Finite Group Databasebeta

← #28402391

Subgroups — #28402391

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
2D4×C22⋊D113C211yesmaximal, characteristic
3#20298943C211yesmaximal, characteristic, complemented
4#20298917C211yesmaximal, characteristic, complemented
5#20298915C211yesmaximal, characteristic, complemented
6#20298886C211yesmaximal, characteristic, complemented
7#20298829C211yesmaximal, characteristic, complemented
8#20298824C211yesmaximal, characteristic, complemented
9#20298796C211yesmaximal, characteristic, complemented
10#20298747C211yesmaximal, characteristic, complemented
11SD16×Dic113C211yesmaximal, characteristic, complemented
12#20298661C211yesmaximal, characteristic, complemented
13C2×#16813543C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#450×C113C211yesmaximal, characteristic, complemented
16C22×C22⋊D113—21no—
17C2×D4×D113C2211yescharacteristic
18C2×#14268634C2211yescharacteristic, complemented
19C22×#11744751C2211yescharacteristic, complemented
20C2×C8×D113C2211yescharacteristic, complemented
21#16813621C2211yescharacteristic, complemented
22#16813618C2211yescharacteristic
23#16813612—21no—
24#16813602—21no—
25#16813599—21no—
26#16813598C2211yescharacteristic, complemented
27#16813596C2211yescharacteristic
28#16813594—21no—
29#16813593C2211yescharacteristic
30#16813591—21no—
31#16813590—21no—
32Q8×Dic113C2211yescharacteristic, complemented
33D4×Dic113C2211yescharacteristic
34C4×C22⋊D113C2211yescharacteristic
35#16813582—21no—
36C2×C4⋊Dic113C2211yescharacteristic, complemented
37C4⋊C4×D113C2211yescharacteristic, complemented
38#16813554C2211yescharacteristic, complemented
39#16813554C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, 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—
72C22×Dic113—21no—
73C2×C4×D113—21no—
74C2×C4×D113C2311yescharacteristic
75#14268634—41no—
76C2×#11744751—41no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C8×D113—41no—
80C4⋊Dic113—21no—
81C4⋊Dic113—21no—
82C4⋊Dic113C2311yescharacteristic
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626D411yescharacteristic
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113D411yescharacteristic
92#14268624—21no—
93#14268624—21no—
94#14268624D411yescharacteristic
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—42no—
137C22⋊D113—42no—
138C22⋊D113—42no—
139C22⋊D113—42no—
140C22⋊D113—81no—
141C22⋊D113SD1614yescomplemented
142C2×Dic113—21no—
143C2×Dic113—21no—
144C2×Dic113—21no—
145C2×Dic113—42no—
146C2×Dic113—81no—
147C2×Dic113C2×D411yescharacteristic
148C2×Dic113C2×D411yescharacteristic
149C2×Dic113C2×D411yescharacteristic
150D452—21no—
151D452—21no—
152C4×D113—21no—
153C4×D113—21no—
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—22no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113—84no—
169C22×C113C2×SD1612yes—
170C22×C113C22×D411yescharacteristic
171C2×D113—21no—
172C2×D113—21no—
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—84no—
177C2×D113C2×SD1612yes—
178C4×C113—21no—
179C4×C113—41no—
180C4×C113—41no—
181C4×C113C2×#4111yescharacteristic
182C4×C113H(5,𝔽2)11yescharacteristic
183Dic113—21no—
184Dic113—21no—
185Dic113—41no—
186Dic113—41no—
187Dic113—41no—
188Dic113C2×SD1612yes—
189C2×C113—22no—
190C2×C113—42no—
191C2×C113—81no—
192C2×C113#54611yescharacteristic
193C2×C113C22×SD1611yescharacteristic
194C2×C113#57611yescharacteristic
195D113—22no—
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#465—1131no—
207#460—1131no—
208#450—1131no—
209#450D11311yescharacteristic, complemented
210C4×SD16—1131no—
211C8×D4—1131no—
212C2×#102—1131no—
213C2×#102—1131no—
214C22×D4—1131no—
215C22×D4—2261no—
216C22×D4C2×D11311yescharacteristic
217C2×SD16—1131no—
218C2×SD16C2×D11311yescharacteristic
219C2×SD16C2×D11311yescharacteristic, complemented
220C22×C8—1131no—
221C22×C8—1131no—
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—1131no—
231#121—2261no—
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#106—1131no—
243C4⋊C8—1131no—
244#103—1131no—
245#102—1131no—
246#102—1131no—
247#102—1131no—
248#102—1131no—
249#102—1131no—
250#102—1131no—
251#102—1131no—
252#102C2×D11311yescharacteristic
253#102C2×D11311yescharacteristic, complemented
254C22⋊C8—1131no—
255C22⋊C8C2×D11311yescharacteristic, complemented
256C4×C8—1131no—
257C24—21no—
258C24—2261no—
259C2×Q8—2261no—
260C2×Q8C22×D11311yescharacteristic
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—1131no—
265C2×D4—1131no—
266C2×D4—4524no—
267C2×D4—4521no—
268C2×D4—2261no—
269C2×D4—2261no—
270C2×D4—2261no—
271C2×D4—2261no—
272C2×D4—2261no—
273C2×D4—2262no—
274C2×D4C22×D11311yescharacteristic
275C2×D4C22×D11311yescharacteristic
276C22×C4—1131no—
277C22×C4—2261no—
278C22×C4—2261no—
279C22×C4—2261no—
280C22×C4C22×D11311yescharacteristic
281SD16—22no—
282SD16—41no—
283SD16—4521no—
284C2×C8—1131no—
285C2×C8—1131no—
286C2×C8—4521no—
287C2×C8—4521no—
288C2×C8C22×D11311yescharacteristic
289C2×C8C22×D11311yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—1131no—
292C4⋊C4—1131no—
293C4⋊C4—1131no—
294C4⋊C4—1131no—
295C4⋊C4—2261no—
296C4⋊C4—2261no—
297C4⋊C4—2261no—
298C4⋊C4—2261no—
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—
308C42—1131no—
309C42—2261no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—1131no—
316C23—9041no—
317C23—4522no—
318C23—4522no—
319C23—2261no—
320C23D4×D11311yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—9041no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—1134no—
329D4—9041no—
330D4—4522no—
331D4—4522no—
332D4—4522no—
333D4—4522no—
334D4—2261no—
335D4—2261no—
336D4#1426864612yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—1131no—
342C2×C4—1131no—
343C2×C4—1131no—
344C2×C4—9041no—
345C2×C4—9041no—
346C2×C4—4522no—
347C2×C4—2261no—
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—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—1132no—
368C22—9044no—
369C22—4521no—
370C22—4521no—
371C22—4521no—
372C22—2261no—
373C22—2261no—
374C22SD16×D11312yes—
375C22C2×D4×D11311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—1132no—
380C4—4521no—
381C4—4521no—
382C4—4521no—
383C4—2261no—
384C4—2261no—
385C4C2×#1426864611yescharacteristic
386C4#1681366711yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—9041no—
391C2—2262no—
392C2#2029923511yescharacteristic
393C2C2×SD16×D11311yescharacteristic
394C2#2029940211yescharacteristic
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#3295
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. #20299306C2semidirect
3. #20298943C2semidirect
4. #20298917C2semidirect
5. #20298915C2semidirect
6. #20298886C2semidirect
7. #20298829C2semidirect
8. #20298824C2semidirect
9. #20298796C2semidirect
10. #20298747C2semidirect
11. SD16×Dic113C2semidirect
12. #20298661C2semidirect
13. C2×#16813543C2semidirect
14. #102×D113C2semidirect
15. #450×C113C2semidirect
18. C2×#14268634C22semidirect
19. C22×#11744751C22semidirect
20. C2×C8×D113C22semidirect
21. #16813621C22semidirect
26. #16813598C22semidirect
32. Q8×Dic113C22semidirect
36. C2×C4⋊Dic113C22semidirect
37. C4⋊C4×D113C22semidirect
38. #16813554C22semidirect
39. #16813554C22semidirect
40. #16813553C22semidirect
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
141. C22⋊D113SD16semidirect
198. C113#3295semidirect
209. #450D113semidirect
219. C2×SD16C2×D113semidirect
228. C22⋊Q8C2×D113semidirect
253. #102C2×D113semidirect
255. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993062
D4×C22⋊D1132
#202989432
#202989172
#202989152
#202988862
#202988292
#202988242
#202987962
#202987472
SD16×Dic1132
#202986612
C2×#168135432
#102×D1132
#450×C1132
#3295113