Finite Group Databasebeta

← C31×#13606 #21470365

Subgroups — C31×#13606 #21470365

Order 7936.

320 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 86 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×#3221C211yesmaximal, characteristic
2C31×#2133C211yesmaximal, characteristic, complemented
3C31×#2129C211yesmaximal, characteristic, complemented
4C31×#1414C212yesmaximal, complemented
5C31×#1406C212yesmaximal, complemented
6C31×#540C411yescharacteristic, complemented
7C31×#536C2211yescharacteristic
8C31×#496C2211yescharacteristic
9C31×#492C411yescharacteristic, complemented
10C31×#491C411yescharacteristic, complemented
11C31×#488C2211yescharacteristic
12C31×#463—21no—
13C31×#461—21no—
14C31×#449—21no—
15C31×#448—21no—
16C31×#433C411yescharacteristic, complemented
17C2×C31×#101—21no—
18C31×#410—21no—
19C31×#356—21no—
20C31×#355C2212yes—
21C31×#354—21no—
22C31×#354C2212yes—
23C2×#41×C31D411yescharacteristic
24C22×Q8×C31D411yescharacteristic
25C2×SD16×C31—21no—
26C2×SD16×C31—21no—
27C2×SD16×C31—21no—
28C2×D8×C31—21no—
29C2×M16×C31—41no—
30C31×C4⋊Q8C2×C411yescharacteristic
31C31×C4⋊Q8D411yescharacteristic
32C31×#127C2×C411yescharacteristic
33C31×#125C2×C411yescharacteristic
34C31×#124D411yescharacteristic
35C31×#124C2311yescharacteristic
36C31×#123—41no—
37C31×#123—41no—
38C31×C22⋊Q8—41no—
39C31×#121—21no—
40C31×#121—41no—
41C4×D4×C31—21no—
42C31×#117—41no—
43C31×#117C2×C411yescharacteristic
44C31×C4⋊C8—21no—
45C31×#103—21no—
46C31×#103—21no—
47C31×#103—21no—
48C31×#102—21no—
49C31×#101—22no—
50C31×#101—41no—
51C31×#99—22no—
52C31×#99—41no—
53C31×C22⋊C8—21no—
54C31×#97C2×C411yescharacteristic
55C4×C8×C31C2×C411yescharacteristic
56#41×C31—81no—
57C2×Q8×C31—21no—
58C2×Q8×C31—81no—
59C2×Q8×C31C22⋊C411yescharacteristic
60C2×Q8×C31C22⋊C411yescharacteristic
61C2×Q8×C31C2×D411yescharacteristic
62C2×D4×C31—21no—
63C2×D4×C31—21no—
64C2×D4×C31—41no—
65C2×D4×C31—41no—
66C2×D4×C31C2×D411yescharacteristic
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—41no—
70C22×C4×C31C22⋊C411yescharacteristic
71SD16×C31—81no—
72SD16×C31—81no—
73SD16×C31—81no—
74D8×C31—81no—
75M16×C31—42no—
76M16×C31—81no—
77C2×C8×C31—21no—
78C2×C8×C31—21no—
79C2×C8×C31—81no—
80C4⋊C4×C31—21no—
81C4⋊C4×C31—21no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—41no—
84C4⋊C4×C31—41no—
85C4⋊C4×C31—81no—
86C22⋊C4×C31—21no—
87C22⋊C4×C31—41no—
88C22⋊C4×C31—41no—
89C22⋊C4×C31—41no—
90C22⋊C4×C31—41no—
91C22⋊C4×C31—42no—
92C42×C31—81no—
93C42×C31C22⋊C411yescharacteristic
94C42×C31C22×C411yescharacteristic
95#13606C3111yesmaximal, characteristic, direct product factor, Sylow
96C23×C31—21no—
97C23×C31—41no—
98C23×C31#9911yescharacteristic
99Q8×C31—41no—
100Q8×C31—41no—
101Q8×C31—41no—
102Q8×C31—81no—
103D4×C31—41no—
104D4×C31—41no—
105D4×C31—41no—
106D4×C31—81no—
107D4×C31—161no—
108D4×C31—161no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—41no—
115C2×C4×C31—41no—
116C2×C4×C31—41no—
117C2×C4×C31—41no—
118C2×C4×C31—41no—
119C2×C4×C31—41no—
120C2×C4×C31—82no—
121C2×C4×C31—161no—
122C2×C4×C31#9911yescharacteristic
123C2×C4×C31C2×C22⋊C411yescharacteristic
124C8×C31—41no—
125C8×C31—41no—
126C8×C31—82no—
127#3221C2×C3111yescharacteristic
128#2133C2×C3111yescharacteristic, complemented
129#2129C2×C3111yescharacteristic, complemented
130#1414C2×C3112yescomplemented
131#1406C2×C3112yescomplemented
132C22×C31—21no—
133C22×C31—41no—
134C22×C31—41no—
135C22×C31—81no—
136C22×C31—81no—
137C22×C31—81no—
138C22×C31—81no—
139C22×C31C2×#9911yescharacteristic
140C4×C31—21no—
141C4×C31—21no—
142C4×C31—41no—
143C4×C31—41no—
144C4×C31—41no—
145C4×C31—41no—
146C4×C31—41no—
147C4×C31—81no—
148C4×C31—162no—
149#540C4×C3111yescharacteristic, complemented
150#536C22×C3111yescharacteristic
151#496C22×C3111yescharacteristic
152#492C4×C3111yescharacteristic, complemented
153#491C4×C3111yescharacteristic, complemented
154#488C22×C3111yescharacteristic
155#463—21no—
156#461—21no—
157#449—21no—
158#448—21no—
159#433C4×C3111yescharacteristic, complemented
160C2×#101—21no—
161#410—21no—
162#356—21no—
163#355C22×C3112yes—
164#354—21no—
165#354C22×C3112yes—
166C2×C31—21no—
167C2×C31—41no—
168C2×C31—81no—
169C2×C31—161no—
170C2×C31#212711yescharacteristic
171C2×#41D4×C3111yescharacteristic
172C22×Q8D4×C3111yescharacteristic
173C2×SD16—21no—
174C2×SD16—21no—
175C2×SD16—21no—
176C2×D8—21no—
177C2×M16—41no—
178C4⋊Q8C2×C4×C3111yescharacteristic
179C4⋊Q8D4×C3111yescharacteristic
180#127C2×C4×C3111yescharacteristic
181#125C2×C4×C3111yescharacteristic
182#124D4×C3111yescharacteristic
183#124C23×C3111yescharacteristic
184#123—41no—
185#123—41no—
186C22⋊Q8—41no—
187#121—21no—
188#121—41no—
189C4×D4—21no—
190#117—41no—
191#117C2×C4×C3111yescharacteristic
192C4⋊C8—21no—
193#103—21no—
194#103—21no—
195#103—21no—
196#102—21no—
197#101—22no—
198#101—41no—
199#99—22no—
200#99—41no—
201C22⋊C8—21no—
202#97C2×C4×C3111yescharacteristic
203C4×C8C2×C4×C3111yescharacteristic
204C31#1360611yescharacteristic, direct product factor, Sylow
205#41—81no—
206C2×Q8—21no—
207C2×Q8—81no—
208C2×Q8C22⋊C4×C3111yescharacteristic
209C2×Q8C22⋊C4×C3111yescharacteristic
210C2×Q8C2×D4×C3111yescharacteristic
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—41no—
214C2×D4—41no—
215C2×D4C2×D4×C3111yescharacteristic
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—41no—
219C22×C4C22⋊C4×C3111yescharacteristic
220SD16—81no—
221SD16—81no—
222SD16—81no—
223D8—81no—
224M16—42no—
225M16—81no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—81no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—81no—
235C22⋊C4—21no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—41no—
240C22⋊C4—42no—
241C42—81no—
242C42C22⋊C4×C3111yescharacteristic
243C42C22×C4×C3111yescharacteristic
244C23—21no—
245C23—41no—
246C23C31×#9911yescharacteristic
247Q8—41no—
248Q8—41no—
249Q8—41no—
250Q8—81no—
251D4—41no—
252D4—41no—
253D4—41no—
254D4—81no—
255D4—161no—
256D4—161no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—82no—
269C2×C4—161no—
270C2×C4C31×#9911yescharacteristic
271C2×C4C2×C22⋊C4×C3111yescharacteristic
272C8—41no—
273C8—41no—
274C8—82no—
275C22—21no—
276C22—41no—
277C22—41no—
278C22—81no—
279C22—81no—
280C22—81no—
281C22—81no—
282C22C2×C31×#9911yescharacteristic
283C4—21no—
284C4—21no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—41no—
290C4—81no—
291C4—162no—
292C2—21no—
293C2—41no—
294C2—81no—
295C2—161no—
296C2C31×#212711yescharacteristic
subgroupG/H
center, socleC2×C31#2127
commutatorC42C22×C4×C31
Frattini, cosocle#124C23×C31
prime radicalC31×#3221C2
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C22×C31 ◁ C22×C4×C31 ◁ C31×#536 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2133C2semidirect
3. C31×#2129C2semidirect
4. C31×#1414C2semidirect
5. C31×#1406C2semidirect
6. C31×#540C4semidirect
9. C31×#492C4semidirect
10. C31×#491C4semidirect
16. C31×#433C4semidirect
95. #13606C31direct (N × H)
128. #2133C2×C31semidirect
129. #2129C2×C31semidirect
130. #1414C2×C31semidirect
131. #1406C2×C31semidirect
149. #540C4×C31semidirect
152. #492C4×C31semidirect
153. #491C4×C31semidirect
159. #433C4×C31semidirect
204. C31#13606direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32212
C31×#21332
C31×#21292
C31×#14142
C31×#14062
#1360631