Finite Group Databasebeta

← C31×#14747 #21471506

Subgroups — C31×#14747 #21471506

Order 7936.

2730 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic
2C2×C31×#394C211yesmaximal, characteristic, complemented
3C2×C31×#386C212yesmaximal, complemented
4C2×C31×#386C212yesmaximal, complemented
5C2×C31×#385C211yesmaximal, characteristic, complemented
6C22×C31×#95C211yesmaximal, characteristic, complemented
7C31×#1442C211yesmaximal, characteristic, complemented
8C31×#1441C211yesmaximal, characteristic, complemented
9C31×#1440C212yesmaximal, complemented
10C31×#1439C212yesmaximal, complemented
11C31×#1438C211yesmaximal, characteristic, complemented
12C23×D4×C31C2212yes—
13C23×D4×C31C2211yescharacteristic
14C24×C4×C31C2212yes—
15C24×C4×C31C2211yescharacteristic
16C2×C31×#121—28no—
17C2×C31×#121—24no—
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2212yes—
27C22×C22⋊C4×C31C2211yescharacteristic
28C31×#394—24no—
29C31×#386—28no—
30C31×#386—28no—
31C31×#385—24no—
32C2×C31×#95—24no—
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2211yescharacteristic
39C2×C31×#95C2212yes—
40C2×C31×#95C2212yes—
41C2×C31×#95C2211yescharacteristic
42C25×C31C2312yes—
43C25×C31C2311yescharacteristic
44C22×D4×C31—24no—
45C22×D4×C31—24no—
46C22×D4×C31—24no—
47C22×D4×C31—24no—
48C22×D4×C31—24no—
49C22×D4×C31—24no—
50C22×D4×C31—24no—
51C22×D4×C31—22no—
52C22×D4×C31—22no—
53C22×D4×C31—22no—
54C22×D4×C31—42no—
55C22×D4×C31D418yes—
56C23×C4×C31—24no—
57C23×C4×C31—24no—
58C23×C4×C31—24no—
59C23×C4×C31—22no—
60C23×C4×C31—24no—
61C23×C4×C31—22no—
62C23×C4×C31—24no—
63C23×C4×C31—24no—
64C23×C4×C31—42no—
65C23×C4×C31—42no—
66C23×C4×C31—42no—
67C23×C4×C31D414yes—
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2311yescharacteristic
73C23×C4×C31C2312yes—
74C23×C4×C31C2312yes—
75C23×C4×C31C2312yes—
76C23×C4×C31C2311yescharacteristic
77C31×#121—232no—
78C2×C4⋊C4×C31—24no—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31—42no—
85C2×C22⋊C4×C31—24no—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—24no—
92C2×C22⋊C4×C31—24no—
93C2×C22⋊C4×C31—24no—
94C2×C22⋊C4×C31—24no—
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—42no—
101C2×C22⋊C4×C31—42no—
102C2×C22⋊C4×C31—42no—
103C2×C22⋊C4×C31—42no—
104C2×C22⋊C4×C31D414yescomplemented
105C31×#95—24no—
106C31×#95—22no—
107C31×#95—22no—
108C31×#95—22no—
109C31×#95—24no—
110C31×#95—24no—
111C31×#95—24no—
112C31×#95—24no—
113C31×#95D414yescomplemented
114C24×C31—21no—
115C24×C31—21no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—21no—
119C24×C31—21no—
120C24×C31—22no—
121C24×C31—22no—
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—22no—
132C24×C31—22no—
133C24×C31—22no—
134C24×C31C2×D414yes—
135C24×C31C2×D414yes—
136C24×C31C2×D412yes—
137C24×C31C2×D412yes—
138C24×C31#4112yes—
139C24×C31#4114yes—
140C24×C31C2411yescharacteristic
141C2×D4×C31—28no—
142C2×D4×C31—216no—
143C2×D4×C31—216no—
144C2×D4×C31—216no—
145C2×D4×C31—48no—
146C2×D4×C31—48no—
147C2×D4×C31—44no—
148C2×D4×C31—48no—
149C2×D4×C31—48no—
150C2×D4×C31—48no—
151C2×D4×C31—48no—
152C2×D4×C31—44no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—216no—
156C22×C4×C31—28no—
157C22×C4×C31—21no—
158C22×C4×C31—22no—
159C22×C4×C31—22no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—22no—
166C22×C4×C31—21no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—22no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—22no—
181C22×C4×C31—21no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—21no—
189C22×C4×C31—28no—
190C22×C4×C31—21no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—22no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—22no—
199C22×C4×C31—21no—
200C22×C4×C31—44no—
201C22×C4×C31—48no—
202C22×C4×C31—48no—
203C22×C4×C31—48no—
204C22×C4×C31—48no—
205C22×C4×C31—48no—
206C22×C4×C31—48no—
207C22×C4×C31—48no—
208C22×C4×C31—48no—
209C22×C4×C31C2×D412yes—
210C22×C4×C31C2×D412yes—
211C22×C4×C31C2×D414yes—
212C22×C4×C31C2×D414yes—
213C22×C4×C31C2×D412yes—
214C22×C4×C31C2×D412yes—
215C22×C4×C31C2×D412yes—
216C22×C4×C31#4114yes—
217C22×C4×C31#4112yes—
218C4⋊C4×C31—28no—
219C4⋊C4×C31—44no—
220C4⋊C4×C31—44no—
221C22⋊C4×C31—216no—
222C22⋊C4×C31—28no—
223C22⋊C4×C31—48no—
224C22⋊C4×C31—48no—
225C22⋊C4×C31—48no—
226C22⋊C4×C31—48no—
227C22⋊C4×C31—44no—
228#14747C3111yesmaximal, characteristic, direct product factor, Sylow
229C23×C31—22no—
230C23×C31—24no—
231C23×C31—24no—
232C23×C31—22no—
233C23×C31—22no—
234C23×C31—22no—
235C23×C31—24no—
236C23×C31—24no—
237C23×C31—24no—
238C23×C31—22no—
239C23×C31—24no—
240C23×C31—24no—
241C23×C31—24no—
242C23×C31—22no—
243C23×C31—24no—
244C23×C31—22no—
245C23×C31—22no—
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—42no—
255C23×C31—42no—
256C23×C31—42no—
257C23×C31—42no—
258C23×C31—42no—
259C23×C31—42no—
260C23×C31—42no—
261C23×C31—42no—
262C23×C31—42no—
263C23×C31—42no—
264C23×C31—42no—
265C23×C31—42no—
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—42no—
280C23×C31—42no—
281C23×C31—42no—
282C23×C31#12014yes—
283C23×C31#12114yes—
284C23×C31#12118yes—
285C23×C31#12318yes—
286C23×C31#12414yes—
287C23×C31C22×D411yescharacteristic
288C23×C31C22×D412yes—
289C23×C31C22×D411yescharacteristic
290C23×C31C22×D411yescharacteristic
291C23×C31C2×#4111yescharacteristic
292C23×C31C2×#4112yes—
293C23×C31C2×#4111yescharacteristic
294C23×C31C2×#4112yes—
295C23×C31H(5,𝔽2)12yes—
296C23×C31H(5,𝔽2)11yescharacteristic
297C23×C312−1+411yescharacteristic
298D4×C31—416no—
299D4×C31—432no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—24no—
303C2×C4×C31—24no—
304C2×C4×C31—22no—
305C2×C4×C31—24no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—24no—
310C2×C4×C31—24no—
311C2×C4×C31—24no—
312C2×C4×C31—24no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—24no—
316C2×C4×C31—24no—
317C2×C4×C31—24no—
318C2×C4×C31—24no—
319C2×C4×C31—24no—
320C2×C4×C31—22no—
321C2×C4×C31—416no—
322C2×C4×C31—432no—
323C2×C4×C31—41no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—42no—
334C2×C4×C31—42no—
335C2×C4×C31—42no—
336C2×C4×C31—42no—
337C2×C4×C31—42no—
338C2×C4×C31—42no—
339C2×C4×C31—42no—
340C2×C4×C31—42no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—42no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—42no—
351C2×C4×C31—42no—
352C2×C4×C31—42no—
353C2×C4×C31—42no—
354C2×C4×C31#12114yes—
355C22×#121C2×C3111yescharacteristic
356C2×#394C2×C3111yescharacteristic, complemented
357C2×#386C2×C3112yescomplemented
358C2×#386C2×C3112yescomplemented
359C2×#385C2×C3111yescharacteristic, complemented
360C22×#95C2×C3111yescharacteristic, complemented
361#1442C2×C3111yescharacteristic, complemented
362#1441C2×C3111yescharacteristic, complemented
363#1440C2×C3112yescomplemented
364#1439C2×C3112yescomplemented
365#1438C2×C3111yescharacteristic, complemented
366C22×C31—24no—
367C22×C31—24no—
368C22×C31—24no—
369C22×C31—24no—
370C22×C31—28no—
371C22×C31—28no—
372C22×C31—24no—
373C22×C31—28no—
374C22×C31—28no—
375C22×C31—24no—
376C22×C31—44no—
377C22×C31—44no—
378C22×C31—44no—
379C22×C31—44no—
380C22×C31—44no—
381C22×C31—44no—
382C22×C31—44no—
383C22×C31—82no—
384C22×C31—82no—
385C22×C31—82no—
386C22×C31—82no—
387C22×C31—82no—
388C22×C31—82no—
389C22×C31—82no—
390C22×C31—82no—
391C22×C31#39418yescomplemented
392C22×C31C2×#12011yescharacteristic
393C22×C31C2×#12111yescharacteristic
394C22×C31C2×#12111yescharacteristic
395C22×C31C2×#12112yes—
396C22×C31C2×#12312yes—
397C22×C31#52512yes—
398C22×C31C2×#12411yescharacteristic
399C22×C31#52912yes—
400C22×C31#53211yescharacteristic
401C22×C31#53411yescharacteristic
402C22×C31#53711yescharacteristic
403C22×C31#53812yes—
404C22×C31#53912yes—
405C22×C31D4212yes—
406C22×C31D4211yescharacteristic
407C22×C31#54612yes—
408C22×C31#54612yes—
409C22×C31#54612yes—
410C22×C31#54711yescharacteristic
411C22×C31#54712yes—
412C22×C31#54811yescharacteristic
413C22×C31#55311yescharacteristic
414C22×C31#55312yes—
415C4×C31—24no—
416C4×C31—44no—
417C4×C31—42no—
418C4×C31—42no—
419C4×C31—44no—
420C4×C31—44no—
421C4×C31—42no—
422C4×C31—81no—
423C4×C31—81no—
424C23×D4C22×C3112yes—
425C23×D4C22×C3111yescharacteristic
426C24×C4C22×C3112yes—
427C24×C4C22×C3111yescharacteristic
428C2×#121—28no—
429C2×#121—24no—
430C22×C4⋊C4C22×C3111yescharacteristic
431C22×C4⋊C4C22×C3111yescharacteristic
432C22×C4⋊C4C22×C3111yescharacteristic
433C22×C22⋊C4C22×C3112yes—
434C22×C22⋊C4C22×C3111yescharacteristic
435C22×C22⋊C4C22×C3112yes—
436C22×C22⋊C4C22×C3112yes—
437C22×C22⋊C4C22×C3112yes—
438C22×C22⋊C4C22×C3112yes—
439C22×C22⋊C4C22×C3111yescharacteristic
440#394—24no—
441#386—28no—
442#386—28no—
443#385—24no—
444C2×#95—24no—
445C2×#95C22×C3111yescharacteristic
446C2×#95C22×C3111yescharacteristic
447C2×#95C22×C3112yes—
448C2×#95C22×C3112yes—
449C2×#95C22×C3112yes—
450C2×#95C22×C3111yescharacteristic
451C2×#95C22×C3112yes—
452C2×#95C22×C3112yes—
453C2×#95C22×C3111yescharacteristic
454C2×C31—28no—
455C2×C31—84no—
456C2×C31C2×#39411yescharacteristic
457C2×C31#241011yescharacteristic
458C2×C31#241611yescharacteristic
459C2×C31#242412yes—
460C2×C31#242512yes—
461C2×C31#243011yescharacteristic
462C2×C31#244312yes—
463C2×C31#244412yes—
464C2×C31#254311yescharacteristic
465C2×C31#263911yescharacteristic
466C2×C31#285011yescharacteristic
467C25C23×C3112yes—
468C25C23×C3111yescharacteristic
469C22×D4—24no—
470C22×D4—24no—
471C22×D4—24no—
472C22×D4—24no—
473C22×D4—24no—
474C22×D4—24no—
475C22×D4—24no—
476C22×D4—22no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—42no—
480C22×D4D4×C3118yes—
481C23×C4—24no—
482C23×C4—24no—
483C23×C4—24no—
484C23×C4—22no—
485C23×C4—24no—
486C23×C4—22no—
487C23×C4—24no—
488C23×C4—24no—
489C23×C4—42no—
490C23×C4—42no—
491C23×C4—42no—
492C23×C4D4×C3114yes—
493C23×C4C23×C3111yescharacteristic
494C23×C4C23×C3111yescharacteristic
495C23×C4C23×C3111yescharacteristic
496C23×C4C23×C3111yescharacteristic
497C23×C4C23×C3111yescharacteristic
498C23×C4C23×C3112yes—
499C23×C4C23×C3112yes—
500C23×C4C23×C3112yes—
501C23×C4C23×C3111yescharacteristic
502#121—232no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—42no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4D4×C3114yescomplemented
530#95—24no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—24no—
535#95—24no—
536#95—24no—
537#95—24no—
538#95D4×C3114yescomplemented
539C31#1474711yescharacteristic, direct product factor, Sylow
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24—21no—
545C24—21no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24C2×D4×C3114yes—
561C24C2×D4×C3114yes—
562C24C2×D4×C3112yes—
563C24C2×D4×C3112yes—
564C24#41×C3112yes—
565C24#41×C3114yes—
566C24C24×C3111yescharacteristic
567C2×D4—28no—
568C2×D4—216no—
569C2×D4—216no—
570C2×D4—216no—
571C2×D4—48no—
572C2×D4—48no—
573C2×D4—44no—
574C2×D4—48no—
575C2×D4—48no—
576C2×D4—48no—
577C2×D4—48no—
578C2×D4—44no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—216no—
582C22×C4—28no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—28no—
616C22×C4—21no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—21no—
626C22×C4—44no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4C2×D4×C3112yes—
636C22×C4C2×D4×C3112yes—
637C22×C4C2×D4×C3114yes—
638C22×C4C2×D4×C3114yes—
639C22×C4C2×D4×C3112yes—
640C22×C4C2×D4×C3112yes—
641C22×C4C2×D4×C3112yes—
642C22×C4#41×C3114yes—
643C22×C4#41×C3112yes—
644C4⋊C4—28no—
645C4⋊C4—44no—
646C4⋊C4—44no—
647C22⋊C4—216no—
648C22⋊C4—28no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—44no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—22no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
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—42no—
706C23—42no—
707C23C31×#12014yes—
708C23C31×#12114yes—
709C23C31×#12118yes—
710C23C31×#12318yes—
711C23C31×#12414yes—
712C23C22×D4×C3111yescharacteristic
713C23C22×D4×C3112yes—
714C23C22×D4×C3111yescharacteristic
715C23C22×D4×C3111yescharacteristic
716C23C2×#41×C3111yescharacteristic
717C23C2×#41×C3112yes—
718C23C2×#41×C3111yescharacteristic
719C23C2×#41×C3112yes—
720C23C31×H(5,𝔽2)12yes—
721C23C31×H(5,𝔽2)11yescharacteristic
722C23C31×2−1+411yescharacteristic
723D4—416no—
724D4—432no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—416no—
747C2×C4—432no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4C31×#12114yes—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—28no—
785C22—28no—
786C22—24no—
787C22—28no—
788C22—28no—
789C22—24no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22C31×#39418yescomplemented
806C22C2×C31×#12011yescharacteristic
807C22C2×C31×#12111yescharacteristic
808C22C2×C31×#12111yescharacteristic
809C22C2×C31×#12112yes—
810C22C2×C31×#12312yes—
811C22C31×#52512yes—
812C22C2×C31×#12411yescharacteristic
813C22C31×#52912yes—
814C22C31×#53211yescharacteristic
815C22C31×#53411yescharacteristic
816C22C31×#53711yescharacteristic
817C22C31×#53812yes—
818C22C31×#53912yes—
819C22D42×C3112yes—
820C22D42×C3111yescharacteristic
821C22C31×#54612yes—
822C22C31×#54612yes—
823C22C31×#54612yes—
824C22C31×#54711yescharacteristic
825C22C31×#54712yes—
826C22C31×#54811yescharacteristic
827C22C31×#55311yescharacteristic
828C22C31×#55312yes—
829C4—24no—
830C4—44no—
831C4—42no—
832C4—42no—
833C4—44no—
834C4—44no—
835C4—42no—
836C4—81no—
837C4—81no—
838C2—28no—
839C2—84no—
840C2C2×C31×#39411yescharacteristic
841C2C31×#241011yescharacteristic
842C2C31×#241611yescharacteristic
843C2C31×#242412yes—
844C2C31×#242512yes—
845C2C31×#243011yescharacteristic
846C2C31×#244312yes—
847C2C31×#244412yes—
848C2C31×#254311yescharacteristic
849C2C31×#263911yescharacteristic
850C2C31×#285011yescharacteristic
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
2. C2×C31×#394C2semidirect
3. C2×C31×#386C2semidirect
4. C2×C31×#386C2semidirect
5. C2×C31×#385C2semidirect
6. C22×C31×#95C2semidirect
7. C31×#1442C2semidirect
8. C31×#1441C2semidirect
9. C31×#1440C2semidirect
10. C31×#1439C2semidirect
11. C31×#1438C2semidirect
104. C2×C22⋊C4×C31D4semidirect
113. C31×#95D4semidirect
228. #14747C31direct (N × H)
356. C2×#394C2×C31semidirect
357. C2×#386C2×C31semidirect
358. C2×#386C2×C31semidirect
359. C2×#385C2×C31semidirect
360. C22×#95C2×C31semidirect
361. #1442C2×C31semidirect
362. #1441C2×C31semidirect
363. #1440C2×C31semidirect
364. #1439C2×C31semidirect
365. #1438C2×C31semidirect
391. C22×C31#394semidirect
529. C2×C22⋊C4D4×C31semidirect
538. #95D4×C31semidirect
539. C31#14747direct (N × H)
805. C22C31×#394semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C2×C31×#3942
C2×C31×#3862
C2×C31×#3852
C22×C31×#952
C31×#14422
C31×#14412
C31×#14402
C31×#14392
C31×#14382
#1474731