Finite Group Databasebeta

← C31×#12241 #21469000

Subgroups — C31×#12241 #21469000

Order 7936.

324 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2769C211yesmaximal, characteristic
2C31×#2061C211yesmaximal, characteristic
3C31×#1617C211yesmaximal, characteristic
4C31×#1611C211yesmaximal, characteristic
5C31×#1353C211yesmaximal, characteristic
6C31×#1346C211yesmaximal, characteristic
7C31×#1324C211yesmaximal, characteristic
8C31×#544C2211yescharacteristic
9C31×#484—21no—
10C31×#483—21no—
11C31×#428—21no—
12C31×#400—21no—
13C31×#400C2211yescharacteristic
14C31×#398—21no—
15C31×#398C2211yescharacteristic
16C31×#389—21no—
17C31×#387—21no—
18C31×#387—21no—
19C31×#383—21no—
20C31×#382C2211yescharacteristic
21C31×#343C2211yescharacteristic
22C31×#339—21no—
23C31×#328—21no—
24C31×#328—21no—
25C31×#324C2211yescharacteristic
26C31×#324C2211yescharacteristic
27C2×M16×C31—21no—
28C31×C4⋊Q8—41no—
29C31×#125—41no—
30C31×C22⋊Q8—21no—
31C31×C22⋊Q8—21no—
32C31×#117—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31D411yescharacteristic
38C2×C4⋊C4×C31D411yescharacteristic
39C2×C4⋊C4×C31D411yescharacteristic
40C2×C4⋊C4×C31C2311yescharacteristic
41C2×C42×C31—21no—
42C2×C42×C31D411yescharacteristic
43C31×#107—41no—
44C31×#107—41no—
45C31×#106—41no—
46C31×#106—41no—
47C31×#103—41no—
48C31×#103—41no—
49C31×C22⋊C8—21no—
50C31×C22⋊C8—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95D411yescharacteristic
61C31×#95D411yescharacteristic
62C2×Q8×C31—21no—
63C2×Q8×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31C2×D411yescharacteristic
71C22×C4×C31C2×D411yescharacteristic
72C22×C4×C31C2×D411yescharacteristic
73M16×C31—22no—
74M16×C31—41no—
75C2×C8×C31—41no—
76C2×C8×C31—41no—
77C2×C8×C31—41no—
78C4⋊C4×C31—21no—
79C4⋊C4×C31—21no—
80C4⋊C4×C31—21no—
81C4⋊C4×C31—21no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—42no—
84C4⋊C4×C31—42no—
85C4⋊C4×C31—41no—
86C4⋊C4×C31—41no—
87C4⋊C4×C31—41no—
88C4⋊C4×C31—41no—
89C4⋊C4×C31—41no—
90C4⋊C4×C31—41no—
91C4⋊C4×C31—41no—
92C4⋊C4×C31—81no—
93C22⋊C4×C31—41no—
94C42×C31—21no—
95C42×C31—21no—
96C42×C31—42no—
97C42×C31—41no—
98#12241C3111yesmaximal, characteristic, direct product factor, Sylow
99C23×C31#12011yescharacteristic
100Q8×C31—81no—
101Q8×C31—81no—
102C2×C4×C31—21no—
103C2×C4×C31—21no—
104C2×C4×C31—22no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—41no—
108C2×C4×C31—41no—
109C2×C4×C31—41no—
110C2×C4×C31—41no—
111C2×C4×C31—41no—
112C2×C4×C31—41no—
113C2×C4×C31—41no—
114C2×C4×C31—41no—
115C2×C4×C31—41no—
116C2×C4×C31—41no—
117C2×C4×C31—41no—
118C2×C4×C31—41no—
119C2×C4×C31—41no—
120C2×C4×C31—41no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—41no—
124C2×C4×C31—41no—
125C2×C4×C31—41no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
128C2×C4×C31#13511yescharacteristic
129C2×C4×C31#13711yescharacteristic
130C8×C31—42no—
131C8×C31—81no—
132C8×C31—81no—
133#2769C2×C3111yescharacteristic
134#2061C2×C3111yescharacteristic
135#1617C2×C3111yescharacteristic
136#1611C2×C3111yescharacteristic
137#1353C2×C3111yescharacteristic
138#1346C2×C3111yescharacteristic
139#1324C2×C3111yescharacteristic
140C22×C31—21no—
141C22×C31—21no—
142C22×C31#45211yescharacteristic
143C22×C31#45611yescharacteristic
144C22×C31B(4,𝔽2)11yescharacteristic
145C4×C31—21no—
146C4×C31—21no—
147C4×C31—42no—
148C4×C31—41no—
149C4×C31—41no—
150C4×C31—81no—
151C4×C31—81no—
152C4×C31—81no—
153C4×C31—81no—
154C4×C31—81no—
155C4×C31—81no—
156C4×C31—81no—
157#544C22×C3111yescharacteristic
158#484—21no—
159#483—21no—
160#428—21no—
161#400—21no—
162#400C22×C3111yescharacteristic
163#398—21no—
164#398C22×C3111yescharacteristic
165#389—21no—
166#387—21no—
167#387—21no—
168#383—21no—
169#382C22×C3111yescharacteristic
170#343C22×C3111yescharacteristic
171#339—21no—
172#328—21no—
173#328—21no—
174#324C22×C3111yescharacteristic
175#324C22×C3111yescharacteristic
176C2×C31—21no—
177C2×C31—21no—
178C2×C31#160311yescharacteristic
179C2×C31#220111yescharacteristic
180C2×C31#220411yescharacteristic
181C2×M16—21no—
182C4⋊Q8—41no—
183#125—41no—
184C22⋊Q8—21no—
185C22⋊Q8—21no—
186#117—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4D4×C3111yescharacteristic
192C2×C4⋊C4D4×C3111yescharacteristic
193C2×C4⋊C4D4×C3111yescharacteristic
194C2×C4⋊C4C23×C3111yescharacteristic
195C2×C42—21no—
196C2×C42D4×C3111yescharacteristic
197#107—41no—
198#107—41no—
199#106—41no—
200#106—41no—
201#103—41no—
202#103—41no—
203C22⋊C8—21no—
204C22⋊C8—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95D4×C3111yescharacteristic
215#95D4×C3111yescharacteristic
216C31#1224111yescharacteristic, direct product factor, Sylow
217C2×Q8—21no—
218C2×Q8—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4C2×D4×C3111yescharacteristic
226C22×C4C2×D4×C3111yescharacteristic
227C22×C4C2×D4×C3111yescharacteristic
228M16—22no—
229M16—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—81no—
248C22⋊C4—41no—
249C42—21no—
250C42—21no—
251C42—42no—
252C42—41no—
253C23C31×#12011yescharacteristic
254Q8—81no—
255Q8—81no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4C31×#13511yescharacteristic
283C2×C4C31×#13711yescharacteristic
284C8—42no—
285C8—81no—
286C8—81no—
287C22—21no—
288C22—21no—
289C22C31×#45211yescharacteristic
290C22C31×#45611yescharacteristic
291C22C31×B(4,𝔽2)11yescharacteristic
292C4—21no—
293C4—21no—
294C4—42no—
295C4—41no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—81no—
300C4—81no—
301C4—81no—
302C4—81no—
303C4—81no—
304C2—21no—
305C2—21no—
306C2C31×#160311yescharacteristic
307C2C31×#220111yescharacteristic
308C2C31×#220411yescharacteristic
subgroupG/H
center, socleC22×C31B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC23×C31#120
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C2×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
98. #12241C31direct (N × H)
216. C31#12241direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#27692
C31×#20612
C31×#16172
C31×#16112
C31×#13532
C31×#13462
C31×#13242
#1224131