Finite Group Databasebeta

← C31×#9036 #21465795

Subgroups — C31×#9036 #21465795

Order 7936.

566 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2921C211yesmaximal, characteristic, complemented
2C31×#2392C211yesmaximal, characteristic
3C31×#1486C212yesmaximal, complemented
4C31×#1458C211yesmaximal, characteristic, complemented
5C31×#1303C212yesmaximal, complemented
6C2×C4×D4×C31—21no—
7C2×C4×D4×C31C2211yescharacteristic
8C2×C31×#117C2211yescharacteristic
9C31×#433—24no—
10C31×#431C2212yes—
11C31×#423C2212yes—
12C31×#407—21no—
13C4×M16×C31—21no—
14C31×#398C411yescharacteristic
15C31×#397C411yescharacteristic
16C31×#396—21no—
17C31×#394—21no—
18C31×#394C411yescharacteristic
19C31×#392C411yescharacteristic
20C4×C4⋊C4×C31C2211yescharacteristic
21C4×C22⋊C4×C31—21no—
22C31×D4⋊C8—24no—
23C31×#324—21no—
24C31×#323—21no—
25C22×D4×C31—21no—
26C22×D4×C31C2×C411yescharacteristic
27C23×C4×C31—21no—
28C23×C4×C31D411yescharacteristic
29C2×M16×C31—22no—
30C4×D4×C31—22no—
31C4×D4×C31—22no—
32C4×D4×C31—44no—
33C31×#117—22no—
34C31×#117—22no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C4⋊C4×C31D411yescharacteristic
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31C2×C411yescharacteristic
46C2×C22⋊C4×C31D411yescharacteristic
47C2×C42×C31—21no—
48C2×C42×C31D411yescharacteristic
49C2×C42×C31C2311yescharacteristic
50C31×C4⋊C8—22no—
51C31×C4⋊C8—22no—
52C31×C4⋊C8D414yescomplemented
53C31×C22⋊C8—24no—
54C31×C22⋊C8—22no—
55C31×#97—22no—
56C4×C8×C31—22no—
57C4×C8×C31—22no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95C2×C411yescharacteristic
61C31×#95C2×C411yescharacteristic
62C24×C31—21no—
63C24×C31C22⋊C411yescharacteristic
64C2×D4×C31—22no—
65C2×D4×C31—42no—
66C2×D4×C31—42no—
67C2×D4×C31—42no—
68C2×D4×C31—42no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—22no—
73C22×C4×C31—22no—
74C22×C4×C31—21no—
75C22×C4×C31—21no—
76C22×C4×C31—41no—
77C22×C4×C31—41no—
78C22×C4×C31—42no—
79C22×C4×C31—42no—
80C22×C4×C31C22⋊C411yescharacteristic
81C22×C4×C31C22⋊C411yescharacteristic
82C22×C4×C31C22⋊C411yescharacteristic
83C22×C4×C31C22×C411yescharacteristic
84C22×C4×C31C2×D411yescharacteristic
85C22×C4×C31C2×D411yescharacteristic
86M16×C31—42no—
87M16×C31—42no—
88C2×C8×C31—24no—
89C2×C8×C31—42no—
90C4⋊C4×C31—22no—
91C4⋊C4×C31—22no—
92C4⋊C4×C31—22no—
93C4⋊C4×C31—42no—
94C4⋊C4×C31—42no—
95C22⋊C4×C31—22no—
96C22⋊C4×C31—22no—
97C22⋊C4×C31—42no—
98C22⋊C4×C31—42no—
99C22⋊C4×C31—42no—
100C22⋊C4×C31—42no—
101C22⋊C4×C31—42no—
102C42×C31—21no—
103C42×C31—21no—
104C42×C31—42no—
105C42×C31C2×D412yes—
106C42×C31#4112yes—
107#9036C3111yesmaximal, characteristic, direct product factor, Sylow
108C23×C31—22no—
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—21no—
112C23×C31—41no—
113C23×C31—41no—
114C23×C31—41no—
115C23×C31—41no—
116C23×C31—41no—
117C23×C31—41no—
118C23×C31—41no—
119C23×C31—41no—
120C23×C31C2×C22⋊C411yescharacteristic
121D4×C31—24no—
122D4×C31—42no—
123D4×C31—48no—
124C2×C4×C31—22no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
132C2×C4×C31—41no—
133C2×C4×C31—41no—
134C2×C4×C31—42no—
135C2×C4×C31—42no—
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—82no—
145C2×C4×C31—82no—
146C2×C4×C31C4×D412yes—
147C2×C4×C31#12011yescharacteristic
148C2×C4×C31#12112yes—
149C2×C4×C31#12311yescharacteristic
150C2×C4×C31#13512yes—
151C2×C4×C31AGL(1,ℤ/8)12yes—
152C8×C31—44no—
153C8×C31—82no—
154#2921C2×C3111yescharacteristic, complemented
155#2392C2×C3111yescharacteristic
156#1486C2×C3112yescomplemented
157#1458C2×C3111yescharacteristic, complemented
158#1303C2×C3112yescomplemented
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—42no—
162C22×C31—42no—
163C22×C31—42no—
164C22×C31—41no—
165C22×C31—41no—
166C22×C31—42no—
167C22×C31—41no—
168C22×C31—81no—
169C22×C31—81no—
170C22×C31—81no—
171C22×C31—81no—
172C22×C31—81no—
173C22×C31#38611yescharacteristic
174C22×C31#41611yescharacteristic
175C22×C31#41811yescharacteristic
176C4×C31—22no—
177C4×C31—22no—
178C4×C31—42no—
179C4×C31—41no—
180C4×C31—41no—
181C4×C31—41no—
182C4×C31—81no—
183C4×C31—81no—
184C4×C31#44912yes—
185C4×C31#48212yes—
186C2×C4×D4—21no—
187C2×C4×D4C22×C3111yescharacteristic
188C2×#117C22×C3111yescharacteristic
189#433—24no—
190#431C22×C3112yes—
191#423C22×C3112yes—
192#407—21no—
193C4×M16—21no—
194#398C4×C3111yescharacteristic
195#397C4×C3111yescharacteristic
196#396—21no—
197#394—21no—
198#394C4×C3111yescharacteristic
199#392C4×C3111yescharacteristic
200C4×C4⋊C4C22×C3111yescharacteristic
201C4×C22⋊C4—21no—
202D4⋊C8—24no—
203#324—21no—
204#323—21no—
205C2×C31—21no—
206C2×C31—21no—
207C2×C31—81no—
208C2×C31—82no—
209C2×C31#187511yescharacteristic
210C2×C31#188411yescharacteristic
211C2×C31#189111yescharacteristic
212C22×D4—21no—
213C22×D4C2×C4×C3111yescharacteristic
214C23×C4—21no—
215C23×C4D4×C3111yescharacteristic
216C2×M16—22no—
217C4×D4—22no—
218C4×D4—22no—
219C4×D4—44no—
220#117—22no—
221#117—22no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4C2×C4×C3111yescharacteristic
225C2×C4⋊C4C2×C4×C3111yescharacteristic
226C2×C4⋊C4D4×C3111yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4C2×C4×C3111yescharacteristic
233C2×C22⋊C4D4×C3111yescharacteristic
234C2×C42—21no—
235C2×C42D4×C3111yescharacteristic
236C2×C42C23×C3111yescharacteristic
237C4⋊C8—22no—
238C4⋊C8—22no—
239C4⋊C8D4×C3114yescomplemented
240C22⋊C8—24no—
241C22⋊C8—22no—
242#97—22no—
243C4×C8—22no—
244C4×C8—22no—
245#95—21no—
246#95—21no—
247#95C2×C4×C3111yescharacteristic
248#95C2×C4×C3111yescharacteristic
249C31#903611yescharacteristic, direct product factor, Sylow
250C24—21no—
251C24C22⋊C4×C3111yescharacteristic
252C2×D4—22no—
253C2×D4—42no—
254C2×D4—42no—
255C2×D4—42no—
256C2×D4—42no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4C22⋊C4×C3111yescharacteristic
269C22×C4C22⋊C4×C3111yescharacteristic
270C22×C4C22⋊C4×C3111yescharacteristic
271C22×C4C22×C4×C3111yescharacteristic
272C22×C4C2×D4×C3111yescharacteristic
273C22×C4C2×D4×C3111yescharacteristic
274M16—42no—
275M16—42no—
276C2×C8—24no—
277C2×C8—42no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C42—21no—
291C42—21no—
292C42—42no—
293C42C2×D4×C3112yes—
294C42#41×C3112yes—
295C23—22no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23C2×C22⋊C4×C3111yescharacteristic
308D4—24no—
309D4—42no—
310D4—48no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4C4×D4×C3112yes—
334C2×C4C31×#12011yescharacteristic
335C2×C4C31×#12112yes—
336C2×C4C31×#12311yescharacteristic
337C2×C4C31×#13512yes—
338C2×C4C31×AGL(1,ℤ/8)12yes—
339C8—44no—
340C8—82no—
341C22—21no—
342C22—21no—
343C22—42no—
344C22—42no—
345C22—42no—
346C22—41no—
347C22—41no—
348C22—42no—
349C22—41no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22C31×#38611yescharacteristic
356C22C31×#41611yescharacteristic
357C22C31×#41811yescharacteristic
358C4—22no—
359C4—22no—
360C4—42no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—81no—
365C4—81no—
366C4C31×#44912yes—
367C4C31×#48212yes—
368C2—21no—
369C2—21no—
370C2—81no—
371C2—82no—
372C2C31×#187511yescharacteristic
373C2C31×#188411yescharacteristic
374C2C31×#189111yescharacteristic
subgroupG/H
centerC2×C4×C31#120
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
socleC22×C31#386
prime radicalC31×#392C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2921C2semidirect
3. C31×#1486C2semidirect
4. C31×#1458C2semidirect
5. C31×#1303C2semidirect
52. C31×C4⋊C8D4semidirect
107. #9036C31direct (N × H)
154. #2921C2×C31semidirect
156. #1486C2×C31semidirect
157. #1458C2×C31semidirect
158. #1303C2×C31semidirect
239. C4⋊C8D4×C31semidirect
249. C31#9036direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29212
C31×#23922
C31×#14862
C31×#14582
C31×#13032
#903631