Finite Group Databasebeta

← #28402395

Subgroups — #28402395

Order 14464.

462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#20299309C211yesmaximal, characteristic, complemented
2D4×D452C211yesmaximal, characteristic
3#20298946C211yesmaximal, characteristic, complemented
4#20298918C212yesmaximal, complemented
5#20298828C212yesmaximal, complemented
6#20298799C211yesmaximal, characteristic, complemented
7#20298750C212yesmaximal, complemented
8C4×#14268635C211yesmaximal, characteristic, complemented
9#20298663C211yesmaximal, characteristic, complemented
10#102×D113C212yesmaximal, complemented
11#476×C113C211yesmaximal, characteristic, complemented
12C22×D452—21no—
13C2×D4×D113C2212yes—
14C2×#14268636C2212yescomplemented
15C2×#14268635C2211yescharacteristic
16C2×C8×D113C2212yescomplemented
17#16813619C2211yescharacteristic
18#16813613—21no—
19#16813602C2212yescomplemented
20#16813598—22no—
21#16813597C2212yes—
22#16813596—21no—
23#16813592—22no—
24C4×Dic226C2211yescharacteristic, complemented
25C4×D452C2211yescharacteristic
26#16813584—21no—
27C4⋊C4×D113C2212yescomplemented
28#16813553C2211yescharacteristic, complemented
29#16813545C2211yescharacteristic, complemented
30#16813544C2212yescomplemented
31#16813543C2211yescharacteristic
32#16813542C2212yescomplemented
33#16813542C2212yescomplemented
34#16813534C2212yescomplemented
35C4×#11744751C2211yescharacteristic, complemented
36C4⋊Q8×C113C2211yescharacteristic, complemented
37C4×D4×C113C2211yescharacteristic
38#106×C113C2212yescomplemented
39C4⋊C8×C113C2211yescharacteristic, complemented
40#102×C113C2212yes—
41C23×D113—22no—
42C2×Dic226C2311yescharacteristic
43C2×D452—22no—
44C2×D452—21no—
45C2×D452—21no—
46C2×D452—44no—
47C2×D452D411yescharacteristic
48C2×D452C2312yes—
49C2×C22⋊D113—22no—
50D4×D113—24no—
51D4×D113—42no—
52C2×C4×D113—22no—
53C2×C4×D113C2312yes—
54#14268636—42no—
55#14268635—22no—
56C2×#11744751C2311yescharacteristic
57C2×#11744751C2311yescharacteristic
58C8×D113—42no—
59C4⋊Dic113—22no—
60C4⋊Dic113D411yescharacteristic
61C4⋊Dic113C2311yescharacteristic
62#14268626—21no—
63#14268626—22no—
64#14268624—22no—
65#14268624—22no—
66#14268624D412yes—
67C4×Dic113—21no—
68C2×Q8×C113—21no—
69C2×D4×C113C2311yescharacteristic
70C22×C4×C113—21no—
71C2×C8×C113C2312yes—
72C4⋊C4×C113—21no—
73C4⋊C4×C113C2312yes—
74C4⋊C4×C113C2311yescharacteristic
75C22⋊C4×C113—21no—
76C42×C113C2311yescharacteristic
77C23×C113—21no—
78C22×D113—22no—
79C22×D113—44no—
80C22×D113—44no—
81C22×D113—82no—
82C22×D113C2×D412yes—
83Q8×C113—81no—
84D4×C113—21no—
85D4×C113#4112yes—
86C2×C4×C113—21no—
87C2×C4×C113—22no—
88C2×C4×C113—42no—
89C2×C4×C113C2×D411yescharacteristic
90C2×C4×C113C2×D411yescharacteristic
91C2×C4×C113C2411yescharacteristic
92C22⋊D113—44no—
93C2×Dic113—21no—
94C2×Dic113—21no—
95C2×Dic113C2×D412yes—
96D452—22no—
97D452—22no—
98D452—44no—
99D452—42no—
100D452—81no—
101D452SD1614yescomplemented
102C4×D113—22no—
103C4×D113—22no—
104C4×D113—82no—
105Dic226—21no—
106Dic226—21no—
107C8×C113—22no—
108#11744751—21no—
109#11744751—21no—
110C22×C113—22no—
111C22×C113—41no—
112C22×C113—41no—
113C22×C113C22×D411yescharacteristic
114C2×D113—22no—
115C2×D113—22no—
116C2×D113—42no—
117C2×D113—42no—
118C2×D113—42no—
119C2×D113—88no—
120C2×D113C2×SD1614yes—
121C4×C113—21no—
122C4×C113—41no—
123C4×C113—42no—
124C4×C113C2×SD1612yes—
125C4×C113C2×#4111yescharacteristic
126C4×C113H(5,𝔽2)11yescharacteristic
127Dic113—22no—
128Dic113—41no—
129Dic113—41no—
130C2×C113—42no—
131C2×C113#54611yescharacteristic
132C2×C113C22×SD1611yescharacteristic
133C2×C113#57611yescharacteristic
134D113—24no—
135D113—82no—
136#3295—1131nomaximal, Sylow
137C113#329511yescharacteristic, complemented, Sylow
138#554—1131no—
139D42—1131no—
140#486—1131no—
141#481—1132no—
142#476D11311yescharacteristic, complemented
143#465—1132no—
144#460—1131no—
145#450—1132no—
146C4×SD16—1131no—
147C8×D4—1131no—
148C2×#102—1132no—
149C22×D4—1132no—
150C22×D4—2261no—
151C2×SD16—1131no—
152C2×SD16—1132no—
153C22×C8—1132no—
154C4⋊Q8C2×D11311yescharacteristic, complemented
155#127—1131no—
156#125—2261no—
157C22⋊Q8—1132no—
158C22⋊Q8—2262no—
159#121—1132no—
160#121—2261no—
161#120—2262no—
162C4×Q8—1131no—
163C4×D4—1131no—
164C4×D4—2261no—
165C4×D4C2×D11311yescharacteristic
166C2×C4⋊C4—1132no—
167#106—1131no—
168#106C2×D11312yescomplemented
169C4⋊C8C2×D11311yescharacteristic, complemented
170#103—1131no—
171#102—1131no—
172#102—1132no—
173#102—1132no—
174#102—1132no—
175#102C2×D11312yes—
176C22⋊C8—1132no—
177C4×C8—1131no—
178C24—2262no—
179C2×Q8—21no—
180C2×Q8—1131no—
181C2×D4—1131no—
182C2×D4—1132no—
183C2×D4—4524no—
184C2×D4—4522no—
185C2×D4—2262no—
186C2×D4—2262no—
187C2×D4—2264no—
188C2×D4—2261no—
189C2×D4—2261no—
190C2×D4C22×D11311yescharacteristic
191C22×C4—21no—
192C22×C4—1132no—
193C22×C4—2262no—
194SD16—4522no—
195SD16—2262no—
196C2×C8—1131no—
197C2×C8—1131no—
198C2×C8—4522no—
199C2×C8C22×D11312yes—
200C4⋊C4—21no—
201C4⋊C4—1131no—
202C4⋊C4—1131no—
203C4⋊C4—2262no—
204C4⋊C4—2262no—
205C4⋊C4—2261no—
206C4⋊C4C22×D11312yes—
207C4⋊C4C22×D11311yescharacteristic
208C22⋊C4—21no—
209C22⋊C4—1132no—
210C22⋊C4—2262no—
211C22⋊C4—2262no—
212C42—2261no—
213C42C22×D11311yescharacteristic
214C23—21no—
215C23—1132no—
216C23—9042no—
217C23—4524no—
218C23—4524no—
219C23—2262no—
220Q8—81no—
221Q8—2261no—
222Q8—2261no—
223D4—21no—
224D4—1134no—
225D4—9041no—
226D4—4524no—
227D4—4524no—
228D4—4522no—
229D4—2262no—
230D4—2262no—
231D4#1426864812yes—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—1132no—
236C2×C4—9042no—
237C2×C4—2261no—
238C2×C4—2261no—
239C2×C4—2262no—
240C2×C4—2262no—
241C2×C4D4×D11311yescharacteristic
242C2×C4D4×D11311yescharacteristic
243C2×C4C23×D11311yescharacteristic
244C8—22no—
245C8—2261no—
246C8—2261no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—1134no—
251C22—9048no—
252C22—4522no—
253C22—4522no—
254C22—4522no—
255C22—2262no—
256C22—2262no—
257C22C2×D4×D11311yescharacteristic
258C4—21no—
259C4—41no—
260C4—42no—
261C4—4521no—
262C4—4521no—
263C4—2262no—
264C4SD16×D11312yes—
265C4C2×#1426864811yescharacteristic
266C4#1681366811yescharacteristic
267C2—42no—
268C2—9042no—
269C2—2264no—
270C2#2029923911yescharacteristic
271C2C2×SD16×D11311yescharacteristic
272C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#476×C113C2
socleC22×C113C22×D4
prime radicalD4×D452C2
hypercenter#476D113
hypocenterC113#3295
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #20299309C2semidirect
3. #20298946C2semidirect
4. #20298918C2semidirect
5. #20298828C2semidirect
6. #20298799C2semidirect
7. #20298750C2semidirect
8. C4×#14268635C2semidirect
9. #20298663C2semidirect
10. #102×D113C2semidirect
11. #476×C113C2semidirect
14. C2×#14268636C22semidirect
16. C2×C8×D113C22semidirect
19. #16813602C22semidirect
24. C4×Dic226C22semidirect
27. C4⋊C4×D113C22semidirect
28. #16813553C22semidirect
29. #16813545C22semidirect
30. #16813544C22semidirect
32. #16813542C22semidirect
33. #16813542C22semidirect
34. #16813534C22semidirect
35. C4×#11744751C22semidirect
36. C4⋊Q8×C113C22semidirect
38. #106×C113C22semidirect
39. C4⋊C8×C113C22semidirect
101. D452SD16semidirect
137. C113#3295semidirect
142. #476D113semidirect
154. C4⋊Q8C2×D113semidirect
168. #106C2×D113semidirect
169. C4⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993092
D4×D4522
#202989462
#202989182
#202988282
#202987992
#202987502
C4×#142686352
#202986632
#102×D1132
#476×C1132
#3295113