Finite Group Databasebeta

← #28400263

Subgroups — #28400263

Order 14464.

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

normal subgroups only

This group has 472 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×#16813653C211yesmaximal, characteristic, complemented
2C2×#16813628C211yesmaximal, characteristic, complemented
3#20299179C211yesmaximal, characteristic
4#20299172C211yesmaximal, characteristic, complemented
5#20298855C212yesmaximal, complemented
6#20298847C212yesmaximal, complemented
7#20298838C212yesmaximal, complemented
8#20298830C212yesmaximal, complemented
9#20298638C211yesmaximal, characteristic, complemented
10#20298595C211yesmaximal, characteristic, complemented
11C2×#103×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C2×#14268647C2211yescharacteristic
14#16813653—24no—
15C2×#14268637C2212yes—
16C2×#14268634C2212yes—
17#16813628—24no—
18C2×#14268631C2211yescharacteristic
19C2×#14268630C2212yes—
20C2×C8×D113C2212yes—
21#16813620—21no—
22#16813611—21no—
23#16813605—22no—
24#16813602—21no—
25#16813602C2212yes—
26#16813598C2212yes—
27#16813598C2212yes—
28#16813597—21no—
29#16813597C2212yes—
30#16813596—22no—
31#16813581C2211yescharacteristic
32#16813555C2212yes—
33#16813553C2212yes—
34#16813547C2211yescharacteristic
35#16813547C2211yescharacteristic
36#16813544C2211yescharacteristic
37#16813544C2211yescharacteristic
38C22×Q8×C113C2211yescharacteristic
39C22×C8×C113C2211yescharacteristic
40C2×C4⋊C4×C113C2211yescharacteristic
41#103×C113C2212yes—
42#103×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⋊D113D412yes—
54C2×C4×D113—21no—
55C2×C4×D113C2312yes—
56#14268637—24no—
57#14268634—24no—
58#14268631D414yescomplemented
59#14268630—24no—
60C2×#11744751C2312yes—
61C8×D113—24no—
62C4⋊Dic113—22no—
63C4⋊Dic113C2311yescharacteristic
64C4⋊Dic113C2311yescharacteristic
65#14268626—22no—
66#14268626—22no—
67C22⋊Dic113—21no—
68#14268624—22no—
69#14268624—22no—
70#14268624—22no—
71#14268624—22no—
72C4×Dic113—21no—
73C2×Q8×C113—21no—
74C2×Q8×C113—22no—
75C2×Q8×C113—22no—
76C2×Q8×C113C2312yes—
77C22×C4×C113—21no—
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×C113C2×D411yescharacteristic
86C22×D113—21no—
87C22×D113C2×D412yes—
88Q8×C113—22no—
89Q8×C113—22no—
90Q8×C113—42no—
91C2×C4×C113—22no—
92C2×C4×C113—22no—
93C2×C4×C113—42no—
94C2×C4×C113—81no—
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113C2×D412yes—
97C2×C4×C113#4112yes—
98C2×C4×C113C2411yescharacteristic
99C22⋊D113—24no—
100C22⋊D113—42no—
101C2×Dic113—21no—
102C2×Dic113—21no—
103C2×Dic113—21no—
104C2×Dic113C2×D412yes—
105D452—22no—
106D452—21no—
107D452—21no—
108D452—82no—
109C4×D113—22no—
110C4×D113—22no—
111C4×D113—42no—
112Dic226—22no—
113Dic226—21no—
114Dic226—21no—
115C8×C113—21no—
116C8×C113—21no—
117#11744751C2×D414yes—
118C22×C113—21no—
119C22×C113—21no—
120C22×C113#12112yes—
121C22×C113C22×D411yescharacteristic
122C2×D113—22no—
123C2×D113—22no—
124C2×D113—22no—
125C2×D113—41no—
126C2×D113—41no—
127C2×D113—41no—
128C4×C113—42no—
129C4×C113—42no—
130C4×C113#12112yes—
131C4×C113C22×D411yescharacteristic
132C4×C113C2×#4111yescharacteristic
133Dic113—22no—
134Dic113—41no—
135Dic113—41no—
136Dic113—41no—
137C2×C113—22no—
138C2×C113C2×#12111yescharacteristic
139C2×C113#57711yescharacteristic
140C2×C113#57811yescharacteristic
141D113—42no—
142D113—81no—
143#3063—1131nomaximal, Sylow
144C113#306311yescharacteristic, complemented, Sylow
145C2×#137—1131no—
146C2×#131—1131no—
147#537—1131no—
148#536—1131no—
149#470—1132no—
150#468—1132no—
151#467—1132no—
152#465—1132no—
153#428—1131no—
154#416—1131no—
155C2×#103D11311yescharacteristic, complemented
156C2×#41—1131no—
157C2×#41—1131no—
158C22×Q8C2×D11311yescharacteristic
159#137—2264no—
160C2×Q16—1132no—
161C2×SD16—1132no—
162#131—2264no—
163C2×M16—1131no—
164C2×M16—1132no—
165C22×C8—1132no—
166C22×C8C2×D11311yescharacteristic
167C4⋊Q8—2261no—
168#124—2261no—
169#123—2262no—
170C22⋊Q8—1132no—
171C22⋊Q8—1132no—
172C22⋊Q8—1132no—
173C22⋊Q8—2261no—
174#121—1132no—
175#121—2261no—
176#121—2262no—
177#117—1131no—
178C2×C4⋊C4C2×D11311yescharacteristic
179#107—1132no—
180#106—1132no—
181#103—1131no—
182#103—1131no—
183#103C2×D11312yes—
184#103C2×D11312yes—
185#102—1131no—
186#102—1131no—
187#41—2262no—
188#41—2262no—
189#41—2262no—
190#41—2262no—
191C2×Q8—21no—
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—1131no—
195C2×Q8—1131no—
196C2×Q8C22×D11312yes—
197C2×D4—1132no—
198C2×D4—1131no—
199C2×D4—1131no—
200C2×D4—2262no—
201C2×D4—2261no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—1132no—
205C22×C4—2261no—
206C22×C4C22×D11311yescharacteristic
207Q16—2264no—
208SD16—2264no—
209M16—1134no—
210M16—2264no—
211C2×C8—22no—
212C2×C8—1132no—
213C2×C8—2264no—
214C2×C8C22×D11311yescharacteristic
215C2×C8C22×D11311yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—1131no—
218C4⋊C4—1131no—
219C4⋊C4—2262no—
220C4⋊C4—2262no—
221C4⋊C4—2262no—
222C4⋊C4C22×D11312yes—
223C22⋊C4—2262no—
224C22⋊C4—2262no—
225C22⋊C4—2262no—
226C22⋊C4—2262no—
227C22⋊C4—2261no—
228C42—2261no—
229C23—1132no—
230C23—2261no—
231C23D4×D11311yescharacteristic
232Q8—22no—
233Q8—22no—
234Q8—42no—
235Q8—2261no—
236Q8—2261no—
237Q8—2262no—
238D4—9042no—
239D4—4522no—
240D4—2264no—
241D4—2262no—
242D4—2261no—
243D4—2261no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—81no—
248C2×C4—1132no—
249C2×C4—4522no—
250C2×C4—2261no—
251C2×C4—2261no—
252C2×C4—2261no—
253C2×C4—2262no—
254C2×C4—2262no—
255C2×C4D4×D11311yescharacteristic
256C2×C4D4×D11312yes—
257C2×C4#1426864712yes—
258C2×C4C23×D11311yescharacteristic
259C8—21no—
260C8—21no—
261C8—1134no—
262C22—21no—
263C22—21no—
264C22—4521no—
265C22—4521no—
266C22—4521no—
267C22—2262no—
268C22—2262no—
269C22—2262no—
270C22#1681359512yes—
271C22C2×D4×D11311yescharacteristic
272C4—42no—
273C4—42no—
274C4—4521no—
275C4—4521no—
276C4—4521no—
277C4—2262no—
278C4#1681359512yes—
279C4C2×D4×D11311yescharacteristic
280C4C2×#1426864711yescharacteristic
281C2—22no—
282C2—9041no—
283C2—4522no—
284C2C2×#1681359511yescharacteristic
285C2#2029940411yescharacteristic
286C2#2029941111yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#103×C113C2
socleC22×C113C22×D4
prime radical#20299179C2
hypercenterC2×#103D113
hypocenterC113#3063
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C2×#16813653C2semidirect
2. C2×#16813628C2semidirect
4. #20299172C2semidirect
5. #20298855C2semidirect
6. #20298847C2semidirect
7. #20298838C2semidirect
8. #20298830C2semidirect
9. #20298638C2semidirect
10. #20298595C2semidirect
11. C2×#103×C113C2semidirect
58. #14268631D4semidirect
144. C113#3063semidirect
155. C2×#103D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136532
C2×#168136282
#202991792
#202991722
#202988552
#202988472
#202988382
#202988302
#202986382
#202985952
C2×#103×C1132
#3063113