Finite Group Databasebeta

← C31×#7830 #21464589

Subgroups — C31×#7830 #21464589

Order 7936.

494 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2733C211yesmaximal, characteristic
2C31×#2095C211yesmaximal, characteristic, complemented
3C31×#2094C212yesmaximal, complemented
4C31×#1272C211yesmaximal, characteristic, complemented
5C31×#1270C212yesmaximal, complemented
6C2×C31×#124—21no—
7C2×C31×#107—21no—
8C2×C31×#106—22no—
9C2×C31×#103—21no—
10C2×C31×#102—22no—
11C31×#394—21no—
12C31×#392—22no—
13C31×#391C2211yescharacteristic
14C31×#390C2212yes—
15C31×#388—22no—
16C31×#384C2211yescharacteristic
17C31×#336C2212yes—
18C31×#336C2211yescharacteristic
19C22×Q8×C31D411yescharacteristic
20C22×D4×C31—21no—
21C22×D4×C31—21no—
22C22×D4×C31D412yes—
23C22×C8×C31—22no—
24C22×C8×C31—21no—
25C31×#124—42no—
26C31×#124—42no—
27C2×C4⋊C4×C31—22no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31D412yes—
30C2×C4⋊C4×C31D411yescharacteristic
31C2×C22⋊C4×C31—22no—
32C2×C22⋊C4×C31—22no—
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31—22no—
35C2×C42×C31—21no—
36C2×C42×C31C2311yescharacteristic
37C31×#107—42no—
38C31×#106—44no—
39C31×#103—42no—
40C31×#102—44no—
41C31×#95—21no—
42C31×#95—22no—
43C24×C31—22no—
44C2×Q8×C31—21no—
45C2×Q8×C31—41no—
46C2×Q8×C31—41no—
47C2×Q8×C31SD1612yes—
48C2×D4×C31—22no—
49C2×D4×C31—22no—
50C2×D4×C31—42no—
51C2×D4×C31—42no—
52C2×D4×C31—42no—
53C2×D4×C31—81no—
54C2×D4×C31—81no—
55C2×D4×C31—82no—
56C2×D4×C31—81no—
57C22×C4×C31—21no—
58C22×C4×C31—21no—
59C22×C4×C31—22no—
60C22×C4×C31—41no—
61C22×C4×C31C2×D411yescharacteristic
62C22×C4×C31C2×D412yes—
63C2×C8×C31—24no—
64C2×C8×C31—22no—
65C2×C8×C31—42no—
66C2×C8×C31—41no—
67C2×C8×C31—42no—
68C2×C8×C31—41no—
69C4⋊C4×C31—42no—
70C4⋊C4×C31—41no—
71C4⋊C4×C31—42no—
72C4⋊C4×C31—41no—
73C4⋊C4×C31—42no—
74C4⋊C4×C31—41no—
75C22⋊C4×C31—44no—
76C22⋊C4×C31—42no—
77C22⋊C4×C31—42no—
78C22⋊C4×C31—42no—
79C22⋊C4×C31—42no—
80C22⋊C4×C31—82no—
81C42×C31—41no—
82C42×C31—42no—
83#7830C3111yesmaximal, characteristic, direct product factor, Sylow
84C23×C31—42no—
85C23×C31—42no—
86C23×C31—42no—
87C23×C31—42no—
88C23×C31—42no—
89C23×C31—42no—
90C23×C31—42no—
91C23×C31#12011yescharacteristic
92Q8×C31—42no—
93Q8×C31—81no—
94D4×C31—44no—
95D4×C31—82no—
96D4×C31—84no—
97D4×C31—84no—
98C2×C4×C31—22no—
99C2×C4×C31—21no—
100C2×C4×C31—22no—
101C2×C4×C31—21no—
102C2×C4×C31—22no—
103C2×C4×C31—41no—
104C2×C4×C31—41no—
105C2×C4×C31—42no—
106C2×C4×C31—42no—
107C2×C4×C31—42no—
108C2×C4×C31—42no—
109C2×C4×C31—41no—
110C2×C4×C31—81no—
111C2×C4×C31—82no—
112C2×C4×C31C2×SD1611yescharacteristic
113C2×C4×C31#13512yes—
114C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C31#13712yes—
116C8×C31—42no—
117C8×C31—44no—
118#2733C2×C3111yescharacteristic
119#2095C2×C3111yescharacteristic, complemented
120#2094C2×C3112yescomplemented
121#1272C2×C3111yescharacteristic, complemented
122#1270C2×C3112yescomplemented
123C22×C31—82no—
124C22×C31—82no—
125C22×C31—82no—
126C22×C31—82no—
127C22×C31—82no—
128C22×C31—82no—
129C22×C31—82no—
130C22×C31#45011yescharacteristic
131C22×C31#45212yes—
132C22×C31#45311yescharacteristic
133C22×C31#45312yes—
134C22×C31#45811yescharacteristic
135C4×C31—21no—
136C4×C31—21no—
137C4×C31—22no—
138C4×C31—22no—
139C4×C31—42no—
140C4×C31—82no—
141C4×C31—81no—
142C4×C31—161no—
143C2×#124—21no—
144C2×#107—21no—
145C2×#106—22no—
146C2×#103—21no—
147C2×#102—22no—
148#394—21no—
149#392—22no—
150#391C22×C3111yescharacteristic
151#390C22×C3112yes—
152#388—22no—
153#384C22×C3111yescharacteristic
154#336C22×C3112yes—
155#336C22×C3111yescharacteristic
156C2×C31—162no—
157C2×C31#161311yescharacteristic
158C2×C31#161812yes—
159C2×C31#163112yes—
160C2×C31#163411yescharacteristic
161C2×C31#165511yescharacteristic
162C22×Q8D4×C3111yescharacteristic
163C22×D4—21no—
164C22×D4—21no—
165C22×D4D4×C3112yes—
166C22×C8—22no—
167C22×C8—21no—
168#124—42no—
169#124—42no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4D4×C3112yes—
173C2×C4⋊C4D4×C3111yescharacteristic
174C2×C22⋊C4—22no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C42—21no—
179C2×C42C23×C3111yescharacteristic
180#107—42no—
181#106—44no—
182#103—42no—
183#102—44no—
184#95—21no—
185#95—22no—
186C31#783011yescharacteristic, direct product factor, Sylow
187C24—22no—
188C2×Q8—21no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8SD16×C3112yes—
192C2×D4—22no—
193C2×D4—22no—
194C2×D4—42no—
195C2×D4—42no—
196C2×D4—42no—
197C2×D4—81no—
198C2×D4—81no—
199C2×D4—82no—
200C2×D4—81no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—41no—
205C22×C4C2×D4×C3111yescharacteristic
206C22×C4C2×D4×C3112yes—
207C2×C8—24no—
208C2×C8—22no—
209C2×C8—42no—
210C2×C8—41no—
211C2×C8—42no—
212C2×C8—41no—
213C4⋊C4—42no—
214C4⋊C4—41no—
215C4⋊C4—42no—
216C4⋊C4—41no—
217C4⋊C4—42no—
218C4⋊C4—41no—
219C22⋊C4—44no—
220C22⋊C4—42no—
221C22⋊C4—42no—
222C22⋊C4—42no—
223C22⋊C4—42no—
224C22⋊C4—82no—
225C42—41no—
226C42—42no—
227C23—42no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—42no—
233C23—42no—
234C23C31×#12011yescharacteristic
235Q8—42no—
236Q8—81no—
237D4—44no—
238D4—82no—
239D4—84no—
240D4—84no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—81no—
254C2×C4—82no—
255C2×C4C2×SD16×C3111yescharacteristic
256C2×C4C31×#13512yes—
257C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
258C2×C4C31×#13712yes—
259C8—42no—
260C8—44no—
261C22—82no—
262C22—82no—
263C22—82no—
264C22—82no—
265C22—82no—
266C22—82no—
267C22—82no—
268C22C31×#45011yescharacteristic
269C22C31×#45212yes—
270C22C31×#45311yescharacteristic
271C22C31×#45312yes—
272C22C31×#45811yescharacteristic
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—42no—
278C4—82no—
279C4—81no—
280C4—161no—
281C2—162no—
282C2C31×#161311yescharacteristic
283C2C31×#161812yes—
284C2C31×#163112yes—
285C2C31×#163411yescharacteristic
286C2C31×#165511yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC31×#2733C2
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2095C2semidirect
3. C31×#2094C2semidirect
4. C31×#1272C2semidirect
5. C31×#1270C2semidirect
83. #7830C31direct (N × H)
119. #2095C2×C31semidirect
120. #2094C2×C31semidirect
121. #1272C2×C31semidirect
122. #1270C2×C31semidirect
186. C31#7830direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#27332
C31×#20952
C31×#20942
C31×#12722
C31×#12702
#783031