Finite Group Databasebeta

← #16857535

Subgroups — #16857535

Order 3968.

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

normal subgroups only

This group has 462 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#14521756C211yesmaximal, characteristic, complemented
2#14521395C211yesmaximal, characteristic, complemented
3#14521365C212yesmaximal, complemented
4#14521339C211yesmaximal, characteristic, complemented
5#14521276C212yesmaximal, complemented
6#14521246C211yesmaximal, characteristic, complemented
7#14521200C212yesmaximal, complemented
8C4×#92480C211yesmaximal, characteristic, complemented
9D4×C31⋊C8C211yesmaximal, characteristic, complemented
10C2×#11758420C212yesmaximal, complemented
11D42×C31C211yesmaximal, characteristic
12C22×D4×C31—21no—
13C22×D4×C31C2212yes—
14C31×#127C2211yescharacteristic
15C31×#121—21no—
16C31×#121C2212yes—
17C31×#120—22no—
18C4×D4×C31C2211yescharacteristic
19C4×D4×C31C2211yescharacteristic
20D4×Dic31—21no—
21C2×#92480C2211yescharacteristic
22C2×#92480C2212yescomplemented
23C2×C4⋊Dic31C2212yescomplemented
24#11758501C2212yescomplemented
25C22×C31⋊C8C2212yescomplemented
26#11758467—21no—
27#11758455—22no—
28#11758446C2211yescharacteristic, complemented
29C4×Dic62C2211yescharacteristic, complemented
30#11758420C2211yescharacteristic
31#11758420C2212yes—
32#11758420C2212yescomplemented
33#11758420C2212yescomplemented
34#11758420C2212yescomplemented
35C22⋊(C31⋊C8)C2212yescomplemented
36#11758398C2211yescharacteristic, complemented
37#11758396C2211yescharacteristic, complemented
38#11758396C2212yescomplemented
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—
54C22×Dic31—22no—
55C2×Dic62—21no—
56C2×Dic62C2311yescharacteristic
57C4⋊C4×C31D411yescharacteristic
58C4⋊C4×C31C2311yescharacteristic
59C22⋊C4×C31—21no—
60C22⋊C4×C31—22no—
61C22⋊C4×C31D412yes—
62C42×C31C2311yescharacteristic
63C22⋊Dic31—22no—
64#92480—22no—
65#92480—42no—
66C4⋊Dic31—21no—
67C4⋊Dic31—22no—
68C4⋊Dic31C2311yescharacteristic
69C4⋊Dic31C2312yes—
70Dic31⋊C4—21no—
71Dic31⋊C4—22no—
72C4×Dic31—21no—
73C2×C31⋊C8—42no—
74C2×C31⋊C8C2311yescharacteristic
75C2×C31⋊C8C2311yescharacteristic
76C2×C31⋊C8C2312yes—
77C23×C31—21no—
78C23×C31—22no—
79C23×C31—44no—
80C23×C31—44no—
81C23×C31—82no—
82C23×C31C2×D412yes—
83D4×C31—22no—
84D4×C31—21no—
85D4×C31—22no—
86D4×C31—44no—
87D4×C31—44no—
88D4×C31—42no—
89D4×C31—81no—
90D4×C31SD1614yescomplemented
91D4×C31#4112yes—
92C2×C4×C31—22no—
93C2×C4×C31—22no—
94C2×C4×C31—21no—
95C2×C4×C31—42no—
96C2×C4×C31C2×D412yes—
97C2×C4×C31C2×D411yescharacteristic
98C2×C4×C31C2×D411yescharacteristic
99C2×C4×C31C2411yescharacteristic
100C2×Dic31—21no—
101C2×Dic31—21no—
102C2×Dic31—22no—
103C2×Dic31—82no—
104Dic62—21no—
105Dic62—21no—
106Dic62—81no—
107C31⋊C8—21no—
108C31⋊C8—21no—
109C31⋊C8—22no—
110#3295—311nomaximal, Sylow
111C22×C31—22no—
112C22×C31—22no—
113C22×C31—22no—
114C22×C31—41no—
115C22×C31—41no—
116C22×C31—42no—
117C22×C31—42no—
118C22×C31—42no—
119C22×C31—88no—
120C22×C31C2×SD1614yes—
121C22×C31C22×D411yescharacteristic
122C4×C31—22no—
123C4×C31—21no—
124C4×C31—41no—
125C4×C31C2×SD1612yes—
126C4×C31C2×#4111yescharacteristic
127C4×C31H(5,𝔽2)11yescharacteristic
128Dic31—41no—
129Dic31—42no—
130Dic31—41no—
131#554—311no—
132D42D3111yescharacteristic
133#486—311no—
134#481—312no—
135#476—311no—
136#465—312no—
137#460—311no—
138#450—312no—
139C4×SD16—311no—
140C8×D4—311no—
141C2×#102—312no—
142C2×C31—24no—
143C2×C31—42no—
144C2×C31—82no—
145C2×C31#54611yescharacteristic
146C2×C31C22×SD1611yescharacteristic
147C2×C31#57611yescharacteristic
148C22×D4—21no—
149C22×D4C2×D3112yes—
150C2×SD16—311no—
151C2×SD16—312no—
152C22×C8—312no—
153C4⋊Q8—311no—
154#127C2×D3111yescharacteristic
155#125—621no—
156C22⋊Q8—312no—
157C22⋊Q8—622no—
158#121—21no—
159#121C2×D3112yes—
160#120—22no—
161C4×Q8—311no—
162C4×D4—621no—
163C4×D4C2×D3111yescharacteristic
164C4×D4C2×D3111yescharacteristic
165C2×C4⋊C4—312no—
166#106—311no—
167#106—312no—
168C4⋊C8—311no—
169#103—311no—
170#102—311no—
171#102—312no—
172#102—312no—
173#102—312no—
174#102—312no—
175C22⋊C8—312no—
176C4×C8—311no—
177C31#329511yescharacteristic, complemented, Sylow
178C24—22no—
179C2×Q8—311no—
180C2×Q8—621no—
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—42no—
187C2×D4—44no—
188C2×D4C22⋊D3111yescharacteristic
189C2×D4C22×D3112yes—
190C2×D4C22×D3111yescharacteristic
191C22×C4—21no—
192C22×C4—622no—
193C22×C4C22×D3112yes—
194SD16—622no—
195SD16—1242no—
196C2×C8—311no—
197C2×C8—311no—
198C2×C8—312no—
199C2×C8—1242no—
200C4⋊C4—311no—
201C4⋊C4—312no—
202C4⋊C4—621no—
203C4⋊C4—622no—
204C4⋊C4—622no—
205C4⋊C4—621no—
206C4⋊C4C22⋊D3111yescharacteristic
207C4⋊C4C22×D3111yescharacteristic
208C22⋊C4—21no—
209C22⋊C4—22no—
210C22⋊C4—622no—
211C22⋊C4C22⋊D3112yes—
212C42—621no—
213C42C22×D3111yescharacteristic
214C23—21no—
215C23—22no—
216C23—44no—
217C23—44no—
218C23—82no—
219C23C2×C22⋊D3112yes—
220Q8—621no—
221Q8—621no—
222Q8—2481no—
223D4—22no—
224D4—21no—
225D4—22no—
226D4—44no—
227D4—44no—
228D4—42no—
229D4—81no—
230D4#9248014yescomplemented
231D4#9249712yes—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—621no—
237C2×C4—621no—
238C2×C4—622no—
239C2×C4—2482no—
240C2×C4C2×C22⋊D3111yescharacteristic
241C2×C4C2×C22⋊D3112yes—
242C2×C4C2×C22⋊D3111yescharacteristic
243C2×C4C23×D3111yescharacteristic
244C8—621no—
245C8—621no—
246C8—622no—
247C22—22no—
248C22—22no—
249C22—22no—
250C22—41no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—88no—
256C22C2×#9248014yes—
257C22C22×C22⋊D3111yescharacteristic
258C4—22no—
259C4—21no—
260C4—41no—
261C4—1241no—
262C4—1241no—
263C4—1242no—
264C4C2×#9248012yes—
265C4C2×#9249711yescharacteristic
266C4#1175856111yescharacteristic
267C2—24no—
268C2—42no—
269C2—82no—
270C2#1452169311yescharacteristic
271C2C22×#9248011yescharacteristic
272C2#1452185211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
Fitting, prime radicalD42×C31C2
socleC22×C31C22×D4
hypercenterD42D31
hypocenterC31#3295
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. #14521756C2semidirect
2. #14521395C2semidirect
3. #14521365C2semidirect
4. #14521339C2semidirect
5. #14521276C2semidirect
6. #14521246C2semidirect
7. #14521200C2semidirect
8. C4×#92480C2semidirect
9. D4×C31⋊C8C2semidirect
10. C2×#11758420C2semidirect
22. C2×#92480C22semidirect
23. C2×C4⋊Dic31C22semidirect
24. #11758501C22semidirect
25. C22×C31⋊C8C22semidirect
28. #11758446C22semidirect
29. C4×Dic62C22semidirect
32. #11758420C22semidirect
33. #11758420C22semidirect
34. #11758420C22semidirect
35. C22⋊(C31⋊C8)C22semidirect
36. #11758398C22semidirect
37. #11758396C22semidirect
38. #11758396C22semidirect
39. C4⋊(C31⋊C8)C22semidirect
40. C4×C31⋊C8C22semidirect
90. D4×C31SD16semidirect
177. C31#3295semidirect
230. D4#92480semidirect

Maximal subgroups

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

subgroupindex
#145217562
#145213952
#145213652
#145213392
#145212762
#145212462
#145212002
C4×#924802
D4×C31⋊C82
C2×#117584202
D42×C312
#329531