Finite Group Databasebeta

← C31×#12699 #21469458

Subgroups — C31×#12699 #21469458

Order 7936.

1146 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1146 conjugacy classes of subgroups — too many to draw. Only its 158 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
1C22×C31×#124C211yesmaximal, characteristic
2C2×C31×#355C214yesmaximal, complemented
3C31×#1784C212yesmaximal, complemented
4C23×Q8×C31C2211yescharacteristic
5C23×D4×C31C411yescharacteristic
6C2×C31×#124—22no—
7C2×C31×#124—28no—
8C2×C31×#124C412yes—
9C2×C31×#124C2212yes—
10C22×C22⋊C4×C31—22no—
11C22×C42×C31C411yescharacteristic
12C2×C31×#101—22no—
13C2×C31×#101C2214yescomplemented
14C31×#407—22no—
15C31×#355—28no—
16C25×C31—21no—
17C22×Q8×C31—24no—
18C22×Q8×C31—42no—
19C22×Q8×C31—42no—
20C22×Q8×C31C2×C411yescharacteristic
21C22×Q8×C31D412yes—
22C22×Q8×C31C2311yescharacteristic
23C22×D4×C31—24no—
24C22×D4×C31—21no—
25C22×D4×C31—42no—
26C22×D4×C31—42no—
27C22×D4×C31C2×C412yes—
28C23×C4×C31—21no—
29C23×C4×C31C2×C411yescharacteristic
30C23×C4×C31D412yes—
31C2×M16×C31—24no—
32C31×#124—216no—
33C31×#124—24no—
34C31×#124—24no—
35C31×#124—24no—
36C31×#124D418yes—
37C2×C22⋊C4×C31—216no—
38C2×C22⋊C4×C31—24no—
39C2×C22⋊C4×C31—24no—
40C2×C42×C31—21no—
41C2×C42×C31—24no—
42C2×C42×C31C2×C412yes—
43C31×#101—28no—
44C31×#101—44no—
45C31×C22⋊C8—44no—
46C24×C31—24no—
47C24×C31—22no—
48C24×C31—42no—
49C24×C31—48no—
50C24×C31—42no—
51C24×C31C22⋊C411yescharacteristic
52C2×Q8×C31—24no—
53C2×Q8×C31—22no—
54C2×Q8×C31—24no—
55C2×Q8×C31—41no—
56C2×Q8×C31—41no—
57C2×Q8×C31—42no—
58C2×Q8×C31—41no—
59C2×Q8×C31—41no—
60C2×Q8×C31—416no—
61C2×Q8×C31C2×D414yes—
62C2×D4×C31—24no—
63C2×D4×C31—22no—
64C2×D4×C31—416no—
65C2×D4×C31—42no—
66C2×D4×C31—42no—
67C2×D4×C31—42no—
68C2×D4×C31—42no—
69C2×D4×C31C22⋊C414yes—
70C22×C4×C31—22no—
71C22×C4×C31—22no—
72C22×C4×C31—22no—
73C22×C4×C31—24no—
74C22×C4×C31—24no—
75C22×C4×C31—22no—
76C22×C4×C31—24no—
77C22×C4×C31—42no—
78C22×C4×C31—44no—
79C22×C4×C31C22⋊C412yes—
80C22×C4×C31C22⋊C411yescharacteristic
81C22×C4×C31C22×C411yescharacteristic
82C22×C4×C31C2×D412yes—
83M16×C31—44no—
84M16×C31—44no—
85C2×C8×C31—44no—
86C22⋊C4×C31—216no—
87C22⋊C4×C31—216no—
88C42×C31—24no—
89C42×C31—22no—
90C42×C31C22⋊C414yes—
91#12699C3111yesmaximal, characteristic, direct product factor, Sylow
92C23×C31—24no—
93C23×C31—21no—
94C23×C31—21no—
95C23×C31—24no—
96C23×C31—48no—
97C23×C31—416no—
98C23×C31—48no—
99C23×C31—42no—
100C23×C31—42no—
101C23×C31—88no—
102C23×C31—84no—
103C23×C31—84no—
104C23×C31#9912yes—
105C23×C31C2×C22⋊C411yescharacteristic
106Q8×C31—44no—
107Q8×C31—48no—
108Q8×C31—44no—
109D4×C31—44no—
110D4×C31—48no—
111D4×C31—44no—
112C2×C4×C31—28no—
113C2×C4×C31—21no—
114C2×C4×C31—22no—
115C2×C4×C31—21no—
116C2×C4×C31—22no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—24no—
120C2×C4×C31—22no—
121C2×C4×C31—22no—
122C2×C4×C31—22no—
123C2×C4×C31—48no—
124C2×C4×C31—48no—
125C2×C4×C31—44no—
126C2×C4×C31#9912yes—
127C2×C4×C31C2×C22⋊C412yes—
128C2×C4×C31#12014yes—
129C8×C31—84no—
130C22×#124C2×C3111yescharacteristic
131C2×#355C2×C3114yescomplemented
132#1784C2×C3112yescomplemented
133C22×C31—24no—
134C22×C31—24no—
135C22×C31—22no—
136C22×C31—22no—
137C22×C31—22no—
138C22×C31—48no—
139C22×C31—44no—
140C22×C31—816no—
141C22×C31—84no—
142C22×C31—84no—
143C22×C31#35514yescomplemented
144C22×C31#37911yescharacteristic
145C22×C31C2×#9911yescharacteristic
146C22×C31C2×#9911yescharacteristic
147C4×C31—24no—
148C4×C31—22no—
149C4×C31—22no—
150C4×C31—44no—
151C4×C31—42no—
152C23×Q8C22×C3111yescharacteristic
153C23×D4C4×C3111yescharacteristic
154C2×#124—22no—
155C2×#124—28no—
156C2×#124C4×C3112yes—
157C2×#124C22×C3112yes—
158C22×C22⋊C4—22no—
159C22×C42C4×C3111yescharacteristic
160C2×#101—22no—
161C2×#101C22×C3114yescomplemented
162#407—22no—
163#355—28no—
164C2×C31—21no—
165C2×C31—24no—
166C2×C31—21no—
167C2×C31—84no—
168C2×C31#178111yescharacteristic
169C2×C31C2×#35512yes—
170C25—21no—
171C22×Q8—24no—
172C22×Q8—42no—
173C22×Q8—42no—
174C22×Q8C2×C4×C3111yescharacteristic
175C22×Q8D4×C3112yes—
176C22×Q8C23×C3111yescharacteristic
177C22×D4—24no—
178C22×D4—21no—
179C22×D4—42no—
180C22×D4—42no—
181C22×D4C2×C4×C3112yes—
182C23×C4—21no—
183C23×C4C2×C4×C3111yescharacteristic
184C23×C4D4×C3112yes—
185C2×M16—24no—
186#124—216no—
187#124—24no—
188#124—24no—
189#124—24no—
190#124D4×C3118yes—
191C2×C22⋊C4—216no—
192C2×C22⋊C4—24no—
193C2×C22⋊C4—24no—
194C2×C42—21no—
195C2×C42—24no—
196C2×C42C2×C4×C3112yes—
197#101—28no—
198#101—44no—
199C22⋊C8—44no—
200C31#1269911yescharacteristic, direct product factor, Sylow
201C24—24no—
202C24—22no—
203C24—42no—
204C24—48no—
205C24—42no—
206C24C22⋊C4×C3111yescharacteristic
207C2×Q8—24no—
208C2×Q8—22no—
209C2×Q8—24no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8—42no—
213C2×Q8—41no—
214C2×Q8—41no—
215C2×Q8—416no—
216C2×Q8C2×D4×C3114yes—
217C2×D4—24no—
218C2×D4—22no—
219C2×D4—42no—
220C2×D4—42no—
221C2×D4—416no—
222C2×D4—42no—
223C2×D4—42no—
224C2×D4C22⋊C4×C3114yes—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—22no—
231C22×C4—24no—
232C22×C4—42no—
233C22×C4—44no—
234C22×C4C22⋊C4×C3112yes—
235C22×C4C22⋊C4×C3111yescharacteristic
236C22×C4C22×C4×C3111yescharacteristic
237C22×C4C2×D4×C3112yes—
238M16—44no—
239M16—44no—
240C2×C8—44no—
241C22⋊C4—216no—
242C22⋊C4—216no—
243C42—24no—
244C42—22no—
245C42C22⋊C4×C3114yes—
246C23—21no—
247C23—24no—
248C23—21no—
249C23—24no—
250C23—48no—
251C23—416no—
252C23—48no—
253C23—42no—
254C23—42no—
255C23—88no—
256C23—84no—
257C23—84no—
258C23C31×#9912yes—
259C23C2×C22⋊C4×C3111yescharacteristic
260Q8—44no—
261Q8—48no—
262Q8—44no—
263D4—44no—
264D4—48no—
265D4—44no—
266C2×C4—28no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—24no—
276C2×C4—22no—
277C2×C4—48no—
278C2×C4—48no—
279C2×C4—44no—
280C2×C4C31×#9912yes—
281C2×C4C2×C22⋊C4×C3112yes—
282C2×C4C31×#12014yes—
283C8—84no—
284C22—24no—
285C22—24no—
286C22—22no—
287C22—22no—
288C22—22no—
289C22—48no—
290C22—44no—
291C22—84no—
292C22—816no—
293C22—84no—
294C22C31×#35514yescomplemented
295C22C31×#37911yescharacteristic
296C22C2×C31×#9911yescharacteristic
297C22C2×C31×#9911yescharacteristic
298C4—24no—
299C4—22no—
300C4—22no—
301C4—44no—
302C4—42no—
303C2—21no—
304C2—21no—
305C2—24no—
306C2—84no—
307C2C31×#178111yescharacteristic
308C2C2×C31×#35512yes—
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC22×Q8C23×C31
prime radicalC23×D4×C31C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C31 ◁ C23×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#355C2semidirect
3. C31×#1784C2semidirect
13. C2×C31×#101C22semidirect
91. #12699C31direct (N × H)
131. C2×#355C2×C31semidirect
132. #1784C2×C31semidirect
143. C22×C31#355semidirect
161. C2×#101C22×C31semidirect
200. C31#12699direct (N × H)
294. C22C31×#355semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1242
C2×C31×#3552
C31×#17842
#1269931