Finite Group Databasebeta

← #28402393

Subgroups — #28402393

Order 14464.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299306C211yesmaximal, characteristic, complemented
2#20299232C211yesmaximal, characteristic
3#20298943C211yesmaximal, characteristic, complemented
4#20298918C211yesmaximal, characteristic, complemented
5#20298914C211yesmaximal, characteristic, complemented
6#20298887C211yesmaximal, characteristic, complemented
7#20298830C211yesmaximal, characteristic, complemented
8#20298796C211yesmaximal, characteristic, complemented
9#20298748C211yesmaximal, characteristic, complemented
10#20298747C211yesmaximal, characteristic, complemented
11#20298683C211yesmaximal, characteristic, complemented
12C8×C22⋊D113C211yesmaximal, characteristic, complemented
13C2×#16813544C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#465×C113C211yesmaximal, characteristic, complemented
16C22×D452C2211yescharacteristic
17C2×D4×D113—21no—
18C2×D4×D113C2211yescharacteristic
19C2×#14268634C2211yescharacteristic
20C2×#14268634C2211yescharacteristic, complemented
21C2×C8×D113C2211yescharacteristic, complemented
22#16813621C2211yescharacteristic, complemented
23#16813618C2211yescharacteristic
24#16813612—21no—
25#16813602—21no—
26#16813599—21no—
27#16813598C2211yescharacteristic, complemented
28#16813597C2211yescharacteristic
29#16813595—21no—
30#16813592—21no—
31#16813590—21no—
32Q8×Dic113C2211yescharacteristic, complemented
33#16813584C2211yescharacteristic
34C4×C22⋊D113C2211yescharacteristic
35#16813582—21no—
36C2×C4⋊Dic113C2211yescharacteristic, complemented
37C4⋊C4×D113C2211yescharacteristic, complemented
38#16813553C2211yescharacteristic, complemented
39#16813553C2211yescharacteristic, complemented
40#16813551C2211yescharacteristic, complemented
41#16813544C2211yescharacteristic
42#16813544C2211yescharacteristic
43#16813544C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic, complemented
45#16813543C2211yescharacteristic, complemented
46#16813543C2211yescharacteristic, complemented
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic, complemented
49C22⋊#11744751C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C2×SD16×C113C2211yescharacteristic, complemented
53C22×C8×C113C2211yescharacteristic, complemented
54C22⋊Q8×C113C2211yescharacteristic, complemented
55#121×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C23×D113—21no—
61C2×Dic226—21no—
62C2×D452—22no—
63C2×D452—21no—
64C2×D452—21no—
65C2×D452—41no—
66C2×D452C2311yescharacteristic
67C2×D452C2311yescharacteristic
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113D411yescharacteristic
72D4×D113—22no—
73D4×D113—41no—
74D4×D113—44no—
75C22×Dic113—21no—
76C2×C4×D113—21no—
77C2×C4×D113—21no—
78C2×C4×D113C2311yescharacteristic
79#14268634—22no—
80#14268634—41no—
81C2×#11744751C2311yescharacteristic
82C2×#11744751C2311yescharacteristic
83C8×D113—41no—
84C4⋊Dic113—21no—
85C4⋊Dic113—21no—
86C4⋊Dic113C2311yescharacteristic
87C4⋊Dic113C2311yescharacteristic
88#14268626—21no—
89#14268626—21no—
90#14268626—21no—
91#14268626D411yescharacteristic
92C22⋊Dic113D411yescharacteristic
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624D411yescharacteristic
97C4×Dic113—21no—
98C4×Dic113C2311yescharacteristic
99C2×Q8×C113C2311yescharacteristic
100C2×D4×C113—21no—
101C2×D4×C113C2311yescharacteristic
102C22×C4×C113C2311yescharacteristic
103SD16×C113—41no—
104C2×C8×C113—41no—
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113—21no—
108C4⋊C4×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C22⋊C4×C113—21no—
112C23×C113—21no—
113C23×C113C2×D411yescharacteristic
114C22×D113—21no—
115C22×D113—21no—
116C22×D113—42no—
117C22×D113—42no—
118C22×D113—42no—
119C22×D113—42no—
120C22×D113—81no—
121C22×D113—81no—
122C22×D113C2×D411yescharacteristic
123Q8×C113—21no—
124Q8×C113—21no—
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—42no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2411yescharacteristic
135C22⋊D113—42no—
136C22⋊D113—42no—
137C22⋊D113—81no—
138C22⋊D113SD1614yescomplemented
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113—81no—
142C2×Dic113C2×D411yescharacteristic
143C2×Dic113C2×D411yescharacteristic
144C2×Dic113C2×D411yescharacteristic
145D452—21no—
146D452—21no—
147D452—21no—
148D452—42no—
149D452—42no—
150D452#4112yes—
151C4×D113—21no—
152C4×D113—21no—
153C4×D113—42no—
154C4×D113—81no—
155Dic226—81no—
156C8×C113—21no—
157C8×C113—21no—
158#11744751—21no—
159#11744751—21no—
160C22×C113—21no—
161C22×C113—21no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113C2×SD1612yes—
166C22×C113C22×D411yescharacteristic
167C2×D113—21no—
168C2×D113—21no—
169C2×D113—22no—
170C2×D113—41no—
171C2×D113—41no—
172C2×D113—41no—
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—84no—
176C2×D113—84no—
177C2×D113C2×SD1612yes—
178C4×C113—21no—
179C4×C113—41no—
180C4×C113—41no—
181C4×C113—41no—
182C4×C113C2×#4111yescharacteristic
183C4×C113H(5,𝔽2)11yescharacteristic
184Dic113—21no—
185Dic113—21no—
186Dic113—41no—
187Dic113—41no—
188Dic113C2×SD1612yes—
189C2×C113—22no—
190C2×C113—81no—
191C2×C113#54611yescharacteristic
192C2×C113C22×SD1611yescharacteristic
193C2×C113#57611yescharacteristic
194D113—22no—
195D113—42no—
196D113—81no—
197#3295—1131nomaximal, Sylow
198C113#329511yescharacteristic, complemented, Sylow
199#554—1131no—
200D42—1131no—
201#486—1131no—
202#481—1131no—
203#481—1131no—
204#476—1131no—
205#465—1131no—
206#465D11311yescharacteristic, complemented
207#460—1131no—
208#450—1131no—
209#450—1131no—
210C4×SD16—1131no—
211C8×D4—1131no—
212C2×#102—1131no—
213C2×#102—1131no—
214C22×D4—1131no—
215C22×D4—1131no—
216C22×D4—2261no—
217C2×SD16—1131no—
218C2×SD16—1131no—
219C2×SD16C2×D11311yescharacteristic, complemented
220C22×C8—1131no—
221C22×C8C2×D11311yescharacteristic, complemented
222C4⋊Q8—1131no—
223#127—1131no—
224#125—2261no—
225C22⋊Q8—1131no—
226C22⋊Q8—2261no—
227C22⋊Q8—2261no—
228C22⋊Q8C2×D11311yescharacteristic, complemented
229#121—1131no—
230#121—2261no—
231#121C2×D11311yescharacteristic
232#120—2261no—
233#120—2261no—
234C4×Q8—1131no—
235C4×D4—1131no—
236C4×D4—1131no—
237C4×D4—2261no—
238C2×C4⋊C4—1131no—
239C2×C4⋊C4—1131no—
240#106—1131no—
241#106—1131no—
242#106C2×D11311yescharacteristic, complemented
243C4⋊C8—1131no—
244#103C2×D11311yescharacteristic, complemented
245#102—1131no—
246#102—1131no—
247#102—1131no—
248#102—1131no—
249#102—1131no—
250#102—1131no—
251#102—1131no—
252#102—1131no—
253#102C2×D11311yescharacteristic, complemented
254C22⋊C8—1131no—
255C22⋊C8—1131no—
256C4×C8—1131no—
257C24—2261no—
258C24—2261no—
259C2×Q8—2261no—
260C2×Q8C22×D11311yescharacteristic
261C2×D4—21no—
262C2×D4—1131no—
263C2×D4—1131no—
264C2×D4—1131no—
265C2×D4—4521no—
266C2×D4—4524no—
267C2×D4—4521no—
268C2×D4—2262no—
269C2×D4—2261no—
270C2×D4—2261no—
271C2×D4—2261no—
272C2×D4—2261no—
273C2×D4—2262no—
274C2×D4—2261no—
275C2×D4C22×D11311yescharacteristic
276C22×C4—1131no—
277C22×C4—2261no—
278C22×C4—2261no—
279C22×C4—2261no—
280C22×C4C22×D11311yescharacteristic
281SD16—41no—
282SD16—4521no—
283SD16—2262no—
284C2×C8—41no—
285C2×C8—1131no—
286C2×C8—1131no—
287C2×C8—4521no—
288C2×C8C22×D11311yescharacteristic
289C2×C8C22×D11311yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—1131no—
292C4⋊C4—1131no—
293C4⋊C4—1131no—
294C4⋊C4—2261no—
295C4⋊C4—2261no—
296C4⋊C4—2261no—
297C4⋊C4—2261no—
298C4⋊C4—2261no—
299C4⋊C4C22×D11311yescharacteristic
300C4⋊C4C22×D11311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—1131no—
304C22⋊C4—1131no—
305C22⋊C4—2261no—
306C22⋊C4—2261no—
307C22⋊C4—2261no—
308C42—1131no—
309C42—2261no—
310C23—21no—
311C23—1131no—
312C23—9041no—
313C23—9041no—
314C23—4522no—
315C23—4522no—
316C23—4522no—
317C23—4522no—
318C23—2261no—
319C23—2261no—
320C23D4×D11311yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—9041no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—1134no—
328D4—1132no—
329D4—9041no—
330D4—4522no—
331D4—4522no—
332D4—4522no—
333D4—4522no—
334D4—2261no—
335D4—2261no—
336D4—2261no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—1131no—
343C2×C4—1131no—
344C2×C4—1131no—
345C2×C4—9041no—
346C2×C4—9041no—
347C2×C4—4522no—
348C2×C4—2261no—
349C2×C4—2261no—
350C2×C4—2261no—
351C2×C4—2261no—
352C2×C4D4×D11311yescharacteristic
353C2×C4C23×D11311yescharacteristic
354C8—21no—
355C8—21no—
356C8—2261no—
357C8—2261no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—1132no—
364C22—9044no—
365C22—9044no—
366C22—4521no—
367C22—4521no—
368C22—4521no—
369C22—4521no—
370C22—4521no—
371C22—2262no—
372C22—2261no—
373C22—2261no—
374C22SD16×D11312yes—
375C22C2×D4×D11311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—1132no—
381C4—4521no—
382C4—4521no—
383C4—2261no—
384C4—2261no—
385C4#41×D11311yescharacteristic
386C4#1681366711yescharacteristic
387C2—22no—
388C2—81no—
389C2—9041no—
390C2—4522no—
391C2—2262no—
392C2#2029923711yescharacteristic
393C2C2×SD16×D11311yescharacteristic
394C2#2029940011yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#465×C113C2
socleC22×C113C22×D4
prime radical#20299232C2
hypercenter#465D113
hypocenterC113#3295
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #20299306C2semidirect
3. #20298943C2semidirect
4. #20298918C2semidirect
5. #20298914C2semidirect
6. #20298887C2semidirect
7. #20298830C2semidirect
8. #20298796C2semidirect
9. #20298748C2semidirect
10. #20298747C2semidirect
11. #20298683C2semidirect
12. C8×C22⋊D113C2semidirect
13. C2×#16813544C2semidirect
14. #102×D113C2semidirect
15. #465×C113C2semidirect
20. C2×#14268634C22semidirect
21. C2×C8×D113C22semidirect
22. #16813621C22semidirect
27. #16813598C22semidirect
32. Q8×Dic113C22semidirect
36. C2×C4⋊Dic113C22semidirect
37. C4⋊C4×D113C22semidirect
38. #16813553C22semidirect
39. #16813553C22semidirect
40. #16813551C22semidirect
43. #16813544C22semidirect
44. #16813544C22semidirect
45. #16813543C22semidirect
46. #16813543C22semidirect
48. #16813542C22semidirect
49. C22⋊#11744751C22semidirect
50. #16813534C22semidirect
51. C8×Dic113C22semidirect
52. C2×SD16×C113C22semidirect
53. C22×C8×C113C22semidirect
54. C22⋊Q8×C113C22semidirect
56. #106×C113C22semidirect
57. #103×C113C22semidirect
58. #102×C113C22semidirect
138. C22⋊D113SD16semidirect
198. C113#3295semidirect
206. #465D113semidirect
219. C2×SD16C2×D113semidirect
221. C22×C8C2×D113semidirect
228. C22⋊Q8C2×D113semidirect
242. #106C2×D113semidirect
244. #103C2×D113semidirect
253. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993062
#202992322
#202989432
#202989182
#202989142
#202988872
#202988302
#202987962
#202987482
#202987472
#202986832
C8×C22⋊D1132
C2×#168135442
#102×D1132
#465×C1132
#3295113