Finite Group Databasebeta

← C31×#13889 #21470648

Subgroups — C31×#13889 #21470648

Order 7936.

1442 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#387C212yesmaximal
2C2×C31×#382C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
5C31×#1444C212yesmaximal
6C31×#1441C212yesmaximal
7C31×#1436C212yesmaximal
8C31×C4⋊#95C211yesmaximal, characteristic
9C31×#1434C211yesmaximal, characteristic
10C31×#1434C211yesmaximal, characteristic
11C31×#1434C211yesmaximal, characteristic
12C22×C4⋊C4×C31C2212yes—
13C22×C4⋊C4×C31C2212yes—
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C42×C31C2212yes—
18C22×C42×C31C2211yescharacteristic
19C22×C42×C31C2211yescharacteristic
20C22×C42×C31C2211yescharacteristic
21C31×#387—28no—
22C31×#382—24no—
23C4×C4⋊C4×C31—24no—
24C4×C4⋊C4×C31C418yescomplemented
25C2×C31×#95C2211yescharacteristic
26C2×C31×#95C2211yescharacteristic
27C2×C31×#95C2211yescharacteristic
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2211yescharacteristic
39C23×C4×C31C2312yes—
40C23×C4×C31C2312yes—
41C23×C4×C31C2311yescharacteristic
42C23×C4×C31C2312yes—
43C23×C4×C31C2312yes—
44C23×C4×C31C2311yescharacteristic
45C23×C4×C31C2311yescharacteristic
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2311yescharacteristic
50C2×C4⋊C4×C31—24no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31—24no—
53C2×C4⋊C4×C31—24no—
54C2×C4⋊C4×C31—24no—
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31—24no—
57C2×C4⋊C4×C31—24no—
58C2×C4⋊C4×C31—42no—
59C2×C4⋊C4×C31—42no—
60C2×C4⋊C4×C31C2×C414yes—
61C2×C4⋊C4×C31C2×C414yes—
62C2×C4⋊C4×C31D414yes—
63C2×C4⋊C4×C31Q814yes—
64C2×C42×C31—22no—
65C2×C42×C31—22no—
66C2×C42×C31—24no—
67C2×C42×C31—22no—
68C2×C42×C31—22no—
69C2×C42×C31—24no—
70C2×C42×C31—24no—
71C2×C42×C31—42no—
72C2×C42×C31C2×C414yes—
73C2×C42×C31C2×C414yes—
74C2×C42×C31C2×C414yes—
75C31×#95—22no—
76C31×#95—24no—
77C31×#95—22no—
78C31×#95—24no—
79C31×#95—24no—
80C31×#95—24no—
81C31×#95—24no—
82C31×#95—24no—
83C31×#95—24no—
84C31×#95—24no—
85C31×#95—22no—
86C31×#95C2×C414yes—
87C31×#95C2×C414yes—
88C31×#95D414yes—
89C24×C31C2411yescharacteristic
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—21no—
93C22×C4×C31—22no—
94C22×C4×C31—22no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—21no—
98C22×C4×C31—22no—
99C22×C4×C31—22no—
100C22×C4×C31—22no—
101C22×C4×C31—21no—
102C22×C4×C31—21no—
103C22×C4×C31—21no—
104C22×C4×C31—22no—
105C22×C4×C31—21no—
106C22×C4×C31—21no—
107C22×C4×C31—21no—
108C22×C4×C31—21no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—21no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31C22×C412yes—
139C22×C4×C31C22×C412yes—
140C22×C4×C31C22×C412yes—
141C22×C4×C31C22×C412yes—
142C22×C4×C31C22×C412yes—
143C22×C4×C31C22×C412yes—
144C22×C4×C31C22×C412yes—
145C22×C4×C31C2×D414yes—
146C22×C4×C31C2×D412yes—
147C22×C4×C31C2×D412yes—
148C22×C4×C31C2×D412yes—
149C22×C4×C31C2×D412yes—
150C22×C4×C31C2×Q812yes—
151C22×C4×C31C2×Q812yes—
152C22×C4×C31C2×Q812yes—
153C22×C4×C31#4114yes—
154C22×C4×C31#4114yes—
155C22×C4×C31#4114yes—
156C22×C4×C31#4112yes—
157C4⋊C4×C31—216no—
158C4⋊C4×C31—28no—
159C4⋊C4×C31—48no—
160C4⋊C4×C31—48no—
161C4⋊C4×C31C4⋊C4116yescomplemented
162C42×C31—28no—
163C42×C31—28no—
164C42×C31—28no—
165C42×C31—48no—
166#13889C3111yesmaximal, characteristic, direct product factor, Sylow
167C23×C31C23×C411yescharacteristic
168C23×C31C22×D411yescharacteristic
169C23×C31C22×D411yescharacteristic
170C23×C31C22×Q811yescharacteristic
171C23×C31C2×#4112yes—
172C23×C31C2×#4112yes—
173C23×C31C2×#4111yescharacteristic
174C23×C31C2×#4112yes—
175C23×C31H(5,𝔽2)11yescharacteristic
176C23×C312−1+412yes—
177C23×C312−1+411yescharacteristic
178C2×C4×C31—22no—
179C2×C4×C31—22no—
180C2×C4×C31—22no—
181C2×C4×C31—22no—
182C2×C4×C31—22no—
183C2×C4×C31—22no—
184C2×C4×C31—22no—
185C2×C4×C31—22no—
186C2×C4×C31—22no—
187C2×C4×C31—22no—
188C2×C4×C31—22no—
189C2×C4×C31—22no—
190C2×C4×C31—24no—
191C2×C4×C31—24no—
192C2×C4×C31—24no—
193C2×C4×C31—24no—
194C2×C4×C31—22no—
195C2×C4×C31—22no—
196C2×C4×C31—24no—
197C2×C4×C31—22no—
198C2×C4×C31—22no—
199C2×C4×C31—22no—
200C2×C4×C31—22no—
201C2×C4×C31—24no—
202C2×C4×C31—24no—
203C2×C4×C31—24no—
204C2×C4×C31—22no—
205C2×C4×C31—22no—
206C2×C4×C31—22no—
207C2×C4×C31—22no—
208C2×C4×C31—22no—
209C2×C4×C31—24no—
210C2×C4×C31—24no—
211C2×C4×C31—24no—
212C2×C4×C31—24no—
213C2×C4×C31—24no—
214C2×C4×C31—24no—
215C2×C4×C31—42no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—42no—
228C2×C4×C31—42no—
229C2×C4×C31—42no—
230C2×C4×C31—42no—
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×C31C2×C4⋊C414yes—
240C2×C4×C31C2×C4⋊C414yes—
241C2×C4×C31C2×C4⋊C414yes—
242C2×C4×C31#11714yes—
243C2×C4×C31#11714yes—
244C2×C4×C31C4×D414yes—
245C2×#387C2×C3112yes—
246C2×#382C2×C3111yescharacteristic
247C2×C4×C4⋊C4C2×C3111yescharacteristic
248C2×C4×C4⋊C4C2×C3111yescharacteristic
249#1444C2×C3112yes—
250#1441C2×C3112yes—
251#1436C2×C3112yes—
252C4⋊#95C2×C3111yescharacteristic
253#1434C2×C3111yescharacteristic
254#1434C2×C3111yescharacteristic
255#1434C2×C3111yescharacteristic
256C22×C31C22×C4⋊C411yescharacteristic
257C22×C31C2×#11711yescharacteristic
258C22×C31C2×#11711yescharacteristic
259C22×C31C2×C4×D411yescharacteristic
260C22×C31C4×#4111yescharacteristic
261C22×C31#51911yescharacteristic
262C22×C31#52011yescharacteristic
263C22×C31#52512yes—
264C22×C31#52912yes—
265C22×C31#53212yes—
266C22×C31#53312yes—
267C22×C31#54112yes—
268C22×C31#54212yes—
269C22×C31D4211yescharacteristic
270C22×C31#54712yes—
271C22×C31#54711yescharacteristic
272C22×C31#54812yes—
273C22×C31D4×Q811yescharacteristic
274C22×C31#55112yes—
275C22×C31#55212yes—
276C22×C31#55212yes—
277C22×C31#55411yescharacteristic
278C22×C31#55712yes—
279C4×C31—24no—
280C4×C31—24no—
281C4×C31—24no—
282C4×C31—24no—
283C4×C31—24no—
284C4×C31—24no—
285C4×C31—44no—
286C4×C31—44no—
287C4×C31—42no—
288C4×C31—82no—
289C4×C31—82no—
290C22×C4⋊C4C22×C3112yes—
291C22×C4⋊C4C22×C3112yes—
292C22×C4⋊C4C22×C3112yes—
293C22×C4⋊C4C22×C3111yescharacteristic
294C22×C4⋊C4C22×C3111yescharacteristic
295C22×C42C22×C3112yes—
296C22×C42C22×C3111yescharacteristic
297C22×C42C22×C3111yescharacteristic
298C22×C42C22×C3111yescharacteristic
299#387—28no—
300#382—24no—
301C4×C4⋊C4—24no—
302C4×C4⋊C4C4×C3118yescomplemented
303C2×#95C22×C3111yescharacteristic
304C2×#95C22×C3111yescharacteristic
305C2×#95C22×C3111yescharacteristic
306C2×#95C22×C3112yes—
307C2×#95C22×C3112yes—
308C2×#95C22×C3112yes—
309C2×#95C22×C3112yes—
310C2×#95C22×C3112yes—
311C2×#95C22×C3112yes—
312C2×#95C22×C3112yes—
313C2×#95C22×C3112yes—
314C2×#95C22×C3111yescharacteristic
315C2×#95C22×C3111yescharacteristic
316C2×#95C22×C3111yescharacteristic
317C2×C31#228511yescharacteristic
318C2×C31#229011yescharacteristic
319C2×C31#232011yescharacteristic
320C2×C31#234311yescharacteristic
321C2×C31#234411yescharacteristic
322C2×C31D4×C4⋊C411yescharacteristic
323C2×C31#235111yescharacteristic
324C2×C31#246112yes—
325C2×C31#246212yes—
326C2×C31#251912yes—
327C2×C31#252012yes—
328C23×C4C23×C3112yes—
329C23×C4C23×C3112yes—
330C23×C4C23×C3111yescharacteristic
331C23×C4C23×C3112yes—
332C23×C4C23×C3112yes—
333C23×C4C23×C3111yescharacteristic
334C23×C4C23×C3111yescharacteristic
335C23×C4C23×C3111yescharacteristic
336C23×C4C23×C3111yescharacteristic
337C23×C4C23×C3111yescharacteristic
338C23×C4C23×C3111yescharacteristic
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4C2×C4×C3114yes—
350C2×C4⋊C4C2×C4×C3114yes—
351C2×C4⋊C4D4×C3114yes—
352C2×C4⋊C4Q8×C3114yes—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—24no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—42no—
361C2×C42C2×C4×C3114yes—
362C2×C42C2×C4×C3114yes—
363C2×C42C2×C4×C3114yes—
364#95—22no—
365#95—24no—
366#95—22no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—22no—
375#95C2×C4×C3114yes—
376#95C2×C4×C3114yes—
377#95D4×C3114yes—
378C31#1388911yescharacteristic, direct product factor, Sylow
379C24C24×C3111yescharacteristic
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4C22×C4×C3112yes—
429C22×C4C22×C4×C3112yes—
430C22×C4C22×C4×C3112yes—
431C22×C4C22×C4×C3112yes—
432C22×C4C22×C4×C3112yes—
433C22×C4C22×C4×C3112yes—
434C22×C4C22×C4×C3112yes—
435C22×C4C2×D4×C3114yes—
436C22×C4C2×D4×C3112yes—
437C22×C4C2×D4×C3112yes—
438C22×C4C2×D4×C3112yes—
439C22×C4C2×D4×C3112yes—
440C22×C4C2×Q8×C3112yes—
441C22×C4C2×Q8×C3112yes—
442C22×C4C2×Q8×C3112yes—
443C22×C4#41×C3114yes—
444C22×C4#41×C3114yes—
445C22×C4#41×C3114yes—
446C22×C4#41×C3112yes—
447C4⋊C4—216no—
448C4⋊C4—28no—
449C4⋊C4—48no—
450C4⋊C4—48no—
451C4⋊C4C4⋊C4×C31116yescomplemented
452C42—28no—
453C42—28no—
454C42—28no—
455C42—48no—
456C23C23×C4×C3111yescharacteristic
457C23C22×D4×C3111yescharacteristic
458C23C22×D4×C3111yescharacteristic
459C23C22×Q8×C3111yescharacteristic
460C23C2×#41×C3112yes—
461C23C2×#41×C3112yes—
462C23C2×#41×C3111yescharacteristic
463C23C2×#41×C3112yes—
464C23C31×H(5,𝔽2)11yescharacteristic
465C23C31×2−1+412yes—
466C23C31×2−1+411yescharacteristic
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
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×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4C2×C4⋊C4×C3114yes—
529C2×C4C2×C4⋊C4×C3114yes—
530C2×C4C2×C4⋊C4×C3114yes—
531C2×C4C31×#11714yes—
532C2×C4C31×#11714yes—
533C2×C4C4×D4×C3114yes—
534C22C22×C4⋊C4×C3111yescharacteristic
535C22C2×C31×#11711yescharacteristic
536C22C2×C31×#11711yescharacteristic
537C22C2×C4×D4×C3111yescharacteristic
538C22C4×#41×C3111yescharacteristic
539C22C31×#51911yescharacteristic
540C22C31×#52011yescharacteristic
541C22C31×#52512yes—
542C22C31×#52912yes—
543C22C31×#53212yes—
544C22C31×#53312yes—
545C22C31×#54112yes—
546C22C31×#54212yes—
547C22D42×C3111yescharacteristic
548C22C31×#54712yes—
549C22C31×#54711yescharacteristic
550C22C31×#54812yes—
551C22D4×Q8×C3111yescharacteristic
552C22C31×#55112yes—
553C22C31×#55212yes—
554C22C31×#55212yes—
555C22C31×#55411yescharacteristic
556C22C31×#55712yes—
557C4—24no—
558C4—24no—
559C4—24no—
560C4—24no—
561C4—24no—
562C4—24no—
563C4—44no—
564C4—44no—
565C4—42no—
566C4—82no—
567C4—82no—
568C2C31×#228511yescharacteristic
569C2C31×#229011yescharacteristic
570C2C31×#232011yescharacteristic
571C2C31×#234311yescharacteristic
572C2C31×#234411yescharacteristic
573C2D4×C4⋊C4×C3111yescharacteristic
574C2C31×#235111yescharacteristic
575C2C31×#246112yes—
576C2C31×#246212yes—
577C2C31×#251912yes—
578C2C31×#252012yes—
subgroupG/H
center, socle, prime radicalC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
24. C4×C4⋊C4×C31C4semidirect
161. C4⋊C4×C31C4⋊C4semidirect
166. #13889C31direct (N × H)
302. C4×C4⋊C4C4×C31semidirect
378. C31#13889direct (N × H)
451. C4⋊C4C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3872
C2×C31×#3822
C2×C4×C4⋊C4×C312
C31×#14442
C31×#14412
C31×#14362
C31×C4⋊#952
C31×#14342
#1388931