Finite Group Databasebeta

← C31×#18374 #21475133

Subgroups — C31×#18374 #21475133

Order 7936.

838 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3502C211yesmaximal, characteristic
2C31×#3236C212yesmaximal
3C31×#2634C211yesmaximal, characteristic
4C31×#1617C214yesmaximal
5C31×#1611C214yesmaximal
6C31×#1515C212yesmaximal
7C31×#1467C211yesmaximal, characteristic
8Q82×C31—22no—
9C31×#557—22no—
10C31×#557—24no—
11C31×#544—21no—
12C31×#544C2214yes—
13C31×#533—22no—
14C31×#533C2212yes—
15C2×C31×#125C2211yescharacteristic
16C31×#519—21no—
17C2×C4×Q8×C31C2211yescharacteristic
18C31×#501—22no—
19C31×#491—22no—
20C31×#484C2214yes—
21C31×#483C2214yes—
22C31×#479—24no—
23C31×#432C2212yes—
24C31×#400—21no—
25C31×#400C2212yes—
26C31×#398C2212yes—
27C31×#395—21no—
28C31×#387—22no—
29C31×#383C2211yescharacteristic
30C31×#328C2218yes—
31C31×#324C2214yes—
32C22×Q8×C31D411yescharacteristic
33C31×C4⋊Q8—22no—
34C31×C4⋊Q8—22no—
35C31×C4⋊Q8—24no—
36C31×C4⋊Q8—28no—
37C31×C4⋊Q8D412yes—
38C31×C4⋊Q8D412yes—
39C31×#125—24no—
40C31×#125—24no—
41C31×#125—28no—
42C31×#125—22no—
43C31×#125—22no—
44C31×#125—22no—
45C31×C22⋊Q8—22no—
46C31×C22⋊Q8—24no—
47C31×C22⋊Q8C2314yes—
48C4×Q8×C31—24no—
49C4×Q8×C31—24no—
50C4×Q8×C31—24no—
51C4×Q8×C31—24no—
52C4×Q8×C31—22no—
53C4×Q8×C31—22no—
54C4×Q8×C31—22no—
55C4×Q8×C31D414yes—
56C31×#117—24no—
57C31×#117—22no—
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—21no—
60C2×C4⋊C4×C31—21no—
61C2×C4⋊C4×C31D411yescharacteristic
62C2×C4⋊C4×C31C2311yescharacteristic
63C2×C4⋊C4×C31C2311yescharacteristic
64C2×C4⋊C4×C31C2312yes—
65C2×C42×C31D412yes—
66C2×C42×C31C2311yescharacteristic
67C31×#107—24no—
68C31×#106—24no—
69C31×C4⋊C8—22no—
70C31×#103—24no—
71C31×#103—24no—
72C31×C22⋊C8C2314yes—
73C31×#97—22no—
74C31×#95—21no—
75C31×#95—22no—
76C31×#95—22no—
77C31×#95—22no—
78C31×#95—21no—
79C31×#95C2312yes—
80C2×Q8×C31—24no—
81C2×Q8×C31—22no—
82C2×Q8×C31—22no—
83C2×Q8×C31—24no—
84C2×Q8×C31C2×D414yes—
85C22×C4×C31—22no—
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31C2×D411yescharacteristic
89C22×C4×C31C2×D412yes—
90C22×C4×C31C2×D412yes—
91C22×C4×C31C2×D411yescharacteristic
92C22×C4×C31C2411yescharacteristic
93C2×C8×C31—24no—
94C4⋊C4×C31—24no—
95C4⋊C4×C31—24no—
96C4⋊C4×C31—24no—
97C4⋊C4×C31—28no—
98C4⋊C4×C31—22no—
99C4⋊C4×C31—22no—
100C4⋊C4×C31—22no—
101C4⋊C4×C31—22no—
102C4⋊C4×C31—24no—
103C4⋊C4×C31—24no—
104C4⋊C4×C31—24no—
105C4⋊C4×C31—22no—
106C4⋊C4×C31—22no—
107C4⋊C4×C31—41no—
108C4⋊C4×C31—42no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31—44no—
111C4⋊C4×C31C2×D414yes—
112C22⋊C4×C31—24no—
113C42×C31—28no—
114C42×C31—22no—
115C42×C31—22no—
116C42×C31—24no—
117C42×C31C2×D412yes—
118C42×C31C2×D412yes—
119#18374C3111yesmaximal, characteristic, direct product factor, Sylow
120C23×C31C22×D411yescharacteristic
121Q8×C31—28no—
122Q8×C31—44no—
123Q8×C31—44no—
124Q8×C31—84no—
125C2×C4×C31—22no—
126C2×C4×C31—22no—
127C2×C4×C31—22no—
128C2×C4×C31—24no—
129C2×C4×C31—24no—
130C2×C4×C31—22no—
131C2×C4×C31—41no—
132C2×C4×C31—41no—
133C2×C4×C31—42no—
134C2×C4×C31—42no—
135C2×C4×C31—42no—
136C2×C4×C31—42no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—42no—
140C2×C4×C31—42no—
141C2×C4×C31#12011yescharacteristic
142C2×C4×C31#12012yes—
143C2×C4×C31#12011yescharacteristic
144C2×C4×C31#13714yes—
145C2×C4×C31C22×D412yes—
146C8×C31—44no—
147#3502C2×C3111yescharacteristic
148#3236C2×C3112yes—
149#2634C2×C3111yescharacteristic
150#1617C2×C3114yes—
151#1611C2×C3114yes—
152#1515C2×C3112yes—
153#1467C2×C3111yescharacteristic
154C22×C31—21no—
155C22×C31—21no—
156C22×C31C2×#12011yescharacteristic
157C22×C31C2×#13712yes—
158C4×C31—22no—
159C4×C31—24no—
160C4×C31—21no—
161C4×C31—21no—
162C4×C31—22no—
163C4×C31—44no—
164C4×C31—42no—
165C4×C31—44no—
166C4×C31—82no—
167C4×C31—81no—
168C4×C31—81no—
169Q82—22no—
170#557—22no—
171#557—24no—
172#544—21no—
173#544C22×C3114yes—
174#533—22no—
175#533C22×C3112yes—
176C2×#125C22×C3111yescharacteristic
177#519—21no—
178C2×C4×Q8C22×C3111yescharacteristic
179#501—22no—
180#491—22no—
181#484C22×C3114yes—
182#483C22×C3114yes—
183#479—24no—
184#432C22×C3112yes—
185#400—21no—
186#400C22×C3112yes—
187#398C22×C3112yes—
188#395—21no—
189#387—22no—
190#383C22×C3111yescharacteristic
191#328C22×C3118yes—
192#324C22×C3114yes—
193C2×C31—22no—
194C2×C31#300411yescharacteristic
195C2×C31#302011yescharacteristic
196C2×C31#302811yescharacteristic
197C22×Q8D4×C3111yescharacteristic
198C4⋊Q8—22no—
199C4⋊Q8—22no—
200C4⋊Q8—24no—
201C4⋊Q8—28no—
202C4⋊Q8D4×C3112yes—
203C4⋊Q8D4×C3112yes—
204#125—24no—
205#125—24no—
206#125—28no—
207#125—22no—
208#125—22no—
209#125—22no—
210C22⋊Q8—22no—
211C22⋊Q8—24no—
212C22⋊Q8C23×C3114yes—
213C4×Q8—24no—
214C4×Q8—24no—
215C4×Q8—24no—
216C4×Q8—24no—
217C4×Q8—22no—
218C4×Q8—22no—
219C4×Q8—22no—
220C4×Q8D4×C3114yes—
221#117—24no—
222#117—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4D4×C3111yescharacteristic
227C2×C4⋊C4C23×C3111yescharacteristic
228C2×C4⋊C4C23×C3111yescharacteristic
229C2×C4⋊C4C23×C3112yes—
230C2×C42D4×C3112yes—
231C2×C42C23×C3111yescharacteristic
232#107—24no—
233#106—24no—
234C4⋊C8—22no—
235#103—24no—
236#103—24no—
237C22⋊C8C23×C3114yes—
238#97—22no—
239#95—21no—
240#95—21no—
241#95—22no—
242#95—22no—
243#95—22no—
244#95C23×C3112yes—
245C31#1837411yescharacteristic, direct product factor, Sylow
246C2×Q8—24no—
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—24no—
250C2×Q8C2×D4×C3114yes—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4C2×D4×C3111yescharacteristic
255C22×C4C2×D4×C3112yes—
256C22×C4C2×D4×C3112yes—
257C22×C4C2×D4×C3111yescharacteristic
258C22×C4C24×C3111yescharacteristic
259C2×C8—24no—
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—24no—
263C4⋊C4—28no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—24no—
269C4⋊C4—24no—
270C4⋊C4—24no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—41no—
274C4⋊C4—42no—
275C4⋊C4—41no—
276C4⋊C4—44no—
277C4⋊C4C2×D4×C3114yes—
278C22⋊C4—24no—
279C42—28no—
280C42—22no—
281C42—22no—
282C42—24no—
283C42C2×D4×C3112yes—
284C42C2×D4×C3112yes—
285C23C22×D4×C3111yescharacteristic
286Q8—28no—
287Q8—44no—
288Q8—44no—
289Q8—84no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4C31×#12011yescharacteristic
307C2×C4C31×#12012yes—
308C2×C4C31×#12011yescharacteristic
309C2×C4C31×#13714yes—
310C2×C4C22×D4×C3112yes—
311C8—44no—
312C22—21no—
313C22—21no—
314C22C2×C31×#12011yescharacteristic
315C22C2×C31×#13712yes—
316C4—22no—
317C4—24no—
318C4—21no—
319C4—21no—
320C4—22no—
321C4—44no—
322C4—42no—
323C4—44no—
324C4—82no—
325C4—81no—
326C4—81no—
327C2—22no—
328C2C31×#300411yescharacteristic
329C2C31×#302011yescharacteristic
330C2C31×#302811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC23×C31C22×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
119. #18374C31direct (N × H)
245. C31#18374direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35022
C31×#32362
C31×#26342
C31×#16172
C31×#16112
C31×#15152
C31×#14672
#1837431