Finite Group Databasebeta

← C31×#23959 #21480718

Subgroups — C31×#23959 #21480718

Order 7936.

1192 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3495C211yesmaximal, characteristic, complemented
2C31×#3005C211yesmaximal, characteristic
3C31×#2896C211yesmaximal, characteristic, complemented
4C31×#2432C211yesmaximal, characteristic, complemented
5C31×#2028C211yesmaximal, characteristic, complemented
6C31×#2027C211yesmaximal, characteristic, complemented
7C31×#2005C211yesmaximal, characteristic, complemented
8C31×#2003C211yesmaximal, characteristic, complemented
9C31×#1901C211yesmaximal, characteristic, complemented
10C31×#1888C211yesmaximal, characteristic, complemented
11C31×#1886C211yesmaximal, characteristic, complemented
12C31×#1883C211yesmaximal, characteristic, complemented
13C31×#1882C211yesmaximal, characteristic, complemented
14C31×#1871C211yesmaximal, characteristic, complemented
15C31×#1826C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C2×C31×#137C2211yescharacteristic
18C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic
20C31×#556—21no—
21C31×#554—21no—
22C31×#552—21no—
23C31×#552—22no—
24C31×#552—21no—
25C31×#551—22no—
26C31×#544C2211yescharacteristic
27C31×#542—21no—
28C31×#541—21no—
29C31×#536C2211yescharacteristic
30C31×#533—21no—
31C2×C31×C4⋊Q8C2211yescharacteristic
32C31×#529—21no—
33C2×C31×#124C2211yescharacteristic
34C31×#525C2211yescharacteristic
35C2×C31×C22⋊Q8C2211yescharacteristic
36C31×#520C2211yescharacteristic
37C31×#519C2211yescharacteristic
38C2×C31×#117C2211yescharacteristic
39C31×#452—21no—
40C31×#452—21no—
41C31×#449—21no—
42C31×#449—21no—
43C2×C31×#104C2211yescharacteristic
44C2×C31×#104C2211yescharacteristic
45C31×#419C2211yescharacteristic
46C31×#419C2211yescharacteristic
47C31×#419C2211yescharacteristic
48C31×#418C2211yescharacteristic
49C31×#418C2211yescharacteristic
50C31×#418C2211yescharacteristic
51C31×#417—21no—
52C31×#417—21no—
53C31×#416—21no—
54C31×#416—21no—
55C2×C31×#101C2211yescharacteristic
56C2×C31×#101C2211yescharacteristic
57C31×#407C2211yescharacteristic
58C31×#394—22no—
59C31×#391C2211yescharacteristic
60C31×#390C2211yescharacteristic
61C31×#385—22no—
62C4×C22⋊C4×C31C2211yescharacteristic
63C31×#343C2211yescharacteristic
64C31×#343C2211yescharacteristic
65C31×#339C2211yescharacteristic
66C31×#339C2211yescharacteristic
67C31×#339C2211yescharacteristic
68C31×#339C2211yescharacteristic
69C31×#339C2211yescharacteristic
70C31×#339C2211yescharacteristic
71C2×#41×C31—22no—
72C2×#41×C31—22no—
73C2×#41×C31—21no—
74C2×#41×C31—21no—
75C2×#41×C31—21no—
76C2×#41×C31—21no—
77C2×#41×C31—41no—
78C2×#41×C31—41no—
79C2×#41×C31C2311yescharacteristic
80C22×Q8×C31C2311yescharacteristic
81C22×Q8×C31C2311yescharacteristic
82C22×D4×C31—21no—
83C22×D4×C31C2311yescharacteristic
84C23×C4×C31—21no—
85C23×C4×C31C2311yescharacteristic
86C31×#137—22no—
87C31×#137—41no—
88C31×AGL(1,ℤ/8)—22no—
89C31×AGL(1,ℤ/8)—41no—
90C2×Q16×C31—21no—
91C2×SD16×C31—21no—
92C2×SD16×C31—21no—
93C2×D8×C31—21no—
94C2×M16×C31—21no—
95C2×M16×C31—41no—
96C2×M16×C31—41no—
97C2×M16×C31C2311yescharacteristic
98C2×M16×C31C2311yescharacteristic
99C2×M16×C31C2311yescharacteristic
100C2×M16×C31C2311yescharacteristic
101C22×C8×C31—21no—
102C31×C4⋊Q8—21no—
103C31×C4⋊Q8—21no—
104C31×C4⋊Q8—21no—
105C31×C4⋊Q8—22no—
106C31×C4⋊Q8—41no—
107C31×#126—22no—
108C31×#126—22no—
109C31×#126—22no—
110C31×#126—22no—
111C31×#125—22no—
112C31×#125—22no—
113C31×#125—22no—
114C31×#125—21no—
115C31×#125—21no—
116C31×#124—22no—
117C31×#124—21no—
118C31×#124—22no—
119C31×#124—41no—
120C31×#123—22no—
121C31×#123—22no—
122C31×#123—21no—
123C31×#123—22no—
124C31×C22⋊Q8—22no—
125C31×C22⋊Q8—22no—
126C31×C22⋊Q8—21no—
127C31×C22⋊Q8—21no—
128C31×C22⋊Q8—21no—
129C31×C22⋊Q8—21no—
130C31×C22⋊Q8—22no—
131C31×C22⋊Q8—21no—
132C31×C22⋊Q8—21no—
133C31×C22⋊Q8D411yescharacteristic
134C31×C22⋊Q8D411yescharacteristic
135C31×#121D411yescharacteristic
136C31×#121D411yescharacteristic
137C31×#120—21no—
138C4×Q8×C31—22no—
139C4×Q8×C31—21no—
140C4×Q8×C31—21no—
141C4×Q8×C31—21no—
142C4×Q8×C31—21no—
143C4×Q8×C31—21no—
144C4×D4×C31—22no—
145C4×D4×C31—21no—
146C4×D4×C31—22no—
147C4×D4×C31—21no—
148C4×D4×C31—21no—
149C31×#117—22no—
150C31×#117—22no—
151C31×#117—21no—
152C31×#117—21no—
153C31×#117—22no—
154C31×#117—21no—
155C31×#117D411yescharacteristic
156C31×#117D411yescharacteristic
157C31×#117C2311yescharacteristic
158C31×#117C2311yescharacteristic
159C31×#117C2311yescharacteristic
160C2×C4⋊C4×C31—21no—
161C2×C4⋊C4×C31—22no—
162C2×C4⋊C4×C31D412yes—
163C2×C4⋊C4×C31D411yescharacteristic
164C2×C4⋊C4×C31D411yescharacteristic
165C2×C4⋊C4×C31C2311yescharacteristic
166C2×C22⋊C4×C31—21no—
167C2×C22⋊C4×C31—21no—
168C2×C22⋊C4×C31—22no—
169C2×C22⋊C4×C31—22no—
170C2×C22⋊C4×C31D412yes—
171C2×C42×C31—21no—
172C2×C42×C31C2311yescharacteristic
173C2×C42×C31C2311yescharacteristic
174C31×#104—41no—
175C31×#104—41no—
176C31×#103—21no—
177C31×#103—21no—
178C31×#103—21no—
179C31×#103—21no—
180C31×#103—21no—
181C31×#103—21no—
182C31×#102—21no—
183C31×#102—21no—
184C31×#102—21no—
185C31×#102—21no—
186C31×#102—21no—
187C31×#102—21no—
188C31×#101—41no—
189C31×#101—41no—
190C31×C22⋊C8—21no—
191C31×C22⋊C8—21no—
192C31×#95—21no—
193C31×#95—22no—
194C24×C31—21no—
195C24×C31C2×D411yescharacteristic
196#41×C31—24no—
197#41×C31—24no—
198#41×C31—21no—
199#41×C31—21no—
200#41×C31—21no—
201#41×C31—21no—
202#41×C31—42no—
203#41×C31—42no—
204#41×C31—42no—
205#41×C31—42no—
206#41×C31—42no—
207#41×C31—42no—
208C2×Q8×C31—22no—
209C2×Q8×C31—21no—
210C2×Q8×C31—21no—
211C2×Q8×C31—21no—
212C2×Q8×C31—21no—
213C2×Q8×C31—21no—
214C2×Q8×C31—21no—
215C2×Q8×C31—21no—
216C2×Q8×C31—21no—
217C2×Q8×C31—21no—
218C2×Q8×C31—21no—
219C2×Q8×C31—21no—
220C2×Q8×C31C2×D411yescharacteristic
221C2×Q8×C31#4112yes—
222C2×D4×C31—21no—
223C2×D4×C31—21no—
224C2×D4×C31—21no—
225C2×D4×C31—21no—
226C2×D4×C31—21no—
227C2×D4×C31—21no—
228C2×D4×C31—21no—
229C2×D4×C31—21no—
230C2×D4×C31—42no—
231C2×D4×C31—42no—
232C2×D4×C31—41no—
233C2×D4×C31—41no—
234C2×D4×C31C2×D411yescharacteristic
235C2×D4×C31#4112yes—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—22no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—42no—
248C22×C4×C31—42no—
249C22×C4×C31—41no—
250C22×C4×C31—41no—
251C22×C4×C31C2×D412yes—
252C22×C4×C31C2×D411yescharacteristic
253C22×C4×C31C2×D411yescharacteristic
254C22×C4×C31C2×D411yescharacteristic
255C22×C4×C31C2×D411yescharacteristic
256C22×C4×C31C2×D411yescharacteristic
257C22×C4×C31C2×D412yes—
258C22×C4×C31C2411yescharacteristic
259Q16×C31—42no—
260SD16×C31—42no—
261SD16×C31—42no—
262D8×C31—42no—
263M16×C31—21no—
264M16×C31—21no—
265M16×C31—21no—
266M16×C31—21no—
267M16×C31—21no—
268M16×C31—21no—
269M16×C31—21no—
270M16×C31—21no—
271M16×C31—42no—
272C2×C8×C31—21no—
273C2×C8×C31—21no—
274C2×C8×C31—21no—
275C2×C8×C31—21no—
276C2×C8×C31—42no—
277C4⋊C4×C31—22no—
278C4⋊C4×C31—22no—
279C4⋊C4×C31—22no—
280C4⋊C4×C31—22no—
281C4⋊C4×C31—22no—
282C4⋊C4×C31—22no—
283C4⋊C4×C31—22no—
284C4⋊C4×C31—22no—
285C4⋊C4×C31—21no—
286C4⋊C4×C31—21no—
287C4⋊C4×C31—22no—
288C4⋊C4×C31—22no—
289C4⋊C4×C31—21no—
290C4⋊C4×C31—21no—
291C4⋊C4×C31—21no—
292C4⋊C4×C31—21no—
293C4⋊C4×C31—44no—
294C4⋊C4×C31C2×D411yescharacteristic
295C4⋊C4×C31C2×D411yescharacteristic
296C4⋊C4×C31C2×D411yescharacteristic
297C4⋊C4×C31C2×D411yescharacteristic
298C4⋊C4×C31C2×D411yescharacteristic
299C4⋊C4×C31C2×D411yescharacteristic
300C22⋊C4×C31—22no—
301C22⋊C4×C31—22no—
302C22⋊C4×C31—22no—
303C22⋊C4×C31—21no—
304C22⋊C4×C31—21no—
305C22⋊C4×C31—22no—
306C22⋊C4×C31—22no—
307C22⋊C4×C31—21no—
308C22⋊C4×C31—21no—
309C22⋊C4×C31—21no—
310C22⋊C4×C31—21no—
311C22⋊C4×C31—21no—
312C22⋊C4×C31—21no—
313C22⋊C4×C31—21no—
314C22⋊C4×C31—44no—
315C22⋊C4×C31—44no—
316C22⋊C4×C31—42no—
317C42×C31—22no—
318C42×C31—22no—
319C42×C31—22no—
320C42×C31—21no—
321C42×C31—21no—
322C42×C31—21no—
323C42×C31—21no—
324C42×C31—21no—
325C42×C31—21no—
326C42×C31—21no—
327C42×C31—21no—
328C42×C31—21no—
329#23959C3111yesmaximal, characteristic, direct product factor, Sylow
330C23×C31—21no—
331C23×C31—21no—
332C23×C31—21no—
333C23×C31—22no—
334C23×C31—41no—
335C23×C31—41no—
336C23×C31—42no—
337C23×C31—42no—
338C23×C31—41no—
339C23×C31—41no—
340C23×C31#12011yescharacteristic
341C23×C31#12011yescharacteristic
342C23×C31C22×D411yescharacteristic
343Q8×C31—22no—
344Q8×C31—21no—
345Q8×C31—22no—
346Q8×C31—21no—
347Q8×C31—41no—
348Q8×C31—41no—
349Q8×C31—41no—
350Q8×C31—41no—
351Q8×C31—41no—
352Q8×C31—41no—
353Q8×C31—82no—
354D4×C31—22no—
355D4×C31—21no—
356D4×C31—22no—
357D4×C31—21no—
358D4×C31—42no—
359D4×C31—44no—
360D4×C31—44no—
361D4×C31—41no—
362D4×C31—41no—
363D4×C31—41no—
364D4×C31—41no—
365D4×C31—81no—
366C2×C4×C31—21no—
367C2×C4×C31—21no—
368C2×C4×C31—21no—
369C2×C4×C31—21no—
370C2×C4×C31—21no—
371C2×C4×C31—21no—
372C2×C4×C31—21no—
373C2×C4×C31—21no—
374C2×C4×C31—21no—
375C2×C4×C31—21no—
376C2×C4×C31—22no—
377C2×C4×C31—21no—
378C2×C4×C31—21no—
379C2×C4×C31—21no—
380C2×C4×C31—21no—
381C2×C4×C31—21no—
382C2×C4×C31—22no—
383C2×C4×C31—21no—
384C2×C4×C31—21no—
385C2×C4×C31—22no—
386C2×C4×C31—22no—
387C2×C4×C31—22no—
388C2×C4×C31—22no—
389C2×C4×C31—44no—
390C2×C4×C31—44no—
391C2×C4×C31—41no—
392C2×C4×C31—42no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31—41no—
397C2×C4×C31—41no—
398C2×C4×C31—42no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402C2×C4×C31—81no—
403C2×C4×C31—82no—
404C2×C4×C31#12011yescharacteristic
405C2×C4×C31#12011yescharacteristic
406C2×C4×C31C22×D411yescharacteristic
407C2×C4×C31C22×D411yescharacteristic
408C2×C4×C31C2×#4111yescharacteristic
409C2×C4×C31C2×#4111yescharacteristic
410C2×C4×C31H(5,𝔽2)11yescharacteristic
411C2×C4×C31H(5,𝔽2)11yescharacteristic
412C8×C31—41no—
413C8×C31—41no—
414C8×C31—41no—
415C8×C31—41no—
416#3495C2×C3111yescharacteristic, complemented
417#3005C2×C3111yescharacteristic
418#2896C2×C3111yescharacteristic, complemented
419#2432C2×C3111yescharacteristic, complemented
420#2028C2×C3111yescharacteristic, complemented
421#2027C2×C3111yescharacteristic, complemented
422#2005C2×C3111yescharacteristic, complemented
423#2003C2×C3111yescharacteristic, complemented
424#1901C2×C3111yescharacteristic, complemented
425#1888C2×C3111yescharacteristic, complemented
426#1886C2×C3111yescharacteristic, complemented
427#1883C2×C3111yescharacteristic, complemented
428#1882C2×C3111yescharacteristic, complemented
429#1871C2×C3111yescharacteristic, complemented
430#1826C2×C3111yescharacteristic, complemented
431C22×C31—21no—
432C22×C31—21no—
433C22×C31—21no—
434C22×C31—21no—
435C22×C31—21no—
436C22×C31—21no—
437C22×C31—21no—
438C22×C31—21no—
439C22×C31—44no—
440C22×C31—42no—
441C22×C31—41no—
442C22×C31—41no—
443C22×C31—41no—
444C22×C31—81no—
445C22×C31—81no—
446C22×C31—82no—
447C22×C31—81no—
448C22×C31—81no—
449C22×C31C2×#12011yescharacteristic
450C22×C31#54611yescharacteristic
451C22×C31#54611yescharacteristic
452C4×C31—21no—
453C4×C31—21no—
454C4×C31—42no—
455C4×C31—42no—
456C4×C31—42no—
457C4×C31—41no—
458C4×C31—42no—
459C4×C31—41no—
460C4×C31—41no—
461C4×C31—41no—
462C4×C31—41no—
463C4×C31—41no—
464C4×C31—41no—
465C4×C31—81no—
466C4×C31#52511yescharacteristic
467C4×C31#53511yescharacteristic
468C4×C31#54611yescharacteristic
469C4×C31#54611yescharacteristic
470C22×#41C22×C3111yescharacteristic
471C2×#137C22×C3111yescharacteristic
472C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
473C22×M16C22×C3111yescharacteristic
474#556—21no—
475#554—21no—
476#552—21no—
477#552—22no—
478#552—21no—
479#551—22no—
480#544C22×C3111yescharacteristic
481#542—21no—
482#541—21no—
483#536C22×C3111yescharacteristic
484#533—21no—
485C2×C4⋊Q8C22×C3111yescharacteristic
486#529—21no—
487C2×#124C22×C3111yescharacteristic
488#525C22×C3111yescharacteristic
489C2×C22⋊Q8C22×C3111yescharacteristic
490#520C22×C3111yescharacteristic
491#519C22×C3111yescharacteristic
492C2×#117C22×C3111yescharacteristic
493#452—21no—
494#452—21no—
495#449—21no—
496#449—21no—
497C2×#104C22×C3111yescharacteristic
498C2×#104C22×C3111yescharacteristic
499#419C22×C3111yescharacteristic
500#419C22×C3111yescharacteristic
501#419C22×C3111yescharacteristic
502#418C22×C3111yescharacteristic
503#418C22×C3111yescharacteristic
504#418C22×C3111yescharacteristic
505#417—21no—
506#417—21no—
507#416—21no—
508#416—21no—
509C2×#101C22×C3111yescharacteristic
510C2×#101C22×C3111yescharacteristic
511#407C22×C3111yescharacteristic
512#394—22no—
513#391C22×C3111yescharacteristic
514#390C22×C3111yescharacteristic
515#385—22no—
516C4×C22⋊C4C22×C3111yescharacteristic
517#343C22×C3111yescharacteristic
518#343C22×C3111yescharacteristic
519#339C22×C3111yescharacteristic
520#339C22×C3111yescharacteristic
521#339C22×C3111yescharacteristic
522#339C22×C3111yescharacteristic
523#339C22×C3111yescharacteristic
524#339C22×C3111yescharacteristic
525C2×C31—21no—
526C2×C31—21no—
527C2×C31—41no—
528C2×C31—41no—
529C2×C31—81no—
530C2×C31—82no—
531C2×C31#240411yescharacteristic
532C2×C31#301811yescharacteristic
533C2×C31#302011yescharacteristic
534C2×#41—22no—
535C2×#41—22no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—41no—
541C2×#41—41no—
542C2×#41C23×C3111yescharacteristic
543C22×Q8C23×C3111yescharacteristic
544C22×Q8C23×C3111yescharacteristic
545C22×D4—21no—
546C22×D4C23×C3111yescharacteristic
547C23×C4—21no—
548C23×C4C23×C3111yescharacteristic
549#137—22no—
550#137—41no—
551AGL(1,ℤ/8)—22no—
552AGL(1,ℤ/8)—41no—
553C2×Q16—21no—
554C2×SD16—21no—
555C2×SD16—21no—
556C2×D8—21no—
557C2×M16—21no—
558C2×M16—41no—
559C2×M16—41no—
560C2×M16C23×C3111yescharacteristic
561C2×M16C23×C3111yescharacteristic
562C2×M16C23×C3111yescharacteristic
563C2×M16C23×C3111yescharacteristic
564C22×C8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567C4⋊Q8—21no—
568C4⋊Q8—22no—
569C4⋊Q8—41no—
570#126—22no—
571#126—22no—
572#126—22no—
573#126—22no—
574#125—22no—
575#125—22no—
576#125—22no—
577#125—21no—
578#125—21no—
579#124—22no—
580#124—21no—
581#124—22no—
582#124—41no—
583#123—22no—
584#123—22no—
585#123—21no—
586#123—22no—
587C22⋊Q8—22no—
588C22⋊Q8—22no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8—22no—
594C22⋊Q8—21no—
595C22⋊Q8—21no—
596C22⋊Q8D4×C3111yescharacteristic
597C22⋊Q8D4×C3111yescharacteristic
598#121D4×C3111yescharacteristic
599#121D4×C3111yescharacteristic
600#120—21no—
601C4×Q8—22no—
602C4×Q8—21no—
603C4×Q8—21no—
604C4×Q8—21no—
605C4×Q8—21no—
606C4×Q8—21no—
607C4×D4—22no—
608C4×D4—21no—
609C4×D4—22no—
610C4×D4—21no—
611C4×D4—21no—
612#117—22no—
613#117—22no—
614#117—21no—
615#117—21no—
616#117—22no—
617#117—21no—
618#117D4×C3111yescharacteristic
619#117D4×C3111yescharacteristic
620#117C23×C3111yescharacteristic
621#117C23×C3111yescharacteristic
622#117C23×C3111yescharacteristic
623C2×C4⋊C4—21no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4D4×C3112yes—
626C2×C4⋊C4D4×C3111yescharacteristic
627C2×C4⋊C4D4×C3111yescharacteristic
628C2×C4⋊C4C23×C3111yescharacteristic
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4D4×C3112yes—
634C2×C42—21no—
635C2×C42C23×C3111yescharacteristic
636C2×C42C23×C3111yescharacteristic
637#104—41no—
638#104—41no—
639#103—21no—
640#103—21no—
641#103—21no—
642#103—21no—
643#103—21no—
644#103—21no—
645#102—21no—
646#102—21no—
647#102—21no—
648#102—21no—
649#102—21no—
650#102—21no—
651#101—41no—
652#101—41no—
653C22⋊C8—21no—
654C22⋊C8—21no—
655#95—21no—
656#95—22no—
657C31#2395911yescharacteristic, direct product factor, Sylow
658C24—21no—
659C24C2×D4×C3111yescharacteristic
660#41—24no—
661#41—24no—
662#41—21no—
663#41—21no—
664#41—21no—
665#41—21no—
666#41—42no—
667#41—42no—
668#41—42no—
669#41—42no—
670#41—42no—
671#41—42no—
672C2×Q8—22no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—21no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8C2×D4×C3111yescharacteristic
685C2×Q8#41×C3112yes—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—41no—
697C2×D4—41no—
698C2×D4C2×D4×C3111yescharacteristic
699C2×D4#41×C3112yes—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—42no—
712C22×C4—42no—
713C22×C4—41no—
714C22×C4—41no—
715C22×C4C2×D4×C3112yes—
716C22×C4C2×D4×C3111yescharacteristic
717C22×C4C2×D4×C3111yescharacteristic
718C22×C4C2×D4×C3111yescharacteristic
719C22×C4C2×D4×C3111yescharacteristic
720C22×C4C2×D4×C3111yescharacteristic
721C22×C4C2×D4×C3112yes—
722C22×C4C24×C3111yescharacteristic
723Q16—42no—
724SD16—42no—
725SD16—42no—
726D8—42no—
727M16—21no—
728M16—21no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—42no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—42no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—22no—
745C4⋊C4—22no—
746C4⋊C4—22no—
747C4⋊C4—22no—
748C4⋊C4—22no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—22no—
752C4⋊C4—22no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—44no—
758C4⋊C4C2×D4×C3111yescharacteristic
759C4⋊C4C2×D4×C3111yescharacteristic
760C4⋊C4C2×D4×C3111yescharacteristic
761C4⋊C4C2×D4×C3111yescharacteristic
762C4⋊C4C2×D4×C3111yescharacteristic
763C4⋊C4C2×D4×C3111yescharacteristic
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—22no—
770C22⋊C4—22no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—42no—
781C42—22no—
782C42—22no—
783C42—22no—
784C42—21no—
785C42—21no—
786C42—21no—
787C42—21no—
788C42—21no—
789C42—21no—
790C42—21no—
791C42—21no—
792C42—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—22no—
797C23—41no—
798C23—41no—
799C23—42no—
800C23—42no—
801C23—41no—
802C23—41no—
803C23C31×#12011yescharacteristic
804C23C31×#12011yescharacteristic
805C23C22×D4×C3111yescharacteristic
806Q8—22no—
807Q8—21no—
808Q8—22no—
809Q8—21no—
810Q8—41no—
811Q8—41no—
812Q8—41no—
813Q8—41no—
814Q8—41no—
815Q8—41no—
816Q8—82no—
817D4—22no—
818D4—21no—
819D4—22no—
820D4—21no—
821D4—42no—
822D4—44no—
823D4—44no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—81no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—81no—
866C2×C4—82no—
867C2×C4C31×#12011yescharacteristic
868C2×C4C31×#12011yescharacteristic
869C2×C4C22×D4×C3111yescharacteristic
870C2×C4C22×D4×C3111yescharacteristic
871C2×C4C2×#41×C3111yescharacteristic
872C2×C4C2×#41×C3111yescharacteristic
873C2×C4C31×H(5,𝔽2)11yescharacteristic
874C2×C4C31×H(5,𝔽2)11yescharacteristic
875C8—41no—
876C8—41no—
877C8—41no—
878C8—41no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—44no—
888C22—42no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—81no—
893C22—81no—
894C22—82no—
895C22—81no—
896C22—81no—
897C22C2×C31×#12011yescharacteristic
898C22C31×#54611yescharacteristic
899C22C31×#54611yescharacteristic
900C4—21no—
901C4—21no—
902C4—42no—
903C4—42no—
904C4—42no—
905C4—41no—
906C4—42no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—81no—
914C4C31×#52511yescharacteristic
915C4C31×#53511yescharacteristic
916C4C31×#54611yescharacteristic
917C4C31×#54611yescharacteristic
918C2—21no—
919C2—21no—
920C2—41no—
921C2—41no—
922C2—82no—
923C2—81no—
924C2C31×#240411yescharacteristic
925C2C31×#301811yescharacteristic
926C2C31×#302011yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3005C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3495C2semidirect
3. C31×#2896C2semidirect
4. C31×#2432C2semidirect
5. C31×#2028C2semidirect
6. C31×#2027C2semidirect
7. C31×#2005C2semidirect
8. C31×#2003C2semidirect
9. C31×#1901C2semidirect
10. C31×#1888C2semidirect
11. C31×#1886C2semidirect
12. C31×#1883C2semidirect
13. C31×#1882C2semidirect
14. C31×#1871C2semidirect
15. C31×#1826C2semidirect
329. #23959C31direct (N × H)
416. #3495C2×C31semidirect
418. #2896C2×C31semidirect
419. #2432C2×C31semidirect
420. #2028C2×C31semidirect
421. #2027C2×C31semidirect
422. #2005C2×C31semidirect
423. #2003C2×C31semidirect
424. #1901C2×C31semidirect
425. #1888C2×C31semidirect
426. #1886C2×C31semidirect
427. #1883C2×C31semidirect
428. #1882C2×C31semidirect
429. #1871C2×C31semidirect
430. #1826C2×C31semidirect
657. C31#23959direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34952
C31×#30052
C31×#28962
C31×#24322
C31×#20282
C31×#20272
C31×#20052
C31×#20032
C31×#19012
C31×#18882
C31×#18862
C31×#18832
C31×#18822
C31×#18712
C31×#18262
#2395931