Finite Group Databasebeta

← C31×#11548 #21468307

Subgroups — C31×#11548 #21468307

Order 7936.

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

normal subgroups only

This group has 380 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×#2484C211yesmaximal, characteristic
2C31×#1464C211yesmaximal, characteristic
3C31×#1458C211yesmaximal, characteristic
4C31×#1326C212yesmaximal
5C31×#1317C212yesmaximal
6C2×C31×#117C2211yescharacteristic
7C22×C4⋊C4×C31C411yescharacteristic
8C31×#432—21no—
9C31×#431—21no—
10C31×#400—21no—
11C31×#398—21no—
12C31×#387—21no—
13C31×#387—21no—
14C31×#385C411yescharacteristic
15C31×#385C2211yescharacteristic
16C31×#381C411yescharacteristic
17C31×#381C411yescharacteristic
18C31×#381C2211yescharacteristic
19C31×#324—21no—
20C31×#324—21no—
21C31×#323C2212yes—
22C31×#323C2212yes—
23C23×C4×C31C2×C411yescharacteristic
24C23×C4×C31C2×C411yescharacteristic
25C23×C4×C31C2×C411yescharacteristic
26C31×#117—41no—
27C31×#117—41no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—41no—
33C2×C4⋊C4×C31—41no—
34C2×C4⋊C4×C31D411yescharacteristic
35C2×C4⋊C4×C31D411yescharacteristic
36C2×C22⋊C4×C31C2×C411yescharacteristic
37C2×C22⋊C4×C31C2×C411yescharacteristic
38C2×C22⋊C4×C31C2×C411yescharacteristic
39C2×C22⋊C4×C31C2311yescharacteristic
40C2×C42×C31D411yescharacteristic
41C2×C42×C31D411yescharacteristic
42C31×C4⋊C8—41no—
43C31×C4⋊C8—41no—
44C31×C22⋊C8—22no—
45C31×C22⋊C8—22no—
46C31×#97—41no—
47C4×C8×C31—41no—
48C31×#95—21no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C24×C31C22×C411yescharacteristic
57C22×C4×C31—21no—
58C22×C4×C31—22no—
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—21no—
64C22×C4×C31—22no—
65C22×C4×C31—41no—
66C22×C4×C31—42no—
67C22×C4×C31—41no—
68C22×C4×C31—41no—
69C22×C4×C31—41no—
70C22×C4×C31C22⋊C411yescharacteristic
71C22×C4×C31C22⋊C411yescharacteristic
72C22×C4×C31C22⋊C411yescharacteristic
73C22×C4×C31C22⋊C411yescharacteristic
74C22×C4×C31C2×D411yescharacteristic
75C22×C4×C31C2×D411yescharacteristic
76C2×C8×C31—42no—
77C2×C8×C31—42no—
78C4⋊C4×C31—41no—
79C4⋊C4×C31—41no—
80C4⋊C4×C31—42no—
81C4⋊C4×C31—42no—
82C4⋊C4×C31—42no—
83C4⋊C4×C31—41no—
84C4⋊C4×C31—41no—
85C22⋊C4×C31—22no—
86C22⋊C4×C31—41no—
87C22⋊C4×C31—41no—
88C22⋊C4×C31—41no—
89C42×C31—21no—
90C42×C31—21no—
91C42×C31—21no—
92C42×C31—21no—
93#11548C3111yesmaximal, characteristic, direct product factor, Sylow
94C23×C31—21no—
95C23×C31—21no—
96C23×C31—41no—
97C23×C31—41no—
98C23×C31C2×C22⋊C411yescharacteristic
99C23×C31#13112yes—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—22no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—42no—
111C2×C4×C31—42no—
112C2×C4×C31—41no—
113C2×C4×C31—42no—
114C2×C4×C31—41no—
115C2×C4×C31—41no—
116C2×C4×C31—41no—
117C2×C4×C31—41no—
118C2×C4×C31—41no—
119C2×C4×C31—42no—
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—41no—
129C2×C4×C31—82no—
130C2×C4×C31#9911yescharacteristic
131C2×C4×C31#9911yescharacteristic
132C8×C31—82no—
133C8×C31—82no—
134#2484C2×C3111yescharacteristic
135#1464C2×C3111yescharacteristic
136#1458C2×C3111yescharacteristic
137#1326C2×C3112yes—
138#1317C2×C3112yes—
139C22×C31—21no—
140C22×C31—21no—
141C22×C31—22no—
142C22×C31—42no—
143C22×C31—42no—
144C22×C31—41no—
145C22×C31—41no—
146C22×C31#40811yescharacteristic
147C22×C31C2×#9911yescharacteristic
148C22×C31#41311yescharacteristic
149C4×C31—21no—
150C4×C31—21no—
151C4×C31—41no—
152C4×C31—41no—
153C4×C31—42no—
154C4×C31—41no—
155C4×C31—41no—
156C4×C31—41no—
157C4×C31—81no—
158C4×C31—81no—
159C4×C31—81no—
160C2×#117C22×C3111yescharacteristic
161C22×C4⋊C4C4×C3111yescharacteristic
162#432—21no—
163#431—21no—
164#400—21no—
165#398—21no—
166#387—21no—
167#387—21no—
168#385C4×C3111yescharacteristic
169#385C22×C3111yescharacteristic
170#381C4×C3111yescharacteristic
171#381C4×C3111yescharacteristic
172#381C22×C3111yescharacteristic
173#324—21no—
174#324—21no—
175#323C22×C3112yes—
176#323C22×C3112yes—
177C2×C31—21no—
178C2×C31—21no—
179C2×C31—42no—
180C2×C31#146811yescharacteristic
181C2×C31#212011yescharacteristic
182C2×C31#212311yescharacteristic
183C23×C4C2×C4×C3111yescharacteristic
184C23×C4C2×C4×C3111yescharacteristic
185C23×C4C2×C4×C3111yescharacteristic
186#117—41no—
187#117—41no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—41no—
193C2×C4⋊C4—41no—
194C2×C4⋊C4D4×C3111yescharacteristic
195C2×C4⋊C4D4×C3111yescharacteristic
196C2×C22⋊C4C2×C4×C3111yescharacteristic
197C2×C22⋊C4C2×C4×C3111yescharacteristic
198C2×C22⋊C4C2×C4×C3111yescharacteristic
199C2×C22⋊C4C23×C3111yescharacteristic
200C2×C42D4×C3111yescharacteristic
201C2×C42D4×C3111yescharacteristic
202C4⋊C8—41no—
203C4⋊C8—41no—
204C22⋊C8—22no—
205C22⋊C8—22no—
206#97—41no—
207C4×C8—41no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216C31#1154811yescharacteristic, direct product factor, Sylow
217C24C22×C4×C3111yescharacteristic
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—41no—
227C22×C4—42no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4C22⋊C4×C3111yescharacteristic
232C22×C4C22⋊C4×C3111yescharacteristic
233C22×C4C22⋊C4×C3111yescharacteristic
234C22×C4C22⋊C4×C3111yescharacteristic
235C22×C4C2×D4×C3111yescharacteristic
236C22×C4C2×D4×C3111yescharacteristic
237C2×C8—42no—
238C2×C8—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C22⋊C4—22no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×C22⋊C4×C3111yescharacteristic
259C23C31×#13112yes—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—82no—
290C2×C4C31×#9911yescharacteristic
291C2×C4C31×#9911yescharacteristic
292C8—82no—
293C8—82no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22C31×#40811yescharacteristic
302C22C2×C31×#9911yescharacteristic
303C22C31×#41311yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—42no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4—81no—
314C4—81no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2C31×#146811yescharacteristic
319C2C31×#212011yescharacteristic
320C2C31×#212311yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC24C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC24×C31C22×C4
LCSG ▷ C24 ▷ C22 ▷ 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
93. #11548C31direct (N × H)
216. C31#11548direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#24842
C31×#14642
C31×#14582
C31×#13262
C31×#13172
#1154831