Finite Group Databasebeta

← C31×#18302 #21475061

Subgroups — C31×#18302 #21475061

Order 7936.

1032 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3458C211yesmaximal, characteristic, complemented
2C31×#3208C212yesmaximal, complemented
3C31×#2619C211yesmaximal, characteristic
4C31×#1599C214yesmaximal, complemented
5C31×#1596C214yesmaximal, complemented
6C31×#1518C212yesmaximal, complemented
7C31×#1458C211yesmaximal, characteristic, complemented
8C31×#544—22no—
9C31×#544—22no—
10C31×#544—21no—
11C31×#544C2212yes—
12C31×#543—21no—
13C31×#543C2212yes—
14C31×#533—24no—
15C31×#533—21no—
16C31×#533C2212yes—
17C2×C31×#127C2211yescharacteristic
18C2×C31×#121—21no—
19C2×C31×#117—21no—
20C2×C31×#117C2211yescharacteristic
21C31×#492—22no—
22C31×#486—22no—
23C31×#460—24no—
24C31×#450C2218yes—
25C31×#431C2212yes—
26C31×#394—21no—
27C31×#394C2212yes—
28C31×#392—21no—
29C31×#392C2212yes—
30C31×#390—21no—
31C31×#382C2211yescharacteristic
32C31×#328C2218yes—
33C31×#324C2212yes—
34C31×#323C2212yes—
35C22×D4×C31—22no—
36C22×D4×C31—21no—
37C22×D4×C31—21no—
38C22×D4×C31C2312yes—
39C23×C4×C31D411yescharacteristic
40C2×SD16×C31—28no—
41C31×C4⋊Q8—24no—
42C31×C4⋊Q8—21no—
43C31×C4⋊Q8—21no—
44C31×C4⋊Q8—24no—
45C31×C4⋊Q8D412yescomplemented
46C31×C4⋊Q8D412yescomplemented
47C31×#127—22no—
48C31×#127—22no—
49C31×#125—24no—
50C31×#125—22no—
51C31×#125—24no—
52C31×#125—22no—
53C31×C22⋊Q8—24no—
54C31×C22⋊Q8—24no—
55C31×C22⋊Q8—24no—
56C31×C22⋊Q8—22no—
57C31×C22⋊Q8—22no—
58C31×C22⋊Q8—22no—
59C31×C22⋊Q8—24no—
60C31×C22⋊Q8C2314yes—
61C31×#121—44no—
62C4×Q8×C31—22no—
63C4×Q8×C31—22no—
64C4×Q8×C31—22no—
65C4×Q8×C31D414yescomplemented
66C31×#117—22no—
67C31×#117—22no—
68C31×#117—22no—
69C31×#117—22no—
70C31×#117—22no—
71C31×#117—22no—
72C2×C4⋊C4×C31—21no—
73C2×C4⋊C4×C31—21no—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31D411yescharacteristic
76C2×C4⋊C4×C31C2311yescharacteristic
77C2×C22⋊C4×C31—22no—
78C2×C22⋊C4×C31—22no—
79C2×C22⋊C4×C31—22no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31D411yescharacteristic
82C2×C22⋊C4×C31C2311yescharacteristic
83C2×C42×C31—22no—
84C2×C42×C31D411yescharacteristic
85C2×C42×C31C2311yescharacteristic
86C31×C4⋊C8—22no—
87C31×#102—28no—
88C31×C22⋊C8C2314yes—
89C4×C8×C31—22no—
90C31×#95—21no—
91C31×#95C2312yes—
92C24×C31—22no—
93C24×C31C2×D411yescharacteristic
94C2×Q8×C31—22no—
95C2×Q8×C31—22no—
96C2×Q8×C31—22no—
97C2×Q8×C31C2×D414yes—
98C2×D4×C31—24no—
99C2×D4×C31—44no—
100C2×D4×C31—42no—
101C2×D4×C31—41no—
102C2×D4×C31—41no—
103C2×D4×C31—42no—
104C2×D4×C31—42no—
105C2×D4×C31—82no—
106C2×D4×C31—82no—
107C2×D4×C31—82no—
108C2×D4×C31—82no—
109C22×C4×C31—21no—
110C22×C4×C31—21no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31SD1614yescomplemented
116C22×C4×C31C2×D411yescharacteristic
117C22×C4×C31C2×D411yescharacteristic
118C22×C4×C31C2×D411yescharacteristic
119C22×C4×C31C2×D411yescharacteristic
120C22×C4×C31C2×D411yescharacteristic
121C22×C4×C31C2411yescharacteristic
122SD16×C31—88no—
123C2×C8×C31—24no—
124C4⋊C4×C31—22no—
125C4⋊C4×C31—22no—
126C4⋊C4×C31—22no—
127C4⋊C4×C31—24no—
128C4⋊C4×C31—24no—
129C4⋊C4×C31—22no—
130C4⋊C4×C31—22no—
131C4⋊C4×C31—22no—
132C4⋊C4×C31—22no—
133C4⋊C4×C31—22no—
134C4⋊C4×C31—24no—
135C4⋊C4×C31—22no—
136C4⋊C4×C31—24no—
137C4⋊C4×C31—42no—
138C4⋊C4×C31C2×D414yes—
139C22⋊C4×C31—24no—
140C22⋊C4×C31—24no—
141C22⋊C4×C31—22no—
142C22⋊C4×C31—22no—
143C22⋊C4×C31—44no—
144C22⋊C4×C31—82no—
145C22⋊C4×C31—82no—
146C42×C31—24no—
147C42×C31—24no—
148C42×C31—21no—
149C42×C31—21no—
150C42×C31C2×D412yes—
151C42×C31C2×D412yes—
152#18302C3111yesmaximal, characteristic, direct product factor, Sylow
153C23×C31—21no—
154C23×C31—21no—
155C23×C31—41no—
156C23×C31—41no—
157C23×C31—42no—
158C23×C31—42no—
159C23×C31—42no—
160C23×C31—42no—
161C23×C31—42no—
162C23×C31—42no—
163C23×C31—42no—
164C23×C31C2×SD1612yes—
165C23×C31C22×D411yescharacteristic
166Q8×C31—44no—
167Q8×C31—82no—
168Q8×C31—82no—
169Q8×C31—82no—
170D4×C31—48no—
171D4×C31—84no—
172D4×C31—88no—
173D4×C31—82no—
174D4×C31—82no—
175C2×C4×C31—21no—
176C2×C4×C31—21no—
177C2×C4×C31—24no—
178C2×C4×C31—24no—
179C2×C4×C31—24no—
180C2×C4×C31—21no—
181C2×C4×C31—21no—
182C2×C4×C31—24no—
183C2×C4×C31—41no—
184C2×C4×C31—41no—
185C2×C4×C31—41no—
186C2×C4×C31—41no—
187C2×C4×C31—42no—
188C2×C4×C31—42no—
189C2×C4×C31—42no—
190C2×C4×C31—82no—
191C2×C4×C31—82no—
192C2×C4×C31#12012yes—
193C2×C4×C31#12011yescharacteristic
194C2×C4×C31#12011yescharacteristic
195C2×C4×C31C2×SD1612yes—
196C2×C4×C31C2×SD1612yes—
197C2×C4×C31#13712yes—
198C2×C4×C31C22×D412yes—
199C8×C31—44no—
200#3458C2×C3111yescharacteristic, complemented
201#3208C2×C3112yescomplemented
202#2619C2×C3111yescharacteristic
203#1599C2×C3114yescomplemented
204#1596C2×C3114yescomplemented
205#1518C2×C3112yescomplemented
206#1458C2×C3111yescharacteristic, complemented
207C22×C31—21no—
208C22×C31—21no—
209C22×C31—22no—
210C22×C31—42no—
211C22×C31—41no—
212C22×C31—41no—
213C22×C31—81no—
214C22×C31—82no—
215C22×C31—82no—
216C22×C31—82no—
217C22×C31—82no—
218C22×C31—82no—
219C22×C31—82no—
220C22×C31—82no—
221C22×C31C2×#12011yescharacteristic
222C22×C31C22×SD1611yescharacteristic
223C22×C31C2×#13711yescharacteristic
224C4×C31—22no—
225C4×C31—22no—
226C4×C31—22no—
227C4×C31—41no—
228C4×C31—44no—
229C4×C31—41no—
230C4×C31—44no—
231C4×C31—82no—
232C4×C31#44812yes—
233C4×C31#44812yes—
234#544—22no—
235#544—22no—
236#544—21no—
237#544C22×C3112yes—
238#543—21no—
239#543C22×C3112yes—
240#533—24no—
241#533—21no—
242#533C22×C3112yes—
243C2×#127C22×C3111yescharacteristic
244C2×#121—21no—
245C2×#117—21no—
246C2×#117C22×C3111yescharacteristic
247#492—22no—
248#486—22no—
249#460—24no—
250#450C22×C3118yes—
251#431C22×C3112yes—
252#394—21no—
253#394C22×C3112yes—
254#392—21no—
255#392C22×C3112yes—
256#390—21no—
257#382C22×C3111yescharacteristic
258#328C22×C3118yes—
259#324C22×C3112yes—
260#323C22×C3112yes—
261C2×C31—21no—
262C2×C31—21no—
263C2×C31—42no—
264C2×C31—162no—
265C2×C31C2×#44811yescharacteristic
266C2×C31#302111yescharacteristic
267C2×C31#302711yescharacteristic
268C22×D4—22no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4C23×C3112yes—
272C23×C4D4×C3111yescharacteristic
273C2×SD16—28no—
274C4⋊Q8—24no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—24no—
278C4⋊Q8D4×C3112yescomplemented
279C4⋊Q8D4×C3112yescomplemented
280#127—22no—
281#127—22no—
282#125—24no—
283#125—22no—
284#125—24no—
285#125—22no—
286C22⋊Q8—24no—
287C22⋊Q8—24no—
288C22⋊Q8—24no—
289C22⋊Q8—22no—
290C22⋊Q8—22no—
291C22⋊Q8—22no—
292C22⋊Q8—24no—
293C22⋊Q8C23×C3114yes—
294#121—44no—
295C4×Q8—22no—
296C4×Q8—22no—
297C4×Q8—22no—
298C4×Q8D4×C3114yescomplemented
299#117—22no—
300#117—22no—
301#117—22no—
302#117—22no—
303#117—22no—
304#117—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4D4×C3111yescharacteristic
309C2×C4⋊C4C23×C3111yescharacteristic
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4D4×C3111yescharacteristic
315C2×C22⋊C4C23×C3111yescharacteristic
316C2×C42—22no—
317C2×C42D4×C3111yescharacteristic
318C2×C42C23×C3111yescharacteristic
319C4⋊C8—22no—
320#102—28no—
321C22⋊C8C23×C3114yes—
322C4×C8—22no—
323#95—21no—
324#95C23×C3112yes—
325C31#1830211yescharacteristic, direct product factor, Sylow
326C24—22no—
327C24C2×D4×C3111yescharacteristic
328C2×Q8—22no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8C2×D4×C3114yes—
332C2×D4—24no—
333C2×D4—44no—
334C2×D4—42no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—42no—
338C2×D4—42no—
339C2×D4—82no—
340C2×D4—82no—
341C2×D4—82no—
342C2×D4—82no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4SD16×C3114yescomplemented
350C22×C4C2×D4×C3111yescharacteristic
351C22×C4C2×D4×C3111yescharacteristic
352C22×C4C2×D4×C3111yescharacteristic
353C22×C4C2×D4×C3111yescharacteristic
354C22×C4C2×D4×C3111yescharacteristic
355C22×C4C24×C3111yescharacteristic
356SD16—88no—
357C2×C8—24no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—24no—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—24no—
369C4⋊C4—22no—
370C4⋊C4—24no—
371C4⋊C4—42no—
372C4⋊C4C2×D4×C3114yes—
373C22⋊C4—24no—
374C22⋊C4—24no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—44no—
378C22⋊C4—82no—
379C22⋊C4—82no—
380C42—24no—
381C42—24no—
382C42—21no—
383C42—21no—
384C42C2×D4×C3112yes—
385C42C2×D4×C3112yes—
386C23—21no—
387C23—21no—
388C23—41no—
389C23—41no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23C2×SD16×C3112yes—
398C23C22×D4×C3111yescharacteristic
399Q8—44no—
400Q8—82no—
401Q8—82no—
402Q8—82no—
403D4—48no—
404D4—84no—
405D4—88no—
406D4—82no—
407D4—82no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—24no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4C31×#12012yes—
426C2×C4C31×#12011yescharacteristic
427C2×C4C31×#12011yescharacteristic
428C2×C4C2×SD16×C3112yes—
429C2×C4C2×SD16×C3112yes—
430C2×C4C31×#13712yes—
431C2×C4C22×D4×C3112yes—
432C8—44no—
433C22—21no—
434C22—21no—
435C22—22no—
436C22—42no—
437C22—41no—
438C22—41no—
439C22—81no—
440C22—82no—
441C22—82no—
442C22—82no—
443C22—82no—
444C22—82no—
445C22—82no—
446C22—82no—
447C22C2×C31×#12011yescharacteristic
448C22C22×SD16×C3111yescharacteristic
449C22C2×C31×#13711yescharacteristic
450C4—22no—
451C4—22no—
452C4—22no—
453C4—41no—
454C4—44no—
455C4—41no—
456C4—44no—
457C4—82no—
458C4C31×#44812yes—
459C4C31×#44812yes—
460C2—21no—
461C2—21no—
462C2—42no—
463C2—162no—
464C2C2×C31×#44811yescharacteristic
465C2C31×#302111yescharacteristic
466C2C31×#302711yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2619C2
LCSG ▷ C22×C4 ▷ 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×#3458C2semidirect
2. C31×#3208C2semidirect
4. C31×#1599C2semidirect
5. C31×#1596C2semidirect
6. C31×#1518C2semidirect
7. C31×#1458C2semidirect
45. C31×C4⋊Q8D4semidirect
46. C31×C4⋊Q8D4semidirect
65. C4×Q8×C31D4semidirect
115. C22×C4×C31SD16semidirect
152. #18302C31direct (N × H)
200. #3458C2×C31semidirect
201. #3208C2×C31semidirect
203. #1599C2×C31semidirect
204. #1596C2×C31semidirect
205. #1518C2×C31semidirect
206. #1458C2×C31semidirect
278. C4⋊Q8D4×C31semidirect
279. C4⋊Q8D4×C31semidirect
298. C4×Q8D4×C31semidirect
325. C31#18302direct (N × H)
349. C22×C4SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#34582
C31×#32082
C31×#26192
C31×#15992
C31×#15962
C31×#15182
C31×#14582
#1830231