Finite Group Databasebeta

← #28401041

Subgroups — #28401041

Order 14464.

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

normal subgroups only

This group has 572 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×#16813650C211yesmaximal, characteristic, complemented
3C2×#16813647C211yesmaximal, characteristic, complemented
4#20299144C211yesmaximal, characteristic, complemented
5C2×#16813611C211yesmaximal, characteristic, complemented
6#20298991C212yesmaximal, complemented
7#20298984C212yesmaximal, complemented
8#20298983C212yesmaximal, complemented
9#20298979C212yesmaximal, complemented
10M16×Dic113C211yesmaximal, characteristic, complemented
11C2×#137×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C22×D452C2211yescharacteristic
14#16813653—24no—
15#16813650—24no—
16#16813647—24no—
17C2×#14268637C2212yescomplemented
18C2×#14268636C2212yes—
19C2×#14268634C2212yes—
20C2×#14268634C2212yescomplemented
21C2×D904C2212yes—
22C2×#14268632C2212yes—
23C2×#14268631C2211yescharacteristic
24#16813620C2211yescharacteristic, complemented
25#16813618C2211yescharacteristic, complemented
26#16813611—22no—
27#16813611C2212yes—
28#16813611C2212yes—
29#16813611C2211yescharacteristic, complemented
30#16813609C2211yescharacteristic, complemented
31#16813594—22no—
32C4×C22⋊D113—22no—
33C2×#14268624—22no—
34C2×C4×Dic113C2211yescharacteristic
35#16813532C2212yescomplemented
36C8×Dic113C2212yescomplemented
37C2×#41×C113C2211yescharacteristic
38C22×Q8×C113C2211yescharacteristic
39#137×C113—24no—
40C2×Q16×C113C2212yescomplemented
41C2×SD16×C113C2212yescomplemented
42C2×M16×C113C2211yescharacteristic
43C23×D113—21no—
44#14268647—22no—
45#14268647—22no—
46C2×Dic226C2311yescharacteristic
47C2×D452—22no—
48C2×D452—22no—
49C2×D452—21no—
50C2×D452C2312yes—
51C2×D452C2311yescharacteristic
52C2×C22⋊D113—21no—
53C2×C22⋊D113—22no—
54C22×Dic113D412yes—
55C2×C4×D113—21no—
56#14268637—24no—
57#14268636—24no—
58#14268634—24no—
59#14268634—24no—
60D904—24no—
61#14268632—24no—
62#14268631D414yescomplemented
63C2×#11744751C2312yes—
64#14268626—22no—
65C22⋊Dic113—22no—
66#14268624—24no—
67#14268624—24no—
68#14268624—22no—
69C4×Dic113D412yes—
70C4×Dic113C2311yescharacteristic
71C4×Dic113C2311yescharacteristic
72#41×C113—22no—
73#41×C113—22no—
74C2×Q8×C113—21no—
75C2×Q8×C113—22no—
76C2×Q8×C113—22no—
77C2×Q8×C113C2312yes—
78C2×Q8×C113C2311yescharacteristic
79C2×D4×C113—21no—
80C2×D4×C113C2311yescharacteristic
81C22×C4×C113—21no—
82C22×C4×C113—21no—
83C22×C4×C113C2311yescharacteristic
84Q16×C113—24no—
85SD16×C113—24no—
86M16×C113D414yescomplemented
87C2×C8×C113C2312yes—
88C23×C113—21no—
89C23×C113C2×D411yescharacteristic
90C22×D113—22no—
91C22×D113—21no—
92C22×D113—44no—
93C22×D113—42no—
94Q8×C113—22no—
95Q8×C113—21no—
96Q8×C113—22no—
97Q8×C113—21no—
98Q8×C113—42no—
99D4×C113—21no—
100D4×C113—21no—
101D4×C113—42no—
102C2×C4×C113—21no—
103C2×C4×C113—22no—
104C2×C4×C113—42no—
105C2×C4×C113—42no—
106C2×C4×C113C2×D411yescharacteristic
107C2×C4×C113C2×D412yes—
108C2×C4×C113C2×D412yes—
109C2×C4×C113C2411yescharacteristic
110C22⋊D113—44no—
111C22⋊D113—42no—
112C2×Dic113—21no—
113C2×Dic113—42no—
114C2×Dic113C2×D412yes—
115C2×Dic113C2×D412yes—
116D452—22no—
117D452—21no—
118D452—22no—
119D452—21no—
120D452—42no—
121C4×D113—42no—
122Dic226—21no—
123Dic226—21no—
124C8×C113C2×D414yes—
125#11744751C2×D414yes—
126C22×C113—22no—
127C22×C113—41no—
128C22×C113—42no—
129C22×C113#12712yes—
130C22×C113C22×D411yescharacteristic
131C2×D113—41no—
132C2×D113—42no—
133C2×D113—42no—
134C2×D113—44no—
135C2×D113—84no—
136C4×C113—41no—
137C4×C113—42no—
138C4×C113#12712yes—
139C4×C113C22×D411yescharacteristic
140C4×C113C22×D411yescharacteristic
141Dic113—22no—
142Dic113—22no—
143Dic113—41no—
144C2×C113—22no—
145C2×C113—81no—
146C2×C113C2×#12711yescharacteristic
147C2×C113#57512yes—
148D113—81no—
149D113—82no—
150#3153—1131nomaximal, Sylow
151C113#315311yescharacteristic, complemented, Sylow
152C2×#137—1131no—
153C2×#137D11311yescharacteristic, complemented
154C2×AGL(1,ℤ/8)—1131no—
155C2×AGL(1,ℤ/8)—1131no—
156#532—1131no—
157C2×#124—1131no—
158#497—1132no—
159#496—1132no—
160#495—1132no—
161#495—1132no—
162C4×M16—1131no—
163C2×#41—1131no—
164C2×#41C2×D11311yescharacteristic
165C22×Q8C2×D11311yescharacteristic
166C22×D4—1131no—
167#137—24no—
168#137—2264no—
169AGL(1,ℤ/8)—2264no—
170AGL(1,ℤ/8)—2264no—
171C2×Q16—1132no—
172C2×Q16C2×D11312yescomplemented
173C2×SD16—1132no—
174C2×SD16—1132no—
175C2×SD16—1132no—
176C2×SD16C2×D11312yescomplemented
177C2×D8—1132no—
178C2×D8—1132no—
179C2×M16—1131no—
180C2×M16C2×D11311yescharacteristic
181C4⋊Q8—1131no—
182#127—1131no—
183#124—1132no—
184#124—1132no—
185#124—1131no—
186#124—1131no—
187#124—2262no—
188#121—2262no—
189C4×D4—2262no—
190C2×C22⋊C4—2262no—
191C2×C42—1131no—
192#97—1132no—
193C4×C8—1132no—
194C24—2261no—
195#41—22no—
196#41—22no—
197#41—2262no—
198#41—2262no—
199C2×Q8—21no—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—1131no—
203C2×Q8C22×D11312yes—
204C2×Q8C22×D11311yescharacteristic
205C2×D4—21no—
206C2×D4—1132no—
207C2×D4—1131no—
208C2×D4—2262no—
209C2×D4—2261no—
210C2×D4—2261no—
211C2×D4—2262no—
212C2×D4—2262no—
213C2×D4C22×D11311yescharacteristic
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—1132no—
217C22×C4—2261no—
218C22×C4C22×D11311yescharacteristic
219Q16—24no—
220Q16—2264no—
221SD16—24no—
222SD16—2264no—
223SD16—2264no—
224SD16—2264no—
225D8—2264no—
226D8—2264no—
227M16—1134no—
228M16C22⋊D11314yescomplemented
229C2×C8—1132no—
230C2×C8C22×D11312yes—
231C4⋊C4—2262no—
232C22⋊C4—2264no—
233C22⋊C4—2264no—
234C22⋊C4—2262no—
235C22⋊C4—2262no—
236C42—1132no—
237C42—1131no—
238C42—1131no—
239C23—21no—
240C23—4524no—
241C23—4522no—
242C23—2262no—
243C23—2261no—
244C23D4×D11311yescharacteristic
245Q8—21no—
246Q8—22no—
247Q8—22no—
248Q8—21no—
249Q8—42no—
250Q8—2261no—
251Q8—2261no—
252D4—21no—
253D4—21no—
254D4—42no—
255D4—4522no—
256D4—4524no—
257D4—4522no—
258D4—2262no—
259D4—2261no—
260D4—2261no—
261D4—2262no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—1132no—
267C2×C4—1132no—
268C2×C4—4522no—
269C2×C4—4522no—
270C2×C4—2261no—
271C2×C4D4×D11311yescharacteristic
272C2×C4D4×D11312yes—
273C2×C4C2×C22⋊D11312yes—
274C2×C4C23×D11311yescharacteristic
275C8—1134no—
276C8C2×C22⋊D11314yes—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—9044no—
281C22—4521no—
282C22—4522no—
283C22—4522no—
284C22—4524no—
285C22#1681361812yes—
286C22C2×D4×D11311yescharacteristic
287C4—41no—
288C4—42no—
289C4—4521no—
290C4—2262no—
291C4—2262no—
292C4#1681361812yes—
293C4C2×D4×D11311yescharacteristic
294C4C22×C22⋊D11311yescharacteristic
295C2—22no—
296C2—81no—
297C2—9042no—
298C2—9041no—
299C2C2×#1681361811yescharacteristic
300C2#2029939712yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#137×C113C2
socleC22×C113C22×D4
hypercenterC2×#137D113
hypocenterC113#3153
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#16813653C2semidirect
2. C2×#16813650C2semidirect
3. C2×#16813647C2semidirect
4. #20299144C2semidirect
5. C2×#16813611C2semidirect
6. #20298991C2semidirect
7. #20298984C2semidirect
8. #20298983C2semidirect
9. #20298979C2semidirect
10. M16×Dic113C2semidirect
11. C2×#137×C113C2semidirect
17. C2×#14268637C22semidirect
20. C2×#14268634C22semidirect
24. #16813620C22semidirect
25. #16813618C22semidirect
29. #16813611C22semidirect
30. #16813609C22semidirect
35. #16813532C22semidirect
36. C8×Dic113C22semidirect
40. C2×Q16×C113C22semidirect
41. C2×SD16×C113C22semidirect
62. #14268631D4semidirect
86. M16×C113D4semidirect
151. C113#3153semidirect
153. C2×#137D113semidirect
172. C2×Q16C2×D113semidirect
176. C2×SD16C2×D113semidirect
228. M16C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136532
C2×#168136502
C2×#168136472
#202991442
C2×#168136112
#202989912
#202989842
#202989832
#202989792
M16×Dic1132
C2×#137×C1132
#3153113