Finite Group Databasebeta

← C31×#10254 #21467013

Subgroups — C31×#10254 #21467013

Order 7936.

634 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3245C211yesmaximal, characteristic, complemented
2C31×#3036C212yesmaximal, complemented
3C31×#1954C211yesmaximal, characteristic, complemented
4C31×#1492C212yesmaximal, complemented
5C31×#1292C211yesmaximal, characteristic, complemented
6C2×C31×AGL(1,ℤ/8)—22no—
7C31×#532C2212yes—
8C2×C4×D4×C31C2211yescharacteristic
9C31×#474—22no—
10C31×#466—22no—
11C31×#463—24no—
12C31×#461—22no—
13C31×#459—22no—
14C31×#459—22no—
15C31×#423C2212yes—
16C2×C31×C4⋊C8C2211yescharacteristic
17C31×#417—22no—
18C2×C31×C22⋊C8—22no—
19C2×C4×C8×C31C2211yescharacteristic
20C31×D4⋊C8—24no—
21C2×#41×C31—22no—
22C22×D4×C31D411yescharacteristic
23C23×C4×C31—21no—
24C31×AGL(1,ℤ/8)—44no—
25C31×AGL(1,ℤ/8)—44no—
26C2×SD16×C31—24no—
27C2×D8×C31—24no—
28C2×D8×C31—22no—
29C2×M16×C31—22no—
30C22×C8×C31—21no—
31C22×C8×C31D412yes—
32C31×C4⋊Q8D412yes—
33C31×#127D412yes—
34C31×#124—22no—
35C31×#121—22no—
36C31×#121—22no—
37C4×D4×C31—22no—
38C4×D4×C31—22no—
39C4×D4×C31—22no—
40C4×D4×C31—22no—
41C2×C4⋊C4×C31D411yescharacteristic
42C2×C22⋊C4×C31—21no—
43C2×C42×C31C2311yescharacteristic
44C31×#107—22no—
45C31×C4⋊C8—22no—
46C31×C4⋊C8—22no—
47C31×C4⋊C8D414yes—
48C31×#103—24no—
49C31×#102—24no—
50C31×#102—24no—
51C31×C22⋊C8—44no—
52C4×C8×C31—22no—
53C24×C31—21no—
54#41×C31—42no—
55#41×C31—42no—
56#41×C31—42no—
57#41×C31—42no—
58C2×Q8×C31—22no—
59C2×D4×C31—22no—
60C2×D4×C31—22no—
61C2×D4×C31—22no—
62C2×D4×C31—22no—
63C2×D4×C31—21no—
64C2×D4×C31—22no—
65C2×D4×C31—42no—
66C2×D4×C31D812yescomplemented
67C22×C4×C31—21no—
68C22×C4×C31—42no—
69C22×C4×C31—42no—
70C22×C4×C31—41no—
71C22×C4×C31—42no—
72C22×C4×C31—41no—
73C22×C4×C31C2×D411yescharacteristic
74C22×C4×C31C2×D411yescharacteristic
75C22×C4×C31#4111yescharacteristic
76SD16×C31—48no—
77D8×C31—48no—
78D8×C31—82no—
79M16×C31—42no—
80M16×C31—42no—
81C2×C8×C31—22no—
82C2×C8×C31—22no—
83C2×C8×C31—24no—
84C2×C8×C31—41no—
85C2×C8×C31—41no—
86C2×C8×C31—42no—
87C4⋊C4×C31—22no—
88C4⋊C4×C31—22no—
89C4⋊C4×C31—22no—
90C22⋊C4×C31—42no—
91C22⋊C4×C31—42no—
92C22⋊C4×C31—42no—
93C42×C31C2×D412yes—
94C42×C31C2×D412yes—
95#10254C3111yesmaximal, characteristic, direct product factor, Sylow
96C23×C31—22no—
97C23×C31—42no—
98C23×C31—42no—
99C23×C31—41no—
100C23×C31—41no—
101C23×C31—42no—
102C23×C31#12111yescharacteristic
103Q8×C31—42no—
104Q8×C31—42no—
105D4×C31—24no—
106D4×C31—44no—
107D4×C31—42no—
108D4×C31—42no—
109D4×C31—42no—
110D4×C31—42no—
111D4×C31—42no—
112D4×C31—82no—
113D4×C31—82no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—41no—
117C2×C4×C31—42no—
118C2×C4×C31—41no—
119C2×C4×C31—42no—
120C2×C4×C31—82no—
121C2×C4×C31—82no—
122C2×C4×C31—82no—
123C2×C4×C31—81no—
124C2×C4×C31—81no—
125C2×C4×C31#12012yes—
126C2×C4×C31#12011yescharacteristic
127C2×C4×C31#12112yes—
128C2×C4×C31#12711yescharacteristic
129C2×C4×C31C2×D811yescharacteristic
130C2×C4×C31#13511yescharacteristic
131C2×C4×C31AGL(1,ℤ/8)12yes—
132C8×C31—42no—
133C8×C31—44no—
134C8×C31—42no—
135#3245C2×C3111yescharacteristic, complemented
136#3036C2×C3112yescomplemented
137#1954C2×C3111yescharacteristic, complemented
138#1492C2×C3112yescomplemented
139#1292C2×C3111yescharacteristic, complemented
140C22×C31—21no—
141C22×C31—21no—
142C22×C31—44no—
143C22×C31—42no—
144C22×C31—82no—
145C22×C31—81no—
146C22×C31—81no—
147C22×C31—82no—
148C22×C31—82no—
149C22×C31—82no—
150C22×C31#39211yescharacteristic
151C22×C31#46611yescharacteristic
152C22×C31#46911yescharacteristic
153C4×C31—21no—
154C4×C31—22no—
155C4×C31—82no—
156C4×C31—81no—
157C4×C31#44712yes—
158C4×C31#44912yes—
159C4×C31#45311yescharacteristic
160C4×C31#45411yescharacteristic
161C2×AGL(1,ℤ/8)—22no—
162#532C22×C3112yes—
163C2×C4×D4C22×C3111yescharacteristic
164#474—22no—
165#466—22no—
166#463—24no—
167#461—22no—
168#459—22no—
169#459—22no—
170#423C22×C3112yes—
171C2×C4⋊C8C22×C3111yescharacteristic
172#417—22no—
173C2×C22⋊C8—22no—
174C2×C4×C8C22×C3111yescharacteristic
175D4⋊C8—24no—
176C2×C31—21no—
177C2×C31—21no—
178C2×C31—82no—
179C2×C31—162no—
180C2×C31#199911yescharacteristic
181C2×C31#200611yescharacteristic
182C2×C31#201711yescharacteristic
183C2×#41—22no—
184C22×D4D4×C3111yescharacteristic
185C23×C4—21no—
186AGL(1,ℤ/8)—44no—
187AGL(1,ℤ/8)—44no—
188C2×SD16—24no—
189C2×D8—24no—
190C2×D8—22no—
191C2×M16—22no—
192C22×C8—21no—
193C22×C8D4×C3112yes—
194C4⋊Q8D4×C3112yes—
195#127D4×C3112yes—
196#124—22no—
197#121—22no—
198#121—22no—
199C4×D4—22no—
200C4×D4—22no—
201C4×D4—22no—
202C4×D4—22no—
203C2×C4⋊C4D4×C3111yescharacteristic
204C2×C22⋊C4—21no—
205C2×C42C23×C3111yescharacteristic
206#107—22no—
207C4⋊C8—22no—
208C4⋊C8—22no—
209C4⋊C8D4×C3114yes—
210#103—24no—
211#102—24no—
212#102—24no—
213C22⋊C8—44no—
214C4×C8—22no—
215C31#1025411yescharacteristic, direct product factor, Sylow
216C24—21no—
217#41—42no—
218#41—42no—
219#41—42no—
220#41—42no—
221C2×Q8—22no—
222C2×D4—22no—
223C2×D4—22no—
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—21no—
227C2×D4—22no—
228C2×D4—42no—
229C2×D4D8×C3112yescomplemented
230C22×C4—21no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—41no—
234C22×C4—42no—
235C22×C4—41no—
236C22×C4C2×D4×C3111yescharacteristic
237C22×C4C2×D4×C3111yescharacteristic
238C22×C4#41×C3111yescharacteristic
239SD16—48no—
240D8—48no—
241D8—82no—
242M16—42no—
243M16—42no—
244C2×C8—22no—
245C2×C8—22no—
246C2×C8—24no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—42no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C42C2×D4×C3112yes—
257C42C2×D4×C3112yes—
258C23—22no—
259C23—42no—
260C23—42no—
261C23—41no—
262C23—41no—
263C23—42no—
264C23C31×#12111yescharacteristic
265Q8—42no—
266Q8—42no—
267D4—24no—
268D4—44no—
269D4—42no—
270D4—42no—
271D4—42no—
272D4—42no—
273D4—42no—
274D4—82no—
275D4—82no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4C31×#12012yes—
288C2×C4C31×#12011yescharacteristic
289C2×C4C31×#12112yes—
290C2×C4C31×#12711yescharacteristic
291C2×C4C2×D8×C3111yescharacteristic
292C2×C4C31×#13511yescharacteristic
293C2×C4C31×AGL(1,ℤ/8)12yes—
294C8—42no—
295C8—44no—
296C8—42no—
297C22—21no—
298C22—21no—
299C22—44no—
300C22—42no—
301C22—82no—
302C22—81no—
303C22—81no—
304C22—82no—
305C22—82no—
306C22—82no—
307C22C31×#39211yescharacteristic
308C22C31×#46611yescharacteristic
309C22C31×#46911yescharacteristic
310C4—21no—
311C4—22no—
312C4—82no—
313C4—81no—
314C4C31×#44712yes—
315C4C31×#44912yes—
316C4C31×#45311yescharacteristic
317C4C31×#45411yescharacteristic
318C2—21no—
319C2—21no—
320C2—82no—
321C2—162no—
322C2C31×#199911yescharacteristic
323C2C31×#200611yescharacteristic
324C2C31×#201711yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC2×C42C23×C31
LCSG ▷ C2×C42 ▷ 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×#3245C2semidirect
2. C31×#3036C2semidirect
3. C31×#1954C2semidirect
4. C31×#1492C2semidirect
5. C31×#1292C2semidirect
66. C2×D4×C31D8semidirect
95. #10254C31direct (N × H)
135. #3245C2×C31semidirect
136. #3036C2×C31semidirect
137. #1954C2×C31semidirect
138. #1492C2×C31semidirect
139. #1292C2×C31semidirect
215. C31#10254direct (N × H)
229. C2×D4D8×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#32452
C31×#30362
C31×#19542
C31×#14922
C31×#12922
#1025431