Finite Group Databasebeta

← #28400063

Subgroups — #28400063

Order 14464.

500 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×#16813651C211yesmaximal, characteristic, complemented
2C2×#16813646C211yesmaximal, characteristic
3#124×D113C211yesmaximal, characteristic, complemented
4C4×#14268646C211yesmaximal, characteristic, complemented
5#20298823C211yesmaximal, characteristic, complemented
6#20298821C211yesmaximal, characteristic, complemented
7#20298819C211yesmaximal, characteristic, complemented
8#20298817C211yesmaximal, characteristic, complemented
9#20298815C211yesmaximal, characteristic, complemented
10#20298813C211yesmaximal, characteristic, complemented
11#20298811C211yesmaximal, characteristic, complemented
12#20298620C211yesmaximal, characteristic, complemented
13#20298605C211yesmaximal, characteristic, complemented
14#20298601C211yesmaximal, characteristic, complemented
15#463×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic
19#16813651—24no—
20#16813646—24no—
21C2×Dic452C2211yescharacteristic, complemented
22C2×#14268637C2211yescharacteristic, complemented
23C2×#14268636C2211yescharacteristic
24C2×#14268635C2211yescharacteristic
25C2×#14268635C2211yescharacteristic, complemented
26C2×#14268632C2211yescharacteristic
27C2×#14268630C2211yescharacteristic
28C2×#14268630C2211yescharacteristic
29#16813611C2211yescharacteristic
30#16813610C2211yescharacteristic
31#16813609C2211yescharacteristic
32#16813608—21no—
33#16813608—21no—
34C4×Dic226C2211yescharacteristic, complemented
35#16813587C2211yescharacteristic, complemented
36D4×Dic113C2211yescharacteristic, complemented
37C4×C22⋊D113—21no—
38#16813582—21no—
39#16813580C2211yescharacteristic
40#16813578—21no—
41C22⋊C4×D113—21no—
42C22⋊C4×D113—21no—
43C2×C4×Dic113—21no—
44C42×D113C2211yescharacteristic
45C4⋊#11744751C2211yescharacteristic, complemented
46#16813551C2211yescharacteristic, complemented
47#16813551C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813546C2211yescharacteristic, complemented
50#16813545C2211yescharacteristic, complemented
51#16813544C2211yescharacteristic
52#16813543C2211yescharacteristic
53#16813542C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic, complemented
55C2×D8×C113C2211yescharacteristic
56#124×C113C2211yescharacteristic
57C4×D4×C113C2211yescharacteristic, complemented
58C4⋊C8×C113C2211yescharacteristic, complemented
59#103×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic
61C23×D113—21no—
62#14268646—22no—
63#14268646D414yes—
64C2×Dic226—21no—
65C2×Dic226C2311yescharacteristic
66C2×Dic226C2311yescharacteristic
67Q8×D113—22no—
68Q8×D113—22no—
69C2×D452C2311yescharacteristic
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72D4×D113—22no—
73D4×D113—22no—
74C22×Dic113—21no—
75C22×Dic113—21no—
76C2×C4×D113—21no—
77C2×C4×D113D411yescharacteristic
78C2×C4×D113D411yescharacteristic
79C2×C4×D113C2311yescharacteristic
80Dic452—22no—
81#14268637—22no—
82#14268636—22no—
83#14268635—22no—
84#14268635—22no—
85#14268632—22no—
86#14268630—22no—
87#14268630—22no—
88C2×#11744751C2311yescharacteristic
89C2×#11744751C2311yescharacteristic
90C4⋊Dic113C2311yescharacteristic
91#14268626—21no—
92#14268626—21no—
93C22⋊Dic113—21no—
94C22⋊Dic113—21no—
95C22⋊Dic113—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624—21no—
99#14268624—21no—
100#14268624—21no—
101C4×Dic113—21no—
102C4×Dic113—21no—
103C4×Dic113—21no—
104C4×Dic113D411yescharacteristic
105C4×Dic113D411yescharacteristic
106C4×Dic113C2311yescharacteristic
107C2×Q8×C113C2311yescharacteristic
108C2×D4×C113C2311yescharacteristic
109C2×D4×C113C2311yescharacteristic
110C22×C4×C113—21no—
111SD16×C113—22no—
112D8×C113—22no—
113C2×C8×C113C2311yescharacteristic
114C2×C8×C113C2311yescharacteristic
115C4⋊C4×C113C2311yescharacteristic
116C22⋊C4×C113—21no—
117C22⋊C4×C113—21no—
118C22⋊C4×C113—21no—
119C42×C113C2311yescharacteristic
120C23×C113—21no—
121C23×C113—21no—
122C22×D113—21no—
123C22×D113—42no—
124C22×D113—42no—
125C22×D113—42no—
126C22×D113C2×D411yescharacteristic
127Q8×C113—21no—
128Q8×C113—21no—
129D4×C113—21no—
130D4×C113—21no—
131D4×C113—21no—
132D4×C113C2×D412yes—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—42no—
136C2×C4×C113C2×D411yescharacteristic
137C2×C4×C113C2×D411yescharacteristic
138C2×C4×C113C2411yescharacteristic
139C22⋊D113—24no—
140C22⋊D113—42no—
141C2×Dic113—21no—
142C2×Dic113—24no—
143C2×Dic113—21no—
144C2×Dic113—21no—
145C2×Dic113—42no—
146C2×Dic113C2×D411yescharacteristic
147C2×Dic113C2×D411yescharacteristic
148C2×Dic113C2×D411yescharacteristic
149D452—21no—
150D452—21no—
151C4×D113—41no—
152C4×D113—41no—
153C4×D113—42no—
154C4×D113C2×D412yes—
155C4×D113#4112yes—
156Dic226—21no—
157Dic226—21no—
158Dic226—21no—
159Dic226—42no—
160Dic226C2×D412yes—
161C8×C113—21no—
162C8×C113—21no—
163#11744751—21no—
164#11744751—21no—
165C22×C113—22no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113—41no—
170C22×C113—41no—
171C22×C113C22×D411yescharacteristic
172C2×D113—21no—
173C2×D113—21no—
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—41no—
177C2×D113—84no—
178C2×D113#12112yes—
179C4×C113—21no—
180C4×C113—21no—
181C4×C113—41no—
182C4×C113—41no—
183C4×C113C22×D411yescharacteristic
184C4×C113C2×#4111yescharacteristic
185Dic113—22no—
186Dic113—21no—
187Dic113—21no—
188Dic113—41no—
189Dic113—41no—
190Dic113#12112yes—
191C2×C113—42no—
192C2×C113—81no—
193C2×C113C2×#12111yescharacteristic
194C2×C113#57511yescharacteristic
195C2×C113#57511yescharacteristic
196D113—22no—
197D113—81no—
198#3040—1131nomaximal, Sylow
199C113#304011yescharacteristic, complemented, Sylow
200C2×#137—1131no—
201C2×AGL(1,ℤ/8)—1131no—
202C2×#124—1131no—
203C4×#41—1131no—
204#464—1131no—
205#464—1131no—
206#464—1131no—
207#464—1131no—
208#463—1131no—
209#463—1131no—
210#463—1131no—
211#463D11311yescharacteristic, complemented
212#423—1131no—
213#419—1131no—
214#418—1131no—
215C2×#41—1131no—
216C22×Q8—1131no—
217C22×D4—1131no—
218#137—2264no—
219AGL(1,ℤ/8)—2264no—
220C2×Q16—1131no—
221C2×Q16—1131no—
222C2×SD16—1131no—
223C2×SD16—1131no—
224C2×SD16—1131no—
225C2×SD16C2×D11311yescharacteristic, complemented
226C2×D8—1131no—
227C2×D8C2×D11311yescharacteristic
228C2×M16—1131no—
229C2×M16—1131no—
230#124—1131no—
231#124—1131no—
232#124—1131no—
233#124—2261no—
234#124—2261no—
235#124C2×D11311yescharacteristic
236C4×Q8—1131no—
237C4×Q8—1131no—
238C4×D4—1131no—
239C4×D4—2261no—
240C4×D4—2261no—
241C4×D4C2×D11311yescharacteristic, complemented
242#117—1131no—
243#117—2261no—
244C2×C22⋊C4—2261no—
245C2×C22⋊C4—2261no—
246C2×C42—1131no—
247C2×C42—2261no—
248C4⋊C8—1131no—
249C4⋊C8—1131no—
250C4⋊C8—1131no—
251C4⋊C8C2×D11311yescharacteristic, complemented
252#103—1131no—
253#103—1131no—
254#103—1131no—
255#103C2×D11311yescharacteristic, complemented
256#102—1131no—
257#102—1131no—
258#102—1131no—
259#102C2×D11311yescharacteristic
260C24—2261no—
261#41—1134no—
262#41—2262no—
263C2×Q8—1131no—
264C2×Q8—1131no—
265C2×Q8—2261no—
266C2×Q8—2262no—
267C2×Q8—2262no—
268C2×Q8C22×D11311yescharacteristic
269C2×D4—1131no—
270C2×D4—2262no—
271C2×D4—2262no—
272C2×D4—2261no—
273C2×D4—2261no—
274C2×D4C22×D11311yescharacteristic
275C2×D4C22×D11311yescharacteristic
276C22×C4—21no—
277C22×C4—1131no—
278C22×C4—1131no—
279C22×C4—1131no—
280C22×C4—2261no—
281C22×C4—2261no—
282C22×C4—2261no—
283Q16—2262no—
284Q16—2262no—
285SD16—22no—
286SD16—2262no—
287SD16—2262no—
288SD16—2262no—
289D8—22no—
290D8—2262no—
291M16—2262no—
292M16—2262no—
293C2×C8—1131no—
294C2×C8—1131no—
295C2×C8C22×D11311yescharacteristic
296C2×C8C22×D11311yescharacteristic
297C4⋊C4—1131no—
298C4⋊C4—2261no—
299C4⋊C4—2261no—
300C4⋊C4C22×D11311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—2261no—
305C22⋊C4—2261no—
306C22⋊C4—2261no—
307C22⋊C4—2261no—
308C22⋊C4—2261no—
309C22⋊C4—2261no—
310C22⋊C4—2261no—
311C22⋊C4—2261no—
312C42—1131no—
313C42—1131no—
314C42—1131no—
315C42—2261no—
316C42—2261no—
317C42—2261no—
318C42C22×D11311yescharacteristic
319C23—21no—
320C23—21no—
321C23—1131no—
322C23—4522no—
323C23—4522no—
324C23—4522no—
325C23—2261no—
326Q8—21no—
327Q8—21no—
328Q8—1132no—
329Q8—4522no—
330Q8—2261no—
331Q8—2261no—
332Q8—2261no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—4522no—
337D4—2264no—
338D4—2261no—
339D4—2261no—
340D4D4×D11312yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—1131no—
345C2×C4—1132no—
346C2×C4—1132no—
347C2×C4—1131no—
348C2×C4—1131no—
349C2×C4—4521no—
350C2×C4—4521no—
351C2×C4—4522no—
352C2×C4—4522no—
353C2×C4—2264no—
354C2×C4—2261no—
355C2×C4—2261no—
356C2×C4—2261no—
357C2×C4D4×D11311yescharacteristic
358C2×C4D4×D11311yescharacteristic
359C2×C4C23×D11311yescharacteristic
360C8—21no—
361C8—21no—
362C8—2261no—
363C8—2261no—
364C22—22no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—1132no—
371C22—9044no—
372C22—4521no—
373C22—4521no—
374C22—4521no—
375C22—2261no—
376C22—2261no—
377C22C2×D4×D11311yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—1132no—
383C4—4521no—
384C4—4521no—
385C4—2262no—
386C4—2261no—
387C4—2261no—
388C4C2×D4×D11311yescharacteristic
389C4#41×D11311yescharacteristic
390C2—42no—
391C2—81no—
392C2—9041no—
393C2—2262no—
394C2#121×D11311yescharacteristic
395C2#2029939411yescharacteristic
396C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#463×C113C2
socleC22×C113C22×D4
prime radicalC2×#16813646C2
hypercenter#463D113
hypocenterC113#3040
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#16813651C2semidirect
3. #124×D113C2semidirect
4. C4×#14268646C2semidirect
5. #20298823C2semidirect
6. #20298821C2semidirect
7. #20298819C2semidirect
8. #20298817C2semidirect
9. #20298815C2semidirect
10. #20298813C2semidirect
11. #20298811C2semidirect
12. #20298620C2semidirect
13. #20298605C2semidirect
14. #20298601C2semidirect
15. #463×C113C2semidirect
21. C2×Dic452C22semidirect
22. C2×#14268637C22semidirect
25. C2×#14268635C22semidirect
34. C4×Dic226C22semidirect
35. #16813587C22semidirect
36. D4×Dic113C22semidirect
45. C4⋊#11744751C22semidirect
46. #16813551C22semidirect
47. #16813551C22semidirect
48. #16813547C22semidirect
49. #16813546C22semidirect
50. #16813545C22semidirect
54. C2×SD16×C113C22semidirect
57. C4×D4×C113C22semidirect
58. C4⋊C8×C113C22semidirect
59. #103×C113C22semidirect
199. C113#3040semidirect
211. #463D113semidirect
225. C2×SD16C2×D113semidirect
241. C4×D4C2×D113semidirect
251. C4⋊C8C2×D113semidirect
255. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136512
C2×#168136462
#124×D1132
C4×#142686462
#202988232
#202988212
#202988192
#202988172
#202988152
#202988132
#202988112
#202986202
#202986052
#202986012
#463×C1132
#3040113