Finite Group Databasebeta

← C31×#36584 #21493343

Subgroups — C31×#36584 #21493343

Order 7936.

1590 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2859C213yesmaximal
2C31×#2571C216yesmaximal
3C31×#2509C2112yesmaximal
4C31×#2351C214yesmaximal
5Q8×C4⋊C4×C31C212yesmaximal
6C4×C31×#125C213yesmaximal
7C42×Q8×C31C211yesmaximal, characteristic
8C2×C31×#125C2213yes—
9C2×C4×Q8×C31C2214yes—
10C2×C4×Q8×C31C2212yes—
11C2×C4×Q8×C31C2211yescharacteristic
12C31×#400C22124yes—
13C31×#389C2216yes—
14C31×#389C22112yes—
15C31×#389C22112yes—
16C31×#389C22112yes—
17C31×#389C22112yes—
18C31×#387C22112yes—
19C31×#384C2216yes—
20C31×#382C2216yes—
21C31×#382C22112yes—
22C31×#382C2211yescharacteristic
23C4×C4⋊C4×C31C2213yes—
24C4×C4⋊C4×C31C2216yes—
25C4×C4⋊C4×C31C22112yes—
26C4×C4⋊C4×C31C2216yes—
27C43×C31C2213yes—
28C22×Q8×C31C2311yescharacteristic
29C31×#125—212no—
30C4×Q8×C31—216no—
31C4×Q8×C31—28no—
32C4×Q8×C31Q818yes—
33C2×C4⋊C4×C31C2316yes—
34C2×C4⋊C4×C31C23112yes—
35C2×C4⋊C4×C31C2316yes—
36C2×C4⋊C4×C31C23112yes—
37C2×C4⋊C4×C31C2312yes—
38C2×C4⋊C4×C31C23112yes—
39C2×C4⋊C4×C31C23112yes—
40C2×C4⋊C4×C31C2313yes—
41C2×C42×C31C2316yes—
42C2×C42×C31C23112yes—
43C2×C42×C31C2313yes—
44C2×C42×C31C2316yes—
45C2×C42×C31C2313yes—
46C2×C42×C31C2311yescharacteristic
47C31×#95C2316yes—
48C31×#95C23112yes—
49C31×#95C23112yes—
50C31×#95C23124yes—
51C31×#95C2314yes—
52C2×Q8×C31C2×Q814yes—
53C2×Q8×C31#4118yes—
54C22×C4×C31C2414yes—
55C22×C4×C31C2416yes—
56C22×C4×C31C24112yes—
57C22×C4×C31C2413yes—
58C22×C4×C31C2412yes—
59C22×C4×C31C2413yes—
60C22×C4×C31C2411yescharacteristic
61C4⋊C4×C31—212no—
62C4⋊C4×C31—224no—
63C4⋊C4×C31—224no—
64C4⋊C4×C31—212no—
65C4⋊C4×C31—24no—
66C4⋊C4×C31—412no—
67C4⋊C4×C31—412no—
68C4⋊C4×C31C2×Q8112yes—
69C42×C31—212no—
70C42×C31—224no—
71C42×C31—26no—
72C42×C31—46no—
73C42×C31C2×Q8112yes—
74C42×C31#4114yes—
75#36584C3111yesmaximal, characteristic, direct product factor, Sylow
76C23×C31C2511yescharacteristic
77Q8×C31#125116yescomplemented
78C2×C4×C31—22no—
79C2×C4×C31—22no—
80C2×C4×C31—26no—
81C2×C4×C31—24no—
82C2×C4×C31—212no—
83C2×C4×C31—26no—
84C2×C4×C31—212no—
85C2×C4×C31—26no—
86C2×C4×C31—24no—
87C2×C4×C31—26no—
88C2×C4×C31—212no—
89C2×C4×C31—24no—
90C2×C4×C31C22×Q816yes—
91C2×C4×C31C22×Q816yes—
92C2×C4×C31C22×Q812yes—
93C2×C4×C31C2×#4114yes—
94C2×C4×C31C2×#41112yes—
95C2×C4×C31C2×#4112yes—
96C2×C4×C312−1+412yes—
97#2859C2×C3113yes—
98#2571C2×C3116yes—
99#2509C2×C31112yes—
100#2351C2×C3114yes—
101Q8×C4⋊C4C2×C3112yes—
102C4×#125C2×C3113yes—
103C42×Q8C2×C3111yescharacteristic
104C22×C31C23×Q811yescharacteristic
105C22×C31C22×#4112yes—
106C22×C31C22×#4111yescharacteristic
107C22×C31C2×2−1+411yescharacteristic
108C22×C31#58512yes—
109C4×C31—24no—
110C4×C31—26no—
111C4×C31—412no—
112C4×C31—44no—
113C4×C31—46no—
114C4×C31C2×#125112yes—
115C4×C31#55714yes—
116C2×#125C22×C3113yes—
117C2×C4×Q8C22×C3114yes—
118C2×C4×Q8C22×C3112yes—
119C2×C4×Q8C22×C3111yescharacteristic
120#400C22×C31124yes—
121#389C22×C3116yes—
122#389C22×C31112yes—
123#389C22×C31112yes—
124#389C22×C31112yes—
125#389C22×C31112yes—
126#387C22×C31112yes—
127#384C22×C3116yes—
128#382C22×C3111yescharacteristic
129#382C22×C3116yes—
130#382C22×C31112yes—
131C4×C4⋊C4C22×C3116yes—
132C4×C4⋊C4C22×C31112yes—
133C4×C4⋊C4C22×C3113yes—
134C4×C4⋊C4C22×C3116yes—
135C43C22×C3113yes—
136C2×C31C22×#12511yescharacteristic
137C2×C31C2×#55711yescharacteristic
138C2×C31#348012yes—
139C2×C31#350411yescharacteristic
140C2×C31#351812yes—
141C22×Q8C23×C3111yescharacteristic
142#125—212no—
143C4×Q8—216no—
144C4×Q8—28no—
145C4×Q8Q8×C3118yes—
146C2×C4⋊C4C23×C3116yes—
147C2×C4⋊C4C23×C31112yes—
148C2×C4⋊C4C23×C3116yes—
149C2×C4⋊C4C23×C31112yes—
150C2×C4⋊C4C23×C3112yes—
151C2×C4⋊C4C23×C31112yes—
152C2×C4⋊C4C23×C31112yes—
153C2×C4⋊C4C23×C3113yes—
154C2×C42C23×C3116yes—
155C2×C42C23×C31112yes—
156C2×C42C23×C3113yes—
157C2×C42C23×C3116yes—
158C2×C42C23×C3113yes—
159C2×C42C23×C3111yescharacteristic
160#95C23×C3114yes—
161#95C23×C3116yes—
162#95C23×C31112yes—
163#95C23×C31112yes—
164#95C23×C31124yes—
165C31#3658411yescharacteristic, direct product factor, Sylow
166C2×Q8C2×Q8×C3114yes—
167C2×Q8#41×C3118yes—
168C22×C4C24×C3114yes—
169C22×C4C24×C3116yes—
170C22×C4C24×C31112yes—
171C22×C4C24×C3113yes—
172C22×C4C24×C3112yes—
173C22×C4C24×C3113yes—
174C22×C4C24×C3111yescharacteristic
175C4⋊C4—212no—
176C4⋊C4—224no—
177C4⋊C4—224no—
178C4⋊C4—212no—
179C4⋊C4—24no—
180C4⋊C4—412no—
181C4⋊C4—412no—
182C4⋊C4C2×Q8×C31112yes—
183C42—212no—
184C42—224no—
185C42—26no—
186C42—46no—
187C42C2×Q8×C31112yes—
188C42#41×C3114yes—
189C23C25×C3111yescharacteristic
190Q8C31×#125116yescomplemented
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—26no—
194C2×C4—24no—
195C2×C4—212no—
196C2×C4—26no—
197C2×C4—212no—
198C2×C4—26no—
199C2×C4—24no—
200C2×C4—26no—
201C2×C4—212no—
202C2×C4—24no—
203C2×C4C22×Q8×C3116yes—
204C2×C4C22×Q8×C3116yes—
205C2×C4C22×Q8×C3112yes—
206C2×C4C2×#41×C3114yes—
207C2×C4C2×#41×C31112yes—
208C2×C4C2×#41×C3112yes—
209C2×C4C31×2−1+412yes—
210C22C23×Q8×C3111yescharacteristic
211C22C22×#41×C3112yes—
212C22C22×#41×C3111yescharacteristic
213C22C2×C31×2−1+411yescharacteristic
214C22C31×#58512yes—
215C4—24no—
216C4—26no—
217C4—412no—
218C4—44no—
219C4—46no—
220C4C2×C31×#125112yes—
221C4C31×#55714yes—
222C2C22×C31×#12511yescharacteristic
223C2C2×C31×#55711yescharacteristic
224C2C31×#348012yes—
225C2C31×#350411yescharacteristic
226C2C31×#351812yes—
subgroupG/H
center, socle, prime radicalC23×C31C25
commutator, Frattini, cosocleC23C25×C31
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C31 ◁ G

Complements

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

NH ≅ G/Ntype
75. #36584C31direct (N × H)
77. Q8×C31#125semidirect
165. C31#36584direct (N × H)
190. Q8C31×#125semidirect

Maximal subgroups

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

subgroupindex
C31×#28592
C31×#25712
C31×#25092
C31×#23512
Q8×C4⋊C4×C312
C4×C31×#1252
C42×Q8×C312
#3658431