—
202C2×D8—111no—
203C2×D8—111no—
204C22×C8—111no—
205C22×C8—111no—
206#126—221no—
207#125C2×D1111yescharacteristic, complemented
208#124C2×D1111yescharacteristic
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#117—111no—
223C2×C4⋊C4—111no—
224C2×C22⋊C4—221no—
225#107—111no—
226#107—111no—
227#106—111no—
228C4⋊C8—111no—
229#103—111no—
230#103C2×D1111yescharacteristic, complemented
231#103C2×D1111yescharacteristic, complemented
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⋊C8—111no—
241C4×C8C2×D1111yescharacteristic, complemented
242C2×C11—81no—
243C2×C11#54611yescharacteristic
244C2×C11C2×#13511yescharacteristic
245C2×C11#57611yescharacteristic
246D11—22no—
247D11—41no—
248D11—42no—
249D11—81no—
250C24—221no—
251#41—222no—
252#41—441no—
253C2×Q8C22×D1111yescharacteristic
254C2×D4—111no—
255C2×D4—111no—
256C2×D4—111no—
257C2×D4—221no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—222no—
262C2×D4—221no—
263C2×D4—441no—
264C2×D4C22×D1111yescharacteristic
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271SD16—441no—
272D8—222no—
273D8—441no—
274C2×C8—111no—
275C2×C8—111no—
276C2×C8—441no—
277C2×C8—441no—
278C2×C8C22×D1111yescharacteristic
279C2×C8C22×D1111yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—111no—
283C4⋊C4—111no—
284C4⋊C4—111no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4C22×D1111yescharacteristic
288C4⋊C4C22×D1111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—111no—
292C22⋊C4—111no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C42—221no—
301C42C22×D1111yescharacteristic
302C11#329711yescharacteristic, complemented, Sylow
303C23—21no—
304C23—111no—
305C23—111no—
306C23—221no—
307C23—221no—
308C23—442no—
309C23—442no—
310C23—881no—
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—112no—
316D4—222no—
317D4—221no—
318D4—221no—
319D4—221no—
320D4—442no—
321D4—442no—
322D4—442no—
323D4—881no—
324D4—881no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—111no—
329C2×C4—111no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—442no—
337C2×C4—881no—
338C2×C4—881no—
339C2×C4—881no—
340C2×C4D4×D1111yescharacteristic
341C2×C4D4×D1111yescharacteristic
342C2×C4C23×D1111yescharacteristic
343C8—21no—
344C8—21no—
345C8—221no—
346C8—221no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—112no—
351C22—221no—
352C22—221no—
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—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—221no—
370C4—221no—
371C4—441no—
372C4—441no—
373C4#41×D1111yescharacteristic
374C4#6704211yescharacteristic
375C2—81no—
376C2—222no—
377C2—441no—
378C2—442no—
379C2—881no—
380C2#1062320711yescharacteristic
381C2D11×#13511yescharacteristic
382C2#1062330011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#488C2
socleC22×C11C22×D4
hypercenter#488D11
hypocenterC11#3297
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #10623226C2semidirect
2. #10623207C2semidirect
3. C11×#488C2semidirect
4. #10622679C2semidirect
5. #10622670C2semidirect
6. #10622424C2semidirect
7. #10622422C2semidirect
8. #10622420C2semidirect
9. #10622417C2semidirect
10. #10622397C2semidirect
11. #10622388C2semidirect
12. #10622386C2semidirect
13. D11×#102C2semidirect
14. C4×D88C2semidirect
15. C8×D44C2semidirect
18. C11×#125C22semidirect
21. C2×#4325C22semidirect
26. C2×C8×D11C22semidirect
30. #66948C22semidirect
33. #66945C22semidirect
41. C4×D44C22semidirect
42. C11×#103C22semidirect
43. C11×#103C22semidirect
46. C4×C8×C11C22semidirect
47. #66899C22semidirect
50. #66885C22semidirect
52. (C2×D11)⋊C8C22semidirect
53. #66882C22semidirect
56. #66872C22semidirect
57. #66871C22semidirect
58. C4⋊(C11⋊C8)C22semidirect
158. #488D11semidirect
207. #125C2×D11semidirect
230. #103C2×D11semidirect
231. #103C2×D11semidirect
241. C4×C8C2×D11semidirect
302. C11#3297semidirect

Maximal subgroups

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

subgroupindex
#106232262
#106232072
C11×#4882
#106226792
#106226702
#106224242
#106224222
#106224202
#106224172
#106223972
#106223882
#106223862
D11×#1022
C4×D882
C8×D442
#329711