Finite Group Databasebeta

← C31×#9450 #21466209

Subgroups — C31×#9450 #21466209

Order 7936.

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

normal subgroups only

This group has 424 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
2C31×#2565C211yesmaximal, characteristic
3C31×#1534C212yesmaximal
4C31×#1467C211yesmaximal, characteristic
5C31×#1285C212yesmaximal
6C2×C31×#125C2211yescharacteristic
7C2×C4×Q8×C31C2211yescharacteristic
8C31×#446—24no—
9C31×#432—21no—
10C31×#432C2212yes—
11C31×#432C2212yes—
12C31×#431—21no—
13C31×#398—21no—
14C31×#398—21no—
15C31×#391C411yescharacteristic
16C31×#391C411yescharacteristic
17C31×#387—21no—
18C31×#387—21no—
19C31×#384C411yescharacteristic
20C31×#382C411yescharacteristic
21C4×C4⋊C4×C31C2211yescharacteristic
22C31×#330—24no—
23C31×#324—21no—
24C31×#324—21no—
25C22×Q8×C31C2×C411yescharacteristic
26C31×#125—22no—
27C31×#125—22no—
28C4×Q8×C31—22no—
29C4×Q8×C31—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C4⋊C4×C31D411yescharacteristic
39C2×C4⋊C4×C31D411yescharacteristic
40C2×C42×C31C2×C411yescharacteristic
41C2×C42×C31C2×C411yescharacteristic
42C2×C42×C31D411yescharacteristic
43C2×C42×C31D411yescharacteristic
44C2×C42×C31C2311yescharacteristic
45C31×C4⋊C8—22no—
46C31×C4⋊C8—22no—
47C31×C4⋊C8—22no—
48C31×C4⋊C8—22no—
49C31×C22⋊C8—22no—
50C31×C22⋊C8—22no—
51C31×#97—22no—
52C31×#97—22no—
53C31×#97D414yes—
54C4×C8×C31—22no—
55C31×#95—21no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95—21no—
61C31×#95—21no—
62C2×Q8×C31—22no—
63C2×Q8×C31—22no—
64C2×Q8×C31—41no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31C22⋊C411yescharacteristic
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—24no—
77C2×C8×C31—42no—
78C4⋊C4×C31—22no—
79C4⋊C4×C31—22no—
80C4⋊C4×C31—22no—
81C4⋊C4×C31—22no—
82C4⋊C4×C31—22no—
83C4⋊C4×C31—42no—
84C4⋊C4×C31—42no—
85C4⋊C4×C31—42no—
86C4⋊C4×C31—41no—
87C4⋊C4×C31—42no—
88C4⋊C4×C31—41no—
89C42×C31—21no—
90C42×C31—21no—
91C42×C31—21no—
92C42×C31—21no—
93C42×C31—41no—
94C42×C31—41no—
95C42×C31C2×D412yes—
96C42×C31#4112yes—
97#9450C3111yesmaximal, characteristic, direct product factor, Sylow
98C23×C31C2×C22⋊C411yescharacteristic
99Q8×C31—44no—
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—21no—
110C2×C4×C31—41no—
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—42no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—41no—
124C2×C4×C31#10112yes—
125C2×C4×C31C4×D412yes—
126C2×C4×C31#12011yescharacteristic
127C2×C4×C31#12112yes—
128C2×C4×C31#12311yescharacteristic
129C8×C31—44no—
130C8×C31—82no—
131#2983C2×C3111yescharacteristic
132#2565C2×C3111yescharacteristic
133#1534C2×C3112yes—
134#1467C2×C3111yescharacteristic
135#1285C2×C3112yes—
136C22×C31—21no—
137C22×C31—21no—
138C22×C31#38611yescharacteristic
139C22×C31C2×#10111yescharacteristic
140C22×C31#41311yescharacteristic
141C4×C31—22no—
142C4×C31—22no—
143C4×C31—22no—
144C4×C31—21no—
145C4×C31—21no—
146C4×C31—42no—
147C4×C31—41no—
148C4×C31—41no—
149C4×C31—41no—
150C4×C31—81no—
151C4×C31—81no—
152C4×C31—81no—
153C2×#125C22×C3111yescharacteristic
154C2×C4×Q8C22×C3111yescharacteristic
155#446—24no—
156#432—21no—
157#432C22×C3112yes—
158#432C22×C3112yes—
159#431—21no—
160#398—21no—
161#398—21no—
162#391C4×C3111yescharacteristic
163#391C4×C3111yescharacteristic
164#387—21no—
165#387—21no—
166#384C4×C3111yescharacteristic
167#382C4×C3111yescharacteristic
168C4×C4⋊C4C22×C3111yescharacteristic
169#330—24no—
170#324—21no—
171#324—21no—
172C2×C31—21no—
173C2×C31—21no—
174C2×C31#188411yescharacteristic
175C2×C31#190111yescharacteristic
176C2×C31#191211yescharacteristic
177C22×Q8C2×C4×C3111yescharacteristic
178#125—22no—
179#125—22no—
180C4×Q8—22no—
181C4×Q8—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4C2×C4×C3111yescharacteristic
188C2×C4⋊C4C2×C4×C3111yescharacteristic
189C2×C4⋊C4C2×C4×C3111yescharacteristic
190C2×C4⋊C4D4×C3111yescharacteristic
191C2×C4⋊C4D4×C3111yescharacteristic
192C2×C42C2×C4×C3111yescharacteristic
193C2×C42C2×C4×C3111yescharacteristic
194C2×C42D4×C3111yescharacteristic
195C2×C42D4×C3111yescharacteristic
196C2×C42C23×C3111yescharacteristic
197C4⋊C8—22no—
198C4⋊C8—22no—
199C4⋊C8—22no—
200C4⋊C8—22no—
201C22⋊C8—22no—
202C22⋊C8—22no—
203#97—22no—
204#97—22no—
205#97D4×C3114yes—
206C4×C8—22no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214C31#945011yescharacteristic, direct product factor, Sylow
215C2×Q8—22no—
216C2×Q8—22no—
217C2×Q8—41no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C22⋊C4×C3111yescharacteristic
223C22×C4C22⋊C4×C3111yescharacteristic
224C22×C4C22⋊C4×C3111yescharacteristic
225C22×C4C22⋊C4×C3111yescharacteristic
226C22×C4C22×C4×C3111yescharacteristic
227C22×C4C2×D4×C3111yescharacteristic
228C22×C4C2×D4×C3111yescharacteristic
229C2×C8—24no—
230C2×C8—42no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—41no—
247C42—41no—
248C42C2×D4×C3112yes—
249C42#41×C3112yes—
250C23C2×C22⋊C4×C3111yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4C31×#10112yes—
277C2×C4C4×D4×C3112yes—
278C2×C4C31×#12011yescharacteristic
279C2×C4C31×#12112yes—
280C2×C4C31×#12311yescharacteristic
281C8—44no—
282C8—82no—
283C22—21no—
284C22—21no—
285C22C31×#38611yescharacteristic
286C22C2×C31×#10111yescharacteristic
287C22C31×#41311yescharacteristic
288C4—22no—
289C4—22no—
290C4—22no—
291C4—21no—
292C4—21no—
293C4—42no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—81no—
300C2—21no—
301C2—21no—
302C2C31×#188411yescharacteristic
303C2C31×#190111yescharacteristic
304C2C31×#191211yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC23×C31C2×C22⋊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
97. #9450C31direct (N × H)
214. C31#9450direct (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×#25652
C31×#15342
C31×#14672
C31×#12852
#945031