Finite Group Databasebeta

← C31×#9490 #21466249

Subgroups — C31×#9490 #21466249

Order 7936.

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

normal subgroups only

This group has 522 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×#2983C211yesmaximal, characteristic, complemented
2C31×#2536C211yesmaximal, characteristic
3C31×#1801C211yesmaximal, characteristic, complemented
4C31×#1486C212yesmaximal
5C31×#1286C212yesmaximal, complemented
6C2×C31×C22⋊Q8—21no—
7C2×C4×Q8×C31C2211yescharacteristic
8C2×C4×D4×C31C2211yescharacteristic
9C31×#446—24no—
10C31×#432—22no—
11C31×#431C2212yes—
12C31×#423C2212yes—
13C2×C31×#101—21no—
14C31×#398C412yes—
15C31×#394C412yes—
16C31×#388—22no—
17C31×#382C2211yescharacteristic
18C31×#380—21no—
19C31×#343—21no—
20C31×D4⋊C8—24no—
21C22×Q8×C31D411yescharacteristic
22C22×D4×C31C2×C411yescharacteristic
23C23×C4×C31—21no—
24C2×M16×C31—22no—
25C31×C22⋊Q8—44no—
26C4×Q8×C31—22no—
27C4×Q8×C31—22no—
28C4×D4×C31—22no—
29C4×D4×C31—22no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31C2×C411yescharacteristic
33C2×C4⋊C4×C31C2×C412yes—
34C2×C4⋊C4×C31D411yescharacteristic
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31—21no—
38C2×C42×C31D412yes—
39C2×C42×C31C2311yescharacteristic
40C31×C4⋊C8—24no—
41C31×C4⋊C8—22no—
42C31×C4⋊C8—22no—
43C31×C4⋊C8—22no—
44C31×#101—42no—
45C31×C22⋊C8—22no—
46C31×#97—24no—
47C4×C8×C31D414yes—
48C31×#95—22no—
49C31×#95—21no—
50C31×#95C2×C412yes—
51C24×C31—21no—
52C2×Q8×C31—22no—
53C2×Q8×C31—21no—
54C2×Q8×C31—22no—
55C2×Q8×C31—21no—
56C2×D4×C31—22no—
57C2×D4×C31—42no—
58C22×C4×C31—22no—
59C22×C4×C31—21no—
60C22×C4×C31—42no—
61C22×C4×C31—42no—
62C22×C4×C31—41no—
63C22×C4×C31—41no—
64C22×C4×C31C22⋊C412yes—
65C22×C4×C31C22⋊C412yes—
66C22×C4×C31C22×C411yescharacteristic
67C22×C4×C31C2×D411yescharacteristic
68C22×C4×C31C2×D411yescharacteristic
69M16×C31—42no—
70M16×C31—42no—
71C2×C8×C31—24no—
72C2×C8×C31—42no—
73C4⋊C4×C31—24no—
74C4⋊C4×C31—22no—
75C4⋊C4×C31—22no—
76C4⋊C4×C31—44no—
77C4⋊C4×C31—42no—
78C22⋊C4×C31—44no—
79C22⋊C4×C31—44no—
80C22⋊C4×C31—41no—
81C22⋊C4×C31—41no—
82C42×C31—22no—
83C42×C31—22no—
84C42×C31C2×D412yes—
85C42×C31#4112yes—
86#9490C3111yesmaximal, characteristic, direct product factor, Sylow
87C23×C31—22no—
88C23×C31—41no—
89C23×C31—41no—
90C23×C31—41no—
91C23×C31—41no—
92C23×C31—41no—
93C23×C31—41no—
94C23×C31C2×C22⋊C411yescharacteristic
95Q8×C31—42no—
96Q8×C31—42no—
97D4×C31—24no—
98D4×C31—42no—
99C2×C4×C31—22no—
100C2×C4×C31—22no—
101C2×C4×C31—22no—
102C2×C4×C31—22no—
103C2×C4×C31—41no—
104C2×C4×C31—41no—
105C2×C4×C31—42no—
106C2×C4×C31—42no—
107C2×C4×C31—42no—
108C2×C4×C31—41no—
109C2×C4×C31—41no—
110C2×C4×C31—42no—
111C2×C4×C31—41no—
112C2×C4×C31—82no—
113C2×C4×C31—82no—
114C2×C4×C31C4×D412yes—
115C2×C4×C31#12011yescharacteristic
116C2×C4×C31#12112yes—
117C2×C4×C31#12311yescharacteristic
118C2×C4×C31AGL(1,ℤ/8)12yes—
119C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C31#13711yescharacteristic
121C8×C31—44no—
122C8×C31—82no—
123#2983C2×C3111yescharacteristic, complemented
124#2536C2×C3111yescharacteristic
125#1801C2×C3111yescharacteristic, complemented
126#1486C2×C3112yes—
127#1286C2×C3112yescomplemented
128C22×C31—21no—
129C22×C31—21no—
130C22×C31—42no—
131C22×C31—42no—
132C22×C31—42no—
133C22×C31—81no—
134C22×C31—81no—
135C22×C31—81no—
136C22×C31—81no—
137C22×C31#38611yescharacteristic
138C22×C31#41711yescharacteristic
139C22×C31#41811yescharacteristic
140C4×C31—22no—
141C4×C31—21no—
142C4×C31—21no—
143C4×C31—42no—
144C4×C31—42no—
145C4×C31—82no—
146C4×C31—81no—
147C4×C31#46812yes—
148C4×C31#46912yes—
149C2×C22⋊Q8—21no—
150C2×C4×Q8C22×C3111yescharacteristic
151C2×C4×D4C22×C3111yescharacteristic
152#446—24no—
153#432—22no—
154#431C22×C3112yes—
155#423C22×C3112yes—
156C2×#101—21no—
157#398C4×C3112yes—
158#394C4×C3112yes—
159#388—22no—
160#382C22×C3111yescharacteristic
161#380—21no—
162#343—21no—
163D4⋊C8—24no—
164C2×C31—21no—
165C2×C31—21no—
166C2×C31—82no—
167C2×C31#189111yescharacteristic
168C2×C31#189511yescharacteristic
169C2×C31#191211yescharacteristic
170C22×Q8D4×C3111yescharacteristic
171C22×D4C2×C4×C3111yescharacteristic
172C23×C4—21no—
173C2×M16—22no—
174C22⋊Q8—44no—
175C4×Q8—22no—
176C4×Q8—22no—
177C4×D4—22no—
178C4×D4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4C2×C4×C3111yescharacteristic
182C2×C4⋊C4C2×C4×C3112yes—
183C2×C4⋊C4D4×C3111yescharacteristic
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—21no—
187C2×C42D4×C3112yes—
188C2×C42C23×C3111yescharacteristic
189C4⋊C8—24no—
190C4⋊C8—22no—
191C4⋊C8—22no—
192C4⋊C8—22no—
193#101—42no—
194C22⋊C8—22no—
195#97—24no—
196C4×C8D4×C3114yes—
197#95—22no—
198#95—21no—
199#95C2×C4×C3112yes—
200C31#949011yescharacteristic, direct product factor, Sylow
201C24—21no—
202C2×Q8—22no—
203C2×Q8—21no—
204C2×Q8—22no—
205C2×Q8—21no—
206C2×D4—22no—
207C2×D4—42no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4C22⋊C4×C3112yes—
215C22×C4C22⋊C4×C3112yes—
216C22×C4C22×C4×C3111yescharacteristic
217C22×C4C2×D4×C3111yescharacteristic
218C22×C4C2×D4×C3111yescharacteristic
219M16—42no—
220M16—42no—
221C2×C8—24no—
222C2×C8—42no—
223C4⋊C4—24no—
224C4⋊C4—22no—
225C4⋊C4—22no—
226C4⋊C4—44no—
227C4⋊C4—42no—
228C22⋊C4—44no—
229C22⋊C4—44no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C42—22no—
233C42—22no—
234C42C2×D4×C3112yes—
235C42#41×C3112yes—
236C23—22no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23C2×C22⋊C4×C3111yescharacteristic
244Q8—42no—
245Q8—42no—
246D4—24no—
247D4—42no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4C4×D4×C3112yes—
264C2×C4C31×#12011yescharacteristic
265C2×C4C31×#12112yes—
266C2×C4C31×#12311yescharacteristic
267C2×C4C31×AGL(1,ℤ/8)12yes—
268C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
269C2×C4C31×#13711yescharacteristic
270C8—44no—
271C8—82no—
272C22—21no—
273C22—21no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—81no—
278C22—81no—
279C22—81no—
280C22—81no—
281C22C31×#38611yescharacteristic
282C22C31×#41711yescharacteristic
283C22C31×#41811yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—42no—
288C4—42no—
289C4—82no—
290C4—81no—
291C4C31×#46812yes—
292C4C31×#46912yes—
293C2—21no—
294C2—21no—
295C2—82no—
296C2C31×#189111yescharacteristic
297C2C31×#189511yescharacteristic
298C2C31×#191211yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31C2×C4
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×#2983C2semidirect
3. C31×#1801C2semidirect
5. C31×#1286C2semidirect
86. #9490C31direct (N × H)
123. #2983C2×C31semidirect
125. #1801C2×C31semidirect
127. #1286C2×C31semidirect
200. C31#9490direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29832
C31×#25362
C31×#18012
C31×#14862
C31×#12862
#949031