Finite Group Databasebeta

← C31×#9146 #21465905

Subgroups — C31×#9146 #21465905

Order 7936.

1010 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2848C211yesmaximal, characteristic
2C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
3C31×#1779C211yesmaximal, characteristic
4C2×C31×#328C212yesmaximal, complemented
5C31×#1294C212yesmaximal, complemented
6C24×C4×C31C2211yescharacteristic
7C2×C31×C22⋊Q8C412yescomplemented
8C2×C31×C22⋊Q8C2211yescharacteristic
9C22×C22⋊C4×C31—21no—
10C22×C42×C31—21no—
11C2×C31×C22⋊C8—22no—
12C2×C31×C22⋊C8C2212yes—
13C31×#385—21no—
14C31×#385—22no—
15C31×#380C412yescomplemented
16C31×#380C2211yescharacteristic
17C31×#379—21no—
18C4×C22⋊C4×C31—24no—
19C2×C31×#95C2212yes—
20C31×#328—24no—
21C25×C31D411yescharacteristic
22C22×Q8×C31C2×C411yescharacteristic
23C23×C4×C31—22no—
24C23×C4×C31—22no—
25C23×C4×C31—22no—
26C23×C4×C31—44no—
27C23×C4×C31C2×C412yes—
28C23×C4×C31D411yescharacteristic
29C23×C4×C31D412yes—
30C23×C4×C31C2311yescharacteristic
31C22×C8×C31—22no—
32C31×C22⋊Q8—22no—
33C31×C22⋊Q8—22no—
34C31×C22⋊Q8—44no—
35C2×C4⋊C4×C31—22no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C4⋊C4×C31C2×C412yes—
39C2×C22⋊C4×C31—28no—
40C2×C22⋊C4×C31—24no—
41C2×C22⋊C4×C31—22no—
42C2×C22⋊C4×C31—22no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C42×C31—24no—
46C2×C42×C31—44no—
47C31×C22⋊C8—22no—
48C31×C22⋊C8—22no—
49C31×C22⋊C8—44no—
50C31×#95—22no—
51C31×#95—22no—
52C31×#95—21no—
53C31×#95D414yes—
54C24×C31—24no—
55C24×C31—21no—
56C24×C31—21no—
57C24×C31—22no—
58C24×C31—22no—
59C24×C31—42no—
60C24×C31C22⋊C412yes—
61C24×C31C2×D411yescharacteristic
62C2×Q8×C31—22no—
63C2×Q8×C31—42no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—24no—
67C22×C4×C31—28no—
68C22×C4×C31—24no—
69C22×C4×C31—24no—
70C22×C4×C31—24no—
71C22×C4×C31—24no—
72C22×C4×C31—24no—
73C22×C4×C31—21no—
74C22×C4×C31—22no—
75C22×C4×C31—21no—
76C22×C4×C31—42no—
77C22×C4×C31—42no—
78C22×C4×C31—42no—
79C22×C4×C31—48no—
80C22×C4×C31—48no—
81C22×C4×C31—44no—
82C22×C4×C31—42no—
83C22×C4×C31—42no—
84C22×C4×C31C22⋊C412yes—
85C22×C4×C31C22×C411yescharacteristic
86C22×C4×C31C2×D411yescharacteristic
87C22×C4×C31C2×D412yes—
88C22×C4×C31#4112yes—
89C2×C8×C31—44no—
90C2×C8×C31—42no—
91C4⋊C4×C31—22no—
92C4⋊C4×C31—42no—
93C4⋊C4×C31—44no—
94C4⋊C4×C31—42no—
95C22⋊C4×C31—216no—
96C22⋊C4×C31—44no—
97C22⋊C4×C31—44no—
98C22⋊C4×C31—41no—
99C22⋊C4×C31—41no—
100C22⋊C4×C31—42no—
101C42×C31—48no—
102#9146C3111yesmaximal, characteristic, direct product factor, Sylow
103C23×C31—22no—
104C23×C31—22no—
105C23×C31—24no—
106C23×C31—24no—
107C23×C31—22no—
108C23×C31—22no—
109C23×C31—22no—
110C23×C31—22no—
111C23×C31—22no—
112C23×C31—22no—
113C23×C31—48no—
114C23×C31—48no—
115C23×C31—42no—
116C23×C31—42no—
117C23×C31—42no—
118C23×C31—42no—
119C23×C31#10414yes—
120C23×C31C2×C22⋊C411yescharacteristic
121C23×C31#12011yescharacteristic
122C23×C31#12311yescharacteristic
123C23×C31#13512yes—
124C23×C31#13712yes—
125Q8×C31—82no—
126C2×C4×C31—24no—
127C2×C4×C31—24no—
128C2×C4×C31—22no—
129C2×C4×C31—22no—
130C2×C4×C31—22no—
131C2×C4×C31—22no—
132C2×C4×C31—28no—
133C2×C4×C31—42no—
134C2×C4×C31—42no—
135C2×C4×C31—48no—
136C2×C4×C31—48no—
137C2×C4×C31—44no—
138C2×C4×C31—48no—
139C2×C4×C31—48no—
140C2×C4×C31—44no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—42no—
144C2×C4×C31—42no—
145C2×C4×C31—42no—
146C2×C4×C31—42no—
147C2×C4×C31—42no—
148C2×C4×C31#9914yes—
149C2×C4×C31C4×D412yes—
150C2×C4×C31#12112yes—
151C8×C31—82no—
152#2848C2×C3111yescharacteristic
153C2×C4×C22⋊C4C2×C3111yescharacteristic
154#1779C2×C3111yescharacteristic
155C2×#328C2×C3112yescomplemented
156#1294C2×C3112yescomplemented
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—24no—
162C22×C31—24no—
163C22×C31—24no—
164C22×C31—24no—
165C22×C31—24no—
166C22×C31—48no—
167C22×C31—48no—
168C22×C31—42no—
169C22×C31—42no—
170C22×C31—42no—
171C22×C31—42no—
172C22×C31#38611yescharacteristic
173C22×C31C2×#9912yes—
174C22×C31#41611yescharacteristic
175C22×C31#41911yescharacteristic
176C22×C31C2×#10412yes—
177C22×C31#45212yes—
178C22×C31#48512yes—
179C4×C31—22no—
180C4×C31—24no—
181C4×C31—22no—
182C4×C31—48no—
183C4×C31—81no—
184C4×C31—81no—
185C4×C31—82no—
186C24×C4C22×C3111yescharacteristic
187C2×C22⋊Q8C4×C3112yescomplemented
188C2×C22⋊Q8C22×C3111yescharacteristic
189C22×C22⋊C4—21no—
190C22×C42—21no—
191C2×C22⋊C8—22no—
192C2×C22⋊C8C22×C3112yes—
193#385—21no—
194#385—22no—
195#380C4×C3112yescomplemented
196#380C22×C3111yescharacteristic
197#379—21no—
198C4×C22⋊C4—24no—
199C2×#95C22×C3112yes—
200#328—24no—
201C2×C31—22no—
202C2×C31—22no—
203C2×C31—44no—
204C2×C31#150112yes—
205C2×C31#150812yes—
206C2×C31#187311yescharacteristic
207C2×C31#189611yescharacteristic
208C2×C31#189811yescharacteristic
209C25D4×C3111yescharacteristic
210C22×Q8C2×C4×C3111yescharacteristic
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—44no—
215C23×C4C2×C4×C3112yes—
216C23×C4D4×C3111yescharacteristic
217C23×C4D4×C3112yes—
218C23×C4C23×C3111yescharacteristic
219C22×C8—22no—
220C22⋊Q8—22no—
221C22⋊Q8—22no—
222C22⋊Q8—44no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4C2×C4×C3111yescharacteristic
226C2×C4⋊C4C2×C4×C3112yes—
227C2×C22⋊C4—24no—
228C2×C22⋊C4—28no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C42—24no—
234C2×C42—44no—
235C22⋊C8—22no—
236C22⋊C8—22no—
237C22⋊C8—44no—
238#95—22no—
239#95—22no—
240#95—21no—
241#95D4×C3114yes—
242C31#914611yescharacteristic, direct product factor, Sylow
243C24—24no—
244C24—21no—
245C24—21no—
246C24—22no—
247C24—22no—
248C24—42no—
249C24C22⋊C4×C3112yes—
250C24C2×D4×C3111yescharacteristic
251C2×Q8—22no—
252C2×Q8—42no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—24no—
256C22×C4—28no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—48no—
269C22×C4—48no—
270C22×C4—44no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4C22⋊C4×C3112yes—
274C22×C4C22×C4×C3111yescharacteristic
275C22×C4C2×D4×C3111yescharacteristic
276C22×C4C2×D4×C3112yes—
277C22×C4#41×C3112yes—
278C2×C8—44no—
279C2×C8—42no—
280C4⋊C4—22no—
281C4⋊C4—42no—
282C4⋊C4—44no—
283C4⋊C4—42no—
284C22⋊C4—216no—
285C22⋊C4—44no—
286C22⋊C4—44no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C42—48no—
291C23—22no—
292C23—22no—
293C23—24no—
294C23—24no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—22no—
300C23—22no—
301C23—48no—
302C23—48no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23—42no—
307C23C31×#10414yes—
308C23C2×C22⋊C4×C3111yescharacteristic
309C23C31×#12011yescharacteristic
310C23C31×#12311yescharacteristic
311C23C31×#13512yes—
312C23C31×#13712yes—
313Q8—82no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—28no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—48no—
324C2×C4—48no—
325C2×C4—44no—
326C2×C4—48no—
327C2×C4—48no—
328C2×C4—44no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4C31×#9914yes—
337C2×C4C4×D4×C3112yes—
338C2×C4C31×#12112yes—
339C8—82no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—24no—
345C22—24no—
346C22—24no—
347C22—24no—
348C22—24no—
349C22—48no—
350C22—48no—
351C22—42no—
352C22—42no—
353C22—42no—
354C22—42no—
355C22C31×#38611yescharacteristic
356C22C2×C31×#9912yes—
357C22C31×#41611yescharacteristic
358C22C31×#41911yescharacteristic
359C22C2×C31×#10412yes—
360C22C31×#45212yes—
361C22C31×#48512yes—
362C4—22no—
363C4—24no—
364C4—22no—
365C4—48no—
366C4—81no—
367C4—81no—
368C4—82no—
369C2—22no—
370C2—22no—
371C2—44no—
372C2C31×#150112yes—
373C2C31×#150812yes—
374C2C31×#187311yescharacteristic
375C2C31×#189611yescharacteristic
376C2C31×#189811yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C31×#328C2semidirect
5. C31×#1294C2semidirect
7. C2×C31×C22⋊Q8C4semidirect
15. C31×#380C4semidirect
102. #9146C31direct (N × H)
155. C2×#328C2×C31semidirect
156. #1294C2×C31semidirect
187. C2×C22⋊Q8C4×C31semidirect
195. #380C4×C31semidirect
242. C31#9146direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28482
C2×C4×C22⋊C4×C312
C31×#17792
C2×C31×#3282
C31×#12942
#914631