Finite Group Databasebeta

← #28402798

Subgroups — #28402798

Order 14464.

448 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299319C211yesmaximal, characteristic, complemented
2D4×C22⋊D113C211yesmaximal, characteristic
3#20298943C211yesmaximal, characteristic, complemented
4#20298923C211yesmaximal, characteristic, complemented
5#20298921C211yesmaximal, characteristic, complemented
6#20298876C211yesmaximal, characteristic, complemented
7#20298846C211yesmaximal, characteristic, complemented
8#20298841C211yesmaximal, characteristic, complemented
9#20298796C211yesmaximal, characteristic, complemented
10#20298747C211yesmaximal, characteristic, complemented
11SD16×Dic113C211yesmaximal, characteristic, complemented
12#20298673C211yesmaximal, characteristic, complemented
13#20298603C211yesmaximal, characteristic, complemented
14#20298601C211yesmaximal, characteristic, complemented
15#450×C113C211yesmaximal, characteristic, complemented
16C22×C22⋊D113—21no—
17C2×D4×D113C2211yescharacteristic
18C2×#14268634C2211yescharacteristic, complemented
19C2×#14268631C2211yescharacteristic, complemented
20C2×#14268630C2211yescharacteristic, complemented
21#16813621C2211yescharacteristic, complemented
22#16813618C2211yescharacteristic
23#16813617—21no—
24#16813615—21no—
25#16813608—21no—
26#16813598C2211yescharacteristic, complemented
27#16813596C2211yescharacteristic
28#16813594—21no—
29#16813593C2211yescharacteristic
30#16813591—21no—
31#16813590—21no—
32Q8×Dic113C2211yescharacteristic, complemented
33#16813587—21no—
34D4×Dic113C2211yescharacteristic
35C4×C22⋊D113C2211yescharacteristic
36#16813581C2211yescharacteristic, complemented
37#16813580C2211yescharacteristic, complemented
38#16813556C2211yescharacteristic, complemented
39#16813555C2211yescharacteristic, complemented
40#16813554C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813546C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic, complemented
45#16813543C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic, complemented
48#16813543C2211yescharacteristic, complemented
49#16813542C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C22×D4×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic, complemented
55C22⋊Q8×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—44no—
68C2×C22⋊D113D411yescharacteristic
69D4×D113—22no—
70D4×D113—41no—
71C22×Dic113—21no—
72C2×C4×D113C2311yescharacteristic
73#14268634—41no—
74#14268631—41no—
75#14268630—41no—
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C4⋊Dic113—21no—
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82#14268626—21no—
83#14268626—21no—
84#14268626D411yescharacteristic
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113D411yescharacteristic
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624D411yescharacteristic
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97C24×C113—21no—
98C2×Q8×C113C2311yescharacteristic
99C2×D4×C113—22no—
100C2×D4×C113—21no—
101C2×D4×C113—41no—
102C2×D4×C113C2311yescharacteristic
103C2×D4×C113C2311yescharacteristic
104C22×C4×C113C2311yescharacteristic
105SD16×C113—22no—
106SD16×C113—41no—
107C2×C8×C113C2311yescharacteristic
108C2×C8×C113C2311yescharacteristic
109C4⋊C4×C113—21no—
110C4⋊C4×C113C2311yescharacteristic
111C22⋊C4×C113—21no—
112C23×C113—21no—
113C23×C113—21no—
114C23×C113—42no—
115C23×C113—42no—
116C23×C113—81no—
117C23×C113C2×D411yescharacteristic
118C22×D113—21no—
119C22×D113—42no—
120C22×D113—42no—
121C22×D113—81no—
122C22×D113C2×D411yescharacteristic
123Q8×C113—21no—
124Q8×C113—21no—
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—21no—
128D4×C113—42no—
129D4×C113#4112yes—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113C2×D411yescharacteristic
135C2×C4×C113C2411yescharacteristic
136C22⋊D113—22no—
137C22⋊D113—42no—
138C22⋊D113—42no—
139C22⋊D113—42no—
140C22⋊D113—42no—
141C22⋊D113—81no—
142C2×Dic113—21no—
143C2×Dic113—21no—
144C2×Dic113—21no—
145C2×Dic113—42no—
146C2×Dic113C2×D411yescharacteristic
147C2×Dic113C2×D411yescharacteristic
148C2×Dic113C2×D411yescharacteristic
149D452—21no—
150D452—21no—
151C4×D113—21no—
152C4×D113—21no—
153Dic226—42no—
154C8×C113—21no—
155C8×C113—21no—
156#11744751—21no—
157#11744751—21no—
158C22×C113—22no—
159C22×C113—21no—
160C22×C113—21no—
161C22×C113—21no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113—84no—
168C22×C113C22×D411yescharacteristic
169C2×D113—21no—
170C2×D113—21no—
171C2×D113—21no—
172C2×D113—41no—
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—84no—
176C4×C113—21no—
177C4×C113—41no—
178C4×C113—41no—
179C4×C113C2×#4111yescharacteristic
180C4×C113H(5,𝔽2)11yescharacteristic
181Dic113—21no—
182Dic113—21no—
183Dic113—41no—
184Dic113—41no—
185Dic113—41no—
186Dic113AGL(1,ℤ/8)12yes—
187C2×C113—42no—
188C2×C113—41no—
189C2×C113—81no—
190C2×C113#54611yescharacteristic
191C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C113#57711yescharacteristic
193D113—41no—
194D113—81no—
195#3324—1131nomaximal, Sylow
196C113#332411yescharacteristic, complemented, Sylow
197#556—1131no—
198D42—1131no—
199#486—1131no—
200#482—1131no—
201#482—1131no—
202#474—1131no—
203#468—1131no—
204#468—1131no—
205#460—1131no—
206#450—1131no—
207#450D11311yescharacteristic, complemented
208C4×SD16—1131no—
209#436—1131no—
210#418—1131no—
211#418—1131no—
212C22×D4—1131no—
213C22×D4—2261no—
214C22×D4C2×D11311yescharacteristic
215C2×SD16—1131no—
216C2×SD16C2×D11311yescharacteristic
217C2×SD16C2×D11311yescharacteristic, complemented
218C2×M16—1131no—
219C2×M16—1131no—
220C4⋊Q8—1131no—
221#127—1131no—
222#126—2261no—
223#126—2261no—
224#124—2261no—
225C22⋊Q8—1131no—
226C22⋊Q8C2×D11311yescharacteristic, complemented
227#121—1131no—
228#121—1131no—
229#121—2261no—
230#120—2261no—
231#120—2261no—
232C4×Q8—1131no—
233C4×Q8—2261no—
234C4×D4—1131no—
235C4×D4—1131no—
236#117—1131no—
237#117—1131no—
238#107—1131no—
239#107—1131no—
240#106—1131no—
241C4⋊C8—1131no—
242#103—1131no—
243#102—1131no—
244#102—1131no—
245#102—1131no—
246#102—1131no—
247#102—1131no—
248#102—1131no—
249#102—1131no—
250#102C2×D11311yescharacteristic
251#102C2×D11311yescharacteristic, complemented
252C22⋊C8—1131no—
253C22⋊C8C2×D11311yescharacteristic, complemented
254C4×C8—1131no—
255C24—21no—
256C24—2261no—
257C2×Q8—2261no—
258C2×Q8C22×D11311yescharacteristic
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—1131no—
263C2×D4—1131no—
264C2×D4—4524no—
265C2×D4—4521no—
266C2×D4—2261no—
267C2×D4—2261no—
268C2×D4—2261no—
269C2×D4—2261no—
270C2×D4—2261no—
271C2×D4—2262no—
272C2×D4C22×D11311yescharacteristic
273C2×D4C22×D11311yescharacteristic
274C22×C4—1131no—
275C22×C4—2261no—
276C22×C4C22×D11311yescharacteristic
277SD16—22no—
278SD16—41no—
279SD16—4521no—
280M16—4521no—
281M16—4521no—
282C2×C8—1131no—
283C2×C8—1131no—
284C2×C8C22×D11311yescharacteristic
285C2×C8C22×D11311yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—1131no—
288C4⋊C4—1131no—
289C4⋊C4—1131no—
290C4⋊C4—1131no—
291C4⋊C4—2261no—
292C4⋊C4—2261no—
293C4⋊C4—2261no—
294C4⋊C4C22×D11311yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—1131no—
297C22⋊C4—1131no—
298C22⋊C4—2261no—
299C22⋊C4—2261no—
300C22⋊C4—2261no—
301C22⋊C4—2261no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C42—1131no—
305C42—2261no—
306C42—2261no—
307C42—2261no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—1131no—
314C23—9041no—
315C23—4522no—
316C23—4522no—
317C23—2261no—
318C23D4×D11311yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—4522no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—9041no—
327D4—4522no—
328D4—4522no—
329D4—4522no—
330D4—4522no—
331D4—2262no—
332D4—2261no—
333D4—2261no—
334D4#1426864612yes—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—1131no—
340C2×C4—1131no—
341C2×C4—1131no—
342C2×C4—4522no—
343C2×C4—2261no—
344C2×C4—2261no—
345C2×C4—2261no—
346C2×C4—2261no—
347C2×C4—2261no—
348C2×C4D4×D11311yescharacteristic
349C2×C4C23×D11311yescharacteristic
350C8—21no—
351C8—21no—
352C8—2261no—
353C8—2261no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—84no—
364C22—9044no—
365C22—4521no—
366C22—4521no—
367C22—4521no—
368C22—2261no—
369C22—2261no—
370C22—2261no—
371C22C2×D4×D11311yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—1132no—
376C4—4521no—
377C4—4521no—
378C4—4521no—
379C4—2261no—
380C4—2261no—
381C4C2×#1426864611yescharacteristic
382C4#1681366711yescharacteristic
383C2—41no—
384C2—42no—
385C2—81no—
386C2—9041no—
387C2—4521no—
388C2#2029923511yescharacteristic
389C2AGL(1,ℤ/8)×D11311yescharacteristic
390C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#450×C113C2
socleC22×C113C22×D4
prime radicalD4×C22⋊D113C2
hypercenter#450D113
hypocenterC113#3324
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #20299319C2semidirect
3. #20298943C2semidirect
4. #20298923C2semidirect
5. #20298921C2semidirect
6. #20298876C2semidirect
7. #20298846C2semidirect
8. #20298841C2semidirect
9. #20298796C2semidirect
10. #20298747C2semidirect
11. SD16×Dic113C2semidirect
12. #20298673C2semidirect
13. #20298603C2semidirect
14. #20298601C2semidirect
15. #450×C113C2semidirect
18. C2×#14268634C22semidirect
19. C2×#14268631C22semidirect
20. C2×#14268630C22semidirect
21. #16813621C22semidirect
26. #16813598C22semidirect
32. Q8×Dic113C22semidirect
36. #16813581C22semidirect
37. #16813580C22semidirect
38. #16813556C22semidirect
39. #16813555C22semidirect
40. #16813554C22semidirect
41. #16813551C22semidirect
42. #16813546C22semidirect
43. #16813544C22semidirect
44. #16813544C22semidirect
47. #16813543C22semidirect
48. #16813543C22semidirect
49. #16813542C22semidirect
50. #16813534C22semidirect
51. C8×Dic113C22semidirect
54. C2×SD16×C113C22semidirect
55. C22⋊Q8×C113C22semidirect
57. #102×C113C22semidirect
58. C22⋊C8×C113C22semidirect
196. C113#3324semidirect
207. #450D113semidirect
217. C2×SD16C2×D113semidirect
226. C22⋊Q8C2×D113semidirect
251. #102C2×D113semidirect
253. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993192
D4×C22⋊D1132
#202989432
#202989232
#202989212
#202988762
#202988462
#202988412
#202987962
#202987472
SD16×Dic1132
#202986732
#202986032
#202986012
#450×C1132
#3324113