Finite Group Databasebeta

← C31×#10425 #21467184

Subgroups — C31×#10425 #21467184

Order 7936.

518 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2819C211yesmaximal, characteristic
2C31×#1959C212yesmaximal, complemented
3C31×#1836C211yesmaximal, characteristic, complemented
4C2×C31×#329C212yesmaximal, complemented
5C31×#1295C211yesmaximal, characteristic, complemented
6C2×C31×#124C2212yes—
7C2×C31×#103—22no—
8C2×C31×#102—22no—
9C2×C31×#97C2212yes—
10C2×C31×#97C2211yescharacteristic
11C31×#394—22no—
12C31×#393—22no—
13C31×#392—22no—
14C31×#384C2211yescharacteristic
15C31×#382C2211yescharacteristic
16C31×#340—22no—
17C31×#329—24no—
18C22×Q8×C31D412yes—
19C22×D4×C31—22no—
20C22×D4×C31D412yes—
21C22×C8×C31—22no—
22C22×C8×C31—21no—
23C31×#124—22no—
24C31×#124—22no—
25C31×#124—22no—
26C31×#124—22no—
27C2×C4⋊C4×C31—22no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31D412yes—
30C2×C22⋊C4×C31—22no—
31C2×C22⋊C4×C31—22no—
32C2×C22⋊C4×C31—22no—
33C2×C22⋊C4×C31—22no—
34C2×C42×C31C2311yescharacteristic
35C31×#103—44no—
36C31×#102—44no—
37C31×#97—22no—
38C31×#97—21no—
39C31×#97—22no—
40C31×#97D412yescomplemented
41C31×#95—22no—
42C31×#95—22no—
43C24×C31—22no—
44C2×Q8×C31—22no—
45C2×Q8×C31—22no—
46C2×Q8×C31—42no—
47C2×Q8×C31—42no—
48C2×D4×C31—22no—
49C2×D4×C31—22no—
50C2×D4×C31—42no—
51C2×D4×C31—42no—
52C2×D4×C31—82no—
53C2×D4×C31—82no—
54C2×D4×C31—82no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—41no—
58C22×C4×C31C2×D412yes—
59C22×C4×C31C2×D411yescharacteristic
60C2×C8×C31—24no—
61C2×C8×C31—22no—
62C2×C8×C31—41no—
63C2×C8×C31—41no—
64C2×C8×C31—42no—
65C2×C8×C31—42no—
66C4⋊C4×C31—42no—
67C4⋊C4×C31—42no—
68C4⋊C4×C31—42no—
69C4⋊C4×C31—42no—
70C22⋊C4×C31—42no—
71C22⋊C4×C31—42no—
72C22⋊C4×C31—42no—
73C22⋊C4×C31—42no—
74C22⋊C4×C31—82no—
75C22⋊C4×C31—82no—
76C42×C31C2×D411yescharacteristic
77C42×C31#4111yescharacteristic
78C42×C31#4112yes—
79#10425C3111yesmaximal, characteristic, direct product factor, Sylow
80C23×C31—42no—
81C23×C31—42no—
82C23×C31—42no—
83C23×C31—42no—
84C23×C31—42no—
85C23×C31—42no—
86C23×C31—42no—
87C23×C31#12011yescharacteristic
88Q8×C31—44no—
89Q8×C31—82no—
90D4×C31—44no—
91D4×C31—82no—
92D4×C31—88no—
93C2×C4×C31—22no—
94C2×C4×C31—21no—
95C2×C4×C31—21no—
96C2×C4×C31—22no—
97C2×C4×C31—42no—
98C2×C4×C31—42no—
99C2×C4×C31—42no—
100C2×C4×C31—42no—
101C2×C4×C31—42no—
102C2×C4×C31—42no—
103C2×C4×C31—82no—
104C2×C4×C31—81no—
105C2×C4×C31#12111yescharacteristic
106C2×C4×C31#12112yes—
107C2×C4×C31#12312yes—
108C2×C4×C31#12411yescharacteristic
109C8×C31—44no—
110C8×C31—42no—
111#2819C2×C3111yescharacteristic
112#1959C2×C3112yescomplemented
113#1836C2×C3111yescharacteristic, complemented
114C2×#329C2×C3112yescomplemented
115#1295C2×C3111yescharacteristic, complemented
116C22×C31—82no—
117C22×C31—82no—
118C22×C31—82no—
119C22×C31—82no—
120C22×C31—82no—
121C22×C31—82no—
122C22×C31—82no—
123C22×C31#39411yescharacteristic
124C22×C31#45312yes—
125C22×C31#45411yescharacteristic
126C22×C31#45511yescharacteristic
127C22×C31#45512yes—
128C4×C31—22no—
129C4×C31—22no—
130C4×C31—21no—
131C4×C31—21no—
132C4×C31—82no—
133C4×C31—82no—
134C4×C31—161no—
135C2×#124C22×C3112yes—
136C2×#103—22no—
137C2×#102—22no—
138C2×#97C22×C3112yes—
139C2×#97C22×C3111yescharacteristic
140#394—22no—
141#393—22no—
142#392—22no—
143#384C22×C3111yescharacteristic
144#382C22×C3111yescharacteristic
145#340—22no—
146#329—24no—
147C2×C31—162no—
148C2×C31#165611yescharacteristic
149C2×C31#165912yes—
150C2×C31#166211yescharacteristic
151C2×C31#203712yes—
152C2×C31#204011yescharacteristic
153C22×Q8D4×C3112yes—
154C22×D4—22no—
155C22×D4D4×C3112yes—
156C22×C8—21no—
157C22×C8—22no—
158#124—22no—
159#124—22no—
160#124—22no—
161#124—22no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4D4×C3112yes—
165C2×C22⋊C4—22no—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C42C23×C3111yescharacteristic
170#103—44no—
171#102—44no—
172#97—22no—
173#97—21no—
174#97—22no—
175#97D4×C3112yescomplemented
176#95—22no—
177#95—22no—
178C31#1042511yescharacteristic, direct product factor, Sylow
179C24—22no—
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—42no—
183C2×Q8—42no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—42no—
187C2×D4—42no—
188C2×D4—82no—
189C2×D4—82no—
190C2×D4—82no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—41no—
194C22×C4C2×D4×C3112yes—
195C22×C4C2×D4×C3111yescharacteristic
196C2×C8—24no—
197C2×C8—22no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—42no—
201C2×C8—42no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C22⋊C4—42no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C22⋊C4—42no—
210C22⋊C4—82no—
211C22⋊C4—82no—
212C42C2×D4×C3111yescharacteristic
213C42#41×C3111yescharacteristic
214C42#41×C3112yes—
215C23—42no—
216C23—42no—
217C23—42no—
218C23—42no—
219C23—42no—
220C23—42no—
221C23—42no—
222C23C31×#12011yescharacteristic
223Q8—44no—
224Q8—82no—
225D4—44no—
226D4—82no—
227D4—88no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—82no—
239C2×C4—81no—
240C2×C4C31×#12111yescharacteristic
241C2×C4C31×#12112yes—
242C2×C4C31×#12312yes—
243C2×C4C31×#12411yescharacteristic
244C8—44no—
245C8—42no—
246C22—82no—
247C22—82no—
248C22—82no—
249C22—82no—
250C22—82no—
251C22—82no—
252C22—82no—
253C22C31×#39411yescharacteristic
254C22C31×#45312yes—
255C22C31×#45411yescharacteristic
256C22C31×#45511yescharacteristic
257C22C31×#45512yes—
258C4—22no—
259C4—22no—
260C4—21no—
261C4—21no—
262C4—82no—
263C4—82no—
264C4—161no—
265C2—162no—
266C2C31×#165611yescharacteristic
267C2C31×#165912yes—
268C2C31×#166211yescharacteristic
269C2C31×#203712yes—
270C2C31×#204011yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC31×#2819C2
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×#1959C2semidirect
3. C31×#1836C2semidirect
4. C2×C31×#329C2semidirect
5. C31×#1295C2semidirect
40. C31×#97D4semidirect
79. #10425C31direct (N × H)
112. #1959C2×C31semidirect
113. #1836C2×C31semidirect
114. C2×#329C2×C31semidirect
115. #1295C2×C31semidirect
175. #97D4×C31semidirect
178. C31#10425direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28192
C31×#19592
C31×#18362
C2×C31×#3292
C31×#12952
#1042531