Finite Group Databasebeta

← C31×#14727 #21471486

Subgroups — C31×#14727 #21471486

Order 7936.

3350 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C31C211yesmaximal, characteristic
2C2×C31×#397C212yesmaximal, complemented
3C2×C31×#385C211yesmaximal, characteristic, complemented
4C2×C31×#379C211yesmaximal, characteristic
5C2×C31×#379C211yesmaximal, characteristic
6C31×#1440C212yesmaximal, complemented
7C31×#1440C212yesmaximal, complemented
8C31×#1439C212yesmaximal, complemented
9C31×C22⋊#95C211yesmaximal, characteristic, complemented
10C31×C22⋊#95C211yesmaximal, characteristic, complemented
11C31×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C31C2211yescharacteristic
13C24×C4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2212yescomplemented
16C22×C22⋊C4×C31—24no—
17C22×C22⋊C4×C31—28no—
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2212yes—
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C31×#397—28no—
31C31×#385—24no—
32C31×#379—24no—
33C31×#379—24no—
34C2×C31×#95C2212yescomplemented
35C2×C31×#95C2212yescomplemented
36C2×C31×#95C2212yescomplemented
37C2×C31×#95C2212yescomplemented
38C2×C31×#95C2212yescomplemented
39C2×C31×#95C2212yescomplemented
40C2×C31×#95C2212yescomplemented
41C25×C31—24no—
42C25×C31—24no—
43C25×C31—22no—
44C25×C31—22no—
45C25×C31—22no—
46C25×C31—22no—
47C25×C31—22no—
48C25×C31—22no—
49C25×C31—42no—
50C25×C31—42no—
51C25×C31D414yes—
52C25×C31C2311yescharacteristic
53C25×C31C2311yescharacteristic
54C25×C31C2311yescharacteristic
55C23×C4×C31—22no—
56C23×C4×C31—22no—
57C23×C4×C31—24no—
58C23×C4×C31—24no—
59C23×C4×C31—22no—
60C23×C4×C31—22no—
61C23×C4×C31—22no—
62C23×C4×C31—22no—
63C23×C4×C31—42no—
64C23×C4×C31—42no—
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2312yes—
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2312yes—
71C23×C4×C31C2312yes—
72C23×C4×C31C2312yes—
73C2×C4⋊C4×C31—24no—
74C2×C4⋊C4×C31—24no—
75C2×C4⋊C4×C31—42no—
76C2×C22⋊C4×C31—232no—
77C2×C22⋊C4×C31—24no—
78C2×C22⋊C4×C31—24no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—24no—
83C2×C22⋊C4×C31—24no—
84C2×C22⋊C4×C31—24no—
85C2×C22⋊C4×C31—24no—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—22no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—24no—
97C2×C22⋊C4×C31—22no—
98C2×C22⋊C4×C31—22no—
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—24no—
102C2×C22⋊C4×C31—24no—
103C2×C22⋊C4×C31—42no—
104C2×C22⋊C4×C31—42no—
105C2×C22⋊C4×C31—42no—
106C2×C22⋊C4×C31—42no—
107C2×C22⋊C4×C31D418yes—
108C2×C22⋊C4×C31D414yes—
109C31×#95—24no—
110C31×#95—24no—
111C31×#95—24no—
112C31×#95—24no—
113C31×#95—42no—
114C31×#95—42no—
115C31×#95—42no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31—22no—
120C24×C31—216no—
121C24×C31—216no—
122C24×C31—28no—
123C24×C31—28no—
124C24×C31—28no—
125C24×C31—22no—
126C24×C31—21no—
127C24×C31—21no—
128C24×C31—21no—
129C24×C31—21no—
130C24×C31—21no—
131C24×C31—21no—
132C24×C31—22no—
133C24×C31—21no—
134C24×C31—21no—
135C24×C31—21no—
136C24×C31—21no—
137C24×C31—21no—
138C24×C31—21no—
139C24×C31—22no—
140C24×C31—22no—
141C24×C31—22no—
142C24×C31—22no—
143C24×C31—28no—
144C24×C31—28no—
145C24×C31—44no—
146C24×C31—44no—
147C24×C31—48no—
148C24×C31—48no—
149C24×C31—48no—
150C24×C31—48no—
151C24×C31—48no—
152C24×C31—48no—
153C24×C31—48no—
154C24×C31—48no—
155C24×C31—48no—
156C24×C31—48no—
157C24×C31—44no—
158C24×C31—44no—
159C24×C31—44no—
160C24×C31—44no—
161C24×C31C2×D412yes—
162C24×C31C2×D414yes—
163C24×C31C2×D412yes—
164C24×C31C2×D412yes—
165C24×C31C2×D412yes—
166C24×C31#4114yes—
167C24×C31#4112yes—
168C24×C31#4112yes—
169C24×C31#4112yes—
170C24×C31#4112yes—
171C24×C31#4112yes—
172C24×C31C2411yescharacteristic
173C22×C4×C31—28no—
174C22×C4×C31—28no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—22no—
181C22×C4×C31—22no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—22no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—21no—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—22no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—22no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—22no—
211C22×C4×C31—22no—
212C22×C4×C31—22no—
213C22×C4×C31—22no—
214C22×C4×C31—22no—
215C22×C4×C31—22no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—22no—
220C22×C4×C31—48no—
221C22×C4×C31—48no—
222C22×C4×C31—48no—
223C22×C4×C31—48no—
224C22×C4×C31—44no—
225C22×C4×C31—44no—
226C22×C4×C31—44no—
227C22×C4×C31—44no—
228C22×C4×C31C2×D414yes—
229C22×C4×C31C2×D414yes—
230C22×C4×C31C2×D414yes—
231C4⋊C4×C31—48no—
232C22⋊C4×C31—216no—
233C22⋊C4×C31—216no—
234C22⋊C4×C31—28no—
235C22⋊C4×C31—48no—
236C22⋊C4×C31—48no—
237C22⋊C4×C31—44no—
238C22⋊C4×C31—44no—
239C22⋊C4×C31—44no—
240C22⋊C4×C31—44no—
241C22⋊C4×C31—44no—
242C22⋊C4×C31—44no—
243C22⋊C4×C31—44no—
244#14727C3111yesmaximal, characteristic, direct product factor, Sylow
245C23×C31—22no—
246C23×C31—22no—
247C23×C31—24no—
248C23×C31—24no—
249C23×C31—22no—
250C23×C31—22no—
251C23×C31—24no—
252C23×C31—24no—
253C23×C31—24no—
254C23×C31—24no—
255C23×C31—24no—
256C23×C31—24no—
257C23×C31—24no—
258C23×C31—24no—
259C23×C31—24no—
260C23×C31—24no—
261C23×C31—232no—
262C23×C31—22no—
263C23×C31—22no—
264C23×C31—22no—
265C23×C31—22no—
266C23×C31—22no—
267C23×C31—22no—
268C23×C31—22no—
269C23×C31—22no—
270C23×C31—24no—
271C23×C31—24no—
272C23×C31—24no—
273C23×C31—24no—
274C23×C31—22no—
275C23×C31—22no—
276C23×C31—22no—
277C23×C31—22no—
278C23×C31—24no—
279C23×C31—24no—
280C23×C31—24no—
281C23×C31—24no—
282C23×C31—24no—
283C23×C31—24no—
284C23×C31—24no—
285C23×C31—24no—
286C23×C31—416no—
287C23×C31—416no—
288C23×C31—416no—
289C23×C31—416no—
290C23×C31—416no—
291C23×C31—432no—
292C23×C31—432no—
293C23×C31—432no—
294C23×C31—432no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31—41no—
300C23×C31—41no—
301C23×C31—41no—
302C23×C31—41no—
303C23×C31—42no—
304C23×C31—42no—
305C23×C31—42no—
306C23×C31—42no—
307C23×C31—42no—
308C23×C31—42no—
309C23×C31—42no—
310C23×C31—42no—
311C23×C31—42no—
312C23×C31—42no—
313C23×C31—42no—
314C23×C31—42no—
315C23×C31—416no—
316C23×C31#12014yes—
317C23×C31#12114yes—
318C23×C31#12314yes—
319C23×C31#12314yes—
320C23×C31#12314yes—
321C23×C31#12314yes—
322C23×C31#12414yes—
323C23×C31#12614yes—
324C23×C31#12614yes—
325C23×C31C22×D411yescharacteristic
326C23×C31C22×D412yes—
327C23×C31C22×D411yescharacteristic
328C23×C31C2×#4111yescharacteristic
329C23×C31C2×#4111yescharacteristic
330C23×C31C2×#4111yescharacteristic
331C23×C31C2×#4111yescharacteristic
332C23×C31C2×#4112yes—
333C23×C31C2×#4111yescharacteristic
334C23×C31H(5,𝔽2)12yes—
335C23×C31H(5,𝔽2)12yes—
336C2×C4×C31—24no—
337C2×C4×C31—24no—
338C2×C4×C31—24no—
339C2×C4×C31—24no—
340C2×C4×C31—24no—
341C2×C4×C31—24no—
342C2×C4×C31—24no—
343C2×C4×C31—24no—
344C2×C4×C31—24no—
345C2×C4×C31—416no—
346C2×C4×C31—416no—
347C2×C4×C31—42no—
348C2×C4×C31—42no—
349C2×C4×C31—42no—
350C2×C4×C31—42no—
351C2×C4×C31—42no—
352C2×C4×C31—42no—
353C2×C4×C31—42no—
354C2×C4×C31—42no—
355C2×C4×C31—42no—
356C2×C4×C31—42no—
357C2×C4×C31—42no—
358C2×C4×C31—42no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—41no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31—42no—
368C2×C4×C31—42no—
369C2×C4×C31—42no—
370C2×C4×C31—42no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—41no—
374C2×C4×C31—41no—
375C2×C4×C31—42no—
376C2×C4×C31—42no—
377C2×C4×C31—42no—
378C2×C4×C31—42no—
379C2×C4×C31—42no—
380C2×C4×C31—42no—
381C2×C4×C31—42no—
382C2×C4×C31—42no—
383C2×C4×C31—42no—
384C2×C4×C31—42no—
385C2×C4×C31—42no—
386C23×C22⋊C4C2×C3111yescharacteristic
387C2×#397C2×C3112yescomplemented
388C2×#385C2×C3111yescharacteristic, complemented
389C2×#379C2×C3111yescharacteristic
390C2×#379C2×C3111yescharacteristic
391#1440C2×C3112yescomplemented
392#1440C2×C3112yescomplemented
393#1439C2×C3112yescomplemented
394C22⋊#95C2×C3111yescharacteristic, complemented
395C22⋊#95C2×C3111yescharacteristic, complemented
396C22⋊#95C2×C3111yescharacteristic, complemented
397C22×C31—24no—
398C22×C31—24no—
399C22×C31—24no—
400C22×C31—24no—
401C22×C31—24no—
402C22×C31—28no—
403C22×C31—28no—
404C22×C31—28no—
405C22×C31—28no—
406C22×C31—24no—
407C22×C31—24no—
408C22×C31—24no—
409C22×C31—24no—
410C22×C31—24no—
411C22×C31—24no—
412C22×C31—24no—
413C22×C31—464no—
414C22×C31—42no—
415C22×C31—42no—
416C22×C31—42no—
417C22×C31—42no—
418C22×C31—42no—
419C22×C31—42no—
420C22×C31—42no—
421C22×C31—44no—
422C22×C31—44no—
423C22×C31—44no—
424C22×C31—44no—
425C22×C31—44no—
426C22×C31—44no—
427C22×C31—44no—
428C22×C31—44no—
429C22×C31—42no—
430C22×C31#39718yescomplemented
431C22×C31C2×#12011yescharacteristic
432C22×C31C2×#12111yescharacteristic
433C22×C31C2×#12311yescharacteristic
434C22×C31C2×#12311yescharacteristic
435C22×C31C2×#12311yescharacteristic
436C22×C31C2×#12311yescharacteristic
437C22×C31#52512yes—
438C22×C31#52512yes—
439C22×C31C2×#12411yescharacteristic
440C22×C31C2×#12611yescharacteristic
441C22×C31C2×#12611yescharacteristic
442C22×C31#53411yescharacteristic
443C22×C31#53411yescharacteristic
444C22×C31#53812yes—
445C22×C31#53812yes—
446C22×C31D4212yes—
447C22×C31#54612yes—
448C22×C31#54612yes—
449C22×C31#54612yes—
450C22×C31#54612yes—
451C22×C31#55112yes—
452C22×C31#55112yes—
453C22×C31#55112yes—
454C4×C31—44no—
455C4×C31—44no—
456C4×C31—44no—
457C4×C31—81no—
458C4×C31—81no—
459C4×C31—81no—
460C4×C31—81no—
461C4×C31—82no—
462C26C22×C3111yescharacteristic
463C24×C4C22×C3111yescharacteristic
464C24×C4C22×C3111yescharacteristic
465C22×C4⋊C4C22×C3112yescomplemented
466C22×C22⋊C4—24no—
467C22×C22⋊C4—28no—
468C22×C22⋊C4C22×C3111yescharacteristic
469C22×C22⋊C4C22×C3112yes—
470C22×C22⋊C4C22×C3111yescharacteristic
471C22×C22⋊C4C22×C3111yescharacteristic
472C22×C22⋊C4C22×C3111yescharacteristic
473C22×C22⋊C4C22×C3111yescharacteristic
474C22×C22⋊C4C22×C3112yes—
475C22×C22⋊C4C22×C3112yes—
476C22×C22⋊C4C22×C3112yes—
477C22×C22⋊C4C22×C3111yescharacteristic
478C22×C22⋊C4C22×C3111yescharacteristic
479C22×C22⋊C4C22×C3111yescharacteristic
480#397—28no—
481#385—24no—
482#379—24no—
483#379—24no—
484C2×#95C22×C3112yescomplemented
485C2×#95C22×C3112yescomplemented
486C2×#95C22×C3112yescomplemented
487C2×#95C22×C3112yescomplemented
488C2×#95C22×C3112yescomplemented
489C2×#95C22×C3112yescomplemented
490C2×#95C22×C3112yescomplemented
491C2×C31—28no—
492C2×C31—44no—
493C2×C31—44no—
494C2×C31C2×#39711yescharacteristic
495C2×C31#240511yescharacteristic
496C2×C31#241011yescharacteristic
497C2×C31#241211yescharacteristic
498C2×C31#241812yes—
499C2×C31#247212yes—
500C2×C31#248012yes—
501C2×C31#248012yes—
502C2×C31#248311yescharacteristic
503C2×C31#262211yescharacteristic
504C2×C31#284911yescharacteristic
505C25—24no—
506C25—24no—
507C25—22no—
508C25—22no—
509C25—22no—
510C25—22no—
511C25—22no—
512C25—22no—
513C25—42no—
514C25—42no—
515C25D4×C3114yes—
516C25C23×C3111yescharacteristic
517C25C23×C3111yescharacteristic
518C25C23×C3111yescharacteristic
519C23×C4—22no—
520C23×C4—22no—
521C23×C4—24no—
522C23×C4—24no—
523C23×C4—22no—
524C23×C4—22no—
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—42no—
528C23×C4—42no—
529C23×C4C23×C3111yescharacteristic
530C23×C4C23×C3111yescharacteristic
531C23×C4C23×C3112yes—
532C23×C4C23×C3111yescharacteristic
533C23×C4C23×C3111yescharacteristic
534C23×C4C23×C3112yes—
535C23×C4C23×C3112yes—
536C23×C4C23×C3112yes—
537C2×C4⋊C4—24no—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—42no—
540C2×C22⋊C4—232no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4D4×C3118yes—
572C2×C22⋊C4D4×C3114yes—
573#95—24no—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—42no—
578#95—42no—
579#95—42no—
580C31#1472711yescharacteristic, direct product factor, Sylow
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—216no—
586C24—216no—
587C24—28no—
588C24—28no—
589C24—28no—
590C24—22no—
591C24—21no—
592C24—21no—
593C24—21no—
594C24—21no—
595C24—21no—
596C24—21no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—28no—
609C24—28no—
610C24—44no—
611C24—44no—
612C24—48no—
613C24—48no—
614C24—48no—
615C24—48no—
616C24—48no—
617C24—48no—
618C24—48no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—44no—
623C24—44no—
624C24—44no—
625C24—44no—
626C24C2×D4×C3112yes—
627C24C2×D4×C3114yes—
628C24C2×D4×C3112yes—
629C24C2×D4×C3112yes—
630C24C2×D4×C3112yes—
631C24#41×C3114yes—
632C24#41×C3112yes—
633C24#41×C3112yes—
634C24#41×C3112yes—
635C24#41×C3112yes—
636C24#41×C3112yes—
637C24C24×C3111yescharacteristic
638C22×C4—28no—
639C22×C4—28no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—22no—
673C22×C4—21no—
674C22×C4—21no—
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—22no—
685C22×C4—48no—
686C22×C4—48no—
687C22×C4—48no—
688C22×C4—48no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4C2×D4×C3114yes—
694C22×C4C2×D4×C3114yes—
695C22×C4C2×D4×C3114yes—
696C4⋊C4—48no—
697C22⋊C4—216no—
698C22⋊C4—216no—
699C22⋊C4—28no—
700C22⋊C4—48no—
701C22⋊C4—48no—
702C22⋊C4—44no—
703C22⋊C4—44no—
704C22⋊C4—44no—
705C22⋊C4—44no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—44no—
709C23—22no—
710C23—22no—
711C23—24no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—232no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—416no—
751C23—416no—
752C23—416no—
753C23—416no—
754C23—416no—
755C23—432no—
756C23—432no—
757C23—432no—
758C23—432no—
759C23—416no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23C31×#12014yes—
781C23C31×#12114yes—
782C23C31×#12314yes—
783C23C31×#12314yes—
784C23C31×#12314yes—
785C23C31×#12314yes—
786C23C31×#12414yes—
787C23C31×#12614yes—
788C23C31×#12614yes—
789C23C22×D4×C3111yescharacteristic
790C23C22×D4×C3112yes—
791C23C22×D4×C3111yescharacteristic
792C23C2×#41×C3111yescharacteristic
793C23C2×#41×C3111yescharacteristic
794C23C2×#41×C3111yescharacteristic
795C23C2×#41×C3111yescharacteristic
796C23C2×#41×C3112yes—
797C23C2×#41×C3111yescharacteristic
798C23C31×H(5,𝔽2)12yes—
799C23C31×H(5,𝔽2)12yes—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—416no—
810C2×C4—416no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—24no—
854C22—24no—
855C22—28no—
856C22—28no—
857C22—28no—
858C22—28no—
859C22—24no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—464no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—44no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—42no—
883C22C31×#39718yescomplemented
884C22C2×C31×#12011yescharacteristic
885C22C2×C31×#12111yescharacteristic
886C22C2×C31×#12311yescharacteristic
887C22C2×C31×#12311yescharacteristic
888C22C2×C31×#12311yescharacteristic
889C22C2×C31×#12311yescharacteristic
890C22C31×#52512yes—
891C22C31×#52512yes—
892C22C2×C31×#12411yescharacteristic
893C22C2×C31×#12611yescharacteristic
894C22C2×C31×#12611yescharacteristic
895C22C31×#53411yescharacteristic
896C22C31×#53411yescharacteristic
897C22C31×#53812yes—
898C22C31×#53812yes—
899C22D42×C3112yes—
900C22C31×#54612yes—
901C22C31×#54612yes—
902C22C31×#54612yes—
903C22C31×#54612yes—
904C22C31×#55112yes—
905C22C31×#55112yes—
906C22C31×#55112yes—
907C4—44no—
908C4—44no—
909C4—44no—
910C4—81no—
911C4—81no—
912C4—81no—
913C4—81no—
914C4—82no—
915C2—28no—
916C2—44no—
917C2—44no—
918C2C2×C31×#39711yescharacteristic
919C2C31×#240511yescharacteristic
920C2C31×#241011yescharacteristic
921C2C31×#241211yescharacteristic
922C2C31×#241812yes—
923C2C31×#247212yes—
924C2C31×#248012yes—
925C2C31×#248012yes—
926C2C31×#248311yescharacteristic
927C2C31×#262211yescharacteristic
928C2C31×#284911yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC26×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#397C2semidirect
3. C2×C31×#385C2semidirect
6. C31×#1440C2semidirect
7. C31×#1440C2semidirect
8. C31×#1439C2semidirect
9. C31×C22⋊#95C2semidirect
10. C31×C22⋊#95C2semidirect
11. C31×C22⋊#95C2semidirect
15. C22×C4⋊C4×C31C22semidirect
34. C2×C31×#95C22semidirect
35. C2×C31×#95C22semidirect
36. C2×C31×#95C22semidirect
37. C2×C31×#95C22semidirect
38. C2×C31×#95C22semidirect
39. C2×C31×#95C22semidirect
40. C2×C31×#95C22semidirect
244. #14727C31direct (N × H)
387. C2×#397C2×C31semidirect
388. C2×#385C2×C31semidirect
391. #1440C2×C31semidirect
392. #1440C2×C31semidirect
393. #1439C2×C31semidirect
394. C22⋊#95C2×C31semidirect
395. C22⋊#95C2×C31semidirect
396. C22⋊#95C2×C31semidirect
430. C22×C31#397semidirect
465. C22×C4⋊C4C22×C31semidirect
484. C2×#95C22×C31semidirect
485. C2×#95C22×C31semidirect
486. C2×#95C22×C31semidirect
487. C2×#95C22×C31semidirect
488. C2×#95C22×C31semidirect
489. C2×#95C22×C31semidirect
490. C2×#95C22×C31semidirect
580. C31#14727direct (N × H)
883. C22C31×#397semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C312
C2×C31×#3972
C2×C31×#3852
C2×C31×#3792
C31×#14402
C31×#14392
C31×C22⋊#952
#1472731