Finite Group Databasebeta

← C31×#18174 #21474933

Subgroups — C31×#18174 #21474933

Order 7936.

962 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3501C211yesmaximal, characteristic
2C31×#3095C212yesmaximal, complemented
3C31×#2395C211yesmaximal, characteristic
4C31×#1617C212yesmaximal, complemented
5C31×#1614C212yesmaximal, complemented
6C31×#1611C212yesmaximal, complemented
7C31×#1608C212yesmaximal, complemented
8C31×#1508C212yesmaximal, complemented
9C31×#1465C211yesmaximal, characteristic
10C31×#554—24no—
11C31×#554—22no—
12D4×Q8×C31—22no—
13C31×#544C2212yes—
14C31×#543—21no—
15C31×#543C2212yes—
16C31×#533—21no—
17C2×C31×C22⋊Q8—21no—
18C2×C31×C22⋊Q8C2212yes—
19C31×#518—21no—
20C2×C4×D4×C31C2211yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C31×#485—24no—
23C31×#484C2214yes—
24C31×#483C2214yes—
25C31×#428—22no—
26C31×#419—22no—
27C31×#407C2212yes—
28C31×#400C2211yescharacteristic
29C31×#399C2211yescharacteristic
30C31×#398C2211yescharacteristic
31C31×#397—21no—
32C31×#397C2211yescharacteristic
33C31×#394—21no—
34C4×C4⋊C4×C31—21no—
35C4×C22⋊C4×C31—21no—
36C4×C22⋊C4×C31C2211yescharacteristic
37C31×#328C2214yes—
38C31×#328C2214yes—
39C31×#324C2212yes—
40C31×#323C2212yes—
41C22×Q8×C31—21no—
42C22×Q8×C31D412yes—
43C22×D4×C31D411yescharacteristic
44C23×C4×C31D411yescharacteristic
45C23×C4×C31C2311yescharacteristic
46C2×M16×C31—22no—
47C31×C4⋊Q8—21no—
48C31×C4⋊Q8—21no—
49C31×C4⋊Q8—24no—
50C31×#125—22no—
51C31×#125—24no—
52C31×C22⋊Q8—22no—
53C31×C22⋊Q8—22no—
54C31×C22⋊Q8—24no—
55C31×C22⋊Q8—24no—
56C31×C22⋊Q8—24no—
57C31×C22⋊Q8—22no—
58C31×C22⋊Q8—22no—
59C31×C22⋊Q8—22no—
60C31×C22⋊Q8—22no—
61C31×C22⋊Q8—24no—
62C31×C22⋊Q8D414yes—
63C31×C22⋊Q8C2314yes—
64C4×Q8×C31—22no—
65C4×Q8×C31—22no—
66C4×D4×C31—24no—
67C4×D4×C31—24no—
68C4×D4×C31—22no—
69C4×D4×C31—22no—
70C31×#117—22no—
71C31×#117—22no—
72C31×#117—22no—
73C2×C4⋊C4×C31—21no—
74C2×C4⋊C4×C31—22no—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31—21no—
77C2×C4⋊C4×C31—21no—
78C2×C4⋊C4×C31D412yes—
79C2×C4⋊C4×C31C2311yescharacteristic
80C2×C4⋊C4×C31C2311yescharacteristic
81C2×C4⋊C4×C31C2311yescharacteristic
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—22no—
84C2×C22⋊C4×C31—21no—
85C2×C22⋊C4×C31—21no—
86C2×C22⋊C4×C31—21no—
87C2×C22⋊C4×C31—21no—
88C2×C22⋊C4×C31D411yescharacteristic
89C2×C22⋊C4×C31C2311yescharacteristic
90C2×C42×C31—21no—
91C2×C42×C31—21no—
92C2×C42×C31D411yescharacteristic
93C31×#107—24no—
94C31×#106—24no—
95C31×#103—24no—
96C31×#103—24no—
97C31×C22⋊C8—22no—
98C31×C22⋊C8C2314yes—
99C31×#95—21no—
100C31×#95—21no—
101C31×#95—21no—
102C31×#95—21no—
103C31×#95C2311yescharacteristic
104C31×#95C2311yescharacteristic
105C24×C31C2×D411yescharacteristic
106C24×C31C2×D411yescharacteristic
107C2×Q8×C31—22no—
108C2×Q8×C31—22no—
109C2×Q8×C31—22no—
110C2×Q8×C31—44no—
111C2×Q8×C31—82no—
112C2×Q8×C31C2×D414yes—
113C2×D4×C31—22no—
114C2×D4×C31—22no—
115C2×D4×C31—22no—
116C22×C4×C31—21no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—21no—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—21no—
126C22×C4×C31—42no—
127C22×C4×C31—42no—
128C22×C4×C31C2×D411yescharacteristic
129C22×C4×C31C2×D412yes—
130C22×C4×C31C2×D411yescharacteristic
131C22×C4×C31C2×D411yescharacteristic
132C22×C4×C31C2×D411yescharacteristic
133C22×C4×C31C2×D412yes—
134C22×C4×C31C2411yescharacteristic
135M16×C31—44no—
136C2×C8×C31—24no—
137C4⋊C4×C31—22no—
138C4⋊C4×C31—24no—
139C4⋊C4×C31—22no—
140C4⋊C4×C31—22no—
141C4⋊C4×C31—24no—
142C4⋊C4×C31—22no—
143C4⋊C4×C31—24no—
144C4⋊C4×C31—22no—
145C4⋊C4×C31—24no—
146C4⋊C4×C31—22no—
147C4⋊C4×C31—22no—
148C4⋊C4×C31—22no—
149C4⋊C4×C31—42no—
150C4⋊C4×C31—42no—
151C4⋊C4×C31C2×D414yes—
152C22⋊C4×C31—24no—
153C22⋊C4×C31—24no—
154C22⋊C4×C31—22no—
155C22⋊C4×C31—24no—
156C22⋊C4×C31—22no—
157C22⋊C4×C31—42no—
158C22⋊C4×C31—42no—
159C22⋊C4×C31—42no—
160C22⋊C4×C31—42no—
161C42×C31—24no—
162C42×C31—21no—
163C42×C31—21no—
164C42×C31—42no—
165C42×C31—41no—
166C42×C31—41no—
167#18174C3111yesmaximal, characteristic, direct product factor, Sylow
168C23×C31—21no—
169C23×C31—21no—
170C23×C31—21no—
171C23×C31—21no—
172C23×C31—41no—
173C23×C31—41no—
174C23×C31—41no—
175C23×C31—41no—
176C23×C31#12012yes—
177C23×C31#13712yes—
178C23×C31C22×D411yescharacteristic
179Q8×C31—44no—
180Q8×C31—44no—
181Q8×C31—82no—
182Q8×C31—82no—
183D4×C31—28no—
184C2×C4×C31—21no—
185C2×C4×C31—21no—
186C2×C4×C31—22no—
187C2×C4×C31—24no—
188C2×C4×C31—22no—
189C2×C4×C31—21no—
190C2×C4×C31—24no—
191C2×C4×C31—24no—
192C2×C4×C31—21no—
193C2×C4×C31—42no—
194C2×C4×C31—41no—
195C2×C4×C31—41no—
196C2×C4×C31—41no—
197C2×C4×C31—42no—
198C2×C4×C31—41no—
199C2×C4×C31—41no—
200C2×C4×C31—41no—
201C2×C4×C31—41no—
202C2×C4×C31—41no—
203C2×C4×C31—41no—
204C2×C4×C31—41no—
205C2×C4×C31—41no—
206C2×C4×C31—41no—
207C2×C4×C31—41no—
208C2×C4×C31—41no—
209C2×C4×C31—81no—
210C2×C4×C31—82no—
211C2×C4×C31—82no—
212C2×C4×C31—82no—
213C2×C4×C31—82no—
214C2×C4×C31#12011yescharacteristic
215C2×C4×C31#12011yescharacteristic
216C2×C4×C31#13712yes—
217C2×C4×C31C22×D412yes—
218C8×C31—44no—
219#3501C2×C3111yescharacteristic
220#3095C2×C3112yescomplemented
221#2395C2×C3111yescharacteristic
222#1617C2×C3112yescomplemented
223#1614C2×C3112yescomplemented
224#1611C2×C3112yescomplemented
225#1608C2×C3112yescomplemented
226#1508C2×C3112yescomplemented
227#1465C2×C3111yescharacteristic
228C22×C31—21no—
229C22×C31—21no—
230C22×C31—22no—
231C22×C31—22no—
232C22×C31—22no—
233C22×C31—22no—
234C22×C31—42no—
235C22×C31—41no—
236C22×C31—41no—
237C22×C31—81no—
238C22×C31—81no—
239C22×C31—81no—
240C22×C31C2×#12011yescharacteristic
241C22×C31C2×#13711yescharacteristic
242C22×C31C2×#13711yescharacteristic
243C4×C31—22no—
244C4×C31—22no—
245C4×C31—21no—
246C4×C31—42no—
247C4×C31—41no—
248C4×C31—44no—
249C4×C31—41no—
250C4×C31—44no—
251C4×C31—81no—
252C4×C31—81no—
253C4×C31—81no—
254C4×C31#45812yes—
255#554—24no—
256#554—22no—
257D4×Q8—22no—
258#544C22×C3112yes—
259#543—21no—
260#543C22×C3112yes—
261#533—21no—
262C2×C22⋊Q8—21no—
263C2×C22⋊Q8C22×C3112yes—
264#518—21no—
265C2×C4×D4C22×C3111yescharacteristic
266C2×#117C22×C3111yescharacteristic
267#485—24no—
268#484C22×C3114yes—
269#483C22×C3114yes—
270#428—22no—
271#419—22no—
272#407C22×C3112yes—
273#400C22×C3111yescharacteristic
274#399C22×C3111yescharacteristic
275#398C22×C3111yescharacteristic
276#397—21no—
277#397C22×C3111yescharacteristic
278#394—21no—
279C4×C4⋊C4—21no—
280C4×C22⋊C4—21no—
281C4×C22⋊C4C22×C3111yescharacteristic
282#328C22×C3114yes—
283#328C22×C3114yes—
284#324C22×C3112yes—
285#323C22×C3112yes—
286C2×C31—21no—
287C2×C31—21no—
288C2×C31—42no—
289C2×C31—42no—
290C2×C31#300411yescharacteristic
291C2×C31#301811yescharacteristic
292C2×C31C2×#45811yescharacteristic
293C22×Q8—21no—
294C22×Q8D4×C3112yes—
295C22×D4D4×C3111yescharacteristic
296C23×C4D4×C3111yescharacteristic
297C23×C4C23×C3111yescharacteristic
298C2×M16—22no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—24no—
302#125—22no—
303#125—24no—
304C22⋊Q8—22no—
305C22⋊Q8—22no—
306C22⋊Q8—24no—
307C22⋊Q8—24no—
308C22⋊Q8—24no—
309C22⋊Q8—22no—
310C22⋊Q8—22no—
311C22⋊Q8—22no—
312C22⋊Q8—22no—
313C22⋊Q8—24no—
314C22⋊Q8D4×C3114yes—
315C22⋊Q8C23×C3114yes—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×D4—24no—
319C4×D4—24no—
320C4×D4—22no—
321C4×D4—22no—
322#117—22no—
323#117—22no—
324#117—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4D4×C3112yes—
331C2×C4⋊C4C23×C3111yescharacteristic
332C2×C4⋊C4C23×C3111yescharacteristic
333C2×C4⋊C4C23×C3111yescharacteristic
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4D4×C3111yescharacteristic
341C2×C22⋊C4C23×C3111yescharacteristic
342C2×C42—21no—
343C2×C42—21no—
344C2×C42D4×C3111yescharacteristic
345#107—24no—
346#106—24no—
347#103—24no—
348#103—24no—
349C22⋊C8—22no—
350C22⋊C8C23×C3114yes—
351#95—21no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95C23×C3111yescharacteristic
356#95C23×C3111yescharacteristic
357C31#1817411yescharacteristic, direct product factor, Sylow
358C24C2×D4×C3111yescharacteristic
359C24C2×D4×C3111yescharacteristic
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—44no—
364C2×Q8—82no—
365C2×Q8C2×D4×C3114yes—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4C2×D4×C3111yescharacteristic
382C22×C4C2×D4×C3112yes—
383C22×C4C2×D4×C3111yescharacteristic
384C22×C4C2×D4×C3111yescharacteristic
385C22×C4C2×D4×C3111yescharacteristic
386C22×C4C2×D4×C3112yes—
387C22×C4C24×C3111yescharacteristic
388M16—44no—
389C2×C8—24no—
390C4⋊C4—22no—
391C4⋊C4—24no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4—24no—
397C4⋊C4—22no—
398C4⋊C4—24no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4C2×D4×C3114yes—
405C22⋊C4—24no—
406C22⋊C4—24no—
407C22⋊C4—22no—
408C22⋊C4—24no—
409C22⋊C4—22no—
410C22⋊C4—42no—
411C22⋊C4—42no—
412C22⋊C4—42no—
413C22⋊C4—42no—
414C42—24no—
415C42—21no—
416C42—21no—
417C42—42no—
418C42—41no—
419C42—41no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23C31×#12012yes—
429C23C31×#13712yes—
430C23C22×D4×C3111yescharacteristic
431Q8—44no—
432Q8—44no—
433Q8—82no—
434Q8—82no—
435D4—28no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—21no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—21no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—81no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4C31×#12011yescharacteristic
467C2×C4C31×#12011yescharacteristic
468C2×C4C31×#13712yes—
469C2×C4C22×D4×C3112yes—
470C8—44no—
471C22—21no—
472C22—21no—
473C22—22no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—42no—
478C22—41no—
479C22—41no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22C2×C31×#12011yescharacteristic
484C22C2×C31×#13711yescharacteristic
485C22C2×C31×#13711yescharacteristic
486C4—22no—
487C4—22no—
488C4—21no—
489C4—42no—
490C4—41no—
491C4—44no—
492C4—41no—
493C4—44no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4C31×#45812yes—
498C2—21no—
499C2—21no—
500C2—42no—
501C2—42no—
502C2C31×#300411yescharacteristic
503C2C31×#301811yescharacteristic
504C2C2×C31×#45811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3095C2semidirect
4. C31×#1617C2semidirect
5. C31×#1614C2semidirect
6. C31×#1611C2semidirect
7. C31×#1608C2semidirect
8. C31×#1508C2semidirect
167. #18174C31direct (N × H)
220. #3095C2×C31semidirect
222. #1617C2×C31semidirect
223. #1614C2×C31semidirect
224. #1611C2×C31semidirect
225. #1608C2×C31semidirect
226. #1508C2×C31semidirect
357. C31#18174direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35012
C31×#30952
C31×#23952
C31×#16172
C31×#16142
C31×#16112
C31×#16082
C31×#15082
C31×#14652
#1817431