Finite Group Databasebeta

← C31×#9441 #21466200

Subgroups — C31×#9441 #21466200

Order 7936.

576 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 118 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×#3153C211yesmaximal, characteristic
2C31×#2372C211yesmaximal, characteristic, complemented
3C31×#1533C211yesmaximal, characteristic, complemented
4C31×#1505C212yesmaximal, complemented
5C31×#1300C212yesmaximal, complemented
6C2×C31×#137—21no—
7C2×C31×AGL(1,ℤ/8)—21no—
8C31×#532C2211yescharacteristic
9C2×C31×#124C2211yescharacteristic
10C31×#497C412yescomplemented
11C31×#496C412yescomplemented
12C31×#495—22no—
13C31×#432C2212yes—
14C4×M16×C31C2211yescharacteristic
15C31×#391—21no—
16C31×#388—22no—
17C31×#386—21no—
18C4×C22⋊C4×C31—22no—
19C31×#376C2212yes—
20C31×#329—22no—
21C31×#327—22no—
22C31×#327—22no—
23C2×#41×C31—21no—
24C22×Q8×C31D411yescharacteristic
25C22×D4×C31D411yescharacteristic
26C23×C4×C31—21no—
27C31×#137—42no—
28C31×#137—42no—
29C31×AGL(1,ℤ/8)—42no—
30C31×AGL(1,ℤ/8)—42no—
31C2×Q16×C31—22no—
32C2×SD16×C31—22no—
33C2×SD16×C31—22no—
34C2×D8×C31—22no—
35C2×M16×C31—21no—
36C31×C4⋊Q8C2×C411yescharacteristic, complemented
37C31×#127C2×C411yescharacteristic, complemented
38C31×#124—21no—
39C31×#124—22no—
40C31×#124C2×C412yes—
41C31×#124D412yes—
42C31×#121—22no—
43C4×D4×C31—22no—
44C2×C4⋊C4×C31—21no—
45C2×C22⋊C4×C31—22no—
46C2×C22⋊C4×C31—22no—
47C2×C22⋊C4×C31—21no—
48C2×C42×C31—22no—
49C2×C42×C31—21no—
50C2×C42×C31C2311yescharacteristic
51C31×C4⋊C8—22no—
52C31×C22⋊C8—22no—
53C31×#97—22no—
54C31×#97C2×C412yescomplemented
55C4×C8×C31—21no—
56C31×#95—22no—
57C31×#95—22no—
58C31×#95D412yes—
59C31×#95D412yes—
60C24×C31—21no—
61#41×C31—41no—
62#41×C31—41no—
63#41×C31—41no—
64#41×C31—41no—
65C2×Q8×C31—21no—
66C2×Q8×C31—21no—
67C2×Q8×C31—41no—
68C2×Q8×C31—41no—
69C2×Q8×C31C22⋊C412yes—
70C2×D4×C31—21no—
71C2×D4×C31—22no—
72C2×D4×C31—21no—
73C2×D4×C31—41no—
74C2×D4×C31—41no—
75C2×D4×C31—41no—
76C2×D4×C31C22⋊C412yes—
77C22×C4×C31—22no—
78C22×C4×C31—21no—
79C22×C4×C31—22no—
80C22×C4×C31—44no—
81C22×C4×C31—41no—
82C22×C4×C31—81no—
83C22×C4×C31C2×D411yescharacteristic
84C22×C4×C31C2×D412yes—
85Q16×C31—44no—
86SD16×C31—44no—
87SD16×C31—44no—
88D8×C31—44no—
89M16×C31—22no—
90M16×C31—22no—
91C2×C8×C31—22no—
92C2×C8×C31—42no—
93C4⋊C4×C31—22no—
94C4⋊C4×C31—81no—
95C22⋊C4×C31—24no—
96C22⋊C4×C31—24no—
97C22⋊C4×C31—44no—
98C22⋊C4×C31—42no—
99C22⋊C4×C31—81no—
100C42×C31—44no—
101C42×C31—81no—
102C42×C31C22×C411yescharacteristic
103C42×C31C2×D411yescharacteristic
104C42×C31#4112yes—
105#9441C3111yesmaximal, characteristic, direct product factor, Sylow
106C23×C31—22no—
107C23×C31—42no—
108C23×C31—42no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31—41no—
112C23×C31#12011yescharacteristic
113Q8×C31—42no—
114Q8×C31—41no—
115Q8×C31—41no—
116Q8×C31—81no—
117D4×C31—42no—
118D4×C31—41no—
119D4×C31—41no—
120D4×C31—81no—
121D4×C31—82no—
122D4×C31—81no—
123D4×C31—81no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—24no—
127C2×C4×C31—22no—
128C2×C4×C31—42no—
129C2×C4×C31—42no—
130C2×C4×C31—42no—
131C2×C4×C31—41no—
132C2×C4×C31—41no—
133C2×C4×C31—42no—
134C2×C4×C31—42no—
135C2×C4×C31—41no—
136C2×C4×C31—42no—
137C2×C4×C31—81no—
138C2×C4×C31—81no—
139C2×C4×C31—84no—
140C2×C4×C31C2×C22⋊C411yescharacteristic
141C2×C4×C31C4×D412yes—
142C2×C4×C31#12112yes—
143C2×C4×C31#12311yescharacteristic
144C8×C31—24no—
145C8×C31—82no—
146#3153C2×C3111yescharacteristic
147#2372C2×C3111yescharacteristic, complemented
148#1533C2×C3111yescharacteristic, complemented
149#1505C2×C3112yescomplemented
150#1300C2×C3112yescomplemented
151C22×C31—22no—
152C22×C31—42no—
153C22×C31—44no—
154C22×C31—81no—
155C22×C31—81no—
156C22×C31—82no—
157C22×C31—81no—
158C22×C31—82no—
159C22×C31#38611yescharacteristic
160C22×C31#45311yescharacteristic
161C22×C31#45311yescharacteristic
162C4×C31—21no—
163C4×C31—21no—
164C4×C31—22no—
165C4×C31—22no—
166C4×C31—44no—
167C4×C31—42no—
168C4×C31—82no—
169C4×C31—81no—
170C2×#137—21no—
171C2×AGL(1,ℤ/8)—21no—
172#532C22×C3111yescharacteristic
173C2×#124C22×C3111yescharacteristic
174#497C4×C3112yescomplemented
175#496C4×C3112yescomplemented
176#495—22no—
177#432C22×C3112yes—
178C4×M16C22×C3111yescharacteristic
179#391—21no—
180#388—22no—
181#386—21no—
182C4×C22⋊C4—22no—
183#376C22×C3112yes—
184#329—22no—
185#327—22no—
186#327—22no—
187C2×C31—21no—
188C2×C31—21no—
189C2×C31—82no—
190C2×C31—161no—
191C2×C31#188711yescharacteristic
192C2×C31#190612yes—
193C2×#41—21no—
194C22×Q8D4×C3111yescharacteristic
195C22×D4D4×C3111yescharacteristic
196C23×C4—21no—
197#137—42no—
198#137—42no—
199AGL(1,ℤ/8)—42no—
200AGL(1,ℤ/8)—42no—
201C2×Q16—22no—
202C2×SD16—22no—
203C2×SD16—22no—
204C2×D8—22no—
205C2×M16—21no—
206C4⋊Q8C2×C4×C3111yescharacteristic, complemented
207#127C2×C4×C3111yescharacteristic, complemented
208#124—21no—
209#124—22no—
210#124C2×C4×C3112yes—
211#124D4×C3112yes—
212#121—22no—
213C4×D4—22no—
214C2×C4⋊C4—21no—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—21no—
218C2×C42—22no—
219C2×C42—21no—
220C2×C42C23×C3111yescharacteristic
221C4⋊C8—22no—
222C22⋊C8—22no—
223#97—22no—
224#97C2×C4×C3112yescomplemented
225C4×C8—21no—
226#95—22no—
227#95—22no—
228#95D4×C3112yes—
229#95D4×C3112yes—
230C31#944111yescharacteristic, direct product factor, Sylow
231C24—21no—
232#41—41no—
233#41—41no—
234#41—41no—
235#41—41no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8C22⋊C4×C3112yes—
241C2×D4—21no—
242C2×D4—22no—
243C2×D4—21no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4C22⋊C4×C3112yes—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—44no—
252C22×C4—41no—
253C22×C4—81no—
254C22×C4C2×D4×C3111yescharacteristic
255C22×C4C2×D4×C3112yes—
256Q16—44no—
257SD16—44no—
258SD16—44no—
259D8—44no—
260M16—22no—
261M16—22no—
262C2×C8—22no—
263C2×C8—42no—
264C4⋊C4—22no—
265C4⋊C4—81no—
266C22⋊C4—24no—
267C22⋊C4—24no—
268C22⋊C4—44no—
269C22⋊C4—42no—
270C22⋊C4—81no—
271C42—44no—
272C42—81no—
273C42C22×C4×C3111yescharacteristic
274C42C2×D4×C3111yescharacteristic
275C42#41×C3112yes—
276C23—22no—
277C23—42no—
278C23—42no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23C31×#12011yescharacteristic
283Q8—42no—
284Q8—41no—
285Q8—41no—
286Q8—81no—
287D4—42no—
288D4—41no—
289D4—41no—
290D4—81no—
291D4—82no—
292D4—81no—
293D4—81no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—24no—
297C2×C4—22no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—84no—
310C2×C4C2×C22⋊C4×C3111yescharacteristic
311C2×C4C4×D4×C3112yes—
312C2×C4C31×#12112yes—
313C2×C4C31×#12311yescharacteristic
314C8—24no—
315C8—82no—
316C22—22no—
317C22—42no—
318C22—44no—
319C22—81no—
320C22—81no—
321C22—82no—
322C22—81no—
323C22—82no—
324C22C31×#38611yescharacteristic
325C22C31×#45311yescharacteristic
326C22C31×#45311yescharacteristic
327C4—21no—
328C4—21no—
329C4—22no—
330C4—22no—
331C4—44no—
332C4—42no—
333C4—82no—
334C4—81no—
335C2—21no—
336C2—21no—
337C2—82no—
338C2—161no—
339C2C31×#188711yescharacteristic
340C2C31×#190612yes—
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3153C2
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
2. C31×#2372C2semidirect
3. C31×#1533C2semidirect
4. C31×#1505C2semidirect
5. C31×#1300C2semidirect
10. C31×#497C4semidirect
11. C31×#496C4semidirect
36. C31×C4⋊Q8C2×C4semidirect
37. C31×#127C2×C4semidirect
54. C31×#97C2×C4semidirect
105. #9441C31direct (N × H)
147. #2372C2×C31semidirect
148. #1533C2×C31semidirect
149. #1505C2×C31semidirect
150. #1300C2×C31semidirect
174. #497C4×C31semidirect
175. #496C4×C31semidirect
206. C4⋊Q8C2×C4×C31semidirect
207. #127C2×C4×C31semidirect
224. #97C2×C4×C31semidirect
230. C31#9441direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31532
C31×#23722
C31×#15332
C31×#15052
C31×#13002
#944131