Finite Group Databasebeta

← C31×#7554 #21464313

Subgroups — C31×#7554 #21464313

Order 7936.

3158 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C42×C31C211yesmaximal, characteristic
2C22×C31×#95C216yesmaximal
3C24×C4×C31C2214yes—
4C24×C4×C31C2213yes—
5C22×C42×C31—212no—
6C22×C42×C31C414yescomplemented
7C2×C31×#95—212no—
8C2×C31×#95—212no—
9C2×C31×#95C4124yescomplemented
10C25×C31C2311yescharacteristic
11C23×C4×C31—212no—
12C23×C4×C31—212no—
13C23×C4×C31—212no—
14C23×C4×C31—212no—
15C23×C4×C31—224no—
16C23×C4×C31C2×C4124yes—
17C23×C4×C31C2×C416yes—
18C23×C4×C31C2×C4112yes—
19C23×C4×C31D4112yes—
20C23×C4×C31D416yes—
21C23×C4×C31Q816yes—
22C2×C42×C31—232no—
23C2×C42×C31—224no—
24C31×#95—248no—
25C24×C31C22×C411yescharacteristic
26C24×C31C22×C416yes—
27C24×C31C2×D416yes—
28C24×C31C2×D413yes—
29C24×C31C2×Q813yes—
30C24×C31#41112yes—
31C22×C4×C31—212no—
32C22×C4×C31—212no—
33C22×C4×C31—248no—
34C22×C4×C31—224no—
35C22×C4×C31—224no—
36C22×C4×C31—224no—
37C22×C4×C31—224no—
38C22×C4×C31—224no—
39C22×C4×C31—224no—
40C22×C4×C31—248no—
41C22×C4×C31—248no—
42C22×C4×C31—44no—
43C22×C4×C31—424no—
44C22×C4×C31—412no—
45C22×C4×C31—412no—
46C22×C4×C31—48no—
47C22×C4×C31—44no—
48C22×C4×C31C42112yes—
49C22×C4×C31C42116yescomplemented
50C22×C4×C31C22⋊C4124yes—
51C22×C4×C31C22⋊C4112yes—
52C22×C4×C31C4⋊C4112yes—
53C22×C4×C31C4⋊C4124yes—
54C42×C31—232no—
55#7554C3111yesmaximal, characteristic, direct product factor, Sylow
56C23×C31C2×C4213yes—
57C23×C31C2×C4214yes—
58C23×C31C2×C22⋊C413yes—
59C23×C31C2×C22⋊C416yes—
60C23×C31C2×C4⋊C413yes—
61C23×C31C2×C4⋊C416yes—
62C23×C31#11716yes—
63C23×C31#117112yes—
64C23×C31C4×D4124yes—
65C23×C31C4×D4112yes—
66C23×C31C4×Q8112yes—
67C23×C31#12014yes—
68C23×C31#121112yes—
69C23×C31C22⋊Q8112yes—
70C23×C31#123112yes—
71C23×C31#12416yes—
72C23×C31#12516yes—
73C23×C31#12618yes—
74C23×C31#12711yescharacteristic
75C23×C31C4⋊Q813yes—
76C2×C4×C31—224no—
77C2×C4×C31—212no—
78C2×C4×C31—224no—
79C2×C4×C31—212no—
80C2×C4×C31—248no—
81C2×C4×C31—248no—
82C2×C4×C31—248no—
83C2×C4×C31—424no—
84C2×C4×C31—448no—
85C2×C4×C31—424no—
86C2×C4×C31#95124yescomplemented
87C23×C42C2×C3111yescharacteristic
88C22×#95C2×C3116yes—
89C22×C31C4311yescharacteristic
90C22×C31C2×#9513yes—
91C22×C31#37613yes—
92C22×C31C4×C22⋊C416yes—
93C22×C31C4×C22⋊C4112yes—
94C22×C31C4×C4⋊C416yes—
95C22×C31C4×C4⋊C4112yes—
96C22×C31#37911yescharacteristic
97C22×C31#38016yes—
98C22×C31#38113yes—
99C22×C31#38213yes—
100C22×C31#38312yes—
101C22×C31#38411yescharacteristic
102C22×C31#385112yes—
103C22×C31#386112yes—
104C22×C31#387124yes—
105C22×C31#388124yes—
106C22×C31#389112yes—
107C22×C31#39016yes—
108C22×C31#39116yes—
109C4×C31—224no—
110C4×C31—416no—
111C24×C4C22×C3114yes—
112C24×C4C22×C3113yes—
113C22×C42—212no—
114C22×C42C4×C3114yescomplemented
115C2×#95—212no—
116C2×#95—212no—
117C2×#95C4×C31124yescomplemented
118C2×C31C4×#9513yes—
119C2×C31C22⋊#9513yes—
120C2×C31#143416yes—
121C2×C31C4⋊#9513yes—
122C2×C31#1436112yes—
123C2×C31#143714yes—
124C25C23×C3111yescharacteristic
125C23×C4—212no—
126C23×C4—212no—
127C23×C4—212no—
128C23×C4—212no—
129C23×C4—224no—
130C23×C4C2×C4×C31124yes—
131C23×C4C2×C4×C31112yes—
132C23×C4C2×C4×C3116yes—
133C23×C4D4×C3116yes—
134C23×C4D4×C31112yes—
135C23×C4Q8×C3116yes—
136C2×C42—232no—
137C2×C42—224no—
138#95—248no—
139C31#755411yescharacteristic, direct product factor, Sylow
140C24C22×C4×C3111yescharacteristic
141C24C22×C4×C3116yes—
142C24C2×D4×C3116yes—
143C24C2×D4×C3113yes—
144C24C2×Q8×C3113yes—
145C24#41×C31112yes—
146C22×C4—212no—
147C22×C4—212no—
148C22×C4—248no—
149C22×C4—224no—
150C22×C4—224no—
151C22×C4—224no—
152C22×C4—224no—
153C22×C4—224no—
154C22×C4—224no—
155C22×C4—248no—
156C22×C4—248no—
157C22×C4—44no—
158C22×C4—424no—
159C22×C4—412no—
160C22×C4—412no—
161C22×C4—48no—
162C22×C4—44no—
163C22×C4C42×C31112yes—
164C22×C4C42×C31116yescomplemented
165C22×C4C22⋊C4×C31124yes—
166C22×C4C22⋊C4×C31112yes—
167C22×C4C4⋊C4×C31112yes—
168C22×C4C4⋊C4×C31124yes—
169C42—232no—
170C23C2×C42×C3113yes—
171C23C2×C42×C3114yes—
172C23C2×C22⋊C4×C3113yes—
173C23C2×C22⋊C4×C3116yes—
174C23C2×C4⋊C4×C3113yes—
175C23C2×C4⋊C4×C3116yes—
176C23C31×#11716yes—
177C23C31×#117112yes—
178C23C4×D4×C31124yes—
179C23C4×D4×C31112yes—
180C23C4×Q8×C31112yes—
181C23C31×#12014yes—
182C23C31×#121112yes—
183C23C31×C22⋊Q8112yes—
184C23C31×#123112yes—
185C23C31×#12416yes—
186C23C31×#12516yes—
187C23C31×#12618yes—
188C23C31×#12711yescharacteristic
189C23C31×C4⋊Q813yes—
190C2×C4—224no—
191C2×C4—212no—
192C2×C4—224no—
193C2×C4—212no—
194C2×C4—248no—
195C2×C4—248no—
196C2×C4—248no—
197C2×C4—424no—
198C2×C4—448no—
199C2×C4—424no—
200C2×C4C31×#95124yescomplemented
201C22C43×C3111yescharacteristic
202C22C2×C31×#9513yes—
203C22C31×#37613yes—
204C22C4×C22⋊C4×C3116yes—
205C22C4×C22⋊C4×C31112yes—
206C22C4×C4⋊C4×C3116yes—
207C22C4×C4⋊C4×C31112yes—
208C22C31×#37911yescharacteristic
209C22C31×#38016yes—
210C22C31×#38113yes—
211C22C31×#38213yes—
212C22C31×#38312yes—
213C22C31×#38411yescharacteristic
214C22C31×#385112yes—
215C22C31×#386112yes—
216C22C31×#387124yes—
217C22C31×#388124yes—
218C22C31×#389112yes—
219C22C31×#39016yes—
220C22C31×#39116yes—
221C4—224no—
222C4—416no—
223C2C4×C31×#9513yes—
224C2C31×C22⋊#9513yes—
225C2C31×#143416yes—
226C2C31×C4⋊#9513yes—
227C2C31×#1436112yes—
228C2C31×#143714yes—
subgroupG/H
center, socle, prime radicalC25×C31C23
commutatorC22C43×C31
Frattini, cosocleC25C23×C31
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
6. C22×C42×C31C4semidirect
9. C2×C31×#95C4semidirect
49. C22×C4×C31C42semidirect
55. #7554C31direct (N × H)
86. C2×C4×C31#95semidirect
114. C22×C42C4×C31semidirect
117. C2×#95C4×C31semidirect
139. C31#7554direct (N × H)
164. C22×C4C42×C31semidirect
200. C2×C4C31×#95semidirect

Maximal subgroups

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

subgroupindex
C23×C42×C312
C22×C31×#952
#755431