Finite Group Databasebeta

← C31×#8492 #21465251

Subgroups — C31×#8492 #21465251

Order 7936.

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

normal subgroups only

This group has 692 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×#3550C211yesmaximal, characteristic
2C31×#1963C211yesmaximal, characteristic
3C31×#1559C212yesmaximal, complemented
4C31×#1536C211yesmaximal, characteristic
5C31×#1506C212yesmaximal, complemented
6C31×#563—22no—
7C31×#559C412yescomplemented
8Q82×C31C412yescomplemented
9C31×#556—22no—
10D4×Q8×C31—22no—
11C31×#542—24no—
12C31×#536—22no—
13C31×#533C2212yes—
14C31×#532C2211yescharacteristic
15C31×#432C2212yes—
16C31×#423C2211yescharacteristic
17C2×C31×#104—22no—
18C31×#376C2211yescharacteristic
19C31×#333—22no—
20C31×#332—22no—
21C31×#329—22no—
22C31×#328—24no—
23C2×#41×C31D412yes—
24C22×Q8×C31—22no—
25C2×M16×C31—21no—
26C31×C4⋊Q8—24no—
27C31×C4⋊Q8—24no—
28C31×C4⋊Q8C2×C411yescharacteristic
29C31×C4⋊Q8D412yes—
30C31×C4⋊Q8D412yes—
31C31×#127C2×C411yescharacteristic
32C31×#126—28no—
33C31×#125—22no—
34C31×#124—24no—
35C31×#124—24no—
36C31×#124D412yes—
37C31×#123—24no—
38C31×#123—24no—
39C31×C22⋊Q8—24no—
40C31×C22⋊Q8—28no—
41C31×C22⋊Q8—22no—
42C31×C22⋊Q8D414yes—
43C31×#121—22no—
44C4×Q8×C31—24no—
45C4×Q8×C31—22no—
46C4×Q8×C31C2×C414yes—
47C4×D4×C31—24no—
48C4×D4×C31—22no—
49C31×#117—22no—
50C31×#117—22no—
51C2×C42×C31—21no—
52C2×C42×C31C2311yescharacteristic
53C31×C4⋊C8—22no—
54C31×C4⋊C8—22no—
55C31×#104—44no—
56C31×C22⋊C8—22no—
57C31×#97—22no—
58C31×#95—22no—
59#41×C31—42no—
60#41×C31—42no—
61C2×Q8×C31—24no—
62C2×Q8×C31—22no—
63C2×Q8×C31—82no—
64C2×Q8×C31—82no—
65C2×Q8×C31C22⋊C414yes—
66C2×Q8×C31C22⋊C412yes—
67C2×D4×C31—22no—
68C2×D4×C31—22no—
69C2×D4×C31C22⋊C412yes—
70C22×C4×C31—24no—
71C22×C4×C31—22no—
72C22×C4×C31—41no—
73C22×C4×C31C2×D411yescharacteristic
74C22×C4×C31C2×D412yes—
75M16×C31—42no—
76C2×C8×C31—42no—
77C2×C8×C31—41no—
78C4⋊C4×C31—28no—
79C4⋊C4×C31—22no—
80C4⋊C4×C31—24no—
81C4⋊C4×C31—22no—
82C4⋊C4×C31—22no—
83C4⋊C4×C31—22no—
84C4⋊C4×C31—24no—
85C4⋊C4×C31C22⋊C414yes—
86C22⋊C4×C31—24no—
87C22⋊C4×C31—28no—
88C22⋊C4×C31—24no—
89C22⋊C4×C31—24no—
90C42×C31—24no—
91C42×C31—24no—
92C42×C31—22no—
93C42×C31—41no—
94C42×C31C22×C411yescharacteristic
95C42×C31C2×D411yescharacteristic
96C42×C31C2×D412yes—
97#8492C3111yesmaximal, characteristic, direct product factor, Sylow
98C23×C31—22no—
99C23×C31#12011yescharacteristic
100Q8×C31—44no—
101Q8×C31—42no—
102Q8×C31—42no—
103Q8×C31—42no—
104Q8×C31—84no—
105D4×C31—42no—
106D4×C31—44no—
107D4×C31—82no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—24no—
111C2×C4×C31—22no—
112C2×C4×C31—24no—
113C2×C4×C31—42no—
114C2×C4×C31—42no—
115C2×C4×C31—42no—
116C2×C4×C31—42no—
117C2×C4×C31—84no—
118C2×C4×C31—82no—
119C2×C4×C31C2×C22⋊C412yes—
120C2×C4×C31C2×C22⋊C411yescharacteristic
121C2×C4×C31#12012yes—
122C2×C4×C31#12011yescharacteristic
123C8×C31—82no—
124C8×C31—81no—
125#3550C2×C3111yescharacteristic
126#1963C2×C3111yescharacteristic
127#1559C2×C3112yescomplemented
128#1536C2×C3111yescharacteristic
129#1506C2×C3112yescomplemented
130C22×C31—21no—
131C22×C31—22no—
132C22×C31—42no—
133C22×C31—44no—
134C22×C31#37911yescharacteristic
135C4×C31—21no—
136C4×C31—22no—
137C4×C31—22no—
138C4×C31—42no—
139C4×C31—44no—
140C4×C31—44no—
141C4×C31—82no—
142C4×C31#45311yescharacteristic
143C4×C31#45511yescharacteristic
144#563—22no—
145#559C4×C3112yescomplemented
146Q82C4×C3112yescomplemented
147#556—22no—
148D4×Q8—22no—
149#542—24no—
150#536—22no—
151#533C22×C3112yes—
152#532C22×C3111yescharacteristic
153#432C22×C3112yes—
154#423C22×C3111yescharacteristic
155C2×#104—22no—
156#376C22×C3111yescharacteristic
157#333—22no—
158#332—22no—
159#329—22no—
160#328—24no—
161C2×C31—41no—
162C2×C31—82no—
163C2×C31#179211yescharacteristic
164C2×C31#179612yes—
165C2×#41D4×C3112yes—
166C22×Q8—22no—
167C2×M16—21no—
168C4⋊Q8—24no—
169C4⋊Q8—24no—
170C4⋊Q8C2×C4×C3111yescharacteristic
171C4⋊Q8D4×C3112yes—
172C4⋊Q8D4×C3112yes—
173#127C2×C4×C3111yescharacteristic
174#126—28no—
175#125—22no—
176#124—24no—
177#124—24no—
178#124D4×C3112yes—
179#123—24no—
180#123—24no—
181C22⋊Q8—24no—
182C22⋊Q8—28no—
183C22⋊Q8—22no—
184C22⋊Q8D4×C3114yes—
185#121—22no—
186C4×Q8—24no—
187C4×Q8—22no—
188C4×Q8C2×C4×C3114yes—
189C4×D4—24no—
190C4×D4—22no—
191#117—22no—
192#117—22no—
193C2×C42—21no—
194C2×C42C23×C3111yescharacteristic
195C4⋊C8—22no—
196C4⋊C8—22no—
197#104—44no—
198C22⋊C8—22no—
199#97—22no—
200#95—22no—
201C31#849211yescharacteristic, direct product factor, Sylow
202#41—42no—
203#41—42no—
204C2×Q8—24no—
205C2×Q8—22no—
206C2×Q8—82no—
207C2×Q8—82no—
208C2×Q8C22⋊C4×C3114yes—
209C2×Q8C22⋊C4×C3112yes—
210C2×D4—22no—
211C2×D4—22no—
212C2×D4C22⋊C4×C3112yes—
213C22×C4—24no—
214C22×C4—22no—
215C22×C4—41no—
216C22×C4C2×D4×C3111yescharacteristic
217C22×C4C2×D4×C3112yes—
218M16—42no—
219C2×C8—42no—
220C2×C8—41no—
221C4⋊C4—28no—
222C4⋊C4—22no—
223C4⋊C4—24no—
224C4⋊C4—22no—
225C4⋊C4—22no—
226C4⋊C4—22no—
227C4⋊C4—24no—
228C4⋊C4C22⋊C4×C3114yes—
229C22⋊C4—24no—
230C22⋊C4—28no—
231C22⋊C4—24no—
232C22⋊C4—24no—
233C42—24no—
234C42—24no—
235C42—22no—
236C42—41no—
237C42C22×C4×C3111yescharacteristic
238C42C2×D4×C3111yescharacteristic
239C42C2×D4×C3112yes—
240C23—22no—
241C23C31×#12011yescharacteristic
242Q8—44no—
243Q8—42no—
244Q8—42no—
245Q8—42no—
246Q8—84no—
247D4—42no—
248D4—44no—
249D4—82no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—24no—
253C2×C4—22no—
254C2×C4—24no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—84no—
260C2×C4—82no—
261C2×C4C2×C22⋊C4×C3112yes—
262C2×C4C2×C22⋊C4×C3111yescharacteristic
263C2×C4C31×#12012yes—
264C2×C4C31×#12011yescharacteristic
265C8—82no—
266C8—81no—
267C22—22no—
268C22—21no—
269C22—44no—
270C22—42no—
271C22C31×#37911yescharacteristic
272C4—22no—
273C4—22no—
274C4—21no—
275C4—44no—
276C4—42no—
277C4—44no—
278C4—82no—
279C4C31×#45311yescharacteristic
280C4C31×#45511yescharacteristic
281C2—41no—
282C2—82no—
283C2C31×#179211yescharacteristic
284C2C31×#179612yes—
subgroupG/H
center, socleC22×C31#379
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#532C22
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
3. C31×#1559C2semidirect
5. C31×#1506C2semidirect
7. C31×#559C4semidirect
8. Q82×C31C4semidirect
97. #8492C31direct (N × H)
127. #1559C2×C31semidirect
129. #1506C2×C31semidirect
145. #559C4×C31semidirect
146. Q82C4×C31semidirect
201. C31#8492direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35502
C31×#19632
C31×#15592
C31×#15362
C31×#15062
#849231