Finite Group Databasebeta

← C31×#12146 #21468905

Subgroups — C31×#12146 #21468905

Order 7936.

380 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2792C211yesmaximal, characteristic, complemented
2C31×#2039C211yesmaximal, characteristic
3C31×#1610C211yesmaximal, characteristic
4C31×#1604C211yesmaximal, characteristic
5C31×#1354C211yesmaximal, characteristic, complemented
6C31×#1346C211yesmaximal, characteristic, complemented
7C31×#1325C211yesmaximal, characteristic, complemented
8C31×#537C2211yescharacteristic
9C31×#480—21no—
10C31×#448—21no—
11C2×C31×#104—21no—
12C31×#417—21no—
13C31×#398—21no—
14C31×#398C2211yescharacteristic
15C31×#395—21no—
16C31×#395C2211yescharacteristic
17C31×#389—21no—
18C31×#389—21no—
19C31×#387—21no—
20C31×#387—21no—
21C31×#384C2211yescharacteristic
22C31×#343C2211yescharacteristic
23C31×#327—21no—
24C31×#327—21no—
25C31×#324C2211yescharacteristic
26C31×#324C2211yescharacteristic
27C2×#41×C31—21no—
28C22×Q8×C31D411yescharacteristic
29C2×SD16×C31—41no—
30C2×M16×C31—21no—
31C31×C22⋊Q8—41no—
32C31×#121—21no—
33C31×#121—21no—
34C31×#121—41no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31—21no—
40C2×C4⋊C4×C31—21no—
41C2×C4⋊C4×C31—21no—
42C2×C4⋊C4×C31D411yescharacteristic
43C2×C4⋊C4×C31D411yescharacteristic
44C2×C4⋊C4×C31C2311yescharacteristic
45C2×C42×C31—21no—
46C2×C42×C31D411yescharacteristic
47C31×#107—41no—
48C31×#104—42no—
49C31×#103—41no—
50C31×#103—41no—
51C31×#102—41no—
52C31×#102—41no—
53C31×C22⋊C8—21no—
54C31×C22⋊C8—21no—
55C31×#95—21no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95—21no—
61C31×#95D411yescharacteristic
62C31×#95D411yescharacteristic
63#41×C31—41no—
64#41×C31—41no—
65#41×C31—41no—
66#41×C31—41no—
67C2×Q8×C31—21no—
68C2×Q8×C31—41no—
69C2×Q8×C31—81no—
70C2×D4×C31—21no—
71C2×D4×C31—21no—
72C2×D4×C31—21no—
73C2×D4×C31—41no—
74C22×C4×C31—21no—
75C22×C4×C31—21no—
76C22×C4×C31—21no—
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—21no—
80C22×C4×C31—41no—
81C22×C4×C31C2×D411yescharacteristic
82C22×C4×C31C2×D411yescharacteristic
83C22×C4×C31C2×D411yescharacteristic
84SD16×C31—82no—
85M16×C31—41no—
86M16×C31—41no—
87C2×C8×C31—41no—
88C2×C8×C31—41no—
89C2×C8×C31—41no—
90C4⋊C4×C31—24no—
91C4⋊C4×C31—21no—
92C4⋊C4×C31—21no—
93C4⋊C4×C31—41no—
94C4⋊C4×C31—41no—
95C4⋊C4×C31—41no—
96C4⋊C4×C31—41no—
97C4⋊C4×C31—41no—
98C4⋊C4×C31—81no—
99C4⋊C4×C31—81no—
100C4⋊C4×C31—81no—
101C4⋊C4×C31—81no—
102C4⋊C4×C31—81no—
103C22⋊C4×C31—41no—
104C22⋊C4×C31—41no—
105C42×C31—21no—
106C42×C31—21no—
107C42×C31—81no—
108#12146C3111yesmaximal, characteristic, direct product factor, Sylow
109C23×C31—41no—
110C23×C31#12011yescharacteristic
111Q8×C31—41no—
112Q8×C31—41no—
113Q8×C31—42no—
114Q8×C31—81no—
115D4×C31—41no—
116D4×C31—41no—
117D4×C31—81no—
118D4×C31—81no—
119D4×C31—81no—
120D4×C31—81no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—22no—
124C2×C4×C31—22no—
125C2×C4×C31—22no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—41no—
129C2×C4×C31—41no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
132C2×C4×C31—41no—
133C2×C4×C31—41no—
134C2×C4×C31—41no—
135C2×C4×C31—41no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—81no—
147C2×C4×C31—81no—
148C2×C4×C31#13511yescharacteristic
149C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
150C8×C31—81no—
151C8×C31—81no—
152C8×C31—81no—
153#2792C2×C3111yescharacteristic, complemented
154#2039C2×C3111yescharacteristic
155#1610C2×C3111yescharacteristic
156#1604C2×C3111yescharacteristic
157#1354C2×C3111yescharacteristic, complemented
158#1346C2×C3111yescharacteristic, complemented
159#1325C2×C3111yescharacteristic, complemented
160C22×C31—21no—
161C22×C31—21no—
162C22×C31—81no—
163C22×C31—81no—
164C22×C31—81no—
165C22×C31#44911yescharacteristic
166C22×C31#45411yescharacteristic
167C22×C31B(4,𝔽2)11yescharacteristic
168C4×C31—21no—
169C4×C31—21no—
170C4×C31—42no—
171C4×C31—42no—
172C4×C31—42no—
173C4×C31—41no—
174C4×C31—41no—
175C4×C31—81no—
176C4×C31—81no—
177C4×C31—81no—
178C4×C31—81no—
179#537C22×C3111yescharacteristic
180#480—21no—
181#448—21no—
182C2×#104—21no—
183#417—21no—
184#398—21no—
185#398C22×C3111yescharacteristic
186#395—21no—
187#395C22×C3111yescharacteristic
188#389—21no—
189#389—21no—
190#387—21no—
191#387—21no—
192#384C22×C3111yescharacteristic
193#343C22×C3111yescharacteristic
194#327—21no—
195#327—21no—
196#324C22×C3111yescharacteristic
197#324C22×C3111yescharacteristic
198C2×C31—21no—
199C2×C31—21no—
200C2×C31—161no—
201C2×C31#159711yescharacteristic
202C2×C31#220011yescharacteristic
203C2×C31#220511yescharacteristic
204C2×#41—21no—
205C22×Q8D4×C3111yescharacteristic
206C2×SD16—41no—
207C2×M16—21no—
208C22⋊Q8—41no—
209#121—21no—
210#121—21no—
211#121—41no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4D4×C3111yescharacteristic
220C2×C4⋊C4D4×C3111yescharacteristic
221C2×C4⋊C4C23×C3111yescharacteristic
222C2×C42—21no—
223C2×C42D4×C3111yescharacteristic
224#107—41no—
225#104—42no—
226#103—41no—
227#103—41no—
228#102—41no—
229#102—41no—
230C22⋊C8—21no—
231C22⋊C8—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95D4×C3111yescharacteristic
239#95D4×C3111yescharacteristic
240C31#1214611yescharacteristic, direct product factor, Sylow
241#41—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—81no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4C2×D4×C3111yescharacteristic
260C22×C4C2×D4×C3111yescharacteristic
261C22×C4C2×D4×C3111yescharacteristic
262SD16—82no—
263M16—41no—
264M16—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C4⋊C4—24no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—81no—
277C4⋊C4—81no—
278C4⋊C4—81no—
279C4⋊C4—81no—
280C4⋊C4—81no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C42—21no—
284C42—21no—
285C42—81no—
286C23—41no—
287C23C31×#12011yescharacteristic
288Q8—41no—
289Q8—41no—
290Q8—42no—
291Q8—81no—
292D4—41no—
293D4—41no—
294D4—81no—
295D4—81no—
296D4—81no—
297D4—81no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4C31×#13511yescharacteristic
326C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
327C8—81no—
328C8—81no—
329C8—81no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22C31×#44911yescharacteristic
336C22C31×#45411yescharacteristic
337C22C31×B(4,𝔽2)11yescharacteristic
338C4—21no—
339C4—21no—
340C4—42no—
341C4—42no—
342C4—42no—
343C4—41no—
344C4—41no—
345C4—81no—
346C4—81no—
347C4—81no—
348C4—81no—
349C2—21no—
350C2—21no—
351C2—161no—
352C2C31×#159711yescharacteristic
353C2C31×#220011yescharacteristic
354C2C31×#220511yescharacteristic
subgroupG/H
center, socleC22×C31B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC31×#537C22
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C2×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2792C2semidirect
5. C31×#1354C2semidirect
6. C31×#1346C2semidirect
7. C31×#1325C2semidirect
108. #12146C31direct (N × H)
153. #2792C2×C31semidirect
157. #1354C2×C31semidirect
158. #1346C2×C31semidirect
159. #1325C2×C31semidirect
240. C31#12146direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#27922
C31×#20392
C31×#16102
C31×#16042
C31×#13542
C31×#13462
C31×#13252
#1214631