Finite Group Databasebeta

← C31×#8495 #21465254

Subgroups — C31×#8495 #21465254

Order 7936.

620 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 142 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×#3556C211yesmaximal, characteristic
2C31×#1995C211yesmaximal, characteristic
3C31×#1559C212yesmaximal
4C31×#1537C211yesmaximal, characteristic
5C31×#1506C212yesmaximal
6C31×#564—22no—
7C31×#557—22no—
8C31×#557—22no—
9C31×#557C414yescomplemented
10C31×#541—24no—
11C31×#541—22no—
12C31×#533C2212yes—
13C31×#533C2211yescharacteristic
14C31×#432C2212yes—
15C31×#423C2211yescharacteristic
16C31×#376C2211yescharacteristic
17C31×#339—22no—
18C31×#333—22no—
19C31×#332—22no—
20C31×#330—22no—
21C31×#328—24no—
22C2×M16×C31—21no—
23C31×C4⋊Q8—22no—
24C31×C4⋊Q8—24no—
25C31×C4⋊Q8C2×C412yes—
26C31×C4⋊Q8D412yes—
27C31×C4⋊Q8D412yes—
28C31×#126—28no—
29C31×#125—22no—
30C31×#125—28no—
31C31×#125—28no—
32C31×#125—24no—
33C31×#125—28no—
34C31×#125—22no—
35C31×#125D412yes—
36C31×C22⋊Q8—22no—
37C31×C22⋊Q8—22no—
38C31×C22⋊Q8D414yes—
39C4×Q8×C31—24no—
40C4×Q8×C31—24no—
41C4×Q8×C31—24no—
42C4×Q8×C31—22no—
43C4×Q8×C31—22no—
44C4×Q8×C31C2×C414yes—
45C31×#117—22no—
46C31×#117D412yes—
47C2×C42×C31—21no—
48C2×C42×C31C2311yescharacteristic
49C31×C4⋊C8—22no—
50C31×C4⋊C8—22no—
51C31×C22⋊C8—22no—
52C31×#97—22no—
53C31×#95—22no—
54C2×Q8×C31—22no—
55C2×Q8×C31—22no—
56C2×Q8×C31C22⋊C414yes—
57C22×C4×C31—41no—
58C22×C4×C31C2×D411yescharacteristic
59C22×C4×C31C2×D412yes—
60M16×C31—42no—
61C2×C8×C31—42no—
62C2×C8×C31—41no—
63C4⋊C4×C31—28no—
64C4⋊C4×C31—28no—
65C4⋊C4×C31—28no—
66C4⋊C4×C31—22no—
67C4⋊C4×C31—24no—
68C4⋊C4×C31—22no—
69C4⋊C4×C31—22no—
70C4⋊C4×C31—22no—
71C4⋊C4×C31—24no—
72C4⋊C4×C31—24no—
73C4⋊C4×C31C22⋊C414yes—
74C4⋊C4×C31C22⋊C414yes—
75C22⋊C4×C31—24no—
76C22⋊C4×C31—22no—
77C42×C31—28no—
78C42×C31—24no—
79C42×C31—22no—
80C42×C31—22no—
81C42×C31—41no—
82C42×C31C22×C411yescharacteristic
83C42×C31C2×D411yescharacteristic
84C42×C31C2×D412yes—
85#8495C3111yesmaximal, characteristic, direct product factor, Sylow
86C23×C31#12011yescharacteristic
87Q8×C31—44no—
88Q8×C31—44no—
89Q8×C31—42no—
90Q8×C31—42no—
91C2×C4×C31—21no—
92C2×C4×C31—21no—
93C2×C4×C31—24no—
94C2×C4×C31—24no—
95C2×C4×C31—24no—
96C2×C4×C31—42no—
97C2×C4×C31—42no—
98C2×C4×C31—82no—
99C2×C4×C31C2×C22⋊C412yes—
100C2×C4×C31C2×C22⋊C411yescharacteristic
101C2×C4×C31#12012yes—
102C2×C4×C31#12011yescharacteristic
103C8×C31—82no—
104C8×C31—81no—
105#3556C2×C3111yescharacteristic
106#1995C2×C3111yescharacteristic
107#1559C2×C3112yes—
108#1537C2×C3111yescharacteristic
109#1506C2×C3112yes—
110C22×C31—21no—
111C22×C31—22no—
112C22×C31#37911yescharacteristic
113C4×C31—21no—
114C4×C31—22no—
115C4×C31—22no—
116C4×C31—44no—
117C4×C31—44no—
118C4×C31—44no—
119C4×C31—82no—
120C4×C31#45411yescharacteristic
121C4×C31#45611yescharacteristic
122#564—22no—
123#557—22no—
124#557—22no—
125#557C4×C3114yescomplemented
126#541—24no—
127#541—22no—
128#533C22×C3112yes—
129#533C22×C3111yescharacteristic
130#432C22×C3112yes—
131#423C22×C3111yescharacteristic
132#376C22×C3111yescharacteristic
133#339—22no—
134#333—22no—
135#332—22no—
136#330—22no—
137#328—24no—
138C2×C31—41no—
139C2×C31#179311yescharacteristic
140C2×C31#179612yes—
141C2×M16—21no—
142C4⋊Q8—22no—
143C4⋊Q8—24no—
144C4⋊Q8C2×C4×C3112yes—
145C4⋊Q8D4×C3112yes—
146C4⋊Q8D4×C3112yes—
147#126—28no—
148#125—22no—
149#125—28no—
150#125—28no—
151#125—24no—
152#125—28no—
153#125—22no—
154#125D4×C3112yes—
155C22⋊Q8—22no—
156C22⋊Q8—22no—
157C22⋊Q8D4×C3114yes—
158C4×Q8—24no—
159C4×Q8—24no—
160C4×Q8—24no—
161C4×Q8—22no—
162C4×Q8—22no—
163C4×Q8C2×C4×C3114yes—
164#117—22no—
165#117D4×C3112yes—
166C2×C42—21no—
167C2×C42C23×C3111yescharacteristic
168C4⋊C8—22no—
169C4⋊C8—22no—
170C22⋊C8—22no—
171#97—22no—
172#95—22no—
173C31#849511yescharacteristic, direct product factor, Sylow
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8C22⋊C4×C3114yes—
177C22×C4—41no—
178C22×C4C2×D4×C3111yescharacteristic
179C22×C4C2×D4×C3112yes—
180M16—42no—
181C2×C8—42no—
182C2×C8—41no—
183C4⋊C4—28no—
184C4⋊C4—28no—
185C4⋊C4—28no—
186C4⋊C4—22no—
187C4⋊C4—24no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—24no—
192C4⋊C4—24no—
193C4⋊C4C22⋊C4×C3114yes—
194C4⋊C4C22⋊C4×C3114yes—
195C22⋊C4—24no—
196C22⋊C4—22no—
197C42—28no—
198C42—24no—
199C42—22no—
200C42—22no—
201C42—41no—
202C42C22×C4×C3111yescharacteristic
203C42C2×D4×C3111yescharacteristic
204C42C2×D4×C3112yes—
205C23C31×#12011yescharacteristic
206Q8—44no—
207Q8—44no—
208Q8—42no—
209Q8—42no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—24no—
213C2×C4—24no—
214C2×C4—24no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—82no—
218C2×C4C2×C22⋊C4×C3112yes—
219C2×C4C2×C22⋊C4×C3111yescharacteristic
220C2×C4C31×#12012yes—
221C2×C4C31×#12011yescharacteristic
222C8—82no—
223C8—81no—
224C22—22no—
225C22—21no—
226C22C31×#37911yescharacteristic
227C4—22no—
228C4—22no—
229C4—21no—
230C4—44no—
231C4—44no—
232C4—44no—
233C4—82no—
234C4C31×#45411yescharacteristic
235C4C31×#45611yescharacteristic
236C2—41no—
237C2C31×#179311yescharacteristic
238C2C31×#179612yes—
subgroupG/H
center, socleC22×C31#379
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC23×C31#120
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
9. C31×#557C4semidirect
85. #8495C31direct (N × H)
125. #557C4×C31semidirect
173. C31#8495direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35562
C31×#19952
C31×#15592
C31×#15372
C31×#15062
#849531