Finite Group Databasebeta

← C31×#14311 #21471070

Subgroups — C31×#14311 #21471070

Order 7936.

2198 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#392C211yesmaximal, characteristic
2C2×C31×#390C211yesmaximal, characteristic, complemented
3C2×C31×#386C212yesmaximal, complemented
4C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#1442C211yesmaximal, characteristic, complemented
6C31×#1440C212yesmaximal, complemented
7C31×#1439C211yesmaximal, characteristic, complemented
8C31×#1438C212yesmaximal, complemented
9C31×#1438C211yesmaximal, characteristic, complemented
10C31×#1437C212yesmaximal, complemented
11C31×#1434C211yesmaximal, characteristic, complemented
12C23×D4×C31C2212yes—
13C23×D4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2211yescharacteristic
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C42×C31C2211yescharacteristic
25C22×C42×C31C2211yescharacteristic
26C31×#392C418yescomplemented
27C31×#390—24no—
28C31×#386—28no—
29C4×C22⋊C4×C31—24no—
30C2×C31×#95C2212yes—
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2211yescharacteristic
39C25×C31C2312yes—
40C25×C31C2311yescharacteristic
41C22×D4×C31—24no—
42C22×D4×C31—24no—
43C22×D4×C31—22no—
44C22×D4×C31—22no—
45C22×D4×C31—42no—
46C22×D4×C31—42no—
47C22×D4×C31—42no—
48C22×D4×C31—42no—
49C22×D4×C31—42no—
50C22×D4×C31—42no—
51C22×D4×C31C2×C418yes—
52C22×D4×C31C2×C414yescomplemented
53C23×C4×C31—22no—
54C23×C4×C31—22no—
55C23×C4×C31—42no—
56C23×C4×C31—42no—
57C23×C4×C31D414yescomplemented
58C23×C4×C31C2312yes—
59C23×C4×C31C2312yes—
60C23×C4×C31C2311yescharacteristic
61C23×C4×C31C2312yes—
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C2×C4⋊C4×C31—22no—
68C2×C4⋊C4×C31—42no—
69C2×C22⋊C4×C31—22no—
70C2×C22⋊C4×C31—22no—
71C2×C22⋊C4×C31—22no—
72C2×C22⋊C4×C31—22no—
73C2×C22⋊C4×C31—22no—
74C2×C22⋊C4×C31—24no—
75C2×C22⋊C4×C31—24no—
76C2×C22⋊C4×C31—24no—
77C2×C22⋊C4×C31—24no—
78C2×C22⋊C4×C31—24no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—24no—
81C2×C22⋊C4×C31—42no—
82C2×C22⋊C4×C31—42no—
83C2×C22⋊C4×C31—42no—
84C2×C22⋊C4×C31—42no—
85C2×C22⋊C4×C31—42no—
86C2×C22⋊C4×C31—42no—
87C2×C22⋊C4×C31—42no—
88C2×C22⋊C4×C31—42no—
89C2×C22⋊C4×C31—42no—
90C2×C22⋊C4×C31—42no—
91C2×C22⋊C4×C31C2×C414yes—
92C2×C22⋊C4×C31C2×C418yescomplemented
93C2×C42×C31—22no—
94C2×C42×C31—42no—
95C2×C42×C31—42no—
96C2×C42×C31D414yescomplemented
97C31×#95—22no—
98C31×#95—22no—
99C31×#95—24no—
100C31×#95—24no—
101C31×#95—22no—
102C31×#95—42no—
103C31×#95—42no—
104C31×#95—42no—
105C31×#95C2×C414yescomplemented
106C24×C31—21no—
107C24×C31—21no—
108C24×C31—21no—
109C24×C31—21no—
110C24×C31—22no—
111C24×C31—22no—
112C24×C31—22no—
113C24×C31—22no—
114C24×C31—22no—
115C24×C31—22no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31—22no—
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×C31C22×C414yes—
129C24×C31C22×C412yes—
130C24×C31C2×D412yes—
131C24×C31#4112yes—
132C24×C31C2411yescharacteristic
133C2×D4×C31—216no—
134C2×D4×C31—28no—
135C2×D4×C31—48no—
136C2×D4×C31—48no—
137C2×D4×C31—48no—
138C2×D4×C31—44no—
139C2×D4×C31—44no—
140C2×D4×C31—48no—
141C2×D4×C31—48no—
142C2×D4×C31—48no—
143C2×D4×C31—48no—
144C2×D4×C31—48no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—21no—
150C22×C4×C31—22no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—22no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—28no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
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—22no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—48no—
187C22×C4×C31—44no—
188C22×C4×C31—44no—
189C22×C4×C31—48no—
190C22×C4×C31C22×C414yes—
191C22×C4×C31C22×C412yes—
192C22×C4×C31C22×C412yes—
193C22×C4×C31C2×D412yes—
194C22×C4×C31C2×D412yes—
195C22×C4×C31C2×D412yes—
196C22×C4×C31C2×D412yes—
197C22×C4×C31C2×D412yes—
198C22×C4×C31#4112yes—
199C22×C4×C31#4112yes—
200C22×C4×C31#4112yes—
201C4⋊C4×C31—44no—
202C22⋊C4×C31—28no—
203C22⋊C4×C31—28no—
204C22⋊C4×C31—48no—
205C22⋊C4×C31—48no—
206C22⋊C4×C31—48no—
207C22⋊C4×C31—48no—
208C22⋊C4×C31—48no—
209C22⋊C4×C31—48no—
210C42×C31—44no—
211C42×C31—44no—
212#14311C3111yesmaximal, characteristic, direct product factor, Sylow
213C23×C31—22no—
214C23×C31—22no—
215C23×C31—24no—
216C23×C31—24no—
217C23×C31—22no—
218C23×C31—22no—
219C23×C31—22no—
220C23×C31—22no—
221C23×C31—24no—
222C23×C31—24no—
223C23×C31—24no—
224C23×C31—24no—
225C23×C31—24no—
226C23×C31—24no—
227C23×C31—24no—
228C23×C31—24no—
229C23×C31—24no—
230C23×C31—24no—
231C23×C31—24no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—42no—
237C23×C31—42no—
238C23×C31—42no—
239C23×C31—42no—
240C23×C31—42no—
241C23×C31—42no—
242C23×C31—42no—
243C23×C31—42no—
244C23×C31—42no—
245C23×C31—42no—
246C23×C31—42no—
247C23×C31—42no—
248C23×C31—42no—
249C23×C31—42no—
250C23×C31—42no—
251C23×C31—42no—
252C23×C31—42no—
253C23×C31—42no—
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×C31C4×D414yes—
271C23×C31C23×C411yescharacteristic
272C23×C31C22×D411yescharacteristic
273C23×C31C22×D411yescharacteristic
274C23×C31C2×#4111yescharacteristic
275C23×C31C2×#4111yescharacteristic
276C23×C31C2×#4111yescharacteristic
277C23×C31C2×#4111yescharacteristic
278C23×C31H(5,𝔽2)12yes—
279C23×C31H(5,𝔽2)12yes—
280C23×C31H(5,𝔽2)12yes—
281C23×C31H(5,𝔽2)12yes—
282D4×C31—416no—
283D4×C31—432no—
284C2×C4×C31—24no—
285C2×C4×C31—22no—
286C2×C4×C31—22no—
287C2×C4×C31—24no—
288C2×C4×C31—22no—
289C2×C4×C31—22no—
290C2×C4×C31—24no—
291C2×C4×C31—24no—
292C2×C4×C31—22no—
293C2×C4×C31—24no—
294C2×C4×C31—24no—
295C2×C4×C31—24no—
296C2×C4×C31—24no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
299C2×C4×C31—22no—
300C2×C4×C31—22no—
301C2×C4×C31—24no—
302C2×C4×C31—22no—
303C2×C4×C31—24no—
304C2×C4×C31—416no—
305C2×C4×C31—41no—
306C2×C4×C31—42no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—42no—
313C2×C4×C31—42no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31—42no—
322C2×C4×C31—42no—
323C2×C4×C31—42no—
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—42no—
331C2×C4×C31—42no—
332C2×C4×C31—42no—
333C2×C4×C31—42no—
334C2×C4×C31C4×D414yes—
335C2×C4×C31#12114yes—
336C2×#392C2×C3111yescharacteristic
337C2×#390C2×C3111yescharacteristic, complemented
338C2×#386C2×C3112yescomplemented
339C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
340#1442C2×C3111yescharacteristic, complemented
341#1440C2×C3112yescomplemented
342#1439C2×C3111yescharacteristic, complemented
343#1438C2×C3112yescomplemented
344#1438C2×C3111yescharacteristic, complemented
345#1437C2×C3112yescomplemented
346#1434C2×C3111yescharacteristic, complemented
347C22×C31—28no—
348C22×C31—24no—
349C22×C31—42no—
350C22×C31—42no—
351C22×C31—44no—
352C22×C31—42no—
353C22×C31—42no—
354C22×C31—42no—
355C22×C31—42no—
356C22×C31—44no—
357C22×C31—44no—
358C22×C31—44no—
359C22×C31—44no—
360C22×C31—44no—
361C22×C31—44no—
362C22×C31—44no—
363C22×C31—44no—
364C22×C31—44no—
365C22×C31—82no—
366C22×C31—82no—
367C22×C31—82no—
368C22×C31—82no—
369C22×C31—82no—
370C22×C31—82no—
371C22×C31—82no—
372C22×C31—82no—
373C22×C31C2×C4×D411yescharacteristic
374C22×C31C2×C4×D411yescharacteristic
375C22×C31C4×#4111yescharacteristic
376C22×C31#51812yes—
377C22×C31#51812yes—
378C22×C31C2×#12111yescharacteristic
379C22×C31#52511yescharacteristic
380C22×C31#52911yescharacteristic
381C22×C31#53211yescharacteristic
382C22×C31#53411yescharacteristic
383C22×C31#53412yes—
384C22×C31#53511yescharacteristic
385C22×C31#53512yes—
386C22×C31#53511yescharacteristic
387C22×C31#53511yescharacteristic
388C22×C31#53812yes—
389C22×C31#53812yes—
390C22×C31#53812yes—
391C22×C31#53812yes—
392C22×C31#53812yes—
393C22×C31#54012yes—
394C22×C31#54012yes—
395C22×C31#54012yes—
396C4×C31—24no—
397C4×C31—24no—
398C4×C31—44no—
399C4×C31—42no—
400C4×C31—42no—
401C4×C31—42no—
402C4×C31—42no—
403C4×C31—82no—
404C4×C31—82no—
405C23×D4C22×C3112yes—
406C23×D4C22×C3111yescharacteristic
407C24×C4C22×C3111yescharacteristic
408C22×C4⋊C4C22×C3111yescharacteristic
409C22×C22⋊C4C22×C3112yes—
410C22×C22⋊C4C22×C3111yescharacteristic
411C22×C22⋊C4C22×C3111yescharacteristic
412C22×C22⋊C4C22×C3112yes—
413C22×C22⋊C4C22×C3112yes—
414C22×C22⋊C4C22×C3112yes—
415C22×C22⋊C4C22×C3112yes—
416C22×C22⋊C4C22×C3112yes—
417C22×C42C22×C3111yescharacteristic
418C22×C42C22×C3111yescharacteristic
419#392C4×C3118yescomplemented
420#390—24no—
421#386—28no—
422C4×C22⋊C4—24no—
423C2×#95C22×C3112yes—
424C2×#95C22×C3111yescharacteristic
425C2×#95C22×C3111yescharacteristic
426C2×#95C22×C3111yescharacteristic
427C2×#95C22×C3112yes—
428C2×#95C22×C3112yes—
429C2×#95C22×C3112yes—
430C2×#95C22×C3112yes—
431C2×#95C22×C3111yescharacteristic
432C2×C31—44no—
433C2×C31—84no—
434C2×C31C4×#12111yescharacteristic
435C2×C31#232111yescharacteristic
436C2×C31#232112yes—
437C2×C31#232811yescharacteristic
438C2×C31#233312yes—
439C2×C31#261711yescharacteristic
440C2×C31#261911yescharacteristic
441C2×C31#263111yescharacteristic
442C2×C31#263511yescharacteristic
443C2×C31#264812yes—
444C2×C31#266112yes—
445C25C23×C3112yes—
446C25C23×C3111yescharacteristic
447C22×D4—24no—
448C22×D4—24no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4—42no—
452C22×D4—42no—
453C22×D4—42no—
454C22×D4—42no—
455C22×D4—42no—
456C22×D4—42no—
457C22×D4C2×C4×C3118yes—
458C22×D4C2×C4×C3114yescomplemented
459C23×C4—22no—
460C23×C4—22no—
461C23×C4—42no—
462C23×C4—42no—
463C23×C4D4×C3114yescomplemented
464C23×C4C23×C3112yes—
465C23×C4C23×C3112yes—
466C23×C4C23×C3111yescharacteristic
467C23×C4C23×C3112yes—
468C23×C4C23×C3111yescharacteristic
469C23×C4C23×C3111yescharacteristic
470C23×C4C23×C3111yescharacteristic
471C23×C4C23×C3111yescharacteristic
472C23×C4C23×C3111yescharacteristic
473C2×C4⋊C4—22no—
474C2×C4⋊C4—42no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4C2×C4×C3114yes—
498C2×C22⋊C4C2×C4×C3118yescomplemented
499C2×C42—22no—
500C2×C42—42no—
501C2×C42—42no—
502C2×C42D4×C3114yescomplemented
503#95—22no—
504#95—22no—
505#95—24no—
506#95—24no—
507#95—22no—
508#95—42no—
509#95—42no—
510#95—42no—
511#95C2×C4×C3114yescomplemented
512C31#1431111yescharacteristic, direct product factor, Sylow
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24C22×C4×C3114yes—
536C24C22×C4×C3112yes—
537C24C2×D4×C3112yes—
538C24#41×C3112yes—
539C24C24×C3111yescharacteristic
540C2×D4—216no—
541C2×D4—28no—
542C2×D4—48no—
543C2×D4—48no—
544C2×D4—48no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—48no—
548C2×D4—48no—
549C2×D4—48no—
550C2×D4—48no—
551C2×D4—48no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—28no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—48no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—48no—
597C22×C4C22×C4×C3114yes—
598C22×C4C22×C4×C3112yes—
599C22×C4C22×C4×C3112yes—
600C22×C4C2×D4×C3112yes—
601C22×C4C2×D4×C3112yes—
602C22×C4C2×D4×C3112yes—
603C22×C4C2×D4×C3112yes—
604C22×C4C2×D4×C3112yes—
605C22×C4#41×C3112yes—
606C22×C4#41×C3112yes—
607C22×C4#41×C3112yes—
608C4⋊C4—44no—
609C22⋊C4—28no—
610C22⋊C4—28no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C42—44no—
618C42—44no—
619C23—22no—
620C23—22no—
621C23—24no—
622C23—24no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23C4×D4×C3114yes—
677C23C23×C4×C3111yescharacteristic
678C23C22×D4×C3111yescharacteristic
679C23C22×D4×C3111yescharacteristic
680C23C2×#41×C3111yescharacteristic
681C23C2×#41×C3111yescharacteristic
682C23C2×#41×C3111yescharacteristic
683C23C2×#41×C3111yescharacteristic
684C23C31×H(5,𝔽2)12yes—
685C23C31×H(5,𝔽2)12yes—
686C23C31×H(5,𝔽2)12yes—
687C23C31×H(5,𝔽2)12yes—
688D4—416no—
689D4—432no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—416no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4C4×D4×C3114yes—
741C2×C4C31×#12114yes—
742C22—28no—
743C22—24no—
744C22—42no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22C2×C4×D4×C3111yescharacteristic
769C22C2×C4×D4×C3111yescharacteristic
770C22C4×#41×C3111yescharacteristic
771C22C31×#51812yes—
772C22C31×#51812yes—
773C22C2×C31×#12111yescharacteristic
774C22C31×#52511yescharacteristic
775C22C31×#52911yescharacteristic
776C22C31×#53211yescharacteristic
777C22C31×#53411yescharacteristic
778C22C31×#53412yes—
779C22C31×#53511yescharacteristic
780C22C31×#53512yes—
781C22C31×#53511yescharacteristic
782C22C31×#53511yescharacteristic
783C22C31×#53812yes—
784C22C31×#53812yes—
785C22C31×#53812yes—
786C22C31×#53812yes—
787C22C31×#53812yes—
788C22C31×#54012yes—
789C22C31×#54012yes—
790C22C31×#54012yes—
791C4—24no—
792C4—24no—
793C4—44no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—82no—
799C4—82no—
800C2—44no—
801C2—84no—
802C2C4×C31×#12111yescharacteristic
803C2C31×#232111yescharacteristic
804C2C31×#232112yes—
805C2C31×#232811yescharacteristic
806C2C31×#233312yes—
807C2C31×#261711yescharacteristic
808C2C31×#261911yescharacteristic
809C2C31×#263111yescharacteristic
810C2C31×#263511yescharacteristic
811C2C31×#264812yes—
812C2C31×#266112yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC2×C31×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#390C2semidirect
3. C2×C31×#386C2semidirect
4. C2×C4×C22⋊C4×C31C2semidirect
5. C31×#1442C2semidirect
6. C31×#1440C2semidirect
7. C31×#1439C2semidirect
8. C31×#1438C2semidirect
9. C31×#1438C2semidirect
10. C31×#1437C2semidirect
11. C31×#1434C2semidirect
26. C31×#392C4semidirect
52. C22×D4×C31C2×C4semidirect
57. C23×C4×C31D4semidirect
92. C2×C22⋊C4×C31C2×C4semidirect
96. C2×C42×C31D4semidirect
105. C31×#95C2×C4semidirect
212. #14311C31direct (N × H)
337. C2×#390C2×C31semidirect
338. C2×#386C2×C31semidirect
339. C2×C4×C22⋊C4C2×C31semidirect
340. #1442C2×C31semidirect
341. #1440C2×C31semidirect
342. #1439C2×C31semidirect
343. #1438C2×C31semidirect
344. #1438C2×C31semidirect
345. #1437C2×C31semidirect
346. #1434C2×C31semidirect
419. #392C4×C31semidirect
458. C22×D4C2×C4×C31semidirect
463. C23×C4D4×C31semidirect
498. C2×C22⋊C4C2×C4×C31semidirect
502. C2×C42D4×C31semidirect
511. #95C2×C4×C31semidirect
512. C31#14311direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3922
C2×C31×#3902
C2×C31×#3862
C2×C4×C22⋊C4×C312
C31×#14422
C31×#14402
C31×#14392
C31×#14382
C31×#14372
C31×#14342
#1431131