Finite Group Databasebeta

← C31×#7403 #21464162

Subgroups — C31×#7403 #21464162

Order 7936.

282 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 46 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×#2013C211yesmaximal, characteristic
2C31×#1393C211yesmaximal, characteristic
3C31×#1318C211yesmaximal, characteristic
4C22×SD16×C31—21no—
5C2×C31×C4⋊Q8C411yescharacteristic, complemented
6C2×C31×#103—21no—
7C2×C31×#99—21no—
8C31×#390C2211yescharacteristic
9C31×#336C411yescharacteristic, complemented
10C31×#324—21no—
11C22×Q8×C31—21no—
12C22×D4×C31D411yescharacteristic
13C2×SD16×C31—42no—
14C2×SD16×C31—42no—
15C2×SD16×C31—41no—
16C2×SD16×C31—41no—
17C22×C8×C31—21no—
18C31×C4⋊Q8—42no—
19C2×C4⋊C4×C31—41no—
20C2×C4⋊C4×C31D411yescharacteristic
21C2×C22⋊C4×C31—41no—
22C2×C22⋊C4×C31—41no—
23C2×C42×C31C2×C411yescharacteristic
24C31×#103—42no—
25C31×#99—22no—
26C31×#99—41no—
27C31×C22⋊C8—41no—
28C24×C31—21no—
29C2×Q8×C31—22no—
30C2×Q8×C31—41no—
31C2×Q8×C31—41no—
32C2×Q8×C31—41no—
33C2×Q8×C31—41no—
34C2×Q8×C31—41no—
35C2×D4×C31—21no—
36C2×D4×C31—41no—
37C2×D4×C31—41no—
38C2×D4×C31D811yescharacteristic
39C2×D4×C31SD1611yescharacteristic
40C22×C4×C31—21no—
41C22×C4×C31—21no—
42C22×C4×C31—41no—
43C22×C4×C31—81no—
44C22×C4×C31C22⋊C411yescharacteristic
45SD16×C31—44no—
46SD16×C31—44no—
47C2×C8×C31—22no—
48C2×C8×C31—41no—
49C2×C8×C31—41no—
50C2×C8×C31—81no—
51C4⋊C4×C31—41no—
52C4⋊C4×C31—42no—
53C4⋊C4×C31—42no—
54C22⋊C4×C31—42no—
55C22⋊C4×C31—82no—
56C22⋊C4×C31—81no—
57C42×C31—41no—
58#7403C3111yesmaximal, characteristic, direct product factor, Sylow
59C23×C31—21no—
60C23×C31—21no—
61C23×C31—41no—
62C23×C31—41no—
63C23×C31—81no—
64C23×C31—81no—
65C23×C31#9911yescharacteristic
66Q8×C31—42no—
67Q8×C31—42no—
68Q8×C31—81no—
69Q8×C31—81no—
70D4×C31—41no—
71D4×C31—41no—
72D4×C31—81no—
73C2×C4×C31—21no—
74C2×C4×C31—21no—
75C2×C4×C31—22no—
76C2×C4×C31—41no—
77C2×C4×C31—41no—
78C2×C4×C31—42no—
79C2×C4×C31—41no—
80C2×C4×C31—81no—
81C2×C4×C31—81no—
82C2×C4×C31—81no—
83C2×C4×C31—82no—
84C2×C4×C31—161no—
85C2×C4×C31—161no—
86C2×C4×C31#10211yescharacteristic
87C2×C4×C31#10411yescharacteristic
88C8×C31—42no—
89C8×C31—161no—
90#2013C2×C3111yescharacteristic
91#1393C2×C3111yescharacteristic
92#1318C2×C3111yescharacteristic
93C22×C31—21no—
94C22×C31—21no—
95C22×C31—41no—
96C22×C31—41no—
97C22×C31—81no—
98C22×C31—81no—
99C22×C31—81no—
100C22×C31—81no—
101C22×C31—161no—
102C22×C31#32711yescharacteristic
103C22×C31AΣL(1,𝔽16)11yescharacteristic
104C22×C31#35311yescharacteristic
105C4×C31—21no—
106C4×C31—21no—
107C4×C31—42no—
108C4×C31—82no—
109C4×C31—81no—
110C4×C31—162no—
111C22×SD16—21no—
112C2×C4⋊Q8C4×C3111yescharacteristic, complemented
113C2×#103—21no—
114C2×#99—21no—
115#390C22×C3111yescharacteristic
116#336C4×C3111yescharacteristic, complemented
117#324—21no—
118C2×C31—21no—
119C2×C31—21no—
120C2×C31—81no—
121C2×C31—81no—
122C2×C31#134311yescharacteristic
123C2×C31#140711yescharacteristic
124C2×C31#140911yescharacteristic
125C22×Q8—21no—
126C22×D4D4×C3111yescharacteristic
127C2×SD16—42no—
128C2×SD16—42no—
129C2×SD16—41no—
130C2×SD16—41no—
131C22×C8—21no—
132C4⋊Q8—42no—
133C2×C4⋊C4—41no—
134C2×C4⋊C4D4×C3111yescharacteristic
135C2×C22⋊C4—41no—
136C2×C22⋊C4—41no—
137C2×C42C2×C4×C3111yescharacteristic
138#103—42no—
139#99—22no—
140#99—41no—
141C22⋊C8—41no—
142C31#740311yescharacteristic, direct product factor, Sylow
143C24—21no—
144C2×Q8—22no—
145C2×Q8—41no—
146C2×Q8—41no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×D4—21no—
151C2×D4—41no—
152C2×D4—41no—
153C2×D4D8×C3111yescharacteristic
154C2×D4SD16×C3111yescharacteristic
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—41no—
158C22×C4—81no—
159C22×C4C22⋊C4×C3111yescharacteristic
160SD16—44no—
161SD16—44no—
162C2×C8—22no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—81no—
166C4⋊C4—41no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C22⋊C4—42no—
170C22⋊C4—82no—
171C22⋊C4—81no—
172C42—41no—
173C23—21no—
174C23—21no—
175C23—41no—
176C23—41no—
177C23—81no—
178C23—81no—
179C23C31×#9911yescharacteristic
180Q8—42no—
181Q8—42no—
182Q8—81no—
183Q8—81no—
184D4—41no—
185D4—41no—
186D4—81no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—82no—
198C2×C4—161no—
199C2×C4—161no—
200C2×C4C31×#10211yescharacteristic
201C2×C4C31×#10411yescharacteristic
202C8—42no—
203C8—161no—
204C22—21no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—81no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22—161no—
213C22C31×#32711yescharacteristic
214C22C31×AΣL(1,𝔽16)11yescharacteristic
215C22C31×#35311yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—82no—
220C4—81no—
221C4—162no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—81no—
226C2C31×#134311yescharacteristic
227C2C31×#140711yescharacteristic
228C2C31×#140911yescharacteristic
subgroupG/H
center, socleC22×C31#353
commutatorC2×C42C2×C4×C31
Frattini, cosocle#390C22×C31
prime radicalC22×D4×C31D4
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C31×#390 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C31×C4⋊Q8C4semidirect
9. C31×#336C4semidirect
58. #7403C31direct (N × H)
112. C2×C4⋊Q8C4×C31semidirect
116. #336C4×C31semidirect
142. C31#7403direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#20132
C31×#13932
C31×#13182
#740331