Finite Group Databasebeta

← C31×#19096 #21475855

Subgroups — C31×#19096 #21475855

Order 7936.

906 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 906 conjugacy classes of subgroups — too many to draw. Only its 218 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×#3567C211yesmaximal, characteristic, complemented
2C31×#3217C213yesmaximal, complemented
3C31×#1658C212yesmaximal, complemented
4C31×#1656C216yesmaximal, complemented
5C31×#1535C213yesmaximal, complemented
6C31×#564C2211yescharacteristic, complemented
7C31×#562C2213yescomplemented
8C31×#553—23no—
9C31×#552—23no—
10C31×#540—23no—
11C31×#539—23no—
12C2×C31×#127C2211yescharacteristic
13C31×#529C2213yes—
14C31×#496C2216yes—
15C31×#490C2216yes—
16C31×#460—23no—
17C31×#459—23no—
18C31×#450—23no—
19C31×#447—23no—
20C31×#432C2213yes—
21C31×#330C2216yescomplemented
22C31×#329C2216yescomplemented
23C22×D4×C31—23no—
24C2×SD16×C31—26no—
25C2×D8×C31—26no—
26C31×#127—21no—
27C31×#127—23no—
28C31×#127C2312yes—
29C31×#126—21no—
30C31×#126—23no—
31C31×#126—23no—
32C31×#125—23no—
33C31×#125—23no—
34C31×#125—23no—
35C31×#125C2313yes—
36C31×#124C2313yes—
37C31×#123—23no—
38C31×#123—23no—
39C31×#123—23no—
40C31×#123—23no—
41C31×#123—23no—
42C31×C22⋊Q8—23no—
43C31×C22⋊Q8—23no—
44C31×C22⋊Q8D413yes—
45C31×#121—23no—
46C31×#121—23no—
47C31×#121—23no—
48C31×#121—23no—
49C31×#121D413yes—
50C4×Q8×C31D413yes—
51C4×D4×C31—23no—
52C4×D4×C31—23no—
53C4×D4×C31—23no—
54C4×D4×C31D413yes—
55C31×#117—23no—
56C31×#117—23no—
57C2×C4⋊C4×C31—23no—
58C2×C42×C31C2311yescharacteristic
59C31×C4⋊C8—23no—
60C31×#102—26no—
61C31×#102—26no—
62C31×C22⋊C8—23no—
63C31×#97C2316yes—
64C24×C31—41no—
65C2×Q8×C31C2×D413yes—
66C2×D4×C31—23no—
67C2×D4×C31—23no—
68C2×D4×C31—23no—
69C2×D4×C31—26no—
70C2×D4×C31—43no—
71C2×D4×C31—86no—
72C2×D4×C31C2×D413yes—
73C22×C4×C31—23no—
74C22×C4×C31—23no—
75C22×C4×C31—23no—
76C22×C4×C31C2×D413yes—
77SD16×C31—86no—
78D8×C31—86no—
79C2×C8×C31—26no—
80C4⋊C4×C31—23no—
81C4⋊C4×C31—23no—
82C4⋊C4×C31—23no—
83C4⋊C4×C31—23no—
84C4⋊C4×C31—23no—
85C4⋊C4×C31—23no—
86C4⋊C4×C31—23no—
87C4⋊C4×C31—23no—
88C4⋊C4×C31C2×D413yes—
89C4⋊C4×C31C2×D413yes—
90C22⋊C4×C31—23no—
91C22⋊C4×C31—23no—
92C22⋊C4×C31—23no—
93C22⋊C4×C31—23no—
94C22⋊C4×C31—23no—
95C22⋊C4×C31—23no—
96C22⋊C4×C31—23no—
97C42×C31—21no—
98C42×C31—21no—
99C42×C31—23no—
100C42×C31C2×D413yes—
101C42×C31C2411yescharacteristic
102#19096C3111yesmaximal, characteristic, direct product factor, Sylow
103C23×C31—23no—
104C23×C31—42no—
105C23×C31—86no—
106C23×C31#12011yescharacteristic
107Q8×C31—43no—
108D4×C31—43no—
109D4×C31—46no—
110D4×C31—46no—
111D4×C31—86no—
112D4×C31—83no—
113D4×C31—83no—
114D4×C31—83no—
115C2×C4×C31—23no—
116C2×C4×C31—23no—
117C2×C4×C31—23no—
118C2×C4×C31—43no—
119C2×C4×C31—83no—
120C2×C4×C31—83no—
121C2×C4×C31—83no—
122C2×C4×C31#12013yes—
123C2×C4×C31C22×D413yes—
124C8×C31—46no—
125#3567C2×C3111yescharacteristic, complemented
126#3217C2×C3113yescomplemented
127#1658C2×C3112yescomplemented
128#1656C2×C3116yescomplemented
129#1535C2×C3113yescomplemented
130C22×C31—23no—
131C22×C31—43no—
132C22×C31—43no—
133C22×C31—43no—
134C22×C31—86no—
135C22×C31—164no—
136C22×C31C2×#12011yescharacteristic
137C4×C31—23no—
138C4×C31—23no—
139C4×C31—43no—
140C4×C31—43no—
141C4×C31—43no—
142#564C22×C3111yescharacteristic, complemented
143#562C22×C3113yescomplemented
144#553—23no—
145#552—23no—
146#540—23no—
147#539—23no—
148C2×#127C22×C3111yescharacteristic
149#529C22×C3113yes—
150#496C22×C3116yes—
151#490C22×C3116yes—
152#460—23no—
153#459—23no—
154#450—23no—
155#447—23no—
156#432C22×C3113yes—
157#330C22×C3116yescomplemented
158#329C22×C3116yescomplemented
159C2×C31—41no—
160C2×C31—83no—
161C2×C31—162no—
162C2×C31#302113yes—
163C22×D4—23no—
164C2×SD16—26no—
165C2×D8—26no—
166#127—21no—
167#127—23no—
168#127C23×C3112yes—
169#126—21no—
170#126—23no—
171#126—23no—
172#125—23no—
173#125—23no—
174#125—23no—
175#125C23×C3113yes—
176#124C23×C3113yes—
177#123—23no—
178#123—23no—
179#123—23no—
180#123—23no—
181#123—23no—
182C22⋊Q8—23no—
183C22⋊Q8—23no—
184C22⋊Q8D4×C3113yes—
185#121—23no—
186#121—23no—
187#121—23no—
188#121—23no—
189#121D4×C3113yes—
190C4×Q8D4×C3113yes—
191C4×D4—23no—
192C4×D4—23no—
193C4×D4—23no—
194C4×D4D4×C3113yes—
195#117—23no—
196#117—23no—
197C2×C4⋊C4—23no—
198C2×C42C23×C3111yescharacteristic
199C4⋊C8—23no—
200#102—26no—
201#102—26no—
202C22⋊C8—23no—
203#97C23×C3116yes—
204C31#1909611yescharacteristic, direct product factor, Sylow
205C24—41no—
206C2×Q8C2×D4×C3113yes—
207C2×D4—23no—
208C2×D4—23no—
209C2×D4—23no—
210C2×D4—26no—
211C2×D4—43no—
212C2×D4—86no—
213C2×D4C2×D4×C3113yes—
214C22×C4—23no—
215C22×C4—23no—
216C22×C4—23no—
217C22×C4C2×D4×C3113yes—
218SD16—86no—
219D8—86no—
220C2×C8—26no—
221C4⋊C4—23no—
222C4⋊C4—23no—
223C4⋊C4—23no—
224C4⋊C4—23no—
225C4⋊C4—23no—
226C4⋊C4—23no—
227C4⋊C4—23no—
228C4⋊C4—23no—
229C4⋊C4C2×D4×C3113yes—
230C4⋊C4C2×D4×C3113yes—
231C22⋊C4—23no—
232C22⋊C4—23no—
233C22⋊C4—23no—
234C22⋊C4—23no—
235C22⋊C4—23no—
236C22⋊C4—23no—
237C22⋊C4—23no—
238C42—21no—
239C42—21no—
240C42—23no—
241C42C2×D4×C3113yes—
242C42C24×C3111yescharacteristic
243C23—23no—
244C23—42no—
245C23—86no—
246C23C31×#12011yescharacteristic
247Q8—43no—
248D4—43no—
249D4—46no—
250D4—46no—
251D4—86no—
252D4—83no—
253D4—83no—
254D4—83no—
255C2×C4—23no—
256C2×C4—23no—
257C2×C4—23no—
258C2×C4—43no—
259C2×C4—83no—
260C2×C4—83no—
261C2×C4—83no—
262C2×C4C31×#12013yes—
263C2×C4C22×D4×C3113yes—
264C8—46no—
265C22—23no—
266C22—43no—
267C22—43no—
268C22—43no—
269C22—86no—
270C22—164no—
271C22C2×C31×#12011yescharacteristic
272C4—23no—
273C4—23no—
274C4—43no—
275C4—43no—
276C4—43no—
277C2—41no—
278C2—83no—
279C2—162no—
280C2C31×#302113yes—
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3567C2semidirect
2. C31×#3217C2semidirect
3. C31×#1658C2semidirect
4. C31×#1656C2semidirect
5. C31×#1535C2semidirect
6. C31×#564C22semidirect
7. C31×#562C22semidirect
21. C31×#330C22semidirect
22. C31×#329C22semidirect
102. #19096C31direct (N × H)
125. #3567C2×C31semidirect
126. #3217C2×C31semidirect
127. #1658C2×C31semidirect
128. #1656C2×C31semidirect
129. #1535C2×C31semidirect
142. #564C22×C31semidirect
143. #562C22×C31semidirect
157. #330C22×C31semidirect
158. #329C22×C31semidirect
204. C31#19096direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35672
C31×#32172
C31×#16582
C31×#16562
C31×#15352
#1909631