Finite Group Databasebeta

← C31×#7645 #21464404

Subgroups — C31×#7645 #21464404

Order 7936.

630 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2297C211yesmaximal, characteristic
2C31×#1817C212yesmaximal, complemented
3C31×#1272C212yesmaximal, complemented
4C31×#1270C212yesmaximal, complemented
5C22×#41×C31C411yescharacteristic
6C2×C31×#117C411yescharacteristic
7C22×C42×C31C2211yescharacteristic
8C2×C31×C22⋊C8—22no—
9C31×#391C411yescharacteristic
10C31×#391C2211yescharacteristic
11C31×#390C411yescharacteristic
12C31×#390C2211yescharacteristic
13C31×#386—22no—
14C4×C22⋊C4×C31—22no—
15C31×#336—22no—
16C31×#336C2214yes—
17C2×#41×C31—22no—
18C2×#41×C31—22no—
19C2×#41×C31—42no—
20C2×#41×C31—42no—
21C22×Q8×C31C2×C411yescharacteristic
22C22×D4×C31—21no—
23C22×D4×C31C2×C411yescharacteristic
24C23×C4×C31—21no—
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31D412yes—
27C22×C8×C31—24no—
28C31×#117—42no—
29C2×C4⋊C4×C31C2×C411yescharacteristic
30C2×C4⋊C4×C31C2×C411yescharacteristic
31C2×C22⋊C4×C31—21no—
32C2×C22⋊C4×C31—22no—
33C2×C22⋊C4×C31—22no—
34C2×C42×C31—21no—
35C2×C42×C31—42no—
36C2×C42×C31C2×C411yescharacteristic
37C2×C42×C31D412yes—
38C2×C42×C31C2311yescharacteristic
39C31×C22⋊C8—44no—
40C31×#95—22no—
41C31×#95—22no—
42C24×C31—21no—
43C24×C31C22⋊C411yescharacteristic
44#41×C31—48no—
45#41×C31—48no—
46C2×Q8×C31—21no—
47C2×Q8×C31—41no—
48C2×Q8×C31—41no—
49C2×Q8×C31M1612yes—
50C2×D4×C31—24no—
51C2×D4×C31—21no—
52C2×D4×C31—41no—
53C2×D4×C31—41no—
54C2×D4×C31—42no—
55C2×D4×C31—42no—
56C2×D4×C31M1612yes—
57C22×C4×C31—22no—
58C22×C4×C31—22no—
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—24no—
62C22×C4×C31—24no—
63C22×C4×C31—21no—
64C22×C4×C31—24no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—42no—
68C22×C4×C31—42no—
69C22×C4×C31—42no—
70C22×C4×C31C22⋊C412yes—
71C22×C4×C31C22⋊C411yescharacteristic
72C22×C4×C31C22×C411yescharacteristic
73C22×C4×C31C2×D412yes—
74C2×C8×C31—44no—
75C2×C8×C31—44no—
76C2×C8×C31—44no—
77C4⋊C4×C31—41no—
78C4⋊C4×C31—41no—
79C22⋊C4×C31—44no—
80C22⋊C4×C31—42no—
81C22⋊C4×C31—44no—
82C42×C31—41no—
83C42×C31—42no—
84C42×C31—41no—
85C42×C31—42no—
86#7645C3111yesmaximal, characteristic, direct product factor, Sylow
87C23×C31—21no—
88C23×C31—21no—
89C23×C31—22no—
90C23×C31—22no—
91C23×C31—22no—
92C23×C31—41no—
93C23×C31—41no—
94C23×C31—42no—
95C23×C31—42no—
96C23×C31#9912yes—
97C23×C31C2×C22⋊C411yescharacteristic
98Q8×C31—42no—
99Q8×C31—42no—
100D4×C31—42no—
101D4×C31—42no—
102D4×C31—48no—
103C2×C4×C31—24no—
104C2×C4×C31—24no—
105C2×C4×C31—21no—
106C2×C4×C31—22no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—22no—
111C2×C4×C31—22no—
112C2×C4×C31—22no—
113C2×C4×C31—22no—
114C2×C4×C31—22no—
115C2×C4×C31—48no—
116C2×C4×C31—48no—
117C2×C4×C31—41no—
118C2×C4×C31—41no—
119C2×C4×C31—41no—
120C2×C4×C31—41no—
121C2×C4×C31—42no—
122C2×C4×C31—42no—
123C2×C4×C31#10012yes—
124C2×C4×C31C2×M1611yescharacteristic
125C2×C4×C31C2×M1611yescharacteristic
126C2×C4×C31#13514yes—
127C8×C31—84no—
128#2297C2×C3111yescharacteristic
129#1817C2×C3112yescomplemented
130#1272C2×C3112yescomplemented
131#1270C2×C3112yescomplemented
132C22×C31—22no—
133C22×C31—24no—
134C22×C31—41no—
135C22×C31—41no—
136C22×C31—42no—
137C22×C31—42no—
138C22×C31—44no—
139C22×C31—81no—
140C22×C31—81no—
141C22×C31—82no—
142C22×C31#40711yescharacteristic
143C22×C31C2×#9911yescharacteristic
144C22×C31C2×#10011yescharacteristic
145C22×C31#41612yes—
146C22×C31#42112yes—
147C4×C31—22no—
148C4×C31—21no—
149C4×C31—21no—
150C4×C31—24no—
151C4×C31—42no—
152C4×C31—42no—
153C4×C31—81no—
154C4×C31—81no—
155C22×#41C4×C3111yescharacteristic
156C2×#117C4×C3111yescharacteristic
157C22×C42C22×C3111yescharacteristic
158C2×C22⋊C8—22no—
159#391C4×C3111yescharacteristic
160#391C22×C3111yescharacteristic
161#390C4×C3111yescharacteristic
162#390C22×C3111yescharacteristic
163#386—22no—
164C4×C22⋊C4—22no—
165#336—22no—
166#336C22×C3114yes—
167C2×C31—42no—
168C2×C31—82no—
169C2×C31#146211yescharacteristic
170C2×C31#148812yes—
171C2×C31#151612yes—
172C2×C31#153611yescharacteristic
173C2×C31#154311yescharacteristic
174C2×#41—22no—
175C2×#41—22no—
176C2×#41—42no—
177C2×#41—42no—
178C22×Q8C2×C4×C3111yescharacteristic
179C22×D4—21no—
180C22×D4C2×C4×C3111yescharacteristic
181C23×C4—21no—
182C23×C4C2×C4×C3111yescharacteristic
183C23×C4D4×C3112yes—
184C22×C8—24no—
185#117—42no—
186C2×C4⋊C4C2×C4×C3111yescharacteristic
187C2×C4⋊C4C2×C4×C3111yescharacteristic
188C2×C22⋊C4—21no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C42—21no—
192C2×C42—42no—
193C2×C42C2×C4×C3111yescharacteristic
194C2×C42D4×C3112yes—
195C2×C42C23×C3111yescharacteristic
196C22⋊C8—44no—
197#95—22no—
198#95—22no—
199C31#764511yescharacteristic, direct product factor, Sylow
200C24—21no—
201C24C22⋊C4×C3111yescharacteristic
202#41—48no—
203#41—48no—
204C2×Q8—21no—
205C2×Q8—41no—
206C2×Q8—41no—
207C2×Q8M16×C3112yes—
208C2×D4—24no—
209C2×D4—21no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4M16×C3112yes—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—24no—
220C22×C4—24no—
221C22×C4—21no—
222C22×C4—24no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4C22⋊C4×C3112yes—
229C22×C4C22⋊C4×C3111yescharacteristic
230C22×C4C22×C4×C3111yescharacteristic
231C22×C4C2×D4×C3112yes—
232C2×C8—44no—
233C2×C8—44no—
234C2×C8—44no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C22⋊C4—44no—
238C22⋊C4—42no—
239C22⋊C4—44no—
240C42—41no—
241C42—42no—
242C42—41no—
243C42—42no—
244C23—21no—
245C23—21no—
246C23—22no—
247C23—22no—
248C23—22no—
249C23—41no—
250C23—41no—
251C23—42no—
252C23—42no—
253C23C31×#9912yes—
254C23C2×C22⋊C4×C3111yescharacteristic
255Q8—42no—
256Q8—42no—
257D4—42no—
258D4—42no—
259D4—48no—
260C2×C4—24no—
261C2×C4—24no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—48no—
273C2×C4—48no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4C31×#10012yes—
281C2×C4C2×M16×C3111yescharacteristic
282C2×C4C2×M16×C3111yescharacteristic
283C2×C4C31×#13514yes—
284C8—84no—
285C22—22no—
286C22—24no—
287C22—41no—
288C22—42no—
289C22—41no—
290C22—42no—
291C22—44no—
292C22—81no—
293C22—82no—
294C22—81no—
295C22C31×#40711yescharacteristic
296C22C2×C31×#9911yescharacteristic
297C22C2×C31×#10011yescharacteristic
298C22C31×#41612yes—
299C22C31×#42112yes—
300C4—22no—
301C4—21no—
302C4—21no—
303C4—24no—
304C4—42no—
305C4—42no—
306C4—81no—
307C4—81no—
308C2—42no—
309C2—82no—
310C2C31×#146211yescharacteristic
311C2C31×#148812yes—
312C2C31×#151612yes—
313C2C31×#153611yescharacteristic
314C2C31×#154311yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×#41×C31C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1817C2semidirect
3. C31×#1272C2semidirect
4. C31×#1270C2semidirect
86. #7645C31direct (N × H)
129. #1817C2×C31semidirect
130. #1272C2×C31semidirect
131. #1270C2×C31semidirect
199. C31#7645direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#22972
C31×#18172
C31×#12722
C31×#12702
#764531