Finite Group Databasebeta

← C31×#8910 #21465669

Subgroups — C31×#8910 #21465669

Order 7936.

500 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2379C211yesmaximal, characteristic
2C31×#1959C211yesmaximal, characteristic
3C31×#1847C212yesmaximal, complemented
4C2×C31×#329C211yesmaximal, characteristic
5C31×#1295C212yesmaximal, complemented
6C2×C31×#124C2211yescharacteristic
7C2×C31×#107—22no—
8C2×C31×#106—22no—
9C2×C31×#103—21no—
10C2×C31×#102—21no—
11C2×C31×#97C2211yescharacteristic
12C2×C31×#97C2212yes—
13C31×#391—21no—
14C31×#388—22no—
15C31×#386—21no—
16C31×#385—22no—
17C31×#384C2211yescharacteristic
18C31×#382C2212yes—
19C31×#329C414yescomplemented
20C22×Q8×C31D411yescharacteristic
21C22×D4×C31D411yescharacteristic
22C23×C4×C31—21no—
23C22×C8×C31—22no—
24C22×C8×C31—21no—
25C31×#124—22no—
26C31×#124C2×C412yes—
27C31×#124Q812yes—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31D412yes—
32C2×C4⋊C4×C31D412yes—
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31—22no—
35C2×C22⋊C4×C31—21no—
36C2×C42×C31—21no—
37C2×C42×C31C2311yescharacteristic
38C31×#107—44no—
39C31×#106—44no—
40C31×#103—42no—
41C31×#102—42no—
42C31×#97—22no—
43C31×#97—22no—
44C31×#97C2×C414yescomplemented
45C31×#95—22no—
46C31×#95—22no—
47C31×#95—22no—
48C24×C31—21no—
49C2×Q8×C31—21no—
50C2×Q8×C31—41no—
51C2×Q8×C31—41no—
52C2×Q8×C31C4⋊C412yes—
53C2×D4×C31—21no—
54C2×D4×C31—41no—
55C2×D4×C31—41no—
56C2×D4×C31C4⋊C412yes—
57C22×C4×C31—21no—
58C22×C4×C31—22no—
59C22×C4×C31—22no—
60C22×C4×C31—41no—
61C22×C4×C31—82no—
62C22×C4×C31—81no—
63C22×C4×C31C2×D411yescharacteristic
64C22×C4×C31C2×D412yes—
65C2×C8×C31—24no—
66C2×C8×C31—24no—
67C2×C8×C31—24no—
68C2×C8×C31—22no—
69C2×C8×C31—41no—
70C2×C8×C31—41no—
71C4⋊C4×C31—42no—
72C4⋊C4×C31—42no—
73C4⋊C4×C31—41no—
74C4⋊C4×C31—41no—
75C4⋊C4×C31—42no—
76C4⋊C4×C31—42no—
77C4⋊C4×C31—81no—
78C22⋊C4×C31—24no—
79C22⋊C4×C31—24no—
80C22⋊C4×C31—82no—
81C22⋊C4×C31—81no—
82C42×C31—81no—
83C42×C31C22×C411yescharacteristic
84C42×C31C2×Q811yescharacteristic
85C42×C31#4112yes—
86#8910C3111yesmaximal, characteristic, direct product factor, Sylow
87C23×C31—22no—
88C23×C31—42no—
89C23×C31—41no—
90C23×C31—41no—
91C23×C31—42no—
92C23×C31#12011yescharacteristic
93Q8×C31—42no—
94Q8×C31—81no—
95D4×C31—42no—
96D4×C31—81no—
97C2×C4×C31—22no—
98C2×C4×C31—21no—
99C2×C4×C31—21no—
100C2×C4×C31—22no—
101C2×C4×C31—22no—
102C2×C4×C31—41no—
103C2×C4×C31—41no—
104C2×C4×C31—42no—
105C2×C4×C31—42no—
106C2×C4×C31—42no—
107C2×C4×C31—42no—
108C2×C4×C31—42no—
109C2×C4×C31—42no—
110C2×C4×C31—84no—
111C2×C4×C31—81no—
112C2×C4×C31—82no—
113C2×C4×C31C2×C4⋊C411yescharacteristic
114C2×C4×C31C4×D412yes—
115C2×C4×C31C22⋊Q812yes—
116C2×C4×C31#12311yescharacteristic
117C8×C31—28no—
118C8×C31—42no—
119#2379C2×C3111yescharacteristic
120#1959C2×C3111yescharacteristic
121#1847C2×C3112yescomplemented
122C2×#329C2×C3111yescharacteristic
123#1295C2×C3112yescomplemented
124C22×C31—42no—
125C22×C31—44no—
126C22×C31—81no—
127C22×C31—81no—
128C22×C31—82no—
129C22×C31#38511yescharacteristic
130C22×C31#45311yescharacteristic
131C22×C31#45312yes—
132C22×C31#45511yescharacteristic
133C22×C31#45612yes—
134C4×C31—21no—
135C4×C31—21no—
136C4×C31—22no—
137C4×C31—22no—
138C4×C31—42no—
139C4×C31—82no—
140C4×C31—82no—
141C4×C31—161no—
142C2×#124C22×C3111yescharacteristic
143C2×#107—22no—
144C2×#106—22no—
145C2×#103—21no—
146C2×#102—21no—
147C2×#97C22×C3111yescharacteristic
148C2×#97C22×C3112yes—
149#391—21no—
150#388—22no—
151#386—21no—
152#385—22no—
153#384C22×C3111yescharacteristic
154#382C22×C3112yes—
155#329C4×C3114yescomplemented
156C2×C31—82no—
157C2×C31#165511yescharacteristic
158C2×C31#166011yescharacteristic
159C2×C31#166112yes—
160C2×C31#185611yescharacteristic
161C2×C31#185912yes—
162C22×Q8D4×C3111yescharacteristic
163C22×D4D4×C3111yescharacteristic
164C23×C4—21no—
165C22×C8—22no—
166C22×C8—21no—
167#124—22no—
168#124C2×C4×C3112yes—
169#124Q8×C3112yes—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4D4×C3112yes—
174C2×C4⋊C4D4×C3112yes—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—21no—
178C2×C42—21no—
179C2×C42C23×C3111yescharacteristic
180#107—44no—
181#106—44no—
182#103—42no—
183#102—42no—
184#97—22no—
185#97—22no—
186#97C2×C4×C3114yescomplemented
187#95—22no—
188#95—22no—
189#95—22no—
190C31#891011yescharacteristic, direct product factor, Sylow
191C24—21no—
192C2×Q8—21no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8C4⋊C4×C3112yes—
196C2×D4—21no—
197C2×D4—41no—
198C2×D4—41no—
199C2×D4C4⋊C4×C3112yes—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—41no—
204C22×C4—82no—
205C22×C4—81no—
206C22×C4C2×D4×C3111yescharacteristic
207C22×C4C2×D4×C3112yes—
208C2×C8—24no—
209C2×C8—24no—
210C2×C8—24no—
211C2×C8—22no—
212C2×C8—41no—
213C2×C8—41no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—81no—
221C22⋊C4—24no—
222C22⋊C4—24no—
223C22⋊C4—82no—
224C22⋊C4—81no—
225C42—81no—
226C42C22×C4×C3111yescharacteristic
227C42C2×Q8×C3111yescharacteristic
228C42#41×C3112yes—
229C23—22no—
230C23—42no—
231C23—41no—
232C23—41no—
233C23—42no—
234C23C31×#12011yescharacteristic
235Q8—42no—
236Q8—81no—
237D4—42no—
238D4—81no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—84no—
253C2×C4—81no—
254C2×C4—82no—
255C2×C4C2×C4⋊C4×C3111yescharacteristic
256C2×C4C4×D4×C3112yes—
257C2×C4C31×C22⋊Q812yes—
258C2×C4C31×#12311yescharacteristic
259C8—28no—
260C8—42no—
261C22—42no—
262C22—44no—
263C22—81no—
264C22—81no—
265C22—82no—
266C22C31×#38511yescharacteristic
267C22C31×#45311yescharacteristic
268C22C31×#45312yes—
269C22C31×#45511yescharacteristic
270C22C31×#45612yes—
271C4—21no—
272C4—21no—
273C4—22no—
274C4—22no—
275C4—42no—
276C4—82no—
277C4—82no—
278C4—161no—
279C2—82no—
280C2C31×#165511yescharacteristic
281C2C31×#166011yescharacteristic
282C2C31×#166112yes—
283C2C31×#185611yescharacteristic
284C2C31×#185912yes—
subgroupG/H
center, socleC23×C31#120
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1847C2semidirect
5. C31×#1295C2semidirect
19. C31×#329C4semidirect
44. C31×#97C2×C4semidirect
86. #8910C31direct (N × H)
121. #1847C2×C31semidirect
123. #1295C2×C31semidirect
155. #329C4×C31semidirect
186. #97C2×C4×C31semidirect
190. C31#8910direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23792
C31×#19592
C31×#18472
C2×C31×#3292
C31×#12952
#891031