Finite Group Databasebeta

← C31×#14621 #21471380

Subgroups — C31×#14621 #21471380

Order 7936.

2018 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#392C211yesmaximal, characteristic
2C2×C31×#386C212yesmaximal, complemented
3C31×#1443C212yesmaximal, complemented
4C31×#1440C212yesmaximal, complemented
5C31×#1439C211yesmaximal, characteristic, complemented
6C31×#1439C212yesmaximal, complemented
7C31×#1438C212yesmaximal, complemented
8C31×#1438C212yesmaximal, complemented
9C31×C22⋊#95C211yesmaximal, characteristic, complemented
10C23×D4×C31C2212yes—
11C23×D4×C31C2211yescharacteristic
12C24×C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C22⋊C4×C31C2211yescharacteristic
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2212yes—
22C31×#392C418yescomplemented
23C31×#386—28no—
24C2×C31×#95C2212yes—
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2211yescharacteristic
33C25×C31C2312yes—
34C25×C31C2311yescharacteristic
35C22×D4×C31—24no—
36C22×D4×C31—24no—
37C22×D4×C31—42no—
38C22×D4×C31—42no—
39C22×D4×C31—42no—
40C22×D4×C31—42no—
41C22×D4×C31—42no—
42C22×D4×C31—42no—
43C22×D4×C31—41no—
44C22×D4×C31—41no—
45C22×D4×C31C2×C418yes—
46C22×D4×C31C2×C414yescomplemented
47C23×C4×C31—42no—
48C23×C4×C31—42no—
49C23×C4×C31—41no—
50C23×C4×C31—41no—
51C23×C4×C31D414yescomplemented
52C23×C4×C31C2312yes—
53C23×C4×C31C2312yes—
54C23×C4×C31C2312yes—
55C23×C4×C31C2311yescharacteristic
56C23×C4×C31C2312yes—
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2312yes—
59C2×C4⋊C4×C31—41no—
60C2×C4⋊C4×C31—42no—
61C2×C22⋊C4×C31—24no—
62C2×C22⋊C4×C31—22no—
63C2×C22⋊C4×C31—24no—
64C2×C22⋊C4×C31—24no—
65C2×C22⋊C4×C31—41no—
66C2×C22⋊C4×C31—41no—
67C2×C22⋊C4×C31—42no—
68C2×C22⋊C4×C31—42no—
69C2×C22⋊C4×C31—42no—
70C2×C22⋊C4×C31—42no—
71C2×C22⋊C4×C31—42no—
72C2×C22⋊C4×C31—42no—
73C2×C22⋊C4×C31—42no—
74C2×C22⋊C4×C31—41no—
75C2×C22⋊C4×C31—41no—
76C2×C22⋊C4×C31—42no—
77C2×C22⋊C4×C31—42no—
78C2×C22⋊C4×C31—42no—
79C2×C22⋊C4×C31—42no—
80C2×C22⋊C4×C31—42no—
81C2×C22⋊C4×C31—42no—
82C2×C22⋊C4×C31—42no—
83C2×C22⋊C4×C31C2×C414yes—
84C2×C22⋊C4×C31C2×C418yescomplemented
85C31×#95—24no—
86C31×#95—24no—
87C31×#95—42no—
88C31×#95—41no—
89C31×#95—42no—
90C31×#95—42no—
91C31×#95—42no—
92C31×#95—42no—
93C31×#95C2×C414yescomplemented
94C24×C31—21no—
95C24×C31—21no—
96C24×C31—21no—
97C24×C31—22no—
98C24×C31—22no—
99C24×C31—22no—
100C24×C31—22no—
101C24×C31—21no—
102C24×C31—22no—
103C24×C31—22no—
104C24×C31—22no—
105C24×C31—22no—
106C24×C31—22no—
107C24×C31—22no—
108C24×C31—22no—
109C24×C31—22no—
110C24×C31—22no—
111C24×C31—22no—
112C24×C31—22no—
113C24×C31—22no—
114C24×C31—22no—
115C24×C31—22no—
116C24×C31C22×C414yes—
117C24×C31C22×C412yes—
118C24×C31C2×D412yes—
119C24×C31#4112yes—
120C24×C31C2411yescharacteristic
121C2×D4×C31—216no—
122C2×D4×C31—48no—
123C2×D4×C31—48no—
124C2×D4×C31—44no—
125C2×D4×C31—48no—
126C2×D4×C31—48no—
127C2×D4×C31—48no—
128C2×D4×C31—48no—
129C2×D4×C31—48no—
130C2×D4×C31—48no—
131C2×D4×C31—44no—
132C2×D4×C31—44no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—21no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—21no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
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—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—44no—
175C22×C4×C31—48no—
176C22×C4×C31—48no—
177C22×C4×C31—44no—
178C22×C4×C31—44no—
179C22×C4×C31C22×C412yes—
180C22×C4×C31C22×C414yes—
181C22×C4×C31C22×C412yes—
182C22×C4×C31C2×D414yes—
183C4⋊C4×C31—44no—
184C22⋊C4×C31—44no—
185C22⋊C4×C31—48no—
186C22⋊C4×C31—48no—
187C22⋊C4×C31—48no—
188C22⋊C4×C31—48no—
189C22⋊C4×C31—44no—
190C22⋊C4×C31—48no—
191C22⋊C4×C31—48no—
192#14621C3111yesmaximal, characteristic, direct product factor, Sylow
193C23×C31—22no—
194C23×C31—24no—
195C23×C31—24no—
196C23×C31—22no—
197C23×C31—24no—
198C23×C31—22no—
199C23×C31—24no—
200C23×C31—22no—
201C23×C31—22no—
202C23×C31—24no—
203C23×C31—24no—
204C23×C31—22no—
205C23×C31—24no—
206C23×C31—24no—
207C23×C31—24no—
208C23×C31—24no—
209C23×C31—24no—
210C23×C31—24no—
211C23×C31—24no—
212C23×C31—42no—
213C23×C31—41no—
214C23×C31—41no—
215C23×C31—42no—
216C23×C31—42no—
217C23×C31—42no—
218C23×C31—41no—
219C23×C31—41no—
220C23×C31—42no—
221C23×C31—42no—
222C23×C31—42no—
223C23×C31—42no—
224C23×C31—42no—
225C23×C31—42no—
226C23×C31—42no—
227C23×C31—42no—
228C23×C31—42no—
229C23×C31—42no—
230C23×C31—42no—
231C23×C31—42no—
232C23×C31—42no—
233C23×C31—42no—
234C23×C31—42no—
235C23×C31—42no—
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×C31C4×D414yes—
251C23×C31C23×C411yescharacteristic
252C23×C31C22×D411yescharacteristic
253C23×C31C2×#4111yescharacteristic
254C23×C31H(5,𝔽2)12yes—
255C23×C31H(5,𝔽2)12yes—
256C23×C31H(5,𝔽2)11yescharacteristic
257C23×C31H(5,𝔽2)12yes—
258C23×C31H(5,𝔽2)12yes—
259C23×C31H(5,𝔽2)11yescharacteristic
260C23×C31H(5,𝔽2)11yescharacteristic
261C23×C312−1+411yescharacteristic
262D4×C31—432no—
263D4×C31—416no—
264C2×C4×C31—24no—
265C2×C4×C31—24no—
266C2×C4×C31—22no—
267C2×C4×C31—24no—
268C2×C4×C31—22no—
269C2×C4×C31—24no—
270C2×C4×C31—24no—
271C2×C4×C31—24no—
272C2×C4×C31—24no—
273C2×C4×C31—24no—
274C2×C4×C31—416no—
275C2×C4×C31—42no—
276C2×C4×C31—42no—
277C2×C4×C31—42no—
278C2×C4×C31—42no—
279C2×C4×C31—41no—
280C2×C4×C31—42no—
281C2×C4×C31—41no—
282C2×C4×C31—42no—
283C2×C4×C31—42no—
284C2×C4×C31—42no—
285C2×C4×C31—42no—
286C2×C4×C31—41no—
287C2×C4×C31—42no—
288C2×C4×C31—41no—
289C2×C4×C31—42no—
290C2×C4×C31—42no—
291C2×C4×C31—42no—
292C2×C4×C31—42no—
293C2×C4×C31—42no—
294C2×C4×C31—42no—
295C2×C4×C31—42no—
296C2×C4×C31—42no—
297C2×C4×C31—42no—
298C2×C4×C31—42no—
299C2×C4×C31—42no—
300C2×C4×C31—42no—
301C2×C4×C31—42no—
302C2×C4×C31—42no—
303C2×C4×C31—42no—
304C2×C4×C31—42no—
305C2×C4×C31—42no—
306C2×C4×C31—42no—
307C2×C4×C31—42no—
308C2×C4×C31—42no—
309C2×C4×C31—42no—
310C2×#392C2×C3111yescharacteristic
311C2×#386C2×C3112yescomplemented
312#1443C2×C3112yescomplemented
313#1440C2×C3112yescomplemented
314#1439C2×C3111yescharacteristic, complemented
315#1439C2×C3112yescomplemented
316#1438C2×C3112yescomplemented
317#1438C2×C3112yescomplemented
318C22⋊#95C2×C3111yescharacteristic, complemented
319C22×C31—28no—
320C22×C31—24no—
321C22×C31—42no—
322C22×C31—44no—
323C22×C31—42no—
324C22×C31—42no—
325C22×C31—44no—
326C22×C31—42no—
327C22×C31—42no—
328C22×C31—44no—
329C22×C31—42no—
330C22×C31—44no—
331C22×C31—44no—
332C22×C31—44no—
333C22×C31—44no—
334C22×C31—44no—
335C22×C31—44no—
336C22×C31—44no—
337C22×C31—82no—
338C22×C31—82no—
339C22×C31—82no—
340C22×C31—82no—
341C22×C31—82no—
342C22×C31—82no—
343C22×C31—82no—
344C22×C31—82no—
345C22×C31C2×C4×D411yescharacteristic
346C22×C31#51812yes—
347C22×C31#51812yes—
348C22×C31#51811yescharacteristic
349C22×C31#52011yescharacteristic
350C22×C31#53412yes—
351C22×C31#53411yescharacteristic
352C22×C31#53512yes—
353C22×C31#53711yescharacteristic
354C22×C31#53812yes—
355C22×C31#53811yescharacteristic
356C22×C31#53812yes—
357C22×C31#53911yescharacteristic
358C22×C31#56011yescharacteristic
359C22×C31#56012yes—
360C22×C31#56012yes—
361C22×C31#56012yes—
362C22×C31#56012yes—
363C22×C31#56011yescharacteristic
364C22×C31#56011yescharacteristic
365C22×C31H(3,𝔽4)11yescharacteristic
366C22×C31#56212yes—
367C22×C31#56212yes—
368C4×C31—44no—
369C4×C31—42no—
370C4×C31—42no—
371C4×C31—44no—
372C4×C31—82no—
373C4×C31—82no—
374C4×C31—82no—
375C23×D4C22×C3112yes—
376C23×D4C22×C3111yescharacteristic
377C24×C4C22×C3111yescharacteristic
378C22×C4⋊C4C22×C3111yescharacteristic
379C22×C22⋊C4C22×C3111yescharacteristic
380C22×C22⋊C4C22×C3112yes—
381C22×C22⋊C4C22×C3112yes—
382C22×C22⋊C4C22×C3112yes—
383C22×C22⋊C4C22×C3112yes—
384C22×C22⋊C4C22×C3112yes—
385C22×C22⋊C4C22×C3111yescharacteristic
386C22×C22⋊C4C22×C3112yes—
387#392C4×C3118yescomplemented
388#386—28no—
389C2×#95C22×C3112yes—
390C2×#95C22×C3112yes—
391C2×#95C22×C3112yes—
392C2×#95C22×C3112yes—
393C2×#95C22×C3112yes—
394C2×#95C22×C3112yes—
395C2×#95C22×C3112yes—
396C2×#95C22×C3111yescharacteristic
397C2×#95C22×C3111yescharacteristic
398C2×C31—44no—
399C2×C31—84no—
400C2×C31#232112yes—
401C2×C31#232511yescharacteristic
402C2×C31#237511yescharacteristic
403C2×C31#237712yes—
404C2×C31#238011yescharacteristic
405C2×C31#281211yescharacteristic
406C2×C31#281312yes—
407C2×C31#281511yescharacteristic
408C2×C31#282411yescharacteristic
409C2×C31#282512yes—
410C2×C31#282611yescharacteristic
411C25C23×C3112yes—
412C25C23×C3111yescharacteristic
413C22×D4—24no—
414C22×D4—24no—
415C22×D4—42no—
416C22×D4—42no—
417C22×D4—42no—
418C22×D4—42no—
419C22×D4—42no—
420C22×D4—42no—
421C22×D4—41no—
422C22×D4—41no—
423C22×D4C2×C4×C3118yes—
424C22×D4C2×C4×C3114yescomplemented
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—41no—
428C23×C4—41no—
429C23×C4D4×C3114yescomplemented
430C23×C4C23×C3112yes—
431C23×C4C23×C3112yes—
432C23×C4C23×C3112yes—
433C23×C4C23×C3111yescharacteristic
434C23×C4C23×C3112yes—
435C23×C4C23×C3111yescharacteristic
436C23×C4C23×C3112yes—
437C2×C4⋊C4—41no—
438C2×C4⋊C4—42no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—41no—
444C2×C22⋊C4—41no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4—42no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—42no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4—42no—
452C2×C22⋊C4—41no—
453C2×C22⋊C4—41no—
454C2×C22⋊C4—42no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4—42no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4C2×C4×C3114yes—
462C2×C22⋊C4C2×C4×C3118yescomplemented
463#95—24no—
464#95—24no—
465#95—42no—
466#95—41no—
467#95—42no—
468#95—42no—
469#95—42no—
470#95—42no—
471#95C2×C4×C3114yescomplemented
472C31#1462111yescharacteristic, direct product factor, Sylow
473C24—21no—
474C24—21no—
475C24—21no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—21no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24C22×C4×C3114yes—
496C24C22×C4×C3112yes—
497C24C2×D4×C3112yes—
498C24#41×C3112yes—
499C24C24×C3111yescharacteristic
500C2×D4—216no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—44no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—44no—
511C2×D4—44no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—44no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4C22×C4×C3112yes—
559C22×C4C22×C4×C3114yes—
560C22×C4C22×C4×C3112yes—
561C22×C4C2×D4×C3114yes—
562C4⋊C4—44no—
563C22⋊C4—44no—
564C22⋊C4—48no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—44no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C23—22no—
572C23—24no—
573C23—24no—
574C23—22no—
575C23—24no—
576C23—22no—
577C23—24no—
578C23—22no—
579C23—22no—
580C23—24no—
581C23—24no—
582C23—22no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—42no—
591C23—41no—
592C23—41no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—41no—
597C23—41no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23C4×D4×C3114yes—
629C23C23×C4×C3111yescharacteristic
630C23C22×D4×C3111yescharacteristic
631C23C2×#41×C3111yescharacteristic
632C23C31×H(5,𝔽2)12yes—
633C23C31×H(5,𝔽2)12yes—
634C23C31×H(5,𝔽2)11yescharacteristic
635C23C31×H(5,𝔽2)12yes—
636C23C31×H(5,𝔽2)12yes—
637C23C31×H(5,𝔽2)11yescharacteristic
638C23C31×H(5,𝔽2)11yescharacteristic
639C23C31×2−1+411yescharacteristic
640D4—432no—
641D4—416no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—416no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C22—28no—
689C22—24no—
690C22—42no—
691C22—44no—
692C22—42no—
693C22—42no—
694C22—44no—
695C22—42no—
696C22—42no—
697C22—44no—
698C22—42no—
699C22—44no—
700C22—44no—
701C22—44no—
702C22—44no—
703C22—44no—
704C22—44no—
705C22—44no—
706C22—82no—
707C22—82no—
708C22—82no—
709C22—82no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—82no—
714C22C2×C4×D4×C3111yescharacteristic
715C22C31×#51812yes—
716C22C31×#51812yes—
717C22C31×#51811yescharacteristic
718C22C31×#52011yescharacteristic
719C22C31×#53412yes—
720C22C31×#53411yescharacteristic
721C22C31×#53512yes—
722C22C31×#53711yescharacteristic
723C22C31×#53812yes—
724C22C31×#53811yescharacteristic
725C22C31×#53812yes—
726C22C31×#53911yescharacteristic
727C22C31×#56011yescharacteristic
728C22C31×#56012yes—
729C22C31×#56012yes—
730C22C31×#56012yes—
731C22C31×#56012yes—
732C22C31×#56011yescharacteristic
733C22C31×#56011yescharacteristic
734C22C31×H(3,𝔽4)11yescharacteristic
735C22C31×#56212yes—
736C22C31×#56212yes—
737C4—44no—
738C4—42no—
739C4—42no—
740C4—44no—
741C4—82no—
742C4—82no—
743C4—82no—
744C2—44no—
745C2—84no—
746C2C31×#232112yes—
747C2C31×#232511yescharacteristic
748C2C31×#237511yescharacteristic
749C2C31×#237712yes—
750C2C31×#238011yescharacteristic
751C2C31×#281211yescharacteristic
752C2C31×#281312yes—
753C2C31×#281511yescharacteristic
754C2C31×#282411yescharacteristic
755C2C31×#282512yes—
756C2C31×#282611yescharacteristic
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×#386C2semidirect
3. C31×#1443C2semidirect
4. C31×#1440C2semidirect
5. C31×#1439C2semidirect
6. C31×#1439C2semidirect
7. C31×#1438C2semidirect
8. C31×#1438C2semidirect
9. C31×C22⋊#95C2semidirect
22. C31×#392C4semidirect
46. C22×D4×C31C2×C4semidirect
51. C23×C4×C31D4semidirect
84. C2×C22⋊C4×C31C2×C4semidirect
93. C31×#95C2×C4semidirect
192. #14621C31direct (N × H)
311. C2×#386C2×C31semidirect
312. #1443C2×C31semidirect
313. #1440C2×C31semidirect
314. #1439C2×C31semidirect
315. #1439C2×C31semidirect
316. #1438C2×C31semidirect
317. #1438C2×C31semidirect
318. C22⋊#95C2×C31semidirect
387. #392C4×C31semidirect
424. C22×D4C2×C4×C31semidirect
429. C23×C4D4×C31semidirect
462. C2×C22⋊C4C2×C4×C31semidirect
471. #95C2×C4×C31semidirect
472. C31#14621direct (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×#3862
C31×#14432
C31×#14402
C31×#14392
C31×#14382
C31×C22⋊#952
#1462131