Finite Group Databasebeta

← C31×#15260 #21472019

Subgroups — C31×#15260 #21472019

Order 7936.

2662 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#123C211yesmaximal, characteristic, complemented
2C22×C31×#121C211yesmaximal, characteristic
3C2×C31×#394C212yesmaximal, complemented
4C2×C31×#386C211yesmaximal, characteristic, complemented
5C2×C31×#385C211yesmaximal, characteristic, complemented
6C31×#1444C212yesmaximal, complemented
7C31×#1440C211yesmaximal, characteristic, complemented
8C31×#1439C212yesmaximal, complemented
9C31×#1438C211yesmaximal, characteristic, complemented
10C31×#1438C211yesmaximal, characteristic, complemented
11C31×C22⋊#95C212yesmaximal, complemented
12C23×D4×C31C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C23×D4×C31C2211yescharacteristic
15C24×C4×C31C2211yescharacteristic
16C24×C4×C31C2211yescharacteristic
17C2×C31×#123—24no—
18C2×C31×#123—28no—
19C2×C31×#121—24no—
20C2×C31×#121—24no—
21C2×C31×#121—24no—
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2212yes—
24C22×C4⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2212yes—
29C22×C22⋊C4×C31C2212yes—
30C22×C22⋊C4×C31C2212yes—
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2212yes—
33C22×C22⋊C4×C31C2211yescharacteristic
34C31×#394—28no—
35C31×#386—24no—
36C31×#385—24no—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2212yes—
41C2×C31×#95C2212yes—
42C2×C31×#95C2212yes—
43C25×C31C2311yescharacteristic
44C25×C31C2311yescharacteristic
45C25×C31C2311yescharacteristic
46C22×D4×C31—22no—
47C22×D4×C31—22no—
48C22×D4×C31—22no—
49C22×D4×C31—22no—
50C22×D4×C31—22no—
51C22×D4×C31—22no—
52C22×D4×C31—24no—
53C22×D4×C31—24no—
54C22×D4×C31—22no—
55C22×D4×C31—24no—
56C22×D4×C31—42no—
57C22×D4×C31—42no—
58C22×D4×C31—42no—
59C22×D4×C31D414yes—
60C22×D4×C31D414yes—
61C23×C4×C31—22no—
62C23×C4×C31—22no—
63C23×C4×C31—22no—
64C23×C4×C31—22no—
65C23×C4×C31—24no—
66C23×C4×C31—22no—
67C23×C4×C31—22no—
68C23×C4×C31—24no—
69C23×C4×C31—42no—
70C23×C4×C31—42no—
71C23×C4×C31C2312yes—
72C23×C4×C31C2312yes—
73C23×C4×C31C2312yes—
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2312yes—
78C23×C4×C31C2311yescharacteristic
79C31×#123—232no—
80C31×#121—232no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31—24no—
85C2×C4⋊C4×C31—24no—
86C2×C4⋊C4×C31—24no—
87C2×C4⋊C4×C31—24no—
88C2×C4⋊C4×C31—24no—
89C2×C4⋊C4×C31—42no—
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—24no—
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—22no—
98C2×C22⋊C4×C31—22no—
99C2×C22⋊C4×C31—24no—
100C2×C22⋊C4×C31—24no—
101C2×C22⋊C4×C31—24no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—24no—
104C2×C22⋊C4×C31—24no—
105C2×C22⋊C4×C31—24no—
106C2×C22⋊C4×C31—24no—
107C2×C22⋊C4×C31—24no—
108C2×C22⋊C4×C31—42no—
109C2×C22⋊C4×C31—42no—
110C2×C22⋊C4×C31—42no—
111C2×C22⋊C4×C31—42no—
112C2×C22⋊C4×C31D414yes—
113C2×C22⋊C4×C31D418yescomplemented
114C31×#95—24no—
115C31×#95—24no—
116C31×#95—24no—
117C31×#95—24no—
118C31×#95—42no—
119C31×#95—42no—
120C24×C31—22no—
121C24×C31—21no—
122C24×C31—21no—
123C24×C31—22no—
124C24×C31—22no—
125C24×C31—22no—
126C24×C31—22no—
127C24×C31—22no—
128C24×C31—22no—
129C24×C31—22no—
130C24×C31—22no—
131C24×C31—22no—
132C24×C31—22no—
133C24×C31—22no—
134C24×C31—21no—
135C24×C31—21no—
136C24×C31—22no—
137C24×C31—22no—
138C24×C31—22no—
139C24×C31—22no—
140C24×C31—22no—
141C24×C31C2×D412yes—
142C24×C31C2×D414yes—
143C24×C31C2×D412yes—
144C24×C31C2×D412yes—
145C24×C31C2×D412yes—
146C24×C31C2×D412yes—
147C24×C31C2411yescharacteristic
148C2×D4×C31—28no—
149C2×D4×C31—28no—
150C2×D4×C31—28no—
151C2×D4×C31—28no—
152C2×D4×C31—28no—
153C2×D4×C31—44no—
154C2×D4×C31—44no—
155C2×D4×C31—48no—
156C2×D4×C31—48no—
157C2×D4×C31—48no—
158C2×D4×C31—48no—
159C2×D4×C31—48no—
160C2×D4×C31—48no—
161C2×D4×C31—44no—
162C2×D4×C31—44no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—22no—
166C22×C4×C31—28no—
167C22×C4×C31—28no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
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—22no—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—22no—
202C22×C4×C31—22no—
203C22×C4×C31—22no—
204C22×C4×C31—22no—
205C22×C4×C31—48no—
206C22×C4×C31—48no—
207C22×C4×C31—48no—
208C22×C4×C31—48no—
209C22×C4×C31—44no—
210C22×C4×C31—44no—
211C22×C4×C31—44no—
212C22×C4×C31—44no—
213C22×C4×C31C2×D412yes—
214C22×C4×C31C2×D414yes—
215C22×C4×C31C2×D414yes—
216C22×C4×C31C2×D412yes—
217C22×C4×C31C2×D412yes—
218C22×C4×C31C2×D412yes—
219C22×C4×C31#4114yes—
220C22×C4×C31#4114yes—
221C4⋊C4×C31—28no—
222C4⋊C4×C31—216no—
223C4⋊C4×C31—48no—
224C22⋊C4×C31—28no—
225C22⋊C4×C31—28no—
226C22⋊C4×C31—28no—
227C22⋊C4×C31—28no—
228C22⋊C4×C31—216no—
229C22⋊C4×C31—48no—
230C22⋊C4×C31—48no—
231C22⋊C4×C31—48no—
232C22⋊C4×C31—44no—
233#15260C3111yesmaximal, characteristic, direct product factor, Sylow
234C23×C31—22no—
235C23×C31—22no—
236C23×C31—22no—
237C23×C31—22no—
238C23×C31—24no—
239C23×C31—22no—
240C23×C31—22no—
241C23×C31—22no—
242C23×C31—22no—
243C23×C31—24no—
244C23×C31—24no—
245C23×C31—24no—
246C23×C31—24no—
247C23×C31—24no—
248C23×C31—24no—
249C23×C31—24no—
250C23×C31—24no—
251C23×C31—24no—
252C23×C31—24no—
253C23×C31—24no—
254C23×C31—24no—
255C23×C31—24no—
256C23×C31—22no—
257C23×C31—22no—
258C23×C31—22no—
259C23×C31—24no—
260C23×C31—24no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—42no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—42no—
267C23×C31—42no—
268C23×C31—42no—
269C23×C31—42no—
270C23×C31—42no—
271C23×C31—42no—
272C23×C31—42no—
273C23×C31—42no—
274C23×C31—42no—
275C23×C31—42no—
276C23×C31—42no—
277C23×C31—42no—
278C23×C31—42no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—42no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—42no—
285C23×C31—42no—
286C23×C31—42no—
287C23×C31—42no—
288C23×C31—42no—
289C23×C31—42no—
290C23×C31—42no—
291C23×C31—42no—
292C23×C31—42no—
293C23×C31—42no—
294C23×C31—42no—
295C23×C31#12014yes—
296C23×C31#12014yes—
297C23×C31C22×D411yescharacteristic
298C23×C31C22×D411yescharacteristic
299C23×C31C22×D411yescharacteristic
300C23×C31C22×D412yes—
301C23×C31C2×#4112yes—
302C23×C31C2×#4112yes—
303C23×C31H(5,𝔽2)12yes—
304C23×C31H(5,𝔽2)12yes—
305C23×C312−1+412yes—
306D4×C31—416no—
307D4×C31—416no—
308D4×C31—416no—
309C2×C4×C31—22no—
310C2×C4×C31—22no—
311C2×C4×C31—24no—
312C2×C4×C31—24no—
313C2×C4×C31—24no—
314C2×C4×C31—22no—
315C2×C4×C31—24no—
316C2×C4×C31—22no—
317C2×C4×C31—22no—
318C2×C4×C31—22no—
319C2×C4×C31—24no—
320C2×C4×C31—22no—
321C2×C4×C31—24no—
322C2×C4×C31—24no—
323C2×C4×C31—24no—
324C2×C4×C31—24no—
325C2×C4×C31—24no—
326C2×C4×C31—24no—
327C2×C4×C31—24no—
328C2×C4×C31—24no—
329C2×C4×C31—416no—
330C2×C4×C31—416no—
331C2×C4×C31—42no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—42no—
335C2×C4×C31—42no—
336C2×C4×C31—42no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—42no—
340C2×C4×C31—42no—
341C2×C4×C31—42no—
342C2×C4×C31—42no—
343C2×C4×C31—42no—
344C2×C4×C31—42no—
345C2×C4×C31—42no—
346C2×C4×C31—42no—
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#12314yescomplemented
359C22×#123C2×C3111yescharacteristic, complemented
360C22×#121C2×C3111yescharacteristic
361C2×#394C2×C3112yescomplemented
362C2×#386C2×C3111yescharacteristic, complemented
363C2×#385C2×C3111yescharacteristic, complemented
364#1444C2×C3112yescomplemented
365#1440C2×C3111yescharacteristic, complemented
366#1439C2×C3112yescomplemented
367#1438C2×C3111yescharacteristic, complemented
368#1438C2×C3111yescharacteristic, complemented
369C22⋊#95C2×C3112yescomplemented
370C22×C31—24no—
371C22×C31—24no—
372C22×C31—24no—
373C22×C31—24no—
374C22×C31—28no—
375C22×C31—42no—
376C22×C31—42no—
377C22×C31—44no—
378C22×C31—44no—
379C22×C31—44no—
380C22×C31—44no—
381C22×C31—44no—
382C22×C31—44no—
383C22×C31—44no—
384C22×C31—44no—
385C22×C31—44no—
386C22×C31—44no—
387C22×C31—44no—
388C22×C31—42no—
389C22×C31—42no—
390C22×C31—42no—
391C22×C31—44no—
392C22×C31—44no—
393C22×C31—82no—
394C22×C31—82no—
395C22×C31—82no—
396C22×C31—82no—
397C22×C31C2×#12011yescharacteristic
398C22×C31C2×#12011yescharacteristic
399C22×C31C2×#12311yescharacteristic
400C22×C31#52511yescharacteristic
401C22×C31#53212yes—
402C22×C31#53411yescharacteristic
403C22×C31#53411yescharacteristic
404C22×C31#53611yescharacteristic
405C22×C31#53712yes—
406C22×C31#54012yes—
407C22×C31#54212yes—
408C22×C31D4212yes—
409C22×C31D4212yes—
410C22×C31#54612yes—
411C22×C31#54612yes—
412C22×C31#54612yes—
413C22×C31#54712yes—
414C22×C31#54712yes—
415C22×C31#54712yes—
416C22×C31#55312yes—
417C22×C31#56212yes—
418C4×C31—24no—
419C4×C31—44no—
420C4×C31—42no—
421C4×C31—42no—
422C4×C31—42no—
423C4×C31—44no—
424C4×C31—44no—
425C4×C31—82no—
426C23×D4C22×C3111yescharacteristic
427C23×D4C22×C3111yescharacteristic
428C23×D4C22×C3111yescharacteristic
429C24×C4C22×C3111yescharacteristic
430C24×C4C22×C3111yescharacteristic
431C2×#123—24no—
432C2×#123—28no—
433C2×#121—24no—
434C2×#121—24no—
435C2×#121—24no—
436C22×C4⋊C4C22×C3111yescharacteristic
437C22×C4⋊C4C22×C3112yes—
438C22×C4⋊C4C22×C3112yes—
439C22×C22⋊C4C22×C3111yescharacteristic
440C22×C22⋊C4C22×C3111yescharacteristic
441C22×C22⋊C4C22×C3111yescharacteristic
442C22×C22⋊C4C22×C3112yes—
443C22×C22⋊C4C22×C3112yes—
444C22×C22⋊C4C22×C3112yes—
445C22×C22⋊C4C22×C3111yescharacteristic
446C22×C22⋊C4C22×C3112yes—
447C22×C22⋊C4C22×C3111yescharacteristic
448#394—28no—
449#386—24no—
450#385—24no—
451C2×#95C22×C3112yes—
452C2×#95C22×C3112yes—
453C2×#95C22×C3112yes—
454C2×#95C22×C3112yes—
455C2×#95C22×C3112yes—
456C2×#95C22×C3112yes—
457C2×C31—44no—
458C2×C31—44no—
459C2×C31—82no—
460C2×C31#240311yescharacteristic
461C2×C31#240511yescharacteristic
462C2×C31#240611yescharacteristic
463C2×C31#242212yes—
464C2×C31#243012yes—
465C2×C31#246412yes—
466C2×C31#267112yes—
467C2×C31#267212yes—
468C2×C31#270112yes—
469C25C23×C3111yescharacteristic
470C25C23×C3111yescharacteristic
471C25C23×C3111yescharacteristic
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—22no—
476C22×D4—22no—
477C22×D4—22no—
478C22×D4—24no—
479C22×D4—24no—
480C22×D4—22no—
481C22×D4—24no—
482C22×D4—42no—
483C22×D4—42no—
484C22×D4—42no—
485C22×D4D4×C3114yes—
486C22×D4D4×C3114yes—
487C23×C4—22no—
488C23×C4—22no—
489C23×C4—22no—
490C23×C4—22no—
491C23×C4—24no—
492C23×C4—22no—
493C23×C4—22no—
494C23×C4—24no—
495C23×C4—42no—
496C23×C4—42no—
497C23×C4C23×C3112yes—
498C23×C4C23×C3112yes—
499C23×C4C23×C3112yes—
500C23×C4C23×C3111yescharacteristic
501C23×C4C23×C3111yescharacteristic
502C23×C4C23×C3111yescharacteristic
503C23×C4C23×C3112yes—
504C23×C4C23×C3111yescharacteristic
505#123—232no—
506#121—232no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—24no—
513C2×C4⋊C4—24no—
514C2×C4⋊C4—24no—
515C2×C4⋊C4—42no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4D4×C3114yes—
539C2×C22⋊C4D4×C3118yescomplemented
540#95—24no—
541#95—24no—
542#95—24no—
543#95—24no—
544#95—42no—
545#95—42no—
546C31#1526011yescharacteristic, direct product factor, Sylow
547C24—22no—
548C24—21no—
549C24—21no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—21no—
562C24—21no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24C2×D4×C3112yes—
569C24C2×D4×C3114yes—
570C24C2×D4×C3112yes—
571C24C2×D4×C3112yes—
572C24C2×D4×C3112yes—
573C24C2×D4×C3112yes—
574C24C24×C3111yescharacteristic
575C2×D4—28no—
576C2×D4—28no—
577C2×D4—28no—
578C2×D4—28no—
579C2×D4—28no—
580C2×D4—44no—
581C2×D4—44no—
582C2×D4—48no—
583C2×D4—48no—
584C2×D4—48no—
585C2×D4—48no—
586C2×D4—48no—
587C2×D4—48no—
588C2×D4—44no—
589C2×D4—44no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—28no—
594C22×C4—28no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4C2×D4×C3112yes—
641C22×C4C2×D4×C3114yes—
642C22×C4C2×D4×C3114yes—
643C22×C4C2×D4×C3112yes—
644C22×C4C2×D4×C3112yes—
645C22×C4C2×D4×C3112yes—
646C22×C4#41×C3114yes—
647C22×C4#41×C3114yes—
648C4⋊C4—28no—
649C4⋊C4—216no—
650C4⋊C4—48no—
651C22⋊C4—28no—
652C22⋊C4—28no—
653C22⋊C4—28no—
654C22⋊C4—28no—
655C22⋊C4—216no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—44no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—24no—
686C23—24no—
687C23—41no—
688C23—41no—
689C23—42no—
690C23—41no—
691C23—41no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—41no—
706C23—41no—
707C23—42no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23C31×#12014yes—
722C23C31×#12014yes—
723C23C22×D4×C3111yescharacteristic
724C23C22×D4×C3111yescharacteristic
725C23C22×D4×C3111yescharacteristic
726C23C22×D4×C3112yes—
727C23C2×#41×C3112yes—
728C23C2×#41×C3112yes—
729C23C31×H(5,𝔽2)12yes—
730C23C31×H(5,𝔽2)12yes—
731C23C31×2−1+412yes—
732D4—416no—
733D4—416no—
734D4—416no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—416no—
756C2×C4—416no—
757C2×C4—42no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4C31×#12314yescomplemented
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—28no—
790C22—42no—
791C22—42no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—44no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—44no—
807C22—44no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22C2×C31×#12011yescharacteristic
813C22C2×C31×#12011yescharacteristic
814C22C2×C31×#12311yescharacteristic
815C22C31×#52511yescharacteristic
816C22C31×#53212yes—
817C22C31×#53411yescharacteristic
818C22C31×#53411yescharacteristic
819C22C31×#53611yescharacteristic
820C22C31×#53712yes—
821C22C31×#54012yes—
822C22C31×#54212yes—
823C22D42×C3112yes—
824C22D42×C3112yes—
825C22C31×#54612yes—
826C22C31×#54612yes—
827C22C31×#54612yes—
828C22C31×#54712yes—
829C22C31×#54712yes—
830C22C31×#54712yes—
831C22C31×#55312yes—
832C22C31×#56212yes—
833C4—24no—
834C4—44no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—44no—
839C4—44no—
840C4—82no—
841C2—44no—
842C2—44no—
843C2—82no—
844C2C31×#240311yescharacteristic
845C2C31×#240511yescharacteristic
846C2C31×#240611yescharacteristic
847C2C31×#242212yes—
848C2C31×#243012yes—
849C2C31×#246412yes—
850C2C31×#267112yes—
851C2C31×#267212yes—
852C2C31×#270112yes—
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC22×C31×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#123C2semidirect
3. C2×C31×#394C2semidirect
4. C2×C31×#386C2semidirect
5. C2×C31×#385C2semidirect
6. C31×#1444C2semidirect
7. C31×#1440C2semidirect
8. C31×#1439C2semidirect
9. C31×#1438C2semidirect
10. C31×#1438C2semidirect
11. C31×C22⋊#95C2semidirect
113. C2×C22⋊C4×C31D4semidirect
233. #15260C31direct (N × H)
358. C2×C4×C31#123semidirect
359. C22×#123C2×C31semidirect
361. C2×#394C2×C31semidirect
362. C2×#386C2×C31semidirect
363. C2×#385C2×C31semidirect
364. #1444C2×C31semidirect
365. #1440C2×C31semidirect
366. #1439C2×C31semidirect
367. #1438C2×C31semidirect
368. #1438C2×C31semidirect
369. C22⋊#95C2×C31semidirect
539. C2×C22⋊C4D4×C31semidirect
546. C31#15260direct (N × H)
784. C2×C4C31×#123semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1232
C22×C31×#1212
C2×C31×#3942
C2×C31×#3862
C2×C31×#3852
C31×#14442
C31×#14402
C31×#14392
C31×#14382
C31×C22⋊#952
#1526031