Finite Group Databasebeta

← C31×#12703 #21469462

Subgroups — C31×#12703 #21469462

Order 7936.

1154 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C2×C31×#535C211yesmaximal, characteristic
2C2×C31×#355C214yesmaximal, complemented
3C31×#1785C212yesmaximal, complemented
4C22×#41×C31C2211yescharacteristic
5C23×D4×C31C411yescharacteristic
6C31×#535—28no—
7C2×C31×#127C412yes—
8C2×C31×#124C2212yes—
9C2×C31×#121—22no—
10C2×C31×#120—22no—
11C2×C31×#117C411yescharacteristic
12C2×C31×#101C2214yescomplemented
13C2×C31×#100—22no—
14C31×#407—22no—
15C31×#355—28no—
16C25×C31—21no—
17C2×#41×C31—24no—
18C2×#41×C31—42no—
19C2×#41×C31—42no—
20C22×Q8×C31C2311yescharacteristic
21C22×D4×C31—24no—
22C22×D4×C31—24no—
23C22×D4×C31—21no—
24C22×D4×C31—42no—
25C22×D4×C31—42no—
26C22×D4×C31C2×C411yescharacteristic
27C22×D4×C31C2×C412yes—
28C22×D4×C31D412yes—
29C23×C4×C31C2×C411yescharacteristic
30C23×C4×C31D412yes—
31C2×M16×C31—24no—
32C31×#127—24no—
33C31×#127—24no—
34C31×#124—24no—
35C31×#124D418yes—
36C31×#121—216no—
37C31×#120—216no—
38C31×#117—24no—
39C2×C4⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—24no—
42C2×C42×C31C2×C412yes—
43C31×#101—28no—
44C31×#100—44no—
45C31×C22⋊C8—44no—
46C24×C31—24no—
47C24×C31—22no—
48C24×C31—42no—
49C24×C31—42no—
50C24×C31—84no—
51C24×C31C22⋊C412yes—
52C24×C31C22⋊C411yescharacteristic
53#41×C31—416no—
54C2×Q8×C31—41no—
55C2×Q8×C31—41no—
56C2×Q8×C31C2×D414yes—
57C2×D4×C31—24no—
58C2×D4×C31—24no—
59C2×D4×C31—216no—
60C2×D4×C31—22no—
61C2×D4×C31—22no—
62C2×D4×C31—24no—
63C2×D4×C31—41no—
64C2×D4×C31—41no—
65C2×D4×C31—42no—
66C2×D4×C31—416no—
67C2×D4×C31—42no—
68C2×D4×C31—42no—
69C2×D4×C31—42no—
70C2×D4×C31—42no—
71C2×D4×C31—88no—
72C2×D4×C31C22⋊C414yes—
73C22×C4×C31—22no—
74C22×C4×C31—22no—
75C22×C4×C31—22no—
76C22×C4×C31—22no—
77C22×C4×C31—24no—
78C22×C4×C31—24no—
79C22×C4×C31—42no—
80C22×C4×C31C22⋊C411yescharacteristic
81C22×C4×C31C22×C411yescharacteristic
82C22×C4×C31C2×D412yes—
83M16×C31—44no—
84M16×C31—44no—
85C2×C8×C31—44no—
86C4⋊C4×C31—24no—
87C22⋊C4×C31—24no—
88C22⋊C4×C31—216no—
89C42×C31—22no—
90C42×C31C22⋊C414yes—
91#12703C3111yesmaximal, characteristic, direct product factor, Sylow
92C23×C31—21no—
93C23×C31—21no—
94C23×C31—24no—
95C23×C31—22no—
96C23×C31—22no—
97C23×C31—22no—
98C23×C31—42no—
99C23×C31—44no—
100C23×C31—48no—
101C23×C31—48no—
102C23×C31—42no—
103C23×C31—42no—
104C23×C31—88no—
105C23×C31—88no—
106C23×C31—88no—
107C23×C31#9912yes—
108C23×C31C2×C22⋊C411yescharacteristic
109Q8×C31—44no—
110D4×C31—48no—
111D4×C31—44no—
112D4×C31—48no—
113D4×C31—44no—
114D4×C31—44no—
115D4×C31—816no—
116C2×C4×C31—28no—
117C2×C4×C31—21no—
118C2×C4×C31—22no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—22no—
122C2×C4×C31—21no—
123C2×C4×C31—24no—
124C2×C4×C31—48no—
125C2×C4×C31—44no—
126C2×C4×C31#9912yes—
127C2×C4×C31C2×C22⋊C412yes—
128C2×C4×C31#12014yes—
129C8×C31—84no—
130C2×#535C2×C3111yescharacteristic
131C2×#355C2×C3114yescomplemented
132#1785C2×C3112yescomplemented
133C22×C31—22no—
134C22×C31—22no—
135C22×C31—42no—
136C22×C31—42no—
137C22×C31—44no—
138C22×C31—48no—
139C22×C31—42no—
140C22×C31—44no—
141C22×C31—42no—
142C22×C31—44no—
143C22×C31—82no—
144C22×C31—84no—
145C22×C31—816no—
146C22×C31—84no—
147C22×C31#37911yescharacteristic
148C22×C31C2×#9911yescharacteristic
149C22×C31C2×#9911yescharacteristic
150C4×C31—24no—
151C4×C31—22no—
152C4×C31—22no—
153C4×C31—44no—
154C22×#41C22×C3111yescharacteristic
155C23×D4C4×C3111yescharacteristic
156#535—28no—
157C2×#127C4×C3112yes—
158C2×#124C22×C3112yes—
159C2×#121—22no—
160C2×#120—22no—
161C2×#117C4×C3111yescharacteristic
162C2×#101C22×C3114yescomplemented
163C2×#100—22no—
164#407—22no—
165#355—28no—
166C2×C31—21no—
167C2×C31—21no—
168C2×C31—42no—
169C2×C31—82no—
170C2×C31—84no—
171C2×C31#178111yescharacteristic
172C2×C31#213412yes—
173C25—21no—
174C2×#41—24no—
175C2×#41—42no—
176C2×#41—42no—
177C22×Q8C23×C3111yescharacteristic
178C22×D4—24no—
179C22×D4—24no—
180C22×D4—21no—
181C22×D4—42no—
182C22×D4—42no—
183C22×D4C2×C4×C3111yescharacteristic
184C22×D4C2×C4×C3112yes—
185C22×D4D4×C3112yes—
186C23×C4C2×C4×C3111yescharacteristic
187C23×C4D4×C3112yes—
188C2×M16—24no—
189#127—24no—
190#127—24no—
191#124—24no—
192#124D4×C3118yes—
193#121—216no—
194#120—216no—
195#117—24no—
196C2×C4⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—24no—
199C2×C42C2×C4×C3112yes—
200#101—28no—
201#100—44no—
202C22⋊C8—44no—
203C31#1270311yescharacteristic, direct product factor, Sylow
204C24—24no—
205C24—22no—
206C24—42no—
207C24—42no—
208C24—84no—
209C24C22⋊C4×C3112yes—
210C24C22⋊C4×C3111yescharacteristic
211#41—416no—
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8C2×D4×C3114yes—
215C2×D4—24no—
216C2×D4—24no—
217C2×D4—216no—
218C2×D4—22no—
219C2×D4—22no—
220C2×D4—24no—
221C2×D4—41no—
222C2×D4—41no—
223C2×D4—42no—
224C2×D4—42no—
225C2×D4—42no—
226C2×D4—416no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4—88no—
230C2×D4C22⋊C4×C3114yes—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—42no—
238C22×C4C22⋊C4×C3111yescharacteristic
239C22×C4C22×C4×C3111yescharacteristic
240C22×C4C2×D4×C3112yes—
241M16—44no—
242M16—44no—
243C2×C8—44no—
244C4⋊C4—24no—
245C22⋊C4—24no—
246C22⋊C4—216no—
247C42—22no—
248C42C22⋊C4×C3114yes—
249C23—21no—
250C23—21no—
251C23—22no—
252C23—24no—
253C23—22no—
254C23—22no—
255C23—42no—
256C23—44no—
257C23—48no—
258C23—48no—
259C23—42no—
260C23—42no—
261C23—88no—
262C23—88no—
263C23—88no—
264C23C31×#9912yes—
265C23C2×C22⋊C4×C3111yescharacteristic
266Q8—44no—
267D4—48no—
268D4—44no—
269D4—48no—
270D4—44no—
271D4—44no—
272D4—816no—
273C2×C4—28no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—24no—
281C2×C4—48no—
282C2×C4—44no—
283C2×C4C31×#9912yes—
284C2×C4C2×C22⋊C4×C3112yes—
285C2×C4C31×#12014yes—
286C8—84no—
287C22—22no—
288C22—22no—
289C22—42no—
290C22—42no—
291C22—44no—
292C22—48no—
293C22—42no—
294C22—44no—
295C22—42no—
296C22—44no—
297C22—82no—
298C22—84no—
299C22—816no—
300C22—84no—
301C22C31×#37911yescharacteristic
302C22C2×C31×#9911yescharacteristic
303C22C2×C31×#9911yescharacteristic
304C4—24no—
305C4—22no—
306C4—22no—
307C4—44no—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—82no—
312C2—84no—
313C2C31×#178111yescharacteristic
314C2C31×#213412yes—
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC22×Q8C23×C31
prime radicalC2×C31×#535C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C22×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#355C2semidirect
3. C31×#1785C2semidirect
12. C2×C31×#101C22semidirect
91. #12703C31direct (N × H)
131. C2×#355C2×C31semidirect
132. #1785C2×C31semidirect
162. C2×#101C22×C31semidirect
203. C31#12703direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5352
C2×C31×#3552
C31×#17852
#1270331