Finite Group Databasebeta

← C31×#11853 #21468612

Subgroups — C31×#11853 #21468612

Order 7936.

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

normal subgroups only

This group has 368 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×#2611C211yesmaximal, characteristic
2C31×#1822C211yesmaximal, characteristic
3C31×#1458C211yesmaximal, characteristic
4C31×#1353C212yesmaximal, complemented
5C31×#1346C212yesmaximal, complemented
6C2×C31×#125C411yescharacteristic
7C2×C31×#117C2211yescharacteristic
8C31×#431—21no—
9C31×#407—21no—
10C31×#400C2211yescharacteristic
11C31×#399C411yescharacteristic
12C31×#398C2211yescharacteristic
13C31×#397C411yescharacteristic
14C31×#389—21no—
15C31×#388—21no—
16C31×#387—21no—
17C31×#385—21no—
18C31×#376C411yescharacteristic
19C31×#343—21no—
20C31×#343C2212yes—
21C31×#324C2212yes—
22C31×#323—21no—
23C23×C4×C31D411yescharacteristic
24C2×M16×C31—22no—
25C31×#125—41no—
26C31×#125—41no—
27C31×#117—41no—
28C31×#117—41no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31C2×C411yescharacteristic
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C4⋊C4×C31D411yescharacteristic
36C2×C4⋊C4×C31C2311yescharacteristic
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31C2×C411yescharacteristic
40C2×C22⋊C4×C31D411yescharacteristic
41C2×C42×C31—21no—
42C2×C42×C31C2×C411yescharacteristic
43C2×C42×C31D411yescharacteristic
44C31×C4⋊C8—41no—
45C31×C22⋊C8—22no—
46C31×C22⋊C8—41no—
47C31×C22⋊C8—41no—
48C4×C8×C31—41no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95C2×C411yescharacteristic
55C31×#95C2×C411yescharacteristic
56C24×C31C22⋊C411yescharacteristic
57C22×C4×C31—21no—
58C22×C4×C31—21no—
59C22×C4×C31—21no—
60C22×C4×C31—22no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—21no—
64C22×C4×C31—41no—
65C22×C4×C31C22⋊C411yescharacteristic
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31C22⋊C411yescharacteristic
68C22×C4×C31C22×C411yescharacteristic
69C22×C4×C31C2×D411yescharacteristic
70C22×C4×C31C2×D411yescharacteristic
71M16×C31—42no—
72M16×C31—42no—
73C2×C8×C31—42no—
74C2×C8×C31—42no—
75C4⋊C4×C31—41no—
76C4⋊C4×C31—41no—
77C4⋊C4×C31—42no—
78C4⋊C4×C31—42no—
79C4⋊C4×C31—41no—
80C4⋊C4×C31—41no—
81C4⋊C4×C31—41no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—42no—
84C22⋊C4×C31—41no—
85C22⋊C4×C31—41no—
86C22⋊C4×C31—42no—
87C22⋊C4×C31—42no—
88C42×C31—21no—
89C42×C31—21no—
90C42×C31—21no—
91C42×C31—21no—
92C42×C31—42no—
93#11853C3111yesmaximal, characteristic, direct product factor, Sylow
94C23×C31—21no—
95C23×C31—21no—
96C23×C31—21no—
97C23×C31—41no—
98C23×C31—41no—
99C23×C31C2×C22⋊C411yescharacteristic
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—21no—
103C2×C4×C31—21no—
104C2×C4×C31—22no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—42no—
110C2×C4×C31—42no—
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#9911yescharacteristic
127C2×C4×C31#9911yescharacteristic
128C2×C4×C31#13512yes—
129C8×C31—82no—
130C8×C31—82no—
131#2611C2×C3111yescharacteristic
132#1822C2×C3111yescharacteristic
133#1458C2×C3111yescharacteristic
134#1353C2×C3112yescomplemented
135#1346C2×C3112yescomplemented
136C22×C31—21no—
137C22×C31—21no—
138C22×C31—42no—
139C22×C31—41no—
140C22×C31—41no—
141C22×C31—41no—
142C22×C31—81no—
143C22×C31C2×#9911yescharacteristic
144C22×C31#41611yescharacteristic
145C22×C31#42111yescharacteristic
146C4×C31—22no—
147C4×C31—21no—
148C4×C31—21no—
149C4×C31—42no—
150C4×C31—41no—
151C4×C31—41no—
152C4×C31—41no—
153C4×C31—41no—
154C4×C31—81no—
155C4×C31—81no—
156C4×C31—81no—
157C2×#125C4×C3111yescharacteristic
158C2×#117C22×C3111yescharacteristic
159#431—21no—
160#407—21no—
161#400C22×C3111yescharacteristic
162#399C4×C3111yescharacteristic
163#398C22×C3111yescharacteristic
164#397C4×C3111yescharacteristic
165#389—21no—
166#388—21no—
167#387—21no—
168#385—21no—
169#376C4×C3111yescharacteristic
170#343—21no—
171#343C22×C3112yes—
172#324C22×C3112yes—
173#323—21no—
174C2×C31—21no—
175C2×C31—21no—
176C2×C31—81no—
177C2×C31#151611yescharacteristic
178C2×C31#212311yescharacteristic
179C2×C31#213211yescharacteristic
180C23×C4D4×C3111yescharacteristic
181C2×M16—22no—
182#125—41no—
183#125—41no—
184#117—41no—
185#117—41no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C2×C4×C3111yescharacteristic
191C2×C4⋊C4C2×C4×C3111yescharacteristic
192C2×C4⋊C4D4×C3111yescharacteristic
193C2×C4⋊C4C23×C3111yescharacteristic
194C2×C22⋊C4—21no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4C2×C4×C3111yescharacteristic
197C2×C22⋊C4D4×C3111yescharacteristic
198C2×C42—21no—
199C2×C42C2×C4×C3111yescharacteristic
200C2×C42D4×C3111yescharacteristic
201C4⋊C8—41no—
202C22⋊C8—22no—
203C22⋊C8—41no—
204C22⋊C8—41no—
205C4×C8—41no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95C2×C4×C3111yescharacteristic
212#95C2×C4×C3111yescharacteristic
213C31#1185311yescharacteristic, direct product factor, Sylow
214C24C22⋊C4×C3111yescharacteristic
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—41no—
223C22×C4C22⋊C4×C3111yescharacteristic
224C22×C4C22⋊C4×C3111yescharacteristic
225C22×C4C22⋊C4×C3111yescharacteristic
226C22×C4C22×C4×C3111yescharacteristic
227C22×C4C2×D4×C3111yescharacteristic
228C22×C4C2×D4×C3111yescharacteristic
229M16—42no—
230M16—42no—
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—41no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—42no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23C2×C22⋊C4×C3111yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—42no—
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×C4—41no—
283C2×C4C31×#9911yescharacteristic
284C2×C4C31×#9911yescharacteristic
285C2×C4C31×#13512yes—
286C8—82no—
287C8—82no—
288C22—21no—
289C22—21no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—81no—
295C22C2×C31×#9911yescharacteristic
296C22C31×#41611yescharacteristic
297C22C31×#42111yescharacteristic
298C4—22no—
299C4—21no—
300C4—21no—
301C4—42no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—81no—
307C4—81no—
308C4—81no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2C31×#151611yescharacteristic
313C2C31×#212311yescharacteristic
314C2C31×#213211yescharacteristic
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 ◁ C22×C4×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1353C2semidirect
5. C31×#1346C2semidirect
93. #11853C31direct (N × H)
134. #1353C2×C31semidirect
135. #1346C2×C31semidirect
213. C31#11853direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26112
C31×#18222
C31×#14582
C31×#13532
C31×#13462
#1185331