Finite Group Databasebeta

← C31×#11806 #21468565

Subgroups — C31×#11806 #21468565

Order 7936.

488 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2619C211yesmaximal, characteristic
2C31×#1822C211yesmaximal, characteristic, complemented
3C31×#1464C211yesmaximal, characteristic, complemented
4C31×#1345C214yesmaximal, complemented
5C2×C31×#127C411yescharacteristic
6C2×C31×#121—21no—
7C2×C31×#117C2211yescharacteristic
8C31×#432—21no—
9C31×#407—21no—
10C31×#394—21no—
11C31×#394C2212yes—
12C31×#392—21no—
13C31×#392C412yes—
14C31×#390—21no—
15C31×#382C411yescharacteristic
16C31×#343—21no—
17C31×#343C2212yes—
18C31×#324C2212yes—
19C31×#323—21no—
20C22×D4×C31—22no—
21C22×D4×C31—21no—
22C22×D4×C31—21no—
23C22×D4×C31C2×C412yes—
24C23×C4×C31D411yescharacteristic
25C2×M16×C31—22no—
26C31×#127—41no—
27C31×#127—41no—
28C31×#121—44no—
29C31×#117—41no—
30C31×#117—41no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31D411yescharacteristic
33C2×C4⋊C4×C31C2311yescharacteristic
34C2×C22⋊C4×C31—22no—
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31C2×C411yescharacteristic
38C2×C22⋊C4×C31D411yescharacteristic
39C2×C42×C31C2×C411yescharacteristic
40C2×C42×C31D411yescharacteristic
41C31×C4⋊C8—41no—
42C31×C22⋊C8—22no—
43C31×C22⋊C8—41no—
44C31×C22⋊C8—41no—
45C31×#97—41no—
46C31×#95—21no—
47C31×#95C2×C412yes—
48C24×C31—22no—
49C24×C31C22⋊C411yescharacteristic
50C2×D4×C31—42no—
51C2×D4×C31—42no—
52C2×D4×C31—42no—
53C2×D4×C31—42no—
54C2×D4×C31—44no—
55C2×D4×C31—41no—
56C2×D4×C31—41no—
57C2×D4×C31—82no—
58C2×D4×C31—82no—
59C2×D4×C31—82no—
60C2×D4×C31—82no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—22no—
64C22×C4×C31—22no—
65C22×C4×C31—41no—
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31C22⋊C411yescharacteristic
68C22×C4×C31C22⋊C411yescharacteristic
69C22×C4×C31C22×C411yescharacteristic
70C22×C4×C31C2×D411yescharacteristic
71C22×C4×C31C2×D411yescharacteristic
72M16×C31—42no—
73M16×C31—42no—
74C2×C8×C31—42no—
75C2×C8×C31—42no—
76C4⋊C4×C31—41no—
77C4⋊C4×C31—41no—
78C4⋊C4×C31—42no—
79C22⋊C4×C31—41no—
80C22⋊C4×C31—41no—
81C22⋊C4×C31—44no—
82C22⋊C4×C31—82no—
83C22⋊C4×C31—82no—
84C42×C31—21no—
85C42×C31—21no—
86C42×C31—21no—
87C42×C31—21no—
88#11806C3111yesmaximal, characteristic, direct product factor, Sylow
89C23×C31—21no—
90C23×C31—21no—
91C23×C31—21no—
92C23×C31—41no—
93C23×C31—41no—
94C23×C31—42no—
95C23×C31—42no—
96C23×C31—42no—
97C23×C31—42no—
98C23×C31—42no—
99C23×C31—42no—
100C23×C31—42no—
101C23×C31C2×C22⋊C411yescharacteristic
102D4×C31—82no—
103D4×C31—82no—
104D4×C31—84no—
105D4×C31—84no—
106D4×C31—88no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—42no—
116C2×C4×C31—42no—
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—42no—
124C2×C4×C31#9911yescharacteristic
125C2×C4×C31#9911yescharacteristic
126C2×C4×C31AGL(1,ℤ/8)12yes—
127C8×C31—82no—
128C8×C31—82no—
129#2619C2×C3111yescharacteristic
130#1822C2×C3111yescharacteristic, complemented
131#1464C2×C3111yescharacteristic, complemented
132#1345C2×C3114yescomplemented
133C22×C31—21no—
134C22×C31—21no—
135C22×C31—42no—
136C22×C31—41no—
137C22×C31—41no—
138C22×C31—41no—
139C22×C31—81no—
140C22×C31—82no—
141C22×C31—82no—
142C22×C31—82no—
143C22×C31—82no—
144C22×C31—82no—
145C22×C31—82no—
146C22×C31—82no—
147C22×C31C2×#9911yescharacteristic
148C22×C31#41811yescharacteristic
149C22×C31#42111yescharacteristic
150C4×C31—22no—
151C4×C31—21no—
152C4×C31—21no—
153C4×C31—41no—
154C4×C31—41no—
155C4×C31—41no—
156C4×C31—41no—
157C4×C31—82no—
158C2×#127C4×C3111yescharacteristic
159C2×#121—21no—
160C2×#117C22×C3111yescharacteristic
161#432—21no—
162#407—21no—
163#394—21no—
164#394C22×C3112yes—
165#392—21no—
166#392C4×C3112yes—
167#390—21no—
168#382C4×C3111yescharacteristic
169#343—21no—
170#343C22×C3112yes—
171#324C22×C3112yes—
172#323—21no—
173C2×C31—21no—
174C2×C31—21no—
175C2×C31—81no—
176C2×C31—162no—
177C2×C31#151011yescharacteristic
178C2×C31#212211yescharacteristic
179C2×C31#213411yescharacteristic
180C22×D4—22no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4C2×C4×C3112yes—
184C23×C4D4×C3111yescharacteristic
185C2×M16—22no—
186#127—41no—
187#127—41no—
188#121—44no—
189#117—41no—
190#117—41no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4D4×C3111yescharacteristic
193C2×C4⋊C4C23×C3111yescharacteristic
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4C2×C4×C3111yescharacteristic
198C2×C22⋊C4D4×C3111yescharacteristic
199C2×C42C2×C4×C3111yescharacteristic
200C2×C42D4×C3111yescharacteristic
201C4⋊C8—41no—
202C22⋊C8—22no—
203C22⋊C8—41no—
204C22⋊C8—41no—
205#97—41no—
206#95—21no—
207#95C2×C4×C3112yes—
208C31#1180611yescharacteristic, direct product factor, Sylow
209C24—22no—
210C24C22⋊C4×C3111yescharacteristic
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—44no—
216C2×D4—41no—
217C2×D4—41no—
218C2×D4—82no—
219C2×D4—82no—
220C2×D4—82no—
221C2×D4—82no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—41no—
227C22×C4C22⋊C4×C3111yescharacteristic
228C22×C4C22⋊C4×C3111yescharacteristic
229C22×C4C22⋊C4×C3111yescharacteristic
230C22×C4C22×C4×C3111yescharacteristic
231C22×C4C2×D4×C3111yescharacteristic
232C22×C4C2×D4×C3111yescharacteristic
233M16—42no—
234M16—42no—
235C2×C8—42no—
236C2×C8—42no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—42no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—44no—
243C22⋊C4—82no—
244C22⋊C4—82no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—42no—
261C23C2×C22⋊C4×C3111yescharacteristic
262D4—82no—
263D4—82no—
264D4—84no—
265D4—84no—
266D4—88no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4C31×#9911yescharacteristic
285C2×C4C31×#9911yescharacteristic
286C2×C4C31×AGL(1,ℤ/8)12yes—
287C8—82no—
288C8—82no—
289C22—21no—
290C22—21no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—82no—
297C22—82no—
298C22—82no—
299C22—82no—
300C22—82no—
301C22—82no—
302C22—82no—
303C22C2×C31×#9911yescharacteristic
304C22C31×#41811yescharacteristic
305C22C31×#42111yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—82no—
314C2—21no—
315C2—21no—
316C2—81no—
317C2—162no—
318C2C31×#151011yescharacteristic
319C2C31×#212211yescharacteristic
320C2C31×#213411yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC31×#2619C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1822C2semidirect
3. C31×#1464C2semidirect
4. C31×#1345C2semidirect
88. #11806C31direct (N × H)
130. #1822C2×C31semidirect
131. #1464C2×C31semidirect
132. #1345C2×C31semidirect
208. C31#11806direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26192
C31×#18222
C31×#14642
C31×#13452
#1180631