Finite Group Databasebeta

← C31×#14722 #21471481

Subgroups — C31×#14722 #21471481

Order 7936.

3246 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic, complemented
2C22×C4×D4×C31C211yesmaximal, characteristic, complemented
3C2×C31×#394C211yesmaximal, characteristic, complemented
4C2×C31×#392C212yesmaximal, complemented
5C2×C31×#392C211yesmaximal, characteristic, complemented
6C2×C31×#386C212yesmaximal, complemented
7C31×#1441C211yesmaximal, characteristic, complemented
8C31×#1439C211yesmaximal, characteristic, complemented
9C31×#1438C212yesmaximal, complemented
10C31×#1437C212yesmaximal, complemented
11C31×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C23×D4×C31C2212yes—
14C23×D4×C31C2211yescharacteristic
15C23×D4×C31C2212yes—
16C24×C4×C31C2211yescharacteristic
17C24×C4×C31C2211yescharacteristic
18C2×C31×#121—24no—
19C2×C31×#121—28no—
20C2×C4×D4×C31—24no—
21C2×C4×D4×C31—24no—
22C2×C4×D4×C31—24no—
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2212yes—
28C22×C22⋊C4×C31C2212yes—
29C22×C22⋊C4×C31C2212yes—
30C22×C22⋊C4×C31C2212yes—
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2212yes—
33C22×C42×C31C2211yescharacteristic
34C31×#394—24no—
35C31×#392—28no—
36C31×#392—24no—
37C31×#386—28no—
38C2×C31×#95C2211yescharacteristic
39C2×C31×#95C2212yes—
40C2×C31×#95C2211yescharacteristic
41C2×C31×#95C2212yes—
42C2×C31×#95C2212yes—
43C2×C31×#95C2212yes—
44C25×C31C2312yes—
45C25×C31C2311yescharacteristic
46C25×C31C2311yescharacteristic
47C22×D4×C31—22no—
48C22×D4×C31—22no—
49C22×D4×C31—22no—
50C22×D4×C31—22no—
51C22×D4×C31—24no—
52C22×D4×C31—24no—
53C22×D4×C31—24no—
54C22×D4×C31—24no—
55C22×D4×C31—24no—
56C22×D4×C31—24no—
57C22×D4×C31—24no—
58C22×D4×C31—24no—
59C22×D4×C31—24no—
60C22×D4×C31—22no—
61C22×D4×C31—24no—
62C22×D4×C31—22no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—24no—
67C22×D4×C31—42no—
68C22×D4×C31—42no—
69C22×D4×C31—42no—
70C22×D4×C31—42no—
71C22×D4×C31—42no—
72C22×D4×C31D414yescomplemented
73C23×C4×C31—22no—
74C23×C4×C31—22no—
75C23×C4×C31—22no—
76C23×C4×C31—22no—
77C23×C4×C31—22no—
78C23×C4×C31—24no—
79C23×C4×C31—24no—
80C23×C4×C31—42no—
81C23×C4×C31—42no—
82C23×C4×C31D414yescomplemented
83C23×C4×C31C2312yes—
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2312yes—
87C23×C4×C31C2312yes—
88C23×C4×C31C2311yescharacteristic
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C31×#121—232no—
92C4×D4×C31—232no—
93C2×C4⋊C4×C31—22no—
94C2×C4⋊C4×C31—22no—
95C2×C4⋊C4×C31—24no—
96C2×C4⋊C4×C31—22no—
97C2×C4⋊C4×C31D414yescomplemented
98C2×C22⋊C4×C31—22no—
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—22no—
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—24no—
109C2×C22⋊C4×C31—24no—
110C2×C22⋊C4×C31—24no—
111C2×C22⋊C4×C31—24no—
112C2×C22⋊C4×C31—24no—
113C2×C22⋊C4×C31—24no—
114C2×C22⋊C4×C31—24no—
115C2×C22⋊C4×C31—24no—
116C2×C22⋊C4×C31—42no—
117C2×C22⋊C4×C31—42no—
118C2×C22⋊C4×C31—42no—
119C2×C22⋊C4×C31—42no—
120C2×C22⋊C4×C31D414yescomplemented
121C2×C22⋊C4×C31D418yescomplemented
122C2×C42×C31—22no—
123C2×C42×C31—22no—
124C2×C42×C31—22no—
125C31×#95—24no—
126C31×#95—24no—
127C31×#95—22no—
128C31×#95—24no—
129C31×#95—22no—
130C31×#95—42no—
131C24×C31—21no—
132C24×C31—21no—
133C24×C31—21no—
134C24×C31—21no—
135C24×C31—22no—
136C24×C31—22no—
137C24×C31—22no—
138C24×C31—21no—
139C24×C31—21no—
140C24×C31—21no—
141C24×C31—21no—
142C24×C31—22no—
143C24×C31—22no—
144C24×C31—22no—
145C24×C31—22no—
146C24×C31—22no—
147C24×C31—22no—
148C24×C31—22no—
149C24×C31—22no—
150C24×C31—22no—
151C24×C31—22no—
152C24×C31—22no—
153C24×C31—22no—
154C24×C31—22no—
155C24×C31—22no—
156C24×C31—22no—
157C24×C31—22no—
158C24×C31—22no—
159C24×C31—22no—
160C24×C31—22no—
161C24×C31C2×D414yes—
162C24×C31C2×D412yes—
163C24×C31C2×D412yes—
164C24×C31C2×D412yes—
165C24×C31C2×D412yes—
166C24×C31#4112yes—
167C24×C31#4112yes—
168C24×C31C2411yescharacteristic
169C2×D4×C31—28no—
170C2×D4×C31—28no—
171C2×D4×C31—28no—
172C2×D4×C31—28no—
173C2×D4×C31—28no—
174C2×D4×C31—28no—
175C2×D4×C31—28no—
176C2×D4×C31—216no—
177C2×D4×C31—216no—
178C2×D4×C31—28no—
179C2×D4×C31—48no—
180C2×D4×C31—48no—
181C2×D4×C31—48no—
182C2×D4×C31—48no—
183C2×D4×C31—48no—
184C2×D4×C31—48no—
185C2×D4×C31—44no—
186C2×D4×C31—48no—
187C2×D4×C31—48no—
188C2×D4×C31—48no—
189C2×D4×C31—48no—
190C2×D4×C31—48no—
191C2×D4×C31—48no—
192C2×D4×C31—48no—
193C2×D4×C31—48no—
194C2×D4×C31—44no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—22no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—22no—
203C22×C4×C31—22no—
204C22×C4×C31—28no—
205C22×C4×C31—22no—
206C22×C4×C31—22no—
207C22×C4×C31—22no—
208C22×C4×C31—22no—
209C22×C4×C31—22no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
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—22no—
221C22×C4×C31—22no—
222C22×C4×C31—22no—
223C22×C4×C31—22no—
224C22×C4×C31—22no—
225C22×C4×C31—28no—
226C22×C4×C31—28no—
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—44no—
235C22×C4×C31—48no—
236C22×C4×C31—48no—
237C22×C4×C31—48no—
238C22×C4×C31—48no—
239C22×C4×C31—44no—
240C22×C4×C31—44no—
241C22×C4×C31C2×D414yes—
242C22×C4×C31C2×D412yes—
243C22×C4×C31C2×D412yes—
244C22×C4×C31C2×D414yes—
245C22×C4×C31C2×D412yes—
246C22×C4×C31C2×D412yes—
247C22×C4×C31C2×D412yes—
248C22×C4×C31C2×D412yes—
249C22×C4×C31C2×D412yes—
250C22×C4×C31C2×D412yes—
251C22×C4×C31#4114yes—
252C22×C4×C31#4112yes—
253C4⋊C4×C31—28no—
254C4⋊C4×C31—28no—
255C22⋊C4×C31—28no—
256C22⋊C4×C31—28no—
257C22⋊C4×C31—216no—
258C22⋊C4×C31—48no—
259C22⋊C4×C31—48no—
260C22⋊C4×C31—48no—
261C22⋊C4×C31—48no—
262C22⋊C4×C31—48no—
263C42×C31—28no—
264#14722C3111yesmaximal, characteristic, direct product factor, Sylow
265C23×C31—22no—
266C23×C31—22no—
267C23×C31—22no—
268C23×C31—22no—
269C23×C31—22no—
270C23×C31—22no—
271C23×C31—22no—
272C23×C31—22no—
273C23×C31—22no—
274C23×C31—22no—
275C23×C31—22no—
276C23×C31—22no—
277C23×C31—22no—
278C23×C31—24no—
279C23×C31—22no—
280C23×C31—22no—
281C23×C31—22no—
282C23×C31—24no—
283C23×C31—24no—
284C23×C31—24no—
285C23×C31—24no—
286C23×C31—24no—
287C23×C31—24no—
288C23×C31—24no—
289C23×C31—24no—
290C23×C31—24no—
291C23×C31—24no—
292C23×C31—24no—
293C23×C31—24no—
294C23×C31—24no—
295C23×C31—24no—
296C23×C31—24no—
297C23×C31—24no—
298C23×C31—41no—
299C23×C31—42no—
300C23×C31—42no—
301C23×C31—42no—
302C23×C31—41no—
303C23×C31—41no—
304C23×C31—41no—
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—42no—
316C23×C31—42no—
317C23×C31—42no—
318C23×C31—42no—
319C23×C31—42no—
320C23×C31—42no—
321C23×C31—42no—
322C23×C31—42no—
323C23×C31—42no—
324C23×C31—42no—
325C23×C31—42no—
326C23×C31—42no—
327C23×C31—42no—
328C23×C31—42no—
329C23×C31—42no—
330C23×C31—42no—
331C23×C31—42no—
332C23×C31—42no—
333C23×C31—42no—
334C23×C31—42no—
335C23×C31—42no—
336C23×C31—42no—
337C23×C31—42no—
338C23×C31—42no—
339C23×C31—42no—
340C23×C31—42no—
341C23×C31—42no—
342C23×C31—42no—
343C23×C31—42no—
344C23×C31#12114yes—
345C23×C31#12114yescomplemented
346C23×C31C22×D411yescharacteristic
347C23×C31C22×D411yescharacteristic
348C23×C31C22×D411yescharacteristic
349C23×C31C22×D412yes—
350C23×C31C22×D411yescharacteristic
351C23×C31C2×#4111yescharacteristic
352C23×C31C2×#4111yescharacteristic
353C23×C31C2×#4111yescharacteristic
354C23×C31C2×#4112yes—
355C23×C31H(5,𝔽2)12yes—
356C23×C31H(5,𝔽2)12yes—
357D4×C31—232no—
358D4×C31—416no—
359D4×C31—432no—
360D4×C31—432no—
361C2×C4×C31—22no—
362C2×C4×C31—22no—
363C2×C4×C31—22no—
364C2×C4×C31—22no—
365C2×C4×C31—22no—
366C2×C4×C31—22no—
367C2×C4×C31—22no—
368C2×C4×C31—22no—
369C2×C4×C31—22no—
370C2×C4×C31—22no—
371C2×C4×C31—24no—
372C2×C4×C31—24no—
373C2×C4×C31—24no—
374C2×C4×C31—24no—
375C2×C4×C31—22no—
376C2×C4×C31—22no—
377C2×C4×C31—24no—
378C2×C4×C31—24no—
379C2×C4×C31—24no—
380C2×C4×C31—24no—
381C2×C4×C31—24no—
382C2×C4×C31—24no—
383C2×C4×C31—24no—
384C2×C4×C31—24no—
385C2×C4×C31—416no—
386C2×C4×C31—416no—
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—42no—
394C2×C4×C31—42no—
395C2×C4×C31—42no—
396C2×C4×C31—42no—
397C2×C4×C31—42no—
398C2×C4×C31—42no—
399C2×C4×C31—42no—
400C2×C4×C31—42no—
401C2×C4×C31—42no—
402C2×C4×C31—42no—
403C2×C4×C31—42no—
404C2×C4×C31—42no—
405C2×C4×C31—42no—
406C2×C4×C31—42no—
407C2×C4×C31—42no—
408C2×C4×C31#12014yes—
409C2×C4×C31#12014yes—
410C2×C4×C31#12114yescomplemented
411C22×#121C2×C3111yescharacteristic, complemented
412C22×C4×D4C2×C3111yescharacteristic, complemented
413C2×#394C2×C3111yescharacteristic, complemented
414C2×#392C2×C3112yescomplemented
415C2×#392C2×C3111yescharacteristic, complemented
416C2×#386C2×C3112yescomplemented
417#1441C2×C3111yescharacteristic, complemented
418#1439C2×C3111yescharacteristic, complemented
419#1438C2×C3112yescomplemented
420#1437C2×C3112yescomplemented
421C22⋊#95C2×C3111yescharacteristic, complemented
422C22×C31—24no—
423C22×C31—24no—
424C22×C31—24no—
425C22×C31—28no—
426C22×C31—24no—
427C22×C31—42no—
428C22×C31—42no—
429C22×C31—42no—
430C22×C31—42no—
431C22×C31—42no—
432C22×C31—42no—
433C22×C31—42no—
434C22×C31—44no—
435C22×C31—44no—
436C22×C31—44no—
437C22×C31—42no—
438C22×C31—42no—
439C22×C31—44no—
440C22×C31—44no—
441C22×C31—44no—
442C22×C31—44no—
443C22×C31—42no—
444C22×C31—44no—
445C22×C31—44no—
446C22×C31—44no—
447C22×C31—44no—
448C22×C31—44no—
449C22×C31—44no—
450C22×C31—44no—
451C22×C31—82no—
452C22×C31—82no—
453C22×C31—82no—
454C22×C31—82no—
455C22×C31—82no—
456C22×C31—82no—
457C22×C31—82no—
458C22×C31—82no—
459C22×C31C2×#12011yescharacteristic
460C22×C31C2×#12011yescharacteristic
461C22×C31C2×#12111yescharacteristic
462C22×C31C2×#12111yescharacteristic
463C22×C31C2×#12111yescharacteristic
464C22×C31#52511yescharacteristic
465C22×C31#52511yescharacteristic
466C22×C31#52511yescharacteristic
467C22×C31#52512yes—
468C22×C31#53212yes—
469C22×C31#53211yescharacteristic
470C22×C31#53411yescharacteristic
471C22×C31#53511yescharacteristic
472C22×C31#53812yes—
473C22×C31#54012yes—
474C22×C31D4212yes—
475C22×C31D4212yes—
476C22×C31D4212yes—
477C22×C31#54612yes—
478C22×C31#54612yes—
479C22×C31#54612yes—
480C22×C31#55012yes—
481C22×C31#55312yes—
482C4×C31—24no—
483C4×C31—24no—
484C4×C31—24no—
485C4×C31—42no—
486C4×C31—44no—
487C4×C31—44no—
488C4×C31—42no—
489C4×C31—82no—
490C23×D4C22×C3111yescharacteristic
491C23×D4C22×C3112yes—
492C23×D4C22×C3111yescharacteristic
493C23×D4C22×C3112yes—
494C24×C4C22×C3111yescharacteristic
495C24×C4C22×C3111yescharacteristic
496C2×#121—24no—
497C2×#121—28no—
498C2×C4×D4—24no—
499C2×C4×D4—24no—
500C2×C4×D4—24no—
501C22×C4⋊C4C22×C3111yescharacteristic
502C22×C4⋊C4C22×C3111yescharacteristic
503C22×C22⋊C4C22×C3112yes—
504C22×C22⋊C4C22×C3111yescharacteristic
505C22×C22⋊C4C22×C3112yes—
506C22×C22⋊C4C22×C3112yes—
507C22×C22⋊C4C22×C3112yes—
508C22×C22⋊C4C22×C3112yes—
509C22×C22⋊C4C22×C3111yescharacteristic
510C22×C22⋊C4C22×C3112yes—
511C22×C42C22×C3111yescharacteristic
512#394—24no—
513#392—28no—
514#392—24no—
515#386—28no—
516C2×#95C22×C3111yescharacteristic
517C2×#95C22×C3112yes—
518C2×#95C22×C3111yescharacteristic
519C2×#95C22×C3112yes—
520C2×#95C22×C3112yes—
521C2×#95C22×C3112yes—
522C2×C31—44no—
523C2×C31—44no—
524C2×C31—84no—
525C2×C31#238811yescharacteristic
526C2×C31#240311yescharacteristic
527C2×C31#240811yescharacteristic
528C2×C31#242412yes—
529C2×C31#242812yes—
530C2×C31#243111yescharacteristic
531C2×C31#245612yes—
532C2×C31#246412yes—
533C2×C31#254311yescharacteristic
534C2×C31#263511yescharacteristic
535C2×C31#284711yescharacteristic
536C25C23×C3112yes—
537C25C23×C3111yescharacteristic
538C25C23×C3111yescharacteristic
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—24no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—22no—
553C22×D4—24no—
554C22×D4—22no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—24no—
559C22×D4—42no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4—42no—
564C22×D4D4×C3114yescomplemented
565C23×C4—22no—
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—24no—
571C23×C4—24no—
572C23×C4—42no—
573C23×C4—42no—
574C23×C4D4×C3114yescomplemented
575C23×C4C23×C3112yes—
576C23×C4C23×C3111yescharacteristic
577C23×C4C23×C3111yescharacteristic
578C23×C4C23×C3112yes—
579C23×C4C23×C3112yes—
580C23×C4C23×C3111yescharacteristic
581C23×C4C23×C3111yescharacteristic
582C23×C4C23×C3111yescharacteristic
583#121—232no—
584C4×D4—232no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—24no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4D4×C3114yescomplemented
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—42no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4D4×C3114yescomplemented
613C2×C22⋊C4D4×C3118yescomplemented
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—22no—
617#95—24no—
618#95—24no—
619#95—22no—
620#95—24no—
621#95—22no—
622#95—42no—
623C31#1472211yescharacteristic, direct product factor, Sylow
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24C2×D4×C3114yes—
655C24C2×D4×C3112yes—
656C24C2×D4×C3112yes—
657C24C2×D4×C3112yes—
658C24C2×D4×C3112yes—
659C24#41×C3112yes—
660C24#41×C3112yes—
661C24C24×C3111yescharacteristic
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—44no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—28no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—48no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4C2×D4×C3114yes—
735C22×C4C2×D4×C3112yes—
736C22×C4C2×D4×C3112yes—
737C22×C4C2×D4×C3114yes—
738C22×C4C2×D4×C3112yes—
739C22×C4C2×D4×C3112yes—
740C22×C4C2×D4×C3112yes—
741C22×C4C2×D4×C3112yes—
742C22×C4C2×D4×C3112yes—
743C22×C4C2×D4×C3112yes—
744C22×C4#41×C3114yes—
745C22×C4#41×C3112yes—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C22⋊C4—28no—
749C22⋊C4—28no—
750C22⋊C4—216no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C42—28no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—24no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—41no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23C31×#12114yes—
837C23C31×#12114yescomplemented
838C23C22×D4×C3111yescharacteristic
839C23C22×D4×C3111yescharacteristic
840C23C22×D4×C3111yescharacteristic
841C23C22×D4×C3112yes—
842C23C22×D4×C3111yescharacteristic
843C23C2×#41×C3111yescharacteristic
844C23C2×#41×C3111yescharacteristic
845C23C2×#41×C3111yescharacteristic
846C23C2×#41×C3112yes—
847C23C31×H(5,𝔽2)12yes—
848C23C31×H(5,𝔽2)12yes—
849D4—232no—
850D4—416no—
851D4—432no—
852D4—432no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4C31×#12014yes—
901C2×C4C31×#12014yes—
902C2×C4C31×#12114yescomplemented
903C22—24no—
904C22—24no—
905C22—24no—
906C22—28no—
907C22—24no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—44no—
916C22—44no—
917C22—44no—
918C22—42no—
919C22—42no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—42no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C2×C31×#12011yescharacteristic
941C22C2×C31×#12011yescharacteristic
942C22C2×C31×#12111yescharacteristic
943C22C2×C31×#12111yescharacteristic
944C22C2×C31×#12111yescharacteristic
945C22C31×#52511yescharacteristic
946C22C31×#52511yescharacteristic
947C22C31×#52511yescharacteristic
948C22C31×#52512yes—
949C22C31×#53212yes—
950C22C31×#53211yescharacteristic
951C22C31×#53411yescharacteristic
952C22C31×#53511yescharacteristic
953C22C31×#53812yes—
954C22C31×#54012yes—
955C22D42×C3112yes—
956C22D42×C3112yes—
957C22D42×C3112yes—
958C22C31×#54612yes—
959C22C31×#54612yes—
960C22C31×#54612yes—
961C22C31×#55012yes—
962C22C31×#55312yes—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—44no—
968C4—44no—
969C4—42no—
970C4—82no—
971C2—44no—
972C2—44no—
973C2—84no—
974C2C31×#238811yescharacteristic
975C2C31×#240311yescharacteristic
976C2C31×#240811yescharacteristic
977C2C31×#242412yes—
978C2C31×#242812yes—
979C2C31×#243111yescharacteristic
980C2C31×#245612yes—
981C2C31×#246412yes—
982C2C31×#254311yescharacteristic
983C2C31×#263511yescharacteristic
984C2C31×#284711yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#121C2semidirect
2. C22×C4×D4×C31C2semidirect
3. C2×C31×#394C2semidirect
4. C2×C31×#392C2semidirect
5. C2×C31×#392C2semidirect
6. C2×C31×#386C2semidirect
7. C31×#1441C2semidirect
8. C31×#1439C2semidirect
9. C31×#1438C2semidirect
10. C31×#1437C2semidirect
11. C31×C22⋊#95C2semidirect
72. C22×D4×C31D4semidirect
82. C23×C4×C31D4semidirect
97. C2×C4⋊C4×C31D4semidirect
120. C2×C22⋊C4×C31D4semidirect
121. C2×C22⋊C4×C31D4semidirect
264. #14722C31direct (N × H)
345. C23×C31#121semidirect
410. C2×C4×C31#121semidirect
411. C22×#121C2×C31semidirect
412. C22×C4×D4C2×C31semidirect
413. C2×#394C2×C31semidirect
414. C2×#392C2×C31semidirect
415. C2×#392C2×C31semidirect
416. C2×#386C2×C31semidirect
417. #1441C2×C31semidirect
418. #1439C2×C31semidirect
419. #1438C2×C31semidirect
420. #1437C2×C31semidirect
421. C22⋊#95C2×C31semidirect
564. C22×D4D4×C31semidirect
574. C23×C4D4×C31semidirect
589. C2×C4⋊C4D4×C31semidirect
612. C2×C22⋊C4D4×C31semidirect
613. C2×C22⋊C4D4×C31semidirect
623. C31#14722direct (N × H)
837. C23C31×#121semidirect
902. C2×C4C31×#121semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C22×C4×D4×C312
C2×C31×#3942
C2×C31×#3922
C2×C31×#3862
C31×#14412
C31×#14392
C31×#14382
C31×#14372
C31×C22⋊#952
#1472231