Finite Group Databasebeta

← C31×#9458 #21466217

Subgroups — C31×#9458 #21466217

Order 7936.

536 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2548C211yesmaximal, characteristic
3C31×#1555C212yesmaximal
4C31×#1467C211yesmaximal, characteristic, complemented
5C31×#1285C212yesmaximal, complemented
6C2×C31×#127C2211yescharacteristic
7C2×C31×#124C412yes—
8C2×C4×Q8×C31C2211yescharacteristic
9C31×#446—24no—
10C31×#432—21no—
11C31×#432C2212yes—
12C31×#432C2212yes—
13C31×#431—21no—
14C31×#394—21no—
15C31×#394—21no—
16C31×#390—21no—
17C31×#390—21no—
18C31×#390C412yes—
19C4×C4⋊C4×C31C2211yescharacteristic
20C31×#331—24no—
21C31×#324—21no—
22C31×#324—21no—
23C22×Q8×C31C2×C411yescharacteristic
24C22×D4×C31—21no—
25C22×D4×C31—21no—
26C22×D4×C31C2×C412yes—
27C31×#127—22no—
28C31×#127—22no—
29C31×#124—44no—
30C4×Q8×C31—22no—
31C4×Q8×C31—22no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31C2×C411yescharacteristic
34C2×C4⋊C4×C31D411yescharacteristic
35C2×C4⋊C4×C31D411yescharacteristic
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—22no—
39C2×C22⋊C4×C31—22no—
40C2×C42×C31C2×C412yes—
41C2×C42×C31D411yescharacteristic
42C2×C42×C31D411yescharacteristic
43C2×C42×C31C2311yescharacteristic
44C31×C4⋊C8—22no—
45C31×C4⋊C8—22no—
46C31×C4⋊C8—22no—
47C31×C4⋊C8D414yes—
48C31×C22⋊C8—22no—
49C31×C22⋊C8—22no—
50C31×#97—22no—
51C31×#97—22no—
52C31×#97—22no—
53C4×C8×C31—22no—
54C31×#95—21no—
55C24×C31—22no—
56C2×Q8×C31—22no—
57C2×Q8×C31—22no—
58C2×Q8×C31—41no—
59C2×D4×C31—24no—
60C2×D4×C31—42no—
61C2×D4×C31—42no—
62C2×D4×C31—42no—
63C2×D4×C31—42no—
64C2×D4×C31—41no—
65C2×D4×C31—42no—
66C2×D4×C31—41no—
67C2×D4×C31—82no—
68C22×C4×C31—22no—
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—42no—
82C22⋊C4×C31—44no—
83C22⋊C4×C31—44no—
84C22⋊C4×C31—82no—
85C22⋊C4×C31—82no—
86C42×C31—21no—
87C42×C31—21no—
88C42×C31—21no—
89C42×C31—21no—
90C42×C31—42no—
91C42×C31C2×D412yes—
92C42×C31#4112yes—
93#9458C3111yesmaximal, characteristic, direct product factor, Sylow
94C23×C31—42no—
95C23×C31—42no—
96C23×C31—42no—
97C23×C31—42no—
98C23×C31—42no—
99C23×C31—42no—
100C23×C31—42no—
101C23×C31C2×C22⋊C411yescharacteristic
102Q8×C31—44no—
103D4×C31—84no—
104D4×C31—82no—
105D4×C31—84no—
106D4×C31—82no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
111C2×C4×C31—22no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—41no—
118C2×C4×C31—41no—
119C2×C4×C31—41no—
120C2×C4×C31—42no—
121C2×C4×C31—42no—
122C2×C4×C31—42no—
123C2×C4×C31#10012yes—
124C2×C4×C31C4×D412yes—
125C2×C4×C31#12011yescharacteristic
126C2×C4×C31#12112yes—
127C2×C4×C31#12311yescharacteristic
128C8×C31—44no—
129C8×C31—82no—
130#2983C2×C3111yescharacteristic, complemented
131#2548C2×C3111yescharacteristic
132#1555C2×C3112yes—
133#1467C2×C3111yescharacteristic, complemented
134#1285C2×C3112yescomplemented
135C22×C31—21no—
136C22×C31—21no—
137C22×C31—82no—
138C22×C31—82no—
139C22×C31—82no—
140C22×C31—82no—
141C22×C31—82no—
142C22×C31—82no—
143C22×C31—82no—
144C22×C31#38611yescharacteristic
145C22×C31C2×#10011yescharacteristic
146C22×C31#41311yescharacteristic
147C4×C31—21no—
148C4×C31—22no—
149C4×C31—22no—
150C4×C31—22no—
151C4×C31—41no—
152C4×C31—41no—
153C4×C31—41no—
154C4×C31—82no—
155C4×C31#45412yes—
156C2×#127C22×C3111yescharacteristic
157C2×#124C4×C3112yes—
158C2×C4×Q8C22×C3111yescharacteristic
159#446—24no—
160#432—21no—
161#432C22×C3112yes—
162#432C22×C3112yes—
163#431—21no—
164#394—21no—
165#394—21no—
166#390—21no—
167#390—21no—
168#390C4×C3112yes—
169C4×C4⋊C4C22×C3111yescharacteristic
170#331—24no—
171#324—21no—
172#324—21no—
173C2×C31—21no—
174C2×C31—21no—
175C2×C31—162no—
176C2×C31#188811yescharacteristic
177C2×C31#190011yescharacteristic
178C2×C31#191011yescharacteristic
179C22×Q8C2×C4×C3111yescharacteristic
180C22×D4—21no—
181C22×D4—21no—
182C22×D4C2×C4×C3112yes—
183#127—22no—
184#127—22no—
185#124—44no—
186C4×Q8—22no—
187C4×Q8—22no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4C2×C4×C3111yescharacteristic
190C2×C4⋊C4D4×C3111yescharacteristic
191C2×C4⋊C4D4×C3111yescharacteristic
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C42C2×C4×C3112yes—
197C2×C42D4×C3111yescharacteristic
198C2×C42D4×C3111yescharacteristic
199C2×C42C23×C3111yescharacteristic
200C4⋊C8—22no—
201C4⋊C8—22no—
202C4⋊C8—22no—
203C4⋊C8D4×C3114yes—
204C22⋊C8—22no—
205C22⋊C8—22no—
206#97—22no—
207#97—22no—
208#97—22no—
209C4×C8—22no—
210#95—21no—
211C31#945811yescharacteristic, direct product factor, Sylow
212C24—22no—
213C2×Q8—22no—
214C2×Q8—22no—
215C2×Q8—41no—
216C2×D4—24no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—42no—
220C2×D4—42no—
221C2×D4—41no—
222C2×D4—42no—
223C2×D4—41no—
224C2×D4—82no—
225C22×C4—22no—
226C22×C4C22⋊C4×C3111yescharacteristic
227C22×C4C22⋊C4×C3111yescharacteristic
228C22×C4C22⋊C4×C3111yescharacteristic
229C22×C4C22⋊C4×C3111yescharacteristic
230C22×C4C22×C4×C3111yescharacteristic
231C22×C4C2×D4×C3111yescharacteristic
232C22×C4C2×D4×C3111yescharacteristic
233C2×C8—24no—
234C2×C8—42no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—42no—
239C22⋊C4—44no—
240C22⋊C4—44no—
241C22⋊C4—82no—
242C22⋊C4—82no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—42no—
248C42C2×D4×C3112yes—
249C42#41×C3112yes—
250C23—42no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23C2×C22⋊C4×C3111yescharacteristic
258Q8—44no—
259D4—84no—
260D4—82no—
261D4—84no—
262D4—82no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4C31×#10012yes—
280C2×C4C4×D4×C3112yes—
281C2×C4C31×#12011yescharacteristic
282C2×C4C31×#12112yes—
283C2×C4C31×#12311yescharacteristic
284C8—44no—
285C8—82no—
286C22—21no—
287C22—21no—
288C22—82no—
289C22—82no—
290C22—82no—
291C22—82no—
292C22—82no—
293C22—82no—
294C22—82no—
295C22C31×#38611yescharacteristic
296C22C2×C31×#10011yescharacteristic
297C22C31×#41311yescharacteristic
298C4—21no—
299C4—22no—
300C4—22no—
301C4—22no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—82no—
306C4C31×#45412yes—
307C2—21no—
308C2—21no—
309C2—162no—
310C2C31×#188811yescharacteristic
311C2C31×#190011yescharacteristic
312C2C31×#191011yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#127C22
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
93. #9458C31direct (N × H)
130. #2983C2×C31semidirect
133. #1467C2×C31semidirect
134. #1285C2×C31semidirect
211. C31#9458direct (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×#25482
C31×#15552
C31×#14672
C31×#12852
#945831