Finite Group Databasebeta

← C31×#21796 #21478555

Subgroups — C31×#21796 #21478555

Order 7936.

1334 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 366 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×#537C211yesmaximal, characteristic
2C31×#2313C212yesmaximal, complemented
3C31×#1964C218yesmaximal, complemented
4C31×#1782C214yesmaximal, complemented
5C22×#41×C31C2212yes—
6C31×#537—28no—
7C2×C31×C22⋊Q8C414yescomplemented
8C2×C31×#121C414yescomplemented
9C2×C31×#121C2214yes—
10C22×C4⋊C4×C31C2211yescharacteristic
11C2×C31×#99C22116yes—
12C31×#387—28no—
13C31×#381C2214yes—
14C31×#380C2214yes—
15C4×C22⋊C4×C31C2214yes—
16C2×#41×C31—28no—
17C2×#41×C31—48no—
18C22×Q8×C31C2×C412yes—
19C22×D4×C31C2×C412yes—
20C22×D4×C31C2×C414yes—
21C22×D4×C31C2314yes—
22C23×C4×C31C2×C414yes—
23C23×C4×C31C2311yescharacteristic
24C23×C4×C31C2312yes—
25C31×C22⋊Q8—216no—
26C31×#121—28no—
27C31×#121—28no—
28C31×#121—216no—
29C2×C4⋊C4×C31—24no—
30C2×C4⋊C4×C31C2×C414yes—
31C2×C4⋊C4×C31C2×C414yes—
32C2×C4⋊C4×C31D418yes—
33C2×C22⋊C4×C31C2×C418yes—
34C2×C22⋊C4×C31C2318yes—
35C2×C42×C31—24no—
36C31×#99—416no—
37C31×#95—24no—
38C31×#95—24no—
39C31×#95—28no—
40C24×C31C22×C414yes—
41C24×C31C2411yescharacteristic
42#41×C31—432no—
43C2×Q8×C31—24no—
44C2×Q8×C31—44no—
45C2×D4×C31—28no—
46C2×D4×C31—216no—
47C2×D4×C31—24no—
48C2×D4×C31—28no—
49C2×D4×C31—44no—
50C2×D4×C31—84no—
51C22×C4×C31—24no—
52C22×C4×C31—28no—
53C22×C4×C31—28no—
54C22×C4×C31—48no—
55C22×C4×C31—82no—
56C22×C4×C31C22×C414yes—
57C22×C4×C31C22×C412yes—
58C22×C4×C31C22×C414yes—
59C22×C4×C31C2×D414yes—
60C22×C4×C31C2×D414yes—
61C22×C4×C31C2×D414yes—
62C4⋊C4×C31—28no—
63C4⋊C4×C31—84no—
64C4⋊C4×C31C22⋊C4116yes—
65C22⋊C4×C31—216no—
66C22⋊C4×C31—216no—
67C42×C31—84no—
68#21796C3111yesmaximal, characteristic, direct product factor, Sylow
69C23×C31—24no—
70C23×C31—28no—
71C23×C31—41no—
72C23×C31—41no—
73C23×C31—44no—
74C23×C31—44no—
75C23×C31C23×C411yescharacteristic
76C23×C31C22×D412yes—
77C23×C31H(5,𝔽2)14yes—
78Q8×C31—48no—
79D4×C31—48no—
80D4×C31—416no—
81D4×C31—88no—
82C2×C4×C31—24no—
83C2×C4×C31—28no—
84C2×C4×C31—24no—
85C2×C4×C31—28no—
86C2×C4×C31—44no—
87C2×C4×C31—44no—
88C2×C4×C31—44no—
89C2×C4×C31—416no—
90C2×C4×C31—48no—
91C2×C4×C31—48no—
92C2×C4×C31—48no—
93C2×C4×C31C2×C22⋊C418yes—
94C2×C4×C31C2×C22⋊C414yes—
95C2×#537C2×C3111yescharacteristic
96#2313C2×C3112yescomplemented
97#1964C2×C3118yescomplemented
98#1782C2×C3114yescomplemented
99C22×C31—22no—
100C22×C31—21no—
101C22×C31—22no—
102C22×C31—21no—
103C22×C31—44no—
104C22×C31—44no—
105C22×C31—44no—
106C22×C31—44no—
107C22×C31—88no—
108C22×C31C22×C22⋊C411yescharacteristic
109C22×C31#51812yes—
110C22×C31#53514yes—
111C4×C31—24no—
112C4×C31—28no—
113C4×C31—44no—
114C4×C31—88no—
115C22×#41C22×C3112yes—
116#537—28no—
117C2×C22⋊Q8C4×C3114yescomplemented
118C2×#121C4×C3114yescomplemented
119C2×#121C22×C3114yes—
120C22×C4⋊C4C22×C3111yescharacteristic
121C2×#99C22×C31116yes—
122#387—28no—
123#381C22×C3114yes—
124#380C22×C3114yes—
125C4×C22⋊C4C22×C3114yes—
126C2×C31—24no—
127C2×C31—22no—
128C2×C31—84no—
129C2×C31#230911yescharacteristic
130C2×C31#288311yescharacteristic
131C2×C31#288411yescharacteristic
132C2×#41—28no—
133C2×#41—48no—
134C22×Q8C2×C4×C3112yes—
135C22×D4C2×C4×C3112yes—
136C22×D4C2×C4×C3114yes—
137C22×D4C23×C3114yes—
138C23×C4C2×C4×C3114yes—
139C23×C4C23×C3111yescharacteristic
140C23×C4C23×C3112yes—
141C22⋊Q8—216no—
142#121—28no—
143#121—28no—
144#121—216no—
145C2×C4⋊C4—24no—
146C2×C4⋊C4C2×C4×C3114yes—
147C2×C4⋊C4C2×C4×C3114yes—
148C2×C4⋊C4D4×C3118yes—
149C2×C22⋊C4C2×C4×C3118yes—
150C2×C22⋊C4C23×C3118yes—
151C2×C42—24no—
152#99—416no—
153#95—24no—
154#95—24no—
155#95—28no—
156C31#2179611yescharacteristic, direct product factor, Sylow
157C24C22×C4×C3114yes—
158C24C24×C3111yescharacteristic
159#41—432no—
160C2×Q8—24no—
161C2×Q8—44no—
162C2×D4—28no—
163C2×D4—216no—
164C2×D4—24no—
165C2×D4—28no—
166C2×D4—44no—
167C2×D4—84no—
168C22×C4—24no—
169C22×C4—28no—
170C22×C4—28no—
171C22×C4—48no—
172C22×C4—82no—
173C22×C4C22×C4×C3114yes—
174C22×C4C22×C4×C3112yes—
175C22×C4C22×C4×C3114yes—
176C22×C4C2×D4×C3114yes—
177C22×C4C2×D4×C3114yes—
178C22×C4C2×D4×C3114yes—
179C4⋊C4—28no—
180C4⋊C4—84no—
181C4⋊C4C22⋊C4×C31116yes—
182C22⋊C4—216no—
183C22⋊C4—216no—
184C42—84no—
185C23—24no—
186C23—28no—
187C23—41no—
188C23—41no—
189C23—44no—
190C23—44no—
191C23C23×C4×C3111yescharacteristic
192C23C22×D4×C3112yes—
193C23C31×H(5,𝔽2)14yes—
194Q8—48no—
195D4—48no—
196D4—416no—
197D4—88no—
198C2×C4—24no—
199C2×C4—28no—
200C2×C4—24no—
201C2×C4—28no—
202C2×C4—44no—
203C2×C4—44no—
204C2×C4—44no—
205C2×C4—416no—
206C2×C4—48no—
207C2×C4—48no—
208C2×C4—48no—
209C2×C4C2×C22⋊C4×C3118yes—
210C2×C4C2×C22⋊C4×C3114yes—
211C22—22no—
212C22—21no—
213C22—22no—
214C22—21no—
215C22—44no—
216C22—44no—
217C22—44no—
218C22—44no—
219C22—88no—
220C22C22×C22⋊C4×C3111yescharacteristic
221C22C31×#51812yes—
222C22C31×#53514yes—
223C4—24no—
224C4—28no—
225C4—44no—
226C4—88no—
227C2—24no—
228C2—22no—
229C2—84no—
230C2C31×#230911yescharacteristic
231C2C31×#288311yescharacteristic
232C2C31×#288411yescharacteristic
subgroupG/H
center, socleC22×C31C22×C22⋊C4
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC2×C31×#537C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2313C2semidirect
3. C31×#1964C2semidirect
4. C31×#1782C2semidirect
7. C2×C31×C22⋊Q8C4semidirect
8. C2×C31×#121C4semidirect
68. #21796C31direct (N × H)
96. #2313C2×C31semidirect
97. #1964C2×C31semidirect
98. #1782C2×C31semidirect
117. C2×C22⋊Q8C4×C31semidirect
118. C2×#121C4×C31semidirect
156. C31#21796direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5372
C31×#23132
C31×#19642
C31×#17822
#2179631