Finite Group Databasebeta

← #28400252

Subgroups — #28400252

Order 14464.

504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16813648C211yesmaximal, characteristic, complemented
2C2×#16813628C211yesmaximal, characteristic, complemented
3#20299179C211yesmaximal, characteristic, complemented
4#20299165C211yesmaximal, characteristic, complemented
5#20298850C212yesmaximal, complemented
6#20298843C212yesmaximal, complemented
7#20298833C212yesmaximal, complemented
8#20298826C212yesmaximal, complemented
9#20298638C211yesmaximal, characteristic, complemented
10#20298595C211yesmaximal, characteristic, complemented
11C2×#102×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C2×#14268647C2211yescharacteristic
14#16813648—24no—
15C2×#14268635C2212yes—
16C2×#14268632C2212yes—
17#16813628—24no—
18C2×#14268631C2211yescharacteristic
19C2×#14268630C2212yescomplemented
20C2×C8×D113C2212yescomplemented
21#16813618—21no—
22#16813609—21no—
23#16813602—21no—
24#16813602C2212yescomplemented
25#16813597—21no—
26#16813597C2212yescomplemented
27#16813596—22no—
28#16813593C2212yes—
29#16813593C2212yes—
30#16813591—22no—
31#16813581C2211yescharacteristic
32#16813555C2212yescomplemented
33#16813553C2212yescomplemented
34#16813547C2211yescharacteristic, complemented
35#16813547C2211yescharacteristic, complemented
36#16813544C2211yescharacteristic, complemented
37#16813544C2211yescharacteristic, complemented
38C22×D4×C113C2211yescharacteristic
39C22×C8×C113C2211yescharacteristic
40C2×C4⋊C4×C113C2211yescharacteristic
41#102×C113C2212yes—
42#102×C113C2212yes—
43#14268647—22no—
44#14268647—22no—
45#14268647—22no—
46#14268647—22no—
47C2×Dic226D411yescharacteristic
48C2×Dic226C2311yescharacteristic
49C2×D452—22no—
50C2×D452D411yescharacteristic
51C2×D452C2311yescharacteristic
52C2×C22⋊D113—21no—
53C2×C22⋊D113—22no—
54C2×C22⋊D113—22no—
55C2×C22⋊D113D412yes—
56C2×C4×D113—21no—
57C2×C4×D113C2312yes—
58#14268635—24no—
59#14268632—24no—
60#14268631D414yescomplemented
61#14268630—24no—
62C2×#11744751C2312yes—
63C8×D113—24no—
64C4⋊Dic113—22no—
65C4⋊Dic113C2311yescharacteristic
66C4⋊Dic113C2311yescharacteristic
67C22⋊Dic113—21no—
68C22⋊Dic113—22no—
69C22⋊Dic113—22no—
70#14268624—22no—
71#14268624—22no—
72C4×Dic113—21no—
73C24×C113—21no—
74C2×D4×C113—22no—
75C2×D4×C113—21no—
76C2×D4×C113—22no—
77C2×D4×C113C2312yes—
78C22×C4×C113—21no—
79C22×C4×C113C2311yescharacteristic
80C2×C8×C113—22no—
81C2×C8×C113C2311yescharacteristic
82C2×C8×C113C2311yescharacteristic
83C4⋊C4×C113—21no—
84C4⋊C4×C113C2312yes—
85C23×C113—22no—
86C23×C113—42no—
87C23×C113—81no—
88C23×C113—81no—
89C23×C113C2×D411yescharacteristic
90C22×D113—21no—
91C22×D113C2×D412yes—
92D4×C113—22no—
93D4×C113—22no—
94D4×C113—42no—
95C2×C4×C113—22no—
96C2×C4×C113—81no—
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2×D412yes—
99C2×C4×C113#4112yes—
100C2×C4×C113C2411yescharacteristic
101C22⋊D113—24no—
102C22⋊D113—42no—
103C22⋊D113—82no—
104C22⋊D113—82no—
105C2×Dic113—21no—
106C2×Dic113—21no—
107C2×Dic113—21no—
108C2×Dic113C2×D412yes—
109D452—22no—
110D452—21no—
111D452—21no—
112D452—82no—
113C4×D113—22no—
114C4×D113—22no—
115C4×D113—42no—
116Dic226—22no—
117Dic226—21no—
118Dic226—21no—
119C8×C113—21no—
120C8×C113—21no—
121#11744751C2×D414yes—
122C22×C113—21no—
123C22×C113—21no—
124C22×C113—42no—
125C22×C113—42no—
126C22×C113—42no—
127C22×C113—84no—
128C22×C113#12112yes—
129C22×C113C22×D411yescharacteristic
130C2×D113—22no—
131C2×D113—22no—
132C2×D113—22no—
133C2×D113—41no—
134C2×D113—41no—
135C2×D113—41no—
136C4×C113—42no—
137C4×C113#12112yes—
138C4×C113C22×D411yescharacteristic
139C4×C113C2×#4111yescharacteristic
140Dic113—22no—
141Dic113—41no—
142Dic113—41no—
143Dic113—41no—
144C2×C113—22no—
145C2×C113—82no—
146C2×C113C2×#12111yescharacteristic
147C2×C113#57611yescharacteristic
148C2×C113#57711yescharacteristic
149D113—42no—
150D113—81no—
151#3062—1131nomaximal, Sylow
152C113#306211yescharacteristic, complemented, Sylow
153C2×AGL(1,ℤ/8)—1131no—
154C2×#131—1131no—
155#537—1131no—
156#535—1131no—
157#469—1132no—
158#468—1132no—
159#466—1132no—
160#465—1132no—
161#428—1131no—
162#416—1131no—
163C2×#102D11311yescharacteristic, complemented
164C2×#41—1131no—
165C2×#41—1131no—
166C22×D4C2×D11311yescharacteristic
167AGL(1,ℤ/8)—2264no—
168C2×SD16—1132no—
169C2×D8—1132no—
170#131—2264no—
171C2×M16—1131no—
172C2×M16—1132no—
173C22×C8—1132no—
174C22×C8C2×D11311yescharacteristic
175#127—2261no—
176#124—2261no—
177C22⋊Q8—1132no—
178C22⋊Q8—2261no—
179#121—1132no—
180#121—1132no—
181#121—1132no—
182#121—2261no—
183#121—2262no—
184#120—2262no—
185#117—1131no—
186C2×C4⋊C4C2×D11311yescharacteristic
187#107—1132no—
188#106—1132no—
189#103—1131no—
190#103—1131no—
191#102—1131no—
192#102—1131no—
193#102C2×D11312yes—
194#102C2×D11312yes—
195C24—21no—
196#41—2262no—
197#41—2262no—
198#41—2262no—
199#41—2262no—
200C2×Q8—1131no—
201C2×Q8—1131no—
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—22no—
205C2×D4—1132no—
206C2×D4—1131no—
207C2×D4—1131no—
208C2×D4—2262no—
209C2×D4—2262no—
210C2×D4—2262no—
211C2×D4—2261no—
212C2×D4C22×D11312yes—
213C22×C4—21no—
214C22×C4—1132no—
215C22×C4—2261no—
216C22×C4C22×D11311yescharacteristic
217SD16—2264no—
218D8—2264no—
219M16—1134no—
220M16—2264no—
221C2×C8—22no—
222C2×C8—1132no—
223C2×C8—2264no—
224C2×C8C22×D11311yescharacteristic
225C2×C8C22×D11311yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—1131no—
228C4⋊C4—1131no—
229C4⋊C4—2262no—
230C4⋊C4C22×D11312yes—
231C22⋊C4—2262no—
232C22⋊C4—2262no—
233C22⋊C4—2262no—
234C22⋊C4—2262no—
235C22⋊C4—2261no—
236C42—2261no—
237C23—22no—
238C23—42no—
239C23—81no—
240C23—81no—
241C23—1132no—
242C23—2261no—
243C23D4×D11311yescharacteristic
244Q8—2261no—
245Q8—2261no—
246Q8—2262no—
247D4—22no—
248D4—22no—
249D4—42no—
250D4—9042no—
251D4—9042no—
252D4—9042no—
253D4—4522no—
254D4—2264no—
255D4—2262no—
256D4—2261no—
257D4—2261no—
258C2×C4—22no—
259C2×C4—81no—
260C2×C4—1132no—
261C2×C4—4522no—
262C2×C4—2261no—
263C2×C4—2261no—
264C2×C4—2261no—
265C2×C4—2262no—
266C2×C4—2262no—
267C2×C4D4×D11311yescharacteristic
268C2×C4D4×D11312yes—
269C2×C4#1426864712yes—
270C2×C4C23×D11311yescharacteristic
271C8—21no—
272C8—21no—
273C8—1134no—
274C22—21no—
275C22—21no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—84no—
280C22—4521no—
281C22—4521no—
282C22—4521no—
283C22—2262no—
284C22—2262no—
285C22—2262no—
286C22#1681359512yes—
287C22C2×D4×D11311yescharacteristic
288C4—42no—
289C4—4521no—
290C4—4521no—
291C4—4521no—
292C4—2262no—
293C4#1681359512yes—
294C4C2×D4×D11311yescharacteristic
295C4C2×#1426864711yescharacteristic
296C2—22no—
297C2—82no—
298C2—9041no—
299C2—4522no—
300C2C2×#1681359511yescharacteristic
301C2#2029939911yescharacteristic
302C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#102×C113C2
socleC22×C113C22×D4
hypercenterC2×#102D113
hypocenterC113#3062
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#16813648C2semidirect
2. C2×#16813628C2semidirect
3. #20299179C2semidirect
4. #20299165C2semidirect
5. #20298850C2semidirect
6. #20298843C2semidirect
7. #20298833C2semidirect
8. #20298826C2semidirect
9. #20298638C2semidirect
10. #20298595C2semidirect
11. C2×#102×C113C2semidirect
19. C2×#14268630C22semidirect
20. C2×C8×D113C22semidirect
24. #16813602C22semidirect
26. #16813597C22semidirect
32. #16813555C22semidirect
33. #16813553C22semidirect
34. #16813547C22semidirect
35. #16813547C22semidirect
36. #16813544C22semidirect
37. #16813544C22semidirect
60. #14268631D4semidirect
152. C113#3062semidirect
163. C2×#102D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
C2×#168136282
#202991792
#202991652
#202988502
#202988432
#202988332
#202988262
#202986382
#202985952
C2×#102×C1132
#3062113