Finite Group Databasebeta

← C31×#10080 #21466839

Subgroups — C31×#10080 #21466839

Order 7936.

552 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 114 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×#490C212yesmaximal
2C31×#2822C211yesmaximal, characteristic, complemented
3C31×#1961C211yesmaximal, characteristic
4C2×C31×#330C212yesmaximal, complemented
5C31×#1295C211yesmaximal, characteristic, complemented
6C2×C31×#127C2211yescharacteristic
7C2×C31×#125C2212yes—
8C31×#490—24no—
9C31×#490—24no—
10C2×C31×#102—22no—
11C2×C31×#102—22no—
12C2×C31×#102—22no—
13C2×C31×#97C2211yescharacteristic
14C2×C31×#97C2212yes—
15C31×#400—22no—
16C31×#398—22no—
17C31×#398—22no—
18C31×#382C2211yescharacteristic
19C31×#330—24no—
20C22×D4×C31—22no—
21C22×D4×C31—21no—
22C22×C8×C31—21no—
23C22×C8×C31—22no—
24C31×#127—22no—
25C31×#127—21no—
26C31×#127D412yes—
27C31×#125—22no—
28C31×#125—22no—
29C31×#125—22no—
30C31×#125—22no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31—22no—
33C2×C4⋊C4×C31—22no—
34C2×C4⋊C4×C31D412yes—
35C2×C4⋊C4×C31D412yes—
36C2×C4⋊C4×C31D412yes—
37C2×C42×C31C2311yescharacteristic
38C31×#102—28no—
39C31×#102—28no—
40C31×#102—44no—
41C31×#97—22no—
42C31×#97—22no—
43C31×#97D414yes—
44C31×#95—24no—
45C31×#95—22no—
46C31×#95—22no—
47C24×C31—41no—
48C2×D4×C31—24no—
49C2×D4×C31—22no—
50C2×D4×C31—42no—
51C2×D4×C31—48no—
52C2×D4×C31—42no—
53C2×D4×C31—42no—
54C2×D4×C31—41no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—22no—
58C22×C4×C31C2×D412yes—
59C22×C4×C31C2×D411yescharacteristic
60C2×C8×C31—22no—
61C2×C8×C31—24no—
62C2×C8×C31—44no—
63C2×C8×C31—41no—
64C2×C8×C31—41no—
65C4⋊C4×C31—22no—
66C4⋊C4×C31—22no—
67C4⋊C4×C31—22no—
68C4⋊C4×C31—22no—
69C4⋊C4×C31—42no—
70C4⋊C4×C31—42no—
71C4⋊C4×C31—42no—
72C4⋊C4×C31—42no—
73C4⋊C4×C31—42no—
74C4⋊C4×C31—82no—
75C42×C31C2×D411yescharacteristic
76C42×C31C2×D412yes—
77C42×C31#4111yescharacteristic
78#10080C3111yesmaximal, characteristic, direct product factor, Sylow
79C23×C31—42no—
80C23×C31—81no—
81C23×C31—84no—
82C23×C31—81no—
83C23×C31#12011yescharacteristic
84D4×C31—48no—
85D4×C31—44no—
86D4×C31—84no—
87D4×C31—82no—
88C2×C4×C31—21no—
89C2×C4×C31—24no—
90C2×C4×C31—21no—
91C2×C4×C31—42no—
92C2×C4×C31—42no—
93C2×C4×C31—42no—
94C2×C4×C31—42no—
95C2×C4×C31—44no—
96C2×C4×C31—44no—
97C2×C4×C31—42no—
98C2×C4×C31#12012yes—
99C2×C4×C31#12112yes—
100C2×C4×C31#12111yescharacteristic
101C2×C4×C31#12711yescharacteristic
102C8×C31—44no—
103C8×C31—42no—
104C2×#490C2×C3112yes—
105#2822C2×C3111yescharacteristic, complemented
106#1961C2×C3111yescharacteristic
107C2×#330C2×C3112yescomplemented
108#1295C2×C3111yescharacteristic, complemented
109C22×C31—84no—
110C22×C31—82no—
111C22×C31—162no—
112C22×C31—162no—
113C22×C31#39211yescharacteristic
114C22×C31#45311yescharacteristic
115C22×C31#45414yes—
116C22×C31#45411yescharacteristic
117C4×C31—22no—
118C4×C31—22no—
119C4×C31—21no—
120C4×C31—21no—
121C4×C31—82no—
122C4×C31—82no—
123C4×C31—82no—
124C2×#127C22×C3111yescharacteristic
125C2×#125C22×C3112yes—
126#490—24no—
127#490—24no—
128C2×#102—22no—
129C2×#102—22no—
130C2×#102—22no—
131C2×#97C22×C3111yescharacteristic
132C2×#97C22×C3112yes—
133#400—22no—
134#398—22no—
135#398—22no—
136#382C22×C3111yescharacteristic
137#330—24no—
138C2×C31—162no—
139C2×C31#165712yes—
140C2×C31#165812yes—
141C2×C31#200312yes—
142C2×C31#200611yescharacteristic
143C22×D4—22no—
144C22×D4—21no—
145C22×C8—21no—
146C22×C8—22no—
147#127—22no—
148#127—21no—
149#127D4×C3112yes—
150#125—22no—
151#125—22no—
152#125—22no—
153#125—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4D4×C3112yes—
158C2×C4⋊C4D4×C3112yes—
159C2×C4⋊C4D4×C3112yes—
160C2×C42C23×C3111yescharacteristic
161#102—28no—
162#102—28no—
163#102—44no—
164#97—22no—
165#97—22no—
166#97D4×C3114yes—
167#95—24no—
168#95—22no—
169#95—22no—
170C31#1008011yescharacteristic, direct product factor, Sylow
171C24—41no—
172C2×D4—24no—
173C2×D4—22no—
174C2×D4—42no—
175C2×D4—48no—
176C2×D4—42no—
177C2×D4—42no—
178C2×D4—41no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4C2×D4×C3112yes—
183C22×C4C2×D4×C3111yescharacteristic
184C2×C8—22no—
185C2×C8—24no—
186C2×C8—44no—
187C2×C8—41no—
188C2×C8—41no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—82no—
199C42C2×D4×C3111yescharacteristic
200C42C2×D4×C3112yes—
201C42#41×C3111yescharacteristic
202C23—42no—
203C23—81no—
204C23—84no—
205C23—81no—
206C23C31×#12011yescharacteristic
207D4—48no—
208D4—44no—
209D4—84no—
210D4—82no—
211C2×C4—21no—
212C2×C4—24no—
213C2×C4—21no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—44no—
217C2×C4—44no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4C31×#12012yes—
222C2×C4C31×#12112yes—
223C2×C4C31×#12111yescharacteristic
224C2×C4C31×#12711yescharacteristic
225C8—44no—
226C8—42no—
227C22—84no—
228C22—82no—
229C22—162no—
230C22—162no—
231C22C31×#39211yescharacteristic
232C22C31×#45311yescharacteristic
233C22C31×#45414yes—
234C22C31×#45411yescharacteristic
235C4—22no—
236C4—22no—
237C4—21no—
238C4—21no—
239C4—82no—
240C4—82no—
241C4—82no—
242C2—162no—
243C2C31×#165712yes—
244C2C31×#165812yes—
245C2C31×#200312yes—
246C2C31×#200611yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#127C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2822C2semidirect
4. C2×C31×#330C2semidirect
5. C31×#1295C2semidirect
78. #10080C31direct (N × H)
105. #2822C2×C31semidirect
107. C2×#330C2×C31semidirect
108. #1295C2×C31semidirect
170. C31#10080direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4902
C31×#28222
C31×#19612
C2×C31×#3302
C31×#12952
#1008031