Finite Group Databasebeta

← C31×#18390 #21475149

Subgroups — C31×#18390 #21475149

Order 7936.

978 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3501C211yesmaximal, characteristic
2C31×#3209C212yesmaximal, complemented
3C31×#2563C211yesmaximal, characteristic
4C31×#1602C218yesmaximal, complemented
5C31×#1503C212yesmaximal, complemented
6C31×#1460C211yesmaximal, characteristic
7C31×#554—22no—
8C31×#554—24no—
9D4×Q8×C31—22no—
10C31×#544—21no—
11C31×#543C2214yes—
12C31×#533C2212yes—
13C2×C31×C4⋊Q8C2211yescharacteristic
14C2×C31×C22⋊Q8—22no—
15C31×#518—21no—
16C2×C4×D4×C31C2211yescharacteristic
17C31×#494—22no—
18C31×#487—22no—
19C31×#462—24no—
20C31×#451C2218yes—
21C31×#431C2212yes—
22C31×#393C2214yes—
23C31×#390—21no—
24C31×#382—21no—
25C31×#380—22no—
26C4×C4⋊C4×C31C2211yescharacteristic
27C31×#328C2218yes—
28C31×#323C2214yes—
29C22×Q8×C31—22no—
30C22×Q8×C31C2312yes—
31C22×D4×C31D411yescharacteristic
32C23×C4×C31D412yes—
33C2×Q16×C31—28no—
34C31×C4⋊Q8—24no—
35C31×C4⋊Q8—22no—
36C31×C4⋊Q8—22no—
37C31×C4⋊Q8D412yes—
38C31×C4⋊Q8D412yes—
39C31×#125—24no—
40C31×#125—22no—
41C31×C22⋊Q8—24no—
42C31×C22⋊Q8—24no—
43C31×C22⋊Q8—28no—
44C31×C22⋊Q8—22no—
45C31×C22⋊Q8—24no—
46C31×C22⋊Q8—28no—
47C31×C22⋊Q8C2314yes—
48C4×Q8×C31—22no—
49C4×Q8×C31D414yes—
50C4×D4×C31—24no—
51C4×D4×C31—24no—
52C4×D4×C31—22no—
53C4×D4×C31—22no—
54C31×#117—22no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—24no—
57C2×C4⋊C4×C31—21no—
58C2×C4⋊C4×C31—21no—
59C2×C4⋊C4×C31—21no—
60C2×C4⋊C4×C31D411yescharacteristic
61C2×C22⋊C4×C31—24no—
62C2×C22⋊C4×C31—24no—
63C2×C22⋊C4×C31C2312yes—
64C2×C42×C31—21no—
65C2×C42×C31C2311yescharacteristic
66C31×C4⋊C8—22no—
67C31×#103—28no—
68C31×C22⋊C8C2314yes—
69C4×C8×C31—22no—
70C31×#95—24no—
71C31×#95C2312yes—
72C24×C31C2×D412yes—
73C2×Q8×C31—24no—
74C2×Q8×C31—22no—
75C2×Q8×C31—24no—
76C2×Q8×C31—82no—
77C2×Q8×C31—84no—
78C2×Q8×C31C2×D414yes—
79C2×D4×C31—22no—
80C2×D4×C31—22no—
81C2×D4×C31Q1614yescomplemented
82C22×C4×C31—24no—
83C22×C4×C31—24no—
84C22×C4×C31—22no—
85C22×C4×C31—22no—
86C22×C4×C31—22no—
87C22×C4×C31—22no—
88C22×C4×C31—44no—
89C22×C4×C31C2×D411yescharacteristic
90C22×C4×C31C2×D412yes—
91C22×C4×C31C2×D411yescharacteristic
92C22×C4×C31C2411yescharacteristic
93Q16×C31—88no—
94C2×C8×C31—24no—
95C4⋊C4×C31—24no—
96C4⋊C4×C31—28no—
97C4⋊C4×C31—22no—
98C4⋊C4×C31—24no—
99C4⋊C4×C31—22no—
100C4⋊C4×C31—22no—
101C4⋊C4×C31—22no—
102C4⋊C4×C31—24no—
103C4⋊C4×C31—42no—
104C4⋊C4×C31—41no—
105C4⋊C4×C31—42no—
106C4⋊C4×C31—41no—
107C4⋊C4×C31C2×D414yes—
108C22⋊C4×C31—28no—
109C22⋊C4×C31—24no—
110C22⋊C4×C31—24no—
111C22⋊C4×C31—84no—
112C42×C31—24no—
113C42×C31—42no—
114C42×C31C2×D412yes—
115C42×C31C2×D412yes—
116#18390C3111yesmaximal, characteristic, direct product factor, Sylow
117C23×C31—22no—
118C23×C31—22no—
119C23×C31—42no—
120C23×C31—42no—
121C23×C31C2×Q1614yes—
122C23×C31C22×D411yescharacteristic
123Q8×C31—44no—
124Q8×C31—48no—
125Q8×C31—44no—
126Q8×C31—84no—
127D4×C31—28no—
128C2×C4×C31—22no—
129C2×C4×C31—24no—
130C2×C4×C31—24no—
131C2×C4×C31—22no—
132C2×C4×C31—41no—
133C2×C4×C31—44no—
134C2×C4×C31—42no—
135C2×C4×C31—42no—
136C2×C4×C31—44no—
137C2×C4×C31—42no—
138C2×C4×C31—42no—
139C2×C4×C31—42no—
140C2×C4×C31—82no—
141C2×C4×C31—84no—
142C2×C4×C31—84no—
143C2×C4×C31#12011yescharacteristic
144C2×C4×C31#12012yes—
145C2×C4×C31#12011yescharacteristic
146C2×C4×C31C2×Q1612yes—
147C2×C4×C31#13712yes—
148C2×C4×C31C22×D412yes—
149C8×C31—44no—
150#3501C2×C3111yescharacteristic
151#3209C2×C3112yescomplemented
152#2563C2×C3111yescharacteristic
153#1602C2×C3118yescomplemented
154#1503C2×C3112yescomplemented
155#1460C2×C3111yescharacteristic
156C22×C31—21no—
157C22×C31—21no—
158C22×C31—24no—
159C22×C31—44no—
160C22×C31—42no—
161C22×C31—42no—
162C22×C31—82no—
163C22×C31C2×#12011yescharacteristic
164C22×C31C22×Q1611yescharacteristic
165C22×C31C2×#13711yescharacteristic
166C4×C31—21no—
167C4×C31—22no—
168C4×C31—42no—
169C4×C31—44no—
170C4×C31—44no—
171C4×C31—82no—
172C4×C31—82no—
173C4×C31#45114yes—
174C4×C31#45512yes—
175#554—22no—
176#554—24no—
177D4×Q8—22no—
178#544—21no—
179#543C22×C3114yes—
180#533C22×C3112yes—
181C2×C4⋊Q8C22×C3111yescharacteristic
182C2×C22⋊Q8—22no—
183#518—21no—
184C2×C4×D4C22×C3111yescharacteristic
185#494—22no—
186#487—22no—
187#462—24no—
188#451C22×C3118yes—
189#431C22×C3112yes—
190#393C22×C3114yes—
191#390—21no—
192#382—21no—
193#380—22no—
194C4×C4⋊C4C22×C3111yescharacteristic
195#328C22×C3118yes—
196#323C22×C3114yes—
197C2×C31—21no—
198C2×C31—21no—
199C2×C31—44no—
200C2×C31C2×#45111yescharacteristic
201C2×C31C2×#45511yescharacteristic
202C2×C31#302711yescharacteristic
203C22×Q8—22no—
204C22×Q8C23×C3112yes—
205C22×D4D4×C3111yescharacteristic
206C23×C4D4×C3112yes—
207C2×Q16—28no—
208C4⋊Q8—24no—
209C4⋊Q8—22no—
210C4⋊Q8—22no—
211C4⋊Q8D4×C3112yes—
212C4⋊Q8D4×C3112yes—
213#125—24no—
214#125—22no—
215C22⋊Q8—24no—
216C22⋊Q8—24no—
217C22⋊Q8—28no—
218C22⋊Q8—22no—
219C22⋊Q8—24no—
220C22⋊Q8—28no—
221C22⋊Q8C23×C3114yes—
222C4×Q8—22no—
223C4×Q8D4×C3114yes—
224C4×D4—24no—
225C4×D4—24no—
226C4×D4—22no—
227C4×D4—22no—
228#117—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—24no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4D4×C3111yescharacteristic
235C2×C22⋊C4—24no—
236C2×C22⋊C4—24no—
237C2×C22⋊C4C23×C3112yes—
238C2×C42—21no—
239C2×C42C23×C3111yescharacteristic
240C4⋊C8—22no—
241#103—28no—
242C22⋊C8C23×C3114yes—
243C4×C8—22no—
244#95—24no—
245#95C23×C3112yes—
246C31#1839011yescharacteristic, direct product factor, Sylow
247C24C2×D4×C3112yes—
248C2×Q8—24no—
249C2×Q8—22no—
250C2×Q8—24no—
251C2×Q8—82no—
252C2×Q8—84no—
253C2×Q8C2×D4×C3114yes—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4Q16×C3114yescomplemented
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—44no—
264C22×C4C2×D4×C3111yescharacteristic
265C22×C4C2×D4×C3112yes—
266C22×C4C2×D4×C3111yescharacteristic
267C22×C4C24×C3111yescharacteristic
268Q16—88no—
269C2×C8—24no—
270C4⋊C4—24no—
271C4⋊C4—28no—
272C4⋊C4—22no—
273C4⋊C4—24no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—24no—
278C4⋊C4—42no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—41no—
282C4⋊C4C2×D4×C3114yes—
283C22⋊C4—28no—
284C22⋊C4—24no—
285C22⋊C4—24no—
286C22⋊C4—84no—
287C42—24no—
288C42—42no—
289C42C2×D4×C3112yes—
290C42C2×D4×C3112yes—
291C23—22no—
292C23—22no—
293C23—42no—
294C23—42no—
295C23C2×Q16×C3114yes—
296C23C22×D4×C3111yescharacteristic
297Q8—44no—
298Q8—48no—
299Q8—44no—
300Q8—84no—
301D4—28no—
302C2×C4—22no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—44no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—82no—
315C2×C4—84no—
316C2×C4—84no—
317C2×C4C31×#12011yescharacteristic
318C2×C4C31×#12012yes—
319C2×C4C31×#12011yescharacteristic
320C2×C4C2×Q16×C3112yes—
321C2×C4C31×#13712yes—
322C2×C4C22×D4×C3112yes—
323C8—44no—
324C22—21no—
325C22—21no—
326C22—24no—
327C22—44no—
328C22—42no—
329C22—42no—
330C22—82no—
331C22C2×C31×#12011yescharacteristic
332C22C22×Q16×C3111yescharacteristic
333C22C2×C31×#13711yescharacteristic
334C4—21no—
335C4—22no—
336C4—42no—
337C4—44no—
338C4—44no—
339C4—82no—
340C4—82no—
341C4C31×#45114yes—
342C4C31×#45512yes—
343C2—21no—
344C2—21no—
345C2—44no—
346C2C2×C31×#45111yescharacteristic
347C2C2×C31×#45511yescharacteristic
348C2C31×#302711yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3209C2semidirect
4. C31×#1602C2semidirect
5. C31×#1503C2semidirect
81. C2×D4×C31Q16semidirect
116. #18390C31direct (N × H)
151. #3209C2×C31semidirect
153. #1602C2×C31semidirect
154. #1503C2×C31semidirect
246. C31#18390direct (N × H)
256. C2×D4Q16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#35012
C31×#32092
C31×#25632
C31×#16022
C31×#15032
C31×#14602
#1839031