Finite Group Databasebeta

← C31×#7608 #21464367

Subgroups — C31×#7608 #21464367

Order 7936.

484 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2293C211yesmaximal, characteristic
2C31×#1839C211yesmaximal, characteristic, complemented
3C31×#1745C211yesmaximal, characteristic, complemented
4C31×#1271C212yesmaximal, complemented
5C31×#1270C212yesmaximal
6C2×C4×D4×C31C411yescharacteristic
7C2×C31×#117—21no—
8C2×C31×#97—21no—
9C31×#390C411yescharacteristic
10C31×#390C2211yescharacteristic
11C31×#389C411yescharacteristic
12C31×#389C2211yescharacteristic
13C31×#388—21no—
14C31×#388—21no—
15C4×C4⋊C4×C31C411yescharacteristic
16C4×C22⋊C4×C31—21no—
17C43×C31C2211yescharacteristic
18C31×#336—21no—
19C31×#336—21no—
20C31×#336—21no—
21C31×#336C2212yes—
22C31×#336C2212yes—
23C22×D4×C31C2×C411yescharacteristic
24C23×C4×C31—21no—
25C22×C8×C31—22no—
26C22×C8×C31—22no—
27C4×D4×C31—22no—
28C4×D4×C31—22no—
29C31×#117—44no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31C2×C411yescharacteristic
33C2×C4⋊C4×C31C2×C411yescharacteristic
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C22⋊C4×C31—21no—
36C2×C22⋊C4×C31—21no—
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C42×C31—21no—
41C2×C42×C31C2×C411yescharacteristic
42C2×C42×C31C2×C411yescharacteristic
43C2×C42×C31D411yescharacteristic
44C2×C42×C31D411yescharacteristic
45C2×C42×C31D411yescharacteristic
46C2×C42×C31D411yescharacteristic
47C2×C42×C31C2311yescharacteristic
48C31×#97—24no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95—21no—
52C24×C31—21no—
53C2×D4×C31—21no—
54C2×D4×C31—41no—
55C2×D4×C31—41no—
56C2×D4×C31M1612yes—
57C22×C4×C31—24no—
58C22×C4×C31—21no—
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—42no—
62C22×C4×C31—42no—
63C22×C4×C31C22⋊C411yescharacteristic
64C22×C4×C31C22⋊C411yescharacteristic
65C22×C4×C31C22⋊C411yescharacteristic
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31C22×C411yescharacteristic
68C22×C4×C31C2×D411yescharacteristic
69C22×C4×C31C2×D411yescharacteristic
70C2×C8×C31—24no—
71C2×C8×C31—42no—
72C2×C8×C31—42no—
73C2×C8×C31—42no—
74C2×C8×C31—42no—
75C2×C8×C31—42no—
76C4⋊C4×C31—21no—
77C4⋊C4×C31—42no—
78C4⋊C4×C31—41no—
79C4⋊C4×C31—41no—
80C4⋊C4×C31—42no—
81C4⋊C4×C31M1612yes—
82C22⋊C4×C31—24no—
83C22⋊C4×C31—42no—
84C22⋊C4×C31—42no—
85C22⋊C4×C31—42no—
86C22⋊C4×C31—42no—
87C42×C31—22no—
88C42×C31—21no—
89C42×C31—21no—
90C42×C31—22no—
91C42×C31—22no—
92C42×C31—41no—
93C42×C31—41no—
94C42×C31—41no—
95C42×C31—42no—
96#7608C3111yesmaximal, characteristic, direct product factor, Sylow
97C23×C31—22no—
98C23×C31—41no—
99C23×C31—41no—
100C23×C31—41no—
101C23×C31—41no—
102C23×C31—41no—
103C23×C31—41no—
104C23×C31C2×C22⋊C411yescharacteristic
105D4×C31—42no—
106D4×C31—42no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—22no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—48no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
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#10412yes—
135C2×C4×C31C2×M1611yescharacteristic
136C2×C4×C31C2×M1611yescharacteristic
137C2×C4×C31#13512yes—
138C2×C4×C31AGL(1,ℤ/8)12yes—
139C8×C31—44no—
140C8×C31—82no—
141#2293C2×C3111yescharacteristic
142#1839C2×C3111yescharacteristic, complemented
143#1745C2×C3111yescharacteristic, complemented
144#1271C2×C3112yescomplemented
145#1270C2×C3112yes—
146C22×C31—42no—
147C22×C31—42no—
148C22×C31—42no—
149C22×C31—81no—
150C22×C31—81no—
151C22×C31—81no—
152C22×C31—81no—
153C22×C31#40711yescharacteristic
154C22×C31#41011yescharacteristic
155C22×C31#41311yescharacteristic
156C22×C31#41611yescharacteristic
157C22×C31#41811yescharacteristic
158C22×C31C2×#10411yescharacteristic
159C22×C31#42111yescharacteristic
160C4×C31—21no—
161C4×C31—21no—
162C4×C31—22no—
163C4×C31—22no—
164C4×C31—22no—
165C4×C31—41no—
166C4×C31—41no—
167C4×C31—42no—
168C4×C31—41no—
169C4×C31—81no—
170C4×C31—81no—
171C2×C4×D4C4×C3111yescharacteristic
172C2×#117—21no—
173C2×#97—21no—
174#390C4×C3111yescharacteristic
175#390C22×C3111yescharacteristic
176#389C4×C3111yescharacteristic
177#389C22×C3111yescharacteristic
178#388—21no—
179#388—21no—
180C4×C4⋊C4C4×C3111yescharacteristic
181C4×C22⋊C4—21no—
182C43C22×C3111yescharacteristic
183#336—21no—
184#336—21no—
185#336—21no—
186#336C22×C3112yes—
187#336C22×C3112yes—
188C2×C31—82no—
189C2×C31#146411yescharacteristic
190C2×C31#148811yescharacteristic
191C2×C31#149011yescharacteristic
192C2×C31#150011yescharacteristic
193C2×C31#151411yescharacteristic
194C2×C31#152911yescharacteristic
195C2×C31#155311yescharacteristic
196C22×D4C2×C4×C3111yescharacteristic
197C23×C4—21no—
198C22×C8—22no—
199C22×C8—22no—
200C4×D4—22no—
201C4×D4—22no—
202#117—44no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×C4×C3111yescharacteristic
206C2×C4⋊C4C2×C4×C3111yescharacteristic
207C2×C4⋊C4C2×C4×C3111yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C42—21no—
214C2×C42C2×C4×C3111yescharacteristic
215C2×C42C2×C4×C3111yescharacteristic
216C2×C42D4×C3111yescharacteristic
217C2×C42D4×C3111yescharacteristic
218C2×C42D4×C3111yescharacteristic
219C2×C42D4×C3111yescharacteristic
220C2×C42C23×C3111yescharacteristic
221#97—24no—
222#95—21no—
223#95—21no—
224#95—21no—
225C31#760811yescharacteristic, direct product factor, Sylow
226C24—21no—
227C2×D4—21no—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4M16×C3112yes—
231C22×C4—24no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4C22⋊C4×C3111yescharacteristic
238C22×C4C22⋊C4×C3111yescharacteristic
239C22×C4C22⋊C4×C3111yescharacteristic
240C22×C4C22⋊C4×C3111yescharacteristic
241C22×C4C22×C4×C3111yescharacteristic
242C22×C4C2×D4×C3111yescharacteristic
243C22×C4C2×D4×C3111yescharacteristic
244C2×C8—24no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4M16×C3112yes—
256C22⋊C4—24no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C42—22no—
262C42—21no—
263C42—21no—
264C42—22no—
265C42—22no—
266C42—41no—
267C42—41no—
268C42—41no—
269C42—42no—
270C23—22no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23C2×C22⋊C4×C3111yescharacteristic
278D4—42no—
279D4—42no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—48no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4C31×#10412yes—
308C2×C4C2×M16×C3111yescharacteristic
309C2×C4C2×M16×C3111yescharacteristic
310C2×C4C31×#13512yes—
311C2×C4C31×AGL(1,ℤ/8)12yes—
312C8—44no—
313C8—82no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22C31×#40711yescharacteristic
322C22C31×#41011yescharacteristic
323C22C31×#41311yescharacteristic
324C22C31×#41611yescharacteristic
325C22C31×#41811yescharacteristic
326C22C2×C31×#10411yescharacteristic
327C22C31×#42111yescharacteristic
328C4—21no—
329C4—21no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—42no—
336C4—41no—
337C4—81no—
338C4—81no—
339C2—82no—
340C2C31×#146411yescharacteristic
341C2C31×#148811yescharacteristic
342C2C31×#149011yescharacteristic
343C2C31×#150011yescharacteristic
344C2C31×#151411yescharacteristic
345C2C31×#152911yescharacteristic
346C2C31×#155311yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1839C2semidirect
3. C31×#1745C2semidirect
4. C31×#1271C2semidirect
96. #7608C31direct (N × H)
142. #1839C2×C31semidirect
143. #1745C2×C31semidirect
144. #1271C2×C31semidirect
225. C31#7608direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#22932
C31×#18392
C31×#17452
C31×#12712
C31×#12702
#760831