Finite Group Databasebeta

← C31×#16249 #21473008

Subgroups — C31×#16249 #21473008

Order 7936.

4102 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#120C212yesmaximal, complemented
2C2×C31×#394C212yesmaximal, complemented
3C2×C31×#392C212yesmaximal, complemented
4C2×C31×#392C211yesmaximal, characteristic, complemented
5C2×C31×#379C211yesmaximal, characteristic, complemented
6C31×#1440C212yesmaximal, complemented
7C31×#1439C211yesmaximal, characteristic, complemented
8C31×#1438C212yesmaximal, complemented
9C31×#1438C212yesmaximal, complemented
10C26×C31C2211yescharacteristic
11C23×D4×C31C2212yes—
12C23×D4×C31C2212yes—
13C23×D4×C31C2212yes—
14C23×D4×C31C2211yescharacteristic, complemented
15C2×C31×#120—28no—
16C2×C31×#120—28no—
17C2×C31×#120—28no—
18C22×C4⋊C4×C31C2211yescharacteristic, complemented
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2212yescomplemented
27C22×C22⋊C4×C31C2212yescomplemented
28C22×C22⋊C4×C31C2212yescomplemented
29C31×#394—28no—
30C31×#392—28no—
31C31×#392—24no—
32C31×#379—24no—
33C2×C31×#95C2212yescomplemented
34C2×C31×#95C2211yescharacteristic, complemented
35C2×C31×#95C2212yescomplemented
36C2×C31×#95C2211yescharacteristic, complemented
37C2×C31×#95C2212yescomplemented
38C25×C31—24no—
39C25×C31—24no—
40C25×C31—22no—
41C25×C31—22no—
42C25×C31—41no—
43C25×C31—41no—
44C25×C31—42no—
45C25×C31—42no—
46C25×C31—41no—
47C25×C31—41no—
48C25×C31D414yescomplemented
49C25×C31C2312yes—
50C25×C31C2312yes—
51C25×C31C2311yescharacteristic
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—24no—
61C22×D4×C31—24no—
62C22×D4×C31—24no—
63C22×D4×C31—24no—
64C22×D4×C31—24no—
65C22×D4×C31—22no—
66C22×D4×C31—42no—
67C22×D4×C31—42no—
68C22×D4×C31—42no—
69C22×D4×C31—42no—
70C22×D4×C31—42no—
71C22×D4×C31—42no—
72C22×D4×C31—42no—
73C22×D4×C31—42no—
74C22×D4×C31—42no—
75C22×D4×C31—41no—
76C22×D4×C31—41no—
77C22×D4×C31D418yescomplemented
78C23×C4×C31C2312yes—
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2312yes—
82C23×C4×C31C2312yes—
83C23×C4×C31C2312yes—
84C31×#120—264no—
85C2×C4⋊C4×C31—24no—
86C2×C4⋊C4×C31—41no—
87C2×C22⋊C4×C31—24no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—24no—
91C2×C22⋊C4×C31—24no—
92C2×C22⋊C4×C31—24no—
93C2×C22⋊C4×C31—24no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—24no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—24no—
99C2×C22⋊C4×C31—24no—
100C2×C22⋊C4×C31—24no—
101C2×C22⋊C4×C31—24no—
102C2×C22⋊C4×C31—24no—
103C2×C22⋊C4×C31—24no—
104C2×C22⋊C4×C31—24no—
105C2×C22⋊C4×C31—41no—
106C2×C22⋊C4×C31—41no—
107C2×C22⋊C4×C31—42no—
108C2×C22⋊C4×C31—42no—
109C2×C22⋊C4×C31—41no—
110C2×C22⋊C4×C31—41no—
111C2×C22⋊C4×C31—42no—
112C2×C22⋊C4×C31—42no—
113C2×C22⋊C4×C31—42no—
114C2×C22⋊C4×C31—42no—
115C2×C22⋊C4×C31D418yescomplemented
116C2×C22⋊C4×C31D414yescomplemented
117C31×#95—24no—
118C31×#95—22no—
119C31×#95—24no—
120C31×#95—41no—
121C31×#95—42no—
122C24×C31—22no—
123C24×C31—22no—
124C24×C31—22no—
125C24×C31—22no—
126C24×C31—22no—
127C24×C31—22no—
128C24×C31—21no—
129C24×C31—21no—
130C24×C31—21no—
131C24×C31—21no—
132C24×C31—22no—
133C24×C31—22no—
134C24×C31—22no—
135C24×C31—22no—
136C24×C31—22no—
137C24×C31—22no—
138C24×C31—22no—
139C24×C31—22no—
140C24×C31—22no—
141C24×C31—22no—
142C24×C31—216no—
143C24×C31—28no—
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—48no—
159C24×C31—44no—
160C24×C31—44no—
161C24×C31—48no—
162C24×C31—48no—
163C24×C31—44no—
164C24×C31—44no—
165C24×C31—48no—
166C24×C31—48no—
167C24×C31—48no—
168C24×C31—44no—
169C24×C31—48no—
170C24×C31—48no—
171C24×C31—44no—
172C24×C31—48no—
173C24×C31—48no—
174C24×C31—44no—
175C24×C31—44no—
176C24×C31—44no—
177C24×C31—48no—
178C24×C31—44no—
179C24×C31C2×D414yes—
180C24×C31C2×D414yes—
181C24×C31C2×D414yes—
182C24×C31C2×D414yes—
183C24×C31C2×D412yes—
184C24×C31C2×D412yes—
185C24×C31#4112yes—
186C24×C31C2411yescharacteristic
187C2×D4×C31—216no—
188C2×D4×C31—216no—
189C2×D4×C31—216no—
190C2×D4×C31—48no—
191C2×D4×C31—48no—
192C2×D4×C31—48no—
193C2×D4×C31—48no—
194C2×D4×C31—48no—
195C2×D4×C31—48no—
196C2×D4×C31—48no—
197C2×D4×C31—44no—
198C2×D4×C31—48no—
199C2×D4×C31—48no—
200C2×D4×C31—48no—
201C2×D4×C31—44no—
202C2×D4×C31—48no—
203C2×D4×C31—48no—
204C2×D4×C31—48no—
205C2×D4×C31—48no—
206C2×D4×C31—48no—
207C2×D4×C31—48no—
208C2×D4×C31—48no—
209C2×D4×C31—48no—
210C2×D4×C31—44no—
211C2×D4×C31—48no—
212C2×D4×C31—48no—
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—22no—
221C22×C4×C31—22no—
222C22×C4×C31—22no—
223C22×C4×C31—22no—
224C22×C4×C31—22no—
225C22×C4×C31—21no—
226C22×C4×C31—22no—
227C22×C4×C31—22no—
228C22×C4×C31—22no—
229C22×C4×C31—22no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—22no—
233C22×C4×C31—22no—
234C22×C4×C31—21no—
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×C31C2×D414yes—
247C22×C4×C31C2×D414yes—
248C22×C4×C31C2×D412yes—
249C22×C4×C31C2×D412yes—
250C22×C4×C31C2×D414yes—
251C4⋊C4×C31—44no—
252C22⋊C4×C31—216no—
253C22⋊C4×C31—216no—
254C22⋊C4×C31—216no—
255C22⋊C4×C31—44no—
256C22⋊C4×C31—48no—
257C22⋊C4×C31—48no—
258C22⋊C4×C31—48no—
259C22⋊C4×C31—48no—
260C22⋊C4×C31—48no—
261C22⋊C4×C31—44no—
262#16249C3111yesmaximal, characteristic, direct product factor, Sylow
263C23×C31—24no—
264C23×C31—24no—
265C23×C31—24no—
266C23×C31—22no—
267C23×C31—24no—
268C23×C31—24no—
269C23×C31—24no—
270C23×C31—24no—
271C23×C31—24no—
272C23×C31—24no—
273C23×C31—22no—
274C23×C31—22no—
275C23×C31—24no—
276C23×C31—22no—
277C23×C31—24no—
278C23×C31—24no—
279C23×C31—22no—
280C23×C31—22no—
281C23×C31—24no—
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—24no—
299C23×C31—24no—
300C23×C31—416no—
301C23×C31—432no—
302C23×C31—432no—
303C23×C31—416no—
304C23×C31—416no—
305C23×C31—416no—
306C23×C31—432no—
307C23×C31—416no—
308C23×C31—432no—
309C23×C31—416no—
310C23×C31—416no—
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—41no—
324C23×C31—41no—
325C23×C31—42no—
326C23×C31—42no—
327C23×C31—42no—
328C23×C31—42no—
329C23×C31—42no—
330C23×C31—42no—
331C23×C31—41no—
332C23×C31—42no—
333C23×C31—42no—
334C23×C31—42no—
335C23×C31—42no—
336C23×C31—41no—
337C23×C31—42no—
338C23×C31—42no—
339C23×C31—42no—
340C23×C31—42no—
341C23×C31—42no—
342C23×C31—42no—
343C23×C31—42no—
344C23×C31—42no—
345C23×C31—42no—
346C23×C31—42no—
347C23×C31—42no—
348C23×C31—42no—
349C23×C31—42no—
350C23×C31—42no—
351C23×C31—42no—
352C23×C31—42no—
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#12018yes—
366C23×C31#12114yes—
367C23×C31C22×D411yescharacteristic
368C23×C31C22×D412yes—
369C23×C31C22×D412yes—
370C23×C31C22×D411yescharacteristic
371C23×C31C2×#4111yescharacteristic
372C23×C31H(5,𝔽2)11yescharacteristic
373C23×C31H(5,𝔽2)11yescharacteristic
374C23×C31H(5,𝔽2)12yes—
375C23×C31H(5,𝔽2)12yes—
376C23×C31H(5,𝔽2)11yescharacteristic
377C23×C31H(5,𝔽2)11yescharacteristic
378D4×C31—432no—
379D4×C31—432no—
380D4×C31—432no—
381D4×C31—416no—
382C2×C4×C31—24no—
383C2×C4×C31—24no—
384C2×C4×C31—24no—
385C2×C4×C31—22no—
386C2×C4×C31—24no—
387C2×C4×C31—22no—
388C2×C4×C31—24no—
389C2×C4×C31—24no—
390C2×C4×C31—24no—
391C2×C4×C31—24no—
392C2×C4×C31—24no—
393C2×C4×C31—24no—
394C2×C4×C31—24no—
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—41no—
406C2×C4×C31—42no—
407C2×C4×C31—42no—
408C2×C4×C31—42no—
409C2×C4×C31—41no—
410C2×C4×C31—42no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—42no—
414C2×C4×C31—42no—
415C2×C4×C31—42no—
416C2×C4×C31—42no—
417C2×C4×C31—42no—
418C2×C4×C31—42no—
419C2×C4×C31—42no—
420C22×#120C2×C3112yescomplemented
421C2×#394C2×C3112yescomplemented
422C2×#392C2×C3112yescomplemented
423C2×#392C2×C3111yescharacteristic, complemented
424C2×#379C2×C3111yescharacteristic, complemented
425#1440C2×C3112yescomplemented
426#1439C2×C3111yescharacteristic, complemented
427#1438C2×C3112yescomplemented
428#1438C2×C3112yescomplemented
429C22×C31—28no—
430C22×C31—24no—
431C22×C31—28no—
432C22×C31—28no—
433C22×C31—28no—
434C22×C31—464no—
435C22×C31—44no—
436C22×C31—44no—
437C22×C31—44no—
438C22×C31—42no—
439C22×C31—44no—
440C22×C31—44no—
441C22×C31—42no—
442C22×C31—42no—
443C22×C31—44no—
444C22×C31—44no—
445C22×C31—44no—
446C22×C31—44no—
447C22×C31—44no—
448C22×C31—42no—
449C22×C31—44no—
450C22×C31—44no—
451C22×C31—44no—
452C22×C31—42no—
453C22×C31—44no—
454C22×C31—44no—
455C22×C31—42no—
456C22×C31—44no—
457C22×C31—44no—
458C22×C31—44no—
459C22×C31—44no—
460C22×C31—44no—
461C22×C31—44no—
462C22×C31—44no—
463C22×C31—82no—
464C22×C31—82no—
465C22×C31—82no—
466C22×C31—82no—
467C22×C31—82no—
468C22×C31—82no—
469C22×C31—82no—
470C22×C31—82no—
471C22×C31C2×#12012yes—
472C22×C31C2×#12111yescharacteristic
473C22×C31#53411yescharacteristic
474C22×C31#53412yes—
475C22×C31#53412yes—
476C22×C31#53412yes—
477C22×C31#53411yescharacteristic
478C22×C31#53411yescharacteristic
479C22×C31#53512yes—
480C22×C31#53512yes—
481C22×C31#53511yescharacteristic
482C22×C31#53811yescharacteristic
483C22×C31#53811yescharacteristic
484C22×C31D4211yescharacteristic
485C22×C31D4211yescharacteristic
486C22×C31D4212yes—
487C22×C31D4212yes—
488C22×C31D4212yes—
489C22×C31#54612yes—
490C22×C31#54612yes—
491C22×C31#56011yescharacteristic
492C22×C31#56012yes—
493C22×C31H(3,𝔽4)11yescharacteristic
494C4×C31—44no—
495C4×C31—44no—
496C4×C31—44no—
497C4×C31—42no—
498C4×C31—42no—
499C4×C31—82no—
500C26C22×C3111yescharacteristic
501C23×D4C22×C3112yes—
502C23×D4C22×C3112yes—
503C23×D4C22×C3112yes—
504C23×D4C22×C3111yescharacteristic, complemented
505C2×#120—28no—
506C2×#120—28no—
507C2×#120—28no—
508C22×C4⋊C4C22×C3111yescharacteristic, complemented
509C22×C22⋊C4C22×C3112yes—
510C22×C22⋊C4C22×C3112yes—
511C22×C22⋊C4C22×C3112yes—
512C22×C22⋊C4C22×C3112yes—
513C22×C22⋊C4C22×C3112yes—
514C22×C22⋊C4C22×C3111yescharacteristic
515C22×C22⋊C4C22×C3111yescharacteristic
516C22×C22⋊C4C22×C3112yescomplemented
517C22×C22⋊C4C22×C3112yescomplemented
518C22×C22⋊C4C22×C3112yescomplemented
519#394—28no—
520#392—28no—
521#392—24no—
522#379—24no—
523C2×#95C22×C3112yescomplemented
524C2×#95C22×C3111yescharacteristic, complemented
525C2×#95C22×C3112yescomplemented
526C2×#95C22×C3111yescharacteristic, complemented
527C2×#95C22×C3112yescomplemented
528C2×C31—48no—
529C2×C31—44no—
530C2×C31—84no—
531C2×C31#240311yescharacteristic
532C2×C31#241012yes—
533C2×C31#261312yes—
534C2×C31#261711yescharacteristic
535C2×C31#266811yescharacteristic
536C2×C31#266911yescharacteristic
537C2×C31#266912yes—
538C2×C31#267011yescharacteristic
539C2×C31#267812yes—
540C2×C31#267911yescharacteristic
541C2×C31#281211yescharacteristic
542C25—24no—
543C25—24no—
544C25—22no—
545C25—22no—
546C25—41no—
547C25—41no—
548C25—42no—
549C25—42no—
550C25—41no—
551C25—41no—
552C25D4×C3114yescomplemented
553C25C23×C3112yes—
554C25C23×C3112yes—
555C25C23×C3111yescharacteristic
556C22×D4—24no—
557C22×D4—24no—
558C22×D4—24no—
559C22×D4—24no—
560C22×D4—24no—
561C22×D4—24no—
562C22×D4—24no—
563C22×D4—24no—
564C22×D4—24no—
565C22×D4—24no—
566C22×D4—24no—
567C22×D4—24no—
568C22×D4—24no—
569C22×D4—22no—
570C22×D4—42no—
571C22×D4—42no—
572C22×D4—42no—
573C22×D4—42no—
574C22×D4—42no—
575C22×D4—42no—
576C22×D4—42no—
577C22×D4—42no—
578C22×D4—42no—
579C22×D4—41no—
580C22×D4—41no—
581C22×D4D4×C3118yescomplemented
582C23×C4C23×C3112yes—
583C23×C4C23×C3111yescharacteristic
584C23×C4C23×C3111yescharacteristic
585C23×C4C23×C3112yes—
586C23×C4C23×C3112yes—
587C23×C4C23×C3112yes—
588#120—264no—
589C2×C4⋊C4—24no—
590C2×C4⋊C4—41no—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—24no—
594C2×C22⋊C4—24no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—22no—
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—24no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4—41no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4—42no—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—42no—
616C2×C22⋊C4—42no—
617C2×C22⋊C4—42no—
618C2×C22⋊C4—42no—
619C2×C22⋊C4D4×C3118yescomplemented
620C2×C22⋊C4D4×C3114yescomplemented
621#95—24no—
622#95—22no—
623#95—24no—
624#95—41no—
625#95—42no—
626C31#1624911yescharacteristic, direct product factor, Sylow
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—216no—
648C24—28no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—48no—
664C24—44no—
665C24—44no—
666C24—48no—
667C24—48no—
668C24—44no—
669C24—44no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—44no—
674C24—48no—
675C24—48no—
676C24—44no—
677C24—48no—
678C24—48no—
679C24—44no—
680C24—44no—
681C24—44no—
682C24—48no—
683C24—44no—
684C24C2×D4×C3114yes—
685C24C2×D4×C3114yes—
686C24C2×D4×C3114yes—
687C24C2×D4×C3114yes—
688C24C2×D4×C3112yes—
689C24C2×D4×C3112yes—
690C24#41×C3112yes—
691C24C24×C3111yescharacteristic
692C2×D4—216no—
693C2×D4—216no—
694C2×D4—216no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—44no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—44no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—44no—
716C2×D4—48no—
717C2×D4—48no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—21no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4C2×D4×C3114yes—
752C22×C4C2×D4×C3114yes—
753C22×C4C2×D4×C3112yes—
754C22×C4C2×D4×C3112yes—
755C22×C4C2×D4×C3114yes—
756C4⋊C4—44no—
757C22⋊C4—216no—
758C22⋊C4—216no—
759C22⋊C4—216no—
760C22⋊C4—44no—
761C22⋊C4—48no—
762C22⋊C4—48no—
763C22⋊C4—48no—
764C22⋊C4—48no—
765C22⋊C4—48no—
766C22⋊C4—44no—
767C23—24no—
768C23—24no—
769C23—24no—
770C23—22no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—22no—
778C23—22no—
779C23—24no—
780C23—22no—
781C23—24no—
782C23—24no—
783C23—22no—
784C23—22no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—24no—
791C23—24no—
792C23—24no—
793C23—24no—
794C23—24no—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—416no—
805C23—432no—
806C23—432no—
807C23—416no—
808C23—416no—
809C23—416no—
810C23—432no—
811C23—416no—
812C23—432no—
813C23—416no—
814C23—416no—
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—41no—
828C23—41no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—41no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—41no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23C31×#12018yes—
870C23C31×#12114yes—
871C23C22×D4×C3111yescharacteristic
872C23C22×D4×C3112yes—
873C23C22×D4×C3112yes—
874C23C22×D4×C3111yescharacteristic
875C23C2×#41×C3111yescharacteristic
876C23C31×H(5,𝔽2)11yescharacteristic
877C23C31×H(5,𝔽2)11yescharacteristic
878C23C31×H(5,𝔽2)12yes—
879C23C31×H(5,𝔽2)12yes—
880C23C31×H(5,𝔽2)11yescharacteristic
881C23C31×H(5,𝔽2)11yescharacteristic
882D4—432no—
883D4—432no—
884D4—432no—
885D4—416no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—22no—
890C2×C4—24no—
891C2×C4—22no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—41no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—41no—
914C2×C4—42no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C22—28no—
925C22—24no—
926C22—28no—
927C22—28no—
928C22—28no—
929C22—464no—
930C22—44no—
931C22—44no—
932C22—44no—
933C22—42no—
934C22—44no—
935C22—44no—
936C22—42no—
937C22—42no—
938C22—44no—
939C22—44no—
940C22—44no—
941C22—44no—
942C22—44no—
943C22—42no—
944C22—44no—
945C22—44no—
946C22—44no—
947C22—42no—
948C22—44no—
949C22—44no—
950C22—42no—
951C22—44no—
952C22—44no—
953C22—44no—
954C22—44no—
955C22—44no—
956C22—44no—
957C22—44no—
958C22—82no—
959C22—82no—
960C22—82no—
961C22—82no—
962C22—82no—
963C22—82no—
964C22—82no—
965C22—82no—
966C22C2×C31×#12012yes—
967C22C2×C31×#12111yescharacteristic
968C22C31×#53411yescharacteristic
969C22C31×#53412yes—
970C22C31×#53412yes—
971C22C31×#53412yes—
972C22C31×#53411yescharacteristic
973C22C31×#53411yescharacteristic
974C22C31×#53512yes—
975C22C31×#53512yes—
976C22C31×#53511yescharacteristic
977C22C31×#53811yescharacteristic
978C22C31×#53811yescharacteristic
979C22D42×C3111yescharacteristic
980C22D42×C3111yescharacteristic
981C22D42×C3112yes—
982C22D42×C3112yes—
983C22D42×C3112yes—
984C22C31×#54612yes—
985C22C31×#54612yes—
986C22C31×#56011yescharacteristic
987C22C31×#56012yes—
988C22C31×H(3,𝔽4)11yescharacteristic
989C4—44no—
990C4—44no—
991C4—44no—
992C4—42no—
993C4—42no—
994C4—82no—
995C2—48no—
996C2—44no—
997C2—84no—
998C2C31×#240311yescharacteristic
999C2C31×#241012yes—
1000C2C31×#261312yes—
1001C2C31×#261711yescharacteristic
1002C2C31×#266811yescharacteristic
1003C2C31×#266911yescharacteristic
1004C2C31×#266912yes—
1005C2C31×#267011yescharacteristic
1006C2C31×#267812yes—
1007C2C31×#267911yescharacteristic
1008C2C31×#281211yescharacteristic
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×#120C2semidirect
2. C2×C31×#394C2semidirect
3. C2×C31×#392C2semidirect
4. C2×C31×#392C2semidirect
5. C2×C31×#379C2semidirect
6. C31×#1440C2semidirect
7. C31×#1439C2semidirect
8. C31×#1438C2semidirect
9. C31×#1438C2semidirect
14. C23×D4×C31C22semidirect
18. C22×C4⋊C4×C31C22semidirect
26. C22×C22⋊C4×C31C22semidirect
27. C22×C22⋊C4×C31C22semidirect
28. C22×C22⋊C4×C31C22semidirect
33. C2×C31×#95C22semidirect
34. C2×C31×#95C22semidirect
35. C2×C31×#95C22semidirect
36. C2×C31×#95C22semidirect
37. C2×C31×#95C22semidirect
48. C25×C31D4semidirect
77. C22×D4×C31D4semidirect
115. C2×C22⋊C4×C31D4semidirect
116. C2×C22⋊C4×C31D4semidirect
262. #16249C31direct (N × H)
420. C22×#120C2×C31semidirect
421. C2×#394C2×C31semidirect
422. C2×#392C2×C31semidirect
423. C2×#392C2×C31semidirect
424. C2×#379C2×C31semidirect
425. #1440C2×C31semidirect
426. #1439C2×C31semidirect
427. #1438C2×C31semidirect
428. #1438C2×C31semidirect
504. C23×D4C22×C31semidirect
508. C22×C4⋊C4C22×C31semidirect
516. C22×C22⋊C4C22×C31semidirect
517. C22×C22⋊C4C22×C31semidirect
518. C22×C22⋊C4C22×C31semidirect
523. C2×#95C22×C31semidirect
524. C2×#95C22×C31semidirect
525. C2×#95C22×C31semidirect
526. C2×#95C22×C31semidirect
527. C2×#95C22×C31semidirect
552. C25D4×C31semidirect
581. C22×D4D4×C31semidirect
619. C2×C22⋊C4D4×C31semidirect
620. C2×C22⋊C4D4×C31semidirect
626. C31#16249direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1202
C2×C31×#3942
C2×C31×#3922
C2×C31×#3792
C31×#14402
C31×#14392
C31×#14382
#1624931