Finite Group Databasebeta

← C31×#32964 #21489723

Subgroups — C31×#32964 #21489723

Order 7936.

1206 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#519C211yesmaximal, characteristic
2C2×C31×#477C211yesmaximal, characteristic, complemented
3C2×C31×#475C211yesmaximal, characteristic, complemented
4C31×#2628C211yesmaximal, characteristic
5C31×#1865C212yesmaximal, complemented
6C31×#1863C212yesmaximal, complemented
7C31×#1854C212yesmaximal
8C31×#1805C211yesmaximal, characteristic, complemented
9C31×#1805C211yesmaximal, characteristic, complemented
10C31×#1798C211yesmaximal, characteristic
11C31×#1787C212yesmaximal
12C23×Q8×C31C2211yescharacteristic
13C2×C31×C4⋊Q8C2211yescharacteristic
14C31×#519—24no—
15C31×#519—24no—
16C2×C4×Q8×C31—21no—
17C2×C4×Q8×C31—21no—
18C2×C4×Q8×C31C2211yescharacteristic
19C2×C4×Q8×C31C2211yescharacteristic
20C2×C4×Q8×C31C2211yescharacteristic
21C2×C4×Q8×C31C2211yescharacteristic
22C2×C31×#117—21no—
23C2×C31×#117—21no—
24C2×C31×#117C2211yescharacteristic
25C2×C31×#117C2211yescharacteristic
26C31×#477—24no—
27C31×#475—24no—
28C2×C31×#107C2212yes—
29C2×C31×#106C2212yes—
30C2×C31×C4⋊C8C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×#103C2212yes—
33C2×C31×#103C2212yes—
34C2×C31×#103C2212yes—
35C2×C31×#103C2212yes—
36C2×C31×C22⋊C8C2212yes—
37C31×#400—21no—
38C31×#399—21no—
39C31×#395—21no—
40C31×#393—21no—
41C31×#389C2212yes—
42C31×#382C2211yescharacteristic
43C31×#380C2212yes—
44C31×#340C2212yes—
45C31×#340C2212yes—
46C31×#336C2212yes—
47C22×Q8×C31—22no—
48C22×Q8×C31—22no—
49C22×Q8×C31—22no—
50C22×Q8×C31—22no—
51C22×Q8×C31—21no—
52C22×Q8×C31—21no—
53C22×Q8×C31—22no—
54C22×Q8×C31Q814yescomplemented
55C22×Q8×C31C2311yescharacteristic
56C22×Q8×C31C2311yescharacteristic
57C23×C4×C31—21no—
58C23×C4×C31C2311yescharacteristic
59C22×C8×C31C2312yes—
60C22×C8×C31C2312yes—
61C31×C4⋊Q8—22no—
62C31×C4⋊Q8—22no—
63C4×Q8×C31—28no—
64C4×Q8×C31—28no—
65C4×Q8×C31—22no—
66C4×Q8×C31—22no—
67C4×Q8×C31—22no—
68C4×Q8×C31—22no—
69C4×Q8×C31—22no—
70C4×Q8×C31—22no—
71C4×Q8×C31D414yes—
72C4×Q8×C31D414yes—
73C31×#117—28no—
74C31×#117—28no—
75C31×#117—22no—
76C31×#117—22no—
77C31×#117—22no—
78C31×#117—22no—
79C2×C4⋊C4×C31—21no—
80C2×C4⋊C4×C31—21no—
81C2×C4⋊C4×C31—21no—
82C2×C4⋊C4×C31—21no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31—22no—
85C2×C4⋊C4×C31D411yescharacteristic
86C2×C4⋊C4×C31D411yescharacteristic
87C2×C4⋊C4×C31C2312yes—
88C2×C4⋊C4×C31C2312yes—
89C2×C4⋊C4×C31C2311yescharacteristic
90C2×C4⋊C4×C31C2311yescharacteristic
91C2×C22⋊C4×C31—21no—
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31D411yescharacteristic
94C2×C22⋊C4×C31D411yescharacteristic
95C2×C42×C31—21no—
96C2×C42×C31—21no—
97C2×C42×C31—21no—
98C2×C42×C31—21no—
99C2×C42×C31—21no—
100C2×C42×C31C2311yescharacteristic
101C2×C42×C31C2311yescharacteristic
102C31×#107—24no—
103C31×#106—24no—
104C31×C4⋊C8—22no—
105C31×C4⋊C8—22no—
106C31×#103—24no—
107C31×#103—24no—
108C31×#103—24no—
109C31×#103—24no—
110C31×C22⋊C8—24no—
111C31×#95—22no—
112C31×#95—21no—
113C31×#95—21no—
114C31×#95—22no—
115C24×C31C2×D411yescharacteristic
116C2×Q8×C31—24no—
117C2×Q8×C31—28no—
118C2×Q8×C31—28no—
119C2×Q8×C31—24no—
120C2×Q8×C31—28no—
121C2×Q8×C31—28no—
122C2×Q8×C31—24no—
123C2×Q8×C31—21no—
124C2×Q8×C31—21no—
125C2×Q8×C31—21no—
126C2×Q8×C31—21no—
127C2×Q8×C31—21no—
128C2×Q8×C31—21no—
129C2×Q8×C31—42no—
130C2×Q8×C31—82no—
131C2×Q8×C31C2×D412yes—
132C2×Q8×C31C2×D412yes—
133C2×Q8×C31C2×Q812yes—
134C2×Q8×C31C2×Q812yes—
135C2×Q8×C31#4112yes—
136C2×Q8×C31#4112yes—
137C22×C4×C31—24no—
138C22×C4×C31—24no—
139C22×C4×C31—24no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31C2×D411yescharacteristic
153C22×C4×C31C2×D411yescharacteristic
154C22×C4×C31C2×D411yescharacteristic
155C22×C4×C31C2×Q812yes—
156C22×C4×C31#4112yes—
157C22×C4×C31C2411yescharacteristic
158C2×C8×C31—22no—
159C2×C8×C31—22no—
160C2×C8×C31—22no—
161C2×C8×C31—22no—
162C2×C8×C31—22no—
163C2×C8×C31—22no—
164C4⋊C4×C31—24no—
165C4⋊C4×C31—24no—
166C4⋊C4×C31—24no—
167C4⋊C4×C31—24no—
168C4⋊C4×C31—22no—
169C4⋊C4×C31—22no—
170C4⋊C4×C31—21no—
171C4⋊C4×C31—21no—
172C4⋊C4×C31—22no—
173C4⋊C4×C31—22no—
174C4⋊C4×C31—22no—
175C4⋊C4×C31—22no—
176C4⋊C4×C31—42no—
177C4⋊C4×C31—82no—
178C4⋊C4×C31C2×D412yes—
179C4⋊C4×C31C2×D412yes—
180C22⋊C4×C31—24no—
181C22⋊C4×C31—22no—
182C22⋊C4×C31—22no—
183C22⋊C4×C31—82no—
184C42×C31—24no—
185C42×C31—24no—
186C42×C31—24no—
187C42×C31—24no—
188C42×C31—24no—
189C42×C31—21no—
190C42×C31—21no—
191C42×C31C2×D412yes—
192C42×C31C2×D412yes—
193#32964C3111yesmaximal, characteristic, direct product factor, Sylow
194C23×C31—21no—
195C23×C31—21no—
196C23×C31—22no—
197C23×C31—22no—
198C23×C31C22⋊Q812yes—
199C23×C31C22×D411yescharacteristic
200Q8×C31—216no—
201Q8×C31—22no—
202Q8×C31—22no—
203Q8×C31—22no—
204Q8×C31—22no—
205Q8×C31—22no—
206Q8×C31—22no—
207Q8×C31—84no—
208Q8×C31C22⋊Q814yes—
209Q8×C31C22⋊Q814yes—
210C2×C4×C31—216no—
211C2×C4×C31—22no—
212C2×C4×C31—22no—
213C2×C4×C31—21no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—22no—
217C2×C4×C31—22no—
218C2×C4×C31—21no—
219C2×C4×C31—22no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
222C2×C4×C31—22no—
223C2×C4×C31—22no—
224C2×C4×C31—22no—
225C2×C4×C31—21no—
226C2×C4×C31—21no—
227C2×C4×C31—22no—
228C2×C4×C31—22no—
229C2×C4×C31—22no—
230C2×C4×C31—22no—
231C2×C4×C31—42no—
232C2×C4×C31—42no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31—42no—
236C2×C4×C31—42no—
237C2×C4×C31—42no—
238C2×C4×C31—42no—
239C2×C4×C31#12012yes—
240C2×C4×C31#12012yes—
241C2×C4×C31C22⋊Q812yes—
242C2×C4×C31C22×D411yescharacteristic
243C2×C4×C31C22×D411yescharacteristic
244C2×C4×C31C22×Q811yescharacteristic
245C2×C4×C31C2×#4111yescharacteristic
246C2×C4×C31C2×#4111yescharacteristic
247C2×C4×C31C2×#4111yescharacteristic
248C8×C31—42no—
249C8×C31—42no—
250C2×#519C2×C3111yescharacteristic
251C2×#477C2×C3111yescharacteristic, complemented
252C2×#475C2×C3111yescharacteristic, complemented
253#2628C2×C3111yescharacteristic
254#1865C2×C3112yescomplemented
255#1863C2×C3112yescomplemented
256#1854C2×C3112yes—
257#1805C2×C3111yescharacteristic, complemented
258#1805C2×C3111yescharacteristic, complemented
259#1798C2×C3111yescharacteristic
260#1787C2×C3112yes—
261C22×C31—24no—
262C22×C31—22no—
263C22×C31—42no—
264C22×C31—41no—
265C22×C31—41no—
266C22×C31C2×#12011yescharacteristic
267C22×C31C2×C22⋊Q811yescharacteristic
268C22×C31#52511yescharacteristic
269C22×C31#57712yes—
270C22×C31#57812yes—
271C4×C31—24no—
272C4×C31—24no—
273C4×C31—22no—
274C4×C31—22no—
275C4×C31—22no—
276C4×C31—41no—
277C4×C31—42no—
278C4×C31—41no—
279C4×C31—42no—
280C4×C31—82no—
281C4×C31—82no—
282C4×C31C2×C22⋊Q811yescharacteristic
283C4×C31C2×C22⋊Q811yescharacteristic
284C4×C31#52511yescharacteristic
285C4×C31#52511yescharacteristic
286C23×Q8C22×C3111yescharacteristic
287C2×C4⋊Q8C22×C3111yescharacteristic
288#519—24no—
289#519—24no—
290C2×C4×Q8—21no—
291C2×C4×Q8—21no—
292C2×C4×Q8C22×C3111yescharacteristic
293C2×C4×Q8C22×C3111yescharacteristic
294C2×C4×Q8C22×C3111yescharacteristic
295C2×C4×Q8C22×C3111yescharacteristic
296C2×#117—21no—
297C2×#117—21no—
298C2×#117C22×C3111yescharacteristic
299C2×#117C22×C3111yescharacteristic
300#477—24no—
301#475—24no—
302C2×#107C22×C3112yes—
303C2×#106C22×C3112yes—
304C2×C4⋊C8C22×C3111yescharacteristic
305C2×C4⋊C8C22×C3111yescharacteristic
306C2×#103C22×C3112yes—
307C2×#103C22×C3112yes—
308C2×#103C22×C3112yes—
309C2×#103C22×C3112yes—
310C2×C22⋊C8C22×C3112yes—
311#400—21no—
312#399—21no—
313#395—21no—
314#393—21no—
315#389C22×C3112yes—
316#382C22×C3111yescharacteristic
317#380C22×C3112yes—
318#340C22×C3112yes—
319#340C22×C3112yes—
320#336C22×C3112yes—
321C2×C31—42no—
322C2×C31#284811yescharacteristic
323C2×C31#301011yescharacteristic
324C2×C31#301111yescharacteristic
325C2×C31#308212yes—
326C2×C31#312112yes—
327C22×Q8—22no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—21no—
332C22×Q8—21no—
333C22×Q8—22no—
334C22×Q8Q8×C3114yescomplemented
335C22×Q8C23×C3111yescharacteristic
336C22×Q8C23×C3111yescharacteristic
337C23×C4—21no—
338C23×C4C23×C3111yescharacteristic
339C22×C8C23×C3112yes—
340C22×C8C23×C3112yes—
341C4⋊Q8—22no—
342C4⋊Q8—22no—
343C4×Q8—28no—
344C4×Q8—28no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×Q8D4×C3114yes—
352C4×Q8D4×C3114yes—
353#117—28no—
354#117—28no—
355#117—22no—
356#117—22no—
357#117—22no—
358#117—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4D4×C3111yescharacteristic
366C2×C4⋊C4D4×C3111yescharacteristic
367C2×C4⋊C4C23×C3112yes—
368C2×C4⋊C4C23×C3112yes—
369C2×C4⋊C4C23×C3111yescharacteristic
370C2×C4⋊C4C23×C3111yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4D4×C3111yescharacteristic
374C2×C22⋊C4D4×C3111yescharacteristic
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42C23×C3111yescharacteristic
381C2×C42C23×C3111yescharacteristic
382#107—24no—
383#106—24no—
384C4⋊C8—22no—
385C4⋊C8—22no—
386#103—24no—
387#103—24no—
388#103—24no—
389#103—24no—
390C22⋊C8—24no—
391#95—22no—
392#95—21no—
393#95—21no—
394#95—22no—
395C31#3296411yescharacteristic, direct product factor, Sylow
396C24C2×D4×C3111yescharacteristic
397C2×Q8—24no—
398C2×Q8—28no—
399C2×Q8—28no—
400C2×Q8—24no—
401C2×Q8—28no—
402C2×Q8—28no—
403C2×Q8—24no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—42no—
411C2×Q8—82no—
412C2×Q8C2×D4×C3112yes—
413C2×Q8C2×D4×C3112yes—
414C2×Q8C2×Q8×C3112yes—
415C2×Q8C2×Q8×C3112yes—
416C2×Q8#41×C3112yes—
417C2×Q8#41×C3112yes—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4C2×D4×C3111yescharacteristic
432C22×C4C2×D4×C3111yescharacteristic
433C22×C4C2×D4×C3111yescharacteristic
434C22×C4C2×D4×C3111yescharacteristic
435C22×C4C2×D4×C3111yescharacteristic
436C22×C4C2×Q8×C3112yes—
437C22×C4#41×C3112yes—
438C22×C4C24×C3111yescharacteristic
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—42no—
458C4⋊C4—82no—
459C4⋊C4C2×D4×C3112yes—
460C4⋊C4C2×D4×C3112yes—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—82no—
465C42—24no—
466C42—24no—
467C42—24no—
468C42—24no—
469C42—24no—
470C42—21no—
471C42—21no—
472C42C2×D4×C3112yes—
473C42C2×D4×C3112yes—
474C23—21no—
475C23—21no—
476C23—22no—
477C23—22no—
478C23C31×C22⋊Q812yes—
479C23C22×D4×C3111yescharacteristic
480Q8—216no—
481Q8—22no—
482Q8—22no—
483Q8—22no—
484Q8—22no—
485Q8—22no—
486Q8—22no—
487Q8—84no—
488Q8C31×C22⋊Q814yes—
489Q8C31×C22⋊Q814yes—
490C2×C4—216no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4C31×#12012yes—
520C2×C4C31×#12012yes—
521C2×C4C31×C22⋊Q812yes—
522C2×C4C22×D4×C3111yescharacteristic
523C2×C4C22×D4×C3111yescharacteristic
524C2×C4C22×Q8×C3111yescharacteristic
525C2×C4C2×#41×C3111yescharacteristic
526C2×C4C2×#41×C3111yescharacteristic
527C2×C4C2×#41×C3111yescharacteristic
528C8—42no—
529C8—42no—
530C22—24no—
531C22—22no—
532C22—42no—
533C22—41no—
534C22—41no—
535C22C2×C31×#12011yescharacteristic
536C22C2×C31×C22⋊Q811yescharacteristic
537C22C31×#52511yescharacteristic
538C22C31×#57712yes—
539C22C31×#57812yes—
540C4—24no—
541C4—24no—
542C4—22no—
543C4—22no—
544C4—22no—
545C4—41no—
546C4—42no—
547C4—41no—
548C4—42no—
549C4—82no—
550C4—82no—
551C4C2×C31×C22⋊Q811yescharacteristic
552C4C2×C31×C22⋊Q811yescharacteristic
553C4C31×#52511yescharacteristic
554C4C31×#52511yescharacteristic
555C2—42no—
556C2C31×#284811yescharacteristic
557C2C31×#301011yescharacteristic
558C2C31×#301111yescharacteristic
559C2C31×#308212yes—
560C2C31×#312112yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#477C2semidirect
3. C2×C31×#475C2semidirect
5. C31×#1865C2semidirect
6. C31×#1863C2semidirect
8. C31×#1805C2semidirect
9. C31×#1805C2semidirect
54. C22×Q8×C31Q8semidirect
193. #32964C31direct (N × H)
251. C2×#477C2×C31semidirect
252. C2×#475C2×C31semidirect
254. #1865C2×C31semidirect
255. #1863C2×C31semidirect
257. #1805C2×C31semidirect
258. #1805C2×C31semidirect
334. C22×Q8Q8×C31semidirect
395. C31#32964direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5192
C2×C31×#4772
C2×C31×#4752
C31×#26282
C31×#18652
C31×#18632
C31×#18542
C31×#18052
C31×#17982
C31×#17872
#3296431