Finite Group Databasebeta

← C31×#14718 #21471477

Subgroups — C31×#14718 #21471477

Order 7936.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#120C211yesmaximal, characteristic
2C23×C22⋊C4×C31C211yesmaximal, characteristic, complemented
3C2×C31×#394C212yesmaximal, complemented
4C2×C31×#386C211yesmaximal, characteristic, complemented
5C2×C31×#386C211yesmaximal, characteristic, complemented
6C2×C31×#385C211yesmaximal, characteristic, complemented
7C2×C31×#379C211yesmaximal, characteristic, complemented
8C31×#1440C212yesmaximal, complemented
9C31×#1439C212yesmaximal, complemented
10C31×#1438C212yesmaximal, complemented
11C31×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C31C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C23×D4×C31C2211yescharacteristic
15C23×D4×C31C2211yescharacteristic
16C24×C4×C31C2211yescharacteristic
17C24×C4×C31C2211yescharacteristic
18C2×C31×#120—24no—
19C2×C31×#120—24no—
20C2×C31×#120—24no—
21C22×C4⋊C4×C31C2212yescomplemented
22C22×C22⋊C4×C31—24no—
23C22×C22⋊C4×C31—28no—
24C22×C22⋊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×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2212yes—
32C22×C22⋊C4×C31C2211yescharacteristic
33C22×C22⋊C4×C31C2212yescomplemented
34C22×C22⋊C4×C31C2212yescomplemented
35C31×#394—28no—
36C31×#386—24no—
37C31×#386—24no—
38C31×#385—24no—
39C31×#379—24no—
40C2×C31×#95C2212yescomplemented
41C2×C31×#95C2212yescomplemented
42C2×C31×#95C2212yescomplemented
43C2×C31×#95C2212yescomplemented
44C2×C31×#95C2212yescomplemented
45C25×C31—24no—
46C25×C31—24no—
47C25×C31—22no—
48C25×C31—22no—
49C25×C31—22no—
50C25×C31—22no—
51C25×C31—22no—
52C25×C31—22no—
53C25×C31—42no—
54C25×C31—42no—
55C25×C31D414yes—
56C25×C31C2311yescharacteristic
57C25×C31C2311yescharacteristic
58C25×C31C2311yescharacteristic
59C25×C31C2311yescharacteristic
60C22×D4×C31—22no—
61C22×D4×C31—22no—
62C22×D4×C31—22no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—22no—
70C22×D4×C31—24no—
71C22×D4×C31—24no—
72C22×D4×C31—22no—
73C22×D4×C31—22no—
74C22×D4×C31—42no—
75C22×D4×C31—42no—
76C22×D4×C31D414yes—
77C23×C4×C31—22no—
78C23×C4×C31—22no—
79C23×C4×C31—24no—
80C23×C4×C31—24no—
81C23×C4×C31—22no—
82C23×C4×C31—22no—
83C23×C4×C31—22no—
84C23×C4×C31—22no—
85C23×C4×C31—42no—
86C23×C4×C31—42no—
87C23×C4×C31C2312yes—
88C23×C4×C31C2312yes—
89C23×C4×C31C2312yes—
90C23×C4×C31C2312yes—
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C23×C4×C31C2311yescharacteristic
94C31×#120—232no—
95C2×C4⋊C4×C31—24no—
96C2×C4⋊C4×C31—24no—
97C2×C4⋊C4×C31—42no—
98C2×C22⋊C4×C31—232no—
99C2×C22⋊C4×C31—24no—
100C2×C22⋊C4×C31—24no—
101C2×C22⋊C4×C31—24no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—22no—
106C2×C22⋊C4×C31—22no—
107C2×C22⋊C4×C31—22no—
108C2×C22⋊C4×C31—24no—
109C2×C22⋊C4×C31—24no—
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—22no—
112C2×C22⋊C4×C31—22no—
113C2×C22⋊C4×C31—22no—
114C2×C22⋊C4×C31—22no—
115C2×C22⋊C4×C31—22no—
116C2×C22⋊C4×C31—24no—
117C2×C22⋊C4×C31—24no—
118C2×C22⋊C4×C31—24no—
119C2×C22⋊C4×C31—22no—
120C2×C22⋊C4×C31—24no—
121C2×C22⋊C4×C31—24no—
122C2×C22⋊C4×C31—24no—
123C2×C22⋊C4×C31—24no—
124C2×C22⋊C4×C31—24no—
125C2×C22⋊C4×C31—42no—
126C2×C22⋊C4×C31—42no—
127C2×C22⋊C4×C31—42no—
128C2×C22⋊C4×C31—42no—
129C2×C22⋊C4×C31D414yes—
130C2×C22⋊C4×C31D418yescomplemented
131C2×C22⋊C4×C31D414yescomplemented
132C31×#95—24no—
133C31×#95—24no—
134C31×#95—24no—
135C31×#95—24no—
136C31×#95—42no—
137C24×C31—22no—
138C24×C31—22no—
139C24×C31—22no—
140C24×C31—22no—
141C24×C31—216no—
142C24×C31—216no—
143C24×C31—28no—
144C24×C31—28no—
145C24×C31—28no—
146C24×C31—22no—
147C24×C31—21no—
148C24×C31—21no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31—21no—
152C24×C31—21no—
153C24×C31—21no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31—21no—
157C24×C31—22no—
158C24×C31—21no—
159C24×C31—21no—
160C24×C31—22no—
161C24×C31—22no—
162C24×C31—22no—
163C24×C31—22no—
164C24×C31—28no—
165C24×C31—28no—
166C24×C31—21no—
167C24×C31—22no—
168C24×C31—21no—
169C24×C31—21no—
170C24×C31—21no—
171C24×C31—21no—
172C24×C31—21no—
173C24×C31—22no—
174C24×C31—22no—
175C24×C31—22no—
176C24×C31—44no—
177C24×C31—44no—
178C24×C31—48no—
179C24×C31—48no—
180C24×C31—48no—
181C24×C31—48no—
182C24×C31—48no—
183C24×C31—48no—
184C24×C31—48no—
185C24×C31—48no—
186C24×C31—48no—
187C24×C31—48no—
188C24×C31—44no—
189C24×C31—44no—
190C24×C31—44no—
191C24×C31—44no—
192C24×C31C2×D412yes—
193C24×C31C2×D412yes—
194C24×C31C2×D414yes—
195C24×C31C2×D412yes—
196C24×C31C2×D412yes—
197C24×C31C2×D412yes—
198C24×C31C2×D412yes—
199C24×C31C2×D412yes—
200C24×C31#4114yes—
201C24×C31#4112yes—
202C24×C31#4112yes—
203C24×C31#4112yes—
204C24×C31C2411yescharacteristic
205C2×D4×C31—28no—
206C2×D4×C31—28no—
207C2×D4×C31—28no—
208C2×D4×C31—28no—
209C2×D4×C31—28no—
210C2×D4×C31—48no—
211C2×D4×C31—48no—
212C2×D4×C31—48no—
213C2×D4×C31—48no—
214C2×D4×C31—44no—
215C2×D4×C31—44no—
216C2×D4×C31—44no—
217C2×D4×C31—44no—
218C2×D4×C31—44no—
219C2×D4×C31—44no—
220C2×D4×C31—44no—
221C2×D4×C31—44no—
222C22×C4×C31—28no—
223C22×C4×C31—28no—
224C22×C4×C31—21no—
225C22×C4×C31—22no—
226C22×C4×C31—22no—
227C22×C4×C31—22no—
228C22×C4×C31—22no—
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—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—22no—
242C22×C4×C31—22no—
243C22×C4×C31—22no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—22no—
248C22×C4×C31—22no—
249C22×C4×C31—22no—
250C22×C4×C31—22no—
251C22×C4×C31—22no—
252C22×C4×C31—22no—
253C22×C4×C31—22no—
254C22×C4×C31—22no—
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—48no—
264C22×C4×C31—48no—
265C22×C4×C31—48no—
266C22×C4×C31—48no—
267C22×C4×C31—44no—
268C22×C4×C31—44no—
269C22×C4×C31—44no—
270C22×C4×C31—44no—
271C22×C4×C31C2×D412yes—
272C22×C4×C31C2×D412yes—
273C22×C4×C31C2×D414yes—
274C22×C4×C31C2×D414yes—
275C22×C4×C31C2×D414yes—
276C22×C4×C31C2×D412yes—
277C4⋊C4×C31—48no—
278C22⋊C4×C31—216no—
279C22⋊C4×C31—28no—
280C22⋊C4×C31—28no—
281C22⋊C4×C31—216no—
282C22⋊C4×C31—28no—
283C22⋊C4×C31—28no—
284C22⋊C4×C31—48no—
285C22⋊C4×C31—48no—
286C22⋊C4×C31—48no—
287C22⋊C4×C31—48no—
288C22⋊C4×C31—44no—
289#14718C3111yesmaximal, characteristic, direct product factor, Sylow
290C23×C31—22no—
291C23×C31—22no—
292C23×C31—24no—
293C23×C31—24no—
294C23×C31—22no—
295C23×C31—22no—
296C23×C31—24no—
297C23×C31—24no—
298C23×C31—24no—
299C23×C31—24no—
300C23×C31—24no—
301C23×C31—24no—
302C23×C31—24no—
303C23×C31—24no—
304C23×C31—24no—
305C23×C31—24no—
306C23×C31—232no—
307C23×C31—22no—
308C23×C31—22no—
309C23×C31—22no—
310C23×C31—22no—
311C23×C31—22no—
312C23×C31—22no—
313C23×C31—22no—
314C23×C31—22no—
315C23×C31—24no—
316C23×C31—24no—
317C23×C31—24no—
318C23×C31—24no—
319C23×C31—22no—
320C23×C31—22no—
321C23×C31—22no—
322C23×C31—22no—
323C23×C31—24no—
324C23×C31—24no—
325C23×C31—24no—
326C23×C31—24no—
327C23×C31—24no—
328C23×C31—24no—
329C23×C31—24no—
330C23×C31—24no—
331C23×C31—22no—
332C23×C31—22no—
333C23×C31—22no—
334C23×C31—24no—
335C23×C31—24no—
336C23×C31—416no—
337C23×C31—416no—
338C23×C31—416no—
339C23×C31—416no—
340C23×C31—416no—
341C23×C31—432no—
342C23×C31—432no—
343C23×C31—432no—
344C23×C31—432no—
345C23×C31—41no—
346C23×C31—41no—
347C23×C31—41no—
348C23×C31—41no—
349C23×C31—41no—
350C23×C31—41no—
351C23×C31—41no—
352C23×C31—41no—
353C23×C31—42no—
354C23×C31—42no—
355C23×C31—42no—
356C23×C31—42no—
357C23×C31—42no—
358C23×C31—42no—
359C23×C31—42no—
360C23×C31—42no—
361C23×C31—42no—
362C23×C31—42no—
363C23×C31—42no—
364C23×C31—42no—
365C23×C31—416no—
366C23×C31—41no—
367C23×C31—41no—
368C23×C31—41no—
369C23×C31—41no—
370C23×C31—41no—
371C23×C31—42no—
372C23×C31—42no—
373C23×C31—41no—
374C23×C31—41no—
375C23×C31—41no—
376C23×C31—42no—
377C23×C31—42no—
378C23×C31—42no—
379C23×C31—42no—
380C23×C31—42no—
381C23×C31—42no—
382C23×C31—42no—
383C23×C31—42no—
384C23×C31#12014yes—
385C23×C31#12014yes—
386C23×C31#12114yes—
387C23×C31#12114yes—
388C23×C31#12114yes—
389C23×C31#12314yes—
390C23×C31#12314yes—
391C23×C31#12314yes—
392C23×C31#12414yes—
393C23×C31C22×D411yescharacteristic
394C23×C31C22×D411yescharacteristic
395C23×C31C22×D411yescharacteristic
396C23×C31C22×D412yes—
397C23×C31C22×D411yescharacteristic
398C23×C31C2×#4111yescharacteristic
399C23×C31C2×#4111yescharacteristic
400C23×C31C2×#4111yescharacteristic
401C23×C31C2×#4112yes—
402C23×C31H(5,𝔽2)12yes—
403C23×C31H(5,𝔽2)12yes—
404D4×C31—416no—
405D4×C31—416no—
406D4×C31—416no—
407C2×C4×C31—24no—
408C2×C4×C31—24no—
409C2×C4×C31—22no—
410C2×C4×C31—22no—
411C2×C4×C31—22no—
412C2×C4×C31—24no—
413C2×C4×C31—22no—
414C2×C4×C31—22no—
415C2×C4×C31—24no—
416C2×C4×C31—24no—
417C2×C4×C31—24no—
418C2×C4×C31—24no—
419C2×C4×C31—24no—
420C2×C4×C31—24no—
421C2×C4×C31—24no—
422C2×C4×C31—24no—
423C2×C4×C31—416no—
424C2×C4×C31—416no—
425C2×C4×C31—42no—
426C2×C4×C31—41no—
427C2×C4×C31—42no—
428C2×C4×C31—41no—
429C2×C4×C31—41no—
430C2×C4×C31—41no—
431C2×C4×C31—41no—
432C2×C4×C31—42no—
433C2×C4×C31—41no—
434C2×C4×C31—42no—
435C2×C4×C31—42no—
436C2×C4×C31—41no—
437C2×C4×C31—41no—
438C2×C4×C31—42no—
439C2×C4×C31—42no—
440C2×C4×C31—42no—
441C2×C4×C31—42no—
442C2×C4×C31—42no—
443C2×C4×C31—42no—
444C2×C4×C31—42no—
445C2×C4×C31—42no—
446C2×C4×C31—42no—
447C2×C4×C31—42no—
448C2×C4×C31—42no—
449C2×C4×C31—42no—
450C2×C4×C31—42no—
451C2×C4×C31—42no—
452C2×C4×C31—42no—
453C2×C4×C31—42no—
454C22×#120C2×C3111yescharacteristic
455C23×C22⋊C4C2×C3111yescharacteristic, complemented
456C2×#394C2×C3112yescomplemented
457C2×#386C2×C3111yescharacteristic, complemented
458C2×#386C2×C3111yescharacteristic, complemented
459C2×#385C2×C3111yescharacteristic, complemented
460C2×#379C2×C3111yescharacteristic, complemented
461#1440C2×C3112yescomplemented
462#1439C2×C3112yescomplemented
463#1438C2×C3112yescomplemented
464C22⋊#95C2×C3111yescharacteristic, complemented
465C22×C31—24no—
466C22×C31—24no—
467C22×C31—24no—
468C22×C31—24no—
469C22×C31—24no—
470C22×C31—24no—
471C22×C31—28no—
472C22×C31—28no—
473C22×C31—28no—
474C22×C31—28no—
475C22×C31—24no—
476C22×C31—24no—
477C22×C31—24no—
478C22×C31—24no—
479C22×C31—24no—
480C22×C31—24no—
481C22×C31—464no—
482C22×C31—42no—
483C22×C31—42no—
484C22×C31—42no—
485C22×C31—42no—
486C22×C31—42no—
487C22×C31—42no—
488C22×C31—42no—
489C22×C31—42no—
490C22×C31—44no—
491C22×C31—44no—
492C22×C31—44no—
493C22×C31—44no—
494C22×C31—44no—
495C22×C31—44no—
496C22×C31—44no—
497C22×C31—44no—
498C22×C31—42no—
499C22×C31—42no—
500C22×C31—42no—
501C22×C31—44no—
502C22×C31—44no—
503C22×C31—81no—
504C22×C31—81no—
505C22×C31—81no—
506C22×C31—81no—
507C22×C31—82no—
508C22×C31—82no—
509C22×C31#39418yescomplemented
510C22×C31C2×#12011yescharacteristic
511C22×C31C2×#12011yescharacteristic
512C22×C31C2×#12111yescharacteristic
513C22×C31C2×#12111yescharacteristic
514C22×C31C2×#12111yescharacteristic
515C22×C31C2×#12311yescharacteristic
516C22×C31C2×#12311yescharacteristic
517C22×C31C2×#12311yescharacteristic
518C22×C31#52512yes—
519C22×C31#52512yes—
520C22×C31C2×#12411yescharacteristic
521C22×C31#53411yescharacteristic
522C22×C31#53411yescharacteristic
523C22×C31#53812yes—
524C22×C31#53812yes—
525C22×C31D4212yes—
526C22×C31D4212yes—
527C22×C31D4212yes—
528C22×C31#54612yes—
529C22×C31#54612yes—
530C22×C31#54612yes—
531C22×C31#54612yes—
532C22×C31#55112yes—
533C4×C31—42no—
534C4×C31—44no—
535C4×C31—42no—
536C4×C31—42no—
537C4×C31—44no—
538C4×C31—44no—
539C4×C31—82no—
540C26C22×C3111yescharacteristic
541C23×D4C22×C3111yescharacteristic
542C23×D4C22×C3111yescharacteristic
543C23×D4C22×C3111yescharacteristic
544C24×C4C22×C3111yescharacteristic
545C24×C4C22×C3111yescharacteristic
546C2×#120—24no—
547C2×#120—24no—
548C2×#120—24no—
549C22×C4⋊C4C22×C3112yescomplemented
550C22×C22⋊C4—24no—
551C22×C22⋊C4—28no—
552C22×C22⋊C4C22×C3112yes—
553C22×C22⋊C4C22×C3111yescharacteristic
554C22×C22⋊C4C22×C3111yescharacteristic
555C22×C22⋊C4C22×C3111yescharacteristic
556C22×C22⋊C4C22×C3112yes—
557C22×C22⋊C4C22×C3112yes—
558C22×C22⋊C4C22×C3111yescharacteristic
559C22×C22⋊C4C22×C3112yes—
560C22×C22⋊C4C22×C3111yescharacteristic
561C22×C22⋊C4C22×C3112yescomplemented
562C22×C22⋊C4C22×C3112yescomplemented
563#394—28no—
564#386—24no—
565#386—24no—
566#385—24no—
567#379—24no—
568C2×#95C22×C3112yescomplemented
569C2×#95C22×C3112yescomplemented
570C2×#95C22×C3112yescomplemented
571C2×#95C22×C3112yescomplemented
572C2×#95C22×C3112yescomplemented
573C2×C31—28no—
574C2×C31—44no—
575C2×C31—44no—
576C2×C31—82no—
577C2×C31C2×#39411yescharacteristic
578C2×C31#240311yescharacteristic
579C2×C31#240511yescharacteristic
580C2×C31#241011yescharacteristic
581C2×C31#241211yescharacteristic
582C2×C31#241812yes—
583C2×C31#242412yes—
584C2×C31#242412yes—
585C2×C31#247212yes—
586C2×C31#262211yescharacteristic
587C2×C31#284911yescharacteristic
588C25—24no—
589C25—24no—
590C25—22no—
591C25—22no—
592C25—22no—
593C25—22no—
594C25—22no—
595C25—22no—
596C25—42no—
597C25—42no—
598C25D4×C3114yes—
599C25C23×C3111yescharacteristic
600C25C23×C3111yescharacteristic
601C25C23×C3111yescharacteristic
602C25C23×C3111yescharacteristic
603C22×D4—22no—
604C22×D4—22no—
605C22×D4—22no—
606C22×D4—22no—
607C22×D4—22no—
608C22×D4—22no—
609C22×D4—22no—
610C22×D4—22no—
611C22×D4—22no—
612C22×D4—22no—
613C22×D4—24no—
614C22×D4—24no—
615C22×D4—22no—
616C22×D4—22no—
617C22×D4—42no—
618C22×D4—42no—
619C22×D4D4×C3114yes—
620C23×C4—22no—
621C23×C4—22no—
622C23×C4—24no—
623C23×C4—24no—
624C23×C4—22no—
625C23×C4—22no—
626C23×C4—22no—
627C23×C4—22no—
628C23×C4—42no—
629C23×C4—42no—
630C23×C4C23×C3112yes—
631C23×C4C23×C3112yes—
632C23×C4C23×C3112yes—
633C23×C4C23×C3112yes—
634C23×C4C23×C3111yescharacteristic
635C23×C4C23×C3111yescharacteristic
636C23×C4C23×C3111yescharacteristic
637#120—232no—
638C2×C4⋊C4—24no—
639C2×C4⋊C4—24no—
640C2×C4⋊C4—42no—
641C2×C22⋊C4—232no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—24no—
660C2×C22⋊C4—24no—
661C2×C22⋊C4—24no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—24no—
664C2×C22⋊C4—24no—
665C2×C22⋊C4—24no—
666C2×C22⋊C4—24no—
667C2×C22⋊C4—24no—
668C2×C22⋊C4—42no—
669C2×C22⋊C4—42no—
670C2×C22⋊C4—42no—
671C2×C22⋊C4—42no—
672C2×C22⋊C4D4×C3114yes—
673C2×C22⋊C4D4×C3118yescomplemented
674C2×C22⋊C4D4×C3114yescomplemented
675#95—24no—
676#95—24no—
677#95—24no—
678#95—24no—
679#95—42no—
680C31#1471811yescharacteristic, direct product factor, Sylow
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—216no—
686C24—216no—
687C24—28no—
688C24—28no—
689C24—28no—
690C24—22no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—22no—
702C24—21no—
703C24—21no—
704C24—22no—
705C24—22no—
706C24—22no—
707C24—22no—
708C24—28no—
709C24—28no—
710C24—21no—
711C24—22no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—22no—
718C24—22no—
719C24—22no—
720C24—44no—
721C24—44no—
722C24—48no—
723C24—48no—
724C24—48no—
725C24—48no—
726C24—48no—
727C24—48no—
728C24—48no—
729C24—48no—
730C24—48no—
731C24—48no—
732C24—44no—
733C24—44no—
734C24—44no—
735C24—44no—
736C24C2×D4×C3112yes—
737C24C2×D4×C3112yes—
738C24C2×D4×C3114yes—
739C24C2×D4×C3112yes—
740C24C2×D4×C3112yes—
741C24C2×D4×C3112yes—
742C24C2×D4×C3112yes—
743C24C2×D4×C3112yes—
744C24#41×C3114yes—
745C24#41×C3112yes—
746C24#41×C3112yes—
747C24#41×C3112yes—
748C24C24×C3111yescharacteristic
749C2×D4—28no—
750C2×D4—28no—
751C2×D4—28no—
752C2×D4—28no—
753C2×D4—28no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—48no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4C2×D4×C3112yes—
816C22×C4C2×D4×C3112yes—
817C22×C4C2×D4×C3114yes—
818C22×C4C2×D4×C3114yes—
819C22×C4C2×D4×C3114yes—
820C22×C4C2×D4×C3112yes—
821C4⋊C4—48no—
822C22⋊C4—216no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—216no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—48no—
829C22⋊C4—48no—
830C22⋊C4—48no—
831C22⋊C4—48no—
832C22⋊C4—44no—
833C23—22no—
834C23—22no—
835C23—24no—
836C23—24no—
837C23—22no—
838C23—22no—
839C23—24no—
840C23—24no—
841C23—24no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—232no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—24no—
870C23—24no—
871C23—24no—
872C23—24no—
873C23—24no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—24no—
878C23—24no—
879C23—416no—
880C23—416no—
881C23—416no—
882C23—416no—
883C23—416no—
884C23—432no—
885C23—432no—
886C23—432no—
887C23—432no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—42no—
905C23—42no—
906C23—42no—
907C23—42no—
908C23—416no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—42no—
915C23—42no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—42no—
920C23—42no—
921C23—42no—
922C23—42no—
923C23—42no—
924C23—42no—
925C23—42no—
926C23—42no—
927C23C31×#12014yes—
928C23C31×#12014yes—
929C23C31×#12114yes—
930C23C31×#12114yes—
931C23C31×#12114yes—
932C23C31×#12314yes—
933C23C31×#12314yes—
934C23C31×#12314yes—
935C23C31×#12414yes—
936C23C22×D4×C3111yescharacteristic
937C23C22×D4×C3111yescharacteristic
938C23C22×D4×C3111yescharacteristic
939C23C22×D4×C3112yes—
940C23C22×D4×C3111yescharacteristic
941C23C2×#41×C3111yescharacteristic
942C23C2×#41×C3111yescharacteristic
943C23C2×#41×C3111yescharacteristic
944C23C2×#41×C3112yes—
945C23C31×H(5,𝔽2)12yes—
946C23C31×H(5,𝔽2)12yes—
947D4—416no—
948D4—416no—
949D4—416no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—416no—
967C2×C4—416no—
968C2×C4—42no—
969C2×C4—41no—
970C2×C4—42no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—42no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22—28no—
1004C22—28no—
1005C22—28no—
1006C22—28no—
1007C22—24no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—464no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—44no—
1026C22—44no—
1027C22—44no—
1028C22—44no—
1029C22—44no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—44no—
1034C22—44no—
1035C22—81no—
1036C22—81no—
1037C22—81no—
1038C22—81no—
1039C22—82no—
1040C22—82no—
1041C22C31×#39418yescomplemented
1042C22C2×C31×#12011yescharacteristic
1043C22C2×C31×#12011yescharacteristic
1044C22C2×C31×#12111yescharacteristic
1045C22C2×C31×#12111yescharacteristic
1046C22C2×C31×#12111yescharacteristic
1047C22C2×C31×#12311yescharacteristic
1048C22C2×C31×#12311yescharacteristic
1049C22C2×C31×#12311yescharacteristic
1050C22C31×#52512yes—
1051C22C31×#52512yes—
1052C22C2×C31×#12411yescharacteristic
1053C22C31×#53411yescharacteristic
1054C22C31×#53411yescharacteristic
1055C22C31×#53812yes—
1056C22C31×#53812yes—
1057C22D42×C3112yes—
1058C22D42×C3112yes—
1059C22D42×C3112yes—
1060C22C31×#54612yes—
1061C22C31×#54612yes—
1062C22C31×#54612yes—
1063C22C31×#54612yes—
1064C22C31×#55112yes—
1065C4—42no—
1066C4—44no—
1067C4—42no—
1068C4—42no—
1069C4—44no—
1070C4—44no—
1071C4—82no—
1072C2—28no—
1073C2—44no—
1074C2—44no—
1075C2—82no—
1076C2C2×C31×#39411yescharacteristic
1077C2C31×#240311yescharacteristic
1078C2C31×#240511yescharacteristic
1079C2C31×#241011yescharacteristic
1080C2C31×#241211yescharacteristic
1081C2C31×#241812yes—
1082C2C31×#242412yes—
1083C2C31×#242412yes—
1084C2C31×#247212yes—
1085C2C31×#262211yescharacteristic
1086C2C31×#284911yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC22×C31×#120C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C31C2semidirect
3. C2×C31×#394C2semidirect
4. C2×C31×#386C2semidirect
5. C2×C31×#386C2semidirect
6. C2×C31×#385C2semidirect
7. C2×C31×#379C2semidirect
8. C31×#1440C2semidirect
9. C31×#1439C2semidirect
10. C31×#1438C2semidirect
11. C31×C22⋊#95C2semidirect
21. C22×C4⋊C4×C31C22semidirect
33. C22×C22⋊C4×C31C22semidirect
34. C22×C22⋊C4×C31C22semidirect
40. C2×C31×#95C22semidirect
41. C2×C31×#95C22semidirect
42. C2×C31×#95C22semidirect
43. C2×C31×#95C22semidirect
44. C2×C31×#95C22semidirect
130. C2×C22⋊C4×C31D4semidirect
131. C2×C22⋊C4×C31D4semidirect
289. #14718C31direct (N × H)
455. C23×C22⋊C4C2×C31semidirect
456. C2×#394C2×C31semidirect
457. C2×#386C2×C31semidirect
458. C2×#386C2×C31semidirect
459. C2×#385C2×C31semidirect
460. C2×#379C2×C31semidirect
461. #1440C2×C31semidirect
462. #1439C2×C31semidirect
463. #1438C2×C31semidirect
464. C22⋊#95C2×C31semidirect
509. C22×C31#394semidirect
549. C22×C4⋊C4C22×C31semidirect
561. C22×C22⋊C4C22×C31semidirect
562. C22×C22⋊C4C22×C31semidirect
568. C2×#95C22×C31semidirect
569. C2×#95C22×C31semidirect
570. C2×#95C22×C31semidirect
571. C2×#95C22×C31semidirect
572. C2×#95C22×C31semidirect
673. C2×C22⋊C4D4×C31semidirect
674. C2×C22⋊C4D4×C31semidirect
680. C31#14718direct (N × H)
1041. C22C31×#394semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1202
C23×C22⋊C4×C312
C2×C31×#3942
C2×C31×#3862
C2×C31×#3852
C2×C31×#3792
C31×#14402
C31×#14392
C31×#14382
C31×C22⋊#952
#1471831