Finite Group Databasebeta

← C31×#10424 #21467183

Subgroups — C31×#10424 #21467183

Order 7936.

534 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2819C211yesmaximal, characteristic
2C31×#1959C212yesmaximal, complemented
3C31×#1847C211yesmaximal, characteristic, complemented
4C2×C31×#329C212yesmaximal, complemented
5C31×#1295C211yesmaximal, characteristic, complemented
6C2×C31×#124C2212yes—
7C2×C31×#107—21no—
8C2×C31×#106—21no—
9C2×C31×#103—22no—
10C2×C31×#102—22no—
11C2×C31×#97C2212yes—
12C2×C31×#97C2211yescharacteristic
13C31×#394—21no—
14C31×#394—21no—
15C31×#393—22no—
16C31×#392—22no—
17C31×#384C2211yescharacteristic
18C31×#382C2211yescharacteristic
19C31×#329—24no—
20C22×Q8×C31D412yes—
21C22×D4×C31—21no—
22C22×D4×C31—21no—
23C22×D4×C31D412yes—
24C22×C8×C31—21no—
25C22×C8×C31—22no—
26C31×#124—22no—
27C31×#124—22no—
28C31×#124—22no—
29C31×#124—22no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31D411yescharacteristic
33C2×C4⋊C4×C31D411yescharacteristic
34C2×C22⋊C4×C31—22no—
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31—22no—
38C2×C42×C31C2311yescharacteristic
39C31×#107—42no—
40C31×#106—42no—
41C31×#103—44no—
42C31×#102—44no—
43C31×#97—22no—
44C31×#97—21no—
45C31×#97—22no—
46C31×#97D412yescomplemented
47C31×#95—21no—
48C31×#95—21no—
49C31×#95—22no—
50C24×C31—22no—
51C2×Q8×C31—22no—
52C2×Q8×C31—22no—
53C2×Q8×C31—42no—
54C2×Q8×C31—42no—
55C2×D4×C31—22no—
56C2×D4×C31—22no—
57C2×D4×C31—42no—
58C2×D4×C31—42no—
59C2×D4×C31—82no—
60C2×D4×C31—81no—
61C2×D4×C31—81no—
62C2×D4×C31—82no—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—22no—
66C22×C4×C31—41no—
67C22×C4×C31C2×D412yes—
68C22×C4×C31C2×D411yescharacteristic
69C2×C8×C31—22no—
70C2×C8×C31—22no—
71C2×C8×C31—22no—
72C2×C8×C31—24no—
73C2×C8×C31—42no—
74C2×C8×C31—42no—
75C4⋊C4×C31—41no—
76C4⋊C4×C31—41no—
77C4⋊C4×C31—42no—
78C4⋊C4×C31—42no—
79C4⋊C4×C31—41no—
80C4⋊C4×C31—41no—
81C22⋊C4×C31—42no—
82C22⋊C4×C31—42no—
83C22⋊C4×C31—42no—
84C22⋊C4×C31—42no—
85C22⋊C4×C31—82no—
86C22⋊C4×C31—82no—
87C42×C31C2×D411yescharacteristic
88C42×C31#4111yescharacteristic
89C42×C31#4112yes—
90#10424C3111yesmaximal, characteristic, direct product factor, Sylow
91C23×C31—42no—
92C23×C31—42no—
93C23×C31—42no—
94C23×C31—42no—
95C23×C31—42no—
96C23×C31—42no—
97C23×C31—42no—
98C23×C31#12011yescharacteristic
99Q8×C31—44no—
100Q8×C31—82no—
101D4×C31—44no—
102D4×C31—82no—
103D4×C31—84no—
104D4×C31—84no—
105C2×C4×C31—21no—
106C2×C4×C31—22no—
107C2×C4×C31—22no—
108C2×C4×C31—21no—
109C2×C4×C31—42no—
110C2×C4×C31—42no—
111C2×C4×C31—42no—
112C2×C4×C31—41no—
113C2×C4×C31—41no—
114C2×C4×C31—42no—
115C2×C4×C31—42no—
116C2×C4×C31—81no—
117C2×C4×C31—82no—
118C2×C4×C31#12111yescharacteristic
119C2×C4×C31#12112yes—
120C2×C4×C31#12312yes—
121C2×C4×C31#12411yescharacteristic
122C8×C31—24no—
123C8×C31—44no—
124#2819C2×C3111yescharacteristic
125#1959C2×C3112yescomplemented
126#1847C2×C3111yescharacteristic, complemented
127C2×#329C2×C3112yescomplemented
128#1295C2×C3111yescharacteristic, complemented
129C22×C31—82no—
130C22×C31—82no—
131C22×C31—82no—
132C22×C31—82no—
133C22×C31—82no—
134C22×C31—82no—
135C22×C31—82no—
136C22×C31#39411yescharacteristic
137C22×C31#45311yescharacteristic
138C22×C31#45312yes—
139C22×C31#45512yes—
140C22×C31#45611yescharacteristic
141C4×C31—22no—
142C4×C31—22no—
143C4×C31—21no—
144C4×C31—21no—
145C4×C31—81no—
146C4×C31—81no—
147C4×C31—82no—
148C4×C31—161no—
149C2×#124C22×C3112yes—
150C2×#107—21no—
151C2×#106—21no—
152C2×#103—22no—
153C2×#102—22no—
154C2×#97C22×C3112yes—
155C2×#97C22×C3111yescharacteristic
156#394—21no—
157#394—21no—
158#393—22no—
159#392—22no—
160#384C22×C3111yescharacteristic
161#382C22×C3111yescharacteristic
162#329—24no—
163C2×C31—162no—
164C2×C31#165511yescharacteristic
165C2×C31#165911yescharacteristic
166C2×C31#166112yes—
167C2×C31#203712yes—
168C2×C31#203911yescharacteristic
169C22×Q8D4×C3112yes—
170C22×D4—21no—
171C22×D4—21no—
172C22×D4D4×C3112yes—
173C22×C8—21no—
174C22×C8—22no—
175#124—22no—
176#124—22no—
177#124—22no—
178#124—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4D4×C3111yescharacteristic
182C2×C4⋊C4D4×C3111yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C42C23×C3111yescharacteristic
188#107—42no—
189#106—42no—
190#103—44no—
191#102—44no—
192#97—22no—
193#97—21no—
194#97—22no—
195#97D4×C3112yescomplemented
196#95—21no—
197#95—21no—
198#95—22no—
199C31#1042411yescharacteristic, direct product factor, Sylow
200C24—22no—
201C2×Q8—22no—
202C2×Q8—22no—
203C2×Q8—42no—
204C2×Q8—42no—
205C2×D4—22no—
206C2×D4—22no—
207C2×D4—42no—
208C2×D4—42no—
209C2×D4—82no—
210C2×D4—81no—
211C2×D4—81no—
212C2×D4—82no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—41no—
217C22×C4C2×D4×C3112yes—
218C22×C4C2×D4×C3111yescharacteristic
219C2×C8—22no—
220C2×C8—22no—
221C2×C8—22no—
222C2×C8—24no—
223C2×C8—42no—
224C2×C8—42no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C22⋊C4—42no—
232C22⋊C4—42no—
233C22⋊C4—42no—
234C22⋊C4—42no—
235C22⋊C4—82no—
236C22⋊C4—82no—
237C42C2×D4×C3111yescharacteristic
238C42#41×C3111yescharacteristic
239C42#41×C3112yes—
240C23—42no—
241C23—42no—
242C23—42no—
243C23—42no—
244C23—42no—
245C23—42no—
246C23—42no—
247C23C31×#12011yescharacteristic
248Q8—44no—
249Q8—82no—
250D4—44no—
251D4—82no—
252D4—84no—
253D4—84no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—81no—
266C2×C4—82no—
267C2×C4C31×#12111yescharacteristic
268C2×C4C31×#12112yes—
269C2×C4C31×#12312yes—
270C2×C4C31×#12411yescharacteristic
271C8—24no—
272C8—44no—
273C22—82no—
274C22—82no—
275C22—82no—
276C22—82no—
277C22—82no—
278C22—82no—
279C22—82no—
280C22C31×#39411yescharacteristic
281C22C31×#45311yescharacteristic
282C22C31×#45312yes—
283C22C31×#45512yes—
284C22C31×#45611yescharacteristic
285C4—22no—
286C4—22no—
287C4—21no—
288C4—21no—
289C4—81no—
290C4—81no—
291C4—82no—
292C4—161no—
293C2—162no—
294C2C31×#165511yescharacteristic
295C2C31×#165911yescharacteristic
296C2C31×#166112yes—
297C2C31×#203712yes—
298C2C31×#203911yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC31×#2819C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1959C2semidirect
3. C31×#1847C2semidirect
4. C2×C31×#329C2semidirect
5. C31×#1295C2semidirect
46. C31×#97D4semidirect
90. #10424C31direct (N × H)
125. #1959C2×C31semidirect
126. #1847C2×C31semidirect
127. C2×#329C2×C31semidirect
128. #1295C2×C31semidirect
195. #97D4×C31semidirect
199. C31#10424direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28192
C31×#19592
C31×#18472
C2×C31×#3292
C31×#12952
#1042431