Finite Group Databasebeta

← C31×#19392 #21476151

Subgroups — C31×#19392 #21476151

Order 7936.

728 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3226C211yesmaximal, characteristic, complemented
2C31×#3036C211yesmaximal, characteristic
3C2×C31×#461C211yesmaximal, characteristic, complemented
4C31×#2972C211yesmaximal, characteristic, complemented
5C31×#1681C214yesmaximal, complemented
6C31×#1673C214yesmaximal, complemented
7C31×#1571C211yesmaximal, characteristic, complemented
8C31×#1546C211yesmaximal, characteristic, complemented
9C31×#1540C211yesmaximal, characteristic, complemented
10C2×C31×AGL(1,ℤ/8)—21no—
11C22×SD16×C31—21no—
12C31×#532C2211yescharacteristic
13C2×C31×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C31C2211yescharacteristic
15C31×#500C2212yescomplemented
16C31×#486C2212yescomplemented
17C31×#480—22no—
18C31×#474—22no—
19C31×#463—22no—
20C31×#461—22no—
21C31×#461C2212yes—
22C31×#461C2214yes—
23C31×#459C2212yes—
24C8×D4×C31—22no—
25C8×D4×C31C2214yes—
26C31×#431C2211yescharacteristic
27C31×#431C2211yescharacteristic
28C31×#423C2211yescharacteristic
29C2×C31×C4⋊C8C2211yescharacteristic
30C31×#417—21no—
31C2×C31×#103—21no—
32C2×C31×C22⋊C8—22no—
33C31×#335C2214yescomplemented
34C31×#332C2212yescomplemented
35C31×#332C2214yescomplemented
36C31×#331C2212yescomplemented
37C2×#41×C31—21no—
38C22×Q8×C31—21no—
39C22×D4×C31D411yescharacteristic
40C23×C4×C31—21no—
41C31×AGL(1,ℤ/8)—44no—
42C2×SD16×C31—24no—
43C2×SD16×C31—22no—
44C2×SD16×C31—44no—
45C2×D8×C31—22no—
46C2×M16×C31—21no—
47C22×C8×C31—21no—
48C22×C8×C31—24no—
49C31×C4⋊Q8—21no—
50C31×C4⋊Q8—21no—
51C31×C4⋊Q8—21no—
52C31×C4⋊Q8C2312yes—
53C31×C4⋊Q8C2311yescharacteristic
54C31×#127C2311yescharacteristic
55C31×#124—21no—
56C31×#121—21no—
57C31×#121—21no—
58C4×D4×C31—21no—
59C4×D4×C31—21no—
60C4×D4×C31—21no—
61C4×D4×C31—21no—
62C4×D4×C31D412yes—
63C4×D4×C31C2312yes—
64C2×C4⋊C4×C31—21no—
65C2×C4⋊C4×C31—21no—
66C2×C4⋊C4×C31D411yescharacteristic
67C2×C22⋊C4×C31—21no—
68C2×C42×C31C2311yescharacteristic
69C31×#107—24no—
70C31×C4⋊C8—21no—
71C31×C4⋊C8—21no—
72C31×C4⋊C8D412yes—
73C31×C4⋊C8C2312yes—
74C31×C4⋊C8C2312yes—
75C31×C4⋊C8C2312yes—
76C31×#103—24no—
77C31×#103—22no—
78C31×#102—24no—
79C31×#102—22no—
80C31×C22⋊C8—21no—
81C31×C22⋊C8—24no—
82C31×C22⋊C8D412yes—
83C4×C8×C31—21no—
84C4×C8×C31C2312yes—
85C24×C31—21no—
86#41×C31—42no—
87#41×C31—42no—
88C2×Q8×C31—21no—
89C2×Q8×C31—22no—
90C2×Q8×C31—41no—
91C2×Q8×C31—42no—
92C2×Q8×C31—42no—
93C2×D4×C31—21no—
94C2×D4×C31—22no—
95C2×D4×C31—21no—
96C2×D4×C31—21no—
97C2×D4×C31—21no—
98C2×D4×C31—41no—
99C2×D4×C31D814yes—
100C2×D4×C31C2×D412yes—
101C22×C4×C31—21no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—41no—
105C22×C4×C31—41no—
106C22×C4×C31—82no—
107C22×C4×C31C2×D411yescharacteristic
108C22×C4×C31C2×D411yescharacteristic
109C22×C4×C31#4111yescharacteristic
110SD16×C31—48no—
111SD16×C31—44no—
112D8×C31—44no—
113M16×C31—42no—
114C2×C8×C31—22no—
115C2×C8×C31—22no—
116C2×C8×C31—22no—
117C2×C8×C31—42no—
118C2×C8×C31—84no—
119C2×C8×C31C2×D414yes—
120C4⋊C4×C31—21no—
121C4⋊C4×C31—22no—
122C4⋊C4×C31—21no—
123C4⋊C4×C31—22no—
124C4⋊C4×C31—21no—
125C4⋊C4×C31—41no—
126C4⋊C4×C31—41no—
127C4⋊C4×C31C2×D412yes—
128C22⋊C4×C31—22no—
129C22⋊C4×C31—22no—
130C22⋊C4×C31—41no—
131C22⋊C4×C31—41no—
132C42×C31C2×D411yescharacteristic
133C42×C31C2×D411yescharacteristic
134C42×C31#4111yescharacteristic
135C42×C31C2411yescharacteristic
136#19392C3111yesmaximal, characteristic, direct product factor, Sylow
137C23×C31—22no—
138C23×C31—24no—
139C23×C31—41no—
140C23×C31—81no—
141C23×C31—81no—
142C23×C31#12111yescharacteristic
143Q8×C31—42no—
144Q8×C31—41no—
145Q8×C31—42no—
146Q8×C31—41no—
147Q8×C31—82no—
148D4×C31—22no—
149D4×C31—24no—
150D4×C31—41no—
151D4×C31—41no—
152D4×C31—42no—
153D4×C31—81no—
154D4×C31—82no—
155D4×C31C2×D814yes—
156C2×C4×C31—22no—
157C2×C4×C31—22no—
158C2×C4×C31—41no—
159C2×C4×C31—44no—
160C2×C4×C31—41no—
161C2×C4×C31—42no—
162C2×C4×C31—82no—
163C2×C4×C31—81no—
164C2×C4×C31—82no—
165C2×C4×C31—82no—
166C2×C4×C31#12111yescharacteristic
167C2×C4×C31#12111yescharacteristic
168C2×C4×C31#12111yescharacteristic
169C2×C4×C31C2×D812yes—
170C2×C4×C31#13512yes—
171C2×C4×C31C22×D411yescharacteristic
172C2×C4×C31C22×D411yescharacteristic
173C2×C4×C31C2×#4111yescharacteristic
174C8×C31—24no—
175C8×C31—42no—
176C8×C31—42no—
177C8×C31—42no—
178#3226C2×C3111yescharacteristic, complemented
179#3036C2×C3111yescharacteristic
180C2×#461C2×C3111yescharacteristic, complemented
181#2972C2×C3111yescharacteristic, complemented
182#1681C2×C3114yescomplemented
183#1673C2×C3114yescomplemented
184#1571C2×C3111yescharacteristic, complemented
185#1546C2×C3111yescharacteristic, complemented
186#1540C2×C3111yescharacteristic, complemented
187C22×C31—21no—
188C22×C31—21no—
189C22×C31—24no—
190C22×C31—42no—
191C22×C31—42no—
192C22×C31—84no—
193C22×C31—81no—
194C22×C31—81no—
195C22×C31—81no—
196C22×C31#46612yes—
197C22×C31C2×#12111yescharacteristic
198C4×C31—21no—
199C4×C31—21no—
200C4×C31—21no—
201C4×C31—42no—
202C4×C31—81no—
203C4×C31—82no—
204C4×C31#46612yes—
205C4×C31C22×D811yescharacteristic
206C4×C31C2×#13511yescharacteristic
207C4×C31#57712yes—
208C2×AGL(1,ℤ/8)—21no—
209C22×SD16—21no—
210#532C22×C3111yescharacteristic
211C2×C4⋊Q8C22×C3111yescharacteristic
212C2×C4×D4C22×C3111yescharacteristic
213#500C22×C3112yescomplemented
214#486C22×C3112yescomplemented
215#480—22no—
216#474—22no—
217#463—22no—
218#461—22no—
219#461C22×C3112yes—
220#461C22×C3114yes—
221#459C22×C3112yes—
222C8×D4—22no—
223C8×D4C22×C3114yes—
224#431C22×C3111yescharacteristic
225#431C22×C3111yescharacteristic
226#423C22×C3111yescharacteristic
227C2×C4⋊C8C22×C3111yescharacteristic
228#417—21no—
229C2×#103—21no—
230C2×C22⋊C8—22no—
231#335C22×C3114yescomplemented
232#332C22×C3112yescomplemented
233#332C22×C3114yescomplemented
234#331C22×C3112yescomplemented
235C2×C31—22no—
236C2×C31—44no—
237C2×C31—161no—
238C2×C31#304211yescharacteristic
239C2×C31C2×#46611yescharacteristic
240C2×C31#306911yescharacteristic
241C2×#41—21no—
242C22×Q8—21no—
243C22×D4D4×C3111yescharacteristic
244C23×C4—21no—
245AGL(1,ℤ/8)—44no—
246C2×SD16—24no—
247C2×SD16—22no—
248C2×SD16—44no—
249C2×D8—22no—
250C2×M16—21no—
251C22×C8—21no—
252C22×C8—24no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8C23×C3112yes—
257C4⋊Q8C23×C3111yescharacteristic
258#127C23×C3111yescharacteristic
259#124—21no—
260#121—21no—
261#121—21no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4D4×C3112yes—
267C4×D4C23×C3112yes—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4D4×C3111yescharacteristic
271C2×C22⋊C4—21no—
272C2×C42C23×C3111yescharacteristic
273#107—24no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8D4×C3112yes—
277C4⋊C8C23×C3112yes—
278C4⋊C8C23×C3112yes—
279C4⋊C8C23×C3112yes—
280#103—24no—
281#103—22no—
282#102—24no—
283#102—22no—
284C22⋊C8—21no—
285C22⋊C8—24no—
286C22⋊C8D4×C3112yes—
287C4×C8—21no—
288C4×C8C23×C3112yes—
289C31#1939211yescharacteristic, direct product factor, Sylow
290C24—21no—
291#41—42no—
292#41—42no—
293C2×Q8—21no—
294C2×Q8—22no—
295C2×Q8—41no—
296C2×Q8—42no—
297C2×Q8—42no—
298C2×D4—21no—
299C2×D4—22no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4D8×C3114yes—
305C2×D4C2×D4×C3112yes—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—82no—
312C22×C4C2×D4×C3111yescharacteristic
313C22×C4C2×D4×C3111yescharacteristic
314C22×C4#41×C3111yescharacteristic
315SD16—48no—
316SD16—44no—
317D8—44no—
318M16—42no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—42no—
323C2×C8—84no—
324C2×C8C2×D4×C3114yes—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—22no—
329C4⋊C4—21no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4C2×D4×C3112yes—
333C22⋊C4—22no—
334C22⋊C4—22no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C42C2×D4×C3111yescharacteristic
338C42C2×D4×C3111yescharacteristic
339C42#41×C3111yescharacteristic
340C42C24×C3111yescharacteristic
341C23—22no—
342C23—24no—
343C23—41no—
344C23—81no—
345C23—81no—
346C23C31×#12111yescharacteristic
347Q8—42no—
348Q8—41no—
349Q8—42no—
350Q8—41no—
351Q8—82no—
352D4—24no—
353D4—22no—
354D4—41no—
355D4—41no—
356D4—42no—
357D4—81no—
358D4—82no—
359D4C2×D8×C3114yes—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—44no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—82no—
367C2×C4—81no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4C31×#12111yescharacteristic
371C2×C4C31×#12111yescharacteristic
372C2×C4C31×#12111yescharacteristic
373C2×C4C2×D8×C3112yes—
374C2×C4C31×#13512yes—
375C2×C4C22×D4×C3111yescharacteristic
376C2×C4C22×D4×C3111yescharacteristic
377C2×C4C2×#41×C3111yescharacteristic
378C8—24no—
379C8—42no—
380C8—42no—
381C8—42no—
382C22—21no—
383C22—21no—
384C22—24no—
385C22—42no—
386C22—42no—
387C22—84no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22C31×#46612yes—
392C22C2×C31×#12111yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—81no—
398C4—82no—
399C4C31×#46612yes—
400C4C22×D8×C3111yescharacteristic
401C4C2×C31×#13511yescharacteristic
402C4C31×#57712yes—
403C2—22no—
404C2—44no—
405C2—161no—
406C2C31×#304211yescharacteristic
407C2C2×C31×#46611yescharacteristic
408C2C31×#306911yescharacteristic
subgroupG/H
center, socleC22×C31C2×#121
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#3036C2
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
1. C31×#3226C2semidirect
3. C2×C31×#461C2semidirect
4. C31×#2972C2semidirect
5. C31×#1681C2semidirect
6. C31×#1673C2semidirect
7. C31×#1571C2semidirect
8. C31×#1546C2semidirect
9. C31×#1540C2semidirect
15. C31×#500C22semidirect
16. C31×#486C22semidirect
33. C31×#335C22semidirect
34. C31×#332C22semidirect
35. C31×#332C22semidirect
36. C31×#331C22semidirect
136. #19392C31direct (N × H)
178. #3226C2×C31semidirect
180. C2×#461C2×C31semidirect
181. #2972C2×C31semidirect
182. #1681C2×C31semidirect
183. #1673C2×C31semidirect
184. #1571C2×C31semidirect
185. #1546C2×C31semidirect
186. #1540C2×C31semidirect
213. #500C22×C31semidirect
214. #486C22×C31semidirect
231. #335C22×C31semidirect
232. #332C22×C31semidirect
233. #332C22×C31semidirect
234. #331C22×C31semidirect
289. C31#19392direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32262
C31×#30362
C2×C31×#4612
C31×#29722
C31×#16812
C31×#16732
C31×#15712
C31×#15462
C31×#15402
#1939231