Finite Group Databasebeta

← C31×#24405 #21481164

Subgroups — C31×#24405 #21481164

Order 7936.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3484C211yesmaximal, characteristic
2C2×C31×#458C211yesmaximal, characteristic, complemented
3C22×C31×#99C211yesmaximal, characteristic, complemented
4C31×#2412C212yesmaximal, complemented
5C31×#2405C211yesmaximal, characteristic, complemented
6C31×#2044C212yesmaximal, complemented
7C31×#2022C212yesmaximal, complemented
8C31×#1898C212yesmaximal, complemented
9C31×#1890C211yesmaximal, characteristic, complemented
10C31×#1867C211yesmaximal, characteristic, complemented
11C31×#1790C211yesmaximal, characteristic, complemented
12C2×C31×H(5,𝔽2)C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C31×#546—22no—
15C31×#546—22no—
16D42×C31—22no—
17D42×C31—22no—
18C31×#535—21no—
19C31×#534—21no—
20C31×#534C2212yes—
21C31×#525—21no—
22C2×C31×#123C2211yescharacteristic
23C2×C31×#123C2212yescomplemented
24C2×C31×#123C2211yescharacteristic, complemented
25C2×C31×#120—21no—
26C2×C31×#120C2212yes—
27C31×#518C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic, complemented
29C22×C22⋊C4×C31C2212yescomplemented
30C31×#458—24no—
31C2×C31×#99—24no—
32C2×C31×#99C2211yescharacteristic
33C2×C31×#99C2211yescharacteristic
34C2×C31×#99C2212yescomplemented
35C2×C31×#99C2212yescomplemented
36C2×C31×#99C2212yescomplemented
37C31×#397—22no—
38C31×#394—21no—
39C31×#394—21no—
40C31×#394—22no—
41C31×#386—22no—
42C31×#386C2211yescharacteristic
43C31×#386C2211yescharacteristic, complemented
44C31×#386C2212yescomplemented
45C31×#385—21no—
46C31×#385C2212yescomplemented
47C31×#381C2212yescomplemented
48C31×#380—22no—
49C31×#379—21no—
50C31×#379C2211yescharacteristic, complemented
51C31×#342C2212yescomplemented
52C31×#342C2212yescomplemented
53C25×C31D411yescharacteristic
54C25×C31C2311yescharacteristic
55C31×H(5,𝔽2)—22no—
56C31×H(5,𝔽2)—22no—
57C31×H(5,𝔽2)—42no—
58C2×#41×C31—21no—
59C2×#41×C31—22no—
60C22×D4×C31—21no—
61C22×D4×C31—22no—
62C22×D4×C31—22no—
63C22×D4×C31—22no—
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31—22no—
67C22×D4×C31—22no—
68C22×D4×C31—42no—
69C22×D4×C31D411yescharacteristic
70C22×D4×C31D411yescharacteristic
71C22×D4×C31D412yes—
72C22×D4×C31D412yes—
73C22×D4×C31C2312yes—
74C22×D4×C31C2311yescharacteristic
75C22×D4×C31C2311yescharacteristic
76C23×C4×C31—22no—
77C23×C4×C31D411yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C31×#127—22no—
81C31×#124—22no—
82C31×#123—22no—
83C31×#123—22no—
84C31×#123—22no—
85C31×#123—22no—
86C31×#123—22no—
87C31×#123—24no—
88C31×#123—42no—
89C31×#123—42no—
90C31×C22⋊Q8—21no—
91C31×C22⋊Q8—21no—
92C31×#121—21no—
93C31×#121—21no—
94C31×#121—22no—
95C31×#121—22no—
96C31×#121—22no—
97C31×#121—22no—
98C31×#121—22no—
99C31×#121—22no—
100C31×#120—22no—
101C31×#120—22no—
102C31×#120—22no—
103C31×#120—22no—
104C31×#120—22no—
105C31×#120—22no—
106C31×#120—22no—
107C31×#120—22no—
108C31×#120—22no—
109C4×D4×C31—22no—
110C4×D4×C31—22no—
111C4×D4×C31—22no—
112C4×D4×C31—22no—
113C31×#117—21no—
114C2×C4⋊C4×C31—22no—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31—21no—
117C2×C4⋊C4×C31—22no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—24no—
122C2×C22⋊C4×C31—22no—
123C2×C22⋊C4×C31—22no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—22no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—22no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31—22no—
135C2×C22⋊C4×C31—42no—
136C2×C22⋊C4×C31D412yes—
137C2×C22⋊C4×C31D412yes—
138C2×C22⋊C4×C31C2312yes—
139C2×C22⋊C4×C31C2311yescharacteristic
140C2×C22⋊C4×C31C2311yescharacteristic
141C2×C22⋊C4×C31C2312yes—
142C2×C22⋊C4×C31C2312yes—
143C31×#99—22no—
144C31×#99—24no—
145C31×#99—24no—
146C31×#99—42no—
147C31×#99D414yescomplemented
148C31×#95—22no—
149C31×#95—22no—
150C31×#95—22no—
151C31×#95—22no—
152C31×#95—21no—
153C31×#95—21no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31—22no—
157C24×C31—21no—
158C24×C31—21no—
159C24×C31—21no—
160C24×C31—22no—
161C24×C31—41no—
162C24×C31—42no—
163C24×C31—42no—
164C24×C31—81no—
165C24×C31—81no—
166C24×C31C2×D411yescharacteristic
167C24×C31C2×D412yes—
168C24×C31C2×D411yescharacteristic
169C24×C31C2×D412yes—
170C24×C31C2×D412yes—
171C24×C31C2×D411yescharacteristic
172C24×C31C2×D411yescharacteristic
173C24×C31C2411yescharacteristic
174#41×C31—44no—
175#41×C31—44no—
176#41×C31—42no—
177#41×C31—42no—
178C2×Q8×C31—21no—
179C2×D4×C31—22no—
180C2×D4×C31—22no—
181C2×D4×C31—22no—
182C2×D4×C31—21no—
183C2×D4×C31—22no—
184C2×D4×C31—22no—
185C2×D4×C31—22no—
186C2×D4×C31—22no—
187C2×D4×C31—22no—
188C2×D4×C31—21no—
189C2×D4×C31—22no—
190C2×D4×C31—22no—
191C2×D4×C31—22no—
192C2×D4×C31—22no—
193C2×D4×C31—21no—
194C2×D4×C31—22no—
195C2×D4×C31—22no—
196C2×D4×C31—22no—
197C2×D4×C31—22no—
198C2×D4×C31—22no—
199C2×D4×C31—22no—
200C2×D4×C31—22no—
201C2×D4×C31—22no—
202C2×D4×C31—22no—
203C2×D4×C31—41no—
204C2×D4×C31—41no—
205C2×D4×C31—44no—
206C2×D4×C31—44no—
207C2×D4×C31—44no—
208C2×D4×C31—44no—
209C2×D4×C31—44no—
210C2×D4×C31—44no—
211C2×D4×C31—42no—
212C2×D4×C31—42no—
213C2×D4×C31—44no—
214C2×D4×C31—82no—
215C2×D4×C31—82no—
216C2×D4×C31—82no—
217C2×D4×C31C2×D412yes—
218C2×D4×C31#4112yes—
219C22×C4×C31—21no—
220C22×C4×C31—22no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—22no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—22no—
227C22×C4×C31—22no—
228C22×C4×C31—21no—
229C22×C4×C31—22no—
230C22×C4×C31—22no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—22no—
237C22×C4×C31—41no—
238C22×C4×C31—44no—
239C22×C4×C31—44no—
240C22×C4×C31—81no—
241C22×C4×C31—82no—
242C22×C4×C31C2×D412yes—
243C22×C4×C31C2×D411yescharacteristic
244C22×C4×C31C2×D411yescharacteristic
245C22×C4×C31C2×D412yes—
246C22×C4×C31C2×D412yes—
247C4⋊C4×C31—21no—
248C4⋊C4×C31—21no—
249C4⋊C4×C31—22no—
250C4⋊C4×C31—22no—
251C4⋊C4×C31—44no—
252C4⋊C4×C31—42no—
253C4⋊C4×C31—42no—
254C4⋊C4×C31—82no—
255C22⋊C4×C31—22no—
256C22⋊C4×C31—22no—
257C22⋊C4×C31—22no—
258C22⋊C4×C31—22no—
259C22⋊C4×C31—22no—
260C22⋊C4×C31—22no—
261C22⋊C4×C31—22no—
262C22⋊C4×C31—22no—
263C22⋊C4×C31—22no—
264C22⋊C4×C31—22no—
265C22⋊C4×C31—22no—
266C22⋊C4×C31—22no—
267C22⋊C4×C31—22no—
268C22⋊C4×C31—21no—
269C22⋊C4×C31—21no—
270C22⋊C4×C31—22no—
271C22⋊C4×C31—22no—
272C22⋊C4×C31—44no—
273C22⋊C4×C31—44no—
274C22⋊C4×C31—42no—
275C22⋊C4×C31—42no—
276C22⋊C4×C31—41no—
277C22⋊C4×C31—42no—
278C22⋊C4×C31—41no—
279C22⋊C4×C31—42no—
280C22⋊C4×C31—81no—
281C22⋊C4×C31—81no—
282C22⋊C4×C31—81no—
283C22⋊C4×C31—82no—
284C22⋊C4×C31C2×D414yescomplemented
285C42×C31—22no—
286#24405C3111yesmaximal, characteristic, direct product factor, Sylow
287C23×C31—21no—
288C23×C31—21no—
289C23×C31—21no—
290C23×C31—22no—
291C23×C31—22no—
292C23×C31—22no—
293C23×C31—24no—
294C23×C31—21no—
295C23×C31—21no—
296C23×C31—21no—
297C23×C31—22no—
298C23×C31—22no—
299C23×C31—21no—
300C23×C31—22no—
301C23×C31—21no—
302C23×C31—21no—
303C23×C31—22no—
304C23×C31—22no—
305C23×C31—42no—
306C23×C31—41no—
307C23×C31—41no—
308C23×C31—41no—
309C23×C31—41no—
310C23×C31—42no—
311C23×C31—42no—
312C23×C31—41no—
313C23×C31—42no—
314C23×C31—42no—
315C23×C31—41no—
316C23×C31—41no—
317C23×C31—41no—
318C23×C31—41no—
319C23×C31—42no—
320C23×C31—42no—
321C23×C31—42no—
322C23×C31—42no—
323C23×C31—42no—
324C23×C31—81no—
325C23×C31—81no—
326C23×C31—82no—
327C23×C31—82no—
328C23×C31—84no—
329C23×C31—81no—
330C23×C31—81no—
331C23×C31—84no—
332C23×C31—84no—
333C23×C31#12011yescharacteristic
334C23×C31#12012yes—
335C23×C31#12011yescharacteristic
336C23×C31#12112yes—
337C23×C31C22×D411yescharacteristic
338C23×C31C22×D412yes—
339C23×C31C22×D411yescharacteristic
340C23×C31C2×#4111yescharacteristic
341C23×C31H(5,𝔽2)12yes—
342Q8×C31—42no—
343D4×C31—24no—
344D4×C31—24no—
345D4×C31—44no—
346D4×C31—42no—
347D4×C31—44no—
348D4×C31—44no—
349D4×C31—44no—
350D4×C31—42no—
351D4×C31—42no—
352D4×C31—42no—
353D4×C31—42no—
354D4×C31—42no—
355D4×C31—42no—
356D4×C31—44no—
357D4×C31—82no—
358D4×C31—82no—
359D4×C31—82no—
360D4×C31—82no—
361C2×C4×C31—21no—
362C2×C4×C31—21no—
363C2×C4×C31—22no—
364C2×C4×C31—22no—
365C2×C4×C31—22no—
366C2×C4×C31—21no—
367C2×C4×C31—21no—
368C2×C4×C31—21no—
369C2×C4×C31—24no—
370C2×C4×C31—22no—
371C2×C4×C31—22no—
372C2×C4×C31—42no—
373C2×C4×C31—42no—
374C2×C4×C31—44no—
375C2×C4×C31—42no—
376C2×C4×C31—42no—
377C2×C4×C31—42no—
378C2×C4×C31—42no—
379C2×C4×C31—42no—
380C2×C4×C31—41no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—42no—
385C2×C4×C31—42no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—42no—
389C2×C4×C31—42no—
390C2×C4×C31—41no—
391C2×C4×C31—41no—
392C2×C4×C31—41no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31—42no—
397C2×C4×C31—42no—
398C2×C4×C31—42no—
399C2×C4×C31—81no—
400C2×C4×C31—81no—
401C2×C4×C31—88no—
402C2×C4×C31#12112yes—
403#3484C2×C3111yescharacteristic
404C2×#458C2×C3111yescharacteristic, complemented
405C22×#99C2×C3111yescharacteristic, complemented
406#2412C2×C3112yescomplemented
407#2405C2×C3111yescharacteristic, complemented
408#2044C2×C3112yescomplemented
409#2022C2×C3112yescomplemented
410#1898C2×C3112yescomplemented
411#1890C2×C3111yescharacteristic, complemented
412#1867C2×C3111yescharacteristic, complemented
413#1790C2×C3111yescharacteristic, complemented
414C22×C31—21no—
415C22×C31—22no—
416C22×C31—21no—
417C22×C31—22no—
418C22×C31—21no—
419C22×C31—21no—
420C22×C31—21no—
421C22×C31—22no—
422C22×C31—22no—
423C22×C31—22no—
424C22×C31—21no—
425C22×C31—21no—
426C22×C31—22no—
427C22×C31—41no—
428C22×C31—41no—
429C22×C31—42no—
430C22×C31—44no—
431C22×C31—44no—
432C22×C31—42no—
433C22×C31—42no—
434C22×C31—42no—
435C22×C31—42no—
436C22×C31—41no—
437C22×C31—41no—
438C22×C31—42no—
439C22×C31—41no—
440C22×C31—42no—
441C22×C31—41no—
442C22×C31—42no—
443C22×C31—41no—
444C22×C31—82no—
445C22×C31—81no—
446C22×C31—81no—
447C22×C31—81no—
448C22×C31—82no—
449C22×C31—84no—
450C22×C31—82no—
451C22×C31—82no—
452C22×C31—81no—
453C22×C31—84no—
454C22×C31—162no—
455C22×C31#45812yescomplemented
456C22×C31C2×#12011yescharacteristic
457C22×C31C2×#12111yescharacteristic
458C22×C31#53411yescharacteristic
459C22×C31D4212yes—
460C22×C31#54612yes—
461C4×C31—22no—
462C4×C31—44no—
463C4×C31—41no—
464C4×C31—42no—
465C4×C31—42no—
466C4×C31—42no—
467C4×C31—81no—
468C4×C31—81no—
469C4×C31—82no—
470C4×C31—81no—
471C4×C31—81no—
472C2×H(5,𝔽2)C22×C3111yescharacteristic
473C23×D4C22×C3111yescharacteristic
474#546—22no—
475#546—22no—
476D42—22no—
477D42—22no—
478#535—21no—
479#534—21no—
480#534C22×C3112yes—
481#525—21no—
482C2×#123C22×C3111yescharacteristic
483C2×#123C22×C3112yescomplemented
484C2×#123C22×C3111yescharacteristic, complemented
485C2×#120—21no—
486C2×#120C22×C3112yes—
487#518C22×C3111yescharacteristic
488C22×C22⋊C4C22×C3111yescharacteristic, complemented
489C22×C22⋊C4C22×C3112yescomplemented
490#458—24no—
491C2×#99—24no—
492C2×#99C22×C3111yescharacteristic
493C2×#99C22×C3111yescharacteristic
494C2×#99C22×C3112yescomplemented
495C2×#99C22×C3112yescomplemented
496C2×#99C22×C3112yescomplemented
497#397—22no—
498#394—21no—
499#394—21no—
500#394—22no—
501#386—22no—
502#386C22×C3111yescharacteristic
503#386C22×C3111yescharacteristic, complemented
504#386C22×C3112yescomplemented
505#385—21no—
506#385C22×C3112yescomplemented
507#381C22×C3112yescomplemented
508#380—22no—
509#379—21no—
510#379C22×C3111yescharacteristic, complemented
511#342C22×C3112yescomplemented
512#342C22×C3112yescomplemented
513C2×C31—22no—
514C2×C31—21no—
515C2×C31—21no—
516C2×C31—22no—
517C2×C31—22no—
518C2×C31—42no—
519C2×C31—41no—
520C2×C31—42no—
521C2×C31—81no—
522C2×C31—82no—
523C2×C31#241011yescharacteristic
524C2×C31C2×#45811yescharacteristic
525C2×C31#302611yescharacteristic
526C25D4×C3111yescharacteristic
527C25C23×C3111yescharacteristic
528H(5,𝔽2)—22no—
529H(5,𝔽2)—22no—
530H(5,𝔽2)—42no—
531C2×#41—21no—
532C2×#41—22no—
533C22×D4—21no—
534C22×D4—22no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—42no—
542C22×D4D4×C3111yescharacteristic
543C22×D4D4×C3111yescharacteristic
544C22×D4D4×C3112yes—
545C22×D4D4×C3112yes—
546C22×D4C23×C3112yes—
547C22×D4C23×C3111yescharacteristic
548C22×D4C23×C3111yescharacteristic
549C23×C4—22no—
550C23×C4D4×C3111yescharacteristic
551C23×C4C23×C3111yescharacteristic
552C23×C4C23×C3111yescharacteristic
553#127—22no—
554#124—22no—
555#123—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—24no—
561#123—42no—
562#123—42no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565#121—21no—
566#121—21no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#120—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586#117—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—22no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—24no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—42no—
609C2×C22⋊C4D4×C3112yes—
610C2×C22⋊C4D4×C3112yes—
611C2×C22⋊C4C23×C3112yes—
612C2×C22⋊C4C23×C3111yescharacteristic
613C2×C22⋊C4C23×C3111yescharacteristic
614C2×C22⋊C4C23×C3112yes—
615C2×C22⋊C4C23×C3112yes—
616#99—22no—
617#99—24no—
618#99—24no—
619#99—42no—
620#99D4×C3114yescomplemented
621#95—22no—
622#95—22no—
623#95—22no—
624#95—21no—
625#95—21no—
626#95—22no—
627C31#2440511yescharacteristic, direct product factor, Sylow
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C3111yescharacteristic
641C24C2×D4×C3112yes—
642C24C2×D4×C3111yescharacteristic
643C24C2×D4×C3112yes—
644C24C2×D4×C3112yes—
645C24C2×D4×C3111yescharacteristic
646C24C2×D4×C3111yescharacteristic
647C24C24×C3111yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C3112yes—
692C2×D4#41×C3112yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C3112yes—
717C22×C4C2×D4×C3111yescharacteristic
718C22×C4C2×D4×C3111yescharacteristic
719C22×C4C2×D4×C3112yes—
720C22×C4C2×D4×C3112yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C3114yescomplemented
759C42—22no—
760C23—22no—
761C23—24no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23C31×#12011yescharacteristic
807C23C31×#12012yes—
808C23C31×#12011yescharacteristic
809C23C31×#12112yes—
810C23C22×D4×C3111yescharacteristic
811C23C22×D4×C3112yes—
812C23C22×D4×C3111yescharacteristic
813C23C2×#41×C3111yescharacteristic
814C23C31×H(5,𝔽2)12yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4C31×#12112yes—
876C22—21no—
877C22—22no—
878C22—21no—
879C22—22no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22C31×#45812yescomplemented
918C22C2×C31×#12011yescharacteristic
919C22C2×C31×#12111yescharacteristic
920C22C31×#53411yescharacteristic
921C22D42×C3112yes—
922C22C31×#54612yes—
923C4—22no—
924C4—44no—
925C4—41no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C31×#241011yescharacteristic
945C2C2×C31×#45811yescharacteristic
946C2C31×#302611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
prime radicalC31×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#458C2semidirect
3. C22×C31×#99C2semidirect
4. C31×#2412C2semidirect
5. C31×#2405C2semidirect
6. C31×#2044C2semidirect
7. C31×#2022C2semidirect
8. C31×#1898C2semidirect
9. C31×#1890C2semidirect
10. C31×#1867C2semidirect
11. C31×#1790C2semidirect
23. C2×C31×#123C22semidirect
24. C2×C31×#123C22semidirect
28. C22×C22⋊C4×C31C22semidirect
29. C22×C22⋊C4×C31C22semidirect
34. C2×C31×#99C22semidirect
35. C2×C31×#99C22semidirect
36. C2×C31×#99C22semidirect
43. C31×#386C22semidirect
44. C31×#386C22semidirect
46. C31×#385C22semidirect
47. C31×#381C22semidirect
50. C31×#379C22semidirect
51. C31×#342C22semidirect
52. C31×#342C22semidirect
147. C31×#99D4semidirect
284. C22⋊C4×C31C2×D4semidirect
286. #24405C31direct (N × H)
404. C2×#458C2×C31semidirect
405. C22×#99C2×C31semidirect
406. #2412C2×C31semidirect
407. #2405C2×C31semidirect
408. #2044C2×C31semidirect
409. #2022C2×C31semidirect
410. #1898C2×C31semidirect
411. #1890C2×C31semidirect
412. #1867C2×C31semidirect
413. #1790C2×C31semidirect
455. C22×C31#458semidirect
483. C2×#123C22×C31semidirect
484. C2×#123C22×C31semidirect
488. C22×C22⋊C4C22×C31semidirect
489. C22×C22⋊C4C22×C31semidirect
494. C2×#99C22×C31semidirect
495. C2×#99C22×C31semidirect
496. C2×#99C22×C31semidirect
503. #386C22×C31semidirect
504. #386C22×C31semidirect
506. #385C22×C31semidirect
507. #381C22×C31semidirect
510. #379C22×C31semidirect
511. #342C22×C31semidirect
512. #342C22×C31semidirect
620. #99D4×C31semidirect
627. C31#24405direct (N × H)
758. C22⋊C4C2×D4×C31semidirect
917. C22C31×#458semidirect

Maximal subgroups

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

subgroupindex
C31×#34842
C2×C31×#4582
C22×C31×#992
C31×#24122
C31×#24052
C31×#20442
C31×#20222
C31×#18982
C31×#18902
C31×#18672
C31×#17902
#2440531