Finite Group Databasebeta

← C31×#8966 #21465725

Subgroups — C31×#8966 #21465725

Order 7936.

626 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2972C211yesmaximal, characteristic
2C4×C31×#123C211yesmaximal, characteristic
3C31×#1817C212yesmaximal, complemented
4C31×#1459C211yesmaximal, characteristic
5C31×#1282C212yesmaximal, complemented
6C2×C31×#123C411yescharacteristic
7C2×C4×D4×C31C2211yescharacteristic
8C22×C42×C31C2211yescharacteristic
9C8×D4×C31—24no—
10C31×#431—21no—
11C2×C31×C22⋊C8—21no—
12C2×C31×C22⋊C8C2212yes—
13C2×C31×C22⋊C8C2212yes—
14C31×#388—21no—
15C31×#387—21no—
16C31×#386C411yescharacteristic
17C31×#385C411yescharacteristic
18C31×#381C411yescharacteristic
19C4×C4⋊C4×C31—21no—
20C4×C22⋊C4×C31—21no—
21C4×C22⋊C4×C31C2211yescharacteristic
22C31×#336—24no—
23C31×#324—21no—
24C31×#323—21no—
25C22×D4×C31C2×C411yescharacteristic
26C23×C4×C31C2×C411yescharacteristic
27C23×C4×C31C2×C411yescharacteristic
28C23×C4×C31D411yescharacteristic
29C23×C4×C31C2311yescharacteristic
30C22×C8×C31—22no—
31C22×C8×C31—22no—
32C22×C8×C31D414yes—
33C31×#123—22no—
34C31×#123C814yescomplemented
35C4×D4×C31—22no—
36C4×D4×C31—22no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31D411yescharacteristic
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31C2×C411yescharacteristic
43C2×C22⋊C4×C31C2×C411yescharacteristic
44C2×C22⋊C4×C31C2×C411yescharacteristic
45C2×C22⋊C4×C31D411yescharacteristic
46C2×C42×C31—22no—
47C2×C42×C31—21no—
48C2×C42×C31—21no—
49C2×C42×C31—21no—
50C2×C42×C31—22no—
51C2×C42×C31D411yescharacteristic
52C31×C4⋊C8—22no—
53C31×C22⋊C8—22no—
54C31×C22⋊C8—22no—
55C31×C22⋊C8—22no—
56C31×C22⋊C8—22no—
57C31×C22⋊C8—22no—
58C4×C8×C31—22no—
59C31×#95—21no—
60C31×#95—21no—
61C31×#95—21no—
62C31×#95—21no—
63C31×#95—21no—
64C24×C31C22⋊C411yescharacteristic
65C24×C31C22×C411yescharacteristic
66C2×D4×C31—22no—
67C2×D4×C31—22no—
68C2×D4×C31C2×C812yes—
69C2×D4×C31M1612yes—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31—22no—
74C22×C4×C31—22no—
75C22×C4×C31—21no—
76C22×C4×C31—22no—
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—21no—
80C22×C4×C31—42no—
81C22×C4×C31—42no—
82C22×C4×C31—42no—
83C22×C4×C31C22⋊C411yescharacteristic
84C22×C4×C31C22⋊C411yescharacteristic
85C22×C4×C31C22⋊C411yescharacteristic
86C22×C4×C31C2×C812yescomplemented
87C22×C4×C31C2×D412yes—
88C22×C4×C31C2×D411yescharacteristic
89C22×C4×C31C2×D411yescharacteristic
90C22×C4×C31#4112yes—
91C2×C8×C31—24no—
92C2×C8×C31—44no—
93C2×C8×C31—44no—
94C2×C8×C31—42no—
95C2×C8×C31—82no—
96C4⋊C4×C31—24no—
97C4⋊C4×C31—22no—
98C4⋊C4×C31—42no—
99C22⋊C4×C31—24no—
100C22⋊C4×C31—22no—
101C22⋊C4×C31—21no—
102C22⋊C4×C31—22no—
103C22⋊C4×C31—22no—
104C22⋊C4×C31—42no—
105C22⋊C4×C31C2×C812yescomplemented
106C42×C31—21no—
107C42×C31—21no—
108C42×C31—42no—
109C42×C31—41no—
110C42×C31—42no—
111C42×C31—41no—
112#8966C3111yesmaximal, characteristic, direct product factor, Sylow
113C23×C31—21no—
114C23×C31—21no—
115C23×C31—41no—
116C23×C31—41no—
117C23×C31—41no—
118C23×C31—41no—
119C23×C31C22⋊C812yes—
120C23×C31C2×C22⋊C411yescharacteristic
121C23×C31C4×D412yes—
122C23×C31C22×C811yescharacteristic
123C23×C31C2×M1611yescharacteristic
124C23×C31#13112yes—
125D4×C31—24no—
126D4×C31—24no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—22no—
130C2×C4×C31—24no—
131C2×C4×C31—22no—
132C2×C4×C31—24no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—22no—
136C2×C4×C31—22no—
137C2×C4×C31—24no—
138C2×C4×C31—41no—
139C2×C4×C31—42no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—42no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—42no—
148C2×C4×C31—42no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—81no—
155C2×C4×C31C22⋊C812yes—
156C2×C4×C31#12011yescharacteristic
157C2×C4×C31#12112yes—
158C2×C4×C31#12311yescharacteristic
159C8×C31—44no—
160C8×C31—82no—
161#2972C2×C3111yescharacteristic
162C4×#123C2×C3111yescharacteristic
163#1817C2×C3112yescomplemented
164#1459C2×C3111yescharacteristic
165#1282C2×C3112yescomplemented
166C22×C31—21no—
167C22×C31—22no—
168C22×C31—21no—
169C22×C31—22no—
170C22×C31—22no—
171C22×C31—41no—
172C22×C31—41no—
173C22×C31—42no—
174C22×C31—42no—
175C22×C31—41no—
176C22×C31—41no—
177C22×C31—81no—
178C22×C31#38611yescharacteristic
179C22×C31C2×C22⋊C811yescharacteristic
180C22×C31#40811yescharacteristic
181C22×C31C8×D412yes—
182C22×C31#43512yes—
183C4×C31—22no—
184C4×C31—22no—
185C4×C31—21no—
186C4×C31—42no—
187C4×C31—42no—
188C4×C31—41no—
189C4×C31—42no—
190C4×C31—41no—
191C4×C31—81no—
192C4×C31#45812yes—
193C2×#123C4×C3111yescharacteristic
194C2×C4×D4C22×C3111yescharacteristic
195C22×C42C22×C3111yescharacteristic
196C8×D4—24no—
197#431—21no—
198C2×C22⋊C8—21no—
199C2×C22⋊C8C22×C3112yes—
200C2×C22⋊C8C22×C3112yes—
201#388—21no—
202#387—21no—
203#386C4×C3111yescharacteristic
204#385C4×C3111yescharacteristic
205#381C4×C3111yescharacteristic
206C4×C4⋊C4—21no—
207C4×C22⋊C4—21no—
208C4×C22⋊C4C22×C3111yescharacteristic
209#336—24no—
210#324—21no—
211#323—21no—
212C2×C31—21no—
213C2×C31—21no—
214C2×C31—22no—
215C2×C31—22no—
216C2×C31—42no—
217C2×C31#186911yescharacteristic
218C2×C31#189011yescharacteristic
219C2×C31#189111yescharacteristic
220C22×D4C2×C4×C3111yescharacteristic
221C23×C4C2×C4×C3111yescharacteristic
222C23×C4C2×C4×C3111yescharacteristic
223C23×C4D4×C3111yescharacteristic
224C23×C4C23×C3111yescharacteristic
225C22×C8—22no—
226C22×C8—22no—
227C22×C8D4×C3114yes—
228#123—22no—
229#123C8×C3114yescomplemented
230C4×D4—22no—
231C4×D4—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4D4×C3111yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4C2×C4×C3111yescharacteristic
238C2×C22⋊C4C2×C4×C3111yescharacteristic
239C2×C22⋊C4C2×C4×C3111yescharacteristic
240C2×C22⋊C4D4×C3111yescharacteristic
241C2×C42—22no—
242C2×C42—21no—
243C2×C42—21no—
244C2×C42—21no—
245C2×C42—22no—
246C2×C42D4×C3111yescharacteristic
247C4⋊C8—22no—
248C22⋊C8—22no—
249C22⋊C8—22no—
250C22⋊C8—22no—
251C22⋊C8—22no—
252C22⋊C8—22no—
253C4×C8—22no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259C31#896611yescharacteristic, direct product factor, Sylow
260C24C22⋊C4×C3111yescharacteristic
261C24C22×C4×C3111yescharacteristic
262C2×D4—22no—
263C2×D4—22no—
264C2×D4C2×C8×C3112yes—
265C2×D4M16×C3112yes—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4C22⋊C4×C3111yescharacteristic
280C22×C4C22⋊C4×C3111yescharacteristic
281C22×C4C22⋊C4×C3111yescharacteristic
282C22×C4C2×C8×C3112yescomplemented
283C22×C4C2×D4×C3112yes—
284C22×C4C2×D4×C3111yescharacteristic
285C22×C4C2×D4×C3111yescharacteristic
286C22×C4#41×C3112yes—
287C2×C8—24no—
288C2×C8—44no—
289C2×C8—44no—
290C2×C8—42no—
291C2×C8—82no—
292C4⋊C4—24no—
293C4⋊C4—22no—
294C4⋊C4—42no—
295C22⋊C4—24no—
296C22⋊C4—22no—
297C22⋊C4—21no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—42no—
301C22⋊C4C2×C8×C3112yescomplemented
302C42—21no—
303C42—21no—
304C42—42no—
305C42—41no—
306C42—42no—
307C42—41no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23C31×C22⋊C812yes—
315C23C2×C22⋊C4×C3111yescharacteristic
316C23C4×D4×C3112yes—
317C23C22×C8×C3111yescharacteristic
318C23C2×M16×C3111yescharacteristic
319C23C31×#13112yes—
320D4—24no—
321D4—24no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—22no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—24no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4C31×C22⋊C812yes—
351C2×C4C31×#12011yescharacteristic
352C2×C4C31×#12112yes—
353C2×C4C31×#12311yescharacteristic
354C8—44no—
355C8—82no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—42no—
364C22—42no—
365C22—41no—
366C22—41no—
367C22—81no—
368C22C31×#38611yescharacteristic
369C22C2×C31×C22⋊C811yescharacteristic
370C22C31×#40811yescharacteristic
371C22C8×D4×C3112yes—
372C22C31×#43512yes—
373C4—22no—
374C4—22no—
375C4—21no—
376C4—42no—
377C4—42no—
378C4—41no—
379C4—42no—
380C4—41no—
381C4—81no—
382C4C31×#45812yes—
383C2—21no—
384C2—21no—
385C2—22no—
386C2—22no—
387C2—42no—
388C2C31×#186911yescharacteristic
389C2C31×#189011yescharacteristic
390C2C31×#189111yescharacteristic
subgroupG/H
centerC2×C4×C31#120
commutatorC23C22×C8×C31
Frattini, cosocleC23×C4C23×C31
socleC22×C31#386
prime radicalC22×D4×C31C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1817C2semidirect
5. C31×#1282C2semidirect
34. C31×#123C8semidirect
86. C22×C4×C31C2×C8semidirect
105. C22⋊C4×C31C2×C8semidirect
112. #8966C31direct (N × H)
163. #1817C2×C31semidirect
165. #1282C2×C31semidirect
229. #123C8×C31semidirect
259. C31#8966direct (N × H)
282. C22×C4C2×C8×C31semidirect
301. C22⋊C4C2×C8×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#29722
C4×C31×#1232
C31×#18172
C31×#14592
C31×#12822
#896631