Finite Group Databasebeta

← C31×#9448 #21466207

Subgroups — C31×#9448 #21466207

Order 7936.

486 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2983C211yesmaximal, characteristic, complemented
2C31×#2545C211yesmaximal, characteristic
3C31×#1533C212yesmaximal
4C31×#1467C211yesmaximal, characteristic, complemented
5C31×#1285C212yesmaximal, complemented
6C2×C31×C4⋊Q8C411yescharacteristic
7C2×C31×#124C411yescharacteristic
8C2×C31×#124C2211yescharacteristic
9C2×C4×Q8×C31C2211yescharacteristic
10C31×#446—24no—
11C31×#432—21no—
12C31×#432C2212yes—
13C31×#432C2212yes—
14C31×#431—21no—
15C31×#396—21no—
16C31×#396—21no—
17C31×#391C411yescharacteristic
18C31×#390C411yescharacteristic
19C31×#388—21no—
20C31×#388—21no—
21C4×C4⋊C4×C31C2211yescharacteristic
22C31×#329—24no—
23C31×#324—21no—
24C31×#324—21no—
25C22×Q8×C31C2×C411yescharacteristic
26C22×Q8×C31C2×C411yescharacteristic
27C22×D4×C31C2×C411yescharacteristic
28C31×C4⋊Q8—42no—
29C31×#124—22no—
30C31×#124—22no—
31C31×#124—42no—
32C4×Q8×C31—22no—
33C4×Q8×C31—22no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C4⋊C4×C31D411yescharacteristic
39C2×C4⋊C4×C31D411yescharacteristic
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C42×C31C2×C411yescharacteristic
47C2×C42×C31C2×C411yescharacteristic
48C2×C42×C31D411yescharacteristic
49C2×C42×C31D411yescharacteristic
50C2×C42×C31C2311yescharacteristic
51C31×C4⋊C8—22no—
52C31×C4⋊C8—22no—
53C31×C4⋊C8—22no—
54C31×C4⋊C8—22no—
55C31×C22⋊C8—22no—
56C31×C22⋊C8—22no—
57C31×#97—22no—
58C31×#97—22no—
59C31×#97D414yes—
60C4×C8×C31—22no—
61C31×#95—21no—
62C31×#95—21no—
63C31×#95—21no—
64C24×C31—21no—
65C2×Q8×C31—22no—
66C2×Q8×C31—22no—
67C2×Q8×C31—22no—
68C2×Q8×C31—41no—
69C2×Q8×C31—41no—
70C2×Q8×C31—41no—
71C2×D4×C31—22no—
72C2×D4×C31—41no—
73C2×D4×C31—41no—
74C22×C4×C31—21no—
75C22×C4×C31—21no—
76C22×C4×C31—21no—
77C22×C4×C31C22⋊C411yescharacteristic
78C22×C4×C31C22⋊C411yescharacteristic
79C22×C4×C31C22⋊C411yescharacteristic
80C22×C4×C31C22⋊C411yescharacteristic
81C22×C4×C31C22×C411yescharacteristic
82C22×C4×C31C2×D411yescharacteristic
83C22×C4×C31C2×D411yescharacteristic
84C2×C8×C31—24no—
85C2×C8×C31—42no—
86C4⋊C4×C31—22no—
87C4⋊C4×C31—22no—
88C4⋊C4×C31—22no—
89C4⋊C4×C31—42no—
90C4⋊C4×C31—42no—
91C4⋊C4×C31—42no—
92C22⋊C4×C31—42no—
93C22⋊C4×C31—42no—
94C22⋊C4×C31—42no—
95C22⋊C4×C31—42no—
96C22⋊C4×C31—41no—
97C22⋊C4×C31—42no—
98C22⋊C4×C31—41no—
99C42×C31—21no—
100C42×C31—21no—
101C42×C31—21no—
102C42×C31—21no—
103C42×C31—41no—
104C42×C31—41no—
105C42×C31C2×D412yes—
106C42×C31#4112yes—
107#9448C3111yesmaximal, characteristic, direct product factor, Sylow
108C23×C31—41no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31—41no—
112C23×C31—41no—
113C23×C31—41no—
114C23×C31—41no—
115C23×C31C2×C22⋊C411yescharacteristic
116Q8×C31—44no—
117Q8×C31—82no—
118D4×C31—82no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—22no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—41no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
132C2×C4×C31—41no—
133C2×C4×C31—41no—
134C2×C4×C31—41no—
135C2×C4×C31—41no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31#10012yes—
142C2×C4×C31C4×D412yes—
143C2×C4×C31#12011yescharacteristic
144C2×C4×C31#12112yes—
145C2×C4×C31#12311yescharacteristic
146C8×C31—44no—
147C8×C31—82no—
148#2983C2×C3111yescharacteristic, complemented
149#2545C2×C3111yescharacteristic
150#1533C2×C3112yes—
151#1467C2×C3111yescharacteristic, complemented
152#1285C2×C3112yescomplemented
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—81no—
156C22×C31—81no—
157C22×C31—81no—
158C22×C31—81no—
159C22×C31—81no—
160C22×C31—81no—
161C22×C31—81no—
162C22×C31#38611yescharacteristic
163C22×C31C2×#10011yescharacteristic
164C22×C31#41311yescharacteristic
165C4×C31—22no—
166C4×C31—22no—
167C4×C31—22no—
168C4×C31—21no—
169C4×C31—21no—
170C4×C31—42no—
171C4×C31—41no—
172C4×C31—41no—
173C4×C31—41no—
174C4×C31—81no—
175C4×C31—81no—
176C2×C4⋊Q8C4×C3111yescharacteristic
177C2×#124C4×C3111yescharacteristic
178C2×#124C22×C3111yescharacteristic
179C2×C4×Q8C22×C3111yescharacteristic
180#446—24no—
181#432—21no—
182#432C22×C3112yes—
183#432C22×C3112yes—
184#431—21no—
185#396—21no—
186#396—21no—
187#391C4×C3111yescharacteristic
188#390C4×C3111yescharacteristic
189#388—21no—
190#388—21no—
191C4×C4⋊C4C22×C3111yescharacteristic
192#329—24no—
193#324—21no—
194#324—21no—
195C2×C31—21no—
196C2×C31—21no—
197C2×C31—161no—
198C2×C31#188411yescharacteristic
199C2×C31#190011yescharacteristic
200C2×C31#191211yescharacteristic
201C22×Q8C2×C4×C3111yescharacteristic
202C22×Q8C2×C4×C3111yescharacteristic
203C22×D4C2×C4×C3111yescharacteristic
204C4⋊Q8—42no—
205#124—22no—
206#124—22no—
207#124—42no—
208C4×Q8—22no—
209C4×Q8—22no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4C2×C4×C3111yescharacteristic
214C2×C4⋊C4D4×C3111yescharacteristic
215C2×C4⋊C4D4×C3111yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C42C2×C4×C3111yescharacteristic
223C2×C42C2×C4×C3111yescharacteristic
224C2×C42D4×C3111yescharacteristic
225C2×C42D4×C3111yescharacteristic
226C2×C42C23×C3111yescharacteristic
227C4⋊C8—22no—
228C4⋊C8—22no—
229C4⋊C8—22no—
230C4⋊C8—22no—
231C22⋊C8—22no—
232C22⋊C8—22no—
233#97—22no—
234#97—22no—
235#97D4×C3114yes—
236C4×C8—22no—
237#95—21no—
238#95—21no—
239#95—21no—
240C31#944811yescharacteristic, direct product factor, Sylow
241C24—21no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—22no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×D4—22no—
249C2×D4—41no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4C22⋊C4×C3111yescharacteristic
255C22×C4C22⋊C4×C3111yescharacteristic
256C22×C4C22⋊C4×C3111yescharacteristic
257C22×C4C22⋊C4×C3111yescharacteristic
258C22×C4C22×C4×C3111yescharacteristic
259C22×C4C2×D4×C3111yescharacteristic
260C22×C4C2×D4×C3111yescharacteristic
261C2×C8—24no—
262C2×C8—42no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—41no—
274C22⋊C4—42no—
275C22⋊C4—41no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—21no—
280C42—41no—
281C42—41no—
282C42C2×D4×C3112yes—
283C42#41×C3112yes—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23C2×C22⋊C4×C3111yescharacteristic
292Q8—44no—
293Q8—82no—
294D4—82no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4C31×#10012yes—
318C2×C4C4×D4×C3112yes—
319C2×C4C31×#12011yescharacteristic
320C2×C4C31×#12112yes—
321C2×C4C31×#12311yescharacteristic
322C8—44no—
323C8—82no—
324C22—21no—
325C22—21no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22C31×#38611yescharacteristic
334C22C2×C31×#10011yescharacteristic
335C22C31×#41311yescharacteristic
336C4—22no—
337C4—22no—
338C4—22no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—81no—
346C4—81no—
347C2—21no—
348C2—21no—
349C2—161no—
350C2C31×#188411yescharacteristic
351C2C31×#190011yescharacteristic
352C2C31×#191211yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31C2×C4
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
1. C31×#2983C2semidirect
4. C31×#1467C2semidirect
5. C31×#1285C2semidirect
107. #9448C31direct (N × H)
148. #2983C2×C31semidirect
151. #1467C2×C31semidirect
152. #1285C2×C31semidirect
240. C31#9448direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29832
C31×#25452
C31×#15332
C31×#14672
C31×#12852
#944831