Finite Group Databasebeta

← C31×#9405 #21466164

Subgroups — C31×#9405 #21466164

Order 7936.

706 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 138 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×#2975C211yesmaximal, characteristic, complemented
2C31×#2541C211yesmaximal, characteristic
3C31×#1800C211yesmaximal, characteristic, complemented
4C31×#1545C212yesmaximal, complemented
5C31×#1303C212yesmaximal, complemented
6C2×C31×#127—21no—
7C2×C31×#127C2211yescharacteristic
8C2×C31×#121—22no—
9C2×C4×D4×C31C2211yescharacteristic
10C31×#436—24no—
11C31×#431C2212yes—
12C31×#423C2212yes—
13C2×C31×#100—21no—
14C31×#407—22no—
15C31×#392C414yes—
16C31×#390—21no—
17C4×C4⋊C4×C31C2211yescharacteristic
18C31×#343—21no—
19C31×#331—24no—
20C22×D4×C31—24no—
21C22×D4×C31—21no—
22C22×D4×C31—21no—
23C22×D4×C31C2×C412yes—
24C22×D4×C31D411yescharacteristic
25C23×C4×C31D412yes—
26C2×M16×C31—24no—
27C2×M16×C31—22no—
28C31×#127—22no—
29C31×#127—22no—
30C31×#127—44no—
31C31×#121—48no—
32C4×D4×C31—22no—
33C4×D4×C31—22no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31D411yescharacteristic
36C2×C22⋊C4×C31—24no—
37C2×C22⋊C4×C31C2×C412yes—
38C2×C42×C31—21no—
39C2×C42×C31C2311yescharacteristic
40C31×C4⋊C8—22no—
41C31×C4⋊C8—22no—
42C31×C4⋊C8D414yescomplemented
43C31×#100—42no—
44C31×C22⋊C8—24no—
45C31×C22⋊C8—22no—
46C4×C8×C31—22no—
47C31×#95C2×C412yes—
48C24×C31—22no—
49C24×C31C22⋊C412yes—
50C2×D4×C31—24no—
51C2×D4×C31—22no—
52C2×D4×C31—21no—
53C2×D4×C31—22no—
54C2×D4×C31—21no—
55C2×D4×C31—44no—
56C2×D4×C31—48no—
57C2×D4×C31—48no—
58C2×D4×C31—41no—
59C2×D4×C31—42no—
60C2×D4×C31—41no—
61C2×D4×C31—42no—
62C2×D4×C31—41no—
63C2×D4×C31—41no—
64C2×D4×C31—84no—
65C2×D4×C31—82no—
66C22×C4×C31—22no—
67C22×C4×C31—22no—
68C22×C4×C31—22no—
69C22×C4×C31—44no—
70C22×C4×C31C22⋊C412yes—
71C22×C4×C31C22×C411yescharacteristic
72C22×C4×C31C2×D411yescharacteristic
73C22×C4×C31C2×D411yescharacteristic
74M16×C31—42no—
75M16×C31—42no—
76M16×C31—84no—
77C2×C8×C31—24no—
78C2×C8×C31—42no—
79C4⋊C4×C31—24no—
80C4⋊C4×C31—22no—
81C22⋊C4×C31—24no—
82C22⋊C4×C31—48no—
83C42×C31—42no—
84C42×C31C2×D412yes—
85C42×C31#4112yes—
86#9405C3111yesmaximal, characteristic, direct product factor, Sylow
87C23×C31—22no—
88C23×C31—22no—
89C23×C31—22no—
90C23×C31—42no—
91C23×C31—42no—
92C23×C31—44no—
93C23×C31—44no—
94C23×C31—42no—
95C23×C31—42no—
96C23×C31—42no—
97C23×C31C2×C22⋊C411yescharacteristic
98D4×C31—42no—
99D4×C31—42no—
100D4×C31—84no—
101D4×C31—82no—
102D4×C31—816no—
103D4×C31—82no—
104D4×C31—82no—
105D4×C31—82no—
106C2×C4×C31—22no—
107C2×C4×C31—24no—
108C2×C4×C31—22no—
109C2×C4×C31—41no—
110C2×C4×C31—42no—
111C2×C4×C31—42no—
112C2×C4×C31—44no—
113C2×C4×C31—42no—
114C2×C4×C31—82no—
115C2×C4×C31C4×D412yes—
116C2×C4×C31#12011yescharacteristic
117C2×C4×C31#12112yes—
118C2×C4×C31#12311yescharacteristic
119C2×C4×C31AGL(1,ℤ/8)12yes—
120C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C31#13711yescharacteristic
122C8×C31—44no—
123C8×C31—82no—
124#2975C2×C3111yescharacteristic, complemented
125#2541C2×C3111yescharacteristic
126#1800C2×C3111yescharacteristic, complemented
127#1545C2×C3112yescomplemented
128#1303C2×C3112yescomplemented
129C22×C31—21no—
130C22×C31—21no—
131C22×C31—44no—
132C22×C31—42no—
133C22×C31—42no—
134C22×C31—42no—
135C22×C31—82no—
136C22×C31—84no—
137C22×C31—84no—
138C22×C31—82no—
139C22×C31—82no—
140C22×C31—82no—
141C22×C31#38611yescharacteristic
142C22×C31#41711yescharacteristic
143C22×C31#41811yescharacteristic
144C4×C31—21no—
145C4×C31—22no—
146C4×C31—44no—
147C4×C31—42no—
148C4×C31#45312yes—
149C4×C31#46812yes—
150C4×C31#46912yes—
151C2×#127—21no—
152C2×#127C22×C3111yescharacteristic
153C2×#121—22no—
154C2×C4×D4C22×C3111yescharacteristic
155#436—24no—
156#431C22×C3112yes—
157#423C22×C3112yes—
158C2×#100—21no—
159#407—22no—
160#392C4×C3114yes—
161#390—21no—
162C4×C4⋊C4C22×C3111yescharacteristic
163#343—21no—
164#331—24no—
165C2×C31—21no—
166C2×C31—21no—
167C2×C31—82no—
168C2×C31—162no—
169C2×C31#188711yescharacteristic
170C2×C31#189511yescharacteristic
171C2×C31#191411yescharacteristic
172C22×D4—24no—
173C22×D4—21no—
174C22×D4—21no—
175C22×D4C2×C4×C3112yes—
176C22×D4D4×C3111yescharacteristic
177C23×C4D4×C3112yes—
178C2×M16—24no—
179C2×M16—22no—
180#127—22no—
181#127—22no—
182#127—44no—
183#121—48no—
184C4×D4—22no—
185C4×D4—22no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4D4×C3111yescharacteristic
188C2×C22⋊C4—24no—
189C2×C22⋊C4C2×C4×C3112yes—
190C2×C42—21no—
191C2×C42C23×C3111yescharacteristic
192C4⋊C8—22no—
193C4⋊C8—22no—
194C4⋊C8D4×C3114yescomplemented
195#100—42no—
196C22⋊C8—24no—
197C22⋊C8—22no—
198C4×C8—22no—
199#95C2×C4×C3112yes—
200C31#940511yescharacteristic, direct product factor, Sylow
201C24—22no—
202C24C22⋊C4×C3112yes—
203C2×D4—24no—
204C2×D4—22no—
205C2×D4—21no—
206C2×D4—22no—
207C2×D4—21no—
208C2×D4—44no—
209C2×D4—48no—
210C2×D4—48no—
211C2×D4—41no—
212C2×D4—42no—
213C2×D4—41no—
214C2×D4—42no—
215C2×D4—41no—
216C2×D4—41no—
217C2×D4—84no—
218C2×D4—82no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—44no—
223C22×C4C22⋊C4×C3112yes—
224C22×C4C22×C4×C3111yescharacteristic
225C22×C4C2×D4×C3111yescharacteristic
226C22×C4C2×D4×C3111yescharacteristic
227M16—42no—
228M16—42no—
229M16—84no—
230C2×C8—24no—
231C2×C8—42no—
232C4⋊C4—24no—
233C4⋊C4—22no—
234C22⋊C4—24no—
235C22⋊C4—48no—
236C42—42no—
237C42C2×D4×C3112yes—
238C42#41×C3112yes—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—42no—
243C23—42no—
244C23—44no—
245C23—44no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23C2×C22⋊C4×C3111yescharacteristic
250D4—42no—
251D4—42no—
252D4—84no—
253D4—82no—
254D4—816no—
255D4—82no—
256D4—82no—
257D4—82no—
258C2×C4—22no—
259C2×C4—24no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—44no—
265C2×C4—42no—
266C2×C4—82no—
267C2×C4C4×D4×C3112yes—
268C2×C4C31×#12011yescharacteristic
269C2×C4C31×#12112yes—
270C2×C4C31×#12311yescharacteristic
271C2×C4C31×AGL(1,ℤ/8)12yes—
272C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
273C2×C4C31×#13711yescharacteristic
274C8—44no—
275C8—82no—
276C22—21no—
277C22—21no—
278C22—44no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—82no—
283C22—84no—
284C22—84no—
285C22—82no—
286C22—82no—
287C22—82no—
288C22C31×#38611yescharacteristic
289C22C31×#41711yescharacteristic
290C22C31×#41811yescharacteristic
291C4—21no—
292C4—22no—
293C4—44no—
294C4—42no—
295C4C31×#45312yes—
296C4C31×#46812yes—
297C4C31×#46912yes—
298C2—21no—
299C2—21no—
300C2—82no—
301C2—162no—
302C2C31×#188711yescharacteristic
303C2C31×#189511yescharacteristic
304C2C31×#191411yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#2541C2
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×#2975C2semidirect
3. C31×#1800C2semidirect
4. C31×#1545C2semidirect
5. C31×#1303C2semidirect
42. C31×C4⋊C8D4semidirect
86. #9405C31direct (N × H)
124. #2975C2×C31semidirect
126. #1800C2×C31semidirect
127. #1545C2×C31semidirect
128. #1303C2×C31semidirect
194. C4⋊C8D4×C31semidirect
200. C31#9405direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29752
C31×#25412
C31×#18002
C31×#15452
C31×#13032
#940531