Finite Group Databasebeta

← C31×#8317 #21465076

Subgroups — C31×#8317 #21465076

Order 7936.

864 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 162 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×#3459C211yesmaximal, characteristic
2C31×#1869C213yesmaximal, complemented
3C31×#1459C213yesmaximal, complemented
4C23×C8×C31C2211yescharacteristic
5C31×#543C411yescharacteristic
6C31×#539—23no—
7C31×#538—23no—
8C31×#534C413yes—
9C31×#529—23no—
10C31×#525—23no—
11C2×C4×D4×C31C2213yes—
12C2×C31×C22⋊C8—23no—
13C2×C31×C22⋊C8C2213yes—
14C31×#336—23no—
15C31×#324—23no—
16C31×#323—23no—
17C2×#41×C31—21no—
18C22×D4×C31C2×C413yes—
19C23×C4×C31D413yes—
20C23×C4×C31C2311yescharacteristic
21C22×C8×C31—23no—
22C22×C8×C31—23no—
23C22×C8×C31—42no—
24C31×#126—26no—
25C31×#125—23no—
26C31×#124—23no—
27C31×#123—26no—
28C31×#123—26no—
29C31×C22⋊Q8—23no—
30C31×C22⋊Q8—23no—
31C31×C22⋊Q8—23no—
32C31×#121—23no—
33C31×#121—23no—
34C31×#121—23no—
35C31×#120—26no—
36C4×Q8×C31—21no—
37C4×D4×C31—23no—
38C4×D4×C31—26no—
39C4×D4×C31—26no—
40C31×#117—23no—
41C2×C4⋊C4×C31D413yes—
42C2×C22⋊C4×C31C2×C413yes—
43C2×C22⋊C4×C31D413yes—
44C2×C42×C31D413yes—
45C31×C22⋊C8—26no—
46C31×C22⋊C8—46no—
47C24×C31C22⋊C413yes—
48C24×C31C22×C411yescharacteristic
49#41×C31—81no—
50#41×C31—81no—
51C2×Q8×C31—21no—
52C2×Q8×C31—21no—
53C2×D4×C31—26no—
54C2×D4×C31—23no—
55C2×D4×C31—23no—
56C2×D4×C31—26no—
57C2×D4×C31—23no—
58C2×D4×C31—23no—
59C22×C4×C31—23no—
60C22×C4×C31—23no—
61C22×C4×C31—41no—
62C22×C4×C31—41no—
63C22×C4×C31—43no—
64C22×C4×C31—43no—
65C22×C4×C31C22⋊C413yes—
66C22×C4×C31C22⋊C413yes—
67C22×C4×C31C22⋊C413yes—
68C22×C4×C31C2×D413yes—
69C22×C4×C31C2×D413yes—
70C2×C8×C31—26no—
71C2×C8×C31—43no—
72C2×C8×C31—41no—
73C2×C8×C31—43no—
74C2×C8×C31—43no—
75C2×C8×C31—43no—
76C4⋊C4×C31—23no—
77C4⋊C4×C31—23no—
78C4⋊C4×C31—23no—
79C4⋊C4×C31—23no—
80C4⋊C4×C31—26no—
81C22⋊C4×C31—26no—
82C22⋊C4×C31—26no—
83C22⋊C4×C31—26no—
84C22⋊C4×C31—26no—
85C42×C31—23no—
86C42×C31—23no—
87#8317C3111yesmaximal, characteristic, direct product factor, Sylow
88C23×C31—23no—
89C23×C31—23no—
90C23×C31—23no—
91C23×C31—41no—
92C23×C31—41no—
93C23×C31—43no—
94C23×C31—43no—
95C23×C31C2×C22⋊C413yes—
96C23×C31#13111yescharacteristic
97C23×C31#13113yes—
98Q8×C31—81no—
99Q8×C31—81no—
100D4×C31—46no—
101D4×C31—46no—
102D4×C31—83no—
103D4×C31—83no—
104C2×C4×C31—23no—
105C2×C4×C31—23no—
106C2×C4×C31—23no—
107C2×C4×C31—23no—
108C2×C4×C31—23no—
109C2×C4×C31—23no—
110C2×C4×C31—23no—
111C2×C4×C31—43no—
112C2×C4×C31—43no—
113C2×C4×C31—43no—
114C2×C4×C31—43no—
115C2×C4×C31—43no—
116C2×C4×C31—83no—
117C2×C4×C31#12013yes—
118C2×C4×C31#12011yescharacteristic
119C8×C31—42no—
120C8×C31—83no—
121#3459C2×C3111yescharacteristic
122#1869C2×C3113yescomplemented
123#1459C2×C3113yescomplemented
124C22×C31—23no—
125C22×C31—23no—
126C22×C31—41no—
127C22×C31—43no—
128C22×C31—46no—
129C22×C31—43no—
130C22×C31—43no—
131C22×C31—43no—
132C22×C31—83no—
133C22×C31#37911yescharacteristic
134C22×C31#40813yes—
135C22×C31#40813yes—
136C4×C31—23no—
137C4×C31—43no—
138C4×C31—43no—
139C4×C31—43no—
140C4×C31B(4,𝔽2)11yescharacteristic
141C4×C31#45811yescharacteristic
142C23×C8C22×C3111yescharacteristic
143#543C4×C3111yescharacteristic
144#539—23no—
145#538—23no—
146#534C4×C3113yes—
147#529—23no—
148#525—23no—
149C2×C4×D4C22×C3113yes—
150C2×C22⋊C8—23no—
151C2×C22⋊C8C22×C3113yes—
152#336—23no—
153#324—23no—
154#323—23no—
155C2×C31—23no—
156C2×C31—23no—
157C2×C31—83no—
158C2×C31#178011yescharacteristic
159C2×C31#179011yescharacteristic
160C2×C31#179111yescharacteristic
161C2×#41—21no—
162C22×D4C2×C4×C3113yes—
163C23×C4D4×C3113yes—
164C23×C4C23×C3111yescharacteristic
165C22×C8—23no—
166C22×C8—23no—
167C22×C8—42no—
168#126—26no—
169#125—23no—
170#124—23no—
171#123—26no—
172#123—26no—
173C22⋊Q8—23no—
174C22⋊Q8—23no—
175C22⋊Q8—23no—
176#121—23no—
177#121—23no—
178#121—23no—
179#120—26no—
180C4×Q8—21no—
181C4×D4—23no—
182C4×D4—26no—
183C4×D4—26no—
184#117—23no—
185C2×C4⋊C4D4×C3113yes—
186C2×C22⋊C4C2×C4×C3113yes—
187C2×C22⋊C4D4×C3113yes—
188C2×C42D4×C3113yes—
189C22⋊C8—26no—
190C22⋊C8—46no—
191C31#831711yescharacteristic, direct product factor, Sylow
192C24C22⋊C4×C3113yes—
193C24C22×C4×C3111yescharacteristic
194#41—81no—
195#41—81no—
196C2×Q8—21no—
197C2×Q8—21no—
198C2×D4—26no—
199C2×D4—23no—
200C2×D4—23no—
201C2×D4—26no—
202C2×D4—23no—
203C2×D4—23no—
204C22×C4—23no—
205C22×C4—23no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—43no—
209C22×C4—43no—
210C22×C4C22⋊C4×C3113yes—
211C22×C4C22⋊C4×C3113yes—
212C22×C4C22⋊C4×C3113yes—
213C22×C4C2×D4×C3113yes—
214C22×C4C2×D4×C3113yes—
215C2×C8—26no—
216C2×C8—43no—
217C2×C8—41no—
218C2×C8—43no—
219C2×C8—43no—
220C2×C8—43no—
221C4⋊C4—23no—
222C4⋊C4—23no—
223C4⋊C4—23no—
224C4⋊C4—23no—
225C4⋊C4—26no—
226C22⋊C4—26no—
227C22⋊C4—26no—
228C22⋊C4—26no—
229C22⋊C4—26no—
230C42—23no—
231C42—23no—
232C23—23no—
233C23—23no—
234C23—23no—
235C23—41no—
236C23—41no—
237C23—43no—
238C23—43no—
239C23C2×C22⋊C4×C3113yes—
240C23C31×#13111yescharacteristic
241C23C31×#13113yes—
242Q8—81no—
243Q8—81no—
244D4—46no—
245D4—46no—
246D4—83no—
247D4—83no—
248C2×C4—23no—
249C2×C4—23no—
250C2×C4—23no—
251C2×C4—23no—
252C2×C4—23no—
253C2×C4—23no—
254C2×C4—23no—
255C2×C4—43no—
256C2×C4—43no—
257C2×C4—43no—
258C2×C4—43no—
259C2×C4—43no—
260C2×C4—83no—
261C2×C4C31×#12013yes—
262C2×C4C31×#12011yescharacteristic
263C8—42no—
264C8—83no—
265C22—23no—
266C22—23no—
267C22—41no—
268C22—43no—
269C22—46no—
270C22—43no—
271C22—43no—
272C22—43no—
273C22—83no—
274C22C31×#37911yescharacteristic
275C22C31×#40813yes—
276C22C31×#40813yes—
277C4—23no—
278C4—43no—
279C4—43no—
280C4—43no—
281C4C31×B(4,𝔽2)11yescharacteristic
282C4C31×#45811yescharacteristic
283C2—23no—
284C2—23no—
285C2—83no—
286C2C31×#178011yescharacteristic
287C2C31×#179011yescharacteristic
288C2C31×#179111yescharacteristic
subgroupG/H
centerC2×C4×C31#120
commutatorC24C22×C4×C31
Frattini, cosocleC23×C4C23×C31
socleC22×C31#379
prime radicalC31×#3459C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1869C2semidirect
3. C31×#1459C2semidirect
87. #8317C31direct (N × H)
122. #1869C2×C31semidirect
123. #1459C2×C31semidirect
191. C31#8317direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34592
C31×#18692
C31×#14592
#831731