Finite Group Databasebeta

← C31×#24626 #21481385

Subgroups — C31×#24626 #21481385

Order 7936.

1110 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#459C211yesmaximal, characteristic, complemented
2C2×C4×D8×C31C211yesmaximal, characteristic, complemented
3C31×#2541C211yesmaximal, characteristic, complemented
4C31×#2354C211yesmaximal, characteristic, complemented
5C31×#2054C212yesmaximal, complemented
6C31×#2011C212yesmaximal, complemented
7C31×#1982C212yesmaximal, complemented
8C31×#1957C211yesmaximal, characteristic, complemented
9C31×#1939C211yesmaximal, characteristic, complemented
10C31×#1925C212yesmaximal, complemented
11C31×#1802C211yesmaximal, characteristic, complemented
12C22×D8×C31C2211yescharacteristic
13C22×D8×C31C2212yes—
14C2×C31×#127C2211yescharacteristic
15C2×C31×#127C2212yes—
16C2×C31×#121—21no—
17C2×C31×#121—21no—
18C2×C4×D4×C31C2211yescharacteristic
19C2×C4×D4×C31C2211yescharacteristic
20C2×C31×#117—21no—
21C31×#459—24no—
22C4×D8×C31—24no—
23C2×C31×#107C2211yescharacteristic
24C2×C31×C4⋊C8C2211yescharacteristic
25C2×C31×C4⋊C8C2212yes—
26C2×C31×#102C2211yescharacteristic
27C2×C31×#102C2211yescharacteristic
28C2×C31×#102C2212yes—
29C2×C31×#102C2212yes—
30C2×C31×#102C2212yes—
31C2×C31×#102C2212yes—
32C2×C4×C8×C31C2211yescharacteristic
33C31×#392—22no—
34C31×#390C2212yes—
35C31×#390C2212yes—
36C31×#388—22no—
37C31×#384C2211yescharacteristic
38C31×#380—21no—
39C4×C4⋊C4×C31C2212yes—
40C4×C4⋊C4×C31C2211yescharacteristic
41C31×#340C2212yes—
42C31×#336C2212yes—
43C22×D4×C31—21no—
44C22×D4×C31—22no—
45C22×D4×C31—22no—
46C22×D4×C31—21no—
47C22×D4×C31C2312yes—
48C22×D4×C31C2311yescharacteristic
49C22×D4×C31C2311yescharacteristic
50C23×C4×C31—21no—
51C23×C4×C31—21no—
52C2×D8×C31—22no—
53C2×D8×C31—22no—
54C2×D8×C31—24no—
55C2×D8×C31—22no—
56C2×D8×C31—42no—
57C2×D8×C31—42no—
58C22×C8×C31C2311yescharacteristic
59C22×C8×C31C2312yes—
60C22×C8×C31C2311yescharacteristic
61C31×#127—24no—
62C31×#127—22no—
63C31×#127—22no—
64C31×#127—42no—
65C31×#121—44no—
66C31×#121—44no—
67C4×D4×C31—22no—
68C4×D4×C31—22no—
69C4×D4×C31—22no—
70C4×D4×C31D414yescomplemented
71C31×#117—44no—
72C2×C4⋊C4×C31—21no—
73C2×C4⋊C4×C31—21no—
74C2×C4⋊C4×C31D411yescharacteristic
75C2×C4⋊C4×C31D411yescharacteristic
76C2×C4⋊C4×C31C2312yes—
77C2×C4⋊C4×C31C2311yescharacteristic
78C2×C4⋊C4×C31C2311yescharacteristic
79C2×C22⋊C4×C31—21no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31—21no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—22no—
84C2×C22⋊C4×C31—22no—
85C2×C42×C31—22no—
86C2×C42×C31C2312yes—
87C2×C42×C31C2311yescharacteristic
88C31×#107—22no—
89C31×C4⋊C8—22no—
90C31×C4⋊C8—42no—
91C31×#102—22no—
92C31×#102—24no—
93C31×#102—22no—
94C31×#102—24no—
95C31×#102—42no—
96C31×#102—42no—
97C4×C8×C31—22no—
98C31×#95—22no—
99C31×#95D412yes—
100C24×C31—21no—
101C24×C31—21no—
102C24×C31—22no—
103C2×D4×C31—21no—
104C2×D4×C31—22no—
105C2×D4×C31—21no—
106C2×D4×C31—21no—
107C2×D4×C31—21no—
108C2×D4×C31—21no—
109C2×D4×C31—21no—
110C2×D4×C31—22no—
111C2×D4×C31—22no—
112C2×D4×C31—22no—
113C2×D4×C31—21no—
114C2×D4×C31—21no—
115C2×D4×C31—21no—
116C2×D4×C31—21no—
117C2×D4×C31—22no—
118C2×D4×C31—22no—
119C2×D4×C31—44no—
120C2×D4×C31—44no—
121C2×D4×C31—44no—
122C2×D4×C31—42no—
123C2×D4×C31—42no—
124C2×D4×C31—44no—
125C2×D4×C31—42no—
126C2×D4×C31—42no—
127C2×D4×C31—81no—
128C2×D4×C31—82no—
129C2×D4×C31—81no—
130C2×D4×C31—82no—
131C2×D4×C31C2×D412yes—
132C2×D4×C31#4112yes—
133C22×C4×C31—21no—
134C22×C4×C31—24no—
135C22×C4×C31—22no—
136C22×C4×C31—21no—
137C22×C4×C31—42no—
138C22×C4×C31—42no—
139C22×C4×C31—42no—
140C22×C4×C31—42no—
141C22×C4×C31—42no—
142C22×C4×C31C2×D412yes—
143C22×C4×C31C2×D411yescharacteristic
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2×D411yescharacteristic
146C22×C4×C31C2411yescharacteristic
147D8×C31—28no—
148D8×C31—48no—
149C2×C8×C31—21no—
150C2×C8×C31—21no—
151C2×C8×C31—21no—
152C2×C8×C31—22no—
153C2×C8×C31—21no—
154C2×C8×C31—22no—
155C2×C8×C31—21no—
156C2×C8×C31—22no—
157C2×C8×C31#4112yes—
158C4⋊C4×C31—22no—
159C4⋊C4×C31—21no—
160C4⋊C4×C31—21no—
161C4⋊C4×C31—22no—
162C4⋊C4×C31—21no—
163C4⋊C4×C31—22no—
164C4⋊C4×C31—42no—
165C4⋊C4×C31—81no—
166C4⋊C4×C31D814yescomplemented
167C4⋊C4×C31C2×D412yes—
168C22⋊C4×C31—24no—
169C22⋊C4×C31—44no—
170C22⋊C4×C31—42no—
171C22⋊C4×C31—44no—
172C22⋊C4×C31—44no—
173C22⋊C4×C31—82no—
174C42×C31—22no—
175C42×C31—22no—
176C42×C31—44no—
177C42×C31C2×D412yes—
178C42×C31#4112yes—
179#24626C3111yesmaximal, characteristic, direct product factor, Sylow
180C23×C31—22no—
181C23×C31—22no—
182C23×C31—41no—
183C23×C31—41no—
184C23×C31—41no—
185C23×C31—41no—
186C23×C31—41no—
187C23×C31—41no—
188C23×C31—41no—
189C23×C31—41no—
190C23×C31—41no—
191C23×C31—41no—
192C23×C31—41no—
193C23×C31—41no—
194C23×C31—42no—
195C23×C31—42no—
196C23×C31—42no—
197C23×C31—42no—
198C23×C31—42no—
199C23×C31—42no—
200C23×C31—42no—
201C23×C31C22×D411yescharacteristic
202D4×C31—22no—
203D4×C31—22no—
204D4×C31—22no—
205D4×C31—22no—
206D4×C31—42no—
207D4×C31—41no—
208D4×C31—42no—
209D4×C31—41no—
210D4×C31—42no—
211D4×C31—41no—
212D4×C31—41no—
213D4×C31—42no—
214D4×C31—88no—
215D4×C31—84no—
216D4×C31—88no—
217D4×C31—84no—
218C2×C4×C31—22no—
219C2×C4×C31—21no—
220C2×C4×C31—22no—
221C2×C4×C31—21no—
222C2×C4×C31—22no—
223C2×C4×C31—22no—
224C2×C4×C31—22no—
225C2×C4×C31—22no—
226C2×C4×C31—41no—
227C2×C4×C31—41no—
228C2×C4×C31—48no—
229C2×C4×C31—41no—
230C2×C4×C31—42no—
231C2×C4×C31—42no—
232C2×C4×C31—41no—
233C2×C4×C31—41no—
234C2×C4×C31—42no—
235C2×C4×C31—84no—
236C2×C4×C31#12112yes—
237C2×C4×C31#12112yes—
238C2×C4×C31C2×D814yes—
239C2×C4×C31C2×D812yes—
240C2×C4×C31AGL(1,ℤ/8)12yes—
241C2×C4×C31C22×D411yescharacteristic
242C2×C4×C31C2×#4111yescharacteristic
243C2×C4×C31C2×#4111yescharacteristic
244C2×C4×C31C2×#4111yescharacteristic
245C2×C4×C31H(5,𝔽2)11yescharacteristic
246C2×C4×C31H(5,𝔽2)11yescharacteristic
247C8×C31—22no—
248C8×C31—41no—
249C8×C31—42no—
250C2×#459C2×C3111yescharacteristic, complemented
251C2×C4×D8C2×C3111yescharacteristic, complemented
252#2541C2×C3111yescharacteristic, complemented
253#2354C2×C3111yescharacteristic, complemented
254#2054C2×C3112yescomplemented
255#2011C2×C3112yescomplemented
256#1982C2×C3112yescomplemented
257#1957C2×C3111yescharacteristic, complemented
258#1939C2×C3111yescharacteristic, complemented
259#1925C2×C3112yescomplemented
260#1802C2×C3111yescharacteristic, complemented
261C22×C31—42no—
262C22×C31—42no—
263C22×C31—42no—
264C22×C31—42no—
265C22×C31—42no—
266C22×C31—42no—
267C22×C31—81no—
268C22×C31—81no—
269C22×C31—81no—
270C22×C31—81no—
271C22×C31—81no—
272C22×C31—81no—
273C22×C31—81no—
274C22×C31—81no—
275C22×C31—82no—
276C22×C31—82no—
277C22×C31—82no—
278C22×C31—82no—
279C22×C31—82no—
280C22×C31—82no—
281C22×C31—82no—
282C22×C31C2×#12111yescharacteristic
283C22×C31#54611yescharacteristic
284C22×C31#55011yescharacteristic
285C22×C31C22×D811yescharacteristic
286C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C31#57611yescharacteristic
288C22×C31#57711yescharacteristic
289C4×C31—24no—
290C4×C31—22no—
291C4×C31—42no—
292C4×C31—42no—
293C4×C31—82no—
294C4×C31—81no—
295C4×C31#45914yes—
296C4×C31#52511yescharacteristic
297C4×C31#53511yescharacteristic
298C4×C31#55311yescharacteristic
299C4×C31#55511yescharacteristic
300C22×D8C22×C3111yescharacteristic
301C22×D8C22×C3112yes—
302C2×#127C22×C3111yescharacteristic
303C2×#127C22×C3112yes—
304C2×#121—21no—
305C2×#121—21no—
306C2×C4×D4C22×C3111yescharacteristic
307C2×C4×D4C22×C3111yescharacteristic
308C2×#117—21no—
309#459—24no—
310C4×D8—24no—
311C2×#107C22×C3111yescharacteristic
312C2×C4⋊C8C22×C3111yescharacteristic
313C2×C4⋊C8C22×C3112yes—
314C2×#102C22×C3111yescharacteristic
315C2×#102C22×C3111yescharacteristic
316C2×#102C22×C3112yes—
317C2×#102C22×C3112yes—
318C2×#102C22×C3112yes—
319C2×#102C22×C3112yes—
320C2×C4×C8C22×C3111yescharacteristic
321#392—22no—
322#390C22×C3112yes—
323#390C22×C3112yes—
324#388—22no—
325#384C22×C3111yescharacteristic
326#380—21no—
327C4×C4⋊C4C22×C3112yes—
328C4×C4⋊C4C22×C3111yescharacteristic
329#340C22×C3112yes—
330#336C22×C3112yes—
331C2×C31—82no—
332C2×C31—82no—
333C2×C31—162no—
334C2×C31#241411yescharacteristic
335C2×C31C2×#45911yescharacteristic
336C2×C31#304511yescharacteristic
337C2×C31#329411yescharacteristic
338C2×C31#332511yescharacteristic
339C2×C31#339111yescharacteristic
340C2×C31#339711yescharacteristic
341C22×D4—21no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—21no—
345C22×D4C23×C3112yes—
346C22×D4C23×C3111yescharacteristic
347C22×D4C23×C3111yescharacteristic
348C23×C4—21no—
349C23×C4—21no—
350C2×D8—22no—
351C2×D8—22no—
352C2×D8—24no—
353C2×D8—22no—
354C2×D8—42no—
355C2×D8—42no—
356C22×C8C23×C3112yes—
357C22×C8C23×C3111yescharacteristic
358C22×C8C23×C3111yescharacteristic
359#127—24no—
360#127—22no—
361#127—22no—
362#127—42no—
363#121—44no—
364#121—44no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4D4×C3114yescomplemented
369#117—44no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4D4×C3111yescharacteristic
373C2×C4⋊C4D4×C3111yescharacteristic
374C2×C4⋊C4C23×C3111yescharacteristic
375C2×C4⋊C4C23×C3112yes—
376C2×C4⋊C4C23×C3111yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C42—22no—
384C2×C42C23×C3112yes—
385C2×C42C23×C3111yescharacteristic
386#107—22no—
387C4⋊C8—22no—
388C4⋊C8—42no—
389#102—22no—
390#102—24no—
391#102—22no—
392#102—24no—
393#102—42no—
394#102—42no—
395C4×C8—22no—
396#95—22no—
397#95D4×C3112yes—
398C31#2462611yescharacteristic, direct product factor, Sylow
399C24—21no—
400C24—21no—
401C24—22no—
402C2×D4—21no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—44no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—81no—
427C2×D4—82no—
428C2×D4—81no—
429C2×D4—82no—
430C2×D4C2×D4×C3112yes—
431C2×D4#41×C3112yes—
432C22×C4—21no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4C2×D4×C3112yes—
442C22×C4C2×D4×C3111yescharacteristic
443C22×C4C2×D4×C3112yes—
444C22×C4C2×D4×C3111yescharacteristic
445C22×C4C24×C3111yescharacteristic
446D8—28no—
447D8—48no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—22no—
452C2×C8—21no—
453C2×C8—22no—
454C2×C8—21no—
455C2×C8—22no—
456C2×C8#41×C3112yes—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—42no—
464C4⋊C4—81no—
465C4⋊C4D8×C3114yescomplemented
466C4⋊C4C2×D4×C3112yes—
467C22⋊C4—24no—
468C22⋊C4—44no—
469C22⋊C4—42no—
470C22⋊C4—44no—
471C22⋊C4—44no—
472C22⋊C4—82no—
473C42—22no—
474C42—22no—
475C42—44no—
476C42C2×D4×C3112yes—
477C42#41×C3112yes—
478C23—22no—
479C23—22no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23C22×D4×C3111yescharacteristic
500D4—22no—
501D4—22no—
502D4—22no—
503D4—22no—
504D4—42no—
505D4—41no—
506D4—42no—
507D4—41no—
508D4—42no—
509D4—41no—
510D4—41no—
511D4—42no—
512D4—88no—
513D4—84no—
514D4—88no—
515D4—84no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—48no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—84no—
534C2×C4C31×#12112yes—
535C2×C4C31×#12112yes—
536C2×C4C2×D8×C3114yes—
537C2×C4C2×D8×C3112yes—
538C2×C4C31×AGL(1,ℤ/8)12yes—
539C2×C4C22×D4×C3111yescharacteristic
540C2×C4C2×#41×C3111yescharacteristic
541C2×C4C2×#41×C3111yescharacteristic
542C2×C4C2×#41×C3111yescharacteristic
543C2×C4C31×H(5,𝔽2)11yescharacteristic
544C2×C4C31×H(5,𝔽2)11yescharacteristic
545C8—22no—
546C8—41no—
547C8—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—82no—
563C22—82no—
564C22—82no—
565C22—82no—
566C22—82no—
567C22—82no—
568C22—82no—
569C22C2×C31×#12111yescharacteristic
570C22C31×#54611yescharacteristic
571C22C31×#55011yescharacteristic
572C22C22×D8×C3111yescharacteristic
573C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
574C22C31×#57611yescharacteristic
575C22C31×#57711yescharacteristic
576C4—24no—
577C4—22no—
578C4—42no—
579C4—42no—
580C4—82no—
581C4—81no—
582C4C31×#45914yes—
583C4C31×#52511yescharacteristic
584C4C31×#53511yescharacteristic
585C4C31×#55311yescharacteristic
586C4C31×#55511yescharacteristic
587C2—82no—
588C2—82no—
589C2—162no—
590C2C31×#241411yescharacteristic
591C2C2×C31×#45911yescharacteristic
592C2C31×#304511yescharacteristic
593C2C31×#329411yescharacteristic
594C2C31×#332511yescharacteristic
595C2C31×#339111yescharacteristic
596C2C31×#339711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#459C2semidirect
2. C2×C4×D8×C31C2semidirect
3. C31×#2541C2semidirect
4. C31×#2354C2semidirect
5. C31×#2054C2semidirect
6. C31×#2011C2semidirect
7. C31×#1982C2semidirect
8. C31×#1957C2semidirect
9. C31×#1939C2semidirect
10. C31×#1925C2semidirect
11. C31×#1802C2semidirect
70. C4×D4×C31D4semidirect
166. C4⋊C4×C31D8semidirect
179. #24626C31direct (N × H)
250. C2×#459C2×C31semidirect
251. C2×C4×D8C2×C31semidirect
252. #2541C2×C31semidirect
253. #2354C2×C31semidirect
254. #2054C2×C31semidirect
255. #2011C2×C31semidirect
256. #1982C2×C31semidirect
257. #1957C2×C31semidirect
258. #1939C2×C31semidirect
259. #1925C2×C31semidirect
260. #1802C2×C31semidirect
368. C4×D4D4×C31semidirect
398. C31#24626direct (N × H)
465. C4⋊C4D8×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4592
C2×C4×D8×C312
C31×#25412
C31×#23542
C31×#20542
C31×#20112
C31×#19822
C31×#19572
C31×#19392
C31×#19252
C31×#18022
#2462631