Finite Group Databasebeta

← #28402809

Subgroups — #28402809

Order 14464.

460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299312C211yesmaximal, characteristic, complemented
2D4×C22⋊D113C211yesmaximal, characteristic, complemented
3#20298943C211yesmaximal, characteristic, complemented
4#20298923C211yesmaximal, characteristic, complemented
5#20298920C211yesmaximal, characteristic, complemented
6#20298886C211yesmaximal, characteristic, complemented
7#20298849C211yesmaximal, characteristic, complemented
8#20298848C211yesmaximal, characteristic, complemented
9#20298791C211yesmaximal, characteristic, complemented
10#20298730C211yesmaximal, characteristic, complemented
11D8×Dic113C211yesmaximal, characteristic, complemented
12#20298673C211yesmaximal, characteristic, complemented
13#20298603C211yesmaximal, characteristic, complemented
14#20298601C211yesmaximal, characteristic, complemented
15#447×C113C211yesmaximal, characteristic, complemented
16C22×C22⋊D113—21no—
17C2×D4×D113C2211yescharacteristic
18C2×#14268632C2211yescharacteristic, complemented
19C2×#14268631C2211yescharacteristic, complemented
20C2×#14268630C2211yescharacteristic, complemented
21#16813621C2211yescharacteristic, complemented
22#16813618C2211yescharacteristic
23#16813609—21no—
24#16813608—21no—
25#16813596C2211yescharacteristic
26#16813594—21no—
27#16813594—21no—
28#16813593C2211yescharacteristic
29#16813593C2211yescharacteristic, complemented
30#16813591—21no—
31#16813590—21no—
32D4×Dic113C2211yescharacteristic
33D4×Dic113C2211yescharacteristic, complemented
34C4×C22⋊D113C2211yescharacteristic
35#16813581C2211yescharacteristic, complemented
36#16813580C2211yescharacteristic, complemented
37#16813578—21no—
38#16813556C2211yescharacteristic, complemented
39#16813554C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813544C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic, complemented
44#16813543C2211yescharacteristic
45#16813543C2211yescharacteristic
46#16813543C2211yescharacteristic, complemented
47#16813543C2211yescharacteristic, complemented
48#16813543C2211yescharacteristic, complemented
49#16813542C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C22×D4×C113C2211yescharacteristic
53C2×D8×C113C2211yescharacteristic
54C2×D8×C113C2211yescharacteristic, complemented
55#121×C113C2211yescharacteristic, complemented
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C2×Dic226—21no—
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113—44no—
69C2×C22⋊D113D411yescharacteristic
70D4×D113—22no—
71D4×D113—41no—
72C22×Dic113—21no—
73C22×Dic113—21no—
74C2×C4×D113C2311yescharacteristic
75#14268632—41no—
76#14268631—41no—
77#14268630—41no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626D411yescharacteristic
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113D411yescharacteristic
91#14268624—21no—
92#14268624—21no—
93#14268624D411yescharacteristic
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97C24×C113—21no—
98C2×D4×C113—22no—
99C2×D4×C113—21no—
100C2×D4×C113—21no—
101C2×D4×C113—41no—
102C2×D4×C113C2311yescharacteristic
103C2×D4×C113C2311yescharacteristic
104C2×D4×C113C2311yescharacteristic
105C22×C4×C113C2311yescharacteristic
106D8×C113—22no—
107D8×C113—41no—
108C2×C8×C113C2311yescharacteristic
109C2×C8×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
111C22⋊C4×C113—21no—
112C23×C113—21no—
113C23×C113—21no—
114C23×C113—21no—
115C23×C113—42no—
116C23×C113—42no—
117C23×C113—81no—
118C23×C113C2×D411yescharacteristic
119C22×D113—21no—
120C22×D113—42no—
121C22×D113—42no—
122C22×D113—81no—
123C22×D113C2×D411yescharacteristic
124D4×C113—21no—
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—21no—
128D4×C113—21no—
129D4×C113—42no—
130D4×C113—81no—
131D4×C113#4112yes—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113C2×D411yescharacteristic
136C2×C4×C113C2411yescharacteristic
137C22⋊D113—22no—
138C22⋊D113—42no—
139C22⋊D113—42no—
140C22⋊D113—42no—
141C22⋊D113—42no—
142C22⋊D113—81no—
143C22⋊D113—81no—
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—42no—
148C2×Dic113—42no—
149C2×Dic113C2×D411yescharacteristic
150C2×Dic113C2×D411yescharacteristic
151C2×Dic113C2×D411yescharacteristic
152D452—21no—
153D452—21no—
154C4×D113—21no—
155C4×D113—21no—
156Dic226—81no—
157C8×C113—21no—
158C8×C113—21no—
159#11744751—21no—
160#11744751—21no—
161C22×C113—22no—
162C22×C113—21no—
163C22×C113—21no—
164C22×C113—21no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113—41no—
170C22×C113—41no—
171C22×C113—41no—
172C22×C113—41no—
173C22×C113—84no—
174C22×C113C22×D411yescharacteristic
175C2×D113—21no—
176C2×D113—21no—
177C2×D113—21no—
178C2×D113—41no—
179C2×D113—41no—
180C2×D113—41no—
181C2×D113—84no—
182C4×C113—21no—
183C4×C113—41no—
184C4×C113C2×#4111yescharacteristic
185C4×C113H(5,𝔽2)11yescharacteristic
186Dic113—21no—
187Dic113—21no—
188Dic113—41no—
189Dic113—41no—
190Dic113—41no—
191Dic113AGL(1,ℤ/8)12yes—
192C2×C113—42no—
193C2×C113—41no—
194C2×C113—81no—
195C2×C113—81no—
196C2×C113#54611yescharacteristic
197C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C113#57611yescharacteristic
199D113—41no—
200D113—81no—
201#3325—1131nomaximal, Sylow
202C113#332511yescharacteristic, complemented, Sylow
203#555—1131no—
204D42—1131no—
205#486—1131no—
206#482—1131no—
207#482—1131no—
208#476—1131no—
209#469—1131no—
210#469—1131no—
211#459—1131no—
212#447—1131no—
213#447D11311yescharacteristic, complemented
214C4×D8—1131no—
215#436—1131no—
216#418—1131no—
217#418—1131no—
218C22×D4—1131no—
219C22×D4—2261no—
220C22×D4C2×D11311yescharacteristic
221C2×D8—1131no—
222C2×D8C2×D11311yescharacteristic
223C2×D8C2×D11311yescharacteristic, complemented
224C2×M16—1131no—
225C2×M16—1131no—
226C4⋊Q8—1131no—
227#127—1131no—
228#124—2261no—
229#124—2261no—
230#121—1131no—
231#121—1131no—
232#121—1131no—
233#121—2261no—
234#121—2261no—
235#121C2×D11311yescharacteristic, complemented
236#120—2261no—
237#120—2261no—
238C4×D4—1131no—
239C4×D4—1131no—
240C4×D4—1131no—
241#117—1131no—
242#117—1131no—
243#117—2261no—
244#107—1131no—
245#106—1131no—
246#106—1131no—
247C4⋊C8—1131no—
248#102—1131no—
249#102—1131no—
250#102—1131no—
251#102—1131no—
252#102—1131no—
253#102—1131no—
254#102—1131no—
255#102—1131no—
256#102C2×D11311yescharacteristic
257#102C2×D11311yescharacteristic, complemented
258C22⋊C8—1131no—
259C22⋊C8C2×D11311yescharacteristic, complemented
260C4×C8—1131no—
261C24—21no—
262C24—2261no—
263C2×Q8—2261no—
264C2×D4—22no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—1131no—
269C2×D4—1131no—
270C2×D4—4524no—
271C2×D4—4521no—
272C2×D4—2261no—
273C2×D4—2261no—
274C2×D4—2261no—
275C2×D4—2261no—
276C2×D4—2261no—
277C2×D4—2261no—
278C2×D4—2262no—
279C2×D4C22×D11311yescharacteristic
280C2×D4C22×D11311yescharacteristic
281C2×D4C22×D11311yescharacteristic
282C22×C4—1131no—
283C22×C4—2261no—
284C22×C4—2261no—
285C22×C4C22×D11311yescharacteristic
286D8—22no—
287D8—41no—
288D8—4521no—
289M16—4521no—
290M16—4521no—
291C2×C8—1131no—
292C2×C8—1131no—
293C2×C8C22×D11311yescharacteristic
294C2×C8C22×D11311yescharacteristic
295C4⋊C4—1131no—
296C4⋊C4—1131no—
297C4⋊C4—1131no—
298C4⋊C4—1131no—
299C4⋊C4—2261no—
300C4⋊C4C22×D11311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—1131no—
303C22⋊C4—1131no—
304C22⋊C4—2261no—
305C22⋊C4—2261no—
306C22⋊C4—2261no—
307C22⋊C4—2261no—
308C22⋊C4—2261no—
309C22⋊C4—2261no—
310C22⋊C4—2261no—
311C42—1131no—
312C42—2261no—
313C42—2261no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—42no—
318C23—42no—
319C23—81no—
320C23—1131no—
321C23—9041no—
322C23—4522no—
323C23—4522no—
324C23—2261no—
325C23D4×D11311yescharacteristic
326Q8—9041no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—81no—
334D4—9041no—
335D4—9041no—
336D4—4522no—
337D4—4522no—
338D4—4522no—
339D4—4522no—
340D4—2262no—
341D4—2261no—
342D4—2261no—
343D4#1426864612yes—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—1131no—
348C2×C4—1131no—
349C2×C4—1131no—
350C2×C4—4522no—
351C2×C4—4522no—
352C2×C4—2261no—
353C2×C4—2261no—
354C2×C4—2261no—
355C2×C4—2261no—
356C2×C4—2261no—
357C2×C4D4×D11311yescharacteristic
358C2×C4C23×D11311yescharacteristic
359C8—21no—
360C8—21no—
361C8—2261no—
362C8—2261no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—84no—
376C22—9044no—
377C22—4521no—
378C22—4521no—
379C22—4521no—
380C22—2261no—
381C22—2261no—
382C22—2261no—
383C22C2×D4×D11311yescharacteristic
384C4—21no—
385C4—41no—
386C4—1132no—
387C4—4521no—
388C4—4521no—
389C4—4521no—
390C4—2261no—
391C4—2261no—
392C4C2×#1426864611yescharacteristic
393C4#1681366711yescharacteristic
394C2—41no—
395C2—42no—
396C2—81no—
397C2—81no—
398C2—9041no—
399C2—4521no—
400C2#2029923511yescharacteristic
401C2AGL(1,ℤ/8)×D11311yescharacteristic
402C2#2029939911yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#447×C113C2
socleC22×C113C22×D4
hypercenter#447D113
hypocenterC113#3325
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #20299312C2semidirect
2. D4×C22⋊D113C2semidirect
3. #20298943C2semidirect
4. #20298923C2semidirect
5. #20298920C2semidirect
6. #20298886C2semidirect
7. #20298849C2semidirect
8. #20298848C2semidirect
9. #20298791C2semidirect
10. #20298730C2semidirect
11. D8×Dic113C2semidirect
12. #20298673C2semidirect
13. #20298603C2semidirect
14. #20298601C2semidirect
15. #447×C113C2semidirect
18. C2×#14268632C22semidirect
19. C2×#14268631C22semidirect
20. C2×#14268630C22semidirect
21. #16813621C22semidirect
29. #16813593C22semidirect
33. D4×Dic113C22semidirect
35. #16813581C22semidirect
36. #16813580C22semidirect
38. #16813556C22semidirect
39. #16813554C22semidirect
40. #16813553C22semidirect
41. #16813551C22semidirect
42. #16813544C22semidirect
43. #16813544C22semidirect
46. #16813543C22semidirect
47. #16813543C22semidirect
48. #16813543C22semidirect
49. #16813542C22semidirect
50. #16813534C22semidirect
51. C8×Dic113C22semidirect
54. C2×D8×C113C22semidirect
55. #121×C113C22semidirect
57. #102×C113C22semidirect
58. C22⋊C8×C113C22semidirect
202. C113#3325semidirect
213. #447D113semidirect
223. C2×D8C2×D113semidirect
235. #121C2×D113semidirect
257. #102C2×D113semidirect
259. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993122
D4×C22⋊D1132
#202989432
#202989232
#202989202
#202988862
#202988492
#202988482
#202987912
#202987302
D8×Dic1132
#202986732
#202986032
#202986012
#447×C1132
#3325113