Finite Group Databasebeta

← C31×#9476 #21466235

Subgroups — C31×#9476 #21466235

Order 7936.

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

normal subgroups only

This group has 818 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×#2406C211yesmaximal, characteristic
2C31×#2274C211yesmaximal, characteristic, complemented
3C31×#1789C212yesmaximal
4C31×#1463C211yesmaximal, characteristic, complemented
5C31×#1284C212yesmaximal, complemented
6C22×#41×C31C2211yescharacteristic
7C2×C31×#123—21no—
8C2×C31×#117—21no—
9C22×C4⋊C4×C31C2211yescharacteristic
10C2×C31×#104—24no—
11C31×#407C2212yes—
12C31×#395C412yescomplemented
13C31×#394C412yescomplemented
14C31×#386—21no—
15C31×#385—22no—
16C31×#381C2211yescharacteristic
17C4×C4⋊C4×C31—24no—
18C4×C22⋊C4×C31—21no—
19C4×C22⋊C4×C31C2212yes—
20C31×#324—22no—
21C2×#41×C31—22no—
22C2×#41×C31—22no—
23C2×#41×C31—44no—
24C22×Q8×C31C2×C411yescharacteristic
25C22×D4×C31—21no—
26C22×D4×C31C2×C411yescharacteristic
27C23×C4×C31—21no—
28C23×C4×C31D411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C23×C4×C31C2311yescharacteristic
31C2×M16×C31—22no—
32C31×#123—44no—
33C31×#117—28no—
34C2×C4⋊C4×C31—22no—
35C2×C4⋊C4×C31—22no—
36C2×C4⋊C4×C31—22no—
37C2×C4⋊C4×C31—22no—
38C2×C4⋊C4×C31C2×C412yes—
39C2×C4⋊C4×C31D412yes—
40C2×C22⋊C4×C31—22no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—22no—
43C2×C22⋊C4×C31—22no—
44C2×C42×C31—22no—
45C2×C42×C31—22no—
46C2×C42×C31D414yes—
47C31×#104—48no—
48C31×C22⋊C8—22no—
49C31×C22⋊C8—22no—
50C31×#95—22no—
51C31×#95—22no—
52C31×#95—22no—
53C31×#95—21no—
54C31×#95C2×C412yes—
55C24×C31—21no—
56C24×C31C2×D411yescharacteristic
57#41×C31—28no—
58#41×C31—44no—
59#41×C31—44no—
60#41×C31—44no—
61C2×Q8×C31—22no—
62C2×Q8×C31—42no—
63C2×D4×C31—24no—
64C2×D4×C31—22no—
65C2×D4×C31—42no—
66C2×D4×C31—42no—
67C2×D4×C31—41no—
68C2×D4×C31—41no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—24no—
72C22×C4×C31—21no—
73C22×C4×C31—24no—
74C22×C4×C31—21no—
75C22×C4×C31—21no—
76C22×C4×C31—22no—
77C22×C4×C31—42no—
78C22×C4×C31—42no—
79C22×C4×C31—42no—
80C22×C4×C31—42no—
81C22×C4×C31—42no—
82C22×C4×C31C22⋊C412yes—
83C22×C4×C31C22⋊C412yes—
84C22×C4×C31C22×C411yescharacteristic
85C22×C4×C31C2×D412yes—
86C22×C4×C31C2×D411yescharacteristic
87C22×C4×C31#4112yes—
88M16×C31—44no—
89C2×C8×C31—42no—
90C4⋊C4×C31—28no—
91C4⋊C4×C31—24no—
92C4⋊C4×C31—24no—
93C4⋊C4×C31—44no—
94C22⋊C4×C31—28no—
95C22⋊C4×C31—44no—
96C22⋊C4×C31—42no—
97C22⋊C4×C31—44no—
98C42×C31—28no—
99C42×C31—44no—
100C42×C31—82no—
101#9476C3111yesmaximal, characteristic, direct product factor, Sylow
102C23×C31—22no—
103C23×C31—22no—
104C23×C31—22no—
105C23×C31—41no—
106C23×C31—41no—
107C23×C31—42no—
108C23×C31—41no—
109C23×C31—42no—
110C23×C31C2×C22⋊C411yescharacteristic
111C23×C31#12011yescharacteristic
112C23×C31#12311yescharacteristic
113Q8×C31—24no—
114Q8×C31—42no—
115D4×C31—24no—
116D4×C31—42no—
117D4×C31—44no—
118D4×C31—44no—
119C2×C4×C31—22no—
120C2×C4×C31—22no—
121C2×C4×C31—24no—
122C2×C4×C31—22no—
123C2×C4×C31—22no—
124C2×C4×C31—24no—
125C2×C4×C31—28no—
126C2×C4×C31—22no—
127C2×C4×C31—22no—
128C2×C4×C31—41no—
129C2×C4×C31—41no—
130C2×C4×C31—42no—
131C2×C4×C31—48no—
132C2×C4×C31—44no—
133C2×C4×C31—41no—
134C2×C4×C31—41no—
135C2×C4×C31—44no—
136C2×C4×C31—42no—
137C2×C4×C31—42no—
138C2×C4×C31—42no—
139C2×C4×C31—42no—
140C2×C4×C31—42no—
141C2×C4×C31—81no—
142C2×C4×C31#10414yescomplemented
143C2×C4×C31C4×D412yes—
144C2×C4×C31#12112yes—
145C8×C31—82no—
146#2406C2×C3111yescharacteristic
147#2274C2×C3111yescharacteristic, complemented
148#1789C2×C3112yes—
149#1463C2×C3111yescharacteristic, complemented
150#1284C2×C3112yescomplemented
151C22×C31—21no—
152C22×C31—21no—
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—21no—
156C22×C31—21no—
157C22×C31—21no—
158C22×C31—44no—
159C22×C31—44no—
160C22×C31—42no—
161C22×C31—82no—
162C22×C31—81no—
163C22×C31—81no—
164C22×C31#38611yescharacteristic
165C22×C31C2×#10412yes—
166C22×C31B(4,𝔽2)12yes—
167C4×C31—22no—
168C4×C31—22no—
169C4×C31—24no—
170C4×C31—48no—
171C4×C31—42no—
172C4×C31—42no—
173C4×C31—82no—
174C22×#41C22×C3111yescharacteristic
175C2×#123—21no—
176C2×#117—21no—
177C22×C4⋊C4C22×C3111yescharacteristic
178C2×#104—24no—
179#407C22×C3112yes—
180#395C4×C3112yescomplemented
181#394C4×C3112yescomplemented
182#386—21no—
183#385—22no—
184#381C22×C3111yescharacteristic
185C4×C4⋊C4—24no—
186C4×C22⋊C4—21no—
187C4×C22⋊C4C22×C3112yes—
188#324—22no—
189C2×C31—22no—
190C2×C31—22no—
191C2×C31—41no—
192C2×C31—82no—
193C2×C31#188911yescharacteristic
194C2×C31#189611yescharacteristic
195C2×C31#191211yescharacteristic
196C2×#41—22no—
197C2×#41—22no—
198C2×#41—44no—
199C22×Q8C2×C4×C3111yescharacteristic
200C22×D4—21no—
201C22×D4C2×C4×C3111yescharacteristic
202C23×C4—21no—
203C23×C4D4×C3111yescharacteristic
204C23×C4D4×C3111yescharacteristic
205C23×C4C23×C3111yescharacteristic
206C2×M16—22no—
207#123—44no—
208#117—28no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4C2×C4×C3112yes—
214C2×C4⋊C4D4×C3112yes—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42D4×C3114yes—
222#104—48no—
223C22⋊C8—22no—
224C22⋊C8—22no—
225#95—22no—
226#95—22no—
227#95—22no—
228#95—21no—
229#95C2×C4×C3112yes—
230C31#947611yescharacteristic, direct product factor, Sylow
231C24—21no—
232C24C2×D4×C3111yescharacteristic
233#41—28no—
234#41—44no—
235#41—44no—
236#41—44no—
237C2×Q8—22no—
238C2×Q8—42no—
239C2×D4—24no—
240C2×D4—22no—
241C2×D4—42no—
242C2×D4—42no—
243C2×D4—41no—
244C2×D4—41no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—24no—
248C22×C4—21no—
249C22×C4—24no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4C22⋊C4×C3112yes—
259C22×C4C22⋊C4×C3112yes—
260C22×C4C22×C4×C3111yescharacteristic
261C22×C4C2×D4×C3112yes—
262C22×C4C2×D4×C3111yescharacteristic
263C22×C4#41×C3112yes—
264M16—44no—
265C2×C8—42no—
266C4⋊C4—28no—
267C4⋊C4—24no—
268C4⋊C4—24no—
269C4⋊C4—44no—
270C22⋊C4—28no—
271C22⋊C4—44no—
272C22⋊C4—42no—
273C22⋊C4—44no—
274C42—28no—
275C42—44no—
276C42—82no—
277C23—22no—
278C23—22no—
279C23—22no—
280C23—41no—
281C23—41no—
282C23—42no—
283C23—42no—
284C23—41no—
285C23C2×C22⋊C4×C3111yescharacteristic
286C23C31×#12011yescharacteristic
287C23C31×#12311yescharacteristic
288Q8—24no—
289Q8—42no—
290D4—24no—
291D4—42no—
292D4—44no—
293D4—44no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—22no—
298C2×C4—24no—
299C2×C4—22no—
300C2×C4—28no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—48no—
307C2×C4—44no—
308C2×C4—41no—
309C2×C4—44no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—81no—
317C2×C4C31×#10414yescomplemented
318C2×C4C4×D4×C3112yes—
319C2×C4C31×#12112yes—
320C8—82no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—44no—
329C22—44no—
330C22—42no—
331C22—82no—
332C22—81no—
333C22—81no—
334C22C31×#38611yescharacteristic
335C22C2×C31×#10412yes—
336C22C31×B(4,𝔽2)12yes—
337C4—22no—
338C4—22no—
339C4—24no—
340C4—48no—
341C4—42no—
342C4—42no—
343C4—82no—
344C2—22no—
345C2—22no—
346C2—41no—
347C2—82no—
348C2C31×#188911yescharacteristic
349C2C31×#189611yescharacteristic
350C2C31×#191211yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×#41×C31C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2274C2semidirect
4. C31×#1463C2semidirect
5. C31×#1284C2semidirect
12. C31×#395C4semidirect
13. C31×#394C4semidirect
101. #9476C31direct (N × H)
142. C2×C4×C31#104semidirect
147. #2274C2×C31semidirect
149. #1463C2×C31semidirect
150. #1284C2×C31semidirect
180. #395C4×C31semidirect
181. #394C4×C31semidirect
230. C31#9476direct (N × H)
317. C2×C4C31×#104semidirect

Maximal subgroups

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

subgroupindex
C31×#24062
C31×#22742
C31×#17892
C31×#14632
C31×#12842
#947631