Finite Group Databasebeta

← C31×#9323 #21466082

Subgroups — C31×#9323 #21466082

Order 7936.

612 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3110C211yesmaximal, characteristic
2C31×#2275C211yesmaximal, characteristic
3C31×#1986C211yesmaximal, characteristic, complemented
4C31×#1506C211yesmaximal, characteristic, complemented
5C31×#1490C211yesmaximal, characteristic
6C31×#1300C211yesmaximal, characteristic, complemented
7C31×#1285C211yesmaximal, characteristic, complemented
8C31×#533C2211yescharacteristic
9C2×C4×D4×C31—21no—
10C2×C4×D4×C31C2211yescharacteristic
11C31×#484—21no—
12C31×#474C412yescomplemented
13C31×#461C412yescomplemented
14C31×#450—21no—
15C31×#440—22no—
16C31×#432C2211yescharacteristic
17C31×#432C2211yescharacteristic
18C4×M16×C31C2211yescharacteristic
19C4×C4⋊C4×C31—21no—
20C4×C4⋊C4×C31C2211yescharacteristic
21C4×C22⋊C4×C31—22no—
22C4×C22⋊C4×C31—21no—
23C31×#376C2211yescharacteristic
24C2×C31×#95—21no—
25C31×#339—22no—
26C31×#328—21no—
27C31×#328—21no—
28C31×D4⋊C8—22no—
29C22×D4×C31D411yescharacteristic
30C23×C4×C31—22no—
31C23×C4×C31—21no—
32C2×SD16×C31—22no—
33C2×M16×C31—21no—
34C31×C4⋊Q8C2×C411yescharacteristic, complemented
35C31×C4⋊Q8C2×C411yescharacteristic, complemented
36C31×#125—21no—
37C31×C22⋊Q8—21no—
38C31×C22⋊Q8—21no—
39C4×Q8×C31—21no—
40C4×Q8×C31—21no—
41C4×D4×C31—28no—
42C4×D4×C31—21no—
43C4×D4×C31—21no—
44C4×D4×C31C2×C412yes—
45C4×D4×C31D412yes—
46C31×#117—21no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31D411yescharacteristic
49C2×C22⋊C4×C31—22no—
50C2×C22⋊C4×C31—21no—
51C2×C42×C31—21no—
52C2×C42×C31—22no—
53C2×C42×C31D412yes—
54C2×C42×C31C2311yescharacteristic
55C31×#107—22no—
56C31×C4⋊C8—21no—
57C31×C4⋊C8C2×C412yescomplemented
58C31×#103—22no—
59C31×#102—22no—
60C31×C22⋊C8—21no—
61C31×C22⋊C8—21no—
62C31×#97—21no—
63C31×#97—21no—
64C31×#97—21no—
65C4×C8×C31—21no—
66C31×#95—22no—
67C31×#95—21no—
68C31×#95—21no—
69C31×#95D411yescharacteristic
70C31×#95D411yescharacteristic
71C24×C31—21no—
72C2×Q8×C31—21no—
73C2×Q8×C31—21no—
74C2×D4×C31—24no—
75C2×D4×C31—21no—
76C2×D4×C31C22⋊C412yes—
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—22no—
80C22×C4×C31—21no—
81C22×C4×C31—28no—
82C22×C4×C31—22no—
83C22×C4×C31—22no—
84C22×C4×C31—82no—
85C22×C4×C31—82no—
86C22×C4×C31—82no—
87C22×C4×C31C2×D411yescharacteristic
88C22×C4×C31C2×D411yescharacteristic
89C22×C4×C31C2×D411yescharacteristic
90SD16×C31—44no—
91M16×C31—22no—
92M16×C31—41no—
93C2×C8×C31—22no—
94C2×C8×C31—41no—
95C2×C8×C31—41no—
96C4⋊C4×C31—24no—
97C4⋊C4×C31—21no—
98C4⋊C4×C31—21no—
99C4⋊C4×C31—21no—
100C4⋊C4×C31—21no—
101C4⋊C4×C31—21no—
102C4⋊C4×C31—41no—
103C4⋊C4×C31—41no—
104C4⋊C4×C31C22⋊C412yes—
105C22⋊C4×C31—28no—
106C22⋊C4×C31—22no—
107C22⋊C4×C31—22no—
108C22⋊C4×C31—41no—
109C42×C31—24no—
110C42×C31—42no—
111C42×C31—41no—
112C42×C31—82no—
113C42×C31C22×C411yescharacteristic
114C42×C31C2×D411yescharacteristic
115C42×C31#4111yescharacteristic
116C42×C31#4111yescharacteristic
117#9323C3111yesmaximal, characteristic, direct product factor, Sylow
118C23×C31—24no—
119C23×C31—22no—
120C23×C31—42no—
121C23×C31—41no—
122C23×C31—41no—
123C23×C31#12011yescharacteristic
124Q8×C31—42no—
125Q8×C31—81no—
126D4×C31—24no—
127D4×C31—22no—
128D4×C31#10414yes—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—22no—
132C2×C4×C31—22no—
133C2×C4×C31—22no—
134C2×C4×C31—24no—
135C2×C4×C31—22no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—42no—
139C2×C4×C31—42no—
140C2×C4×C31—41no—
141C2×C4×C31—42no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—82no—
147C2×C4×C31—82no—
148C2×C4×C31—88no—
149C2×C4×C31C2×C22⋊C411yescharacteristic
150C2×C4×C31C4×D411yescharacteristic
151C2×C4×C31C4×D411yescharacteristic
152C2×C4×C31#12111yescharacteristic
153C2×C4×C31#12111yescharacteristic
154C2×C4×C31#12311yescharacteristic
155C8×C31—42no—
156C8×C31—42no—
157C8×C31—81no—
158#3110C2×C3111yescharacteristic
159#2275C2×C3111yescharacteristic
160#1986C2×C3111yescharacteristic, complemented
161#1506C2×C3111yescharacteristic, complemented
162#1490C2×C3111yescharacteristic
163#1300C2×C3111yescharacteristic, complemented
164#1285C2×C3111yescharacteristic, complemented
165C22×C31—21no—
166C22×C31—21no—
167C22×C31—24no—
168C22×C31—44no—
169C22×C31—44no—
170C22×C31—42no—
171C22×C31—42no—
172C22×C31#38611yescharacteristic
173C22×C31#45511yescharacteristic
174C22×C31#45611yescharacteristic
175C4×C31—21no—
176C4×C31—21no—
177C4×C31—21no—
178C4×C31—21no—
179C4×C31—21no—
180C4×C31—42no—
181C4×C31—44no—
182C4×C31—42no—
183C4×C31—42no—
184C4×C31—81no—
185C4×C31—81no—
186C4×C31C2×#10412yes—
187#533C22×C3111yescharacteristic
188C2×C4×D4—21no—
189C2×C4×D4C22×C3111yescharacteristic
190#484—21no—
191#474C4×C3112yescomplemented
192#461C4×C3112yescomplemented
193#450—21no—
194#440—22no—
195#432C22×C3111yescharacteristic
196#432C22×C3111yescharacteristic
197C4×M16C22×C3111yescharacteristic
198C4×C4⋊C4—21no—
199C4×C4⋊C4C22×C3111yescharacteristic
200C4×C22⋊C4—22no—
201C4×C22⋊C4—21no—
202#376C22×C3111yescharacteristic
203C2×#95—21no—
204#339—22no—
205#328—21no—
206#328—21no—
207D4⋊C8—22no—
208C2×C31—21no—
209C2×C31—21no—
210C2×C31—44no—
211C2×C31#188211yescharacteristic
212C2×C31#189611yescharacteristic
213C2×C31#190411yescharacteristic
214C22×D4D4×C3111yescharacteristic
215C23×C4—22no—
216C23×C4—21no—
217C2×SD16—22no—
218C2×M16—21no—
219C4⋊Q8C2×C4×C3111yescharacteristic, complemented
220C4⋊Q8C2×C4×C3111yescharacteristic, complemented
221#125—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×D4—28no—
227C4×D4—21no—
228C4×D4—21no—
229C4×D4C2×C4×C3112yes—
230C4×D4D4×C3112yes—
231#117—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4D4×C3111yescharacteristic
234C2×C22⋊C4—22no—
235C2×C22⋊C4—21no—
236C2×C42—21no—
237C2×C42—22no—
238C2×C42D4×C3112yes—
239C2×C42C23×C3111yescharacteristic
240#107—22no—
241C4⋊C8—21no—
242C4⋊C8C2×C4×C3112yescomplemented
243#103—22no—
244#102—22no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247#97—21no—
248#97—21no—
249#97—21no—
250C4×C8—21no—
251#95—22no—
252#95—21no—
253#95—21no—
254#95D4×C3111yescharacteristic
255#95D4×C3111yescharacteristic
256C31#932311yescharacteristic, direct product factor, Sylow
257C24—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×D4—24no—
261C2×D4—21no—
262C2×D4C22⋊C4×C3112yes—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—28no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—82no—
271C22×C4—82no—
272C22×C4—82no—
273C22×C4C2×D4×C3111yescharacteristic
274C22×C4C2×D4×C3111yescharacteristic
275C22×C4C2×D4×C3111yescharacteristic
276SD16—44no—
277M16—22no—
278M16—41no—
279C2×C8—22no—
280C2×C8—41no—
281C2×C8—41no—
282C4⋊C4—24no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4C22⋊C4×C3112yes—
291C22⋊C4—28no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—41no—
295C42—24no—
296C42—42no—
297C42—41no—
298C42—82no—
299C42C22×C4×C3111yescharacteristic
300C42C2×D4×C3111yescharacteristic
301C42#41×C3111yescharacteristic
302C42#41×C3111yescharacteristic
303C23—24no—
304C23—22no—
305C23—42no—
306C23—41no—
307C23—41no—
308C23C31×#12011yescharacteristic
309Q8—42no—
310Q8—81no—
311D4—24no—
312D4—22no—
313D4C31×#10414yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—88no—
334C2×C4C2×C22⋊C4×C3111yescharacteristic
335C2×C4C4×D4×C3111yescharacteristic
336C2×C4C4×D4×C3111yescharacteristic
337C2×C4C31×#12111yescharacteristic
338C2×C4C31×#12111yescharacteristic
339C2×C4C31×#12311yescharacteristic
340C8—42no—
341C8—42no—
342C8—81no—
343C22—21no—
344C22—21no—
345C22—24no—
346C22—44no—
347C22—44no—
348C22—42no—
349C22—42no—
350C22C31×#38611yescharacteristic
351C22C31×#45511yescharacteristic
352C22C31×#45611yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—42no—
359C4—44no—
360C4—42no—
361C4—42no—
362C4—81no—
363C4—81no—
364C4C2×C31×#10412yes—
365C2—21no—
366C2—21no—
367C2—44no—
368C2C31×#188211yescharacteristic
369C2C31×#189611yescharacteristic
370C2C31×#190411yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1986C2semidirect
4. C31×#1506C2semidirect
6. C31×#1300C2semidirect
7. C31×#1285C2semidirect
12. C31×#474C4semidirect
13. C31×#461C4semidirect
34. C31×C4⋊Q8C2×C4semidirect
35. C31×C4⋊Q8C2×C4semidirect
57. C31×C4⋊C8C2×C4semidirect
117. #9323C31direct (N × H)
160. #1986C2×C31semidirect
161. #1506C2×C31semidirect
163. #1300C2×C31semidirect
164. #1285C2×C31semidirect
191. #474C4×C31semidirect
192. #461C4×C31semidirect
219. C4⋊Q8C2×C4×C31semidirect
220. C4⋊Q8C2×C4×C31semidirect
242. C4⋊C8C2×C4×C31semidirect
256. C31#9323direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31102
C31×#22752
C31×#19862
C31×#15062
C31×#14902
C31×#13002
C31×#12852
#932331