Finite Group Databasebeta

← #28401044

Subgroups — #28401044

Order 14464.

564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16813653C211yesmaximal, characteristic, complemented
2C2×#16813648C211yesmaximal, characteristic, complemented
3C2×#16813644C211yesmaximal, characteristic, complemented
4#20299172C211yesmaximal, characteristic, complemented
5#20299165C211yesmaximal, characteristic, complemented
6#20298989C212yesmaximal, complemented
7#20298984C212yesmaximal, complemented
8#20298979C212yesmaximal, complemented
9#20298969C212yesmaximal, complemented
10#20298553C211yesmaximal, characteristic, complemented
11C22×SD16×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C2×#14268647C2211yescharacteristic
14#16813653—24no—
15#16813648—24no—
16#16813644—24no—
17C2×Dic452C2211yescharacteristic, complemented
18C2×#14268637C2212yescomplemented
19C2×#14268636C2211yescharacteristic, complemented
20C2×#14268636C2211yescharacteristic, complemented
21C2×#14268635C2212yes—
22C2×#14268634C2212yescomplemented
23C2×D904C2211yescharacteristic, complemented
24C2×#14268632C2212yes—
25C2×#14268631C2211yescharacteristic
26#16813620C2212yescomplemented
27#16813618C2212yes—
28#16813611C2212yescomplemented
29#16813609C2212yes—
30#16813605—22no—
31#16813598—22no—
32#16813593—22no—
33#16813591—22no—
34#16813581C2211yescharacteristic
35#16813532C2212yescomplemented
36C8×Dic113C2212yescomplemented
37C22×Q8×C113C2211yescharacteristic
38C22×D4×C113C2211yescharacteristic
39C2×SD16×C113—24no—
40C2×SD16×C113C2212yes—
41C2×SD16×C113C2212yes—
42C22×C8×C113C2211yescharacteristic
43#14268647—22no—
44#14268647—22no—
45#14268647—22no—
46#14268647—22no—
47C2×Dic226C2311yescharacteristic
48C2×Dic226C2311yescharacteristic
49C2×D452C2311yescharacteristic
50C2×D452C2311yescharacteristic
51C2×C22⋊D113—21no—
52C2×C22⋊D113—21no—
53C2×C22⋊D113—24no—
54C2×C4×D113—21no—
55C2×C4×D113—21no—
56Dic452—22no—
57#14268637—24no—
58#14268636—22no—
59#14268636—22no—
60#14268635—24no—
61#14268634—24no—
62D904—22no—
63#14268632—24no—
64#14268631D414yescomplemented
65C2×#11744751C2312yes—
66C4⋊Dic113D412yes—
67#14268626—24no—
68C22⋊Dic113—24no—
69C22⋊Dic113D412yes—
70#14268624—24no—
71C4×Dic113C2312yes—
72C24×C113—21no—
73C2×Q8×C113—21no—
74C2×Q8×C113—22no—
75C2×Q8×C113—22no—
76C2×Q8×C113C2312yes—
77C2×D4×C113—22no—
78C2×D4×C113—22no—
79C2×D4×C113—21no—
80C2×D4×C113C2312yes—
81C22×C4×C113—21no—
82C22×C4×C113C2311yescharacteristic
83SD16×C113—24no—
84SD16×C113—24no—
85C2×C8×C113D414yescomplemented
86C2×C8×C113C2311yescharacteristic
87C2×C8×C113C2311yescharacteristic
88C23×C113—22no—
89C23×C113—42no—
90C23×C113—82no—
91C23×C113C2×D411yescharacteristic
92C22×D113—21no—
93C22×D113—21no—
94Q8×C113—22no—
95Q8×C113—22no—
96Q8×C113—42no—
97D4×C113—22no—
98D4×C113—22no—
99D4×C113—42no—
100C2×C4×C113—22no—
101C2×C4×C113—42no—
102C2×C4×C113C2×D411yescharacteristic
103C2×C4×C113C2×D412yes—
104C2×C4×C113C2×D412yes—
105C2×C4×C113C2411yescharacteristic
106C22⋊D113—42no—
107C22⋊D113—42no—
108C22⋊D113—84no—
109C2×Dic113—21no—
110C2×Dic113—21no—
111C2×Dic113C2×D414yes—
112D452—21no—
113D452—21no—
114D452—21no—
115D452—21no—
116C4×D113—42no—
117C4×D113—42no—
118Dic226—21no—
119Dic226—21no—
120Dic226—21no—
121Dic226—21no—
122C8×C113C2×D412yes—
123C8×C113C2×D412yes—
124#11744751C2×D414yes—
125C22×C113—22no—
126C22×C113—42no—
127C22×C113—44no—
128C22×C113—84no—
129C22×C113#12712yes—
130C22×C113C22×D411yescharacteristic
131C2×D113—41no—
132C2×D113—41no—
133C2×D113—42no—
134C2×D113—42no—
135C4×C113—42no—
136C4×C113#12712yes—
137C4×C113C22×D411yescharacteristic
138C4×C113C22×D411yescharacteristic
139Dic113—24no—
140Dic113—41no—
141Dic113—41no—
142C2×C113—22no—
143C2×C113—82no—
144C2×C113C2×#12711yescharacteristic
145C2×C113#57712yes—
146D113—81no—
147D113—81no—
148#3154—1131nomaximal, Sylow
149C113#315411yescharacteristic, complemented, Sylow
150C2×#137—1131no—
151C2×AGL(1,ℤ/8)—1131no—
152C2×#135—1131no—
153C22×SD16D11311yescharacteristic, complemented
154#536—1131no—
155#535—1131no—
156#497—1132no—
157#496—1132no—
158#495—1132no—
159#492—1132no—
160#405—1131no—
161C2×#41—1131no—
162C2×#41—1131no—
163C22×Q8C2×D11311yescharacteristic
164C22×D4C2×D11311yescharacteristic
165#137—2264no—
166AGL(1,ℤ/8)—2264no—
167#135—2264no—
168C2×Q16—1132no—
169C2×Q16—1131no—
170C2×SD16—24no—
171C2×SD16—1132no—
172C2×SD16—1132no—
173C2×SD16—1131no—
174C2×SD16—1131no—
175C2×SD16C2×D11312yes—
176C2×SD16C2×D11312yes—
177C2×D8—1132no—
178C2×D8—1131no—
179C2×M16—1131no—
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#117—1131no—
190#97—1132no—
191C4×C8—1132no—
192C24—21no—
193#41—2262no—
194#41—2262no—
195#41—2262no—
196#41—2262no—
197C2×Q8—21no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—1131no—
201C2×Q8—1131no—
202C2×Q8C22×D11312yes—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—22no—
206C2×D4—1131no—
207C2×D4—1131no—
208C2×D4—2264no—
209C2×D4—2261no—
210C2×D4—2261no—
211C2×D4C22×D11312yes—
212C22×C4—21no—
213C22×C4—2261no—
214C22×C4—2261no—
215C22×C4C22×D11311yescharacteristic
216Q16—2264no—
217Q16—2262no—
218SD16—24no—
219SD16—24no—
220SD16—2264no—
221SD16—2264no—
222SD16—2262no—
223SD16—2262no—
224D8—2264no—
225D8—2262no—
226M16—1134no—
227C2×C8—1132no—
228C2×C8C22⋊D11314yescomplemented
229C2×C8C22×D11311yescharacteristic
230C2×C8C22×D11311yescharacteristic
231C4⋊C4—1132no—
232C4⋊C4—2264no—
233C22⋊C4—1132no—
234C22⋊C4—2264no—
235C22⋊C4—2264no—
236C42—1132no—
237C23—22no—
238C23—42no—
239C23—82no—
240C23—2261no—
241C23—2261no—
242C23D4×D11311yescharacteristic
243Q8—22no—
244Q8—22no—
245Q8—42no—
246Q8—2261no—
247Q8—2261no—
248Q8—2261no—
249Q8—2261no—
250D4—22no—
251D4—22no—
252D4—42no—
253D4—9044no—
254D4—4522no—
255D4—4522no—
256D4—2261no—
257D4—2261no—
258D4—2261no—
259D4—2261no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—1134no—
263C2×C4—4522no—
264C2×C4—4522no—
265C2×C4—2261no—
266C2×C4—2261no—
267C2×C4D4×D11311yescharacteristic
268C2×C4D4×D11312yes—
269C2×C4C2×C22⋊D11312yes—
270C2×C4C23×D11311yescharacteristic
271C8—1134no—
272C8C2×C22⋊D11312yes—
273C8C2×C22⋊D11312yes—
274C22—22no—
275C22—42no—
276C22—44no—
277C22—84no—
278C22—4521no—
279C22—4521no—
280C22—4522no—
281C22—4522no—
282C22#1681361812yes—
283C22C2×D4×D11311yescharacteristic
284C4—42no—
285C4—4521no—
286C4—4521no—
287C4—2264no—
288C4#1681361812yes—
289C4C2×D4×D11311yescharacteristic
290C4C22×C22⋊D11311yescharacteristic
291C2—22no—
292C2—82no—
293C2—9041no—
294C2—9041no—
295C2C2×#1681361811yescharacteristic
296C2#2029940412yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC22×SD16×C113C2
socleC22×C113C22×D4
hypercenterC22×SD16D113
hypocenterC113#3154
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16813653C2semidirect
2. C2×#16813648C2semidirect
3. C2×#16813644C2semidirect
4. #20299172C2semidirect
5. #20299165C2semidirect
6. #20298989C2semidirect
7. #20298984C2semidirect
8. #20298979C2semidirect
9. #20298969C2semidirect
10. #20298553C2semidirect
11. C22×SD16×C113C2semidirect
17. C2×Dic452C22semidirect
18. C2×#14268637C22semidirect
19. C2×#14268636C22semidirect
20. C2×#14268636C22semidirect
22. C2×#14268634C22semidirect
23. C2×D904C22semidirect
26. #16813620C22semidirect
28. #16813611C22semidirect
35. #16813532C22semidirect
36. C8×Dic113C22semidirect
64. #14268631D4semidirect
85. C2×C8×C113D4semidirect
149. C113#3154semidirect
153. C22×SD16D113semidirect
228. C2×C8C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136532
C2×#168136482
C2×#168136442
#202991722
#202991652
#202989892
#202989842
#202989792
#202989692
#202985532
C22×SD16×C1132
#3154113