Finite Group Databasebeta

← C31×#9157 #21465916

Subgroups — C31×#9157 #21465916

Order 7936.

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

normal subgroups only

This group has 648 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×#2854C211yesmaximal, characteristic
2C2×C31×#383C211yesmaximal, characteristic, complemented
3C31×#1817C211yesmaximal, characteristic, complemented
4C2×C31×#327C212yesmaximal
5C31×#1294C212yesmaximal, complemented
6C2×C31×#123—21no—
7C2×C31×#121C2211yescharacteristic
8C22×C42×C31C2211yescharacteristic
9C2×C31×C22⋊C8C2212yes—
10C31×#390C412yescomplemented
11C31×#389C412yescomplemented
12C31×#388—22no—
13C31×#386—21no—
14C31×#383—24no—
15C31×#380C2211yescharacteristic
16C2×C31×#95—21no—
17C2×C31×#95—21no—
18C2×C31×#95C2212yes—
19C31×#336—22no—
20C31×#327—24no—
21C22×D4×C31—21no—
22C22×D4×C31C2×C411yescharacteristic
23C23×C4×C31—22no—
24C23×C4×C31D411yescharacteristic
25C23×C4×C31D411yescharacteristic
26C23×C4×C31C2311yescharacteristic
27C22×C8×C31—22no—
28C31×#123—44no—
29C31×#121—22no—
30C31×#121—22no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31C2×C411yescharacteristic
33C2×C4⋊C4×C31C2×C412yes—
34C2×C22⋊C4×C31—21no—
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31—21no—
38C2×C42×C31—22no—
39C2×C42×C31—22no—
40C2×C42×C31C2×C412yes—
41C2×C42×C31D412yes—
42C31×C22⋊C8—22no—
43C31×C22⋊C8—22no—
44C31×#95—24no—
45C31×#95—24no—
46C31×#95—22no—
47C31×#95—22no—
48C31×#95—21no—
49C31×#95D414yes—
50C24×C31—21no—
51C24×C31C2×D411yescharacteristic
52C2×D4×C31—22no—
53C2×D4×C31—42no—
54C2×D4×C31—41no—
55C2×D4×C31—41no—
56C2×D4×C31—42no—
57C2×D4×C31—42no—
58C22×C4×C31—21no—
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—21no—
62C22×C4×C31—22no—
63C22×C4×C31—22no—
64C22×C4×C31—22no—
65C22×C4×C31—21no—
66C22×C4×C31—24no—
67C22×C4×C31—42no—
68C22×C4×C31—42no—
69C22×C4×C31—44no—
70C22×C4×C31—44no—
71C22×C4×C31—42no—
72C22×C4×C31—42no—
73C22×C4×C31C22⋊C412yes—
74C22×C4×C31C22⋊C412yes—
75C22×C4×C31C22×C411yescharacteristic
76C22×C4×C31C2×D411yescharacteristic
77C22×C4×C31C2×D412yes—
78C22×C4×C31#4112yes—
79C2×C8×C31—44no—
80C2×C8×C31—42no—
81C4⋊C4×C31—22no—
82C4⋊C4×C31—44no—
83C4⋊C4×C31—42no—
84C22⋊C4×C31—44no—
85C22⋊C4×C31—44no—
86C22⋊C4×C31—42no—
87C22⋊C4×C31—42no—
88C42×C31—24no—
89C42×C31—24no—
90#9157C3111yesmaximal, characteristic, direct product factor, Sylow
91C23×C31—22no—
92C23×C31—22no—
93C23×C31—41no—
94C23×C31—42no—
95C23×C31—41no—
96C23×C31—41no—
97C23×C31—42no—
98C23×C31C2×C22⋊C411yescharacteristic
99C23×C31#12011yescharacteristic
100C23×C31#12311yescharacteristic
101C23×C31#13512yes—
102C23×C31AGL(1,ℤ/8)12yes—
103D4×C31—82no—
104D4×C31—82no—
105D4×C31—82no—
106C2×C4×C31—22no—
107C2×C4×C31—22no—
108C2×C4×C31—22no—
109C2×C4×C31—22no—
110C2×C4×C31—22no—
111C2×C4×C31—22no—
112C2×C4×C31—22no—
113C2×C4×C31—22no—
114C2×C4×C31—42no—
115C2×C4×C31—42no—
116C2×C4×C31—42no—
117C2×C4×C31—42no—
118C2×C4×C31—42no—
119C2×C4×C31—42no—
120C2×C4×C31—44no—
121C2×C4×C31—44no—
122C2×C4×C31—41no—
123C2×C4×C31—42no—
124C2×C4×C31—41no—
125C2×C4×C31—42no—
126C2×C4×C31—41no—
127C2×C4×C31—42no—
128C2×C4×C31—44no—
129C2×C4×C31—84no—
130C2×C4×C31—84no—
131C2×C4×C31C4×D412yes—
132C2×C4×C31#12112yes—
133C8×C31—82no—
134#2854C2×C3111yescharacteristic
135C2×#383C2×C3111yescharacteristic, complemented
136#1817C2×C3111yescharacteristic, complemented
137C2×#327C2×C3112yes—
138#1294C2×C3112yescomplemented
139C22×C31—21no—
140C22×C31—21no—
141C22×C31—21no—
142C22×C31—21no—
143C22×C31—24no—
144C22×C31—24no—
145C22×C31—81no—
146C22×C31—81no—
147C22×C31—81no—
148C22×C31—82no—
149C22×C31—82no—
150C22×C31#38611yescharacteristic
151C22×C31#41012yes—
152C22×C31#41611yescharacteristic
153C22×C31#41811yescharacteristic
154C22×C31#42112yes—
155C22×C31#44912yes—
156C22×C31#48212yes—
157C4×C31—22no—
158C4×C31—22no—
159C4×C31—42no—
160C4×C31—42no—
161C4×C31—84no—
162C4×C31—81no—
163C4×C31—82no—
164C2×#123—21no—
165C2×#121C22×C3111yescharacteristic
166C22×C42C22×C3111yescharacteristic
167C2×C22⋊C8C22×C3112yes—
168#390C4×C3112yescomplemented
169#389C4×C3112yescomplemented
170#388—22no—
171#386—21no—
172#383—24no—
173#380C22×C3111yescharacteristic
174C2×#95—21no—
175C2×#95—21no—
176C2×#95C22×C3112yes—
177#336—22no—
178#327—24no—
179C2×C31—22no—
180C2×C31—22no—
181C2×C31—161no—
182C2×C31#151412yes—
183C2×C31#152112yes—
184C2×C31#187511yescharacteristic
185C2×C31#189711yescharacteristic
186C2×C31#189911yescharacteristic
187C22×D4—21no—
188C22×D4C2×C4×C3111yescharacteristic
189C23×C4—22no—
190C23×C4D4×C3111yescharacteristic
191C23×C4D4×C3111yescharacteristic
192C23×C4C23×C3111yescharacteristic
193C22×C8—22no—
194#123—44no—
195#121—22no—
196#121—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4C2×C4×C3111yescharacteristic
199C2×C4⋊C4C2×C4×C3112yes—
200C2×C22⋊C4—21no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—21no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42C2×C4×C3112yes—
207C2×C42D4×C3112yes—
208C22⋊C8—22no—
209C22⋊C8—22no—
210#95—24no—
211#95—24no—
212#95—22no—
213#95—22no—
214#95—21no—
215#95D4×C3114yes—
216C31#915711yescharacteristic, direct product factor, Sylow
217C24—21no—
218C24C2×D4×C3111yescharacteristic
219C2×D4—22no—
220C2×D4—42no—
221C2×D4—41no—
222C2×D4—41no—
223C2×D4—42no—
224C2×D4—42no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—24no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—44no—
237C22×C4—44no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4C22⋊C4×C3112yes—
241C22×C4C22⋊C4×C3112yes—
242C22×C4C22×C4×C3111yescharacteristic
243C22×C4C2×D4×C3111yescharacteristic
244C22×C4C2×D4×C3112yes—
245C22×C4#41×C3112yes—
246C2×C8—44no—
247C2×C8—42no—
248C4⋊C4—22no—
249C4⋊C4—42no—
250C4⋊C4—44no—
251C22⋊C4—44no—
252C22⋊C4—44no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C42—24no—
256C42—24no—
257C23—22no—
258C23—22no—
259C23—42no—
260C23—41no—
261C23—41no—
262C23—42no—
263C23—41no—
264C23C2×C22⋊C4×C3111yescharacteristic
265C23C31×#12011yescharacteristic
266C23C31×#12311yescharacteristic
267C23C31×#13512yes—
268C23C31×AGL(1,ℤ/8)12yes—
269D4—82no—
270D4—82no—
271D4—82no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—44no—
294C2×C4—41no—
295C2×C4—84no—
296C2×C4—84no—
297C2×C4C4×D4×C3112yes—
298C2×C4C31×#12112yes—
299C8—82no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—24no—
305C22—24no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22—82no—
310C22—82no—
311C22C31×#38611yescharacteristic
312C22C31×#41012yes—
313C22C31×#41611yescharacteristic
314C22C31×#41811yescharacteristic
315C22C31×#42112yes—
316C22C31×#44912yes—
317C22C31×#48212yes—
318C4—22no—
319C4—22no—
320C4—42no—
321C4—42no—
322C4—84no—
323C4—81no—
324C4—82no—
325C2—22no—
326C2—22no—
327C2—161no—
328C2C31×#151412yes—
329C2C31×#152112yes—
330C2C31×#187511yescharacteristic
331C2C31×#189711yescharacteristic
332C2C31×#189911yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#383C2semidirect
3. C31×#1817C2semidirect
5. C31×#1294C2semidirect
10. C31×#390C4semidirect
11. C31×#389C4semidirect
90. #9157C31direct (N × H)
135. C2×#383C2×C31semidirect
136. #1817C2×C31semidirect
138. #1294C2×C31semidirect
168. #390C4×C31semidirect
169. #389C4×C31semidirect
216. C31#9157direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28542
C2×C31×#3832
C31×#18172
C2×C31×#3272
C31×#12942
#915731