Finite Group Databasebeta

← C31×#11803 #21468562

Subgroups — C31×#11803 #21468562

Order 7936.

478 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C2×C31×#398C211yesmaximal, characteristic
2C31×#1821C211yesmaximal, characteristic
3C31×#1463C211yesmaximal, characteristic
4C31×#1346C214yesmaximal, complemented
5C22×C4⋊C4×C31—21no—
6C22×C4⋊C4×C31C411yescharacteristic
7C22×C4⋊C4×C31C2211yescharacteristic
8C31×#407—21no—
9C31×#407—21no—
10C31×#398—21no—
11C31×#398—21no—
12C31×#398C412yes—
13C31×#398C2212yes—
14C2×C31×#95—21no—
15C2×C31×#95C411yescharacteristic
16C31×#343—21no—
17C31×#343C2212yes—
18C31×#324—21no—
19C31×#324C2212yes—
20C23×C4×C31—21no—
21C23×C4×C31—21no—
22C23×C4×C31C2×C411yescharacteristic
23C23×C4×C31D411yescharacteristic
24C23×C4×C31D411yescharacteristic
25C2×M16×C31—22no—
26C2×M16×C31—41no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31—41no—
31C2×C4⋊C4×C31—41no—
32C2×C4⋊C4×C31—44no—
33C2×C4⋊C4×C31—41no—
34C2×C4⋊C4×C31—41no—
35C2×C4⋊C4×C31C2×C412yes—
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C4⋊C4×C31D411yescharacteristic
38C2×C4⋊C4×C31D411yescharacteristic
39C2×C4⋊C4×C31C2311yescharacteristic
40C31×C22⋊C8—22no—
41C31×C22⋊C8—41no—
42C31×C22⋊C8—41no—
43C31×C22⋊C8—41no—
44C31×#95—21no—
45C31×#95—22no—
46C31×#95—22no—
47C31×#95C2×C412yes—
48C24×C31C22⋊C411yescharacteristic
49C22×C4×C31—24no—
50C22×C4×C31—21no—
51C22×C4×C31—21no—
52C22×C4×C31—21no—
53C22×C4×C31—21no—
54C22×C4×C31—21no—
55C22×C4×C31—22no—
56C22×C4×C31—21no—
57C22×C4×C31—22no—
58C22×C4×C31—22no—
59C22×C4×C31—41no—
60C22×C4×C31—42no—
61C22×C4×C31—42no—
62C22×C4×C31—42no—
63C22×C4×C31—42no—
64C22×C4×C31—42no—
65C22×C4×C31—42no—
66C22×C4×C31—41no—
67C22×C4×C31—41no—
68C22×C4×C31C22⋊C411yescharacteristic
69C22×C4×C31C22⋊C411yescharacteristic
70C22×C4×C31C22⋊C411yescharacteristic
71C22×C4×C31C22×C411yescharacteristic
72C22×C4×C31C2×D411yescharacteristic
73C22×C4×C31C2×D411yescharacteristic
74M16×C31—42no—
75M16×C31—42no—
76M16×C31—82no—
77C2×C8×C31—42no—
78C2×C8×C31—42no—
79C4⋊C4×C31—41no—
80C4⋊C4×C31—41no—
81C4⋊C4×C31—41no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—42no—
84C4⋊C4×C31—44no—
85C4⋊C4×C31—42no—
86C4⋊C4×C31—44no—
87#11803C3111yesmaximal, characteristic, direct product factor, Sylow
88C23×C31—22no—
89C23×C31—22no—
90C23×C31—21no—
91C23×C31—21no—
92C23×C31#9911yescharacteristic
93C23×C31#9911yescharacteristic
94C23×C31C2×C22⋊C411yescharacteristic
95C2×C4×C31—21no—
96C2×C4×C31—21no—
97C2×C4×C31—24no—
98C2×C4×C31—21no—
99C2×C4×C31—21no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—21no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—42no—
106C2×C4×C31—42no—
107C2×C4×C31—48no—
108C2×C4×C31—42no—
109C2×C4×C31—42no—
110C2×C4×C31—42no—
111C2×C4×C31—42no—
112C2×C4×C31—42no—
113C2×C4×C31—41no—
114C2×C4×C31—41no—
115C2×C4×C31—41no—
116C2×C4×C31—41no—
117C2×C4×C31—42no—
118C2×C4×C31—42no—
119C2×C4×C31—42no—
120C2×C4×C31—81no—
121C2×C4×C31—82no—
122C2×C4×C31—82no—
123C2×C4×C31AGL(1,ℤ/8)12yes—
124C8×C31—82no—
125C8×C31—82no—
126C2×#398C2×C3111yescharacteristic
127#1821C2×C3111yescharacteristic
128#1463C2×C3111yescharacteristic
129#1346C2×C3114yescomplemented
130C22×C31—24no—
131C22×C31—24no—
132C22×C31—21no—
133C22×C31—21no—
134C22×C31—21no—
135C22×C31—21no—
136C22×C31—21no—
137C22×C31—21no—
138C22×C31#35212yes—
139C22×C31#35612yes—
140C22×C31C2×#9911yescharacteristic
141C22×C31#41811yescharacteristic
142C22×C31#42111yescharacteristic
143C4×C31—22no—
144C4×C31—44no—
145C4×C31—41no—
146C4×C31—41no—
147C4×C31—41no—
148C4×C31—41no—
149C4×C31—41no—
150C4×C31—82no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4C4×C3111yescharacteristic
153C22×C4⋊C4C22×C3111yescharacteristic
154#407—21no—
155#407—21no—
156#398—21no—
157#398—21no—
158#398C4×C3112yes—
159#398C22×C3112yes—
160C2×#95—21no—
161C2×#95C4×C3111yescharacteristic
162#343—21no—
163#343C22×C3112yes—
164#324—21no—
165#324C22×C3112yes—
166C2×C31—21no—
167C2×C31—22no—
168C2×C31—22no—
169C2×C31—21no—
170C2×C31#151011yescharacteristic
171C2×C31C2×#35211yescharacteristic
172C2×C31C2×#35611yescharacteristic
173C23×C4—21no—
174C23×C4—21no—
175C23×C4C2×C4×C3111yescharacteristic
176C23×C4D4×C3111yescharacteristic
177C23×C4D4×C3111yescharacteristic
178C2×M16—22no—
179C2×M16—41no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—44no—
188C2×C4⋊C4C2×C4×C3112yes—
189C2×C4⋊C4C2×C4×C3111yescharacteristic
190C2×C4⋊C4D4×C3111yescharacteristic
191C2×C4⋊C4D4×C3111yescharacteristic
192C2×C4⋊C4C23×C3111yescharacteristic
193C22⋊C8—22no—
194C22⋊C8—41no—
195C22⋊C8—41no—
196C22⋊C8—41no—
197#95—22no—
198#95—21no—
199#95—22no—
200#95C2×C4×C3112yes—
201C31#1180311yescharacteristic, direct product factor, Sylow
202C24C22⋊C4×C3111yescharacteristic
203C22×C4—24no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—41no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4C22⋊C4×C3111yescharacteristic
223C22×C4C22⋊C4×C3111yescharacteristic
224C22×C4C22⋊C4×C3111yescharacteristic
225C22×C4C22×C4×C3111yescharacteristic
226C22×C4C2×D4×C3111yescharacteristic
227C22×C4C2×D4×C3111yescharacteristic
228M16—42no—
229M16—42no—
230M16—82no—
231C2×C8—42no—
232C2×C8—42no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—44no—
240C4⋊C4—44no—
241C23—21no—
242C23—21no—
243C23—22no—
244C23—22no—
245C23C31×#9911yescharacteristic
246C23C31×#9911yescharacteristic
247C23C2×C22⋊C4×C3111yescharacteristic
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—24no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—48no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4C31×AGL(1,ℤ/8)12yes—
277C8—82no—
278C8—82no—
279C22—24no—
280C22—24no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C31×#35212yes—
288C22C31×#35612yes—
289C22C2×C31×#9911yescharacteristic
290C22C31×#41811yescharacteristic
291C22C31×#42111yescharacteristic
292C4—22no—
293C4—44no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—82no—
300C2—21no—
301C2—21no—
302C2—22no—
303C2—22no—
304C2C31×#151011yescharacteristic
305C2C2×C31×#35211yescharacteristic
306C2C2×C31×#35611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C31 ◁ C22×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1346C2semidirect
87. #11803C31direct (N × H)
129. #1346C2×C31semidirect
201. C31#11803direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3982
C31×#18212
C31×#14632
C31×#13462
#1180331