Finite Group Databasebeta

← C31×#61889 #21518648

Subgroups — C31×#61889 #21518648

Order 7936.

1706 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3502C211yesmaximal, characteristic, complemented
2C2×C31×#556C211yesmaximal, characteristic
3C31×#3398C218yesmaximal, complemented
4C31×#3369C218yesmaximal, complemented
5C31×#3215C214yesmaximal
6C31×#3209C212yesmaximal, complemented
7C31×#3113C214yesmaximal, complemented
8C31×#3101C212yesmaximal
9C31×#2983C211yesmaximal, characteristic, complemented
10Q82×C31C2214yescomplemented
11C31×#557—24no—
12C31×#557C2214yescomplemented
13C31×#556—24no—
14C31×#556C2218yes—
15C31×#544—21no—
16C31×#544—22no—
17C31×#533C2212yes—
18C31×#533C2214yes—
19C2×C31×C4⋊Q8C2211yescharacteristic
20C2×C31×#126—22no—
21C2×C31×#124C2212yes—
22C2×C31×C22⋊Q8—21no—
23C31×#519—21no—
24C2×C4×Q8×C31C2212yes—
25C2×C4×Q8×C31C2211yescharacteristic
26C2×C4×D4×C31C2211yescharacteristic
27C2×C31×#117—21no—
28C31×#497C2218yes—
29C31×#494C2214yescomplemented
30C31×#489C2218yes—
31C31×#487C2214yescomplemented
32C31×#483C2214yes—
33C31×#476C2214yes—
34C31×#475C2218yescomplemented
35C31×#464C22116yes—
36C31×#462C2218yescomplemented
37C31×#462C2218yescomplemented
38C31×#461C2214yes—
39C31×#451C2218yes—
40C31×#450C2214yes—
41C31×#446C2218yescomplemented
42C31×#441C22116yescomplemented
43C4×SD16×C31C2218yes—
44C31×#432C2214yes—
45C31×#431C2212yes—
46C22×Q8×C31D411yescharacteristic
47C22×Q8×C31C2312yes—
48C22×D4×C31C2311yescharacteristic
49C23×C4×C31—21no—
50C2×Q16×C31C23116yes—
51C2×SD16×C31C2318yes—
52C31×C4⋊Q8—24no—
53C31×C4⋊Q8—28no—
54C31×C4⋊Q8—22no—
55C31×C4⋊Q8C2312yes—
56C31×C4⋊Q8C2314yes—
57C31×C4⋊Q8C2314yes—
58C31×C4⋊Q8C2314yes—
59C31×C4⋊Q8C2312yes—
60C31×#126—216no—
61C31×#125—24no—
62C31×#125—28no—
63C31×#125—22no—
64C31×#125—24no—
65C31×#124—24no—
66C31×#124C2318yes—
67C31×C22⋊Q8—28no—
68C31×C22⋊Q8—24no—
69C31×C22⋊Q8—22no—
70C31×C22⋊Q8C2314yes—
71C4×Q8×C31—24no—
72C4×Q8×C31—24no—
73C4×Q8×C31—24no—
74C4×Q8×C31—22no—
75C4×Q8×C31—24no—
76C4×Q8×C31D414yes—
77C4×Q8×C31C2314yes—
78C4×Q8×C31C2318yes—
79C4×Q8×C31C2318yes—
80C4×Q8×C31C2314yes—
81C4×D4×C31—22no—
82C4×D4×C31C2314yes—
83C31×#117—24no—
84C31×#117—22no—
85C31×#117—28no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31D411yescharacteristic
90C2×C4⋊C4×C31D412yes—
91C2×C4⋊C4×C31C2311yescharacteristic
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—21no—
94C2×C22⋊C4×C31—22no—
95C2×C42×C31—22no—
96C2×C42×C31C2311yescharacteristic
97C2×C42×C31C2312yes—
98C31×#106C2318yes—
99C31×C4⋊C8C2314yes—
100C31×C4⋊C8C2318yes—
101C31×#103C2318yes—
102C31×#103C23116yes—
103C31×#102C2318yes—
104C31×C22⋊C8C2314yes—
105C31×#97C2318yes—
106C4×C8×C31C2314yes—
107C24×C31—21no—
108C2×Q8×C31—24no—
109C2×Q8×C31—22no—
110C2×Q8×C31—24no—
111C2×Q8×C31—22no—
112C2×Q8×C31—44no—
113C2×Q8×C31C2×D414yes—
114C2×Q8×C31C2414yes—
115C2×Q8×C31C2414yes—
116C2×D4×C31—21no—
117C2×D4×C31—42no—
118C2×D4×C31C2412yes—
119C22×C4×C31—21no—
120C22×C4×C31—22no—
121C22×C4×C31—24no—
122C22×C4×C31—44no—
123C22×C4×C31C2×D412yes—
124C22×C4×C31C2×D412yes—
125C22×C4×C31C2×D411yescharacteristic
126C22×C4×C31C2×D411yescharacteristic
127C22×C4×C31C2411yescharacteristic
128Q16×C31—416no—
129SD16×C31—48no—
130C2×C8×C31C2418yes—
131C4⋊C4×C31—24no—
132C4⋊C4×C31—28no—
133C4⋊C4×C31—24no—
134C4⋊C4×C31—21no—
135C4⋊C4×C31—24no—
136C4⋊C4×C31—22no—
137C4⋊C4×C31—24no—
138C4⋊C4×C31—22no—
139C4⋊C4×C31—24no—
140C4⋊C4×C31—24no—
141C4⋊C4×C31—22no—
142C4⋊C4×C31—28no—
143C4⋊C4×C31—24no—
144C4⋊C4×C31C2×D414yes—
145C4⋊C4×C31C2×D418yes—
146C4⋊C4×C31C2414yes—
147C4⋊C4×C31C2412yes—
148C22⋊C4×C31—24no—
149C22⋊C4×C31—28no—
150C22⋊C4×C31—24no—
151C22⋊C4×C31—28no—
152C42×C31—28no—
153C42×C31—28no—
154C42×C31—24no—
155C42×C31C2×D412yes—
156C42×C31C2×D414yes—
157C42×C31C2412yes—
158C42×C31C2414yes—
159#61889C3111yesmaximal, characteristic, direct product factor, Sylow
160C23×C31—22no—
161C23×C31—42no—
162C23×C31—42no—
163C23×C31—42no—
164C23×C31C22×D411yescharacteristic
165Q8×C31—28no—
166Q8×C31—28no—
167Q8×C31—28no—
168Q8×C31—44no—
169Q8×C31—84no—
170Q8×C31—82no—
171D4×C31—24no—
172D4×C31—42no—
173C2×C4×C31—24no—
174C2×C4×C31—22no—
175C2×C4×C31—22no—
176C2×C4×C31—24no—
177C2×C4×C31—24no—
178C2×C4×C31—24no—
179C2×C4×C31—42no—
180C2×C4×C31—41no—
181C2×C4×C31—44no—
182C2×C4×C31—42no—
183C2×C4×C31—48no—
184C2×C4×C31#13714yes—
185C2×C4×C31C22×D414yes—
186C2×C4×C31C22×D414yes—
187C2×C4×C31C22×D411yescharacteristic
188C2×C4×C31C22×D412yes—
189C2×C4×C31C22×D412yes—
190C2×C4×C31C2511yescharacteristic
191C8×C31—28no—
192#3502C2×C3111yescharacteristic, complemented
193C2×#556C2×C3111yescharacteristic
194#3398C2×C3118yescomplemented
195#3369C2×C3118yescomplemented
196#3215C2×C3114yes—
197#3209C2×C3112yescomplemented
198#3113C2×C3114yescomplemented
199#3101C2×C3112yes—
200#2983C2×C3111yescharacteristic, complemented
201C22×C31—21no—
202C22×C31—21no—
203C22×C31—42no—
204C22×C31—42no—
205C22×C31—42no—
206C22×C31—84no—
207C22×C31C2×#13712yes—
208C22×C31C23×D411yescharacteristic
209C4×C31—24no—
210C4×C31—22no—
211C4×C31—21no—
212C4×C31—24no—
213C4×C31—44no—
214C4×C31—44no—
215C4×C31—44no—
216C4×C31—42no—
217C4×C31C2×#13714yes—
218C4×C31#58512yes—
219Q82C22×C3114yescomplemented
220#557—24no—
221#557C22×C3114yescomplemented
222#556—24no—
223#556C22×C3118yes—
224#544—21no—
225#544—22no—
226#533C22×C3112yes—
227#533C22×C3114yes—
228C2×C4⋊Q8C22×C3111yescharacteristic
229C2×#126—22no—
230C2×#124C22×C3112yes—
231C2×C22⋊Q8—21no—
232#519—21no—
233C2×C4×Q8C22×C3112yes—
234C2×C4×Q8C22×C3111yescharacteristic
235C2×C4×D4C22×C3111yescharacteristic
236C2×#117—21no—
237#497C22×C3118yes—
238#494C22×C3114yescomplemented
239#489C22×C3118yes—
240#487C22×C3114yescomplemented
241#483C22×C3114yes—
242#476C22×C3114yes—
243#475C22×C3118yescomplemented
244#464C22×C31116yes—
245#462C22×C3118yescomplemented
246#462C22×C3118yescomplemented
247#461C22×C3114yes—
248#451C22×C3118yes—
249#450C22×C3114yes—
250#446C22×C3118yescomplemented
251#441C22×C31116yescomplemented
252C4×SD16C22×C3118yes—
253#432C22×C3114yes—
254#431C22×C3112yes—
255C2×C31—22no—
256C2×C31—82no—
257C2×C31#348711yescharacteristic
258C2×C31C22×#13711yescharacteristic
259C2×C31#358611yescharacteristic
260C22×Q8D4×C3111yescharacteristic
261C22×Q8C23×C3112yes—
262C22×D4C23×C3111yescharacteristic
263C23×C4—21no—
264C2×Q16C23×C31116yes—
265C2×SD16C23×C3118yes—
266C4⋊Q8—24no—
267C4⋊Q8—28no—
268C4⋊Q8—22no—
269C4⋊Q8C23×C3114yes—
270C4⋊Q8C23×C3112yes—
271C4⋊Q8C23×C3114yes—
272C4⋊Q8C23×C3114yes—
273C4⋊Q8C23×C3112yes—
274#126—216no—
275#125—24no—
276#125—28no—
277#125—22no—
278#125—24no—
279#124—24no—
280#124C23×C3118yes—
281C22⋊Q8—28no—
282C22⋊Q8—24no—
283C22⋊Q8—22no—
284C22⋊Q8C23×C3114yes—
285C4×Q8—24no—
286C4×Q8—24no—
287C4×Q8—24no—
288C4×Q8—22no—
289C4×Q8—24no—
290C4×Q8D4×C3114yes—
291C4×Q8C23×C3118yes—
292C4×Q8C23×C3114yes—
293C4×Q8C23×C3118yes—
294C4×Q8C23×C3114yes—
295C4×D4—22no—
296C4×D4C23×C3114yes—
297#117—24no—
298#117—22no—
299#117—28no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4D4×C3111yescharacteristic
304C2×C4⋊C4D4×C3112yes—
305C2×C4⋊C4C23×C3111yescharacteristic
306C2×C22⋊C4—22no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—22no—
309C2×C42—22no—
310C2×C42C23×C3111yescharacteristic
311C2×C42C23×C3112yes—
312#106C23×C3118yes—
313C4⋊C8C23×C3114yes—
314C4⋊C8C23×C3118yes—
315#103C23×C3118yes—
316#103C23×C31116yes—
317#102C23×C3118yes—
318C22⋊C8C23×C3114yes—
319#97C23×C3118yes—
320C4×C8C23×C3114yes—
321C31#6188911yescharacteristic, direct product factor, Sylow
322C24—21no—
323C2×Q8—24no—
324C2×Q8—22no—
325C2×Q8—24no—
326C2×Q8—22no—
327C2×Q8—44no—
328C2×Q8C2×D4×C3114yes—
329C2×Q8C24×C3114yes—
330C2×Q8C24×C3114yes—
331C2×D4—21no—
332C2×D4—42no—
333C2×D4C24×C3112yes—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—44no—
338C22×C4C2×D4×C3112yes—
339C22×C4C2×D4×C3112yes—
340C22×C4C2×D4×C3111yescharacteristic
341C22×C4C2×D4×C3111yescharacteristic
342C22×C4C24×C3111yescharacteristic
343Q16—416no—
344SD16—48no—
345C2×C8C24×C3118yes—
346C4⋊C4—24no—
347C4⋊C4—28no—
348C4⋊C4—24no—
349C4⋊C4—21no—
350C4⋊C4—24no—
351C4⋊C4—22no—
352C4⋊C4—24no—
353C4⋊C4—22no—
354C4⋊C4—24no—
355C4⋊C4—24no—
356C4⋊C4—22no—
357C4⋊C4—28no—
358C4⋊C4—24no—
359C4⋊C4C2×D4×C3114yes—
360C4⋊C4C2×D4×C3118yes—
361C4⋊C4C24×C3114yes—
362C4⋊C4C24×C3112yes—
363C22⋊C4—24no—
364C22⋊C4—28no—
365C22⋊C4—24no—
366C22⋊C4—28no—
367C42—28no—
368C42—28no—
369C42—24no—
370C42C2×D4×C3112yes—
371C42C2×D4×C3114yes—
372C42C24×C3112yes—
373C42C24×C3114yes—
374C23—22no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23C22×D4×C3111yescharacteristic
379Q8—28no—
380Q8—28no—
381Q8—28no—
382Q8—44no—
383Q8—84no—
384Q8—82no—
385D4—24no—
386D4—42no—
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—44no—
396C2×C4—42no—
397C2×C4—48no—
398C2×C4C31×#13714yes—
399C2×C4C22×D4×C3114yes—
400C2×C4C22×D4×C3114yes—
401C2×C4C22×D4×C3111yescharacteristic
402C2×C4C22×D4×C3112yes—
403C2×C4C22×D4×C3112yes—
404C2×C4C25×C3111yescharacteristic
405C8—28no—
406C22—21no—
407C22—21no—
408C22—42no—
409C22—42no—
410C22—42no—
411C22—84no—
412C22C2×C31×#13712yes—
413C22C23×D4×C3111yescharacteristic
414C4—21no—
415C4—24no—
416C4—24no—
417C4—22no—
418C4—44no—
419C4—44no—
420C4—42no—
421C4—44no—
422C4C2×C31×#13714yes—
423C4C31×#58512yes—
424C2—22no—
425C2—82no—
426C2C31×#348711yescharacteristic
427C2C22×C31×#13711yescharacteristic
428C2C31×#358611yescharacteristic
subgroupG/H
center, socleC22×C31C23×D4
commutator, Frattini, cosocleC2×C4C25×C31
prime radicalC22×D4×C31C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3502C2semidirect
3. C31×#3398C2semidirect
4. C31×#3369C2semidirect
6. C31×#3209C2semidirect
7. C31×#3113C2semidirect
9. C31×#2983C2semidirect
10. Q82×C31C22semidirect
12. C31×#557C22semidirect
29. C31×#494C22semidirect
31. C31×#487C22semidirect
34. C31×#475C22semidirect
36. C31×#462C22semidirect
37. C31×#462C22semidirect
41. C31×#446C22semidirect
42. C31×#441C22semidirect
159. #61889C31direct (N × H)
192. #3502C2×C31semidirect
194. #3398C2×C31semidirect
195. #3369C2×C31semidirect
197. #3209C2×C31semidirect
198. #3113C2×C31semidirect
200. #2983C2×C31semidirect
219. Q82C22×C31semidirect
221. #557C22×C31semidirect
238. #494C22×C31semidirect
240. #487C22×C31semidirect
243. #475C22×C31semidirect
245. #462C22×C31semidirect
246. #462C22×C31semidirect
250. #446C22×C31semidirect
251. #441C22×C31semidirect
321. C31#61889direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35022
C2×C31×#5562
C31×#33982
C31×#33692
C31×#32152
C31×#32092
C31×#31132
C31×#31012
C31×#29832
#6188931