Finite Group Databasebeta

← #16857524

Subgroups — #16857524

Order 3968.

494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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#14521703C211yesmaximal, characteristic, complemented
2#14521395C211yesmaximal, characteristic, complemented
3#14521360C212yesmaximal, complemented
4#14521329C211yesmaximal, characteristic, complemented
5#14521283C212yesmaximal, complemented
6#14521241C211yesmaximal, characteristic, complemented
7#14521183C212yesmaximal, complemented
8C4×#92479C211yesmaximal, characteristic, complemented
9D4×C31⋊C8C211yesmaximal, characteristic, complemented
10C2×#11758420C212yesmaximal, complemented
11D42×C31C211yesmaximal, characteristic, complemented
12C22×D4×C31—21no—
13C22×D4×C31C2212yes—
14C2×#92497—21no—
15C31×#127C2211yescharacteristic
16C31×#121—21no—
17C31×#121C2212yes—
18C31×#120—22no—
19C4×D4×C31C2211yescharacteristic
20C4×D4×C31C2211yescharacteristic
21C2×#92479C2211yescharacteristic
22C2×#92479C2212yescomplemented
23#11758507C2212yescomplemented
24C2×C4⋊Dic31C2212yescomplemented
25C22×C31⋊C8C2212yescomplemented
26#11758474—21no—
27#11758463—22no—
28C4×D124C2211yescharacteristic, complemented
29#11758446C2211yescharacteristic, complemented
30#11758420C2211yescharacteristic
31#11758420C2212yes—
32#11758420C2212yescomplemented
33#11758420C2212yescomplemented
34#11758420C2212yescomplemented
35C22⋊(C31⋊C8)C2212yescomplemented
36#11758397C2211yescharacteristic, complemented
37#11758395C2211yescharacteristic, complemented
38#11758395C2212yescomplemented
39C4⋊(C31⋊C8)C2211yescharacteristic, complemented
40C4×C31⋊C8C2211yescharacteristic, complemented
41C24×C31—22no—
42C2×D4×C31—24no—
43C2×D4×C31—22no—
44C2×D4×C31—22no—
45C2×D4×C31—21no—
46C2×D4×C31—21no—
47C2×D4×C31—42no—
48C2×D4×C31—44no—
49C2×D4×C31D411yescharacteristic
50C2×D4×C31C2312yes—
51C2×D4×C31C2311yescharacteristic
52C22×C4×C31—21no—
53C22×C4×C31C2312yes—
54C2×C22⋊D31—22no—
55C22×Dic31—22no—
56#92497—44no—
57C2×D124C2311yescharacteristic
58C2×C4×D31—21no—
59C2×Dic62—21no—
60C4⋊C4×C31D411yescharacteristic
61C4⋊C4×C31C2311yescharacteristic
62C22⋊C4×C31—21no—
63C22⋊C4×C31—22no—
64C22⋊C4×C31D412yes—
65C42×C31C2311yescharacteristic
66#92479—22no—
67#92479—42no—
68(C2×D31)⋊C4—21no—
69(C2×D31)⋊C4—22no—
70C4⋊Dic31—21no—
71C4⋊Dic31—22no—
72C4⋊Dic31C2312yes—
73C4⋊Dic31C2311yescharacteristic
74C2×C31⋊C8—42no—
75C2×C31⋊C8C2311yescharacteristic
76C2×C31⋊C8C2311yescharacteristic
77C2×C31⋊C8C2312yes—
78C23×C31—21no—
79C23×C31—22no—
80C23×C31—44no—
81C23×C31—44no—
82C23×C31—82no—
83C23×C31C2×D412yes—
84C22×D31—21no—
85D4×C31—22no—
86D4×C31—21no—
87D4×C31—22no—
88D4×C31—44no—
89D4×C31—44no—
90D4×C31—42no—
91D4×C31—81no—
92D4×C31D814yescomplemented
93D4×C31#4112yescomplemented
94C2×C4×C31—22no—
95C2×C4×C31—22no—
96C2×C4×C31—21no—
97C2×C4×C31—42no—
98C2×C4×C31C2×D411yescharacteristic
99C2×C4×C31C2×D412yes—
100C2×C4×C31C2×D411yescharacteristic
101C2×C4×C31C2411yescharacteristic
102C22⋊D31—44no—
103C2×Dic31—22no—
104C2×Dic31—21no—
105C2×Dic31—44no—
106D124—21no—
107D124—21no—
108C4×D31—42no—
109Dic62—42no—
110C31⋊C8—21no—
111C31⋊C8—21no—
112C31⋊C8—22no—
113#3294—311nomaximal, Sylow
114C22×C31—22no—
115C22×C31—22no—
116C22×C31—22no—
117C22×C31—41no—
118C22×C31—41no—
119C22×C31—42no—
120C22×C31—42no—
121C22×C31—42no—
122C22×C31—88no—
123C22×C31C2×D814yes—
124C22×C31C22×D411yescharacteristic
125C2×D31—41no—
126C2×D31—41no—
127C2×D31—41no—
128C4×C31—22no—
129C4×C31—21no—
130C4×C31—41no—
131C4×C31C2×D812yes—
132C4×C31C2×#4111yescharacteristic
133C4×C31H(5,𝔽2)11yescharacteristic
134Dic31—42no—
135Dic31—41no—
136#547—311no—
137D42D3111yescharacteristic, complemented
138#486—311no—
139#480—312no—
140#474—311no—
141#466—312no—
142#459—311no—
143#447—312no—
144C4×D8—311no—
145C8×D4—311no—
146C2×#102—312no—
147C2×C31—24no—
148C2×C31—42no—
149C2×C31—82no—
150C2×C31#54611yescharacteristic
151C2×C31C22×D811yescharacteristic
152C2×C31#57711yescharacteristic
153D31—81no—
154C2×#41—621no—
155C22×D4—21no—
156C22×D4C2×D3112yes—
157C2×D8—311no—
158C2×D8—312no—
159C22×C8—312no—
160C4⋊Q8—311no—
161#127C2×D3111yescharacteristic
162#123—622no—
163C22⋊Q8—621no—
164#121—21no—
165#121—312no—
166#121C2×D3112yes—
167#120—22no—
168C4×D4—311no—
169C4×D4C2×D3111yescharacteristic
170C4×D4C2×D3111yescharacteristic
171C2×C4⋊C4—312no—
172#107—311no—
173#107—312no—
174C4⋊C8—311no—
175#102—311no—
176#102—312no—
177#102—312no—
178#102—312no—
179#102—312no—
180#102—311no—
181C22⋊C8—312no—
182C4×C8—311no—
183C31#329411yescharacteristic, complemented, Sylow
184C24—22no—
185#41—1244no—
186C2×Q8—621no—
187C2×D4—24no—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—21no—
192C2×D4—42no—
193C2×D4—44no—
194C2×D4—311no—
195C2×D4—622no—
196C2×D4C22⋊D3111yescharacteristic
197C2×D4C22×D3112yes—
198C2×D4C22×D3111yescharacteristic
199C22×C4—21no—
200C22×C4—622no—
201C22×C4—621no—
202C22×C4C22×D3112yes—
203D8—622no—
204D8—1242no—
205C2×C8—311no—
206C2×C8—311no—
207C2×C8—312no—
208C2×C8—1242no—
209C4⋊C4—311no—
210C4⋊C4—312no—
211C4⋊C4—622no—
212C4⋊C4—621no—
213C4⋊C4C22⋊D3111yescharacteristic
214C4⋊C4C22×D3111yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—22no—
217C22⋊C4—621no—
218C22⋊C4—622no—
219C22⋊C4C22⋊D3112yes—
220C42C22×D3111yescharacteristic
221C23—21no—
222C23—22no—
223C23—44no—
224C23—44no—
225C23—82no—
226C23—621no—
227C23C2×C22⋊D3112yes—
228Q8—1242no—
229D4—22no—
230D4—21no—
231D4—22no—
232D4—44no—
233D4—44no—
234D4—42no—
235D4—81no—
236D4—621no—
237D4—621no—
238D4—1244no—
239D4#9247914yescomplemented
240D4#9249712yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—42no—
245C2×C4—621no—
246C2×C4—622no—
247C2×C4—1244no—
248C2×C4—1242no—
249C2×C4C2×C22⋊D3111yescharacteristic
250C2×C4C2×C22⋊D3112yes—
251C2×C4C2×C22⋊D3111yescharacteristic
252C2×C4C23×D3111yescharacteristic
253C8—621no—
254C8—621no—
255C8—622no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—41no—
260C22—41no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—88no—
265C22—1241no—
266C22—1241no—
267C22—1241no—
268C22C2×#9247914yes—
269C22C22×C22⋊D3111yescharacteristic
270C4—21no—
271C4—22no—
272C4—41no—
273C4—1241no—
274C4—1242no—
275C4C2×#9247912yes—
276C4C2×#9249711yescharacteristic
277C4#1175856111yescharacteristic
278C2—24no—
279C2—42no—
280C2—82no—
281C2—2481no—
282C2#1452169311yescharacteristic
283C2C22×#9247911yescharacteristic
284C2#1452186011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingD42×C31C2
socleC22×C31C22×D4
hypercenterD42D31
hypocenterC31#3294
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #14521703C2semidirect
2. #14521395C2semidirect
3. #14521360C2semidirect
4. #14521329C2semidirect
5. #14521283C2semidirect
6. #14521241C2semidirect
7. #14521183C2semidirect
8. C4×#92479C2semidirect
9. D4×C31⋊C8C2semidirect
10. C2×#11758420C2semidirect
11. D42×C31C2semidirect
22. C2×#92479C22semidirect
23. #11758507C22semidirect
24. C2×C4⋊Dic31C22semidirect
25. C22×C31⋊C8C22semidirect
28. C4×D124C22semidirect
29. #11758446C22semidirect
32. #11758420C22semidirect
33. #11758420C22semidirect
34. #11758420C22semidirect
35. C22⋊(C31⋊C8)C22semidirect
36. #11758397C22semidirect
37. #11758395C22semidirect
38. #11758395C22semidirect
39. C4⋊(C31⋊C8)C22semidirect
40. C4×C31⋊C8C22semidirect
92. D4×C31D8semidirect
93. D4×C31#41semidirect
137. D42D31semidirect
183. C31#3294semidirect
239. D4#92479semidirect
240. D4#92497semidirect

Maximal subgroups

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

subgroupindex
#145217032
#145213952
#145213602
#145213292
#145212832
#145212412
#145211832
C4×#924792
D4×C31⋊C82
C2×#117584202
D42×C312
#329431