Finite Group Databasebeta

← C31×#14186 #21470945

Subgroups — C31×#14186 #21470945

Order 7936.

1786 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C31C211yesmaximal, characteristic
2C2×C31×#395C211yesmaximal, characteristic
3C2×C31×#389C212yesmaximal
4C2×C31×#387C211yesmaximal, characteristic
5C31×#1446C211yesmaximal, characteristic
6C31×#1444C211yesmaximal, characteristic
7C31×#1441C211yesmaximal, characteristic
8C31×#1436C212yesmaximal
9C31×#1436C212yesmaximal
10C31×#1436C212yesmaximal
11C4×C31×#95C211yesmaximal, characteristic
12C23×Q8×C31C2211yescharacteristic
13C2×C4×Q8×C31—28no—
14C2×C4×Q8×C31—24no—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2212yes—
18C22×C4⋊C4×C31C2212yes—
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2212yes—
21C22×C42×C31C2212yes—
22C22×C42×C31C2212yes—
23C22×C42×C31C2211yescharacteristic
24C31×#395C418yescomplemented
25C31×#389—28no—
26C31×#387—24no—
27C2×C31×#95C2211yescharacteristic
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2212yes—
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C22×Q8×C31—24no—
41C22×Q8×C31—22no—
42C22×Q8×C31—22no—
43C22×Q8×C31—24no—
44C22×Q8×C31C2×C414yes—
45C23×C4×C31C2311yescharacteristic
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2312yes—
50C23×C4×C31C2312yes—
51C23×C4×C31C2312yes—
52C23×C4×C31C2311yescharacteristic
53C23×C4×C31C2312yes—
54C23×C4×C31C2311yescharacteristic
55C23×C4×C31C2311yescharacteristic
56C4×Q8×C31—232no—
57C2×C4⋊C4×C31—24no—
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—24no—
60C2×C4⋊C4×C31—24no—
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31—24no—
63C2×C4⋊C4×C31—24no—
64C2×C4⋊C4×C31—22no—
65C2×C4⋊C4×C31—22no—
66C2×C4⋊C4×C31—24no—
67C2×C4⋊C4×C31—24no—
68C2×C4⋊C4×C31—24no—
69C2×C4⋊C4×C31—42no—
70C2×C4⋊C4×C31C2×C414yes—
71C2×C4⋊C4×C31C2×C418yes—
72C2×C4⋊C4×C31D418yes—
73C2×C42×C31—24no—
74C2×C42×C31—24no—
75C2×C42×C31—24no—
76C2×C42×C31—24no—
77C2×C42×C31—24no—
78C2×C42×C31—24no—
79C2×C42×C31—42no—
80C2×C42×C31D414yes—
81C31×#95—22no—
82C31×#95—22no—
83C31×#95—22no—
84C31×#95—22no—
85C31×#95—24no—
86C31×#95—24no—
87C31×#95—22no—
88C31×#95—24no—
89C31×#95—24no—
90C31×#95—42no—
91C31×#95C2×C418yes—
92C31×#95C2×C414yes—
93C31×#95Q818yescomplemented
94C24×C31C2411yescharacteristic
95C2×Q8×C31—28no—
96C2×Q8×C31—28no—
97C2×Q8×C31—216no—
98C2×Q8×C31—28no—
99C2×Q8×C31—216no—
100C22×C4×C31—22no—
101C22×C4×C31—22no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—21no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—21no—
114C22×C4×C31—21no—
115C22×C4×C31—21no—
116C22×C4×C31—22no—
117C22×C4×C31—21no—
118C22×C4×C31—21no—
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—21no—
127C22×C4×C31—22no—
128C22×C4×C31—21no—
129C22×C4×C31—22no—
130C22×C4×C31—21no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—21no—
134C22×C4×C31—21no—
135C22×C4×C31—21no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—21no—
139C22×C4×C31—21no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31C22×C412yes—
149C22×C4×C31C22×C412yes—
150C22×C4×C31C22×C414yes—
151C22×C4×C31C22×C412yes—
152C22×C4×C31C22×C414yes—
153C22×C4×C31C2×D414yes—
154C22×C4×C31C2×D414yes—
155C22×C4×C31C2×D412yes—
156C22×C4×C31C2×D412yes—
157C22×C4×C31C2×D414yes—
158C22×C4×C31C2×D412yes—
159C22×C4×C31C2×Q814yes—
160C22×C4×C31C2×Q814yes—
161C22×C4×C31C2×Q814yes—
162C22×C4×C31#4112yes—
163C22×C4×C31#4114yes—
164C22×C4×C31#4114yes—
165C4⋊C4×C31—28no—
166C4⋊C4×C31—216no—
167C4⋊C4×C31—28no—
168C4⋊C4×C31—216no—
169C4⋊C4×C31—48no—
170C4⋊C4×C31—44no—
171C42×C31—216no—
172C42×C31—28no—
173C42×C31—48no—
174#14186C3111yesmaximal, characteristic, direct product factor, Sylow
175C23×C31C23×C411yescharacteristic
176C23×C31C22×D411yescharacteristic
177C23×C31C22×D412yes—
178C23×C31C22×Q812yes—
179C23×C31C2×#4111yescharacteristic
180C23×C31C2×#4112yes—
181C23×C31C2×#4112yes—
182C23×C31H(5,𝔽2)11yescharacteristic
183C23×C312−1+411yescharacteristic
184C23×C312−1+411yescharacteristic
185C23×C312−1+411yescharacteristic
186Q8×C31—232no—
187C2×C4×C31—24no—
188C2×C4×C31—24no—
189C2×C4×C31—24no—
190C2×C4×C31—24no—
191C2×C4×C31—24no—
192C2×C4×C31—22no—
193C2×C4×C31—24no—
194C2×C4×C31—22no—
195C2×C4×C31—22no—
196C2×C4×C31—24no—
197C2×C4×C31—24no—
198C2×C4×C31—24no—
199C2×C4×C31—24no—
200C2×C4×C31—22no—
201C2×C4×C31—22no—
202C2×C4×C31—22no—
203C2×C4×C31—24no—
204C2×C4×C31—24no—
205C2×C4×C31—24no—
206C2×C4×C31—24no—
207C2×C4×C31—24no—
208C2×C4×C31—24no—
209C2×C4×C31—24no—
210C2×C4×C31—24no—
211C2×C4×C31—22no—
212C2×C4×C31—22no—
213C2×C4×C31—24no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—24no—
217C2×C4×C31—24no—
218C2×C4×C31—24no—
219C2×C4×C31—24no—
220C2×C4×C31—24no—
221C2×C4×C31—24no—
222C2×C4×C31—41no—
223C2×C4×C31—42no—
224C2×C4×C31—41no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—41no—
228C2×C4×C31—41no—
229C2×C4×C31—42no—
230C2×C4×C31—41no—
231C2×C4×C31—41no—
232C2×C4×C31—42no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31—42no—
236C2×C4×C31—42no—
237C2×C4×C31—41no—
238C2×C4×C31—41no—
239C2×C4×C31—41no—
240C2×C4×C31—41no—
241C2×C4×C31—41no—
242C2×C4×C31—41no—
243C2×C4×C31—42no—
244C2×C4×C31—42no—
245C2×C4×C31—42no—
246C2×C4×C31—42no—
247C2×C4×C31C4×D414yes—
248C2×C4×C31C4×D418yes—
249C2×C4×C31C4×Q818yescomplemented
250C2×C4×C31#12014yes—
251C2×C4×C31C4⋊Q814yes—
252C22×C4×Q8C2×C3111yescharacteristic
253C2×#395C2×C3111yescharacteristic
254C2×#389C2×C3112yes—
255C2×#387C2×C3111yescharacteristic
256#1446C2×C3111yescharacteristic
257#1444C2×C3111yescharacteristic
258#1441C2×C3111yescharacteristic
259#1436C2×C3112yes—
260#1436C2×C3112yes—
261#1436C2×C3112yes—
262C4×#95C2×C3111yescharacteristic
263C22×C31C2×C4×D411yescharacteristic
264C22×C31C2×C4×D412yes—
265C22×C31C2×C4×Q812yes—
266C22×C31#51911yescharacteristic
267C22×C31#52011yescharacteristic
268C22×C31C2×#12011yescharacteristic
269C22×C31#52511yescharacteristic
270C22×C31#52512yes—
271C22×C31C2×C4⋊Q811yescharacteristic
272C22×C31#53211yescharacteristic
273C22×C31#53312yes—
274C22×C31#53611yescharacteristic
275C22×C31#53711yescharacteristic
276C22×C31#54111yescharacteristic
277C22×C31#54211yescharacteristic
278C22×C31#54612yes—
279C22×C31#54712yes—
280C22×C31D4×Q812yes—
281C22×C31D4×Q812yes—
282C22×C31#55212yes—
283C22×C31#55412yes—
284C22×C31#55612yes—
285C22×C31#55712yes—
286C4×C31—28no—
287C4×C31—24no—
288C4×C31—24no—
289C4×C31—28no—
290C4×C31—24no—
291C4×C31—42no—
292C4×C31—44no—
293C4×C31—44no—
294C4×C31—42no—
295C4×C31—81no—
296C4×C31—81no—
297C23×Q8C22×C3111yescharacteristic
298C2×C4×Q8—28no—
299C2×C4×Q8—24no—
300C22×C4⋊C4C22×C3111yescharacteristic
301C22×C4⋊C4C22×C3111yescharacteristic
302C22×C4⋊C4C22×C3112yes—
303C22×C4⋊C4C22×C3112yes—
304C22×C4⋊C4C22×C3111yescharacteristic
305C22×C4⋊C4C22×C3112yes—
306C22×C42C22×C3112yes—
307C22×C42C22×C3112yes—
308C22×C42C22×C3111yescharacteristic
309#395C4×C3118yescomplemented
310#389—28no—
311#387—24no—
312C2×#95C22×C3111yescharacteristic
313C2×#95C22×C3112yes—
314C2×#95C22×C3112yes—
315C2×#95C22×C3111yescharacteristic
316C2×#95C22×C3111yescharacteristic
317C2×#95C22×C3111yescharacteristic
318C2×#95C22×C3112yes—
319C2×#95C22×C3112yes—
320C2×#95C22×C3111yescharacteristic
321C2×#95C22×C3112yes—
322C2×#95C22×C3111yescharacteristic
323C2×#95C22×C3112yes—
324C2×#95C22×C3112yes—
325C2×C31C4×#12011yescharacteristic
326C2×C31C4×C4⋊Q811yescharacteristic
327C2×C31#232311yescharacteristic
328C2×C31#236012yes—
329C2×C31#236512yes—
330C2×C31#243011yescharacteristic
331C2×C31#243411yescharacteristic
332C2×C31#246212yes—
333C2×C31#246512yes—
334C2×C31#258411yescharacteristic
335C2×C31#260411yescharacteristic
336C22×Q8—24no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—24no—
340C22×Q8C2×C4×C3114yes—
341C23×C4C23×C3111yescharacteristic
342C23×C4C23×C3111yescharacteristic
343C23×C4C23×C3111yescharacteristic
344C23×C4C23×C3111yescharacteristic
345C23×C4C23×C3112yes—
346C23×C4C23×C3112yes—
347C23×C4C23×C3112yes—
348C23×C4C23×C3111yescharacteristic
349C23×C4C23×C3112yes—
350C23×C4C23×C3111yescharacteristic
351C23×C4C23×C3111yescharacteristic
352C4×Q8—232no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4C2×C4×C3114yes—
367C2×C4⋊C4C2×C4×C3118yes—
368C2×C4⋊C4D4×C3118yes—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—42no—
376C2×C42D4×C3114yes—
377#95—22no—
378#95—22no—
379#95—22no—
380#95—22no—
381#95—24no—
382#95—24no—
383#95—22no—
384#95—24no—
385#95—24no—
386#95—42no—
387#95C2×C4×C3118yes—
388#95C2×C4×C3114yes—
389#95Q8×C3118yescomplemented
390C31#1418611yescharacteristic, direct product factor, Sylow
391C24C24×C3111yescharacteristic
392C2×Q8—28no—
393C2×Q8—28no—
394C2×Q8—216no—
395C2×Q8—28no—
396C2×Q8—216no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4C22×C4×C3112yes—
446C22×C4C22×C4×C3112yes—
447C22×C4C22×C4×C3114yes—
448C22×C4C22×C4×C3112yes—
449C22×C4C22×C4×C3114yes—
450C22×C4C2×D4×C3114yes—
451C22×C4C2×D4×C3114yes—
452C22×C4C2×D4×C3112yes—
453C22×C4C2×D4×C3112yes—
454C22×C4C2×D4×C3114yes—
455C22×C4C2×D4×C3112yes—
456C22×C4C2×Q8×C3114yes—
457C22×C4C2×Q8×C3114yes—
458C22×C4C2×Q8×C3114yes—
459C22×C4#41×C3112yes—
460C22×C4#41×C3114yes—
461C22×C4#41×C3114yes—
462C4⋊C4—28no—
463C4⋊C4—216no—
464C4⋊C4—28no—
465C4⋊C4—216no—
466C4⋊C4—48no—
467C4⋊C4—44no—
468C42—216no—
469C42—28no—
470C42—48no—
471C23C23×C4×C3111yescharacteristic
472C23C22×D4×C3111yescharacteristic
473C23C22×D4×C3112yes—
474C23C22×Q8×C3112yes—
475C23C2×#41×C3111yescharacteristic
476C23C2×#41×C3112yes—
477C23C2×#41×C3112yes—
478C23C31×H(5,𝔽2)11yescharacteristic
479C23C31×2−1+411yescharacteristic
480C23C31×2−1+411yescharacteristic
481C23C31×2−1+411yescharacteristic
482Q8—232no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4C4×D4×C3114yes—
544C2×C4C4×D4×C3118yes—
545C2×C4C4×Q8×C3118yescomplemented
546C2×C4C31×#12014yes—
547C2×C4C31×C4⋊Q814yes—
548C22C2×C4×D4×C3111yescharacteristic
549C22C2×C4×D4×C3112yes—
550C22C2×C4×Q8×C3112yes—
551C22C31×#51911yescharacteristic
552C22C31×#52011yescharacteristic
553C22C2×C31×#12011yescharacteristic
554C22C31×#52511yescharacteristic
555C22C31×#52512yes—
556C22C2×C31×C4⋊Q811yescharacteristic
557C22C31×#53211yescharacteristic
558C22C31×#53312yes—
559C22C31×#53611yescharacteristic
560C22C31×#53711yescharacteristic
561C22C31×#54111yescharacteristic
562C22C31×#54211yescharacteristic
563C22C31×#54612yes—
564C22C31×#54712yes—
565C22D4×Q8×C3112yes—
566C22D4×Q8×C3112yes—
567C22C31×#55212yes—
568C22C31×#55412yes—
569C22C31×#55612yes—
570C22C31×#55712yes—
571C4—28no—
572C4—24no—
573C4—24no—
574C4—28no—
575C4—24no—
576C4—42no—
577C4—44no—
578C4—44no—
579C4—42no—
580C4—81no—
581C4—81no—
582C2C4×C31×#12011yescharacteristic
583C2C4×C31×C4⋊Q811yescharacteristic
584C2C31×#232311yescharacteristic
585C2C31×#236012yes—
586C2C31×#236512yes—
587C2C31×#243011yescharacteristic
588C2C31×#243411yescharacteristic
589C2C31×#246212yes—
590C2C31×#246512yes—
591C2C31×#258411yescharacteristic
592C2C31×#260411yescharacteristic
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. C31×#395C4semidirect
93. C31×#95Q8semidirect
174. #14186C31direct (N × H)
249. C2×C4×C31C4×Q8semidirect
309. #395C4×C31semidirect
389. #95Q8×C31semidirect
390. C31#14186direct (N × H)
545. C2×C4C4×Q8×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C312
C2×C31×#3952
C2×C31×#3892
C2×C31×#3872
C31×#14462
C31×#14442
C31×#14412
C31×#14362
C4×C31×#952
#1418631