Finite Group Databasebeta

← C31×#11529 #21468288

Subgroups — C31×#11529 #21468288

Order 7936.

596 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C4×C31×#127C211yesmaximal, characteristic
2C31×#1465C212yesmaximal, complemented
3C31×#1325C212yesmaximal, complemented
4C31×#1318C212yesmaximal, complemented
5C2×C31×#127C411yescharacteristic
6C2×C4×D4×C31—22no—
7C2×C4×D4×C31C411yescharacteristic
8C2×C4×D4×C31C2211yescharacteristic
9C31×#407—22no—
10C31×#390—22no—
11C31×#390C411yescharacteristic
12C31×#390C2211yescharacteristic
13C31×#384C2211yescharacteristic
14C43×C31C411yescharacteristic
15C31×#324C2214yes—
16C31×#323—22no—
17C22×D4×C31—22no—
18C22×D4×C31C2×C411yescharacteristic
19C22×D4×C31C2×C411yescharacteristic
20C23×C4×C31—21no—
21C23×C4×C31D412yes—
22C2×M16×C31—42no—
23C31×#127—22no—
24C31×#127—22no—
25C4×D4×C31—41no—
26C4×D4×C31—41no—
27C4×D4×C31—48no—
28C4×D4×C31—41no—
29C4×D4×C31—41no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31C2×C411yescharacteristic
32C2×C4⋊C4×C31C2311yescharacteristic
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31—21no—
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31D412yes—
37C2×C42×C31—21no—
38C2×C42×C31—21no—
39C2×C42×C31C2×C411yescharacteristic
40C2×C42×C31C2×C411yescharacteristic
41C2×C42×C31C2×C411yescharacteristic
42C31×C22⋊C8—24no—
43C31×C22⋊C8—42no—
44C24×C31—21no—
45C24×C31C22⋊C412yes—
46C2×D4×C31—28no—
47C2×D4×C31—21no—
48C2×D4×C31—21no—
49C2×D4×C31—21no—
50C2×D4×C31—41no—
51C2×D4×C31—41no—
52C2×D4×C31—44no—
53C2×D4×C31—44no—
54C2×D4×C31—41no—
55C2×D4×C31—41no—
56C2×D4×C31M1612yescomplemented
57C22×C4×C31—21no—
58C22×C4×C31—21no—
59C22×C4×C31—22no—
60C22×C4×C31—22no—
61C22×C4×C31—21no—
62C22×C4×C31—44no—
63C22×C4×C31—44no—
64C22×C4×C31—41no—
65C22×C4×C31—41no—
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31C22⋊C411yescharacteristic
68C22×C4×C31C22×C411yescharacteristic
69C22×C4×C31C2×D412yes—
70M16×C31—84no—
71C2×C8×C31—44no—
72C4⋊C4×C31—41no—
73C4⋊C4×C31—44no—
74C4⋊C4×C31—41no—
75C22⋊C4×C31—42no—
76C22⋊C4×C31—44no—
77C22⋊C4×C31—44no—
78C22⋊C4×C31—42no—
79C42×C31—24no—
80C42×C31—21no—
81C42×C31—21no—
82C42×C31—21no—
83C42×C31—42no—
84C42×C31—41no—
85C42×C31M1612yescomplemented
86#11529C3111yesmaximal, characteristic, direct product factor, Sylow
87C23×C31—22no—
88C23×C31—22no—
89C23×C31—22no—
90C23×C31—22no—
91C23×C31—42no—
92C23×C31—42no—
93C23×C31—42no—
94C23×C31—42no—
95C23×C31—41no—
96C23×C31—41no—
97C23×C31C2×C22⋊C411yescharacteristic
98D4×C31—42no—
99D4×C31—416no—
100D4×C31—42no—
101D4×C31—42no—
102D4×C31—42no—
103C2×C4×C31—22no—
104C2×C4×C31—22no—
105C2×C4×C31—22no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—22no—
109C2×C4×C31—22no—
110C2×C4×C31—21no—
111C2×C4×C31—22no—
112C2×C4×C31—41no—
113C2×C4×C31—41no—
114C2×C4×C31—44no—
115C2×C4×C31—41no—
116C2×C4×C31—42no—
117C2×C4×C31—42no—
118C2×C4×C31—41no—
119C2×C4×C31—82no—
120C2×C4×C31—82no—
121C2×C4×C31—82no—
122C2×C4×C31#9911yescharacteristic
123C2×C4×C31#9911yescharacteristic
124C2×C4×C31C2×M1611yescharacteristic
125C2×C4×C31C2×M1611yescharacteristic
126C8×C31—84no—
127C4×#127C2×C3111yescharacteristic
128#1465C2×C3112yescomplemented
129#1325C2×C3112yescomplemented
130#1318C2×C3112yescomplemented
131C22×C31—21no—
132C22×C31—21no—
133C22×C31—44no—
134C22×C31—44no—
135C22×C31—42no—
136C22×C31—42no—
137C22×C31—42no—
138C22×C31—42no—
139C22×C31—82no—
140C22×C31—82no—
141C22×C31—81no—
142C22×C31—81no—
143C22×C31#40711yescharacteristic
144C22×C31C2×#9911yescharacteristic
145C22×C31#41311yescharacteristic
146C4×C31—24no—
147C4×C31—21no—
148C4×C31—21no—
149C4×C31—21no—
150C4×C31—42no—
151C4×C31—42no—
152C4×C31—41no—
153C4×C31—81no—
154C4×C31#35312yes—
155C2×#127C4×C3111yescharacteristic
156C2×C4×D4—22no—
157C2×C4×D4C4×C3111yescharacteristic
158C2×C4×D4C22×C3111yescharacteristic
159#407—22no—
160#390—22no—
161#390C4×C3111yescharacteristic
162#390C22×C3111yescharacteristic
163#384C22×C3111yescharacteristic
164C43C4×C3111yescharacteristic
165#324C22×C3114yes—
166#323—22no—
167C2×C31—21no—
168C2×C31—21no—
169C2×C31—82no—
170C2×C31—82no—
171C2×C31#146511yescharacteristic
172C2×C31C2×#35311yescharacteristic
173C2×C31#213211yescharacteristic
174C22×D4—22no—
175C22×D4C2×C4×C3111yescharacteristic
176C22×D4C2×C4×C3111yescharacteristic
177C23×C4—21no—
178C23×C4D4×C3112yes—
179C2×M16—42no—
180#127—22no—
181#127—22no—
182C4×D4—41no—
183C4×D4—41no—
184C4×D4—48no—
185C4×D4—41no—
186C4×D4—41no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4C2×C4×C3111yescharacteristic
189C2×C4⋊C4C23×C3111yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4—21no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4D4×C3112yes—
194C2×C42—21no—
195C2×C42—21no—
196C2×C42C2×C4×C3111yescharacteristic
197C2×C42C2×C4×C3111yescharacteristic
198C2×C42C2×C4×C3111yescharacteristic
199C22⋊C8—24no—
200C22⋊C8—42no—
201C31#1152911yescharacteristic, direct product factor, Sylow
202C24—21no—
203C24C22⋊C4×C3112yes—
204C2×D4—28no—
205C2×D4—21no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—44no—
213C2×D4—44no—
214C2×D4M16×C3112yescomplemented
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—44no—
221C22×C4—44no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4C22⋊C4×C3111yescharacteristic
225C22×C4C22⋊C4×C3111yescharacteristic
226C22×C4C22×C4×C3111yescharacteristic
227C22×C4C2×D4×C3112yes—
228M16—84no—
229C2×C8—44no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—44no—
233C22⋊C4—42no—
234C22⋊C4—44no—
235C22⋊C4—44no—
236C22⋊C4—42no—
237C42—24no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—41no—
242C42—42no—
243C42M16×C3112yescomplemented
244C23—22no—
245C23—22no—
246C23—22no—
247C23—22no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23—41no—
253C23—41no—
254C23C2×C22⋊C4×C3111yescharacteristic
255D4—42no—
256D4—416no—
257D4—42no—
258D4—42no—
259D4—42no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—44no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—82no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4C31×#9911yescharacteristic
280C2×C4C31×#9911yescharacteristic
281C2×C4C2×M16×C3111yescharacteristic
282C2×C4C2×M16×C3111yescharacteristic
283C8—84no—
284C22—21no—
285C22—21no—
286C22—44no—
287C22—44no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—82no—
293C22—82no—
294C22—81no—
295C22—81no—
296C22C31×#40711yescharacteristic
297C22C2×C31×#9911yescharacteristic
298C22C31×#41311yescharacteristic
299C4—24no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—42no—
304C4—42no—
305C4—41no—
306C4—81no—
307C4C31×#35312yes—
308C2—21no—
309C2—21no—
310C2—82no—
311C2—82no—
312C2C31×#146511yescharacteristic
313C2C2×C31×#35311yescharacteristic
314C2C31×#213211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC2×C31×#127C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1465C2semidirect
3. C31×#1325C2semidirect
4. C31×#1318C2semidirect
56. C2×D4×C31M16semidirect
85. C42×C31M16semidirect
86. #11529C31direct (N × H)
128. #1465C2×C31semidirect
129. #1325C2×C31semidirect
130. #1318C2×C31semidirect
201. C31#11529direct (N × H)
214. C2×D4M16×C31semidirect
243. C42M16×C31semidirect

Maximal subgroups

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

subgroupindex
C4×C31×#1272
C31×#14652
C31×#13252
C31×#13182
#1152931