Finite Group Databasebeta

← #28401050

Subgroups — #28401050

Order 14464.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16813655C211yesmaximal, characteristic, complemented
2C2×#16813650C211yesmaximal, characteristic, complemented
3C2×#16813644C211yesmaximal, characteristic, complemented
4C22×#14268636C211yesmaximal, characteristic, complemented
5#20299174C211yesmaximal, characteristic, complemented
6#20299167C211yesmaximal, characteristic, complemented
7#20298992C212yesmaximal, complemented
8#20298987C212yesmaximal, complemented
9#20298982C212yesmaximal, complemented
10#20298971C212yesmaximal, complemented
11#405×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C2×#14268647C2211yescharacteristic
14C22×Dic226C2211yescharacteristic
15C22×D452C2211yescharacteristic
16#16813655—24no—
17#16813650—24no—
18#16813644—24no—
19C2×Dic452C2211yescharacteristic, complemented
20C2×Dic452C2212yescomplemented
21C2×#14268636—24no—
22C2×#14268636C2212yes—
23C2×#14268636C2212yes—
24C2×#14268636C2212yes—
25C2×#14268636C2211yescharacteristic, complemented
26C2×#14268636C2211yescharacteristic, complemented
27C2×#14268636C2212yescomplemented
28C2×D904C2212yes—
29C2×D904C2211yescharacteristic, complemented
30#16813622C2212yescomplemented
31#16813619C2212yes—
32#16813610C2212yes—
33#16813610C2212yescomplemented
34#16813606—22no—
35#16813602—22no—
36#16813597—22no—
37#16813592—22no—
38C2×M16×C113C2211yescharacteristic
39C22×C8×C113C2211yescharacteristic
40#117×C113C2211yescharacteristic
41#97×C113C2212yescomplemented
42C4×C8×C113C2212yescomplemented
43C23×D113—21no—
44#14268647—22no—
45#14268647—22no—
46#14268647—22no—
47#14268647—22no—
48C2×Dic226—22no—
49C2×Dic226—22no—
50C2×Dic226—21no—
51C2×Dic226C2311yescharacteristic
52C2×Dic226C2312yes—
53C2×Dic226C2311yescharacteristic
54C2×D452—22no—
55C2×D452—22no—
56C2×D452—21no—
57C2×D452—24no—
58C2×D452C2312yes—
59C2×D452C2311yescharacteristic
60C2×D452C2311yescharacteristic
61C2×C22⋊D113—21no—
62C2×C22⋊D113—21no—
63C22×Dic113—21no—
64C2×C4×D113—21no—
65C2×C4×D113—21no—
66Dic452—22no—
67Dic452—24no—
68#14268636—24no—
69#14268636—24no—
70#14268636—24no—
71#14268636—22no—
72#14268636—22no—
73#14268636—24no—
74D904—24no—
75D904—22no—
76C4⋊Dic113—24no—
77#14268624—24no—
78#14268624—24no—
79C22×C4×C113C2311yescharacteristic
80M16×C113D414yescomplemented
81C2×C8×C113D414yescomplemented
82C2×C8×C113C2312yes—
83C2×C8×C113C2311yescharacteristic
84C2×C8×C113C2311yescharacteristic
85C4⋊C4×C113D412yes—
86C22⋊C4×C113D412yes—
87C42×C113C2312yes—
88C23×C113C2×D411yescharacteristic
89C22×D113—21no—
90C22×D113—22no—
91C22×D113—21no—
92C22×D113—42no—
93C22×D113—82no—
94C2×C4×C113C2×D414yes—
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113C2×D412yes—
97C2×C4×C113C2×D412yes—
98C2×C4×C113C2411yescharacteristic
99C22⋊D113—42no—
100C22⋊D113—42no—
101C2×Dic113—21no—
102C2×Dic113—22no—
103C2×Dic113—21no—
104C2×Dic113—42no—
105D452—21no—
106D452—22no—
107D452—21no—
108D452—21no—
109D452—22no—
110D452—21no—
111D452—42no—
112D452—84no—
113C4×D113—42no—
114C4×D113—42no—
115Dic226—22no—
116Dic226—21no—
117Dic226—22no—
118Dic226—21no—
119Dic226—21no—
120Dic226—21no—
121Dic226—42no—
122C8×C113C2×D412yes—
123C8×C113C2×D412yes—
124C8×C113C2×D414yes—
125C22×C113—22no—
126C22×C113#12712yes—
127C22×C113C22×D411yescharacteristic
128C2×D113—41no—
129C2×D113—41no—
130C2×D113—42no—
131C2×D113—42no—
132C2×D113—44no—
133C2×D113—42no—
134C2×D113—84no—
135C4×C113—24no—
136C4×C113#12712yes—
137C4×C113C22×D411yescharacteristic
138C4×C113C22×D411yescharacteristic
139Dic113—42no—
140Dic113—41no—
141Dic113—41no—
142C2×C113—22no—
143C2×C113C2×#12711yescharacteristic
144C2×C113#57712yes—
145D113—81no—
146D113—81no—
147D113—82no—
148#3154—1131nomaximal, Sylow
149C113#315411yescharacteristic, complemented, Sylow
150C2×#137—1131no—
151C2×AGL(1,ℤ/8)—1131no—
152C2×#135—1131no—
153C22×SD16—1131no—
154#536—1131no—
155#535—1131no—
156#497—1132no—
157#496—1132no—
158#495—1132no—
159#492—1132no—
160#405D11311yescharacteristic, complemented
161C2×#41—1131no—
162C2×#41—1131no—
163C22×Q8—1131no—
164C22×D4—1131no—
165#137—2264no—
166AGL(1,ℤ/8)—2264no—
167#135—2264no—
168C2×Q16—1131no—
169C2×Q16—1132no—
170C2×SD16—1132no—
171C2×SD16—1132no—
172C2×SD16—1131no—
173C2×SD16—1131no—
174C2×SD16—1132no—
175C2×SD16—1132no—
176C2×SD16—2264no—
177C2×D8—1131no—
178C2×D8—1132no—
179C2×M16C2×D11311yescharacteristic
180C22×C8C2×D11311yescharacteristic
181C4⋊Q8—1132no—
182#127—1132no—
183#124—1132no—
184#124—1132no—
185#123—2262no—
186C22⋊Q8—2262no—
187#121—2262no—
188#120—2262no—
189#117C2×D11311yescharacteristic
190#97C2×D11312yescomplemented
191C4×C8C2×D11312yescomplemented
192C24—2261no—
193#41—2262no—
194#41—2262no—
195#41—2262no—
196#41—2262no—
197C2×Q8—1131no—
198C2×Q8—1132no—
199C2×Q8—1131no—
200C2×Q8—2262no—
201C2×Q8—2262no—
202C2×Q8—2261no—
203C2×D4—1131no—
204C2×D4—1132no—
205C2×D4—1131no—
206C2×D4—2261no—
207C2×D4—2261no—
208C2×D4—2264no—
209C2×D4—2261no—
210C2×D4—2262no—
211C2×D4—2262no—
212C22×C4—2261no—
213C22×C4—2261no—
214C22×C4—2261no—
215C22×C4C22×D11311yescharacteristic
216Q16—2262no—
217Q16—2264no—
218SD16—2264no—
219SD16—2264no—
220SD16—2262no—
221SD16—2262no—
222SD16—2264no—
223SD16—2264no—
224D8—2262no—
225D8—2264no—
226M16D45214yescomplemented
227C2×C8D45214yescomplemented
228C2×C8C22×D11311yescharacteristic
229C2×C8C22×D11312yes—
230C2×C8C22×D11311yescharacteristic
231C4⋊C4—2264no—
232C4⋊C4D45212yes—
233C22⋊C4—2264no—
234C22⋊C4—2264no—
235C22⋊C4D45212yes—
236C42C22×D11312yes—
237C23—9042no—
238C23—4522no—
239C23—2261no—
240C23—2262no—
241C23—2261no—
242C23C2×D45211yescharacteristic
243Q8—4522no—
244Q8—2262no—
245Q8—2261no—
246Q8—2262no—
247Q8—2261no—
248Q8—2261no—
249Q8—2261no—
250D4—9044no—
251D4—4522no—
252D4—4522no—
253D4—4522no—
254D4—2261no—
255D4—2262no—
256D4—2261no—
257D4—2261no—
258D4—2262no—
259D4—2261no—
260C2×C4—4522no—
261C2×C4—4522no—
262C2×C4—4522no—
263C2×C4—2261no—
264C2×C4—2262no—
265C2×C4—2261no—
266C2×C4C2×D45214yes—
267C2×C4C2×D45211yescharacteristic
268C2×C4C2×D45212yes—
269C2×C4C2×D45212yes—
270C2×C4C23×D11311yescharacteristic
271C8C2×D45212yes—
272C8C2×D45212yes—
273C8C2×D45214yes—
274C22—22no—
275C22—9044no—
276C22—4521no—
277C22—4521no—
278C22—4522no—
279C22—4522no—
280C22—4524no—
281C22—4522no—
282C22#1681361912yes—
283C22C22×D45211yescharacteristic
284C4—24no—
285C4—4521no—
286C4—4521no—
287C4—4522no—
288C4#1681361912yes—
289C4C22×D45211yescharacteristic
290C4C22×D45211yescharacteristic
291C2—22no—
292C2—9042no—
293C2—9041no—
294C2—9041no—
295C2C2×#1681361911yescharacteristic
296C2#2029941012yes—
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#405×C113C2
socleC22×C113C22×D4
hypercenter#405D113
hypocenterC113#3154
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
1. C2×#16813655C2semidirect
2. C2×#16813650C2semidirect
3. C2×#16813644C2semidirect
4. C22×#14268636C2semidirect
5. #20299174C2semidirect
6. #20299167C2semidirect
7. #20298992C2semidirect
8. #20298987C2semidirect
9. #20298982C2semidirect
10. #20298971C2semidirect
11. #405×C113C2semidirect
19. C2×Dic452C22semidirect
20. C2×Dic452C22semidirect
25. C2×#14268636C22semidirect
26. C2×#14268636C22semidirect
27. C2×#14268636C22semidirect
29. C2×D904C22semidirect
30. #16813622C22semidirect
33. #16813610C22semidirect
41. #97×C113C22semidirect
42. C4×C8×C113C22semidirect
80. M16×C113D4semidirect
81. C2×C8×C113D4semidirect
149. C113#3154semidirect
160. #405D113semidirect
190. #97C2×D113semidirect
191. C4×C8C2×D113semidirect
226. M16D452semidirect
227. C2×C8D452semidirect

Maximal subgroups

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

subgroupindex
C2×#168136552
C2×#168136502
C2×#168136442
C22×#142686362
#202991742
#202991672
#202989922
#202989872
#202989822
#202989712
#405×C1132
#3154113