Finite Group Databasebeta

← C31×#15267 #21472026

Subgroups — C31×#15267 #21472026

Order 7936.

4234 conjugacy classes of subgroups.

The subgroup lattice has 980 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×#390C212yesmaximal, complemented
6C2×C31×#379C211yesmaximal, characteristic, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1438C212yesmaximal, complemented
9C31×#1437C211yesmaximal, characteristic, 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×C31C2212yescomplemented
19C22×C22⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2212yescomplemented
27C22×C22⋊C4×C31C2212yescomplemented
28C22×C22⋊C4×C31C2212yescomplemented
29C22×C42×C31C2211yescharacteristic, complemented
30C31×#394—28no—
31C31×#392—28no—
32C31×#392—24no—
33C31×#390—28no—
34C31×#379—24no—
35C2×C31×#95C2212yescomplemented
36C2×C31×#95C2211yescharacteristic, complemented
37C2×C31×#95C2212yescomplemented
38C2×C31×#95C2211yescharacteristic, complemented
39C25×C31—24no—
40C25×C31—24no—
41C25×C31—24no—
42C25×C31—22no—
43C25×C31—24no—
44C25×C31—41no—
45C25×C31—41no—
46C25×C31—42no—
47C25×C31—42no—
48C25×C31C2312yes—
49C25×C31C2311yescharacteristic
50C25×C31C2312yes—
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—24no—
61C22×D4×C31—24no—
62C22×D4×C31—24no—
63C22×D4×C31—24no—
64C22×D4×C31—24no—
65C22×D4×C31—24no—
66C22×D4×C31—22no—
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—41no—
75C22×D4×C31—41no—
76C22×D4×C31D418yescomplemented
77C23×C4×C31C2312yes—
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2312yes—
81C23×C4×C31C2312yes—
82C23×C4×C31C2312yes—
83C31×#120—264no—
84C2×C4⋊C4×C31—24no—
85C2×C4⋊C4×C31—24no—
86C2×C4⋊C4×C31—42no—
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—22no—
95C2×C22⋊C4×C31—24no—
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—24no—
106C2×C22⋊C4×C31—24no—
107C2×C22⋊C4×C31—41no—
108C2×C22⋊C4×C31—41no—
109C2×C22⋊C4×C31—42no—
110C2×C22⋊C4×C31—42no—
111C2×C22⋊C4×C31—42no—
112C2×C22⋊C4×C31—42no—
113C2×C22⋊C4×C31D418yescomplemented
114C2×C22⋊C4×C31D418yescomplemented
115C2×C22⋊C4×C31D414yescomplemented
116C2×C42×C31—24no—
117C2×C42×C31—41no—
118C31×#95—22no—
119C31×#95—24no—
120C31×#95—24no—
121C31×#95—41no—
122C24×C31—22no—
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—21no—
132C24×C31—21no—
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—216no—
142C24×C31—28no—
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—48no—
158C24×C31—48no—
159C24×C31—44no—
160C24×C31—48no—
161C24×C31—44no—
162C24×C31—48no—
163C24×C31—48no—
164C24×C31—48no—
165C24×C31—48no—
166C24×C31—48no—
167C24×C31—44no—
168C24×C31—48no—
169C24×C31—48no—
170C24×C31—48no—
171C24×C31—48no—
172C24×C31—44no—
173C24×C31—44no—
174C24×C31—48no—
175C24×C31—44no—
176C24×C31C2×D414yes—
177C24×C31C2×D414yes—
178C24×C31C2×D414yes—
179C24×C31C2×D414yes—
180C24×C31C2×D412yes—
181C24×C31#4114yes—
182C24×C31C2411yescharacteristic
183C2×D4×C31—216no—
184C2×D4×C31—216no—
185C2×D4×C31—216no—
186C2×D4×C31—216no—
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—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—44no—
207C2×D4×C31—48no—
208C2×D4×C31—48no—
209C22×C4×C31—22no—
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—22no—
221C22×C4×C31—22no—
222C22×C4×C31—22no—
223C22×C4×C31—21no—
224C22×C4×C31—22no—
225C22×C4×C31—21no—
226C22×C4×C31—22no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
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—22no—
236C22×C4×C31—22no—
237C22×C4×C31—22no—
238C22×C4×C31—22no—
239C22×C4×C31—22no—
240C22×C4×C31C2×D414yes—
241C22×C4×C31C2×D412yes—
242C22×C4×C31C2×D412yes—
243C22×C4×C31C2×D414yes—
244C22×C4×C31C2×D414yes—
245C22×C4×C31C2×D414yes—
246C22×C4×C31C2×D414yes—
247C4⋊C4×C31—48no—
248C22⋊C4×C31—216no—
249C22⋊C4×C31—216no—
250C22⋊C4×C31—216no—
251C22⋊C4×C31—44no—
252C22⋊C4×C31—48no—
253C22⋊C4×C31—48no—
254C22⋊C4×C31—48no—
255C22⋊C4×C31—48no—
256C22⋊C4×C31—44no—
257C22⋊C4×C31—48no—
258C42×C31—44no—
259#15267C3111yesmaximal, characteristic, direct product factor, Sylow
260C23×C31—24no—
261C23×C31—24no—
262C23×C31—24no—
263C23×C31—22no—
264C23×C31—24no—
265C23×C31—22no—
266C23×C31—24no—
267C23×C31—24no—
268C23×C31—24no—
269C23×C31—24no—
270C23×C31—24no—
271C23×C31—24no—
272C23×C31—24no—
273C23×C31—24no—
274C23×C31—24no—
275C23×C31—24no—
276C23×C31—24no—
277C23×C31—24no—
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—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—432no—
296C23×C31—432no—
297C23×C31—432no—
298C23×C31—432no—
299C23×C31—416no—
300C23×C31—416no—
301C23×C31—432no—
302C23×C31—432no—
303C23×C31—416no—
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—42no—
316C23×C31—41no—
317C23×C31—42no—
318C23×C31—41no—
319C23×C31—42no—
320C23×C31—42no—
321C23×C31—42no—
322C23×C31—42no—
323C23×C31—42no—
324C23×C31—42no—
325C23×C31—42no—
326C23×C31—41no—
327C23×C31—42no—
328C23×C31—41no—
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—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#12118yes—
359C23×C31#12714yes—
360C23×C31C22×D412yes—
361C23×C31C22×D412yes—
362C23×C31C22×D412yes—
363C23×C31C22×D411yescharacteristic
364C23×C31C2×#4112yes—
365C23×C31H(5,𝔽2)11yescharacteristic
366C23×C31H(5,𝔽2)11yescharacteristic
367C23×C31H(5,𝔽2)12yes—
368C23×C31H(5,𝔽2)12yes—
369D4×C31—432no—
370D4×C31—432no—
371D4×C31—432no—
372D4×C31—416no—
373C2×C4×C31—24no—
374C2×C4×C31—24no—
375C2×C4×C31—24no—
376C2×C4×C31—24no—
377C2×C4×C31—24no—
378C2×C4×C31—24no—
379C2×C4×C31—24no—
380C2×C4×C31—24no—
381C2×C4×C31—22no—
382C2×C4×C31—22no—
383C2×C4×C31—24no—
384C2×C4×C31—24no—
385C2×C4×C31—24no—
386C2×C4×C31—24no—
387C2×C4×C31—24no—
388C2×C4×C31—24no—
389C2×C4×C31—42no—
390C2×C4×C31—42no—
391C2×C4×C31—42no—
392C2×C4×C31—42no—
393C2×C4×C31—42no—
394C2×C4×C31—42no—
395C2×C4×C31—41no—
396C2×C4×C31—42no—
397C2×C4×C31—41no—
398C2×C4×C31—42no—
399C2×C4×C31—42no—
400C2×C4×C31—42no—
401C2×C4×C31—41no—
402C2×C4×C31—41no—
403C2×C4×C31—42no—
404C2×C4×C31—42no—
405C2×C4×C31—42no—
406C2×C4×C31—42no—
407C2×C4×C31—42no—
408C2×C4×C31—42no—
409C2×C4×C31—42no—
410C2×C4×C31#12018yescomplemented
411C22×#120C2×C3112yescomplemented
412C2×#394C2×C3112yescomplemented
413C2×#392C2×C3112yescomplemented
414C2×#392C2×C3111yescharacteristic, complemented
415C2×#390C2×C3112yescomplemented
416C2×#379C2×C3111yescharacteristic, complemented
417#1439C2×C3112yescomplemented
418#1438C2×C3112yescomplemented
419#1437C2×C3111yescharacteristic, complemented
420C22×C31—28no—
421C22×C31—28no—
422C22×C31—28no—
423C22×C31—28no—
424C22×C31—24no—
425C22×C31—464no—
426C22×C31—44no—
427C22×C31—44no—
428C22×C31—44no—
429C22×C31—44no—
430C22×C31—42no—
431C22×C31—44no—
432C22×C31—44no—
433C22×C31—44no—
434C22×C31—44no—
435C22×C31—44no—
436C22×C31—44no—
437C22×C31—44no—
438C22×C31—42no—
439C22×C31—44no—
440C22×C31—44no—
441C22×C31—44no—
442C22×C31—44no—
443C22×C31—44no—
444C22×C31—44no—
445C22×C31—44no—
446C22×C31—44no—
447C22×C31—44no—
448C22×C31—44no—
449C22×C31—44no—
450C22×C31—44no—
451C22×C31—44no—
452C22×C31—82no—
453C22×C31—82no—
454C22×C31—82no—
455C22×C31—82no—
456C22×C31—82no—
457C22×C31—82no—
458C22×C31—82no—
459C22×C31—82no—
460C22×C31C2×#12012yes—
461C22×C31C2×#12112yes—
462C22×C31#52511yescharacteristic
463C22×C31C2×#12711yescharacteristic
464C22×C31#53412yes—
465C22×C31#53411yescharacteristic
466C22×C31#53512yes—
467C22×C31#53512yes—
468C22×C31#53812yes—
469C22×C31D4211yescharacteristic
470C22×C31D4212yes—
471C22×C31D4211yescharacteristic
472C22×C31D4212yes—
473C22×C31D4212yes—
474C22×C31D4212yes—
475C22×C31#54612yes—
476C22×C31#54612yes—
477C22×C31#54612yes—
478C22×C31#54612yes—
479C22×C31#56011yescharacteristic
480C22×C31H(3,𝔽4)11yescharacteristic
481C4×C31—28no—
482C4×C31—44no—
483C4×C31—42no—
484C4×C31—42no—
485C4×C31—44no—
486C4×C31—82no—
487C26C22×C3111yescharacteristic
488C23×D4C22×C3112yes—
489C23×D4C22×C3112yes—
490C23×D4C22×C3112yes—
491C23×D4C22×C3111yescharacteristic, complemented
492C2×#120—28no—
493C2×#120—28no—
494C2×#120—28no—
495C22×C4⋊C4C22×C3112yescomplemented
496C22×C22⋊C4C22×C3111yescharacteristic
497C22×C22⋊C4C22×C3112yes—
498C22×C22⋊C4C22×C3112yes—
499C22×C22⋊C4C22×C3112yes—
500C22×C22⋊C4C22×C3112yes—
501C22×C22⋊C4C22×C3112yes—
502C22×C22⋊C4C22×C3111yescharacteristic
503C22×C22⋊C4C22×C3112yescomplemented
504C22×C22⋊C4C22×C3112yescomplemented
505C22×C22⋊C4C22×C3112yescomplemented
506C22×C42C22×C3111yescharacteristic, complemented
507#394—28no—
508#392—28no—
509#392—24no—
510#390—28no—
511#379—24no—
512C2×#95C22×C3112yescomplemented
513C2×#95C22×C3111yescharacteristic, complemented
514C2×#95C22×C3112yescomplemented
515C2×#95C22×C3111yescharacteristic, complemented
516C2×C31—48no—
517C2×C31—44no—
518C2×C31—84no—
519C2×C31#240812yes—
520C2×C31#241012yes—
521C2×C31#242412yes—
522C2×C31#243312yes—
523C2×C31#253911yescharacteristic
524C2×C31#266911yescharacteristic
525C2×C31#267012yes—
526C2×C31#267812yes—
527C2×C31#267911yescharacteristic
528C25—24no—
529C25—24no—
530C25—24no—
531C25—22no—
532C25—24no—
533C25—41no—
534C25—41no—
535C25—42no—
536C25—42no—
537C25C23×C3112yes—
538C25C23×C3111yescharacteristic
539C25C23×C3112yes—
540C22×D4—24no—
541C22×D4—24no—
542C22×D4—24no—
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—24no—
553C22×D4—24no—
554C22×D4—24no—
555C22×D4—22no—
556C22×D4—42no—
557C22×D4—42no—
558C22×D4—42no—
559C22×D4—42no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4—41no—
564C22×D4—41no—
565C22×D4D4×C3118yescomplemented
566C23×C4C23×C3112yes—
567C23×C4C23×C3111yescharacteristic
568C23×C4C23×C3111yescharacteristic
569C23×C4C23×C3112yes—
570C23×C4C23×C3112yes—
571C23×C4C23×C3112yes—
572#120—264no—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—24no—
575C2×C4⋊C4—42no—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—24no—
580C2×C22⋊C4—24no—
581C2×C22⋊C4—24no—
582C2×C22⋊C4—24no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—24no—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—24no—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—24no—
594C2×C22⋊C4—24no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—41no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—42no—
599C2×C22⋊C4—42no—
600C2×C22⋊C4—42no—
601C2×C22⋊C4—42no—
602C2×C22⋊C4D4×C3118yescomplemented
603C2×C22⋊C4D4×C3118yescomplemented
604C2×C22⋊C4D4×C3114yescomplemented
605C2×C42—24no—
606C2×C42—41no—
607#95—22no—
608#95—24no—
609#95—24no—
610#95—41no—
611C31#1526711yescharacteristic, direct product factor, Sylow
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—21no—
622C24—21no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—216no—
632C24—28no—
633C24—22no—
634C24—22no—
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—48no—
648C24—48no—
649C24—44no—
650C24—48no—
651C24—44no—
652C24—48no—
653C24—48no—
654C24—48no—
655C24—48no—
656C24—48no—
657C24—44no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—48no—
662C24—44no—
663C24—44no—
664C24—48no—
665C24—44no—
666C24C2×D4×C3114yes—
667C24C2×D4×C3114yes—
668C24C2×D4×C3114yes—
669C24C2×D4×C3114yes—
670C24C2×D4×C3112yes—
671C24#41×C3114yes—
672C24C24×C3111yescharacteristic
673C2×D4—216no—
674C2×D4—216no—
675C2×D4—216no—
676C2×D4—216no—
677C2×D4—48no—
678C2×D4—48no—
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—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—48no—
691C2×D4—44no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—44no—
697C2×D4—48no—
698C2×D4—48no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—21no—
718C22×C4—21no—
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×C4C2×D4×C3114yes—
731C22×C4C2×D4×C3112yes—
732C22×C4C2×D4×C3112yes—
733C22×C4C2×D4×C3114yes—
734C22×C4C2×D4×C3114yes—
735C22×C4C2×D4×C3114yes—
736C22×C4C2×D4×C3114yes—
737C4⋊C4—48no—
738C22⋊C4—216no—
739C22⋊C4—216no—
740C22⋊C4—216no—
741C22⋊C4—44no—
742C22⋊C4—48no—
743C22⋊C4—48no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C22⋊C4—44no—
747C22⋊C4—48no—
748C42—44no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—22no—
753C23—24no—
754C23—22no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—24no—
764C23—24no—
765C23—24no—
766C23—24no—
767C23—24no—
768C23—24no—
769C23—24no—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—432no—
785C23—432no—
786C23—432no—
787C23—432no—
788C23—416no—
789C23—416no—
790C23—432no—
791C23—432no—
792C23—416no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—41no—
806C23—42no—
807C23—41no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—41no—
816C23—42no—
817C23—41no—
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—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23C31×#12118yes—
848C23C31×#12714yes—
849C23C22×D4×C3112yes—
850C23C22×D4×C3112yes—
851C23C22×D4×C3112yes—
852C23C22×D4×C3111yescharacteristic
853C23C2×#41×C3112yes—
854C23C31×H(5,𝔽2)11yescharacteristic
855C23C31×H(5,𝔽2)11yescharacteristic
856C23C31×H(5,𝔽2)12yes—
857C23C31×H(5,𝔽2)12yes—
858D4—432no—
859D4—432no—
860D4—432no—
861D4—416no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—41no—
885C2×C4—42no—
886C2×C4—41no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4C31×#12018yescomplemented
900C22—28no—
901C22—28no—
902C22—28no—
903C22—28no—
904C22—24no—
905C22—464no—
906C22—44no—
907C22—44no—
908C22—44no—
909C22—44no—
910C22—42no—
911C22—44no—
912C22—44no—
913C22—44no—
914C22—44no—
915C22—44no—
916C22—44no—
917C22—44no—
918C22—42no—
919C22—44no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
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×#12012yes—
941C22C2×C31×#12112yes—
942C22C31×#52511yescharacteristic
943C22C2×C31×#12711yescharacteristic
944C22C31×#53412yes—
945C22C31×#53411yescharacteristic
946C22C31×#53512yes—
947C22C31×#53512yes—
948C22C31×#53812yes—
949C22D42×C3111yescharacteristic
950C22D42×C3112yes—
951C22D42×C3111yescharacteristic
952C22D42×C3112yes—
953C22D42×C3112yes—
954C22D42×C3112yes—
955C22C31×#54612yes—
956C22C31×#54612yes—
957C22C31×#54612yes—
958C22C31×#54612yes—
959C22C31×#56011yescharacteristic
960C22C31×H(3,𝔽4)11yescharacteristic
961C4—28no—
962C4—44no—
963C4—42no—
964C4—42no—
965C4—44no—
966C4—82no—
967C2—48no—
968C2—44no—
969C2—84no—
970C2C31×#240812yes—
971C2C31×#241012yes—
972C2C31×#242412yes—
973C2C31×#243312yes—
974C2C31×#253911yescharacteristic
975C2C31×#266911yescharacteristic
976C2C31×#267012yes—
977C2C31×#267812yes—
978C2C31×#267911yescharacteristic
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×#390C2semidirect
6. C2×C31×#379C2semidirect
7. C31×#1439C2semidirect
8. C31×#1438C2semidirect
9. C31×#1437C2semidirect
14. C23×D4×C31C22semidirect
18. C22×C4⋊C4×C31C22semidirect
26. C22×C22⋊C4×C31C22semidirect
27. C22×C22⋊C4×C31C22semidirect
28. C22×C22⋊C4×C31C22semidirect
29. C22×C42×C31C22semidirect
35. C2×C31×#95C22semidirect
36. C2×C31×#95C22semidirect
37. C2×C31×#95C22semidirect
38. C2×C31×#95C22semidirect
76. C22×D4×C31D4semidirect
113. C2×C22⋊C4×C31D4semidirect
114. C2×C22⋊C4×C31D4semidirect
115. C2×C22⋊C4×C31D4semidirect
259. #15267C31direct (N × H)
410. C2×C4×C31#120semidirect
411. C22×#120C2×C31semidirect
412. C2×#394C2×C31semidirect
413. C2×#392C2×C31semidirect
414. C2×#392C2×C31semidirect
415. C2×#390C2×C31semidirect
416. C2×#379C2×C31semidirect
417. #1439C2×C31semidirect
418. #1438C2×C31semidirect
419. #1437C2×C31semidirect
491. C23×D4C22×C31semidirect
495. C22×C4⋊C4C22×C31semidirect
503. C22×C22⋊C4C22×C31semidirect
504. C22×C22⋊C4C22×C31semidirect
505. C22×C22⋊C4C22×C31semidirect
506. C22×C42C22×C31semidirect
512. C2×#95C22×C31semidirect
513. C2×#95C22×C31semidirect
514. C2×#95C22×C31semidirect
515. C2×#95C22×C31semidirect
565. C22×D4D4×C31semidirect
602. C2×C22⋊C4D4×C31semidirect
603. C2×C22⋊C4D4×C31semidirect
604. C2×C22⋊C4D4×C31semidirect
611. C31#15267direct (N × H)
899. C2×C4C31×#120semidirect

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×#3902
C2×C31×#3792
C31×#14392
C31×#14382
C31×#14372
#1526731