Finite Group Databasebeta

← C31×#13461 #21470220

Subgroups — C31×#13461 #21470220

Order 7936.

540 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2683C211yesmaximal, characteristic
2C31×#1867C212yesmaximal
3C31×#1856C211yesmaximal, characteristic
4C31×#1393C211yesmaximal, characteristic
5C31×#1390C212yesmaximal
6C2×C31×C22⋊Q8—22no—
7C31×#518C2211yescharacteristic
8C31×#428—21no—
9C2×C31×#100C2211yescharacteristic
10C2×C31×#99C2212yes—
11C31×#396—22no—
12C31×#395—21no—
13C31×#390C2211yescharacteristic
14C31×#389—21no—
15C31×#386C2212yes—
16C31×#385—22no—
17C31×#342—22no—
18C31×#339—21no—
19C22×Q8×C31—21no—
20C22×D4×C31C2311yescharacteristic
21C23×C4×C31D412yes—
22C2×M16×C31—21no—
23C31×C22⋊Q8—48no—
24C4×D4×C31—41no—
25C4×D4×C31—41no—
26C31×#117—21no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—42no—
32C2×C4⋊C4×C31D411yescharacteristic
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31—22no—
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31D412yes—
38C2×C42×C31D411yescharacteristic
39C31×#107—41no—
40C31×#106—41no—
41C31×#100—21no—
42C31×#100Q812yescomplemented
43C31×#99—22no—
44C31×#99Q814yescomplemented
45C31×#95—21no—
46C31×#95—22no—
47C31×#95—42no—
48C24×C31C2×D412yes—
49C2×Q8×C31—44no—
50C2×Q8×C31—81no—
51C2×D4×C31—41no—
52C2×D4×C31—41no—
53C2×D4×C31C2×Q811yescharacteristic
54C2×D4×C31C2×Q812yes—
55C2×D4×C31#4111yescharacteristic
56C22×C4×C31—22no—
57C22×C4×C31—21no—
58C22×C4×C31—22no—
59C22×C4×C31—21no—
60C22×C4×C31—22no—
61C22×C4×C31—22no—
62C22×C4×C31—44no—
63C22×C4×C31—42no—
64C22×C4×C31—42no—
65C22×C4×C31C2×D411yescharacteristic
66M16×C31—22no—
67M16×C31—41no—
68C2×C8×C31—41no—
69C4⋊C4×C31—24no—
70C4⋊C4×C31—21no—
71C4⋊C4×C31—21no—
72C4⋊C4×C31—44no—
73C4⋊C4×C31—44no—
74C4⋊C4×C31—41no—
75C4⋊C4×C31—81no—
76C4⋊C4×C31—84no—
77C22⋊C4×C31—24no—
78C22⋊C4×C31—44no—
79C22⋊C4×C31—44no—
80C22⋊C4×C31—42no—
81C22⋊C4×C31—42no—
82C22⋊C4×C31—41no—
83C22⋊C4×C31—42no—
84C42×C31—41no—
85C42×C31—41no—
86#13461C3111yesmaximal, characteristic, direct product factor, Sylow
87C23×C31—22no—
88C23×C31—22no—
89C23×C31—42no—
90C23×C31—42no—
91C23×C31#12011yescharacteristic
92C23×C31C22⋊Q812yes—
93C23×C31C4⋊Q812yes—
94Q8×C31—84no—
95D4×C31—41no—
96D4×C31—42no—
97D4×C31—41no—
98C2×C4×C31—21no—
99C2×C4×C31—21no—
100C2×C4×C31—22no—
101C2×C4×C31—24no—
102C2×C4×C31—42no—
103C2×C4×C31—41no—
104C2×C4×C31—42no—
105C2×C4×C31—41no—
106C2×C4×C31—44no—
107C2×C4×C31—44no—
108C2×C4×C31—42no—
109C2×C4×C31—42no—
110C2×C4×C31—42no—
111C2×C4×C31—41no—
112C2×C4×C31—41no—
113C2×C4×C31—41no—
114C2×C4×C31—42no—
115C2×C4×C31—82no—
116C2×C4×C31—82no—
117C2×C4×C31—82no—
118C2×C4×C31—82no—
119C2×C4×C31—82no—
120C2×C4×C31C22⋊Q811yescharacteristic
121C2×C4×C31C4⋊Q811yescharacteristic
122C8×C31—42no—
123#2683C2×C3111yescharacteristic
124#1867C2×C3112yes—
125#1856C2×C3111yescharacteristic
126#1393C2×C3111yescharacteristic
127#1390C2×C3112yes—
128C22×C31—21no—
129C22×C31—21no—
130C22×C31—22no—
131C22×C31—22no—
132C22×C31—42no—
133C22×C31—42no—
134C22×C31—42no—
135C22×C31—42no—
136C22×C31—82no—
137C22×C31#39511yescharacteristic
138C22×C31B(4,𝔽2)11yescharacteristic
139C22×C31#45811yescharacteristic
140C4×C31—21no—
141C4×C31—21no—
142C4×C31—42no—
143C4×C31—44no—
144C4×C31—82no—
145C4×C31—84no—
146C4×C31—81no—
147C4×C31—81no—
148C4×C31—81no—
149C2×C22⋊Q8—22no—
150#518C22×C3111yescharacteristic
151#428—21no—
152C2×#100C22×C3111yescharacteristic
153C2×#99C22×C3112yes—
154#396—22no—
155#395—21no—
156#390C22×C3111yescharacteristic
157#389—21no—
158#386C22×C3112yes—
159#385—22no—
160#342—22no—
161#339—21no—
162C2×C31—21no—
163C2×C31—21no—
164C2×C31—42no—
165C2×C31—42no—
166C2×C31#206211yescharacteristic
167C2×C31#219611yescharacteristic
168C2×C31#220111yescharacteristic
169C22×Q8—21no—
170C22×D4C23×C3111yescharacteristic
171C23×C4D4×C3112yes—
172C2×M16—21no—
173C22⋊Q8—48no—
174C4×D4—41no—
175C4×D4—41no—
176#117—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4D4×C3111yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4D4×C3112yes—
188C2×C42D4×C3111yescharacteristic
189#107—41no—
190#106—41no—
191#100—21no—
192#100Q8×C3112yescomplemented
193#99—22no—
194#99Q8×C3114yescomplemented
195#95—21no—
196#95—22no—
197#95—42no—
198C31#1346111yescharacteristic, direct product factor, Sylow
199C24C2×D4×C3112yes—
200C2×Q8—44no—
201C2×Q8—81no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4C2×Q8×C3111yescharacteristic
205C2×D4C2×Q8×C3112yes—
206C2×D4#41×C3111yescharacteristic
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—44no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4C2×D4×C3111yescharacteristic
217M16—22no—
218M16—41no—
219C2×C8—41no—
220C4⋊C4—24no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—41no—
224C4⋊C4—44no—
225C4⋊C4—44no—
226C4⋊C4—81no—
227C4⋊C4—84no—
228C22⋊C4—24no—
229C22⋊C4—44no—
230C22⋊C4—44no—
231C22⋊C4—42no—
232C22⋊C4—42no—
233C22⋊C4—41no—
234C22⋊C4—42no—
235C42—41no—
236C42—41no—
237C23—22no—
238C23—22no—
239C23—42no—
240C23—42no—
241C23C31×#12011yescharacteristic
242C23C31×C22⋊Q812yes—
243C23C31×C4⋊Q812yes—
244Q8—84no—
245D4—41no—
246D4—42no—
247D4—41no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—44no—
257C2×C4—44no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—82no—
266C2×C4—82no—
267C2×C4—82no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4C31×C22⋊Q811yescharacteristic
271C2×C4C31×C4⋊Q811yescharacteristic
272C8—42no—
273C22—21no—
274C22—21no—
275C22—22no—
276C22—22no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—82no—
282C22C31×#39511yescharacteristic
283C22C31×B(4,𝔽2)11yescharacteristic
284C22C31×#45811yescharacteristic
285C4—21no—
286C4—21no—
287C4—42no—
288C4—44no—
289C4—82no—
290C4—84no—
291C4—81no—
292C4—81no—
293C4—81no—
294C2—21no—
295C2—21no—
296C2—42no—
297C2—42no—
298C2C31×#206211yescharacteristic
299C2C31×#219611yescharacteristic
300C2C31×#220111yescharacteristic
subgroupG/H
center, socleC22×C31B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C31
prime radicalC22×D4×C31C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
42. C31×#100Q8semidirect
44. C31×#99Q8semidirect
86. #13461C31direct (N × H)
192. #100Q8×C31semidirect
194. #99Q8×C31semidirect
198. C31#13461direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26832
C31×#18672
C31×#18562
C31×#13932
C31×#13902
#1346131