Finite Group Databasebeta

← C31×#12803 #21469562

Subgroups — C31×#12803 #21469562

Order 7936.

480 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2326C211yesmaximal, characteristic
2C2×C31×#355C212yesmaximal
3C31×#1801C212yesmaximal, complemented
4C31×#1394C212yesmaximal, complemented
5C2×C31×#124C2211yescharacteristic
6C2×C4×Q8×C31C2211yescharacteristic
7C2×C4×D4×C31C411yescharacteristic
8C31×#423—22no—
9C2×C31×#101C2214yes—
10C31×#391C2211yescharacteristic
11C31×#390C411yescharacteristic
12C31×#388—22no—
13C31×#385—22no—
14C31×#384C411yescharacteristic
15C31×#376C411yescharacteristic
16C31×#355—24no—
17C31×#343—22no—
18C22×Q8×C31C2311yescharacteristic
19C22×D4×C31C2×C411yescharacteristic
20C23×C4×C31—21no—
21C2×M16×C31—24no—
22C31×#124—22no—
23C31×#124D412yes—
24C31×#124Q812yes—
25C4×Q8×C31—42no—
26C4×D4×C31—42no—
27C2×C4⋊C4×C31—22no—
28C2×C4⋊C4×C31C2×C411yescharacteristic
29C2×C4⋊C4×C31C2×C411yescharacteristic
30C2×C4⋊C4×C31D412yes—
31C2×C22⋊C4×C31—22no—
32C2×C22⋊C4×C31—21no—
33C2×C22⋊C4×C31—22no—
34C2×C42×C31C2×C411yescharacteristic
35C2×C42×C31C2×C411yescharacteristic
36C2×C42×C31C2×C411yescharacteristic
37C2×C42×C31D412yes—
38C31×C4⋊C8—44no—
39C31×#101—24no—
40C31×#101—24no—
41C31×#95—21no—
42C31×#95—21no—
43C31×#95—22no—
44C24×C31—21no—
45C2×Q8×C31—41no—
46C2×Q8×C31—41no—
47C2×Q8×C31C2×D411yescharacteristic
48C2×Q8×C31C2×Q811yescharacteristic
49C2×Q8×C31#4112yes—
50C2×D4×C31—21no—
51C2×D4×C31—41no—
52C2×D4×C31—41no—
53C2×D4×C31C4⋊C412yes—
54C22×C4×C31—21no—
55C22×C4×C31—21no—
56C22×C4×C31—21no—
57C22×C4×C31—42no—
58C22×C4×C31—82no—
59C22×C4×C31C22⋊C411yescharacteristic
60C22×C4×C31C22⋊C412yes—
61C22×C4×C31C22⋊C411yescharacteristic
62C22×C4×C31C22×C411yescharacteristic
63C22×C4×C31C2×D412yes—
64M16×C31—44no—
65M16×C31—44no—
66C2×C8×C31—44no—
67C4⋊C4×C31—41no—
68C4⋊C4×C31—42no—
69C4⋊C4×C31—41no—
70C4⋊C4×C31—82no—
71C22⋊C4×C31—24no—
72C22⋊C4×C31—24no—
73C22⋊C4×C31—42no—
74C22⋊C4×C31—82no—
75C42×C31—24no—
76C42×C31—22no—
77C42×C31—21no—
78C42×C31—41no—
79C42×C31C4⋊C412yes—
80#12803C3111yesmaximal, characteristic, direct product factor, Sylow
81C23×C31—22no—
82C23×C31—42no—
83C23×C31—42no—
84C23×C31—41no—
85C23×C31—41no—
86C23×C31C2×C22⋊C411yescharacteristic
87Q8×C31—41no—
88Q8×C31—41no—
89Q8×C31—42no—
90D4×C31—42no—
91D4×C31—42no—
92C2×C4×C31—21no—
93C2×C4×C31—22no—
94C2×C4×C31—21no—
95C2×C4×C31—22no—
96C2×C4×C31—22no—
97C2×C4×C31—21no—
98C2×C4×C31—22no—
99C2×C4×C31—41no—
100C2×C4×C31—41no—
101C2×C4×C31—41no—
102C2×C4×C31—42no—
103C2×C4×C31—41no—
104C2×C4×C31—41no—
105C2×C4×C31—42no—
106C2×C4×C31—41no—
107C2×C4×C31—41no—
108C2×C4×C31—41no—
109C2×C4×C31—84no—
110C2×C4×C31#9912yes—
111C2×C4×C31C2×C4⋊C411yescharacteristic
112C2×C4×C31#11711yescharacteristic
113C2×C4×C31#12112yes—
114C2×C4×C31C22⋊Q812yes—
115C8×C31—84no—
116#2326C2×C3111yescharacteristic
117C2×#355C2×C3112yes—
118#1801C2×C3112yescomplemented
119#1394C2×C3112yescomplemented
120C22×C31—21no—
121C22×C31—21no—
122C22×C31—44no—
123C22×C31—42no—
124C22×C31—82no—
125C22×C31—81no—
126C22×C31—81no—
127C22×C31#38011yescharacteristic
128C22×C31C2×#9911yescharacteristic
129C22×C31#41011yescharacteristic
130C4×C31—22no—
131C4×C31—21no—
132C4×C31—21no—
133C4×C31—22no—
134C4×C31—22no—
135C4×C31—42no—
136C4×C31—42no—
137C4×C31—41no—
138C4×C31—81no—
139C4×C31—81no—
140C2×#124C22×C3111yescharacteristic
141C2×C4×Q8C22×C3111yescharacteristic
142C2×C4×D4C4×C3111yescharacteristic
143#423—22no—
144C2×#101C22×C3114yes—
145#391C22×C3111yescharacteristic
146#390C4×C3111yescharacteristic
147#388—22no—
148#385—22no—
149#384C4×C3111yescharacteristic
150#376C4×C3111yescharacteristic
151#355—24no—
152#343—22no—
153C2×C31—21no—
154C2×C31—21no—
155C2×C31—82no—
156C2×C31#179911yescharacteristic
157C2×C31#213311yescharacteristic
158C2×C31#213411yescharacteristic
159C22×Q8C23×C3111yescharacteristic
160C22×D4C2×C4×C3111yescharacteristic
161C23×C4—21no—
162C2×M16—24no—
163#124—22no—
164#124D4×C3112yes—
165#124Q8×C3112yes—
166C4×Q8—42no—
167C4×D4—42no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4C2×C4×C3111yescharacteristic
170C2×C4⋊C4C2×C4×C3111yescharacteristic
171C2×C4⋊C4D4×C3112yes—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—21no—
174C2×C22⋊C4—22no—
175C2×C42C2×C4×C3111yescharacteristic
176C2×C42C2×C4×C3111yescharacteristic
177C2×C42C2×C4×C3111yescharacteristic
178C2×C42D4×C3112yes—
179C4⋊C8—44no—
180#101—24no—
181#101—24no—
182#95—21no—
183#95—21no—
184#95—22no—
185C31#1280311yescharacteristic, direct product factor, Sylow
186C24—21no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8C2×D4×C3111yescharacteristic
190C2×Q8C2×Q8×C3111yescharacteristic
191C2×Q8#41×C3112yes—
192C2×D4—21no—
193C2×D4—41no—
194C2×D4—41no—
195C2×D4C4⋊C4×C3112yes—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—42no—
200C22×C4—82no—
201C22×C4C22⋊C4×C3111yescharacteristic
202C22×C4C22⋊C4×C3112yes—
203C22×C4C22⋊C4×C3111yescharacteristic
204C22×C4C22×C4×C3111yescharacteristic
205C22×C4C2×D4×C3112yes—
206M16—44no—
207M16—44no—
208C2×C8—44no—
209C4⋊C4—41no—
210C4⋊C4—42no—
211C4⋊C4—41no—
212C4⋊C4—82no—
213C22⋊C4—24no—
214C22⋊C4—24no—
215C22⋊C4—42no—
216C22⋊C4—82no—
217C42—24no—
218C42—22no—
219C42—21no—
220C42—41no—
221C42C4⋊C4×C3112yes—
222C23—22no—
223C23—42no—
224C23—42no—
225C23—41no—
226C23—41no—
227C23C2×C22⋊C4×C3111yescharacteristic
228Q8—41no—
229Q8—41no—
230Q8—42no—
231D4—42no—
232D4—42no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—84no—
251C2×C4C31×#9912yes—
252C2×C4C2×C4⋊C4×C3111yescharacteristic
253C2×C4C31×#11711yescharacteristic
254C2×C4C31×#12112yes—
255C2×C4C31×C22⋊Q812yes—
256C8—84no—
257C22—21no—
258C22—21no—
259C22—44no—
260C22—42no—
261C22—82no—
262C22—81no—
263C22—81no—
264C22C31×#38011yescharacteristic
265C22C2×C31×#9911yescharacteristic
266C22C31×#41011yescharacteristic
267C4—22no—
268C4—21no—
269C4—21no—
270C4—22no—
271C4—22no—
272C4—42no—
273C4—41no—
274C4—42no—
275C4—81no—
276C4—81no—
277C2—21no—
278C2—21no—
279C2—82no—
280C2C31×#179911yescharacteristic
281C2C31×#213311yescharacteristic
282C2C31×#213411yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC22×Q8C23×C31
prime radicalC22×D4×C31C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1801C2semidirect
4. C31×#1394C2semidirect
80. #12803C31direct (N × H)
118. #1801C2×C31semidirect
119. #1394C2×C31semidirect
185. C31#12803direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23262
C2×C31×#3552
C31×#18012
C31×#13942
#1280331