Finite Group Databasebeta

← C31×#9485 #21466244

Subgroups — C31×#9485 #21466244

Order 7936.

626 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 150 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×#2972C211yesmaximal, characteristic, complemented
2C31×#2535C211yesmaximal, characteristic
3C31×#1800C211yesmaximal, characteristic, complemented
4C31×#1486C212yesmaximal, complemented
5C31×#1286C212yesmaximal, complemented
6C2×C31×#121—21no—
7C2×C4×D4×C31C2211yescharacteristic
8C2×C4×D4×C31C2211yescharacteristic
9C8×D4×C31—24no—
10C31×#431C2212yes—
11C31×#423C2212yes—
12C2×C31×#100—21no—
13C2×C31×C22⋊C8—22no—
14C31×#397C412yes—
15C31×#392C412yes—
16C31×#386—22no—
17C31×#382C2211yescharacteristic
18C31×#380—21no—
19C31×#343—21no—
20C31×D4⋊C8—24no—
21C22×D4×C31—22no—
22C22×D4×C31C2×C411yescharacteristic
23C22×D4×C31D411yescharacteristic
24C23×C4×C31—21no—
25C23×C4×C31D412yes—
26C2×M16×C31—22no—
27C22×C8×C31—24no—
28C31×#121—42no—
29C31×#121—42no—
30C4×D4×C31—22no—
31C4×D4×C31—22no—
32C4×D4×C31—22no—
33C4×D4×C31—22no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31D411yescharacteristic
37C2×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—22no—
40C2×C22⋊C4×C31C2×C412yes—
41C2×C42×C31C2311yescharacteristic
42C31×C4⋊C8—22no—
43C31×C4⋊C8—22no—
44C31×C4⋊C8—22no—
45C31×#100—42no—
46C31×C22⋊C8—24no—
47C31×C22⋊C8—22no—
48C4×C8×C31D414yescomplemented
49C31×#95—22no—
50C31×#95—21no—
51C31×#95C2×C412yes—
52C24×C31—21no—
53C24×C31C22⋊C412yes—
54C2×D4×C31—22no—
55C2×D4×C31—22no—
56C2×D4×C31—22no—
57C2×D4×C31—42no—
58C2×D4×C31—44no—
59C2×D4×C31—44no—
60C2×D4×C31—82no—
61C2×D4×C31D812yes—
62C2×D4×C31SD1612yes—
63C22×C4×C31—22no—
64C22×C4×C31—22no—
65C22×C4×C31—22no—
66C22×C4×C31—21no—
67C22×C4×C31—42no—
68C22×C4×C31—41no—
69C22×C4×C31—41no—
70C22×C4×C31—42no—
71C22×C4×C31—82no—
72C22×C4×C31C22⋊C412yes—
73C22×C4×C31C22×C411yescharacteristic
74C22×C4×C31C2×D411yescharacteristic
75C22×C4×C31C2×D411yescharacteristic
76M16×C31—42no—
77M16×C31—42no—
78C2×C8×C31—24no—
79C2×C8×C31—42no—
80C2×C8×C31—84no—
81C4⋊C4×C31—22no—
82C4⋊C4×C31—22no—
83C4⋊C4×C31—41no—
84C4⋊C4×C31—41no—
85C22⋊C4×C31—24no—
86C22⋊C4×C31—44no—
87C22⋊C4×C31—41no—
88C22⋊C4×C31—41no—
89C22⋊C4×C31—82no—
90C42×C31C2×D412yes—
91C42×C31#4112yes—
92#9485C3111yesmaximal, characteristic, direct product factor, Sylow
93C23×C31—22no—
94C23×C31—22no—
95C23×C31—22no—
96C23×C31—42no—
97C23×C31—42no—
98C23×C31—41no—
99C23×C31—41no—
100C23×C31—41no—
101C23×C31—41no—
102C23×C31—41no—
103C23×C31—41no—
104C23×C31#10214yes—
105C23×C31C2×C22⋊C411yescharacteristic
106D4×C31—24no—
107D4×C31—24no—
108D4×C31—24no—
109D4×C31—42no—
110D4×C31—88no—
111C2×C4×C31—22no—
112C2×C4×C31—41no—
113C2×C4×C31—41no—
114C2×C4×C31—44no—
115C2×C4×C31—42no—
116C2×C4×C31—42no—
117C2×C4×C31—42no—
118C2×C4×C31—41no—
119C2×C4×C31—41no—
120C2×C4×C31—42no—
121C2×C4×C31—41no—
122C2×C4×C31—82no—
123C2×C4×C31—82no—
124C2×C4×C31—82no—
125C2×C4×C31C4×D412yes—
126C2×C4×C31#12011yescharacteristic
127C2×C4×C31#12112yes—
128C2×C4×C31#12311yescharacteristic
129C2×C4×C31C2×D811yescharacteristic
130C2×C4×C31C2×SD1611yescharacteristic
131C2×C4×C31#13512yes—
132C8×C31—44no—
133C8×C31—82no—
134#2972C2×C3111yescharacteristic, complemented
135#2535C2×C3111yescharacteristic
136#1800C2×C3111yescharacteristic, complemented
137#1486C2×C3112yescomplemented
138#1286C2×C3112yescomplemented
139C22×C31—21no—
140C22×C31—21no—
141C22×C31—24no—
142C22×C31—44no—
143C22×C31—42no—
144C22×C31—42no—
145C22×C31—42no—
146C22×C31—42no—
147C22×C31—42no—
148C22×C31—82no—
149C22×C31—81no—
150C22×C31—81no—
151C22×C31—81no—
152C22×C31—81no—
153C22×C31#38611yescharacteristic
154C22×C31C2×#10211yescharacteristic
155C22×C31#41611yescharacteristic
156C4×C31—22no—
157C4×C31—21no—
158C4×C31—21no—
159C4×C31—42no—
160C4×C31—82no—
161C4×C31—81no—
162C4×C31#46512yes—
163C4×C31#46612yes—
164C2×#121—21no—
165C2×C4×D4C22×C3111yescharacteristic
166C2×C4×D4C22×C3111yescharacteristic
167C8×D4—24no—
168#431C22×C3112yes—
169#423C22×C3112yes—
170C2×#100—21no—
171C2×C22⋊C8—22no—
172#397C4×C3112yes—
173#392C4×C3112yes—
174#386—22no—
175#382C22×C3111yescharacteristic
176#380—21no—
177#343—21no—
178D4⋊C8—24no—
179C2×C31—21no—
180C2×C31—21no—
181C2×C31—44no—
182C2×C31—82no—
183C2×C31#189111yescharacteristic
184C2×C31#189311yescharacteristic
185C2×C31#191111yescharacteristic
186C22×D4—22no—
187C22×D4C2×C4×C3111yescharacteristic
188C22×D4D4×C3111yescharacteristic
189C23×C4—21no—
190C23×C4D4×C3112yes—
191C2×M16—22no—
192C22×C8—24no—
193#121—42no—
194#121—42no—
195C4×D4—22no—
196C4×D4—22no—
197C4×D4—22no—
198C4×D4—22no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4C2×C4×C3111yescharacteristic
201C2×C4⋊C4D4×C3111yescharacteristic
202C2×C22⋊C4—22no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4C2×C4×C3112yes—
206C2×C42C23×C3111yescharacteristic
207C4⋊C8—22no—
208C4⋊C8—22no—
209C4⋊C8—22no—
210#100—42no—
211C22⋊C8—24no—
212C22⋊C8—22no—
213C4×C8D4×C3114yescomplemented
214#95—22no—
215#95—21no—
216#95C2×C4×C3112yes—
217C31#948511yescharacteristic, direct product factor, Sylow
218C24—21no—
219C24C22⋊C4×C3112yes—
220C2×D4—22no—
221C2×D4—22no—
222C2×D4—22no—
223C2×D4—42no—
224C2×D4—44no—
225C2×D4—44no—
226C2×D4—82no—
227C2×D4D8×C3112yes—
228C2×D4SD16×C3112yes—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—42no—
237C22×C4—82no—
238C22×C4C22⋊C4×C3112yes—
239C22×C4C22×C4×C3111yescharacteristic
240C22×C4C2×D4×C3111yescharacteristic
241C22×C4C2×D4×C3111yescharacteristic
242M16—42no—
243M16—42no—
244C2×C8—24no—
245C2×C8—42no—
246C2×C8—84no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C22⋊C4—24no—
252C22⋊C4—44no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—82no—
256C42C2×D4×C3112yes—
257C42#41×C3112yes—
258C23—22no—
259C23—22no—
260C23—22no—
261C23—42no—
262C23—42no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23C31×#10214yes—
270C23C2×C22⋊C4×C3111yescharacteristic
271D4—24no—
272D4—24no—
273D4—24no—
274D4—42no—
275D4—88no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—44no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—82no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4C4×D4×C3112yes—
291C2×C4C31×#12011yescharacteristic
292C2×C4C31×#12112yes—
293C2×C4C31×#12311yescharacteristic
294C2×C4C2×D8×C3111yescharacteristic
295C2×C4C2×SD16×C3111yescharacteristic
296C2×C4C31×#13512yes—
297C8—44no—
298C8—82no—
299C22—21no—
300C22—21no—
301C22—24no—
302C22—44no—
303C22—42no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—42no—
308C22—82no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22C31×#38611yescharacteristic
314C22C2×C31×#10211yescharacteristic
315C22C31×#41611yescharacteristic
316C4—22no—
317C4—21no—
318C4—21no—
319C4—42no—
320C4—82no—
321C4—81no—
322C4C31×#46512yes—
323C4C31×#46612yes—
324C2—21no—
325C2—21no—
326C2—44no—
327C2—82no—
328C2C31×#189111yescharacteristic
329C2C31×#189311yescharacteristic
330C2C31×#191111yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#2535C2
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×#2972C2semidirect
3. C31×#1800C2semidirect
4. C31×#1486C2semidirect
5. C31×#1286C2semidirect
48. C4×C8×C31D4semidirect
92. #9485C31direct (N × H)
134. #2972C2×C31semidirect
136. #1800C2×C31semidirect
137. #1486C2×C31semidirect
138. #1286C2×C31semidirect
213. C4×C8D4×C31semidirect
217. C31#9485direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29722
C31×#25352
C31×#18002
C31×#14862
C31×#12862
#948531