Finite Group Databasebeta

← #28400093

Subgroups — #28400093

Order 14464.

490 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813654C211yesmaximal, characteristic, complemented
2C2×SD16×D113C211yesmaximal, characteristic, complemented
3#20299166C211yesmaximal, characteristic
4#20299074C211yesmaximal, characteristic, complemented
5#20298823C211yesmaximal, characteristic, complemented
6#20298822C211yesmaximal, characteristic, complemented
7#20298817C211yesmaximal, characteristic, complemented
8#20298799C211yesmaximal, characteristic, complemented
9#20298798C211yesmaximal, characteristic, complemented
10#20298797C211yesmaximal, characteristic, complemented
11#20298796C211yesmaximal, characteristic, complemented
12#20298623C211yesmaximal, characteristic, complemented
13#20298601C211yesmaximal, characteristic, complemented
14#20298593C211yesmaximal, characteristic, complemented
15#464×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic
19#16813654—24no—
20C2×#14268637C2211yescharacteristic, complemented
21C2×#14268636C2211yescharacteristic
22C2×#14268636C2211yescharacteristic, complemented
23C2×#14268635C2211yescharacteristic
24C2×#14268634C2211yescharacteristic
25C2×#14268634C2211yescharacteristic, complemented
26SD16×D113—24no—
27C2×#14268630C2211yescharacteristic
28C2×C8×D113C2211yescharacteristic
29#16813619C2211yescharacteristic
30#16813618C2211yescharacteristic
31#16813611C2211yescharacteristic
32#16813595—21no—
33#16813595—21no—
34#16813592—21no—
35#16813592—21no—
36Q8×Dic113C2211yescharacteristic, complemented
37C4×Dic226—21no—
38C4×Dic226C2211yescharacteristic, complemented
39#16813587—21no—
40#16813587C2211yescharacteristic, complemented
41#16813580—21no—
42#16813580C2211yescharacteristic
43#16813579—21no—
44#16813579C2211yescharacteristic
45C4⋊#11744751C2211yescharacteristic, complemented
46#16813551C2211yescharacteristic, complemented
47#16813551C2211yescharacteristic, complemented
48#16813546C2211yescharacteristic, complemented
49#16813544C2211yescharacteristic
50#16813544C2211yescharacteristic, complemented
51#16813543C2211yescharacteristic
52#16813542C2211yescharacteristic
53#16813542C2211yescharacteristic, complemented
54C2×Q16×C113C2211yescharacteristic, complemented
55C2×SD16×C113C2211yescharacteristic
56#124×C113C2211yescharacteristic
57C4×Q8×C113C2211yescharacteristic, complemented
58C4⋊C8×C113C2211yescharacteristic, complemented
59#103×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic
61C23×D113—21no—
62#14268648—22no—
63#14268648—22no—
64C2×Dic226—21no—
65C2×Dic226C2311yescharacteristic
66Q8×D113—22no—
67Q8×D113D414yescomplemented
68C2×D452—21no—
69C2×D452—21no—
70C2×D452—21no—
71C2×D452C2311yescharacteristic
72C2×D452C2311yescharacteristic
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76D4×D113—22no—
77D4×D113—22no—
78C2×C4×D113—21no—
79C2×C4×D113—21no—
80C2×C4×D113C2311yescharacteristic
81#14268637—22no—
82#14268636—22no—
83#14268636—22no—
84#14268635—22no—
85#14268634—22no—
86#14268634—22no—
87#14268630—22no—
88C2×#11744751C2311yescharacteristic
89C2×#11744751C2311yescharacteristic
90C8×D113—22no—
91C4⋊Dic113—21no—
92C4⋊Dic113C2311yescharacteristic
93#14268626—21no—
94#14268626—21no—
95#14268626D411yescharacteristic
96#14268626D411yescharacteristic
97#14268624—21no—
98#14268624—21no—
99#14268624—21no—
100#14268624D411yescharacteristic
101#14268624D411yescharacteristic
102C4×Dic113—21no—
103C4×Dic113—21no—
104C4×Dic113—21no—
105C4×Dic113—21no—
106C4×Dic113C2311yescharacteristic
107C2×Q8×C113C2311yescharacteristic
108C2×Q8×C113C2311yescharacteristic
109C2×D4×C113C2311yescharacteristic
110Q16×C113—22no—
111SD16×C113—22no—
112C2×C8×C113C2311yescharacteristic
113C2×C8×C113C2311yescharacteristic
114C4⋊C4×C113—21no—
115C4⋊C4×C113C2311yescharacteristic
116C22⋊C4×C113—21no—
117C22⋊C4×C113—21no—
118C42×C113—21no—
119C42×C113C2311yescharacteristic
120C23×C113—21no—
121C22×D113—21no—
122C22×D113—21no—
123C22×D113—42no—
124C22×D113—81no—
125C22×D113—81no—
126C22×D113C2×D411yescharacteristic
127Q8×C113—21no—
128Q8×C113—21no—
129Q8×C113—21no—
130Q8×C113C2×D412yes—
131D4×C113—21no—
132D4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113C2×D411yescharacteristic
137C2×C4×C113C2×D411yescharacteristic
138C2×C4×C113C2411yescharacteristic
139C22⋊D113—42no—
140C22⋊D113—81no—
141C22⋊D113—81no—
142C2×Dic113—21no—
143C2×Dic113—21no—
144C2×Dic113C2×D411yescharacteristic
145C2×Dic113C2×D411yescharacteristic
146C2×Dic113C2×D411yescharacteristic
147D452—21no—
148D452—21no—
149D452—21no—
150D452—21no—
151D452—42no—
152D452—81no—
153D452—81no—
154C4×D113—24no—
155C4×D113—42no—
156C4×D113C2×D412yes—
157C4×D113#4112yes—
158Dic226—21no—
159Dic226—24no—
160Dic226C2×D412yes—
161C8×C113—21no—
162C8×C113—21no—
163#11744751—21no—
164#11744751—21no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113C22×D411yescharacteristic
169C2×D113—21no—
170C2×D113—21no—
171C2×D113—41no—
172C2×D113—41no—
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—41no—
177C2×D113—84no—
178C2×D113#12112yes—
179C4×C113—22no—
180C4×C113—21no—
181C4×C113—21no—
182C4×C113—41no—
183C4×C113—41no—
184C4×C113C22×D411yescharacteristic
185C4×C113C2×#4111yescharacteristic
186Dic113—22no—
187Dic113—21no—
188Dic113—21no—
189Dic113—41no—
190Dic113#12112yes—
191C2×C113—81no—
192C2×C113C2×#12111yescharacteristic
193C2×C113#57711yescharacteristic
194C2×C113#57711yescharacteristic
195D113—22no—
196D113—81no—
197D113—81no—
198#3043—1131nomaximal, Sylow
199C113#304311yescharacteristic, complemented, Sylow
200C2×#137—1131no—
201C22×SD16—1131no—
202#535—1131no—
203#519—1131no—
204#464—1131no—
205#464—1131no—
206#464—1131no—
207#464D11311yescharacteristic, complemented
208#460—1131no—
209#460—1131no—
210#460—1131no—
211#460—1131no—
212#424—1131no—
213#418—1131no—
214#416—1131no—
215C2×#41—1131no—
216C22×Q8—1131no—
217C22×D4—1131no—
218#137—2264no—
219C2×Q16—1131no—
220C2×Q16C2×D11311yescharacteristic, complemented
221C2×SD16—1131no—
222C2×SD16—1131no—
223C2×SD16—1131no—
224C2×SD16—1131no—
225C2×SD16—1131no—
226C2×SD16—2264no—
227C2×SD16C2×D11311yescharacteristic
228C2×M16—1131no—
229C22×C8—1131no—
230#127—1131no—
231#127—1131no—
232#124—1131no—
233#124C2×D11311yescharacteristic
234#121—2261no—
235#121—2261no—
236#120—2261no—
237#120—2261no—
238C4×Q8—1131no—
239C4×Q8—1131no—
240C4×Q8—1131no—
241C4×Q8—2261no—
242C4×Q8—2261no—
243C4×Q8C2×D11311yescharacteristic, complemented
244#117—1131no—
245#117—1131no—
246#117—2261no—
247#117—2261no—
248C4⋊C8—1131no—
249C4⋊C8—1131no—
250C4⋊C8—1131no—
251C4⋊C8C2×D11311yescharacteristic, complemented
252#103—1131no—
253#103C2×D11311yescharacteristic, complemented
254#102—1131no—
255#102—1131no—
256#102—1131no—
257#102—1131no—
258#102—1131no—
259#102C2×D11311yescharacteristic
260C24—2261no—
261#41—2262no—
262#41—2262no—
263C2×Q8—1134no—
264C2×Q8—1131no—
265C2×Q8—2261no—
266C2×Q8—2262no—
267C2×Q8C22×D11311yescharacteristic
268C2×Q8C22×D11311yescharacteristic
269C2×D4—1131no—
270C2×D4—1131no—
271C2×D4—2261no—
272C2×D4—2262no—
273C2×D4—2262no—
274C2×D4—2261no—
275C2×D4—2261no—
276C2×D4—2261no—
277C2×D4—2261no—
278C2×D4—2261no—
279C2×D4C22×D11311yescharacteristic
280C22×C4—1131no—
281C22×C4—2261no—
282C22×C4—2261no—
283Q16—22no—
284Q16—2262no—
285SD16—22no—
286SD16—2262no—
287SD16—2262no—
288SD16—2262no—
289SD16—2262no—
290SD16—2262no—
291M16—2262no—
292C2×C8—1131no—
293C2×C8—1131no—
294C2×C8—2262no—
295C2×C8C22×D11311yescharacteristic
296C2×C8C22×D11311yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—1131no—
299C4⋊C4—1131no—
300C4⋊C4—1131no—
301C4⋊C4—2261no—
302C4⋊C4—2261no—
303C4⋊C4—2261no—
304C4⋊C4C22×D11311yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—1131no—
308C22⋊C4—1131no—
309C22⋊C4—2261no—
310C22⋊C4—2261no—
311C22⋊C4—2261no—
312C42—21no—
313C42—1131no—
314C42—2261no—
315C42—2261no—
316C42—2261no—
317C42—2261no—
318C42C22×D11311yescharacteristic
319C23—21no—
320C23—1131no—
321C23—9041no—
322C23—9041no—
323C23—4522no—
324C23—2261no—
325C23—2261no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—1132no—
330Q8—2264no—
331Q8—2261no—
332Q8D4×D11312yes—
333D4—21no—
334D4—21no—
335D4—9041no—
336D4—9041no—
337D4—9041no—
338D4—9041no—
339D4—4522no—
340D4—4522no—
341D4—2261no—
342D4—2261no—
343D4—2261no—
344D4—2261no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—1131no—
349C2×C4—1132no—
350C2×C4—1132no—
351C2×C4—1131no—
352C2×C4—1131no—
353C2×C4—4522no—
354C2×C4—2264no—
355C2×C4—2261no—
356C2×C4—2261no—
357C2×C4D4×D11311yescharacteristic
358C2×C4D4×D11311yescharacteristic
359C2×C4C23×D11311yescharacteristic
360C8—21no—
361C8—21no—
362C8—2261no—
363C8—2261no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—1132no—
368C22—9044no—
369C22—4521no—
370C22—4521no—
371C22—4521no—
372C22—4521no—
373C22—4521no—
374C22—4521no—
375C22—2261no—
376C22—2261no—
377C22C2×D4×D11311yescharacteristic
378C4—22no—
379C4—21no—
380C4—21no—
381C4—41no—
382C4—41no—
383C4—1132no—
384C4—4521no—
385C4—2262no—
386C4—2261no—
387C4—2261no—
388C4C2×D4×D11311yescharacteristic
389C4#41×D11311yescharacteristic
390C2—81no—
391C2—9041no—
392C2—9041no—
393C2—2262no—
394C2#121×D11311yescharacteristic
395C2#2029940511yescharacteristic
396C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#464×C113C2
socleC22×C113C22×D4
prime radical#20299166C2
hypercenter#464D113
hypocenterC113#3043
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#16813654C2semidirect
2. C2×SD16×D113C2semidirect
4. #20299074C2semidirect
5. #20298823C2semidirect
6. #20298822C2semidirect
7. #20298817C2semidirect
8. #20298799C2semidirect
9. #20298798C2semidirect
10. #20298797C2semidirect
11. #20298796C2semidirect
12. #20298623C2semidirect
13. #20298601C2semidirect
14. #20298593C2semidirect
15. #464×C113C2semidirect
20. C2×#14268637C22semidirect
22. C2×#14268636C22semidirect
25. C2×#14268634C22semidirect
36. Q8×Dic113C22semidirect
38. C4×Dic226C22semidirect
40. #16813587C22semidirect
45. C4⋊#11744751C22semidirect
46. #16813551C22semidirect
47. #16813551C22semidirect
48. #16813546C22semidirect
50. #16813544C22semidirect
53. #16813542C22semidirect
54. C2×Q16×C113C22semidirect
57. C4×Q8×C113C22semidirect
58. C4⋊C8×C113C22semidirect
59. #103×C113C22semidirect
67. Q8×D113D4semidirect
199. C113#3043semidirect
207. #464D113semidirect
220. C2×Q16C2×D113semidirect
243. C4×Q8C2×D113semidirect
251. C4⋊C8C2×D113semidirect
253. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136542
C2×SD16×D1132
#202991662
#202990742
#202988232
#202988222
#202988172
#202987992
#202987982
#202987972
#202987962
#202986232
#202986012
#202985932
#464×C1132
#3043113