Finite Group Databasebeta

← C31×#7326 #21464085

Subgroups — C31×#7326 #21464085

Order 7936.

374 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 78 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
1C31×#1463C212yesmaximal
2C31×#1445C211yesmaximal, characteristic
3C22×C4⋊C4×C31C2211yescharacteristic
4C31×#407—22no—
5C2×C31×#95—22no—
6C2×C31×#95C411yescharacteristic
7C2×C31×#95C411yescharacteristic
8C31×#324—22no—
9C31×#324C414yescomplemented
10C23×C4×C31—21no—
11C23×C4×C31—21no—
12C23×C4×C31C2×C411yescharacteristic
13C23×C4×C31D412yes—
14C2×M16×C31—42no—
15C2×C4⋊C4×C31—41no—
16C2×C4⋊C4×C31—41no—
17C2×C4⋊C4×C31C2×C412yes—
18C2×C4⋊C4×C31D411yescharacteristic
19C2×C4⋊C4×C31Q811yescharacteristic
20C31×C22⋊C8—24no—
21C31×C22⋊C8—42no—
22C31×#95—44no—
23C31×#95—41no—
24C31×#95—41no—
25C24×C31C22⋊C411yescharacteristic
26C22×C4×C31—21no—
27C22×C4×C31—21no—
28C22×C4×C31—22no—
29C22×C4×C31—22no—
30C22×C4×C31—22no—
31C22×C4×C31—22no—
32C22×C4×C31—42no—
33C22×C4×C31—42no—
34C22×C4×C31—42no—
35C22×C4×C31—42no—
36C22×C4×C31—42no—
37C22×C4×C31—42no—
38C22×C4×C31—41no—
39C22×C4×C31—41no—
40C22×C4×C31—42no—
41C22×C4×C31—41no—
42C22×C4×C31—41no—
43C22×C4×C31C4211yescharacteristic
44C22×C4×C31C22⋊C412yes—
45C22×C4×C31C4⋊C411yescharacteristic
46C22×C4×C31C4⋊C412yes—
47M16×C31—82no—
48M16×C31—82no—
49C2×C8×C31—44no—
50C4⋊C4×C31—42no—
51C4⋊C4×C31—41no—
52C4⋊C4×C31—41no—
53#7326C3111yesmaximal, characteristic, direct product factor, Sylow
54C23×C31—22no—
55C23×C31—21no—
56C23×C31—21no—
57C23×C31—21no—
58C23×C31—21no—
59C23×C31#9511yescharacteristic
60C23×C31#9911yescharacteristic
61C23×C31#9911yescharacteristic
62C2×C4×C31—22no—
63C2×C4×C31—21no—
64C2×C4×C31—21no—
65C2×C4×C31—22no—
66C2×C4×C31—22no—
67C2×C4×C31—22no—
68C2×C4×C31—42no—
69C2×C4×C31—42no—
70C2×C4×C31—42no—
71C2×C4×C31—42no—
72C2×C4×C31—42no—
73C2×C4×C31—42no—
74C2×C4×C31—44no—
75C2×C4×C31—44no—
76C2×C4×C31—42no—
77C2×C4×C31—42no—
78C2×C4×C31—82no—
79C2×C4×C31—82no—
80C2×C4×C31—82no—
81C2×C4×C31—81no—
82C2×C4×C31—81no—
83C2×C4×C31—81no—
84C2×C4×C31—81no—
85C8×C31—84no—
86#1463C2×C3112yes—
87#1445C2×C3111yescharacteristic
88C22×C31—22no—
89C22×C31—22no—
90C22×C31—22no—
91C22×C31—22no—
92C22×C31—21no—
93C22×C31—21no—
94C22×C31—21no—
95C22×C31—21no—
96C22×C31—21no—
97C22×C31—21no—
98C22×C31#34211yescharacteristic
99C22×C31#34412yes—
100C22×C31#35311yescharacteristic
101C22×C31#35411yescharacteristic
102C22×C31#35511yescharacteristic
103C22×C31#35611yescharacteristic
104C4×C31—41no—
105C4×C31—41no—
106C4×C31—42no—
107C4×C31—42no—
108C4×C31—82no—
109C4×C31—82no—
110C22×C4⋊C4C22×C3111yescharacteristic
111#407—22no—
112C2×#95—22no—
113C2×#95C4×C3111yescharacteristic
114C2×#95C4×C3111yescharacteristic
115#324—22no—
116#324C4×C3114yescomplemented
117C2×C31—21no—
118C2×C31—21no—
119C2×C31—22no—
120C2×C31—21no—
121C2×C31—21no—
122C2×C31#130611yescharacteristic
123C2×C31#139311yescharacteristic
124C2×C31#139411yescharacteristic
125C23×C4—21no—
126C23×C4—21no—
127C23×C4C2×C4×C3111yescharacteristic
128C23×C4D4×C3112yes—
129C2×M16—42no—
130C2×C4⋊C4—41no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4C2×C4×C3112yes—
133C2×C4⋊C4D4×C3111yescharacteristic
134C2×C4⋊C4Q8×C3111yescharacteristic
135C22⋊C8—24no—
136C22⋊C8—42no—
137#95—41no—
138#95—41no—
139#95—44no—
140C31#732611yescharacteristic, direct product factor, Sylow
141C24C22⋊C4×C3111yescharacteristic
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4—42no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—42no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4C42×C3111yescharacteristic
160C22×C4C22⋊C4×C3112yes—
161C22×C4C4⋊C4×C3111yescharacteristic
162C22×C4C4⋊C4×C3112yes—
163M16—82no—
164M16—82no—
165C2×C8—44no—
166C4⋊C4—42no—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C23—22no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23C31×#9511yescharacteristic
175C23C31×#9911yescharacteristic
176C23C31×#9911yescharacteristic
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—44no—
190C2×C4—44no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—82no—
194C2×C4—82no—
195C2×C4—82no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—81no—
200C8—84no—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22C31×#34211yescharacteristic
212C22C31×#34412yes—
213C22C31×#35311yescharacteristic
214C22C31×#35411yescharacteristic
215C22C31×#35511yescharacteristic
216C22C31×#35611yescharacteristic
217C4—41no—
218C4—41no—
219C4—42no—
220C4—42no—
221C4—82no—
222C4—82no—
223C2—21no—
224C2—21no—
225C2—22no—
226C2—21no—
227C2—21no—
228C2C31×#130611yescharacteristic
229C2C31×#139311yescharacteristic
230C2C31×#139411yescharacteristic
subgroupG/H
center, socleC22×C31#342
commutatorC22×C4C42×C31
Frattini, cosocleC22×C4⋊C4C22×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C31 ◁ C22×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
9. C31×#324C4semidirect
53. #7326C31direct (N × H)
116. #324C4×C31semidirect
140. C31#7326direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#14632
C31×#14452
#732631