Finite Group Databasebeta

← C31×#9317 #21466076

Subgroups — C31×#9317 #21466076

Order 7936.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3079C211yesmaximal, characteristic
2C31×#2988C211yesmaximal, characteristic
3C31×#1981C211yesmaximal, characteristic, complemented
4C31×#1806C211yesmaximal, characteristic
5C31×#1549C211yesmaximal, characteristic, complemented
6C31×#1303C211yesmaximal, characteristic, complemented
7C31×#1292C211yesmaximal, characteristic, complemented
8C2×C31×C4⋊Q8C2211yescharacteristic
9C4×#41×C31C2211yescharacteristic
10C31×#477C412yescomplemented
11C31×#476C412yescomplemented
12C31×#475—21no—
13C31×#474—21no—
14C8×Q8×C31—21no—
15C8×D4×C31—22no—
16C8×D4×C31—21no—
17C31×#431—21no—
18C31×#431C2211yescharacteristic
19C31×#428—21no—
20C31×#423C2211yescharacteristic
21C31×#423C2211yescharacteristic
22C2×C31×C4⋊C8—21no—
23C2×C31×C4⋊C8C2211yescharacteristic
24C2×C31×#104—21no—
25C31×#417—21no—
26C2×C31×#103—22no—
27C4×C4⋊C4×C31C2211yescharacteristic
28C31×#339—21no—
29C31×#332—21no—
30C31×#332—21no—
31C2×#41×C31D411yescharacteristic
32C22×Q8×C31—21no—
33C2×M16×C31—21no—
34C2×M16×C31—21no—
35C22×C8×C31—22no—
36C22×C8×C31D412yes—
37C31×C4⋊Q8—21no—
38C31×C4⋊Q8—21no—
39C31×C4⋊Q8—21no—
40C31×C4⋊Q8C2×C412yes—
41C4×Q8×C31C2×C411yescharacteristic
42C4×Q8×C31D411yescharacteristic
43C4×D4×C31—21no—
44C4×D4×C31—21no—
45C4×D4×C31C2×C411yescharacteristic
46C4×D4×C31D411yescharacteristic
47C31×#117—21no—
48C31×#117D411yescharacteristic
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C42×C31—21no—
53C2×C42×C31—21no—
54C2×C42×C31C2311yescharacteristic
55C31×#107—22no—
56C31×#106—22no—
57C31×C4⋊C8—22no—
58C31×C4⋊C8—21no—
59C31×C4⋊C8—21no—
60C31×C4⋊C8—21no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8C2×C412yes—
64C31×C4⋊C8D411yescharacteristic
65C31×C4⋊C8D411yescharacteristic
66C31×#104—42no—
67C31×#103—22no—
68C31×#103—44no—
69C31×#102—22no—
70C31×C22⋊C8—22no—
71C31×C22⋊C8—21no—
72C4×C8×C31—22no—
73C4×C8×C31—21no—
74C31×#95—21no—
75#41×C31—21no—
76#41×C31—21no—
77#41×C31SD1612yes—
78#41×C31Q1612yes—
79C2×Q8×C31—22no—
80C2×Q8×C31—42no—
81C2×Q8×C31—42no—
82C2×Q8×C31—41no—
83C2×Q8×C31C22⋊C411yescharacteristic
84C2×D4×C31—21no—
85C2×D4×C31C22⋊C411yescharacteristic
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31—21no—
89C22×C4×C31—41no—
90C22×C4×C31—41no—
91C22×C4×C31C2×D411yescharacteristic
92C22×C4×C31C2×D411yescharacteristic
93C22×C4×C31#4111yescharacteristic
94M16×C31—41no—
95M16×C31—41no—
96M16×C31—41no—
97M16×C31—41no—
98C2×C8×C31—22no—
99C2×C8×C31—21no—
100C2×C8×C31—22no—
101C2×C8×C31—21no—
102C2×C8×C31—42no—
103C2×C8×C31—41no—
104C2×C8×C31—82no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—21no—
107C4⋊C4×C31—22no—
108C4⋊C4×C31—22no—
109C4⋊C4×C31—22no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31—41no—
112C4⋊C4×C31—41no—
113C4⋊C4×C31C22⋊C411yescharacteristic
114C4⋊C4×C31C22⋊C411yescharacteristic
115C22⋊C4×C31—21no—
116C22⋊C4×C31—21no—
117C22⋊C4×C31—21no—
118C42×C31—21no—
119C42×C31—21no—
120C42×C31—21no—
121C42×C31—41no—
122C42×C31—41no—
123C42×C31C22×C411yescharacteristic
124C42×C31C2×D411yescharacteristic
125C42×C31C2×D411yescharacteristic
126C42×C31#4111yescharacteristic
127#9317C3111yesmaximal, characteristic, direct product factor, Sylow
128C23×C31—21no—
129C23×C31#12111yescharacteristic
130Q8×C31—21no—
131Q8×C31—44no—
132Q8×C31—81no—
133Q8×C31—81no—
134Q8×C31#10312yescomplemented
135D4×C31—22no—
136D4×C31—22no—
137D4×C31—21no—
138D4×C31#10312yescomplemented
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—22no—
143C2×C4×C31—22no—
144C2×C4×C31—21no—
145C2×C4×C31—21no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—42no—
150C2×C4×C31—42no—
151C2×C4×C31—81no—
152C2×C4×C31—81no—
153C2×C4×C31—82no—
154C2×C4×C31—81no—
155C2×C4×C31C2×C22⋊C411yescharacteristic
156C2×C4×C31C4×D411yescharacteristic
157C2×C4×C31C4×D411yescharacteristic
158C2×C4×C31#12011yescharacteristic
159C2×C4×C31#12111yescharacteristic
160C2×C4×C31#12311yescharacteristic
161C2×C4×C31C2×SD1611yescharacteristic
162C2×C4×C31C2×Q1611yescharacteristic
163C2×C4×C31#13511yescharacteristic
164C2×C4×C31#13511yescharacteristic
165C8×C31—42no—
166C8×C31—42no—
167C8×C31—41no—
168C8×C31—41no—
169C8×C31—81no—
170#3079C2×C3111yescharacteristic
171#2988C2×C3111yescharacteristic
172#1981C2×C3111yescharacteristic, complemented
173#1806C2×C3111yescharacteristic
174#1549C2×C3111yescharacteristic, complemented
175#1303C2×C3111yescharacteristic, complemented
176#1292C2×C3111yescharacteristic, complemented
177C22×C31—21no—
178C22×C31—21no—
179C22×C31—22no—
180C22×C31—41no—
181C22×C31—41no—
182C22×C31#38611yescharacteristic
183C22×C31#46511yescharacteristic
184C22×C31#46711yescharacteristic
185C4×C31—21no—
186C4×C31—22no—
187C4×C31—21no—
188C4×C31—21no—
189C4×C31—41no—
190C4×C31—41no—
191C4×C31—82no—
192C4×C31—82no—
193C4×C31C2×#10311yescharacteristic
194C4×C31#41611yescharacteristic
195C4×C31#45311yescharacteristic
196C4×C31#45411yescharacteristic
197C4×C31#46511yescharacteristic
198C4×C31#46711yescharacteristic
199C2×C4⋊Q8C22×C3111yescharacteristic
200C4×#41C22×C3111yescharacteristic
201#477C4×C3112yescomplemented
202#476C4×C3112yescomplemented
203#475—21no—
204#474—21no—
205C8×Q8—21no—
206C8×D4—22no—
207C8×D4—21no—
208#431—21no—
209#431C22×C3111yescharacteristic
210#428—21no—
211#423C22×C3111yescharacteristic
212#423C22×C3111yescharacteristic
213C2×C4⋊C8—21no—
214C2×C4⋊C8C22×C3111yescharacteristic
215C2×#104—21no—
216#417—21no—
217C2×#103—22no—
218C4×C4⋊C4C22×C3111yescharacteristic
219#339—21no—
220#332—21no—
221#332—21no—
222C2×C31—21no—
223C2×C31—21no—
224C2×C31—42no—
225C2×C31#188311yescharacteristic
226C2×C31#189211yescharacteristic
227C2×C31#190211yescharacteristic
228C2×#41D4×C3111yescharacteristic
229C22×Q8—21no—
230C2×M16—21no—
231C2×M16—21no—
232C22×C8—22no—
233C22×C8D4×C3112yes—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8C2×C4×C3112yes—
238C4×Q8C2×C4×C3111yescharacteristic
239C4×Q8D4×C3111yescharacteristic
240C4×D4—21no—
241C4×D4—21no—
242C4×D4C2×C4×C3111yescharacteristic
243C4×D4D4×C3111yescharacteristic
244#117—21no—
245#117D4×C3111yescharacteristic
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C42—21no—
250C2×C42—21no—
251C2×C42C23×C3111yescharacteristic
252#107—22no—
253#106—22no—
254C4⋊C8—22no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8C2×C4×C3112yes—
261C4⋊C8D4×C3111yescharacteristic
262C4⋊C8D4×C3111yescharacteristic
263#104—42no—
264#103—22no—
265#103—44no—
266#102—22no—
267C22⋊C8—22no—
268C22⋊C8—21no—
269C4×C8—22no—
270C4×C8—21no—
271#95—21no—
272C31#931711yescharacteristic, direct product factor, Sylow
273#41—21no—
274#41—21no—
275#41SD16×C3112yes—
276#41Q16×C3112yes—
277C2×Q8—22no—
278C2×Q8—42no—
279C2×Q8—42no—
280C2×Q8—41no—
281C2×Q8C22⋊C4×C3111yescharacteristic
282C2×D4—21no—
283C2×D4C22⋊C4×C3111yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4C2×D4×C3111yescharacteristic
290C22×C4C2×D4×C3111yescharacteristic
291C22×C4#41×C3111yescharacteristic
292M16—41no—
293M16—41no—
294M16—41no—
295M16—41no—
296C2×C8—22no—
297C2×C8—21no—
298C2×C8—22no—
299C2×C8—21no—
300C2×C8—42no—
301C2×C8—41no—
302C2×C8—82no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4C22⋊C4×C3111yescharacteristic
312C4⋊C4C22⋊C4×C3111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C42—21no—
317C42—21no—
318C42—21no—
319C42—41no—
320C42—41no—
321C42C22×C4×C3111yescharacteristic
322C42C2×D4×C3111yescharacteristic
323C42C2×D4×C3111yescharacteristic
324C42#41×C3111yescharacteristic
325C23—21no—
326C23C31×#12111yescharacteristic
327Q8—21no—
328Q8—44no—
329Q8—81no—
330Q8—81no—
331Q8C31×#10312yescomplemented
332D4—22no—
333D4—22no—
334D4—21no—
335D4C31×#10312yescomplemented
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—82no—
351C2×C4—81no—
352C2×C4C2×C22⋊C4×C3111yescharacteristic
353C2×C4C4×D4×C3111yescharacteristic
354C2×C4C4×D4×C3111yescharacteristic
355C2×C4C31×#12011yescharacteristic
356C2×C4C31×#12111yescharacteristic
357C2×C4C31×#12311yescharacteristic
358C2×C4C2×SD16×C3111yescharacteristic
359C2×C4C2×Q16×C3111yescharacteristic
360C2×C4C31×#13511yescharacteristic
361C2×C4C31×#13511yescharacteristic
362C8—42no—
363C8—42no—
364C8—41no—
365C8—41no—
366C8—81no—
367C22—21no—
368C22—21no—
369C22—22no—
370C22—41no—
371C22—41no—
372C22C31×#38611yescharacteristic
373C22C31×#46511yescharacteristic
374C22C31×#46711yescharacteristic
375C4—21no—
376C4—22no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—82no—
382C4—82no—
383C4C2×C31×#10311yescharacteristic
384C4C31×#41611yescharacteristic
385C4C31×#45311yescharacteristic
386C4C31×#45411yescharacteristic
387C4C31×#46511yescharacteristic
388C4C31×#46711yescharacteristic
389C2—21no—
390C2—21no—
391C2—42no—
392C2C31×#188311yescharacteristic
393C2C31×#189211yescharacteristic
394C2C31×#190211yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×#41×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×#1981C2semidirect
5. C31×#1549C2semidirect
6. C31×#1303C2semidirect
7. C31×#1292C2semidirect
10. C31×#477C4semidirect
11. C31×#476C4semidirect
127. #9317C31direct (N × H)
134. Q8×C31#103semidirect
138. D4×C31#103semidirect
172. #1981C2×C31semidirect
174. #1549C2×C31semidirect
175. #1303C2×C31semidirect
176. #1292C2×C31semidirect
201. #477C4×C31semidirect
202. #476C4×C31semidirect
272. C31#9317direct (N × H)
331. Q8C31×#103semidirect
335. D4C31×#103semidirect

Maximal subgroups

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

subgroupindex
C31×#30792
C31×#29882
C31×#19812
C31×#18062
C31×#15492
C31×#13032
C31×#12922
#931731