Finite Group Databasebeta

← C31×#7674 #21464433

Subgroups — C31×#7674 #21464433

Order 7936.

550 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2854C211yesmaximal, characteristic
2C31×#1749C211yesmaximal, characteristic, complemented
3C4×C31×C22⋊C8C211yesmaximal, characteristic, complemented
4C31×#1271C212yesmaximal, complemented
5C31×#1270C212yesmaximal, complemented
6C2×C31×#123—21no—
7C2×C31×#121C411yescharacteristic
8C22×C42×C31C2211yescharacteristic
9C2×C31×C22⋊C8—21no—
10C2×C31×C22⋊C8—21no—
11C2×C31×#97—21no—
12C2×C4×C8×C31—21no—
13C31×#390C411yescharacteristic
14C31×#390C2211yescharacteristic
15C31×#389C411yescharacteristic
16C31×#389C2211yescharacteristic
17C31×#388—21no—
18C31×#388—21no—
19C31×#386—21no—
20C31×#380C411yescharacteristic
21C31×#336C2212yes—
22C31×#336C2212yes—
23C22×D4×C31—21no—
24C22×D4×C31C2×C411yescharacteristic
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31D411yescharacteristic
27C23×C4×C31D411yescharacteristic
28C22×C8×C31—22no—
29C22×C8×C31—22no—
30C31×#123—44no—
31C31×#121—42no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C42×C31—42no—
44C2×C42×C31C2×C411yescharacteristic
45C2×C42×C31D411yescharacteristic
46C2×C42×C31D411yescharacteristic
47C2×C42×C31C2311yescharacteristic
48C31×C22⋊C8—24no—
49C31×C22⋊C8—24no—
50C31×#97—42no—
51C4×C8×C31—42no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C24×C31—21no—
56C24×C31C22⋊C411yescharacteristic
57C2×D4×C31—22no—
58C2×D4×C31—41no—
59C2×D4×C31—41no—
60C2×D4×C31—42no—
61C2×D4×C31—42no—
62C2×D4×C31—42no—
63C22×C4×C31—22no—
64C22×C4×C31—22no—
65C22×C4×C31—22no—
66C22×C4×C31—22no—
67C22×C4×C31—22no—
68C22×C4×C31—22no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—41no—
73C22×C4×C31—41no—
74C22×C4×C31—41no—
75C22×C4×C31C22⋊C411yescharacteristic
76C22×C4×C31C22⋊C411yescharacteristic
77C22×C4×C31C22⋊C411yescharacteristic
78C22×C4×C31C22×C411yescharacteristic
79C22×C4×C31C2×D411yescharacteristic
80C22×C4×C31C2×D411yescharacteristic
81C2×C8×C31—24no—
82C2×C8×C31—24no—
83C2×C8×C31—42no—
84C2×C8×C31—42no—
85C2×C8×C31—42no—
86C2×C8×C31—42no—
87C4⋊C4×C31—22no—
88C4⋊C4×C31—42no—
89C4⋊C4×C31—41no—
90C4⋊C4×C31—41no—
91C4⋊C4×C31—42no—
92C22⋊C4×C31—42no—
93C22⋊C4×C31—42no—
94C22⋊C4×C31—42no—
95C22⋊C4×C31—42no—
96C22⋊C4×C31—42no—
97C22⋊C4×C31—42no—
98C42×C31—22no—
99C42×C31—22no—
100C42×C31—41no—
101C42×C31—41no—
102#7674C3111yesmaximal, characteristic, direct product factor, Sylow
103C23×C31—21no—
104C23×C31—21no—
105C23×C31—21no—
106C23×C31—21no—
107C23×C31—21no—
108C23×C31—21no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31—41no—
112C23×C31—41no—
113C23×C31—41no—
114C23×C31—41no—
115C23×C31—41no—
116C23×C31#10412yes—
117C23×C31C2×C22⋊C411yescharacteristic
118D4×C31—82no—
119D4×C31—84no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—44no—
134C2×C4×C31—44no—
135C2×C4×C31—44no—
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#9912yes—
146C2×C4×C31#10412yes—
147C2×C4×C31#13112yes—
148C2×C4×C31#13512yes—
149C2×C4×C31AGL(1,ℤ/8)12yes—
150C8×C31—44no—
151C8×C31—44no—
152#2854C2×C3111yescharacteristic
153#1749C2×C3111yescharacteristic, complemented
154C4×C22⋊C8C2×C3111yescharacteristic, complemented
155#1271C2×C3112yescomplemented
156#1270C2×C3112yescomplemented
157C22×C31—22no—
158C22×C31—22no—
159C22×C31—22no—
160C22×C31—41no—
161C22×C31—41no—
162C22×C31—41no—
163C22×C31—41no—
164C22×C31—81no—
165C22×C31—81no—
166C22×C31—81no—
167C22×C31—81no—
168C22×C31—81no—
169C22×C31—81no—
170C22×C31—81no—
171C22×C31#40811yescharacteristic
172C22×C31C2×#9911yescharacteristic
173C22×C31#41311yescharacteristic
174C22×C31#41611yescharacteristic
175C22×C31#41811yescharacteristic
176C22×C31C2×#10411yescharacteristic
177C22×C31C2×#10411yescharacteristic
178C4×C31—22no—
179C4×C31—22no—
180C4×C31—22no—
181C4×C31—22no—
182C4×C31—22no—
183C4×C31—41no—
184C4×C31—81no—
185C4×C31—81no—
186C4×C31—81no—
187C2×#123—21no—
188C2×#121C4×C3111yescharacteristic
189C22×C42C22×C3111yescharacteristic
190C2×C22⋊C8—21no—
191C2×C22⋊C8—21no—
192C2×#97—21no—
193C2×C4×C8—21no—
194#390C4×C3111yescharacteristic
195#390C22×C3111yescharacteristic
196#389C4×C3111yescharacteristic
197#389C22×C3111yescharacteristic
198#388—21no—
199#388—21no—
200#386—21no—
201#380C4×C3111yescharacteristic
202#336C22×C3112yes—
203#336C22×C3112yes—
204C2×C31—42no—
205C2×C31—161no—
206C2×C31#146811yescharacteristic
207C2×C31#148411yescharacteristic
208C2×C31#149411yescharacteristic
209C2×C31#150111yescharacteristic
210C2×C31#150711yescharacteristic
211C2×C31#152411yescharacteristic
212C2×C31#155311yescharacteristic
213C22×D4—21no—
214C22×D4C2×C4×C3111yescharacteristic
215C23×C4C2×C4×C3111yescharacteristic
216C23×C4D4×C3111yescharacteristic
217C23×C4D4×C3111yescharacteristic
218C22×C8—22no—
219C22×C8—22no—
220#123—44no—
221#121—42no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4C2×C4×C3111yescharacteristic
225C2×C4⋊C4C2×C4×C3111yescharacteristic
226C2×C4⋊C4C2×C4×C3111yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C42—42no—
234C2×C42C2×C4×C3111yescharacteristic
235C2×C42D4×C3111yescharacteristic
236C2×C42D4×C3111yescharacteristic
237C2×C42C23×C3111yescharacteristic
238C22⋊C8—24no—
239C22⋊C8—24no—
240#97—42no—
241C4×C8—42no—
242#95—21no—
243#95—21no—
244#95—21no—
245C31#767411yescharacteristic, direct product factor, Sylow
246C24—21no—
247C24C22⋊C4×C3111yescharacteristic
248C2×D4—22no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—42no—
252C2×D4—42no—
253C2×D4—42no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4C22⋊C4×C3111yescharacteristic
267C22×C4C22⋊C4×C3111yescharacteristic
268C22×C4C22⋊C4×C3111yescharacteristic
269C22×C4C22×C4×C3111yescharacteristic
270C22×C4C2×D4×C3111yescharacteristic
271C22×C4C2×D4×C3111yescharacteristic
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—42no—
275C2×C8—42no—
276C2×C8—42no—
277C2×C8—42no—
278C4⋊C4—22no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C42—22no—
290C42—22no—
291C42—41no—
292C42—41no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23C31×#10412yes—
307C23C2×C22⋊C4×C3111yescharacteristic
308D4—82no—
309D4—84no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—44no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4C31×#9912yes—
336C2×C4C31×#10412yes—
337C2×C4C31×#13112yes—
338C2×C4C31×#13512yes—
339C2×C4C31×AGL(1,ℤ/8)12yes—
340C8—44no—
341C8—44no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22C31×#40811yescharacteristic
357C22C2×C31×#9911yescharacteristic
358C22C31×#41311yescharacteristic
359C22C31×#41611yescharacteristic
360C22C31×#41811yescharacteristic
361C22C2×C31×#10411yescharacteristic
362C22C2×C31×#10411yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—41no—
369C4—81no—
370C4—81no—
371C4—81no—
372C2—42no—
373C2—161no—
374C2C31×#146811yescharacteristic
375C2C31×#148411yescharacteristic
376C2C31×#149411yescharacteristic
377C2C31×#150111yescharacteristic
378C2C31×#150711yescharacteristic
379C2C31×#152411yescharacteristic
380C2C31×#155311yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1749C2semidirect
3. C4×C31×C22⋊C8C2semidirect
4. C31×#1271C2semidirect
5. C31×#1270C2semidirect
102. #7674C31direct (N × H)
153. #1749C2×C31semidirect
154. C4×C22⋊C8C2×C31semidirect
155. #1271C2×C31semidirect
156. #1270C2×C31semidirect
245. C31#7674direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28542
C31×#17492
C4×C31×C22⋊C82
C31×#12712
C31×#12702
#767431