Finite Group Databasebeta

← C31×#33305 #21490064

Subgroups — C31×#33305 #21490064

Order 7936.

1450 conjugacy classes of subgroups; only the 414 normal subgroups are shown.

normal subgroups only

This group has 1450 conjugacy classes of subgroups — too many to draw. Only its 414 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
1C2×C31×#497C218yesmaximal, complemented
2C2×C31×#494C212yesmaximal, complemented
3C2×C31×#492C212yesmaximal
4C31×#2868C211yesmaximal, characteristic, complemented
5C31×#2858C211yesmaximal, characteristic
6C4×C31×#97C211yesmaximal, characteristic, complemented
7C22×Q16×C31C2218yes—
8C22×SD16×C31C2218yes—
9C2×C31×C4⋊Q8C2211yescharacteristic
10C2×C31×C4⋊Q8C2212yes—
11C2×C31×C4⋊Q8C2214yes—
12C2×C31×#127C2211yescharacteristic
13C2×C31×#124C2214yes—
14C31×#497—232no—
15C31×#494—28no—
16C31×#492—28no—
17C2×C31×#97C2214yes—
18C2×C4×C8×C31C2212yes—
19C31×#390—24no—
20C31×#384—24no—
21C43×C31C2211yescharacteristic
22C22×Q8×C31C2312yes—
23C22×Q8×C31C2314yes—
24C22×D4×C31—22no—
25C22×D4×C31C2312yes—
26C2×Q16×C31—216no—
27C2×Q16×C31—232no—
28C2×SD16×C31—216no—
29C2×SD16×C31—232no—
30C22×C8×C31C2314yes—
31C31×C4⋊Q8—24no—
32C31×C4⋊Q8—24no—
33C31×C4⋊Q8—24no—
34C31×C4⋊Q8—216no—
35C31×#127—24no—
36C31×#124—216no—
37C2×C4⋊C4×C31—28no—
38C2×C4⋊C4×C31—24no—
39C2×C4⋊C4×C31—22no—
40C2×C22⋊C4×C31—28no—
41C2×C42×C31D414yes—
42C2×C42×C31C2311yescharacteristic
43C2×C42×C31C2312yes—
44C31×#97D4116yescomplemented
45C4×C8×C31D418yes—
46C24×C31—22no—
47C2×Q8×C31—28no—
48C2×Q8×C31—24no—
49C2×Q8×C31—216no—
50C2×Q8×C31—24no—
51C2×Q8×C31—24no—
52C2×D4×C31—28no—
53C2×D4×C31—24no—
54C2×D4×C31—44no—
55C2×D4×C31—48no—
56C22×C4×C31—22no—
57C22×C4×C31—24no—
58C22×C4×C31C2×D414yes—
59C22×C4×C31C2×D412yes—
60C22×C4×C31C2411yescharacteristic
61Q16×C31—432no—
62SD16×C31—432no—
63C2×C8×C31C2×D418yes—
64C2×C8×C31C2×D4116yes—
65C4⋊C4×C31—416no—
66C4⋊C4×C31—48no—
67C4⋊C4×C31—44no—
68C22⋊C4×C31—416no—
69C42×C31—28no—
70C42×C31C2×D414yes—
71C42×C31C2×D418yes—
72#33305C3111yesmaximal, characteristic, direct product factor, Sylow
73C23×C31—44no—
74C23×C31—42no—
75C23×C31—48no—
76C23×C31C22×D411yescharacteristic
77Q8×C31—48no—
78Q8×C31—48no—
79Q8×C31—48no—
80D4×C31—48no—
81D4×C31—88no—
82C2×C4×C31—28no—
83C2×C4×C31—44no—
84C2×C4×C31—42no—
85C2×C4×C31—44no—
86C2×C4×C31—48no—
87C2×C4×C31#12718yes—
88C2×C4×C31#12714yes—
89C2×C4×C31#13718yes—
90C2×C4×C31C22×D412yes—
91C2×C4×C31C22×D414yes—
92C8×C31#127116yes—
93C2×#497C2×C3118yescomplemented
94C2×#494C2×C3112yescomplemented
95C2×#492C2×C3112yes—
96#2868C2×C3111yescharacteristic, complemented
97#2858C2×C3111yescharacteristic
98C4×#97C2×C3111yescharacteristic, complemented
99C22×C31—82no—
100C22×C31—84no—
101C22×C31—88no—
102C22×C31C2×#12711yescharacteristic
103C22×C31C2×#12712yes—
104C22×C31C2×#13714yes—
105C4×C31—28no—
106C4×C31—82no—
107C4×C31—84no—
108C4×C31#49718yescomplemented
109C4×C31C2×#12714yes—
110C22×Q16C22×C3118yes—
111C22×SD16C22×C3118yes—
112C2×C4⋊Q8C22×C3111yescharacteristic
113C2×C4⋊Q8C22×C3112yes—
114C2×C4⋊Q8C22×C3114yes—
115C2×#127C22×C3111yescharacteristic
116C2×#124C22×C3114yes—
117#497—232no—
118#494—28no—
119#492—28no—
120C2×#97C22×C3114yes—
121C2×C4×C8C22×C3112yes—
122#390—24no—
123#384—24no—
124C43C22×C3111yescharacteristic
125C2×C31—162no—
126C2×C31#286711yescharacteristic
127C2×C31C2×#49712yes—
128C2×C31#315214yes—
129C22×Q8C23×C3112yes—
130C22×Q8C23×C3114yes—
131C22×D4—22no—
132C22×D4C23×C3112yes—
133C2×Q16—216no—
134C2×Q16—232no—
135C2×SD16—216no—
136C2×SD16—232no—
137C22×C8C23×C3114yes—
138C4⋊Q8—24no—
139C4⋊Q8—24no—
140C4⋊Q8—24no—
141C4⋊Q8—216no—
142#127—24no—
143#124—216no—
144C2×C4⋊C4—28no—
145C2×C4⋊C4—24no—
146C2×C4⋊C4—22no—
147C2×C22⋊C4—28no—
148C2×C42D4×C3114yes—
149C2×C42C23×C3112yes—
150C2×C42C23×C3111yescharacteristic
151#97D4×C31116yescomplemented
152C4×C8D4×C3118yes—
153C31#3330511yescharacteristic, direct product factor, Sylow
154C24—22no—
155C2×Q8—28no—
156C2×Q8—24no—
157C2×Q8—216no—
158C2×Q8—24no—
159C2×Q8—24no—
160C2×D4—28no—
161C2×D4—24no—
162C2×D4—44no—
163C2×D4—48no—
164C22×C4—22no—
165C22×C4—24no—
166C22×C4C2×D4×C3114yes—
167C22×C4C2×D4×C3112yes—
168C22×C4C24×C3111yescharacteristic
169Q16—432no—
170SD16—432no—
171C2×C8C2×D4×C3118yes—
172C2×C8C2×D4×C31116yes—
173C4⋊C4—416no—
174C4⋊C4—48no—
175C4⋊C4—44no—
176C22⋊C4—416no—
177C42—28no—
178C42C2×D4×C3114yes—
179C42C2×D4×C3118yes—
180C23—44no—
181C23—42no—
182C23—48no—
183C23C22×D4×C3111yescharacteristic
184Q8—48no—
185Q8—48no—
186Q8—48no—
187D4—48no—
188D4—88no—
189C2×C4—28no—
190C2×C4—44no—
191C2×C4—42no—
192C2×C4—44no—
193C2×C4—48no—
194C2×C4C31×#12718yes—
195C2×C4C31×#12714yes—
196C2×C4C31×#13718yes—
197C2×C4C22×D4×C3112yes—
198C2×C4C22×D4×C3114yes—
199C8C31×#127116yes—
200C22—82no—
201C22—84no—
202C22—88no—
203C22C2×C31×#12711yescharacteristic
204C22C2×C31×#12712yes—
205C22C2×C31×#13714yes—
206C4—28no—
207C4—82no—
208C4—84no—
209C4C31×#49718yescomplemented
210C4C2×C31×#12714yes—
211C2—162no—
212C2C31×#286711yescharacteristic
213C2C2×C31×#49712yes—
214C2C31×#315214yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#497C2semidirect
2. C2×C31×#494C2semidirect
4. C31×#2868C2semidirect
6. C4×C31×#97C2semidirect
44. C31×#97D4semidirect
72. #33305C31direct (N × H)
93. C2×#497C2×C31semidirect
94. C2×#494C2×C31semidirect
96. #2868C2×C31semidirect
98. C4×#97C2×C31semidirect
108. C4×C31#497semidirect
151. #97D4×C31semidirect
153. C31#33305direct (N × H)
209. C4C31×#497semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4972
C2×C31×#4942
C2×C31×#4922
C31×#28682
C31×#28582
C4×C31×#972
#3330531