Finite Group Databasebeta

← C31×#7285 #21464044

Subgroups — C31×#7285 #21464044

Order 7936.

324 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 82 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×#1870C211yesmaximal, characteristic
2C31×#1460C211yesmaximal, characteristic
3C31×#1459C211yesmaximal, characteristic
4C22×M16×C31C411yescharacteristic
5C2×C4×D4×C31C2211yescharacteristic
6C31×#431—21no—
7C2×C31×C22⋊C8—21no—
8C2×C31×C22⋊C8—21no—
9C2×C31×C22⋊C8C411yescharacteristic
10C31×#336—21no—
11C31×#324C412yes—
12C31×#323—21no—
13C31×#323—21no—
14C31×#323C412yes—
15C22×D4×C31Q811yescharacteristic
16C23×C4×C31C2×C411yescharacteristic
17C23×C4×C31D411yescharacteristic
18C2×M16×C31—42no—
19C2×M16×C31—41no—
20C22×C8×C31—21no—
21C22×C8×C31—21no—
22C22×C8×C31—41no—
23C4×D4×C31—41no—
24C4×D4×C31—41no—
25C2×C4⋊C4×C31C2×C411yescharacteristic
26C2×C22⋊C4×C31C2×C411yescharacteristic
27C2×C22⋊C4×C31D411yescharacteristic
28C2×C42×C31D411yescharacteristic
29C31×C4⋊C8—41no—
30C31×C22⋊C8—22no—
31C31×C22⋊C8—22no—
32C31×C22⋊C8—42no—
33C31×C22⋊C8—41no—
34C31×C22⋊C8—41no—
35C4×C8×C31—41no—
36C24×C31C4⋊C411yescharacteristic
37C24×C31C4⋊C411yescharacteristic
38C2×D4×C31—22no—
39C2×D4×C31—22no—
40C2×D4×C31—41no—
41C22×C4×C31—21no—
42C22×C4×C31—21no—
43C22×C4×C31—21no—
44C22×C4×C31—21no—
45C22×C4×C31—41no—
46C22×C4×C31—41no—
47C22×C4×C31—41no—
48C22×C4×C31—41no—
49C22×C4×C31C4211yescharacteristic
50C22×C4×C31C22⋊C411yescharacteristic
51C22×C4×C31C22⋊C411yescharacteristic
52C22×C4×C31C22⋊C411yescharacteristic
53C22×C4×C31C4⋊C411yescharacteristic
54M16×C31—42no—
55M16×C31—42no—
56C2×C8×C31—22no—
57C2×C8×C31—41no—
58C2×C8×C31—41no—
59C2×C8×C31—42no—
60C2×C8×C31—42no—
61C2×C8×C31—41no—
62C2×C8×C31—41no—
63C2×C8×C31—41no—
64C2×C8×C31—81no—
65C2×C8×C31—81no—
66C4⋊C4×C31—41no—
67C22⋊C4×C31—41no—
68C22⋊C4×C31—41no—
69C42×C31—21no—
70C42×C31—21no—
71#7285C3111yesmaximal, characteristic, direct product factor, Sylow
72C23×C31—21no—
73C23×C31—21no—
74C23×C31—21no—
75C23×C31—21no—
76C23×C31—21no—
77C23×C31—41no—
78C23×C31—41no—
79C23×C31—41no—
80C23×C31—41no—
81C23×C31#9511yescharacteristic
82C23×C31#10812yes—
83D4×C31—44no—
84C2×C4×C31—21no—
85C2×C4×C31—21no—
86C2×C4×C31—21no—
87C2×C4×C31—21no—
88C2×C4×C31—21no—
89C2×C4×C31—21no—
90C2×C4×C31—21no—
91C2×C4×C31—42no—
92C2×C4×C31—41no—
93C2×C4×C31—41no—
94C2×C4×C31—41no—
95C2×C4×C31—41no—
96C2×C4×C31—41no—
97C2×C4×C31—41no—
98C2×C4×C31—41no—
99C2×C4×C31—81no—
100C2×C4×C31#9911yescharacteristic
101C2×C4×C31#9911yescharacteristic
102C2×C4×C31#10812yes—
103C8×C31—42no—
104C8×C31—81no—
105C8×C31—82no—
106C8×C31—82no—
107#1870C2×C3111yescharacteristic
108#1460C2×C3111yescharacteristic
109#1459C2×C3111yescharacteristic
110C22×C31—21no—
111C22×C31—21no—
112C22×C31—22no—
113C22×C31—42no—
114C22×C31—41no—
115C22×C31—41no—
116C22×C31—41no—
117C22×C31—41no—
118C22×C31—41no—
119C22×C31—81no—
120C22×C31—81no—
121C22×C31—81no—
122C22×C31#34111yescharacteristic
123C22×C31#34111yescharacteristic
124C22×C31#34211yescharacteristic
125C4×C31—22no—
126C4×C31—21no—
127C4×C31—41no—
128C4×C31—41no—
129C4×C31—41no—
130C4×C31AΣL(1,𝔽16)11yescharacteristic
131C4×C31#35211yescharacteristic
132C22×M16C4×C3111yescharacteristic
133C2×C4×D4C22×C3111yescharacteristic
134#431—21no—
135C2×C22⋊C8—21no—
136C2×C22⋊C8—21no—
137C2×C22⋊C8C4×C3111yescharacteristic
138#336—21no—
139#324C4×C3112yes—
140#323—21no—
141#323—21no—
142#323C4×C3112yes—
143C2×C31—21no—
144C2×C31—21no—
145C2×C31—42no—
146C2×C31—81no—
147C2×C31#129811yescharacteristic
148C2×C31#139011yescharacteristic
149C2×C31#139511yescharacteristic
150C22×D4Q8×C3111yescharacteristic
151C23×C4C2×C4×C3111yescharacteristic
152C23×C4D4×C3111yescharacteristic
153C2×M16—42no—
154C2×M16—41no—
155C22×C8—21no—
156C22×C8—21no—
157C22×C8—41no—
158C4×D4—41no—
159C4×D4—41no—
160C2×C4⋊C4C2×C4×C3111yescharacteristic
161C2×C22⋊C4C2×C4×C3111yescharacteristic
162C2×C22⋊C4D4×C3111yescharacteristic
163C2×C42D4×C3111yescharacteristic
164C4⋊C8—41no—
165C22⋊C8—22no—
166C22⋊C8—22no—
167C22⋊C8—42no—
168C22⋊C8—41no—
169C22⋊C8—41no—
170C4×C8—41no—
171C31#728511yescharacteristic, direct product factor, Sylow
172C24C4⋊C4×C3111yescharacteristic
173C24C4⋊C4×C3111yescharacteristic
174C2×D4—22no—
175C2×D4—22no—
176C2×D4—41no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4C42×C3111yescharacteristic
186C22×C4C22⋊C4×C3111yescharacteristic
187C22×C4C22⋊C4×C3111yescharacteristic
188C22×C4C22⋊C4×C3111yescharacteristic
189C22×C4C4⋊C4×C3111yescharacteristic
190M16—42no—
191M16—42no—
192C2×C8—22no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—42no—
196C2×C8—42no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—81no—
201C2×C8—81no—
202C4⋊C4—41no—
203C22⋊C4—41no—
204C22⋊C4—41no—
205C42—21no—
206C42—21no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—21no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23C31×#9511yescharacteristic
217C23C31×#10812yes—
218D4—44no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—81no—
235C2×C4C31×#9911yescharacteristic
236C2×C4C31×#9911yescharacteristic
237C2×C4C31×#10812yes—
238C8—42no—
239C8—81no—
240C8—82no—
241C8—82no—
242C22—21no—
243C22—21no—
244C22—22no—
245C22—42no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—81no—
252C22—81no—
253C22—81no—
254C22C31×#34111yescharacteristic
255C22C31×#34111yescharacteristic
256C22C31×#34211yescharacteristic
257C4—22no—
258C4—21no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4C31×AΣL(1,𝔽16)11yescharacteristic
263C4C31×#35211yescharacteristic
264C2—21no—
265C2—21no—
266C2—42no—
267C2—81no—
268C2C31×#129811yescharacteristic
269C2C31×#139011yescharacteristic
270C2C31×#139511yescharacteristic
subgroupG/H
centerC2×C4×C31#99
commutatorC22×C4C42×C31
Frattini, cosocleC2×C4×D4C22×C31
socleC22×C31#342
prime radicalC22×D4×C31Q8
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
71. #7285C31direct (N × H)
171. C31#7285direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#18702
C31×#14602
C31×#14592
#728531