Finite Group Databasebeta

← C31×#14025 #21470784

Subgroups — C31×#14025 #21470784

Order 7936.

3422 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#127C211yesmaximal, characteristic
2C22×C4×D4×C31C211yesmaximal, characteristic, complemented
3C2×C31×#390C211yesmaximal, characteristic, complemented
4C2×C31×#390C211yesmaximal, characteristic, complemented
5C2×C31×#390C211yesmaximal, characteristic, complemented
6C2×C31×#386C214yesmaximal, complemented
7C31×#1438C214yesmaximal, complemented
8C31×C4⋊#95C211yesmaximal, characteristic, complemented
9C4×C31×#95C211yesmaximal, characteristic, complemented
10C23×D4×C31C2211yescharacteristic
11C23×D4×C31C2214yes—
12C23×D4×C31C2211yescharacteristic
13C24×C4×C31C2212yes—
14C2×C31×#127—24no—
15C2×C31×#127—24no—
16C2×C31×#127C418yescomplemented
17C2×C4×D4×C31—24no—
18C2×C4×D4×C31—24no—
19C2×C4×D4×C31—24no—
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2214yes—
25C22×C22⋊C4×C31C2214yes—
26C22×C22⋊C4×C31C2212yes—
27C22×C42×C31C2211yescharacteristic
28C22×C42×C31C2211yescharacteristic
29C22×C42×C31C2211yescharacteristic
30C31×#390—24no—
31C31×#390—24no—
32C31×#390—24no—
33C31×#386—216no—
34C2×C31×#95C2212yes—
35C2×C31×#95C2214yes—
36C2×C31×#95C2212yes—
37C25×C31C2312yes—
38C25×C31C2312yes—
39C22×D4×C31—28no—
40C22×D4×C31—28no—
41C22×D4×C31—22no—
42C22×D4×C31—22no—
43C22×D4×C31—22no—
44C22×D4×C31—22no—
45C22×D4×C31—28no—
46C22×D4×C31—22no—
47C22×D4×C31—22no—
48C22×D4×C31—22no—
49C22×D4×C31—22no—
50C22×D4×C31—28no—
51C22×D4×C31—22no—
52C22×D4×C31—22no—
53C22×D4×C31—44no—
54C22×D4×C31—44no—
55C22×D4×C31C2×C414yes—
56C22×D4×C31C2×C414yescomplemented
57C22×D4×C31C2×C4116yescomplemented
58C22×D4×C31D414yes—
59C22×D4×C31D414yes—
60C23×C4×C31—24no—
61C23×C4×C31—24no—
62C23×C4×C31—24no—
63C23×C4×C31—28no—
64C23×C4×C31—44no—
65C23×C4×C31C2312yes—
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2312yes—
68C23×C4×C31C2312yes—
69C23×C4×C31C2312yes—
70C23×C4×C31C2311yescharacteristic
71C23×C4×C31C2311yescharacteristic
72C31×#127—232no—
73C4×D4×C31—232no—
74C2×C4⋊C4×C31—22no—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31D414yescomplemented
80C2×C22⋊C4×C31—24no—
81C2×C22⋊C4×C31—24no—
82C2×C22⋊C4×C31—24no—
83C2×C22⋊C4×C31—28no—
84C2×C22⋊C4×C31—28no—
85C2×C22⋊C4×C31—28no—
86C2×C22⋊C4×C31—28no—
87C2×C22⋊C4×C31—28no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—44no—
91C2×C22⋊C4×C31—44no—
92C2×C22⋊C4×C31—44no—
93C2×C42×C31—22no—
94C2×C42×C31—22no—
95C2×C42×C31—22no—
96C2×C42×C31—22no—
97C2×C42×C31—22no—
98C2×C42×C31—22no—
99C2×C42×C31—22no—
100C2×C42×C31C2×C414yescomplemented
101C2×C42×C31D414yescomplemented
102C31×#95—28no—
103C31×#95—24no—
104C31×#95D418yescomplemented
105C24×C31—22no—
106C24×C31—22no—
107C24×C31—24no—
108C24×C31—22no—
109C24×C31—22no—
110C24×C31—24no—
111C24×C31—24no—
112C24×C31—24no—
113C24×C31—22no—
114C24×C31—22no—
115C24×C31—24no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31—22no—
120C24×C31—24no—
121C24×C31—24no—
122C24×C31—24no—
123C24×C31C22×C414yes—
124C24×C31C22×C414yes—
125C24×C31C2×D414yes—
126C24×C31C2×D414yes—
127C24×C31C2411yescharacteristic
128C2×D4×C31—232no—
129C2×D4×C31—28no—
130C2×D4×C31—28no—
131C2×D4×C31—28no—
132C2×D4×C31—28no—
133C2×D4×C31—28no—
134C2×D4×C31—232no—
135C2×D4×C31—28no—
136C2×D4×C31—28no—
137C2×D4×C31—28no—
138C2×D4×C31—28no—
139C2×D4×C31—416no—
140C2×D4×C31—416no—
141C2×D4×C31—416no—
142C2×D4×C31—416no—
143C2×D4×C31—416no—
144C2×D4×C31—44no—
145C2×D4×C31—44no—
146C2×D4×C31—44no—
147C2×D4×C31—44no—
148C2×D4×C31C22⋊C4116yescomplemented
149C22×C4×C31—21no—
150C22×C4×C31—21no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—216no—
157C22×C4×C31—24no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
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—24no—
171C22×C4×C31—24no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—24no—
176C22×C4×C31—416no—
177C22×C4×C31—416no—
178C22×C4×C31—48no—
179C22×C4×C31—48no—
180C22×C4×C31C22×C414yes—
181C22×C4×C31C22×C412yes—
182C22×C4×C31C2×D414yes—
183C22×C4×C31C2×D412yes—
184C22×C4×C31C2×D414yes—
185C22×C4×C31C2×D414yes—
186C22×C4×C31C2×D414yes—
187C22×C4×C31C2×D412yes—
188C22×C4×C31C2×D412yes—
189C22×C4×C31C2×D412yes—
190C22×C4×C31C2×D412yes—
191C22×C4×C31C2×D412yes—
192C22×C4×C31#4114yes—
193C22×C4×C31#4112yes—
194C22×C4×C31#4112yes—
195C4⋊C4×C31—28no—
196C4⋊C4×C31—44no—
197C22⋊C4×C31—216no—
198C22⋊C4×C31—416no—
199C22⋊C4×C31—416no—
200C22⋊C4×C31—48no—
201C22⋊C4×C31—48no—
202C42×C31—28no—
203C42×C31—28no—
204C42×C31—44no—
205#14025C3111yesmaximal, characteristic, direct product factor, Sylow
206C23×C31—28no—
207C23×C31—24no—
208C23×C31—24no—
209C23×C31—28no—
210C23×C31—24no—
211C23×C31—24no—
212C23×C31—24no—
213C23×C31—24no—
214C23×C31—28no—
215C23×C31—28no—
216C23×C31—28no—
217C23×C31—28no—
218C23×C31—24no—
219C23×C31—24no—
220C23×C31—28no—
221C23×C31—24no—
222C23×C31—28no—
223C23×C31—42no—
224C23×C31—44no—
225C23×C31—42no—
226C23×C31—42no—
227C23×C31—42no—
228C23×C31—44no—
229C23×C31—44no—
230C23×C31—44no—
231C23×C31—44no—
232C23×C31—44no—
233C23×C31—42no—
234C23×C31—42no—
235C23×C31—42no—
236C23×C31—42no—
237C23×C31—42no—
238C23×C31—44no—
239C23×C31—42no—
240C23×C31—42no—
241C23×C31—42no—
242C23×C31—44no—
243C23×C31—44no—
244C23×C31—44no—
245C23×C31—44no—
246C23×C31—44no—
247C23×C31—44no—
248C23×C31—44no—
249C23×C31—44no—
250C23×C31—44no—
251C23×C31C2×C22⋊C418yes—
252C23×C31C23×C411yescharacteristic
253C23×C31C22×D411yescharacteristic
254C23×C31C22×D411yescharacteristic
255C23×C31C22×D411yescharacteristic
256C23×C31C22×D411yescharacteristic
257C23×C31C22×D412yes—
258C23×C31C2×#4111yescharacteristic
259C23×C31C2×#4111yescharacteristic
260C23×C31C2×#4112yes—
261C23×C31H(5,𝔽2)12yes—
262C23×C31H(5,𝔽2)12yes—
263D4×C31—232no—
264D4×C31—464no—
265D4×C31—416no—
266C2×C4×C31—24no—
267C2×C4×C31—24no—
268C2×C4×C31—22no—
269C2×C4×C31—22no—
270C2×C4×C31—24no—
271C2×C4×C31—24no—
272C2×C4×C31—24no—
273C2×C4×C31—24no—
274C2×C4×C31—24no—
275C2×C4×C31—24no—
276C2×C4×C31—22no—
277C2×C4×C31—24no—
278C2×C4×C31—24no—
279C2×C4×C31—22no—
280C2×C4×C31—22no—
281C2×C4×C31—24no—
282C2×C4×C31—24no—
283C2×C4×C31—28no—
284C2×C4×C31—432no—
285C2×C4×C31—42no—
286C2×C4×C31—42no—
287C2×C4×C31—42no—
288C2×C4×C31—42no—
289C2×C4×C31—44no—
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—44no—
298C2×C4×C31—44no—
299C2×C4×C31C2×C22⋊C414yes—
300C2×C4×C31C4×D414yes—
301C2×C4×C31C4×D414yes—
302C2×C4×C31C4×D418yescomplemented
303C2×C4×C31#12014yes—
304C2×C4×C31#12114yes—
305C2×C4×C31#12114yes—
306C2×C4×C31#12314yes—
307C2×C4×C31#12714yescomplemented
308C22×#127C2×C3111yescharacteristic
309C22×C4×D4C2×C3111yescharacteristic, complemented
310C2×#390C2×C3111yescharacteristic, complemented
311C2×#390C2×C3111yescharacteristic, complemented
312C2×#390C2×C3111yescharacteristic, complemented
313C2×#386C2×C3114yescomplemented
314#1438C2×C3114yescomplemented
315C4⋊#95C2×C3111yescharacteristic, complemented
316C4×#95C2×C3111yescharacteristic, complemented
317C22×C31—216no—
318C22×C31—28no—
319C22×C31—44no—
320C22×C31—44no—
321C22×C31—48no—
322C22×C31—48no—
323C22×C31—44no—
324C22×C31—44no—
325C22×C31—48no—
326C22×C31—44no—
327C22×C31—44no—
328C22×C31—44no—
329C22×C31—44no—
330C22×C31—48no—
331C22×C31—48no—
332C22×C31—44no—
333C22×C31—84no—
334C22×C31—82no—
335C22×C31—82no—
336C22×C31—84no—
337C22×C31—82no—
338C22×C31—82no—
339C22×C31C22×C22⋊C411yescharacteristic
340C22×C31C2×C4×D411yescharacteristic
341C22×C31C2×C4×D412yes—
342C22×C31C2×C4×D411yescharacteristic
343C22×C31#51812yes—
344C22×C31C2×#12011yescharacteristic
345C22×C31C2×#12111yescharacteristic
346C22×C31C2×#12111yescharacteristic
347C22×C31C2×#12311yescharacteristic
348C22×C31C2×#12711yescharacteristic
349C22×C31#53212yes—
350C22×C31#53211yescharacteristic
351C22×C31#53511yescharacteristic
352C22×C31#53511yescharacteristic
353C22×C31#54012yes—
354C22×C31D4212yes—
355C22×C31D4212yes—
356C22×C31D4212yes—
357C22×C31#54612yes—
358C22×C31#54612yes—
359C22×C31#55012yes—
360C22×C31#55012yes—
361C22×C31#55912yes—
362C4×C31—28no—
363C4×C31—24no—
364C4×C31—44no—
365C4×C31—42no—
366C4×C31—44no—
367C4×C31—82no—
368C4×C31#38618yescomplemented
369C23×D4C22×C3111yescharacteristic
370C23×D4C22×C3114yes—
371C23×D4C22×C3111yescharacteristic
372C24×C4C22×C3112yes—
373C2×#127—24no—
374C2×#127—24no—
375C2×#127C4×C3118yescomplemented
376C2×C4×D4—24no—
377C2×C4×D4—24no—
378C2×C4×D4—24no—
379C22×C4⋊C4C22×C3111yescharacteristic
380C22×C4⋊C4C22×C3111yescharacteristic
381C22×C22⋊C4C22×C3112yes—
382C22×C22⋊C4C22×C3112yes—
383C22×C22⋊C4C22×C3114yes—
384C22×C22⋊C4C22×C3114yes—
385C22×C22⋊C4C22×C3112yes—
386C22×C42C22×C3111yescharacteristic
387C22×C42C22×C3111yescharacteristic
388C22×C42C22×C3111yescharacteristic
389#390—24no—
390#390—24no—
391#390—24no—
392#386—216no—
393C2×#95C22×C3112yes—
394C2×#95C22×C3114yes—
395C2×#95C22×C3112yes—
396C2×C31—48no—
397C2×C31—84no—
398C2×C31C2×#38611yescharacteristic
399C2×C31C4×#12711yescharacteristic
400C2×C31#232811yescharacteristic
401C2×C31D4×C22⋊C412yes—
402C2×C31#236612yes—
403C2×C31#242812yes—
404C2×C31#243111yescharacteristic
405C2×C31#243311yescharacteristic
406C2×C31#244512yes—
407C2×C31#254111yescharacteristic
408C2×C31#254411yescharacteristic
409C25C23×C3112yes—
410C25C23×C3112yes—
411C22×D4—28no—
412C22×D4—28no—
413C22×D4—22no—
414C22×D4—22no—
415C22×D4—22no—
416C22×D4—22no—
417C22×D4—28no—
418C22×D4—22no—
419C22×D4—22no—
420C22×D4—22no—
421C22×D4—22no—
422C22×D4—28no—
423C22×D4—22no—
424C22×D4—22no—
425C22×D4—44no—
426C22×D4—44no—
427C22×D4C2×C4×C3114yes—
428C22×D4C2×C4×C3114yescomplemented
429C22×D4C2×C4×C31116yescomplemented
430C22×D4D4×C3114yes—
431C22×D4D4×C3114yes—
432C23×C4—24no—
433C23×C4—24no—
434C23×C4—24no—
435C23×C4—28no—
436C23×C4—44no—
437C23×C4C23×C3112yes—
438C23×C4C23×C3111yescharacteristic
439C23×C4C23×C3112yes—
440C23×C4C23×C3112yes—
441C23×C4C23×C3112yes—
442C23×C4C23×C3111yescharacteristic
443C23×C4C23×C3111yescharacteristic
444#127—232no—
445C4×D4—232no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4D4×C3114yescomplemented
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—28no—
456C2×C22⋊C4—28no—
457C2×C22⋊C4—28no—
458C2×C22⋊C4—28no—
459C2×C22⋊C4—28no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—44no—
463C2×C22⋊C4—44no—
464C2×C22⋊C4—44no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42C2×C4×C3114yescomplemented
473C2×C42D4×C3114yescomplemented
474#95—28no—
475#95—24no—
476#95D4×C3118yescomplemented
477C31#1402511yescharacteristic, direct product factor, Sylow
478C24—22no—
479C24—22no—
480C24—24no—
481C24—22no—
482C24—22no—
483C24—24no—
484C24—24no—
485C24—24no—
486C24—22no—
487C24—22no—
488C24—24no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—24no—
494C24—24no—
495C24—24no—
496C24C22×C4×C3114yes—
497C24C22×C4×C3114yes—
498C24C2×D4×C3114yes—
499C24C2×D4×C3114yes—
500C24C24×C3111yescharacteristic
501C2×D4—232no—
502C2×D4—28no—
503C2×D4—28no—
504C2×D4—28no—
505C2×D4—28no—
506C2×D4—28no—
507C2×D4—232no—
508C2×D4—28no—
509C2×D4—28no—
510C2×D4—28no—
511C2×D4—28no—
512C2×D4—416no—
513C2×D4—416no—
514C2×D4—416no—
515C2×D4—416no—
516C2×D4—416no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4C22⋊C4×C31116yescomplemented
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—216no—
530C22×C4—24no—
531C22×C4—21no—
532C22×C4—21no—
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—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—416no—
550C22×C4—416no—
551C22×C4—48no—
552C22×C4—48no—
553C22×C4C22×C4×C3114yes—
554C22×C4C22×C4×C3112yes—
555C22×C4C2×D4×C3114yes—
556C22×C4C2×D4×C3112yes—
557C22×C4C2×D4×C3114yes—
558C22×C4C2×D4×C3114yes—
559C22×C4C2×D4×C3114yes—
560C22×C4C2×D4×C3112yes—
561C22×C4C2×D4×C3112yes—
562C22×C4C2×D4×C3112yes—
563C22×C4C2×D4×C3112yes—
564C22×C4C2×D4×C3112yes—
565C22×C4#41×C3114yes—
566C22×C4#41×C3112yes—
567C22×C4#41×C3112yes—
568C4⋊C4—28no—
569C4⋊C4—44no—
570C22⋊C4—216no—
571C22⋊C4—416no—
572C22⋊C4—416no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C42—28no—
576C42—28no—
577C42—44no—
578C23—28no—
579C23—24no—
580C23—24no—
581C23—28no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—28no—
587C23—28no—
588C23—28no—
589C23—28no—
590C23—24no—
591C23—24no—
592C23—28no—
593C23—24no—
594C23—28no—
595C23—42no—
596C23—44no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—44no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23—44no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—44no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—44no—
615C23—44no—
616C23—44no—
617C23—44no—
618C23—44no—
619C23—44no—
620C23—44no—
621C23—44no—
622C23—44no—
623C23C2×C22⋊C4×C3118yes—
624C23C23×C4×C3111yescharacteristic
625C23C22×D4×C3111yescharacteristic
626C23C22×D4×C3111yescharacteristic
627C23C22×D4×C3111yescharacteristic
628C23C22×D4×C3111yescharacteristic
629C23C22×D4×C3112yes—
630C23C2×#41×C3111yescharacteristic
631C23C2×#41×C3111yescharacteristic
632C23C2×#41×C3112yes—
633C23C31×H(5,𝔽2)12yes—
634C23C31×H(5,𝔽2)12yes—
635D4—232no—
636D4—464no—
637D4—416no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—28no—
656C2×C4—432no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—44no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4C2×C22⋊C4×C3114yes—
672C2×C4C4×D4×C3114yes—
673C2×C4C4×D4×C3114yes—
674C2×C4C4×D4×C3118yescomplemented
675C2×C4C31×#12014yes—
676C2×C4C31×#12114yes—
677C2×C4C31×#12114yes—
678C2×C4C31×#12314yes—
679C2×C4C31×#12714yescomplemented
680C22—216no—
681C22—28no—
682C22—44no—
683C22—48no—
684C22—48no—
685C22—44no—
686C22—44no—
687C22—48no—
688C22—44no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—48no—
693C22—48no—
694C22—44no—
695C22—44no—
696C22—84no—
697C22—82no—
698C22—82no—
699C22—84no—
700C22—82no—
701C22—82no—
702C22C22×C22⋊C4×C3111yescharacteristic
703C22C2×C4×D4×C3111yescharacteristic
704C22C2×C4×D4×C3112yes—
705C22C2×C4×D4×C3111yescharacteristic
706C22C31×#51812yes—
707C22C2×C31×#12011yescharacteristic
708C22C2×C31×#12111yescharacteristic
709C22C2×C31×#12111yescharacteristic
710C22C2×C31×#12311yescharacteristic
711C22C2×C31×#12711yescharacteristic
712C22C31×#53212yes—
713C22C31×#53211yescharacteristic
714C22C31×#53511yescharacteristic
715C22C31×#53511yescharacteristic
716C22C31×#54012yes—
717C22D42×C3112yes—
718C22D42×C3112yes—
719C22D42×C3112yes—
720C22C31×#54612yes—
721C22C31×#54612yes—
722C22C31×#55012yes—
723C22C31×#55012yes—
724C22C31×#55912yes—
725C4—28no—
726C4—24no—
727C4—44no—
728C4—42no—
729C4—44no—
730C4—82no—
731C4C31×#38618yescomplemented
732C2—48no—
733C2—84no—
734C2C2×C31×#38611yescharacteristic
735C2C4×C31×#12711yescharacteristic
736C2C31×#232811yescharacteristic
737C2D4×C22⋊C4×C3112yes—
738C2C31×#236612yes—
739C2C31×#242812yes—
740C2C31×#243111yescharacteristic
741C2C31×#243311yescharacteristic
742C2C31×#244512yes—
743C2C31×#254111yescharacteristic
744C2C31×#254411yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC22×C31×#127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×D4×C31C2semidirect
3. C2×C31×#390C2semidirect
4. C2×C31×#390C2semidirect
5. C2×C31×#390C2semidirect
6. C2×C31×#386C2semidirect
7. C31×#1438C2semidirect
8. C31×C4⋊#95C2semidirect
9. C4×C31×#95C2semidirect
16. C2×C31×#127C4semidirect
56. C22×D4×C31C2×C4semidirect
57. C22×D4×C31C2×C4semidirect
79. C2×C4⋊C4×C31D4semidirect
100. C2×C42×C31C2×C4semidirect
101. C2×C42×C31D4semidirect
104. C31×#95D4semidirect
148. C2×D4×C31C22⋊C4semidirect
205. #14025C31direct (N × H)
302. C2×C4×C31C4×D4semidirect
307. C2×C4×C31#127semidirect
309. C22×C4×D4C2×C31semidirect
310. C2×#390C2×C31semidirect
311. C2×#390C2×C31semidirect
312. C2×#390C2×C31semidirect
313. C2×#386C2×C31semidirect
314. #1438C2×C31semidirect
315. C4⋊#95C2×C31semidirect
316. C4×#95C2×C31semidirect
368. C4×C31#386semidirect
375. C2×#127C4×C31semidirect
428. C22×D4C2×C4×C31semidirect
429. C22×D4C2×C4×C31semidirect
451. C2×C4⋊C4D4×C31semidirect
472. C2×C42C2×C4×C31semidirect
473. C2×C42D4×C31semidirect
476. #95D4×C31semidirect
477. C31#14025direct (N × H)
521. C2×D4C22⋊C4×C31semidirect
674. C2×C4C4×D4×C31semidirect
679. C2×C4C31×#127semidirect
731. C4C31×#386semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1272
C22×C4×D4×C312
C2×C31×#3902
C2×C31×#3862
C31×#14382
C31×C4⋊#952
C4×C31×#952
#1402531