Finite Group Databasebeta

← #28400572

Subgroups — #28400572

Order 14464.

492 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299145C211yesmaximal, characteristic, complemented
2C4×D4×D113C211yesmaximal, characteristic, complemented
3#20298913C211yesmaximal, characteristic, complemented
4#20298910C211yesmaximal, characteristic, complemented
5#20298877C211yesmaximal, characteristic, complemented
6#20298876C211yesmaximal, characteristic, complemented
7#20298792C211yesmaximal, characteristic, complemented
8#20298791C211yesmaximal, characteristic, complemented
9#20298733C211yesmaximal, characteristic, complemented
10#20298730C211yesmaximal, characteristic, complemented
11C4×D904C211yesmaximal, characteristic, complemented
12C4×#14268632C211yesmaximal, characteristic, complemented
13C4×#14268632C211yesmaximal, characteristic, complemented
14#20298649C211yesmaximal, characteristic, complemented
15C4×D8×C113C211yesmaximal, characteristic, complemented
16C2×#14268647—21no—
17C2×D4×D113C2211yescharacteristic
18C22×C4×D113—21no—
19C2×D904C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21C2×#14268632C2211yescharacteristic
22#16813621C2211yescharacteristic, complemented
23#16813618C2211yescharacteristic, complemented
24#16813608—21no—
25#16813597C2211yescharacteristic
26#16813595—21no—
27#16813593C2211yescharacteristic
28C4×D452C2211yescharacteristic
29C4×D452C2211yescharacteristic, complemented
30D4×Dic113C2211yescharacteristic
31#16813584C2211yescharacteristic
32C4×C22⋊D113—21no—
33C4×C22⋊D113—21no—
34#16813582—21no—
35C4⋊C4×D113C2211yescharacteristic
36C22⋊C4×D113—21no—
37C42×D113C2211yescharacteristic
38#16813556C2211yescharacteristic, complemented
39#16813555C2211yescharacteristic, complemented
40#16813555C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813551C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic
44#16813544C2211yescharacteristic, complemented
45#16813543C2211yescharacteristic
46#16813543C2211yescharacteristic, complemented
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic, complemented
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51C4×#11744751C2211yescharacteristic, complemented
52C2×D8×C113C2211yescharacteristic
53C4×D4×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic, complemented
55#107×C113C2211yescharacteristic, complemented
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic, complemented
58C4×C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268647—44no—
61C2×Dic226—21no—
62C2×D452—21no—
63C2×D452C2311yescharacteristic
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69D4×D113—22no—
70D4×D113—22no—
71C22×Dic113—21no—
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76C2×C4×D113—44no—
77C2×C4×D113D411yescharacteristic
78C2×C4×D113D411yescharacteristic
79C2×C4×D113C2311yescharacteristic
80D904—22no—
81#14268632—22no—
82#14268632—22no—
83C2×#11744751C2311yescharacteristic
84C2×#11744751C2311yescharacteristic
85C4⋊Dic113C2311yescharacteristic
86C4⋊Dic113C2311yescharacteristic
87#14268626—21no—
88#14268626—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95C4×Dic113D411yescharacteristic
96C4×Dic113D411yescharacteristic
97C4×Dic113C2311yescharacteristic
98C2×D4×C113C2311yescharacteristic
99C2×D4×C113C2311yescharacteristic
100C22×C4×C113—21no—
101C22×C4×C113—21no—
102D8×C113—22no—
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C4⋊C4×C113C2311yescharacteristic
107C22⋊C4×C113—21no—
108C22⋊C4×C113—21no—
109C42×C113C2311yescharacteristic
110C23×C113—21no—
111C23×C113—21no—
112C22×D113—24no—
113C22×D113—21no—
114C22×D113—21no—
115C22×D113—42no—
116C22×D113—42no—
117C22×D113C2×D411yescharacteristic
118D4×C113—21no—
119D4×C113—21no—
120D4×C113—21no—
121D4×C113#4112yescomplemented
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—42no—
125C2×C4×C113—42no—
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2411yescharacteristic
129C22⋊D113—24no—
130C22⋊D113—42no—
131C22⋊D113—42no—
132C22⋊D113—42no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—42no—
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139D452—21no—
140D452—21no—
141D452—21no—
142D452—42no—
143D452#4112yescomplemented
144C4×D113—21no—
145C4×D113—21no—
146C4×D113—41no—
147C4×D113—42no—
148C4×D113—42no—
149C4×D113—42no—
150C4×D113—42no—
151C4×D113D814yescomplemented
152Dic226—42no—
153C8×C113—21no—
154C8×C113—21no—
155#11744751—21no—
156#11744751—21no—
157C22×C113—22no—
158C22×C113—41no—
159C22×C113—41no—
160C22×C113—41no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113C22×D411yescharacteristic
164C2×D113—21no—
165C2×D113—21no—
166C2×D113—22no—
167C2×D113—48no—
168C2×D113—41no—
169C2×D113—41no—
170C2×D113—41no—
171C2×D113—41no—
172C2×D113—41no—
173C2×D113C2×D812yes—
174C4×C113—21no—
175C4×C113—41no—
176C4×C113—41no—
177C4×C113C2×D812yes—
178C4×C113C2×#4111yescharacteristic
179C4×C113C2×#4111yescharacteristic
180Dic113—21no—
181Dic113—21no—
182Dic113—41no—
183Dic113—41no—
184Dic113C2×D812yes—
185C2×C113—42no—
186C2×C113—81no—
187C2×C113#52511yescharacteristic
188C2×C113C22×D811yescharacteristic
189C2×C113#57511yescharacteristic
190D113—22no—
191D113—42no—
192D113—81no—
193#3100—1131nomaximal, Sylow
194C113#310011yescharacteristic, complemented, Sylow
195#532—1131no—
196C2×C4×D4—1131no—
197#480—1131no—
198#480—1131no—
199#474—1131no—
200#474—1131no—
201#459—1131no—
202#459—1131no—
203#447—1131no—
204#447—1131no—
205C4×D8—1131no—
206C4×D8—1131no—
207C4×D8—1131no—
208C4×D8D11311yescharacteristic, complemented
209#431—1131no—
210C2×#41—2261no—
211C22×D4—1131no—
212C23×C4—2261no—
213C2×D8—1131no—
214C2×D8—1131no—
215C2×D8—1131no—
216C2×D8C2×D11311yescharacteristic
217C4⋊Q8—1131no—
218#127—1131no—
219#124—2261no—
220#121—1131no—
221#121—1131no—
222#121—2261no—
223C4×D4—1131no—
224C4×D4—1131no—
225C4×D4—1131no—
226C4×D4—1131no—
227C4×D4—2261no—
228C4×D4—2261no—
229C4×D4—2261no—
230C4×D4C2×D11311yescharacteristic
231C4×D4C2×D11311yescharacteristic, complemented
232C2×C4⋊C4—1131no—
233C2×C22⋊C4—2261no—
234C2×C42—1131no—
235#107—1131no—
236#107—1131no—
237#107—1131no—
238#107C2×D11311yescharacteristic, complemented
239C4⋊C8—1131no—
240C4⋊C8—1131no—
241#102—1131no—
242#102—1131no—
243#102—1131no—
244#102—1131no—
245#102—1131no—
246#102—1131no—
247#102C2×D11311yescharacteristic
248#102C2×D11311yescharacteristic, complemented
249C22⋊C8—1131no—
250C22⋊C8—1131no—
251C4×C8—1131no—
252C4×C8C2×D11311yescharacteristic, complemented
253C24—2261no—
254#41—4524no—
255C2×Q8—2261no—
256C2×D4—1131no—
257C2×D4—1131no—
258C2×D4—2261no—
259C2×D4—2261no—
260C2×D4—2261no—
261C2×D4—2261no—
262C2×D4—2262no—
263C2×D4—2261no—
264C2×D4—2262no—
265C2×D4C22×D11311yescharacteristic
266C2×D4C22×D11311yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—1131no—
270C22×C4—1131no—
271C22×C4—1131no—
272C22×C4—4524no—
273C22×C4—2261no—
274C22×C4—2261no—
275C22×C4—2261no—
276C22×C4—2261no—
277C22×C4—2261no—
278D8—22no—
279D8—2262no—
280D8—2262no—
281D8—2262no—
282C2×C8—1131no—
283C2×C8—1131no—
284C2×C8C22×D11311yescharacteristic
285C2×C8C22×D11311yescharacteristic
286C4⋊C4—1131no—
287C4⋊C4—1131no—
288C4⋊C4—2261no—
289C4⋊C4—2261no—
290C4⋊C4C22×D11311yescharacteristic
291C4⋊C4C22×D11311yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C22⋊C4—2261no—
300C42—1131no—
301C42—1131no—
302C42—1131no—
303C42C22×D11311yescharacteristic
304C23—21no—
305C23—21no—
306C23—1131no—
307C23—4522no—
308C23—4522no—
309C23—2264no—
310C23—2261no—
311C23—2261no—
312Q8—4522no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—1132no—
317D4—4522no—
318D4—4522no—
319D4—4522no—
320D4—4522no—
321D4—2264no—
322D4—2261no—
323D4—2261no—
324D4—2261no—
325D4#1426864712yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—1131no—
331C2×C4—1134no—
332C2×C4—1131no—
333C2×C4—1131no—
334C2×C4—4521no—
335C2×C4—4522no—
336C2×C4—4522no—
337C2×C4—4522no—
338C2×C4—4522no—
339C2×C4—4522no—
340C2×C4—2261no—
341C2×C4—2261no—
342C2×C4—2261no—
343C2×C4—2261no—
344C2×C4D4×D11311yescharacteristic
345C2×C4D4×D11311yescharacteristic
346C2×C4C23×D11311yescharacteristic
347C8—21no—
348C8—21no—
349C8—2261no—
350C8—2261no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—1132no—
358C22—4528no—
359C22—4521no—
360C22—4521no—
361C22—4521no—
362C22—4521no—
363C22—4521no—
364C22—2262no—
365C22—2261no—
366C22—2261no—
367C22C2×D4×D11311yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—1132no—
372C4—4521no—
373C4—4521no—
374C4—2261no—
375C4—2261no—
376C4D8×D11312yes—
377C4#41×D11311yescharacteristic
378C4C2×#1426864711yescharacteristic
379C2—42no—
380C2—81no—
381C2—9041no—
382C2—4522no—
383C2—2262no—
384C2#2029910711yescharacteristic
385C2C2×D8×D11311yescharacteristic
386C2#2029939511yescharacteristic
subgroupG/H
centerC2×C4D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC4×D8×C113C2
socleC22×C113C22×D4
hypercenterC4×D8D113
hypocenterC113#3100
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #20299145C2semidirect
2. C4×D4×D113C2semidirect
3. #20298913C2semidirect
4. #20298910C2semidirect
5. #20298877C2semidirect
6. #20298876C2semidirect
7. #20298792C2semidirect
8. #20298791C2semidirect
9. #20298733C2semidirect
10. #20298730C2semidirect
11. C4×D904C2semidirect
12. C4×#14268632C2semidirect
13. C4×#14268632C2semidirect
14. #20298649C2semidirect
15. C4×D8×C113C2semidirect
22. #16813621C22semidirect
23. #16813618C22semidirect
29. C4×D452C22semidirect
38. #16813556C22semidirect
39. #16813555C22semidirect
40. #16813555C22semidirect
41. #16813551C22semidirect
42. #16813551C22semidirect
44. #16813544C22semidirect
46. #16813543C22semidirect
48. #16813542C22semidirect
51. C4×#11744751C22semidirect
54. C4×D4×C113C22semidirect
55. #107×C113C22semidirect
57. #102×C113C22semidirect
58. C4×C8×C113C22semidirect
121. D4×C113#41semidirect
143. D452#41semidirect
151. C4×D113D8semidirect
194. C113#3100semidirect
208. C4×D8D113semidirect
231. C4×D4C2×D113semidirect
238. #107C2×D113semidirect
248. #102C2×D113semidirect
252. C4×C8C2×D113semidirect
325. D4#14268647semidirect

Maximal subgroups

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

subgroupindex
#202991452
C4×D4×D1132
#202989132
#202989102
#202988772
#202988762
#202987922
#202987912
#202987332
#202987302
C4×D9042
C4×#142686322
#202986492
C4×D8×C1132
#3100113