Finite Group Databasebeta

← #28401540

Subgroups — #28401540

Order 14464.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299133C211yesmaximal, characteristic, complemented
2#124×D113C211yesmaximal, characteristic, complemented
3#20298982C211yesmaximal, characteristic, complemented
4#20298980C211yesmaximal, characteristic, complemented
5#20298955C211yesmaximal, characteristic, complemented
6#20298823C211yesmaximal, characteristic, complemented
7#20298819C211yesmaximal, characteristic, complemented
8#20298816C211yesmaximal, characteristic, complemented
9#20298812C211yesmaximal, characteristic, complemented
10#20298755C211yesmaximal, characteristic, complemented
11#20298750C211yesmaximal, characteristic, complemented
12#20298738C211yesmaximal, characteristic, complemented
13#20298733C211yesmaximal, characteristic
14#20298649C211yesmaximal, characteristic, complemented
15#488×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×Dic452C2211yescharacteristic, complemented
19C2×#14268637C2211yescharacteristic, complemented
20C2×#14268636C2211yescharacteristic
21C2×#14268636C2211yescharacteristic, complemented
22C2×#14268635C2211yescharacteristic
23C2×#14268634C2211yescharacteristic, complemented
24C2×D904C2211yescharacteristic
25C2×#14268632C2211yescharacteristic
26#16813617—21no—
27#16813611C2211yescharacteristic
28#16813610C2211yescharacteristic
29#16813610C2211yescharacteristic, complemented
30#16813609C2211yescharacteristic
31#16813608—21no—
32#16813608—21no—
33#16813607—21no—
34#16813602C2211yescharacteristic
35#16813597C2211yescharacteristic
36#16813587C2211yescharacteristic, complemented
37#16813584—21no—
38#16813584C2211yescharacteristic, complemented
39#16813580—21no—
40C22⋊C4×D113—21no—
41C22⋊C4×D113—21no—
42C42×D113C2211yescharacteristic
43#16813551C2211yescharacteristic, complemented
44#16813551C2211yescharacteristic, complemented
45#16813545C2211yescharacteristic, complemented
46#16813545C2211yescharacteristic, complemented
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51C4×#11744751C2211yescharacteristic, complemented
52#125×C113C2211yescharacteristic, complemented
53#124×C113C2211yescharacteristic
54#103×C113C2211yescharacteristic, complemented
55#103×C113C2211yescharacteristic, complemented
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C4×C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C2×Dic226—21no—
61C2×Dic226C2311yescharacteristic
62C2×Dic226C2311yescharacteristic
63Q8×D113—41no—
64Q8×D113—41no—
65C2×D452—21no—
66C2×D452C2311yescharacteristic
67C2×D452C2311yescharacteristic
68C2×C22⋊D113—21no—
69D4×D113—41no—
70D4×D113—41no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113D411yescharacteristic
74C2×C4×D113D411yescharacteristic
75C2×C4×D113C2311yescharacteristic
76Dic452—41no—
77#14268637—41no—
78#14268636—41no—
79#14268636—41no—
80#14268635—41no—
81#14268634—41no—
82D904—41no—
83#14268632—41no—
84C2×#11744751C2311yescharacteristic
85C2×#11744751C2311yescharacteristic
86C4⋊Dic113—21no—
87#14268626—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624—21no—
99C4×Dic113—21no—
100C4×Dic113D411yescharacteristic
101C4×Dic113D411yescharacteristic
102C4×Dic113C2311yescharacteristic
103C2×Q8×C113C2311yescharacteristic
104C2×D4×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113—21no—
108C4⋊C4×C113—21no—
109C4⋊C4×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
111C22⋊C4×C113—21no—
112C22⋊C4×C113—21no—
113C42×C113C2311yescharacteristic
114C23×C113—21no—
115C22×D113—21no—
116C22×D113—21no—
117C22×D113—42no—
118C22×D113—42no—
119C22×D113—42no—
120C22×D113C2×D411yescharacteristic
121Q8×C113—21no—
122Q8×C113—21no—
123D4×C113—21no—
124D4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2411yescharacteristic
131C22⋊D113—42no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137D452—21no—
138D452—21no—
139D452—21no—
140D452—21no—
141D452—42no—
142C4×D113—22no—
143C4×D113—21no—
144C4×D113—21no—
145C4×D113—41no—
146C4×D113—42no—
147C4×D113—42no—
148Dic226—21no—
149Dic226—21no—
150Dic226—21no—
151Dic226—21no—
152Dic226—42no—
153C8×C113—21no—
154C8×C113—21no—
155#11744751—21no—
156#11744751—21no—
157C22×C113—41no—
158C22×C113—41no—
159C22×C113—41no—
160C22×C113C22×D411yescharacteristic
161C2×D113—21no—
162C2×D113—21no—
163C2×D113—41no—
164C2×D113—41no—
165C2×D113—41no—
166C2×D113—41no—
167C2×D113—41no—
168C2×D113—41no—
169C2×D113—84no—
170C2×D113#13512yes—
171C4×C113—21no—
172C4×C113—21no—
173C4×C113—41no—
174C4×C113—41no—
175C4×C113—41no—
176C4×C113H(5,𝔽2)11yescharacteristic
177C4×C113H(5,𝔽2)11yescharacteristic
178Dic113—21no—
179Dic113—21no—
180Dic113—21no—
181Dic113—41no—
182Dic113—41no—
183C2×C113—81no—
184C2×C113#53511yescharacteristic
185C2×C113C2×#13511yescharacteristic
186C2×C113#57511yescharacteristic
187D113—22no—
188D113—81no—
189D113—81no—
190#3211—1131nomaximal, Sylow
191C113#321111yescharacteristic, complemented, Sylow
192#529—1131no—
193C2×#124—1131no—
194#495—1131no—
195#495—1131no—
196#488—1131no—
197#488D11311yescharacteristic, complemented
198#464—1131no—
199#464—1131no—
200#463—1131no—
201#463—1131no—
202#451—1131no—
203#450—1131no—
204#448—1131no—
205#447—1131no—
206#431—1131no—
207C22×Q8—1131no—
208C22×D4—1131no—
209C2×Q16—1131no—
210C2×Q16—1131no—
211C2×SD16—1131no—
212C2×SD16—1131no—
213C2×SD16—1131no—
214C2×SD16—1131no—
215C2×D8—1131no—
216C2×D8—1131no—
217#126—2261no—
218#125C2×D11311yescharacteristic, complemented
219#124—1131no—
220#124—1131no—
221#124—1131no—
222#124—1131no—
223#124—2261no—
224#124—2261no—
225#124C2×D11311yescharacteristic
226#123—2261no—
227C22⋊Q8—1131no—
228#121—1131no—
229C4×Q8—1131no—
230C4×D4—1131no—
231C4×D4—2261no—
232#117—2261no—
233C2×C22⋊C4—2261no—
234C2×C22⋊C4—2261no—
235C2×C42—1131no—
236C4⋊C8—1131no—
237C4⋊C8—1131no—
238#103—1131no—
239#103—1131no—
240#103C2×D11311yescharacteristic, complemented
241#103C2×D11311yescharacteristic, complemented
242#102—1131no—
243#102—1131no—
244#102C2×D11311yescharacteristic
245#102C2×D11311yescharacteristic
246C22⋊C8—1131no—
247C22⋊C8—1131no—
248C4×C8—1131no—
249C4×C8C2×D11311yescharacteristic, complemented
250C24—2261no—
251C2×Q8—1131no—
252C2×Q8—1131no—
253C2×Q8—4521no—
254C2×Q8—4521no—
255C2×Q8—2261no—
256C2×Q8C22×D11311yescharacteristic
257C2×D4—1131no—
258C2×D4—1131no—
259C2×D4—4521no—
260C2×D4—4521no—
261C2×D4—2261no—
262C2×D4—2261no—
263C2×D4C22×D11311yescharacteristic
264C22×C4—1131no—
265C22×C4—1131no—
266C22×C4—1131no—
267C22×C4—2261no—
268C22×C4—2261no—
269Q16—4521no—
270Q16—4521no—
271SD16—4521no—
272SD16—4521no—
273SD16—4521no—
274SD16—4521no—
275D8—4521no—
276D8—4521no—
277C2×C8—1131no—
278C2×C8—1131no—
279C2×C8C22×D11311yescharacteristic
280C2×C8C22×D11311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—2261no—
284C4⋊C4—2261no—
285C4⋊C4C22×D11311yescharacteristic
286C4⋊C4C22×D11311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C22⋊C4—2261no—
300C42—1131no—
301C42—1131no—
302C42—1131no—
303C42—2261no—
304C42C22×D11311yescharacteristic
305C23—21no—
306C23—1131no—
307C23—4522no—
308C23—4522no—
309C23—4522no—
310C23—2261no—
311C23—2261no—
312Q8—21no—
313Q8—21no—
314Q8—4522no—
315Q8—2261no—
316Q8—2261no—
317Q8—2261no—
318Q8—2261no—
319D4—21no—
320D4—21no—
321D4—4522no—
322D4—4522no—
323D4—2261no—
324D4—2261no—
325D4—2261no—
326D4—2261no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—1131no—
331C2×C4—1131no—
332C2×C4—1131no—
333C2×C4—4521no—
334C2×C4—4522no—
335C2×C4—4522no—
336C2×C4—2262no—
337C2×C4—2261no—
338C2×C4—2261no—
339C2×C4—2261no—
340C2×C4—2261no—
341C2×C4D4×D11311yescharacteristic
342C2×C4D4×D11311yescharacteristic
343C2×C4C23×D11311yescharacteristic
344C8—21no—
345C8—21no—
346C8—2261no—
347C8—2261no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—1132no—
352C22—9044no—
353C22—4521no—
354C22—4521no—
355C22—4521no—
356C22—4521no—
357C22—4521no—
358C22—4521no—
359C22—2261no—
360C22—2261no—
361C22C2×D4×D11311yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—4521no—
368C4—4521no—
369C4—2261no—
370C4—2261no—
371C4—2261no—
372C4#1681366811yescharacteristic
373C4#1681366811yescharacteristic
374C2—81no—
375C2—9041no—
376C2—9041no—
377C2—2262no—
378C2#2029916611yescharacteristic
379C2#135×D11311yescharacteristic
380C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#488×C113C2
socleC22×C113C22×D4
prime radical#20298733C2
hypercenter#488D113
hypocenterC113#3211
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #20299133C2semidirect
2. #124×D113C2semidirect
3. #20298982C2semidirect
4. #20298980C2semidirect
5. #20298955C2semidirect
6. #20298823C2semidirect
7. #20298819C2semidirect
8. #20298816C2semidirect
9. #20298812C2semidirect
10. #20298755C2semidirect
11. #20298750C2semidirect
12. #20298738C2semidirect
14. #20298649C2semidirect
15. #488×C113C2semidirect
18. C2×Dic452C22semidirect
19. C2×#14268637C22semidirect
21. C2×#14268636C22semidirect
23. C2×#14268634C22semidirect
29. #16813610C22semidirect
36. #16813587C22semidirect
38. #16813584C22semidirect
43. #16813551C22semidirect
44. #16813551C22semidirect
45. #16813545C22semidirect
46. #16813545C22semidirect
51. C4×#11744751C22semidirect
52. #125×C113C22semidirect
54. #103×C113C22semidirect
55. #103×C113C22semidirect
58. C4×C8×C113C22semidirect
191. C113#3211semidirect
197. #488D113semidirect
218. #125C2×D113semidirect
240. #103C2×D113semidirect
241. #103C2×D113semidirect
249. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991332
#124×D1132
#202989822
#202989802
#202989552
#202988232
#202988192
#202988162
#202988122
#202987552
#202987502
#202987382
#202987332
#202986492
#488×C1132
#3211113