Finite Group Databasebeta

← C31×#13894 #21470653

Subgroups — C31×#13894 #21470653

Order 7936.

2546 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C31C211yesmaximal, characteristic
2C2×C31×#386C212yesmaximal
3C2×C31×#381C211yesmaximal, characteristic, complemented
4C22×C31×#95C211yesmaximal, characteristic, complemented
5C31×#1445C212yesmaximal, complemented
6C31×#1440C212yesmaximal, complemented
7C31×#1434C211yesmaximal, characteristic, complemented
8C31×#1434C211yesmaximal, characteristic, complemented
9C31×C22⋊#95C211yesmaximal, characteristic, complemented
10C31×C22⋊#95C212yesmaximal, complemented
11C31×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C24×C4×C31C2212yes—
14C24×C4×C31C2211yescharacteristic
15C24×C4×C31C2211yescharacteristic
16C2×C4×D4×C31—28no—
17C2×C4×D4×C31C418yescomplemented
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C42×C31C2211yescharacteristic
25C31×#386—28no—
26C31×#381—24no—
27C2×C31×#95—24no—
28C2×C31×#95C2211yescharacteristic
29C2×C31×#95C2212yes—
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2211yescharacteristic
40C25×C31C2311yescharacteristic
41C25×C31C2311yescharacteristic
42C22×D4×C31—22no—
43C22×D4×C31—24no—
44C22×D4×C31—22no—
45C22×D4×C31C2×C414yes—
46C22×D4×C31D418yes—
47C23×C4×C31—24no—
48C23×C4×C31—24no—
49C23×C4×C31—24no—
50C23×C4×C31—24no—
51C23×C4×C31—22no—
52C23×C4×C31—22no—
53C23×C4×C31—24no—
54C23×C4×C31—22no—
55C23×C4×C31—22no—
56C23×C4×C31—24no—
57C23×C4×C31—24no—
58C23×C4×C31—42no—
59C23×C4×C31—42no—
60C23×C4×C31—42no—
61C23×C4×C31—42no—
62C23×C4×C31C2×C414yes—
63C23×C4×C31C2×C414yescomplemented
64C23×C4×C31C2312yes—
65C23×C4×C31C2312yes—
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2312yes—
70C23×C4×C31C2312yes—
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2311yescharacteristic
73C4×D4×C31—232no—
74C2×C4⋊C4×C31—24no—
75C2×C4⋊C4×C31C2×C414yescomplemented
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—24no—
82C2×C22⋊C4×C31—24no—
83C2×C22⋊C4×C31—24no—
84C2×C22⋊C4×C31—24no—
85C2×C22⋊C4×C31—42no—
86C2×C22⋊C4×C31—42no—
87C2×C22⋊C4×C31C2×C414yes—
88C2×C22⋊C4×C31C2×C414yescomplemented
89C2×C42×C31—24no—
90C2×C42×C31C2×C414yescomplemented
91C31×#95—24no—
92C31×#95—22no—
93C31×#95—24no—
94C31×#95—22no—
95C31×#95—24no—
96C31×#95—24no—
97C31×#95—24no—
98C31×#95—22no—
99C31×#95—42no—
100C31×#95—42no—
101C31×#95—42no—
102C31×#95D414yescomplemented
103C24×C31—21no—
104C24×C31—21no—
105C24×C31—22no—
106C24×C31—22no—
107C24×C31—21no—
108C24×C31—21no—
109C24×C31—21no—
110C24×C31—22no—
111C24×C31—21no—
112C24×C31—22no—
113C24×C31—21no—
114C24×C31—21no—
115C24×C31—21no—
116C24×C31—22no—
117C24×C31—21no—
118C24×C31C22×C412yes—
119C24×C31C22×C412yes—
120C24×C31C2×D414yes—
121C24×C31C2×D414yes—
122C24×C31#4112yes—
123C24×C31#4114yes—
124C24×C31#4112yes—
125C24×C31C2411yescharacteristic
126C2×D4×C31—28no—
127C2×D4×C31—28no—
128C2×D4×C31—216no—
129C2×D4×C31—216no—
130C2×D4×C31C22⋊C4116yes—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—21no—
134C22×C4×C31—21no—
135C22×C4×C31—22no—
136C22×C4×C31—216no—
137C22×C4×C31—28no—
138C22×C4×C31—28no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
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—21no—
149C22×C4×C31—21no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—21no—
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—21no—
163C22×C4×C31—28no—
164C22×C4×C31—28no—
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—22no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—44no—
180C22×C4×C31—44no—
181C22×C4×C31—48no—
182C22×C4×C31—48no—
183C22×C4×C31—48no—
184C22×C4×C31—48no—
185C22×C4×C31—48no—
186C22×C4×C31—48no—
187C22×C4×C31—48no—
188C22×C4×C31—48no—
189C22×C4×C31—48no—
190C22×C4×C31—48no—
191C22×C4×C31C22×C412yes—
192C22×C4×C31C22×C412yes—
193C22×C4×C31C22×C412yes—
194C22×C4×C31C22×C412yes—
195C22×C4×C31C22×C412yes—
196C22×C4×C31C2×D414yes—
197C22×C4×C31C2×D414yes—
198C22×C4×C31C2×D412yes—
199C22×C4×C31#4114yes—
200C22×C4×C31#4112yes—
201C4⋊C4×C31—28no—
202C22⋊C4×C31—28no—
203C22⋊C4×C31—28no—
204C22⋊C4×C31—48no—
205C22⋊C4×C31—48no—
206C22⋊C4×C31—48no—
207C42×C31—28no—
208#13894C3111yesmaximal, characteristic, direct product factor, Sylow
209C23×C31—22no—
210C23×C31—22no—
211C23×C31—22no—
212C23×C31—22no—
213C23×C31—24no—
214C23×C31—24no—
215C23×C31—24no—
216C23×C31—24no—
217C23×C31—24no—
218C23×C31—22no—
219C23×C31—24no—
220C23×C31—24no—
221C23×C31—24no—
222C23×C31—22no—
223C23×C31—24no—
224C23×C31—22no—
225C23×C31—22no—
226C23×C31—24no—
227C23×C31—22no—
228C23×C31—22no—
229C23×C31—22no—
230C23×C31—22no—
231C23×C31—22no—
232C23×C31—22no—
233C23×C31—24no—
234C23×C31—24no—
235C23×C31—24no—
236C23×C31—24no—
237C23×C31—24no—
238C23×C31—24no—
239C23×C31—42no—
240C23×C31—42no—
241C23×C31—42no—
242C23×C31—42no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—42no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—42no—
249C23×C31C2×C22⋊C414yes—
250C23×C31C2×C22⋊C414yes—
251C23×C31#11714yes—
252C23×C31#11714yes—
253C23×C31#12318yes—
254C23×C31#12318yes—
255C23×C31C23×C411yescharacteristic
256C23×C31C22×D412yes—
257C23×C31C22×D411yescharacteristic
258C23×C31C2×#4112yes—
259C23×C31C2×#4111yescharacteristic
260C23×C31C2×#4111yescharacteristic
261C23×C31C2×#4111yescharacteristic
262C23×C31C2×#4112yes—
263C23×C31H(5,𝔽2)12yes—
264C23×C31H(5,𝔽2)11yescharacteristic
265C23×C312−1+411yescharacteristic
266D4×C31—232no—
267C2×C4×C31—22no—
268C2×C4×C31—22no—
269C2×C4×C31—22no—
270C2×C4×C31—22no—
271C2×C4×C31—24no—
272C2×C4×C31—24no—
273C2×C4×C31—24no—
274C2×C4×C31—24no—
275C2×C4×C31—22no—
276C2×C4×C31—22no—
277C2×C4×C31—22no—
278C2×C4×C31—22no—
279C2×C4×C31—22no—
280C2×C4×C31—22no—
281C2×C4×C31—22no—
282C2×C4×C31—22no—
283C2×C4×C31—22no—
284C2×C4×C31—24no—
285C2×C4×C31—24no—
286C2×C4×C31—24no—
287C2×C4×C31—24no—
288C2×C4×C31—24no—
289C2×C4×C31—24no—
290C2×C4×C31—416no—
291C2×C4×C31—416no—
292C2×C4×C31—432no—
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×C4×C31—42no—
311C2×C4×C31—42no—
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×C31C2×C22⋊C414yes—
322C2×C4×C31C4×D414yes—
323C22×C4×D4C2×C3111yescharacteristic
324C2×#386C2×C3112yes—
325C2×#381C2×C3111yescharacteristic, complemented
326C22×#95C2×C3111yescharacteristic, complemented
327#1445C2×C3112yescomplemented
328#1440C2×C3112yescomplemented
329#1434C2×C3111yescharacteristic, complemented
330#1434C2×C3111yescharacteristic, complemented
331C22⋊#95C2×C3111yescharacteristic, complemented
332C22⋊#95C2×C3112yescomplemented
333C22⋊#95C2×C3111yescharacteristic, complemented
334C22×C31—24no—
335C22×C31—24no—
336C22×C31—24no—
337C22×C31—24no—
338C22×C31—24no—
339C22×C31—28no—
340C22×C31—28no—
341C22×C31—28no—
342C22×C31—28no—
343C22×C31—24no—
344C22×C31—24no—
345C22×C31—24no—
346C22×C31—24no—
347C22×C31—42no—
348C22×C31—42no—
349C22×C31—42no—
350C22×C31—44no—
351C22×C31—44no—
352C22×C31—44no—
353C22×C31—44no—
354C22×C31—42no—
355C22×C31#38118yescomplemented
356C22×C31C22×C22⋊C411yescharacteristic
357C22×C31C2×#11711yescharacteristic
358C22×C31C2×#11711yescharacteristic
359C22×C31C2×C4×D411yescharacteristic
360C22×C31C4×#4111yescharacteristic
361C22×C31#51811yescharacteristic
362C22×C31#52011yescharacteristic
363C22×C31C2×#12312yes—
364C22×C31C2×#12312yes—
365C22×C31#52512yes—
366C22×C31#52912yes—
367C22×C31#53812yes—
368C22×C31#53912yes—
369C22×C31D4212yes—
370C22×C31#54612yes—
371C22×C31#54612yes—
372C22×C31#54611yescharacteristic
373C22×C31#54712yes—
374C22×C31#54811yescharacteristic
375C22×C31#55112yes—
376C22×C31#55211yescharacteristic
377C22×C31#55311yescharacteristic
378C22×C31#55312yes—
379C4×C31—24no—
380C4×C31—24no—
381C4×C31—42no—
382C4×C31—42no—
383C4×C31—42no—
384C4×C31—44no—
385C4×C31—44no—
386C4×C31—82no—
387C4×C31—82no—
388C23×D4C22×C3111yescharacteristic
389C24×C4C22×C3112yes—
390C24×C4C22×C3111yescharacteristic
391C24×C4C22×C3111yescharacteristic
392C2×C4×D4—28no—
393C2×C4×D4C4×C3118yescomplemented
394C22×C4⋊C4C22×C3111yescharacteristic
395C22×C22⋊C4C22×C3112yes—
396C22×C22⋊C4C22×C3112yes—
397C22×C22⋊C4C22×C3112yes—
398C22×C22⋊C4C22×C3111yescharacteristic
399C22×C22⋊C4C22×C3111yescharacteristic
400C22×C42C22×C3111yescharacteristic
401#386—28no—
402#381—24no—
403C2×#95—24no—
404C2×#95C22×C3111yescharacteristic
405C2×#95C22×C3112yes—
406C2×#95C22×C3111yescharacteristic
407C2×#95C22×C3111yescharacteristic
408C2×#95C22×C3112yes—
409C2×#95C22×C3112yes—
410C2×#95C22×C3112yes—
411C2×#95C22×C3112yes—
412C2×#95C22×C3112yes—
413C2×#95C22×C3112yes—
414C2×#95C22×C3112yes—
415C2×#95C22×C3111yescharacteristic
416C2×C31—28no—
417C2×C31—44no—
418C2×C31C2×#38111yescharacteristic
419C2×C31#229011yescharacteristic
420C2×C31#231811yescharacteristic
421C2×C31D4×C22⋊C411yescharacteristic
422C2×C31#233911yescharacteristic
423C2×C31#235211yescharacteristic
424C2×C31#235311yescharacteristic
425C2×C31#241812yes—
426C2×C31#241912yes—
427C2×C31#244312yes—
428C2×C31#244412yes—
429C25C23×C3111yescharacteristic
430C25C23×C3111yescharacteristic
431C22×D4—22no—
432C22×D4—24no—
433C22×D4—22no—
434C22×D4C2×C4×C3114yes—
435C22×D4D4×C3118yes—
436C23×C4—24no—
437C23×C4—24no—
438C23×C4—24no—
439C23×C4—24no—
440C23×C4—22no—
441C23×C4—22no—
442C23×C4—24no—
443C23×C4—22no—
444C23×C4—22no—
445C23×C4—24no—
446C23×C4—24no—
447C23×C4—42no—
448C23×C4—42no—
449C23×C4—42no—
450C23×C4—42no—
451C23×C4C2×C4×C3114yes—
452C23×C4C2×C4×C3114yescomplemented
453C23×C4C23×C3112yes—
454C23×C4C23×C3112yes—
455C23×C4C23×C3111yescharacteristic
456C23×C4C23×C3111yescharacteristic
457C23×C4C23×C3111yescharacteristic
458C23×C4C23×C3112yes—
459C23×C4C23×C3112yes—
460C23×C4C23×C3111yescharacteristic
461C23×C4C23×C3111yescharacteristic
462C4×D4—232no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4C2×C4×C3114yescomplemented
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4C2×C4×C3114yes—
477C2×C22⋊C4C2×C4×C3114yescomplemented
478C2×C42—24no—
479C2×C42C2×C4×C3114yescomplemented
480#95—24no—
481#95—22no—
482#95—24no—
483#95—22no—
484#95—24no—
485#95—24no—
486#95—24no—
487#95—22no—
488#95—42no—
489#95—42no—
490#95—42no—
491#95D4×C3114yescomplemented
492C31#1389411yescharacteristic, direct product factor, Sylow
493C24—21no—
494C24—21no—
495C24—22no—
496C24—22no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—22no—
501C24—21no—
502C24—22no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—22no—
507C24—21no—
508C24C22×C4×C3112yes—
509C24C22×C4×C3112yes—
510C24C2×D4×C3114yes—
511C24C2×D4×C3114yes—
512C24#41×C3112yes—
513C24#41×C3114yes—
514C24#41×C3112yes—
515C24C24×C3111yescharacteristic
516C2×D4—28no—
517C2×D4—28no—
518C2×D4—216no—
519C2×D4—216no—
520C2×D4C22⋊C4×C31116yes—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—216no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4C22×C4×C3112yes—
582C22×C4C22×C4×C3112yes—
583C22×C4C22×C4×C3112yes—
584C22×C4C22×C4×C3112yes—
585C22×C4C22×C4×C3112yes—
586C22×C4C2×D4×C3114yes—
587C22×C4C2×D4×C3114yes—
588C22×C4C2×D4×C3112yes—
589C22×C4#41×C3114yes—
590C22×C4#41×C3112yes—
591C4⋊C4—28no—
592C22⋊C4—28no—
593C22⋊C4—28no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C42—28no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—24no—
613C23—22no—
614C23—22no—
615C23—24no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—41no—
633C23—41no—
634C23—42no—
635C23—41no—
636C23—41no—
637C23—42no—
638C23C2×C22⋊C4×C3114yes—
639C23C2×C22⋊C4×C3114yes—
640C23C31×#11714yes—
641C23C31×#11714yes—
642C23C31×#12318yes—
643C23C31×#12318yes—
644C23C23×C4×C3111yescharacteristic
645C23C22×D4×C3112yes—
646C23C22×D4×C3111yescharacteristic
647C23C2×#41×C3112yes—
648C23C2×#41×C3111yescharacteristic
649C23C2×#41×C3111yescharacteristic
650C23C2×#41×C3111yescharacteristic
651C23C2×#41×C3112yes—
652C23C31×H(5,𝔽2)12yes—
653C23C31×H(5,𝔽2)11yescharacteristic
654C23C31×2−1+411yescharacteristic
655D4—232no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—416no—
680C2×C4—416no—
681C2×C4—432no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4C2×C22⋊C4×C3114yes—
711C2×C4C4×D4×C3114yes—
712C22—24no—
713C22—24no—
714C22—24no—
715C22—24no—
716C22—24no—
717C22—28no—
718C22—28no—
719C22—28no—
720C22—28no—
721C22—24no—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—42no—
733C22C31×#38118yescomplemented
734C22C22×C22⋊C4×C3111yescharacteristic
735C22C2×C31×#11711yescharacteristic
736C22C2×C31×#11711yescharacteristic
737C22C2×C4×D4×C3111yescharacteristic
738C22C4×#41×C3111yescharacteristic
739C22C31×#51811yescharacteristic
740C22C31×#52011yescharacteristic
741C22C2×C31×#12312yes—
742C22C2×C31×#12312yes—
743C22C31×#52512yes—
744C22C31×#52912yes—
745C22C31×#53812yes—
746C22C31×#53912yes—
747C22D42×C3112yes—
748C22C31×#54612yes—
749C22C31×#54612yes—
750C22C31×#54611yescharacteristic
751C22C31×#54712yes—
752C22C31×#54811yescharacteristic
753C22C31×#55112yes—
754C22C31×#55211yescharacteristic
755C22C31×#55311yescharacteristic
756C22C31×#55312yes—
757C4—24no—
758C4—24no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—44no—
763C4—44no—
764C4—82no—
765C4—82no—
766C2—28no—
767C2—44no—
768C2C2×C31×#38111yescharacteristic
769C2C31×#229011yescharacteristic
770C2C31×#231811yescharacteristic
771C2D4×C22⋊C4×C3111yescharacteristic
772C2C31×#233911yescharacteristic
773C2C31×#235211yescharacteristic
774C2C31×#235311yescharacteristic
775C2C31×#241812yes—
776C2C31×#241912yes—
777C2C31×#244312yes—
778C2C31×#244412yes—
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
3. C2×C31×#381C2semidirect
4. C22×C31×#95C2semidirect
5. C31×#1445C2semidirect
6. C31×#1440C2semidirect
7. C31×#1434C2semidirect
8. C31×#1434C2semidirect
9. C31×C22⋊#95C2semidirect
10. C31×C22⋊#95C2semidirect
11. C31×C22⋊#95C2semidirect
17. C2×C4×D4×C31C4semidirect
63. C23×C4×C31C2×C4semidirect
75. C2×C4⋊C4×C31C2×C4semidirect
88. C2×C22⋊C4×C31C2×C4semidirect
90. C2×C42×C31C2×C4semidirect
102. C31×#95D4semidirect
208. #13894C31direct (N × H)
325. C2×#381C2×C31semidirect
326. C22×#95C2×C31semidirect
327. #1445C2×C31semidirect
328. #1440C2×C31semidirect
329. #1434C2×C31semidirect
330. #1434C2×C31semidirect
331. C22⋊#95C2×C31semidirect
332. C22⋊#95C2×C31semidirect
333. C22⋊#95C2×C31semidirect
355. C22×C31#381semidirect
393. C2×C4×D4C4×C31semidirect
452. C23×C4C2×C4×C31semidirect
464. C2×C4⋊C4C2×C4×C31semidirect
477. C2×C22⋊C4C2×C4×C31semidirect
479. C2×C42C2×C4×C31semidirect
491. #95D4×C31semidirect
492. C31#13894direct (N × H)
733. C22C31×#381semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C312
C2×C31×#3862
C2×C31×#3812
C22×C31×#952
C31×#14452
C31×#14402
C31×#14342
C31×C22⋊#952
#1389431