Finite Group Databasebeta

← #28401372

Subgroups — #28401372

Order 14464.

514 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813593C211yesmaximal, characteristic, complemented
2#121×D113C211yesmaximal, characteristic, complemented
3#20298917C211yesmaximal, characteristic, complemented
4#20298915C212yesmaximal, complemented
5#20298914C211yesmaximal, characteristic, complemented
6#20298850C212yesmaximal, complemented
7#20298848C212yesmaximal, complemented
8#20298732C211yesmaximal, characteristic, complemented
9#20298730C212yesmaximal, complemented
10#20298560C211yesmaximal, characteristic, complemented
11#447×C113C211yesmaximal, characteristic, complemented
12C22×C22⋊D113—21no—
13C2×D4×D113—21no—
14C2×D4×D113C2211yescharacteristic, complemented
15C22×C4×D113C2211yescharacteristic
16C2×#14268632C2212yescomplemented
17C2×#14268630C2212yescomplemented
18#16813597C2211yescharacteristic, complemented
19#16813596C2211yescharacteristic
20#16813595—21no—
21#16813594—21no—
22#16813593—21no—
23#16813593—21no—
24#16813593C2212yes—
25#16813593C2211yescharacteristic, complemented
26#16813593C2212yescomplemented
27C2×C4⋊Dic113C2211yescharacteristic, complemented
28C4⋊C4×D113C2211yescharacteristic, complemented
29C2×C22⋊Dic113—21no—
30C22⋊C4×D113—21no—
31#16813554C2212yescomplemented
32#16813553C2212yescomplemented
33#16813544C2212yescomplemented
34#16813543C2212yescomplemented
35#16813543C2212yescomplemented
36C22⋊#11744751C2211yescharacteristic, complemented
37#16813534C2212yescomplemented
38C22×D4×C113C2211yescharacteristic, complemented
39C2×D8×C113C2212yescomplemented
40#121×C113C2211yescharacteristic
41#102×C113C2212yescomplemented
42C22⋊C8×C113C2211yescharacteristic, complemented
43C23×D113—21no—
44C23×D113D411yescharacteristic
45C2×D452—21no—
46C2×D452C2311yescharacteristic
47C2×C22⋊D113—21no—
48C2×C22⋊D113—22no—
49C2×C22⋊D113—22no—
50C2×C22⋊D113—21no—
51C2×C22⋊D113—21no—
52C2×C22⋊D113—44no—
53D4×D113—42no—
54D4×D113—44no—
55C22×Dic113—21no—
56C22×Dic113D411yescharacteristic
57C2×C4×D113—21no—
58C2×C4×D113—42no—
59C2×C4×D113D411yescharacteristic
60C2×C4×D113D411yescharacteristic
61C2×C4×D113C2311yescharacteristic
62C2×C4×D113C2311yescharacteristic
63#14268632—42no—
64#14268630—42no—
65C2×#11744751C2312yes—
66C4⋊Dic113—21no—
67C4⋊Dic113C2311yescharacteristic
68C4⋊Dic113C2312yes—
69#14268626—21no—
70C22⋊Dic113—21no—
71C22⋊Dic113—22no—
72C22⋊Dic113—22no—
73#14268624—21no—
74#14268624—21no—
75C24×C113—21no—
76C2×D4×C113—21no—
77C2×D4×C113—21no—
78C2×D4×C113—42no—
79C2×D4×C113C2312yes—
80C2×D4×C113C2311yescharacteristic
81C22×C4×C113C2311yescharacteristic
82D8×C113—42no—
83C2×C8×C113C2312yes—
84C4⋊C4×C113C2311yescharacteristic
85C22⋊C4×C113—21no—
86C23×C113—21no—
87C23×C113—22no—
88C23×C113—42no—
89C23×C113—42no—
90C23×C113—42no—
91C23×C113C2×D411yescharacteristic
92C22×D113—22no—
93C22×D113—22no—
94C22×D113—21no—
95C22×D113—41no—
96C22×D113—42no—
97C22×D113—42no—
98C22×D113—42no—
99C22×D113C2×D411yescharacteristic
100C22×D113C2×D411yescharacteristic
101D4×C113—22no—
102D4×C113—22no—
103D4×C113—22no—
104D4×C113—42no—
105D4×C113—42no—
106C2×C4×C113—22no—
107C2×C4×C113—21no—
108C2×C4×C113C2×D411yescharacteristic
109C2×C4×C113C2411yescharacteristic
110C22⋊D113—42no—
111C22⋊D113—42no—
112C22⋊D113—44no—
113C22⋊D113—42no—
114C22⋊D113—44no—
115C2×Dic113—21no—
116C2×Dic113—22no—
117C2×Dic113—41no—
118C2×Dic113—42no—
119C2×Dic113C2×D411yescharacteristic
120C2×Dic113C2×D411yescharacteristic
121D452—22no—
122D452—42no—
123C4×D113—22no—
124C4×D113—22no—
125C4×D113—41no—
126C4×D113—41no—
127C4×D113—42no—
128C8×C113—22no—
129#11744751—22no—
130C22×C113—21no—
131C22×C113—21no—
132C22×C113—41no—
133C22×C113—42no—
134C22×C113—42no—
135C22×C113—41no—
136C22×C113—41no—
137C22×C113—42no—
138C22×C113—84no—
139C22×C113AGL(1,ℤ/8)12yes—
140C22×C113C22×D411yescharacteristic
141C2×D113—21no—
142C2×D113—21no—
143C2×D113—21no—
144C2×D113—21no—
145C2×D113—21no—
146C2×D113—44no—
147C2×D113—41no—
148C2×D113—41no—
149C2×D113—41no—
150C2×D113—84no—
151C2×D113AGL(1,ℤ/8)12yes—
152C4×C113—21no—
153C4×C113—41no—
154C4×C113H(5,𝔽2)12yes—
155Dic113—21no—
156Dic113—21no—
157Dic113—41no—
158Dic113—42no—
159C2×C113—22no—
160C2×C113—81no—
161C2×C113—82no—
162C2×C113#53411yescharacteristic
163C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
164C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
165D113—22no—
166D113—41no—
167D113—81no—
168#3192—1131nomaximal, Sylow
169C113#319211yescharacteristic, complemented, Sylow
170C2×#121—1131no—
171C2×#121—1131no—
172#481—1131no—
173#481—1132no—
174#481—1131no—
175#469—1132no—
176#469—1132no—
177#447—1131no—
178#447—1132no—
179#447D11311yescharacteristic, complemented
180#407—1131no—
181C22×D4—1131no—
182C22×D4—2261no—
183C22×D4—2261no—
184C22×D4C2×D11311yescharacteristic, complemented
185C23×C4—1131no—
186C2×D8—1132no—
187C2×D8C2×D11312yescomplemented
188C2×M16—1132no—
189#121—1132no—
190#121—1131no—
191#121—1132no—
192#121—1131no—
193#121—1131no—
194#121—2261no—
195#121—2261no—
196#121—2261no—
197#121—2261no—
198#121C2×D11311yescharacteristic
199C2×C4⋊C4—1131no—
200C2×C4⋊C4—1131no—
201C2×C22⋊C4—2261no—
202C2×C22⋊C4—2261no—
203#106—1132no—
204#106—1132no—
205#102—1132no—
206#102—1132no—
207#102—1132no—
208#102C2×D11312yescomplemented
209C22⋊C8—1131no—
210C22⋊C8—1132no—
211C22⋊C8C2×D11311yescharacteristic, complemented
212C24—21no—
213C24—1131no—
214C24—2261no—
215C2×D4—21no—
216C2×D4—21no—
217C2×D4—42no—
218C2×D4—1131no—
219C2×D4—4524no—
220C2×D4—4524no—
221C2×D4—4522no—
222C2×D4—2261no—
223C2×D4—2261no—
224C2×D4—2262no—
225C2×D4—2261no—
226C2×D4—2262no—
227C2×D4—2261no—
228C2×D4C22×D11311yescharacteristic
229C2×D4C22×D11312yes—
230C22×C4—1131no—
231C22×C4—1131no—
232C22×C4—1131no—
233C22×C4—1131no—
234C22×C4—1131no—
235C22×C4—4522no—
236C22×C4—2261no—
237C22×C4—2261no—
238C22×C4C22×D11311yescharacteristic
239D8—42no—
240D8—4522no—
241M16—4522no—
242C2×C8—1132no—
243C2×C8C22×D11312yes—
244C4⋊C4—1131no—
245C4⋊C4—1132no—
246C4⋊C4—2261no—
247C4⋊C4—2261no—
248C4⋊C4C22×D11311yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—2261no—
251C22⋊C4—2261no—
252C22⋊C4—2262no—
253C22⋊C4—2262no—
254C22⋊C4—2261no—
255C23—21no—
256C23—22no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—1131no—
261C23—1131no—
262C23—4521no—
263C23—4522no—
264C23—4522no—
265C23—4522no—
266C23—2262no—
267C23—2261no—
268C23—2262no—
269C23D4×D11311yescharacteristic
270D4—22no—
271D4—22no—
272D4—22no—
273D4—42no—
274D4—42no—
275D4—4522no—
276D4—4524no—
277D4—4524no—
278D4—4522no—
279D4—4522no—
280D4—4522no—
281D4—2262no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—1131no—
285C2×C4—1131no—
286C2×C4—4521no—
287C2×C4—4521no—
288C2×C4—4522no—
289C2×C4—4522no—
290C2×C4—4521no—
291C2×C4—2262no—
292C2×C4—2261no—
293C2×C4—2262no—
294C2×C4—2262no—
295C2×C4D4×D11311yescharacteristic
296C2×C4C23×D11311yescharacteristic
297C8—22no—
298C8—2262no—
299C22—21no—
300C22—21no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22—42no—
305C22—42no—
306C22—41no—
307C22—84no—
308C22—1132no—
309C22—9044no—
310C22—4524no—
311C22—4521no—
312C22—4521no—
313C22—4521no—
314C22—2261no—
315C22—2261no—
316C22—2261no—
317C22—2261no—
318C22—2261no—
319C22#1681364612yes—
320C22C2×D4×D11311yescharacteristic
321C4—21no—
322C4—41no—
323C4—4522no—
324C4—4521no—
325C4—2261no—
326C4—2261no—
327C4#1681366712yes—
328C2—22no—
329C2—82no—
330C2—81no—
331C2—9041no—
332C2—4521no—
333C2—2262no—
334C2#2029915811yescharacteristic
335C2AGL(1,ℤ/8)×D11311yescharacteristic
336C2C2×#1681364611yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#447×C113C2
socleC22×C113C22×D4
hypercenter#447D113
hypocenterC113#3192
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#16813593C2semidirect
2. #121×D113C2semidirect
3. #20298917C2semidirect
4. #20298915C2semidirect
5. #20298914C2semidirect
6. #20298850C2semidirect
7. #20298848C2semidirect
8. #20298732C2semidirect
9. #20298730C2semidirect
10. #20298560C2semidirect
11. #447×C113C2semidirect
14. C2×D4×D113C22semidirect
16. C2×#14268632C22semidirect
17. C2×#14268630C22semidirect
18. #16813597C22semidirect
25. #16813593C22semidirect
26. #16813593C22semidirect
27. C2×C4⋊Dic113C22semidirect
28. C4⋊C4×D113C22semidirect
31. #16813554C22semidirect
32. #16813553C22semidirect
33. #16813544C22semidirect
34. #16813543C22semidirect
35. #16813543C22semidirect
36. C22⋊#11744751C22semidirect
37. #16813534C22semidirect
38. C22×D4×C113C22semidirect
39. C2×D8×C113C22semidirect
41. #102×C113C22semidirect
42. C22⋊C8×C113C22semidirect
169. C113#3192semidirect
179. #447D113semidirect
184. C22×D4C2×D113semidirect
187. C2×D8C2×D113semidirect
208. #102C2×D113semidirect
211. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135932
#121×D1132
#202989172
#202989152
#202989142
#202988502
#202988482
#202987322
#202987302
#202985602
#447×C1132
#3192113