Finite Group Databasebeta

← C31×#14513 #21471272

Subgroups — C31×#14513 #21471272

Order 7936.

1918 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#390C211yesmaximal, characteristic
2C2×C31×#386C211yesmaximal, characteristic
3C2×C31×#386C211yesmaximal, characteristic
4C31×#1442C212yesmaximal, complemented
5C31×#1439C212yesmaximal, complemented
6C31×#1439C212yesmaximal, complemented
7C31×#1436C212yesmaximal, complemented
8C31×C22⋊#95C212yesmaximal, complemented
9C31×C22⋊#95C212yesmaximal, complemented
10C23×D4×C31C2211yescharacteristic
11C24×C4×C31C2211yescharacteristic
12C24×C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2212yes—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C42×C31C2211yescharacteristic
22C31×#390—24no—
23C31×#386—24no—
24C31×#386C418yescomplemented
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C25×C31C2311yescharacteristic
35C25×C31C2311yescharacteristic
36C22×D4×C31—41no—
37C22×D4×C31—41no—
38C22×D4×C31—41no—
39C22×D4×C31—41no—
40C22×D4×C31C2×C414yes—
41C22×D4×C31D414yes—
42C22×D4×C31Q814yes—
43C23×C4×C31—22no—
44C23×C4×C31—24no—
45C23×C4×C31—41no—
46C23×C4×C31—41no—
47C23×C4×C31—41no—
48C23×C4×C31—41no—
49C23×C4×C31—42no—
50C23×C4×C31—42no—
51C23×C4×C31—42no—
52C23×C4×C31C2×C414yescomplemented
53C23×C4×C31C2312yes—
54C23×C4×C31C2312yes—
55C23×C4×C31C2312yes—
56C23×C4×C31C2312yes—
57C23×C4×C31C2312yes—
58C23×C4×C31C2312yes—
59C23×C4×C31C2311yescharacteristic
60C2×C4⋊C4×C31—22no—
61C2×C4⋊C4×C31—24no—
62C2×C4⋊C4×C31—41no—
63C2×C4⋊C4×C31—41no—
64C2×C4⋊C4×C31—42no—
65C2×C4⋊C4×C31—42no—
66C2×C22⋊C4×C31—24no—
67C2×C22⋊C4×C31—22no—
68C2×C22⋊C4×C31—24no—
69C2×C22⋊C4×C31—24no—
70C2×C22⋊C4×C31—24no—
71C2×C22⋊C4×C31—24no—
72C2×C22⋊C4×C31—24no—
73C2×C22⋊C4×C31—42no—
74C2×C22⋊C4×C31—42no—
75C2×C22⋊C4×C31—41no—
76C2×C22⋊C4×C31—41no—
77C2×C22⋊C4×C31—42no—
78C2×C22⋊C4×C31—42no—
79C2×C22⋊C4×C31—42no—
80C2×C22⋊C4×C31—41no—
81C2×C22⋊C4×C31—41no—
82C2×C22⋊C4×C31C2×C418yes—
83C2×C22⋊C4×C31C2×C414yescomplemented
84C2×C42×C31—22no—
85C2×C42×C31—41no—
86C2×C42×C31—41no—
87C31×#95—24no—
88C31×#95—24no—
89C31×#95—42no—
90C31×#95—42no—
91C31×#95—42no—
92C31×#95—42no—
93C31×#95—42no—
94C31×#95—42no—
95C31×#95C2×C418yescomplemented
96C24×C31—22no—
97C24×C31—22no—
98C24×C31—22no—
99C24×C31—22no—
100C24×C31—22no—
101C24×C31—22no—
102C24×C31—22no—
103C24×C31—22no—
104C24×C31—21no—
105C24×C31—21no—
106C24×C31—21no—
107C24×C31—21no—
108C24×C31—21no—
109C24×C31—21no—
110C24×C31—21no—
111C24×C31—21no—
112C24×C31C22×C412yes—
113C24×C31C22×C412yes—
114C24×C31C2×D412yes—
115C24×C31C2×D412yes—
116C24×C31C2×Q812yes—
117C24×C31C2×Q812yes—
118C24×C31C2411yescharacteristic
119C2×D4×C31—44no—
120C2×D4×C31—44no—
121C2×D4×C31—44no—
122C2×D4×C31—44no—
123C2×D4×C31—44no—
124C2×D4×C31—44no—
125C2×D4×C31C4⋊C4116yescomplemented
126C22×C4×C31—21no—
127C22×C4×C31—21no—
128C22×C4×C31—21no—
129C22×C4×C31—21no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
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—22no—
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—22no—
152C22×C4×C31—22no—
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—48no—
169C22×C4×C31—44no—
170C22×C4×C31—44no—
171C22×C4×C31—48no—
172C22×C4×C31—48no—
173C22×C4×C31—44no—
174C22×C4×C31—48no—
175C22×C4×C31—44no—
176C22×C4×C31—44no—
177C22×C4×C31—44no—
178C22×C4×C31C22×C414yes—
179C22×C4×C31C22×C414yes—
180C22×C4×C31C22×C412yes—
181C22×C4×C31C2×D412yes—
182C22×C4×C31C2×Q812yes—
183C22×C4×C31#4114yes—
184C22×C4×C31#4114yes—
185C4⋊C4×C31—44no—
186C4⋊C4×C31—48no—
187C22⋊C4×C31—48no—
188C22⋊C4×C31—44no—
189C22⋊C4×C31—48no—
190C22⋊C4×C31—48no—
191C22⋊C4×C31—48no—
192C22⋊C4×C31—44no—
193C42×C31—44no—
194#14513C3111yesmaximal, characteristic, direct product factor, Sylow
195C23×C31—24no—
196C23×C31—24no—
197C23×C31—22no—
198C23×C31—24no—
199C23×C31—22no—
200C23×C31—24no—
201C23×C31—22no—
202C23×C31—22no—
203C23×C31—22no—
204C23×C31—22no—
205C23×C31—22no—
206C23×C31—22no—
207C23×C31—22no—
208C23×C31—22no—
209C23×C31—22no—
210C23×C31—22no—
211C23×C31—24no—
212C23×C31—24no—
213C23×C31—24no—
214C23×C31—24no—
215C23×C31—24no—
216C23×C31—24no—
217C23×C31—24no—
218C23×C31—24no—
219C23×C31—42no—
220C23×C31—42no—
221C23×C31—42no—
222C23×C31—42no—
223C23×C31—42no—
224C23×C31—42no—
225C23×C31—42no—
226C23×C31—42no—
227C23×C31—41no—
228C23×C31—41no—
229C23×C31—42no—
230C23×C31—42no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31—42no—
234C23×C31—41no—
235C23×C31—42no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31C2×C4⋊C414yes—
240C23×C31C2×C4⋊C414yes—
241C23×C31C23×C411yescharacteristic
242C23×C31C22×D411yescharacteristic
243C23×C31C22×Q811yescharacteristic
244C23×C31C2×#4112yes—
245C23×C31C2×#4112yes—
246C23×C31H(5,𝔽2)11yescharacteristic
247C23×C31H(5,𝔽2)11yescharacteristic
248C23×C31H(5,𝔽2)11yescharacteristic
249C23×C31H(5,𝔽2)11yescharacteristic
250C23×C31H(5,𝔽2)12yes—
251C23×C31H(5,𝔽2)12yes—
252D4×C31—416no—
253C2×C4×C31—22no—
254C2×C4×C31—22no—
255C2×C4×C31—22no—
256C2×C4×C31—22no—
257C2×C4×C31—22no—
258C2×C4×C31—22no—
259C2×C4×C31—24no—
260C2×C4×C31—24no—
261C2×C4×C31—24no—
262C2×C4×C31—24no—
263C2×C4×C31—24no—
264C2×C4×C31—24no—
265C2×C4×C31—24no—
266C2×C4×C31—24no—
267C2×C4×C31—24no—
268C2×C4×C31—24no—
269C2×C4×C31—24no—
270C2×C4×C31—24no—
271C2×C4×C31—416no—
272C2×C4×C31—416no—
273C2×C4×C31—42no—
274C2×C4×C31—42no—
275C2×C4×C31—42no—
276C2×C4×C31—42no—
277C2×C4×C31—42no—
278C2×C4×C31—42no—
279C2×C4×C31—42no—
280C2×C4×C31—42no—
281C2×C4×C31—42no—
282C2×C4×C31—42no—
283C2×C4×C31—42no—
284C2×C4×C31—42no—
285C2×C4×C31—42no—
286C2×C4×C31—42no—
287C2×C4×C31—42no—
288C2×C4×C31—42no—
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×C31C2×C4⋊C414yes—
304C2×#390C2×C3111yescharacteristic
305C2×#386C2×C3111yescharacteristic
306C2×#386C2×C3111yescharacteristic
307#1442C2×C3112yescomplemented
308#1439C2×C3112yescomplemented
309#1439C2×C3112yescomplemented
310#1436C2×C3112yescomplemented
311C22⋊#95C2×C3112yescomplemented
312C22⋊#95C2×C3112yescomplemented
313C22×C31—24no—
314C22×C31—24no—
315C22×C31—28no—
316C22×C31—28no—
317C22×C31—44no—
318C22×C31—44no—
319C22×C31—42no—
320C22×C31—42no—
321C22×C31—42no—
322C22×C31—42no—
323C22×C31—42no—
324C22×C31—42no—
325C22×C31—44no—
326C22×C31—44no—
327C22×C31—42no—
328C22×C31—42no—
329C22×C31—42no—
330C22×C31—42no—
331C22×C31—44no—
332C22×C31—44no—
333C22×C31—42no—
334C22×C31—42no—
335C22×C31C22×C4⋊C411yescharacteristic
336C22×C31C4×#4112yes—
337C22×C31#51811yescharacteristic
338C22×C31#51811yescharacteristic
339C22×C31#51812yes—
340C22×C31#53411yescharacteristic
341C22×C31#53411yescharacteristic
342C22×C31#53812yes—
343C22×C31#53812yes—
344C22×C31#54012yes—
345C22×C31#54012yes—
346C22×C31#54311yescharacteristic
347C22×C31#54311yescharacteristic
348C22×C31#54612yes—
349C22×C31#54612yes—
350C22×C31#55111yescharacteristic
351C22×C31#55312yes—
352C22×C31#55412yes—
353C22×C31#55412yes—
354C22×C31#55911yescharacteristic
355C22×C31#56012yes—
356C22×C31#56011yescharacteristic
357C22×C31H(3,𝔽4)11yescharacteristic
358C4×C31—24no—
359C4×C31—44no—
360C4×C31—44no—
361C4×C31—44no—
362C4×C31—44no—
363C4×C31—82no—
364C4×C31—82no—
365C23×D4C22×C3111yescharacteristic
366C24×C4C22×C3111yescharacteristic
367C24×C4C22×C3111yescharacteristic
368C22×C4⋊C4C22×C3112yes—
369C22×C4⋊C4C22×C3111yescharacteristic
370C22×C22⋊C4C22×C3112yes—
371C22×C22⋊C4C22×C3112yes—
372C22×C22⋊C4C22×C3112yes—
373C22×C22⋊C4C22×C3111yescharacteristic
374C22×C22⋊C4C22×C3112yes—
375C22×C22⋊C4C22×C3111yescharacteristic
376C22×C42C22×C3111yescharacteristic
377#390—24no—
378#386—24no—
379#386C4×C3118yescomplemented
380C2×#95C22×C3112yes—
381C2×#95C22×C3112yes—
382C2×#95C22×C3112yes—
383C2×#95C22×C3112yes—
384C2×#95C22×C3112yes—
385C2×#95C22×C3112yes—
386C2×#95C22×C3112yes—
387C2×#95C22×C3112yes—
388C2×#95C22×C3112yes—
389C2×C31—44no—
390C2×C31—44no—
391C2×C31#231511yescharacteristic
392C2×C31#233312yes—
393C2×C31#234912yes—
394C2×C31#237411yescharacteristic
395C2×C31#237511yescharacteristic
396C2×C31#268411yescharacteristic
397C2×C31#268812yes—
398C2×C31#270911yescharacteristic
399C2×C31#274811yescharacteristic
400C2×C31#278012yes—
401C2×C31#280411yescharacteristic
402C25C23×C3111yescharacteristic
403C25C23×C3111yescharacteristic
404C22×D4—41no—
405C22×D4—41no—
406C22×D4—41no—
407C22×D4—41no—
408C22×D4C2×C4×C3114yes—
409C22×D4D4×C3114yes—
410C22×D4Q8×C3114yes—
411C23×C4—22no—
412C23×C4—24no—
413C23×C4—41no—
414C23×C4—41no—
415C23×C4—41no—
416C23×C4—41no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4C2×C4×C3114yescomplemented
421C23×C4C23×C3112yes—
422C23×C4C23×C3112yes—
423C23×C4C23×C3112yes—
424C23×C4C23×C3112yes—
425C23×C4C23×C3112yes—
426C23×C4C23×C3112yes—
427C23×C4C23×C3111yescharacteristic
428C2×C4⋊C4—22no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—41no—
431C2×C4⋊C4—41no—
432C2×C4⋊C4—42no—
433C2×C4⋊C4—42no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—42no—
442C2×C22⋊C4—42no—
443C2×C22⋊C4—41no—
444C2×C22⋊C4—41no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4—42no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4—41no—
449C2×C22⋊C4—41no—
450C2×C22⋊C4C2×C4×C3118yes—
451C2×C22⋊C4C2×C4×C3114yescomplemented
452C2×C42—22no—
453C2×C42—41no—
454C2×C42—41no—
455#95—24no—
456#95—24no—
457#95—42no—
458#95—42no—
459#95—42no—
460#95—42no—
461#95—42no—
462#95—42no—
463#95C2×C4×C3118yescomplemented
464C31#1451311yescharacteristic, direct product factor, Sylow
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—21no—
481C24C22×C4×C3112yes—
482C24C22×C4×C3112yes—
483C24C2×D4×C3112yes—
484C24C2×D4×C3112yes—
485C24C2×Q8×C3112yes—
486C24C2×Q8×C3112yes—
487C24C24×C3111yescharacteristic
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4C4⋊C4×C31116yescomplemented
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—48no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—44no—
543C22×C4—48no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4C22×C4×C3114yes—
548C22×C4C22×C4×C3114yes—
549C22×C4C22×C4×C3112yes—
550C22×C4C2×D4×C3112yes—
551C22×C4C2×Q8×C3112yes—
552C22×C4#41×C3114yes—
553C22×C4#41×C3114yes—
554C4⋊C4—44no—
555C4⋊C4—48no—
556C22⋊C4—48no—
557C22⋊C4—44no—
558C22⋊C4—48no—
559C22⋊C4—48no—
560C22⋊C4—48no—
561C22⋊C4—44no—
562C42—44no—
563C23—24no—
564C23—24no—
565C23—22no—
566C23—24no—
567C23—22no—
568C23—24no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—41no—
596C23—41no—
597C23—42no—
598C23—42no—
599C23—41no—
600C23—41no—
601C23—42no—
602C23—41no—
603C23—42no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23C2×C4⋊C4×C3114yes—
608C23C2×C4⋊C4×C3114yes—
609C23C23×C4×C3111yescharacteristic
610C23C22×D4×C3111yescharacteristic
611C23C22×Q8×C3111yescharacteristic
612C23C2×#41×C3112yes—
613C23C2×#41×C3112yes—
614C23C31×H(5,𝔽2)11yescharacteristic
615C23C31×H(5,𝔽2)11yescharacteristic
616C23C31×H(5,𝔽2)11yescharacteristic
617C23C31×H(5,𝔽2)11yescharacteristic
618C23C31×H(5,𝔽2)12yes—
619C23C31×H(5,𝔽2)12yes—
620D4—416no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—416no—
640C2×C4—416no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4C2×C4⋊C4×C3114yes—
672C22—24no—
673C22—24no—
674C22—28no—
675C22—28no—
676C22—44no—
677C22—44no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—44no—
685C22—44no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—44no—
691C22—44no—
692C22—42no—
693C22—42no—
694C22C22×C4⋊C4×C3111yescharacteristic
695C22C4×#41×C3112yes—
696C22C31×#51811yescharacteristic
697C22C31×#51811yescharacteristic
698C22C31×#51812yes—
699C22C31×#53411yescharacteristic
700C22C31×#53411yescharacteristic
701C22C31×#53812yes—
702C22C31×#53812yes—
703C22C31×#54012yes—
704C22C31×#54012yes—
705C22C31×#54311yescharacteristic
706C22C31×#54311yescharacteristic
707C22C31×#54612yes—
708C22C31×#54612yes—
709C22C31×#55111yescharacteristic
710C22C31×#55312yes—
711C22C31×#55412yes—
712C22C31×#55412yes—
713C22C31×#55911yescharacteristic
714C22C31×#56012yes—
715C22C31×#56011yescharacteristic
716C22C31×H(3,𝔽4)11yescharacteristic
717C4—24no—
718C4—44no—
719C4—44no—
720C4—44no—
721C4—44no—
722C4—82no—
723C4—82no—
724C2—44no—
725C2—44no—
726C2C31×#231511yescharacteristic
727C2C31×#233312yes—
728C2C31×#234912yes—
729C2C31×#237411yescharacteristic
730C2C31×#237511yescharacteristic
731C2C31×#268411yescharacteristic
732C2C31×#268812yes—
733C2C31×#270911yescharacteristic
734C2C31×#274811yescharacteristic
735C2C31×#278012yes—
736C2C31×#280411yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1442C2semidirect
5. C31×#1439C2semidirect
6. C31×#1439C2semidirect
7. C31×#1436C2semidirect
8. C31×C22⋊#95C2semidirect
9. C31×C22⋊#95C2semidirect
24. C31×#386C4semidirect
52. C23×C4×C31C2×C4semidirect
83. C2×C22⋊C4×C31C2×C4semidirect
95. C31×#95C2×C4semidirect
125. C2×D4×C31C4⋊C4semidirect
194. #14513C31direct (N × H)
307. #1442C2×C31semidirect
308. #1439C2×C31semidirect
309. #1439C2×C31semidirect
310. #1436C2×C31semidirect
311. C22⋊#95C2×C31semidirect
312. C22⋊#95C2×C31semidirect
379. #386C4×C31semidirect
420. C23×C4C2×C4×C31semidirect
451. C2×C22⋊C4C2×C4×C31semidirect
463. #95C2×C4×C31semidirect
464. C31#14513direct (N × H)
494. C2×D4C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3902
C2×C31×#3862
C31×#14422
C31×#14392
C31×#14362
C31×C22⋊#952
#1451331