Finite Group Databasebeta

← C31×#9199 #21465958

Subgroups — C31×#9199 #21465958

Order 7936.

684 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2626C211yesmaximal, characteristic
2C31×#2315C211yesmaximal, characteristic
3C31×#1520C212yesmaximal, complemented
4C2×C31×#323C211yesmaximal, characteristic
5C31×#1289C212yesmaximal, complemented
6C2×C31×C22⋊Q8C2211yescharacteristic
7C22×C22⋊C4×C31—21no—
8C22×C22⋊C4×C31C2211yescharacteristic
9C2×C31×C22⋊C8C2212yes—
10C31×#399C412yescomplemented
11C31×#396—22no—
12C31×#393C412yescomplemented
13C31×#385—21no—
14C31×#385—24no—
15C31×#380—21no—
16C31×#380C2211yescharacteristic
17C31×#380C2212yes—
18C31×#379—21no—
19C31×#328—24no—
20C31×#323—22no—
21C25×C31D411yescharacteristic
22C22×Q8×C31C2×C411yescharacteristic, complemented
23C23×C4×C31—22no—
24C23×C4×C31D411yescharacteristic
25C23×C4×C31C2311yescharacteristic
26C22×C8×C31—22no—
27C31×C22⋊Q8—22no—
28C31×C22⋊Q8—22no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—22no—
34C2×C4⋊C4×C31C2×C411yescharacteristic, complemented
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—22no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—22no—
42C2×C22⋊C4×C31—22no—
43C2×C22⋊C4×C31—42no—
44C2×C22⋊C4×C31—42no—
45C2×C22⋊C4×C31C2×C412yes—
46C2×C22⋊C4×C31D412yes—
47C31×C22⋊C8—22no—
48C31×C22⋊C8—22no—
49C31×#95—22no—
50C31×#95—22no—
51C31×#95C2×C412yescomplemented
52C31×#95D414yes—
53C24×C31—21no—
54C24×C31—21no—
55C24×C31—21no—
56C24×C31—21no—
57C24×C31—81no—
58C24×C31—81no—
59C24×C31C22⋊C412yes—
60C24×C31SD1612yes—
61C24×C31Q1612yes—
62C24×C31C2×D411yescharacteristic
63C2×Q8×C31—22no—
64C2×Q8×C31—81no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—22no—
69C22×C4×C31—21no—
70C22×C4×C31—24no—
71C22×C4×C31—44no—
72C22×C4×C31—81no—
73C22×C4×C31—81no—
74C22×C4×C31—82no—
75C22×C4×C31—82no—
76C22×C4×C31C22⋊C412yes—
77C22×C4×C31C22×C411yescharacteristic
78C22×C4×C31C2×D412yes—
79C22×C4×C31C2×D411yescharacteristic
80C22×C4×C31#4112yes—
81C2×C8×C31—42no—
82C2×C8×C31—82no—
83C4⋊C4×C31—22no—
84C4⋊C4×C31—42no—
85C4⋊C4×C31—81no—
86C4⋊C4×C31—82no—
87C4⋊C4×C31—82no—
88C4⋊C4×C31—82no—
89C22⋊C4×C31—24no—
90C22⋊C4×C31—24no—
91C22⋊C4×C31—44no—
92C22⋊C4×C31—41no—
93C22⋊C4×C31—41no—
94C22⋊C4×C31—42no—
95C22⋊C4×C31—41no—
96C22⋊C4×C31—42no—
97C22⋊C4×C31—41no—
98C22⋊C4×C31—82no—
99C22⋊C4×C31—82no—
100#9199C3111yesmaximal, characteristic, direct product factor, Sylow
101C23×C31—22no—
102C23×C31—22no—
103C23×C31—22no—
104C23×C31—22no—
105C23×C31—22no—
106C23×C31—22no—
107C23×C31—41no—
108C23×C31—41no—
109C23×C31—42no—
110C23×C31—42no—
111C23×C31—42no—
112C23×C31—42no—
113C23×C31—81no—
114C23×C31—81no—
115C23×C31—82no—
116C23×C31—82no—
117C23×C31—82no—
118C23×C31—82no—
119C23×C31#10314yes—
120C23×C31C2×C22⋊C411yescharacteristic
121C23×C31#12011yescharacteristic
122C23×C31#12311yescharacteristic
123C23×C31C2×SD1611yescharacteristic
124C23×C31C2×Q1611yescharacteristic
125C23×C31AGL(1,ℤ/8)11yescharacteristic
126C23×C31#13711yescharacteristic
127Q8×C31—82no—
128C2×C4×C31—22no—
129C2×C4×C31—41no—
130C2×C4×C31—42no—
131C2×C4×C31—42no—
132C2×C4×C31—41no—
133C2×C4×C31—42no—
134C2×C4×C31—42no—
135C2×C4×C31—42no—
136C2×C4×C31—42no—
137C2×C4×C31—42no—
138C2×C4×C31—42no—
139C2×C4×C31—44no—
140C2×C4×C31—44no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—42no—
144C2×C4×C31—44no—
145C2×C4×C31—81no—
146C2×C4×C31—88no—
147C2×C4×C31C4×D412yes—
148C2×C4×C31#12112yes—
149C8×C31—82no—
150#2626C2×C3111yescharacteristic
151#2315C2×C3111yescharacteristic
152#1520C2×C3112yescomplemented
153C2×#323C2×C3111yescharacteristic
154#1289C2×C3112yescomplemented
155C22×C31—21no—
156C22×C31—21no—
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—24no—
162C22×C31—41no—
163C22×C31—41no—
164C22×C31—41no—
165C22×C31—41no—
166C22×C31—44no—
167C22×C31—44no—
168C22×C31—44no—
169C22×C31—42no—
170C22×C31—42no—
171C22×C31—82no—
172C22×C31—82no—
173C22×C31—82no—
174C22×C31#38611yescharacteristic
175C22×C31C2×#10311yescharacteristic
176C22×C31#41711yescharacteristic
177C22×C31#45011yescharacteristic
178C22×C31#45111yescharacteristic
179C22×C31#48311yescharacteristic
180C22×C31#48411yescharacteristic
181C4×C31—22no—
182C4×C31—22no—
183C4×C31—42no—
184C4×C31—82no—
185C4×C31—84no—
186C4×C31—81no—
187C4×C31—81no—
188C2×C22⋊Q8C22×C3111yescharacteristic
189C22×C22⋊C4—21no—
190C22×C22⋊C4C22×C3111yescharacteristic
191C2×C22⋊C8C22×C3112yes—
192#399C4×C3112yescomplemented
193#396—22no—
194#393C4×C3112yescomplemented
195#385—21no—
196#385—24no—
197#380—21no—
198#380C22×C3111yescharacteristic
199#380C22×C3112yes—
200#379—21no—
201#328—24no—
202#323—22no—
203C2×C31—21no—
204C2×C31—21no—
205C2×C31—21no—
206C2×C31—21no—
207C2×C31—21no—
208C2×C31—21no—
209C2×C31—44no—
210C2×C31#187211yescharacteristic
211C2×C31#191111yescharacteristic
212C2×C31#191311yescharacteristic
213C25D4×C3111yescharacteristic
214C22×Q8C2×C4×C3111yescharacteristic, complemented
215C23×C4—22no—
216C23×C4D4×C3111yescharacteristic
217C23×C4C23×C3111yescharacteristic
218C22×C8—22no—
219C22⋊Q8—22no—
220C22⋊Q8—22no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4C2×C4×C3111yescharacteristic, complemented
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—42no—
236C2×C22⋊C4—42no—
237C2×C22⋊C4C2×C4×C3112yes—
238C2×C22⋊C4D4×C3112yes—
239C22⋊C8—22no—
240C22⋊C8—22no—
241#95—22no—
242#95—22no—
243#95C2×C4×C3112yescomplemented
244#95D4×C3114yes—
245C31#919911yescharacteristic, direct product factor, Sylow
246C24—21no—
247C24—21no—
248C24—21no—
249C24—21no—
250C24—81no—
251C24—81no—
252C24C22⋊C4×C3112yes—
253C24SD16×C3112yes—
254C24Q16×C3112yes—
255C24C2×D4×C3111yescharacteristic
256C2×Q8—22no—
257C2×Q8—81no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—24no—
264C22×C4—44no—
265C22×C4—81no—
266C22×C4—81no—
267C22×C4—82no—
268C22×C4—82no—
269C22×C4C22⋊C4×C3112yes—
270C22×C4C22×C4×C3111yescharacteristic
271C22×C4C2×D4×C3112yes—
272C22×C4C2×D4×C3111yescharacteristic
273C22×C4#41×C3112yes—
274C2×C8—42no—
275C2×C8—82no—
276C4⋊C4—22no—
277C4⋊C4—42no—
278C4⋊C4—81no—
279C4⋊C4—82no—
280C4⋊C4—82no—
281C4⋊C4—82no—
282C22⋊C4—24no—
283C22⋊C4—24no—
284C22⋊C4—44no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—82no—
292C22⋊C4—82no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—41no—
300C23—41no—
301C23—42no—
302C23—42no—
303C23—42no—
304C23—42no—
305C23—81no—
306C23—81no—
307C23—82no—
308C23—82no—
309C23—82no—
310C23—82no—
311C23C31×#10314yes—
312C23C2×C22⋊C4×C3111yescharacteristic
313C23C31×#12011yescharacteristic
314C23C31×#12311yescharacteristic
315C23C2×SD16×C3111yescharacteristic
316C23C2×Q16×C3111yescharacteristic
317C23C31×AGL(1,ℤ/8)11yescharacteristic
318C23C31×#13711yescharacteristic
319Q8—82no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—44no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—88no—
339C2×C4C4×D4×C3112yes—
340C2×C4C31×#12112yes—
341C8—82no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—24no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—44no—
354C22—44no—
355C22—44no—
356C22—42no—
357C22—42no—
358C22—82no—
359C22—82no—
360C22—82no—
361C22C31×#38611yescharacteristic
362C22C2×C31×#10311yescharacteristic
363C22C31×#41711yescharacteristic
364C22C31×#45011yescharacteristic
365C22C31×#45111yescharacteristic
366C22C31×#48311yescharacteristic
367C22C31×#48411yescharacteristic
368C4—22no—
369C4—22no—
370C4—42no—
371C4—84no—
372C4—82no—
373C4—81no—
374C4—81no—
375C2—21no—
376C2—21no—
377C2—21no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—44no—
382C2C31×#187211yescharacteristic
383C2C31×#191111yescharacteristic
384C2C31×#191311yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1520C2semidirect
5. C31×#1289C2semidirect
10. C31×#399C4semidirect
12. C31×#393C4semidirect
22. C22×Q8×C31C2×C4semidirect
34. C2×C4⋊C4×C31C2×C4semidirect
51. C31×#95C2×C4semidirect
100. #9199C31direct (N × H)
152. #1520C2×C31semidirect
154. #1289C2×C31semidirect
192. #399C4×C31semidirect
194. #393C4×C31semidirect
214. C22×Q8C2×C4×C31semidirect
226. C2×C4⋊C4C2×C4×C31semidirect
243. #95C2×C4×C31semidirect
245. C31#9199direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26262
C31×#23152
C31×#15202
C2×C31×#3232
C31×#12892
#919931