Finite Group Databasebeta

← #28400513

Subgroups — #28400513

Order 14464.

462 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D113C211yesmaximal, characteristic
2#117×D113C211yesmaximal, characteristic, complemented
3#20298923C211yesmaximal, characteristic, complemented
4#20298922C211yesmaximal, characteristic, complemented
5#20298919C211yesmaximal, characteristic, complemented
6#20298918C211yesmaximal, characteristic, complemented
7#20298915C211yesmaximal, characteristic, complemented
8#20298913C211yesmaximal, characteristic, complemented
9#20298910C211yesmaximal, characteristic, complemented
10#20298639C211yesmaximal, characteristic, complemented
11#20298637C211yesmaximal, characteristic, complemented
12#20298601C211yesmaximal, characteristic, complemented
13#20298601C211yesmaximal, characteristic, complemented
14#20298560C211yesmaximal, characteristic, complemented
15#482×C113C211yesmaximal, characteristic, complemented
16C2×D4×D113—21no—
17C2×D4×D113C2211yescharacteristic
18C22×C4×D113C2211yescharacteristic
19C2×#14268630C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21#16813597C2211yescharacteristic
22#16813596C2211yescharacteristic
23#16813595—21no—
24#16813594—21no—
25#16813593C2211yescharacteristic
26#16813581C2211yescharacteristic, complemented
27#16813580C2211yescharacteristic
28#16813580C2211yescharacteristic
29#16813579—21no—
30#16813578—21no—
31C4⋊C4×D113C2211yescharacteristic
32C4⋊C4×D113C2211yescharacteristic, complemented
33C4⋊C4×D113C2211yescharacteristic, complemented
34C22⋊C4×D113—21no—
35C22⋊C4×D113—21no—
36C42×D113—21no—
37#16813556C2211yescharacteristic, complemented
38#16813555C2211yescharacteristic, complemented
39#16813555C2211yescharacteristic, complemented
40#16813554C2211yescharacteristic, complemented
41#16813553C2211yescharacteristic, complemented
42#16813553C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic, complemented
45#16813543C2211yescharacteristic, complemented
46#16813543C2211yescharacteristic, complemented
47#16813542C2211yescharacteristic, complemented
48#16813542C2211yescharacteristic, complemented
49C22⋊#11744751C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic, complemented
51#16813534C2211yescharacteristic, complemented
52#121×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic, complemented
54#107×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56#102×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C23×D113D411yescharacteristic
61C2×D452—21no—
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66D4×D113—22no—
67D4×D113—22no—
68D4×D113—44no—
69C22×Dic113D411yescharacteristic
70C2×C4×D113—22no—
71C2×C4×D113—22no—
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74C2×C4×D113—21no—
75C2×C4×D113D411yescharacteristic
76C2×C4×D113D411yescharacteristic
77C2×C4×D113C2311yescharacteristic
78C2×C4×D113C2311yescharacteristic
79#14268630—22no—
80#14268630—22no—
81C2×#11744751C2311yescharacteristic
82C2×#11744751C2311yescharacteristic
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85C4⋊Dic113C2311yescharacteristic
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95C4×Dic113—21no—
96C4×Dic113—21no—
97C4×Dic113—21no—
98C2×D4×C113—21no—
99C2×D4×C113C2311yescharacteristic
100C22×C4×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C2×C8×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C22⋊C4×C113—21no—
108C42×C113—21no—
109C23×C113—21no—
110C23×C113C2×D411yescharacteristic
111C22×D113—22no—
112C22×D113—22no—
113C22×D113—21no—
114C22×D113—41no—
115C22×D113—42no—
116C22×D113—42no—
117C22×D113—42no—
118C22×D113C2×D411yescharacteristic
119C22×D113C2×D411yescharacteristic
120D4×C113—21no—
121D4×C113—21no—
122D4×C113—42no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2411yescharacteristic
130C22⋊D113—42no—
131C22⋊D113—42no—
132C22⋊D113—42no—
133C2×Dic113—22no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139D452—21no—
140D452—21no—
141D452—42no—
142C4×D113—22no—
143C4×D113—21no—
144C4×D113—21no—
145C4×D113—22no—
146C4×D113—42no—
147C4×D113—42no—
148C4×D113—42no—
149C4×D113#4112yes—
150C4×D113#4112yes—
151C8×C113—21no—
152C8×C113—21no—
153#11744751—21no—
154#11744751—21no—
155C22×C113—21no—
156C22×C113—21no—
157C22×C113—21no—
158C22×C113—41no—
159C22×C113—41no—
160C22×C113—41no—
161C22×C113C22×D411yescharacteristic
162C2×D113—21no—
163C2×D113—21no—
164C2×D113—21no—
165C2×D113—21no—
166C2×D113—44no—
167C2×D113—41no—
168C2×D113—41no—
169C2×D113—41no—
170C2×D113—84no—
171C2×D113#12312yes—
172C2×D113AGL(1,ℤ/8)12yes—
173C4×C113—21no—
174C4×C113—41no—
175C4×C113—41no—
176C4×C113—41no—
177C4×C113C2×#4111yescharacteristic
178C4×C113C2×#4111yescharacteristic
179Dic113—21no—
180Dic113—41no—
181Dic113—41no—
182Dic113—41no—
183Dic113#12312yes—
184C2×C113—41no—
185C2×C113—81no—
186C2×C113C2×#12311yescharacteristic
187C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
188C2×C113#57511yescharacteristic
189D113—22no—
190D113—22no—
191D113—81no—
192#3094—1131nomaximal, Sylow
193C113#309411yescharacteristic, complemented, Sylow
194C2×#121—1131no—
195C2×#117—1131no—
196#482—1131no—
197#482—1131no—
198#482—1131no—
199#482D11311yescharacteristic, complemented
200#481—1131no—
201#481—1131no—
202#480—1131no—
203#480—1131no—
204#428—1131no—
205#428—1131no—
206#418—1131no—
207#418—1131no—
208#407—1131no—
209C22×D4—1131no—
210C22×D4—2261no—
211C23×C4—1131no—
212C2×M16—1131no—
213C2×M16—1131no—
214#121—1131no—
215#121—1131no—
216#121—1131no—
217#121—2261no—
218#121—2261no—
219#121C2×D11311yescharacteristic
220#117—1131no—
221#117—1131no—
222#117—1131no—
223#117—2261no—
224#117—2261no—
225#117C2×D11311yescharacteristic, complemented
226C2×C4⋊C4—1131no—
227C2×C4⋊C4—1131no—
228C2×C4⋊C4—1131no—
229C2×C22⋊C4—2261no—
230C2×C22⋊C4—2261no—
231C2×C42—2261no—
232#107—1131no—
233#107—1131no—
234#107—1131no—
235#107C2×D11311yescharacteristic, complemented
236#106—1131no—
237#106—1131no—
238#106—1131no—
239#106C2×D11311yescharacteristic, complemented
240#102—1131no—
241#102—1131no—
242#102—1131no—
243#102—1131no—
244#102—1131no—
245#102—1131no—
246#102C2×D11311yescharacteristic, complemented
247#102C2×D11311yescharacteristic, complemented
248C22⋊C8—1131no—
249C22⋊C8—1131no—
250C22⋊C8—1131no—
251C22⋊C8C2×D11311yescharacteristic, complemented
252C24—1131no—
253C24—2261no—
254C2×D4—21no—
255C2×D4—1131no—
256C2×D4—4524no—
257C2×D4—2261no—
258C2×D4—2262no—
259C2×D4—2262no—
260C2×D4—2261no—
261C2×D4—2261no—
262C2×D4—2261no—
263C2×D4C22×D11311yescharacteristic
264C22×C4—1131no—
265C22×C4—1131no—
266C22×C4—1131no—
267C22×C4—1131no—
268C22×C4—1131no—
269C22×C4—2262no—
270C22×C4—2262no—
271C22×C4—2261no—
272C22×C4—2261no—
273C22×C4—2261no—
274C22×C4C22×D11311yescharacteristic
275M16—2262no—
276M16—2262no—
277C2×C8—1131no—
278C2×C8—1131no—
279C2×C8C22×D11311yescharacteristic
280C2×C8C22×D11311yescharacteristic
281C4⋊C4—1131no—
282C4⋊C4—1131no—
283C4⋊C4—1131no—
284C4⋊C4—2261no—
285C4⋊C4—2261no—
286C4⋊C4—2261no—
287C4⋊C4C22×D11311yescharacteristic
288C4⋊C4C22×D11311yescharacteristic
289C4⋊C4C22×D11311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C42—21no—
299C42—2261no—
300C42—2261no—
301C42—2261no—
302C23—21no—
303C23—1131no—
304C23—1131no—
305C23—4521no—
306C23—4522no—
307C23—4522no—
308C23—4522no—
309C23—2262no—
310C23—2262no—
311C23—2261no—
312C23D4×D11311yescharacteristic
313D4—21no—
314D4—21no—
315D4—42no—
316D4—4522no—
317D4—4522no—
318D4—4522no—
319D4—4522no—
320D4—2261no—
321D4—2261no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—1131no—
328C2×C4—1132no—
329C2×C4—1132no—
330C2×C4—1131no—
331C2×C4—4522no—
332C2×C4—4522no—
333C2×C4—4522no—
334C2×C4—2262no—
335C2×C4—2262no—
336C2×C4—2262no—
337C2×C4—2261no—
338C2×C4—2261no—
339C2×C4—2261no—
340C2×C4—2261no—
341C2×C4—2261no—
342C2×C4D4×D11311yescharacteristic
343C2×C4C23×D11311yescharacteristic
344C8—21no—
345C8—21no—
346C8—2261no—
347C8—2261no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—1132no—
355C22—1132no—
356C22—9044no—
357C22—4524no—
358C22—4521no—
359C22—4521no—
360C22—4521no—
361C22—2261no—
362C22—2261no—
363C22—2261no—
364C22—2261no—
365C22C2×D4×D11311yescharacteristic
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—1132no—
371C4—4521no—
372C4—4521no—
373C4—4521no—
374C4—2261no—
375C4#41×D11311yescharacteristic
376C4#41×D11311yescharacteristic
377C2—41no—
378C2—81no—
379C2—9041no—
380C2—2262no—
381C2—2262no—
382C2#123×D11311yescharacteristic
383C2AGL(1,ℤ/8)×D11311yescharacteristic
384C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#482×C113C2
socleC22×C113C22×D4
prime radical#121×D113C2
hypercenter#482D113
hypocenterC113#3094
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #117×D113C2semidirect
3. #20298923C2semidirect
4. #20298922C2semidirect
5. #20298919C2semidirect
6. #20298918C2semidirect
7. #20298915C2semidirect
8. #20298913C2semidirect
9. #20298910C2semidirect
10. #20298639C2semidirect
11. #20298637C2semidirect
12. #20298601C2semidirect
13. #20298601C2semidirect
14. #20298560C2semidirect
15. #482×C113C2semidirect
26. #16813581C22semidirect
32. C4⋊C4×D113C22semidirect
33. C4⋊C4×D113C22semidirect
37. #16813556C22semidirect
38. #16813555C22semidirect
39. #16813555C22semidirect
40. #16813554C22semidirect
41. #16813553C22semidirect
42. #16813553C22semidirect
43. #16813544C22semidirect
44. #16813544C22semidirect
45. #16813543C22semidirect
46. #16813543C22semidirect
47. #16813542C22semidirect
48. #16813542C22semidirect
49. C22⋊#11744751C22semidirect
50. #16813534C22semidirect
51. #16813534C22semidirect
53. #117×C113C22semidirect
54. #107×C113C22semidirect
55. #106×C113C22semidirect
56. #102×C113C22semidirect
57. #102×C113C22semidirect
58. C22⋊C8×C113C22semidirect
193. C113#3094semidirect
199. #482D113semidirect
225. #117C2×D113semidirect
235. #107C2×D113semidirect
239. #106C2×D113semidirect
246. #102C2×D113semidirect
247. #102C2×D113semidirect
251. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#121×D1132
#117×D1132
#202989232
#202989222
#202989192
#202989182
#202989152
#202989132
#202989102
#202986392
#202986372
#202986012
#202985602
#482×C1132
#3094113