Finite Group Databasebeta

← C31×#13431 #21470190

Subgroups — C31×#13431 #21470190

Order 7936.

402 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 86 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×#3202C211yesmaximal, characteristic
2C31×#2135C212yesmaximal
3C31×#1915C212yesmaximal
4C31×#1858C211yesmaximal, characteristic
5C31×#1392C211yesmaximal, characteristic
6C31×#568C2211yescharacteristic
7C31×#536C2212yes—
8C31×#485—22no—
9C31×#470—21no—
10C31×#467—21no—
11C31×#451—22no—
12C31×#430—21no—
13C31×#413C2212yes—
14C31×#413C2211yescharacteristic
15C2×C31×#101—22no—
16C31×#408C2211yescharacteristic
17C31×#356—24no—
18C31×#344—22no—
19C31×#341—21no—
20C2×#41×C31C2311yescharacteristic
21C22×Q8×C31D412yes—
22C2×Q16×C31—21no—
23C2×Q16×C31—21no—
24C31×#131—42no—
25C2×M16×C31—22no—
26C2×M16×C31—21no—
27C2×M16×C31—21no—
28C2×M16×C31—22no—
29C2×M16×C31D411yescharacteristic
30C22×C8×C31D411yescharacteristic
31C31×C4⋊Q8—22no—
32C31×#124—22no—
33C31×#123—22no—
34C31×#123—22no—
35C31×C22⋊Q8—22no—
36C31×C22⋊Q8—22no—
37C31×#117D412yes—
38C31×#108—42no—
39C31×#107—21no—
40C31×#106—21no—
41C31×#103—22no—
42C31×#103—22no—
43C31×#101—22no—
44C31×#101—44no—
45C31×#101D412yes—
46C31×#100—21no—
47C31×#100—22no—
48C31×C22⋊C8—22no—
49#41×C31—41no—
50#41×C31—41no—
51C2×Q8×C31—22no—
52C2×Q8×C31—22no—
53C2×Q8×C31—42no—
54C2×Q8×C31—42no—
55C2×Q8×C31C2×D411yescharacteristic
56C2×D4×C31#4111yescharacteristic
57C2×D4×C31#4112yes—
58C22×C4×C31—22no—
59C22×C4×C31C2×D412yes—
60C22×C4×C31C2×D411yescharacteristic
61Q16×C31—81no—
62Q16×C31—81no—
63M16×C31—24no—
64M16×C31—22no—
65M16×C31—22no—
66M16×C31—41no—
67M16×C31—41no—
68M16×C31—41no—
69M16×C31—42no—
70M16×C31—42no—
71C2×C8×C31—21no—
72C2×C8×C31—21no—
73C2×C8×C31—41no—
74C2×C8×C31—41no—
75C2×C8×C31—42no—
76C2×C8×C31—41no—
77C2×C8×C31—42no—
78C4⋊C4×C31—22no—
79C4⋊C4×C31—42no—
80C4⋊C4×C31—42no—
81C22⋊C4×C31—22no—
82C22⋊C4×C31—42no—
83C22⋊C4×C31—42no—
84C42×C31—22no—
85#13431C3111yesmaximal, characteristic, direct product factor, Sylow
86C23×C31#12312yes—
87C23×C31#12411yescharacteristic
88Q8×C31—41no—
89Q8×C31—42no—
90Q8×C31—42no—
91Q8×C31—82no—
92D4×C31—41no—
93D4×C31—42no—
94C2×C4×C31—21no—
95C2×C4×C31—22no—
96C2×C4×C31—21no—
97C2×C4×C31—22no—
98C2×C4×C31—44no—
99C2×C4×C31—42no—
100C2×C4×C31—42no—
101C2×C4×C31#12011yescharacteristic
102C2×C4×C31#12112yes—
103C2×C4×C31#12111yescharacteristic
104C8×C31—42no—
105C8×C31—41no—
106C8×C31—42no—
107C8×C31—41no—
108C8×C31—82no—
109#3202C2×C3111yescharacteristic
110#2135C2×C3112yes—
111#1915C2×C3112yes—
112#1858C2×C3111yescharacteristic
113#1392C2×C3111yescharacteristic
114C22×C31—22no—
115C22×C31—21no—
116C22×C31—42no—
117C22×C31—41no—
118C22×C31#39411yescharacteristic
119C4×C31—21no—
120C4×C31—22no—
121C4×C31—82no—
122C4×C31—82no—
123C4×C31B(4,𝔽2)11yescharacteristic
124C4×C31#45811yescharacteristic
125#568C22×C3111yescharacteristic
126#536C22×C3112yes—
127#485—22no—
128#470—21no—
129#467—21no—
130#451—22no—
131#430—21no—
132#413C22×C3112yes—
133#413C22×C3111yescharacteristic
134C2×#101—22no—
135#408C22×C3111yescharacteristic
136#356—24no—
137#344—22no—
138#341—21no—
139C2×C31—21no—
140C2×C31—42no—
141C2×C31—41no—
142C2×C31#204411yescharacteristic
143C2×#41C23×C3111yescharacteristic
144C22×Q8D4×C3112yes—
145C2×Q16—21no—
146C2×Q16—21no—
147#131—42no—
148C2×M16—21no—
149C2×M16—22no—
150C2×M16—21no—
151C2×M16—22no—
152C2×M16D4×C3111yescharacteristic
153C22×C8D4×C3111yescharacteristic
154C4⋊Q8—22no—
155#124—22no—
156#123—22no—
157#123—22no—
158C22⋊Q8—22no—
159C22⋊Q8—22no—
160#117D4×C3112yes—
161#108—42no—
162#107—21no—
163#106—21no—
164#103—22no—
165#103—22no—
166#101—22no—
167#101—44no—
168#101D4×C3112yes—
169#100—21no—
170#100—22no—
171C22⋊C8—22no—
172C31#1343111yescharacteristic, direct product factor, Sylow
173#41—41no—
174#41—41no—
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—42no—
178C2×Q8—42no—
179C2×Q8C2×D4×C3111yescharacteristic
180C2×D4#41×C3111yescharacteristic
181C2×D4#41×C3112yes—
182C22×C4—22no—
183C22×C4C2×D4×C3112yes—
184C22×C4C2×D4×C3111yescharacteristic
185Q16—81no—
186Q16—81no—
187M16—24no—
188M16—22no—
189M16—22no—
190M16—41no—
191M16—41no—
192M16—41no—
193M16—42no—
194M16—42no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—42no—
200C2×C8—41no—
201C2×C8—42no—
202C4⋊C4—22no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C22⋊C4—22no—
206C22⋊C4—42no—
207C22⋊C4—42no—
208C42—22no—
209C23C31×#12312yes—
210C23C31×#12411yescharacteristic
211Q8—41no—
212Q8—42no—
213Q8—42no—
214Q8—82no—
215D4—41no—
216D4—42no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—44no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4C31×#12011yescharacteristic
225C2×C4C31×#12112yes—
226C2×C4C31×#12111yescharacteristic
227C8—42no—
228C8—41no—
229C8—42no—
230C8—41no—
231C8—82no—
232C22—22no—
233C22—21no—
234C22—42no—
235C22—41no—
236C22C31×#39411yescharacteristic
237C4—21no—
238C4—22no—
239C4—82no—
240C4—82no—
241C4C31×B(4,𝔽2)11yescharacteristic
242C4C31×#45811yescharacteristic
243C2—21no—
244C2—42no—
245C2—41no—
246C2C31×#204411yescharacteristic
subgroupG/H
center, socleC2×C31#2044
commutator, Frattini, cosocleC2×#41C23×C31
prime radicalC2×#41×C31C23
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C2×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
85. #13431C31direct (N × H)
172. C31#13431direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32022
C31×#21352
C31×#19152
C31×#18582
C31×#13922
#1343131