Finite Group Databasebeta

← #28401341

Subgroups — #28401341

Order 14464.

472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#20299109C211yesmaximal, characteristic, complemented
2C2×#16813596C211yesmaximal, characteristic, complemented
3#20298934C211yesmaximal, characteristic, complemented
4#20298923C212yesmaximal, complemented
5#20298917C211yesmaximal, characteristic, complemented
6#20298834C212yesmaximal, complemented
7#20298827C212yesmaximal, complemented
8#20298751C211yesmaximal, characteristic, complemented
9#20298745C212yesmaximal, complemented
10#20298734C211yesmaximal, characteristic, complemented
11C2×C22⋊C8×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic, complemented
13C22×D452C2211yescharacteristic
14C22×C22⋊D113—21no—
15C2×#14268636C2212yescomplemented
16C2×D904C2212yescomplemented
17#16813605—21no—
18#16813601C2211yescharacteristic
19#16813601C2211yescharacteristic, complemented
20#16813596—21no—
21#16813596—21no—
22#16813596C2212yes—
23#16813596C2212yes—
24#16813596C2211yescharacteristic
25#16813596C2211yescharacteristic, complemented
26#16813591—21no—
27C4×C22⋊D113—21no—
28C4×C22⋊D113—21no—
29#16813581C2211yescharacteristic, complemented
30C2×C4⋊Dic113C2211yescharacteristic
31C2×#14268624—21no—
32#16813556C2212yescomplemented
33#16813554C2212yescomplemented
34#16813547C2212yescomplemented
35#16813544C2212yescomplemented
36#16813544C2212yescomplemented
37#16813544C2212yescomplemented
38C23×C4×C113C2211yescharacteristic
39C22×C8×C113C2212yescomplemented
40C22⋊C8×C113C2211yescharacteristic
41C22⋊C8×C113C2211yescharacteristic
42C22⋊C8×C113C2212yescomplemented
43C23×D113—21no—
44#14268647—42no—
45C2×Dic226C2311yescharacteristic
46C2×D452—21no—
47C2×D452—42no—
48C2×D452C2312yes—
49C2×D452C2311yescharacteristic
50C2×C22⋊D113—21no—
51C2×C22⋊D113—21no—
52C2×C22⋊D113—21no—
53C2×C22⋊D113—22no—
54C2×C22⋊D113—22no—
55C2×C22⋊D113—44no—
56C22×Dic113—21no—
57C2×C4×D113—21no—
58#14268636—42no—
59D904—42no—
60C4⋊Dic113—21no—
61C4⋊Dic113C2312yes—
62C4⋊Dic113C2311yescharacteristic
63C4⋊Dic113C2311yescharacteristic
64#14268626—21no—
65#14268626—21no—
66C22⋊Dic113—21no—
67C22⋊Dic113—21no—
68C22⋊Dic113—21no—
69#14268624—22no—
70#14268624—22no—
71#14268624—21no—
72#14268624—21no—
73C4×Dic113—21no—
74C24×C113D411yescharacteristic
75C22×C4×C113—42no—
76C22×C4×C113D411yescharacteristic
77C22×C4×C113D411yescharacteristic
78C22×C4×C113D411yescharacteristic
79C22×C4×C113C2311yescharacteristic
80C22×C4×C113C2311yescharacteristic
81C22×C4×C113C2311yescharacteristic
82C2×C8×C113—42no—
83C2×C8×C113C2312yes—
84C2×C8×C113C2312yes—
85C23×C113—22no—
86C23×C113—22no—
87C23×C113—41no—
88C23×C113C2×D411yescharacteristic
89C23×C113C2×D411yescharacteristic
90C23×C113C2×D411yescharacteristic
91C22×D113—21no—
92C22×D113—22no—
93C22×D113—42no—
94C22×D113—42no—
95C22×D113—42no—
96C2×C4×C113—22no—
97C2×C4×C113—22no—
98C2×C4×C113—22no—
99C2×C4×C113—41no—
100C2×C4×C113—41no—
101C2×C4×C113—41no—
102C2×C4×C113C2×D411yescharacteristic
103C2×C4×C113C2×D411yescharacteristic
104C2×C4×C113C2×D411yescharacteristic
105C2×C4×C113C2411yescharacteristic
106C22⋊D113—44no—
107C22⋊D113—42no—
108C22⋊D113—42no—
109C22⋊D113—42no—
110C22⋊D113—44no—
111C2×Dic113—21no—
112C2×Dic113—21no—
113C2×Dic113—22no—
114C2×Dic113—21no—
115C2×Dic113—42no—
116D452—22no—
117D452—22no—
118D452—22no—
119D452—42no—
120C4×D113—42no—
121Dic226—22no—
122C8×C113—22no—
123C8×C113—22no—
124C22×C113—21no—
125C22×C113—21no—
126C22×C113—21no—
127C22×C113—21no—
128C22×C113—21no—
129C22×C113—21no—
130C22×C113—21no—
131C22×C113—44no—
132C22×C113#13512yes—
133C22×C113AGL(1,ℤ/8)12yes—
134C22×C113C22×D411yescharacteristic
135C2×D113—41no—
136C2×D113—42no—
137C2×D113—41no—
138C2×D113—42no—
139C2×D113—42no—
140C2×D113—41no—
141C2×D113—84no—
142C4×C113—21no—
143C4×C113—21no—
144C4×C113—21no—
145C4×C113H(5,𝔽2)12yes—
146Dic113—41no—
147Dic113—41no—
148Dic113—42no—
149Dic113—41no—
150C2×C113—22no—
151C2×C113—22no—
152C2×C113—41no—
153C2×C113#53411yescharacteristic
154C2×C113C2×#13511yescharacteristic
155C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
156D113—81no—
157D113—82no—
158#3188—1131nomaximal, Sylow
159C113#318811yescharacteristic, complemented, Sylow
160#525—1131no—
161C2×#121—1131no—
162#484—1131no—
163#482—1132no—
164#481—1131no—
165#466—1132no—
166#465—1132no—
167#450—1131no—
168#449—1132no—
169#447—1131no—
170C2×C22⋊C8D11311yescharacteristic, complemented
171C2×#41—1131no—
172C22×D4—1131no—
173C22×D4—2261no—
174C23×C4C2×D11311yescharacteristic
175C2×SD16—1132no—
176C2×D8—1132no—
177C22×C8C2×D11312yescomplemented
178#123—2261no—
179C22⋊Q8—1131no—
180C22⋊Q8—1131no—
181#121—1132no—
182#121—1132no—
183#121—1131no—
184#121—1131no—
185#121—2261no—
186#121—2261no—
187#120—2261no—
188C4×D4—2261no—
189C4×D4—2261no—
190#117—1131no—
191C2×C4⋊C4—1131no—
192C2×C22⋊C4—2261no—
193#107—1132no—
194#106—1132no—
195#103—1132no—
196#102—1132no—
197#102—1132no—
198#102—1132no—
199C22⋊C8C2×D11311yescharacteristic
200C22⋊C8C2×D11311yescharacteristic
201C22⋊C8C2×D11312yescomplemented
202C24—2261no—
203C24D45211yescharacteristic
204#41—4522no—
205C2×Q8—1131no—
206C2×D4—1131no—
207C2×D4—1132no—
208C2×D4—4522no—
209C2×D4—4524no—
210C2×D4—2261no—
211C2×D4—2261no—
212C2×D4—2261no—
213C2×D4—2262no—
214C2×D4—2262no—
215C2×D4—2261no—
216C22×C4—42no—
217C22×C4—2261no—
218C22×C4—2261no—
219C22×C4D45211yescharacteristic
220C22×C4D45211yescharacteristic
221C22×C4D45211yescharacteristic
222C22×C4C22×D11311yescharacteristic
223C22×C4C22×D11311yescharacteristic
224C22×C4C22×D11311yescharacteristic
225SD16—4522no—
226D8—4522no—
227C2×C8—42no—
228C2×C8C22×D11312yes—
229C2×C8C22×D11312yes—
230C4⋊C4—1131no—
231C4⋊C4—1131no—
232C4⋊C4—1132no—
233C4⋊C4—2261no—
234C4⋊C4—2261no—
235C4⋊C4—2261no—
236C22⋊C4—2261no—
237C22⋊C4—2261no—
238C22⋊C4—2261no—
239C22⋊C4—2262no—
240C22⋊C4—2262no—
241C22⋊C4—2261no—
242C22⋊C4—2261no—
243C42—2261no—
244C23—22no—
245C23—22no—
246C23—41no—
247C23—4522no—
248C23—4522no—
249C23—4522no—
250C23—2261no—
251C23—2262no—
252C23C2×D45211yescharacteristic
253C23C2×D45211yescharacteristic
254C23C2×D45211yescharacteristic
255Q8—2262no—
256D4—4522no—
257D4—4524no—
258D4—4522no—
259D4—4522no—
260D4—4524no—
261D4—4522no—
262D4—2262no—
263D4—2262no—
264D4—2262no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—4522no—
272C2×C4—4522no—
273C2×C4—2261no—
274C2×C4—2261no—
275C2×C4—2262no—
276C2×C4—2261no—
277C2×C4C2×D45211yescharacteristic
278C2×C4C2×D45211yescharacteristic
279C2×C4C2×D45211yescharacteristic
280C2×C4C23×D11311yescharacteristic
281C8—22no—
282C8—22no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—44no—
291C22—9044no—
292C22—4521no—
293C22—4522no—
294C22—4522no—
295C22—4521no—
296C22—4521no—
297C22—4522no—
298C22#1681364412yes—
299C22#1681365012yes—
300C22C22×D45211yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—4521no—
305C4—4522no—
306C4—4521no—
307C4—4521no—
308C4#1681366712yes—
309C2—22no—
310C2—22no—
311C2—41no—
312C2—9042no—
313C2—9041no—
314C2#2029916011yescharacteristic
315C2C2×#1681364411yescharacteristic
316C2C2×#1681365011yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×C22⋊C8×C113C2
socleC22×C113C22×D4
hypercenterC2×C22⋊C8D113
hypocenterC113#3188
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #20299109C2semidirect
2. C2×#16813596C2semidirect
3. #20298934C2semidirect
4. #20298923C2semidirect
5. #20298917C2semidirect
6. #20298834C2semidirect
7. #20298827C2semidirect
8. #20298751C2semidirect
9. #20298745C2semidirect
10. #20298734C2semidirect
11. C2×C22⋊C8×C113C2semidirect
12. C2×#14268647C22semidirect
15. C2×#14268636C22semidirect
16. C2×D904C22semidirect
19. #16813601C22semidirect
25. #16813596C22semidirect
29. #16813581C22semidirect
32. #16813556C22semidirect
33. #16813554C22semidirect
34. #16813547C22semidirect
35. #16813544C22semidirect
36. #16813544C22semidirect
37. #16813544C22semidirect
39. C22×C8×C113C22semidirect
42. C22⋊C8×C113C22semidirect
159. C113#3188semidirect
170. C2×C22⋊C8D113semidirect
177. C22×C8C2×D113semidirect
201. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991092
C2×#168135962
#202989342
#202989232
#202989172
#202988342
#202988272
#202987512
#202987452
#202987342
C2×C22⋊C8×C1132
#3188113