Finite Group Databasebeta

← C31×#25563 #21482322

Subgroups — C31×#25563 #21482322

Order 7936.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3490C211yesmaximal, characteristic, complemented
2C31×#2410C212yesmaximal, complemented
3C31×#2405C211yesmaximal, characteristic, complemented
4C31×#2062C211yesmaximal, characteristic, complemented
5C31×#2044C211yesmaximal, characteristic, complemented
6C31×#2029C211yesmaximal, characteristic, complemented
7C31×#2021C211yesmaximal, characteristic, complemented
8C31×#1898C212yesmaximal, complemented
9C31×#1889C212yesmaximal, complemented
10C31×#1867C212yesmaximal, complemented
11C2×C31×#342C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C31×#551—22no—
14C31×#551—22no—
15C31×#546—22no—
16C31×#546—22no—
17C31×#543C2211yescharacteristic
18C31×#538—21no—
19C31×#538—21no—
20C31×#534C2211yescharacteristic
21C31×#525—21no—
22C31×#525—21no—
23C2×C31×#123—21no—
24C2×C31×#121—22no—
25C2×C31×#120C2212yes—
26C2×C31×#120C2212yes—
27C31×#518C2212yes—
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2212yes—
30C2×C31×#99C2212yes—
31C2×C31×#99C2212yes—
32C31×#394—21no—
33C31×#394—21no—
34C31×#394—22no—
35C31×#392—22no—
36C31×#386—21no—
37C31×#386—22no—
38C31×#386C2212yes—
39C31×#385C2212yes—
40C31×#385C2211yescharacteristic
41C31×#385C2211yescharacteristic
42C31×#379C2211yescharacteristic
43C31×#379C2212yes—
44C31×#379C2211yescharacteristic
45C31×#379C2211yescharacteristic
46C31×#342C2212yes—
47C31×#342C2211yescharacteristic
48C31×#342C2212yes—
49C31×#342C2212yes—
50C31×#342C2211yescharacteristic
51C25×C31C2311yescharacteristic
52C25×C31C2311yescharacteristic
53C2×#41×C31—21no—
54C2×#41×C31—21no—
55C22×D4×C31—22no—
56C22×D4×C31—21no—
57C22×D4×C31—22no—
58C22×D4×C31—21no—
59C22×D4×C31—22no—
60C22×D4×C31—44no—
61C22×D4×C31D412yescomplemented
62C22×D4×C31D412yescomplemented
63C22×D4×C31C2312yes—
64C23×C4×C31—22no—
65C23×C4×C31D411yescharacteristic, complemented
66C23×C4×C31D411yescharacteristic, complemented
67C23×C4×C31C2311yescharacteristic
68C31×#126—22no—
69C31×#126—22no—
70C31×#124—22no—
71C31×#124—22no—
72C31×#123—22no—
73C31×#123—22no—
74C31×#123—22no—
75C31×#123—22no—
76C31×#123—22no—
77C31×#123—44no—
78C31×C22⋊Q8—21no—
79C31×C22⋊Q8—21no—
80C31×C22⋊Q8—21no—
81C31×C22⋊Q8—21no—
82C31×C22⋊Q8—22no—
83C31×C22⋊Q8—22no—
84C31×#121—21no—
85C31×#121—21no—
86C31×#121—22no—
87C31×#121—22no—
88C31×#121—21no—
89C31×#121—21no—
90C31×#121—48no—
91C31×#120—22no—
92C31×#120—22no—
93C31×#120—22no—
94C31×#120—22no—
95C31×#120—22no—
96C31×#120—24no—
97C31×#120—42no—
98C4×D4×C31—22no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31—22no—
102C4×D4×C31—22no—
103C4×D4×C31—22no—
104C31×#117—21no—
105C31×#117—21no—
106C31×#117—22no—
107C2×C4⋊C4×C31—22no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—22no—
112C2×C22⋊C4×C31—22no—
113C2×C22⋊C4×C31—24no—
114C2×C22⋊C4×C31—22no—
115C2×C22⋊C4×C31—22no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—22no—
118C2×C22⋊C4×C31—22no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—22no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—42no—
126C2×C22⋊C4×C31D411yescharacteristic, complemented
127C2×C22⋊C4×C31D411yescharacteristic, complemented
128C2×C22⋊C4×C31D412yescomplemented
129C2×C22⋊C4×C31D412yescomplemented
130C2×C22⋊C4×C31C2311yescharacteristic
131C2×C22⋊C4×C31C2311yescharacteristic
132C2×C22⋊C4×C31C2312yes—
133C2×C22⋊C4×C31C2311yescharacteristic
134C2×C22⋊C4×C31C2311yescharacteristic
135C2×C22⋊C4×C31C2312yes—
136C2×C22⋊C4×C31C2312yes—
137C31×#99—24no—
138C31×#99—42no—
139C31×#95—22no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95—22no—
143C24×C31—22no—
144C24×C31—21no—
145C24×C31—21no—
146C24×C31—21no—
147C24×C31—22no—
148C24×C31—22no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31—42no—
152C24×C31—42no—
153C24×C31—81no—
154C24×C31—81no—
155C24×C31C2×D412yes—
156C24×C31C2×D411yescharacteristic
157C24×C31C2×D412yes—
158C24×C31C2×D412yes—
159C24×C31C2×D411yescharacteristic
160C24×C31C2411yescharacteristic
161#41×C31—82no—
162#41×C31—82no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×D4×C31—28no—
166C2×D4×C31—24no—
167C2×D4×C31—22no—
168C2×D4×C31—22no—
169C2×D4×C31—22no—
170C2×D4×C31—22no—
171C2×D4×C31—22no—
172C2×D4×C31—22no—
173C2×D4×C31—22no—
174C2×D4×C31—22no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—22no—
178C2×D4×C31—22no—
179C2×D4×C31—44no—
180C2×D4×C31—42no—
181C2×D4×C31—44no—
182C2×D4×C31—42no—
183C2×D4×C31—44no—
184C2×D4×C31—42no—
185C2×D4×C31—44no—
186C2×D4×C31—42no—
187C2×D4×C31—41no—
188C2×D4×C31—41no—
189C2×D4×C31—44no—
190C2×D4×C31—44no—
191C2×D4×C31—82no—
192C2×D4×C31—82no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—22no—
196C22×C4×C31—21no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—22no—
205C22×C4×C31—42no—
206C22×C4×C31—44no—
207C22×C4×C31—42no—
208C22×C4×C31—44no—
209C22×C4×C31—81no—
210C22×C4×C31—82no—
211C22×C4×C31C2×D412yes—
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D412yes—
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2×D412yes—
217C22×C4×C31C2×D411yescharacteristic
218C4⋊C4×C31—22no—
219C4⋊C4×C31—22no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—22no—
225C4⋊C4×C31—22no—
226C4⋊C4×C31—44no—
227C4⋊C4×C31—42no—
228C4⋊C4×C31—42no—
229C22⋊C4×C31—22no—
230C22⋊C4×C31—22no—
231C22⋊C4×C31—22no—
232C22⋊C4×C31—22no—
233C22⋊C4×C31—22no—
234C22⋊C4×C31—22no—
235C22⋊C4×C31—22no—
236C22⋊C4×C31—22no—
237C22⋊C4×C31—22no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—22no—
240C22⋊C4×C31—22no—
241C22⋊C4×C31—22no—
242C22⋊C4×C31—22no—
243C22⋊C4×C31—22no—
244C22⋊C4×C31—22no—
245C22⋊C4×C31—22no—
246C22⋊C4×C31—21no—
247C22⋊C4×C31—22no—
248C22⋊C4×C31—21no—
249C22⋊C4×C31—44no—
250C22⋊C4×C31—44no—
251C22⋊C4×C31—44no—
252C22⋊C4×C31—44no—
253C22⋊C4×C31—42no—
254C22⋊C4×C31—42no—
255C22⋊C4×C31—42no—
256C22⋊C4×C31—81no—
257C22⋊C4×C31—81no—
258C22⋊C4×C31—82no—
259C22⋊C4×C31—81no—
260C22⋊C4×C31#4114yescomplemented
261C42×C31—22no—
262C42×C31—22no—
263#25563C3111yesmaximal, characteristic, direct product factor, Sylow
264C23×C31—21no—
265C23×C31—21no—
266C23×C31—22no—
267C23×C31—22no—
268C23×C31—22no—
269C23×C31—24no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—22no—
273C23×C31—22no—
274C23×C31—22no—
275C23×C31—24no—
276C23×C31—22no—
277C23×C31—22no—
278C23×C31—22no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—42no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—42no—
286C23×C31—42no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—42no—
290C23×C31—41no—
291C23×C31—42no—
292C23×C31—42no—
293C23×C31—42no—
294C23×C31—42no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—42no—
299C23×C31—42no—
300C23×C31—84no—
301C23×C31—84no—
302C23×C31—82no—
303C23×C31—82no—
304C23×C31—82no—
305C23×C31—82no—
306C23×C31#12012yes—
307C23×C31#12011yescharacteristic
308C23×C31#12011yescharacteristic
309C23×C31C22×D411yescharacteristic
310C23×C31C22×D412yes—
311C23×C31C2×#4112yes—
312C23×C31H(5,𝔽2)11yescharacteristic
313C23×C312−1+411yescharacteristic
314Q8×C31—81no—
315Q8×C31—81no—
316D4×C31—44no—
317D4×C31—48no—
318D4×C31—44no—
319D4×C31—42no—
320D4×C31—42no—
321D4×C31—42no—
322D4×C31—42no—
323D4×C31—44no—
324D4×C31—44no—
325D4×C31—82no—
326D4×C31—82no—
327D4×C31—81no—
328D4×C31—81no—
329D4×C31—88no—
330C2×C4×C31—24no—
331C2×C4×C31—22no—
332C2×C4×C31—22no—
333C2×C4×C31—21no—
334C2×C4×C31—21no—
335C2×C4×C31—22no—
336C2×C4×C31—22no—
337C2×C4×C31—21no—
338C2×C4×C31—21no—
339C2×C4×C31—24no—
340C2×C4×C31—22no—
341C2×C4×C31—22no—
342C2×C4×C31—42no—
343C2×C4×C31—41no—
344C2×C4×C31—42no—
345C2×C4×C31—42no—
346C2×C4×C31—42no—
347C2×C4×C31—41no—
348C2×C4×C31—42no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—42no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—42no—
355C2×C4×C31—41no—
356C2×C4×C31—41no—
357C2×C4×C31—42no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—42no—
361C2×C4×C31—41no—
362C2×C4×C31—41no—
363C2×C4×C31—42no—
364C2×C4×C31—81no—
365C2×C4×C31—81no—
366C2×C4×C31—82no—
367C2×C4×C31—82no—
368C2×C4×C31—88no—
369#3490C2×C3111yescharacteristic, complemented
370#2410C2×C3112yescomplemented
371#2405C2×C3111yescharacteristic, complemented
372#2062C2×C3111yescharacteristic, complemented
373#2044C2×C3111yescharacteristic, complemented
374#2029C2×C3111yescharacteristic, complemented
375#2021C2×C3111yescharacteristic, complemented
376#1898C2×C3112yescomplemented
377#1889C2×C3112yescomplemented
378#1867C2×C3112yescomplemented
379C2×#342C2×C3111yescharacteristic, complemented
380C22×C31—21no—
381C22×C31—21no—
382C22×C31—22no—
383C22×C31—21no—
384C22×C31—22no—
385C22×C31—21no—
386C22×C31—21no—
387C22×C31—22no—
388C22×C31—21no—
389C22×C31—22no—
390C22×C31—21no—
391C22×C31—22no—
392C22×C31—42no—
393C22×C31—41no—
394C22×C31—41no—
395C22×C31—44no—
396C22×C31—42no—
397C22×C31—42no—
398C22×C31—44no—
399C22×C31—44no—
400C22×C31—42no—
401C22×C31—42no—
402C22×C31—44no—
403C22×C31—42no—
404C22×C31—42no—
405C22×C31—42no—
406C22×C31—42no—
407C22×C31—82no—
408C22×C31—81no—
409C22×C31—81no—
410C22×C31—82no—
411C22×C31—82no—
412C22×C31—82no—
413C22×C31—82no—
414C22×C31—81no—
415C22×C31—81no—
416C22×C31—82no—
417C22×C31—81no—
418C22×C31—81no—
419C22×C31B(4,𝔽2)12yes—
420C22×C31C2×#12011yescharacteristic
421C22×C31#53211yescharacteristic
422C22×C31#53711yescharacteristic
423C22×C31#54612yes—
424C22×C31#54712yes—
425C4×C31—44no—
426C4×C31—42no—
427C4×C31—42no—
428C4×C31—41no—
429C4×C31—41no—
430C4×C31—42no—
431C4×C31—41no—
432C4×C31—41no—
433C4×C31—42no—
434C4×C31—81no—
435C4×C31—81no—
436C4×C31—82no—
437C23×D4C22×C3111yescharacteristic
438#551—22no—
439#551—22no—
440#546—22no—
441#546—22no—
442#543C22×C3111yescharacteristic
443#538—21no—
444#538—21no—
445#534C22×C3111yescharacteristic
446#525—21no—
447#525—21no—
448C2×#123—21no—
449C2×#121—22no—
450C2×#120C22×C3112yes—
451C2×#120C22×C3112yes—
452#518C22×C3112yes—
453C22×C22⋊C4C22×C3111yescharacteristic
454C22×C22⋊C4C22×C3112yes—
455C2×#99C22×C3112yes—
456C2×#99C22×C3112yes—
457#394—21no—
458#394—21no—
459#394—22no—
460#392—22no—
461#386—21no—
462#386—22no—
463#386C22×C3112yes—
464#385C22×C3112yes—
465#385C22×C3111yescharacteristic
466#385C22×C3111yescharacteristic
467#379C22×C3111yescharacteristic
468#379C22×C3112yes—
469#379C22×C3111yescharacteristic
470#379C22×C3111yescharacteristic
471#342C22×C3112yes—
472#342C22×C3111yescharacteristic
473#342C22×C3112yes—
474#342C22×C3112yes—
475#342C22×C3111yescharacteristic
476C2×C31—22no—
477C2×C31—21no—
478C2×C31—21no—
479C2×C31—22no—
480C2×C31—22no—
481C2×C31—41no—
482C2×C31—42no—
483C2×C31—82no—
484C2×C31—82no—
485C2×C31#243011yescharacteristic
486C2×C31C2×B(4,𝔽2)11yescharacteristic
487C2×C31#302611yescharacteristic
488C25C23×C3111yescharacteristic
489C25C23×C3111yescharacteristic
490C2×#41—21no—
491C2×#41—21no—
492C22×D4—22no—
493C22×D4—21no—
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—44no—
498C22×D4D4×C3112yescomplemented
499C22×D4D4×C3112yescomplemented
500C22×D4C23×C3112yes—
501C23×C4—22no—
502C23×C4D4×C3111yescharacteristic, complemented
503C23×C4D4×C3111yescharacteristic, complemented
504C23×C4C23×C3111yescharacteristic
505#126—22no—
506#126—22no—
507#124—22no—
508#124—22no—
509#123—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—44no—
515C22⋊Q8—21no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—22no—
520C22⋊Q8—22no—
521#121—21no—
522#121—21no—
523#121—22no—
524#121—22no—
525#121—21no—
526#121—21no—
527#121—48no—
528#120—22no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—24no—
534#120—42no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541#117—21no—
542#117—21no—
543#117—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4D4×C3111yescharacteristic, complemented
564C2×C22⋊C4D4×C3111yescharacteristic, complemented
565C2×C22⋊C4D4×C3112yescomplemented
566C2×C22⋊C4D4×C3112yescomplemented
567C2×C22⋊C4C23×C3112yes—
568C2×C22⋊C4C23×C3111yescharacteristic
569C2×C22⋊C4C23×C3111yescharacteristic
570C2×C22⋊C4C23×C3111yescharacteristic
571C2×C22⋊C4C23×C3111yescharacteristic
572C2×C22⋊C4C23×C3112yes—
573C2×C22⋊C4C23×C3112yes—
574#99—24no—
575#99—42no—
576#95—22no—
577#95—21no—
578#95—21no—
579#95—22no—
580C31#2556311yescharacteristic, direct product factor, Sylow
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C3112yes—
594C24C2×D4×C3111yescharacteristic
595C24C2×D4×C3112yes—
596C24C2×D4×C3112yes—
597C24C2×D4×C3111yescharacteristic
598C24C24×C3111yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C3112yes—
650C22×C4C2×D4×C3111yescharacteristic
651C22×C4C2×D4×C3112yes—
652C22×C4C2×D4×C3111yescharacteristic
653C22×C4C2×D4×C3111yescharacteristic
654C22×C4C2×D4×C3112yes—
655C22×C4C2×D4×C3111yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C3114yescomplemented
699C42—22no—
700C42—22no—
701C23—22no—
702C23—24no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23C31×#12012yes—
744C23C31×#12011yescharacteristic
745C23C31×#12011yescharacteristic
746C23C22×D4×C3111yescharacteristic
747C23C22×D4×C3112yes—
748C23C2×#41×C3112yes—
749C23C31×H(5,𝔽2)11yescharacteristic
750C23C31×2−1+411yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—44no—
757D4—44no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—21no—
808C22—22no—
809C22—21no—
810C22—22no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C31×B(4,𝔽2)12yes—
846C22C2×C31×#12011yescharacteristic
847C22C31×#53211yescharacteristic
848C22C31×#53711yescharacteristic
849C22C31×#54612yes—
850C22C31×#54712yes—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—42no—
857C4—41no—
858C4—41no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2C31×#243011yescharacteristic
873C2C2×C31×B(4,𝔽2)11yescharacteristic
874C2C31×#302611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3490C2semidirect
2. C31×#2410C2semidirect
3. C31×#2405C2semidirect
4. C31×#2062C2semidirect
5. C31×#2044C2semidirect
6. C31×#2029C2semidirect
7. C31×#2021C2semidirect
8. C31×#1898C2semidirect
9. C31×#1889C2semidirect
10. C31×#1867C2semidirect
11. C2×C31×#342C2semidirect
61. C22×D4×C31D4semidirect
62. C22×D4×C31D4semidirect
65. C23×C4×C31D4semidirect
66. C23×C4×C31D4semidirect
126. C2×C22⋊C4×C31D4semidirect
127. C2×C22⋊C4×C31D4semidirect
128. C2×C22⋊C4×C31D4semidirect
129. C2×C22⋊C4×C31D4semidirect
260. C22⋊C4×C31#41semidirect
263. #25563C31direct (N × H)
369. #3490C2×C31semidirect
370. #2410C2×C31semidirect
371. #2405C2×C31semidirect
372. #2062C2×C31semidirect
373. #2044C2×C31semidirect
374. #2029C2×C31semidirect
375. #2021C2×C31semidirect
376. #1898C2×C31semidirect
377. #1889C2×C31semidirect
378. #1867C2×C31semidirect
379. C2×#342C2×C31semidirect
498. C22×D4D4×C31semidirect
499. C22×D4D4×C31semidirect
502. C23×C4D4×C31semidirect
503. C23×C4D4×C31semidirect
563. C2×C22⋊C4D4×C31semidirect
564. C2×C22⋊C4D4×C31semidirect
565. C2×C22⋊C4D4×C31semidirect
566. C2×C22⋊C4D4×C31semidirect
580. C31#25563direct (N × H)
698. C22⋊C4#41×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#34902
C31×#24102
C31×#24052
C31×#20622
C31×#20442
C31×#20292
C31×#20212
C31×#18982
C31×#18892
C31×#18672
C2×C31×#3422
#2556331