Finite Group Databasebeta

← C31×#19077 #21475836

Subgroups — C31×#19077 #21475836

Order 7936.

996 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 230 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×#3550C211yesmaximal, characteristic, complemented
2C31×#3151C211yesmaximal, characteristic
3C31×#3138C212yesmaximal, complemented
4C31×#1657C218yesmaximal, complemented
5C31×#1526C212yesmaximal, complemented
6C31×#1525C211yesmaximal, characteristic, complemented
7C2×C31×AGL(1,ℤ/8)—22no—
8C31×#563C2214yescomplemented
9C31×#559—21no—
10Q82×C31—21no—
11C31×#556—22no—
12D4×Q8×C31—22no—
13C31×#542—24no—
14C31×#536—22no—
15C31×#533C2212yes—
16C31×#532C2211yescharacteristic
17C2×C31×#127C2211yescharacteristic
18C31×#496C2214yes—
19C31×#493—21no—
20C31×#492—21no—
21C31×#490C2218yes—
22C31×#486—22no—
23C31×#486—22no—
24C31×#418—24no—
25C4×M16×C31C2212yes—
26C4×M16×C31C2211yescharacteristic
27C31×#330C2218yescomplemented
28C31×#329C2214yescomplemented
29C2×#41×C31D412yes—
30C22×Q8×C31—22no—
31C22×D4×C31—22no—
32C22×D4×C31—21no—
33C31×AGL(1,ℤ/8)—48no—
34C2×SD16×C31—24no—
35C2×D8×C31—24no—
36C2×M16×C31—21no—
37C2×M16×C31—22no—
38C31×C4⋊Q8—24no—
39C31×C4⋊Q8—24no—
40C31×C4⋊Q8D411yescharacteristic
41C31×C4⋊Q8D412yes—
42C31×C4⋊Q8D412yes—
43C31×#127—22no—
44C31×#127—21no—
45C31×#127D411yescharacteristic
46C31×#127C2312yes—
47C31×#126—28no—
48C31×#125C2314yes—
49C31×#124—24no—
50C31×#124—24no—
51C31×#124C2312yes—
52C31×#123—24no—
53C31×#123—24no—
54C31×C22⋊Q8—24no—
55C31×C22⋊Q8—22no—
56C31×C22⋊Q8—22no—
57C31×C22⋊Q8—28no—
58C31×#121—22no—
59C4×Q8×C31—24no—
60C4×Q8×C31—22no—
61C4×Q8×C31—22no—
62C4×D4×C31—24no—
63C4×D4×C31—22no—
64C31×#117—22no—
65C31×#117D414yes—
66C2×C42×C31C2311yescharacteristic
67C31×#102—28no—
68C31×#102—28no—
69C31×#97C2314yes—
70C31×#97C2312yes—
71C4×C8×C31—22no—
72C4×C8×C31—21no—
73C24×C31—41no—
74#41×C31—44no—
75C2×Q8×C31—24no—
76C2×Q8×C31—22no—
77C2×Q8×C31—22no—
78C2×Q8×C31—84no—
79C2×Q8×C31C2×D412yes—
80C2×D4×C31—22no—
81C2×D4×C31—22no—
82C2×D4×C31—24no—
83C2×D4×C31—22no—
84C2×D4×C31—44no—
85C2×D4×C31—48no—
86C2×D4×C31—41no—
87C2×D4×C31—42no—
88C2×D4×C31C2×D412yes—
89C22×C4×C31—24no—
90C22×C4×C31—22no—
91C22×C4×C31C2×D412yes—
92C22×C4×C31C2×D411yescharacteristic
93SD16×C31—48no—
94D8×C31—48no—
95M16×C31—24no—
96M16×C31—44no—
97C2×C8×C31—22no—
98C2×C8×C31—24no—
99C4⋊C4×C31—28no—
100C4⋊C4×C31—22no—
101C4⋊C4×C31—22no—
102C4⋊C4×C31—22no—
103C4⋊C4×C31—24no—
104C4⋊C4×C31—24no—
105C4⋊C4×C31C2×D414yes—
106C4⋊C4×C31C2×D414yes—
107C22⋊C4×C31—24no—
108C22⋊C4×C31—28no—
109C22⋊C4×C31—24no—
110C22⋊C4×C31—24no—
111C42×C31—24no—
112C42×C31—24no—
113C42×C31C2×D412yes—
114C42×C31C2×D411yescharacteristic
115C42×C31C2411yescharacteristic
116#19077C3111yesmaximal, characteristic, direct product factor, Sylow
117C23×C31—22no—
118C23×C31—42no—
119C23×C31—82no—
120C23×C31—84no—
121C23×C31#12011yescharacteristic
122Q8×C31—42no—
123Q8×C31—44no—
124Q8×C31—44no—
125Q8×C31—84no—
126D4×C31—42no—
127D4×C31—44no—
128D4×C31—48no—
129D4×C31—44no—
130D4×C31—82no—
131D4×C31—82no—
132D4×C31—84no—
133C2×C4×C31—22no—
134C2×C4×C31—24no—
135C2×C4×C31—24no—
136C2×C4×C31—22no—
137C2×C4×C31—24no—
138C2×C4×C31—44no—
139C2×C4×C31—84no—
140C2×C4×C31#12011yescharacteristic
141C2×C4×C31#12012yes—
142C2×C4×C31C22×D412yes—
143C2×C4×C31C22×D411yescharacteristic
144C8×C31—24no—
145C8×C31—44no—
146#3550C2×C3111yescharacteristic, complemented
147#3151C2×C3111yescharacteristic
148#3138C2×C3112yescomplemented
149#1657C2×C3118yescomplemented
150#1526C2×C3112yescomplemented
151#1525C2×C3111yescharacteristic, complemented
152C22×C31—21no—
153C22×C31—22no—
154C22×C31—42no—
155C22×C31—44no—
156C22×C31—82no—
157C22×C31—84no—
158C22×C31—164no—
159C22×C31C2×#12011yescharacteristic
160C4×C31—21no—
161C4×C31—22no—
162C4×C31—42no—
163C4×C31—44no—
164C4×C31—44no—
165C4×C31#45312yes—
166C4×C31#45414yes—
167C2×AGL(1,ℤ/8)—22no—
168#563C22×C3114yescomplemented
169#559—21no—
170Q82—21no—
171#556—22no—
172D4×Q8—22no—
173#542—24no—
174#536—22no—
175#533C22×C3112yes—
176#532C22×C3111yescharacteristic
177C2×#127C22×C3111yescharacteristic
178#496C22×C3114yes—
179#493—21no—
180#492—21no—
181#490C22×C3118yes—
182#486—22no—
183#486—22no—
184#418—24no—
185C4×M16C22×C3112yes—
186C4×M16C22×C3111yescharacteristic
187#330C22×C3118yescomplemented
188#329C22×C3114yescomplemented
189C2×C31—41no—
190C2×C31—82no—
191C2×C31—162no—
192C2×C31C2×#45311yescharacteristic
193C2×C31C2×#45412yes—
194C2×#41D4×C3112yes—
195C22×Q8—22no—
196C22×D4—21no—
197C22×D4—22no—
198AGL(1,ℤ/8)—48no—
199C2×SD16—24no—
200C2×D8—24no—
201C2×M16—21no—
202C2×M16—22no—
203C4⋊Q8—24no—
204C4⋊Q8—24no—
205C4⋊Q8D4×C3111yescharacteristic
206C4⋊Q8D4×C3112yes—
207C4⋊Q8D4×C3112yes—
208#127—22no—
209#127—21no—
210#127D4×C3111yescharacteristic
211#127C23×C3112yes—
212#126—28no—
213#125C23×C3114yes—
214#124—24no—
215#124—24no—
216#124C23×C3112yes—
217#123—24no—
218#123—24no—
219C22⋊Q8—24no—
220C22⋊Q8—22no—
221C22⋊Q8—22no—
222C22⋊Q8—28no—
223#121—22no—
224C4×Q8—24no—
225C4×Q8—22no—
226C4×Q8—22no—
227C4×D4—24no—
228C4×D4—22no—
229#117—22no—
230#117D4×C3114yes—
231C2×C42C23×C3111yescharacteristic
232#102—28no—
233#102—28no—
234#97C23×C3114yes—
235#97C23×C3112yes—
236C4×C8—22no—
237C4×C8—21no—
238C31#1907711yescharacteristic, direct product factor, Sylow
239C24—41no—
240#41—44no—
241C2×Q8—24no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—84no—
245C2×Q8C2×D4×C3112yes—
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—24no—
249C2×D4—22no—
250C2×D4—44no—
251C2×D4—48no—
252C2×D4—41no—
253C2×D4—42no—
254C2×D4C2×D4×C3112yes—
255C22×C4—24no—
256C22×C4—22no—
257C22×C4C2×D4×C3112yes—
258C22×C4C2×D4×C3111yescharacteristic
259SD16—48no—
260D8—48no—
261M16—24no—
262M16—44no—
263C2×C8—22no—
264C2×C8—24no—
265C4⋊C4—28no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—24no—
270C4⋊C4—24no—
271C4⋊C4C2×D4×C3114yes—
272C4⋊C4C2×D4×C3114yes—
273C22⋊C4—24no—
274C22⋊C4—28no—
275C22⋊C4—24no—
276C22⋊C4—24no—
277C42—24no—
278C42—24no—
279C42C2×D4×C3112yes—
280C42C2×D4×C3111yescharacteristic
281C42C24×C3111yescharacteristic
282C23—22no—
283C23—42no—
284C23—82no—
285C23—84no—
286C23C31×#12011yescharacteristic
287Q8—42no—
288Q8—44no—
289Q8—44no—
290Q8—84no—
291D4—42no—
292D4—44no—
293D4—48no—
294D4—44no—
295D4—82no—
296D4—82no—
297D4—84no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—22no—
302C2×C4—24no—
303C2×C4—44no—
304C2×C4—84no—
305C2×C4C31×#12011yescharacteristic
306C2×C4C31×#12012yes—
307C2×C4C22×D4×C3112yes—
308C2×C4C22×D4×C3111yescharacteristic
309C8—24no—
310C8—44no—
311C22—21no—
312C22—22no—
313C22—42no—
314C22—44no—
315C22—82no—
316C22—84no—
317C22—164no—
318C22C2×C31×#12011yescharacteristic
319C4—21no—
320C4—22no—
321C4—42no—
322C4—44no—
323C4—44no—
324C4C31×#45312yes—
325C4C31×#45414yes—
326C2—41no—
327C2—82no—
328C2—162no—
329C2C2×C31×#45311yescharacteristic
330C2C2×C31×#45412yes—
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#3151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3550C2semidirect
3. C31×#3138C2semidirect
4. C31×#1657C2semidirect
5. C31×#1526C2semidirect
6. C31×#1525C2semidirect
8. C31×#563C22semidirect
27. C31×#330C22semidirect
28. C31×#329C22semidirect
116. #19077C31direct (N × H)
146. #3550C2×C31semidirect
148. #3138C2×C31semidirect
149. #1657C2×C31semidirect
150. #1526C2×C31semidirect
151. #1525C2×C31semidirect
168. #563C22×C31semidirect
187. #330C22×C31semidirect
188. #329C22×C31semidirect
238. C31#19077direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35502
C31×#31512
C31×#31382
C31×#16572
C31×#15262
C31×#15252
#1907731