Finite Group Databasebeta

← C31×#16258 #21473017

Subgroups — C31×#16258 #21473017

Order 7936.

2706 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic, complemented
2C2×C31×#392C211yesmaximal, characteristic, complemented
3C2×C31×#392C212yesmaximal, complemented
4C2×C31×#386C211yesmaximal, characteristic, complemented
5C2×C31×#381C211yesmaximal, characteristic, complemented
6C31×#1442C211yesmaximal, characteristic, complemented
7C31×#1440C212yesmaximal, complemented
8C31×#1439C211yesmaximal, characteristic, complemented
9C31×#1438C212yesmaximal, complemented
10C31×#1438C211yesmaximal, characteristic, complemented
11C31×#1438C212yesmaximal, complemented
12C23×D4×C31C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C23×D4×C31C2212yes—
15C23×D4×C31C2212yes—
16C24×C4×C31C2211yescharacteristic
17C2×C31×#121—28no—
18C2×C31×#121—24no—
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2212yes—
29C31×#392—28no—
30C31×#392—24no—
31C31×#386—24no—
32C31×#381—24no—
33C2×C31×#95C2212yes—
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2212yes—
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2211yescharacteristic
41C25×C31C2312yes—
42C25×C31C2311yescharacteristic
43C25×C31C2311yescharacteristic
44C22×D4×C31—24no—
45C22×D4×C31—24no—
46C22×D4×C31—24no—
47C22×D4×C31—22no—
48C22×D4×C31—22no—
49C22×D4×C31—24no—
50C22×D4×C31—24no—
51C22×D4×C31—24no—
52C22×D4×C31—22no—
53C22×D4×C31—24no—
54C22×D4×C31—22no—
55C22×D4×C31—22no—
56C22×D4×C31—22no—
57C22×D4×C31—42no—
58C22×D4×C31—42no—
59C22×D4×C31—42no—
60C22×D4×C31—42no—
61C22×D4×C31—42no—
62C22×D4×C31—42no—
63C22×D4×C31—42no—
64C22×D4×C31—42no—
65C22×D4×C31—42no—
66C22×D4×C31—42no—
67C22×D4×C31D418yescomplemented
68C23×C4×C31—24no—
69C23×C4×C31—22no—
70C23×C4×C31—22no—
71C23×C4×C31—42no—
72C23×C4×C31D414yescomplemented
73C23×C4×C31C2312yes—
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2312yes—
78C23×C4×C31C2312yes—
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C31×#121—232no—
82C2×C4⋊C4×C31—24no—
83C2×C4⋊C4×C31—22no—
84C2×C22⋊C4×C31—24no—
85C2×C22⋊C4×C31—24no—
86C2×C22⋊C4×C31—24no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—24no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—24no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—24no—
97C2×C22⋊C4×C31—22no—
98C2×C22⋊C4×C31—42no—
99C2×C22⋊C4×C31—42no—
100C2×C22⋊C4×C31—42no—
101C2×C22⋊C4×C31—42no—
102C2×C22⋊C4×C31—42no—
103C2×C22⋊C4×C31—42no—
104C2×C22⋊C4×C31—42no—
105C2×C22⋊C4×C31—42no—
106C2×C22⋊C4×C31—42no—
107C2×C22⋊C4×C31—42no—
108C2×C22⋊C4×C31—42no—
109C31×#95—24no—
110C31×#95—22no—
111C31×#95—22no—
112C31×#95—22no—
113C31×#95—24no—
114C31×#95—42no—
115C31×#95—42no—
116C31×#95D414yescomplemented
117C24×C31—21no—
118C24×C31—21no—
119C24×C31—21no—
120C24×C31—21no—
121C24×C31—22no—
122C24×C31—22no—
123C24×C31—22no—
124C24×C31—21no—
125C24×C31—21no—
126C24×C31—21no—
127C24×C31—22no—
128C24×C31—22no—
129C24×C31—22no—
130C24×C31—22no—
131C24×C31—21no—
132C24×C31—22no—
133C24×C31—21no—
134C24×C31—21no—
135C24×C31—22no—
136C24×C31—22no—
137C24×C31—22no—
138C24×C31—21no—
139C24×C31—22no—
140C24×C31—22no—
141C24×C31—22no—
142C24×C31—22no—
143C24×C31—22no—
144C24×C31—22no—
145C24×C31—22no—
146C24×C31—22no—
147C24×C31—22no—
148C24×C31—21no—
149C24×C31—22no—
150C24×C31C2×D414yes—
151C24×C31C2×D414yes—
152C24×C31C2×D412yes—
153C24×C31#4112yes—
154C24×C31C2411yescharacteristic
155C2×D4×C31—28no—
156C2×D4×C31—28no—
157C2×D4×C31—216no—
158C2×D4×C31—48no—
159C2×D4×C31—48no—
160C2×D4×C31—48no—
161C2×D4×C31—48no—
162C2×D4×C31—48no—
163C2×D4×C31—48no—
164C2×D4×C31—48no—
165C2×D4×C31—44no—
166C2×D4×C31—48no—
167C2×D4×C31—48no—
168C2×D4×C31—48no—
169C2×D4×C31—48no—
170C2×D4×C31—48no—
171C2×D4×C31—48no—
172C2×D4×C31—44no—
173C2×D4×C31—48no—
174C2×D4×C31—48no—
175C2×D4×C31—48no—
176C2×D4×C31—48no—
177C2×D4×C31—44no—
178C2×D4×C31—44no—
179C22×C4×C31—22no—
180C22×C4×C31—22no—
181C22×C4×C31—28no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—22no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—22no—
202C22×C4×C31—28no—
203C22×C4×C31—22no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—22no—
208C22×C4×C31—21no—
209C22×C4×C31—22no—
210C22×C4×C31—21no—
211C22×C4×C31—22no—
212C22×C4×C31—22no—
213C22×C4×C31—22no—
214C22×C4×C31—22no—
215C22×C4×C31—22no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—21no—
219C22×C4×C31—22no—
220C22×C4×C31—44no—
221C22×C4×C31—48no—
222C22×C4×C31—48no—
223C22×C4×C31C2×D414yes—
224C22×C4×C31C2×D412yes—
225C22×C4×C31C2×D414yes—
226C22×C4×C31C2×D412yes—
227C22×C4×C31C2×D412yes—
228C22×C4×C31#4112yes—
229C22×C4×C31#4112yes—
230C4⋊C4×C31—28no—
231C22⋊C4×C31—216no—
232C22⋊C4×C31—48no—
233C22⋊C4×C31—48no—
234C22⋊C4×C31—44no—
235C22⋊C4×C31—48no—
236C22⋊C4×C31—48no—
237C22⋊C4×C31—44no—
238C22⋊C4×C31—48no—
239C22⋊C4×C31—44no—
240#16258C3111yesmaximal, characteristic, direct product factor, Sylow
241C23×C31—22no—
242C23×C31—22no—
243C23×C31—22no—
244C23×C31—24no—
245C23×C31—24no—
246C23×C31—22no—
247C23×C31—22no—
248C23×C31—22no—
249C23×C31—24no—
250C23×C31—24no—
251C23×C31—24no—
252C23×C31—24no—
253C23×C31—24no—
254C23×C31—22no—
255C23×C31—24no—
256C23×C31—24no—
257C23×C31—24no—
258C23×C31—24no—
259C23×C31—24no—
260C23×C31—24no—
261C23×C31—22no—
262C23×C31—24no—
263C23×C31—24no—
264C23×C31—22no—
265C23×C31—42no—
266C23×C31—42no—
267C23×C31—42no—
268C23×C31—42no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—42no—
274C23×C31—42no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—42no—
278C23×C31—42no—
279C23×C31—41no—
280C23×C31—42no—
281C23×C31—42no—
282C23×C31—42no—
283C23×C31—42no—
284C23×C31—42no—
285C23×C31—42no—
286C23×C31—42no—
287C23×C31—42no—
288C23×C31—41no—
289C23×C31—42no—
290C23×C31—42no—
291C23×C31—41no—
292C23×C31—42no—
293C23×C31—41no—
294C23×C31—42no—
295C23×C31—42no—
296C23×C31—42no—
297C23×C31—42no—
298C23×C31—42no—
299C23×C31—42no—
300C23×C31—42no—
301C23×C31—42no—
302C23×C31—42no—
303C23×C31—42no—
304C23×C31—42no—
305C23×C31—42no—
306C23×C31—42no—
307C23×C31—42no—
308C23×C31—42no—
309C23×C31—42no—
310C23×C31—41no—
311C23×C31—42no—
312C23×C31—42no—
313C23×C31—41no—
314C23×C31—42no—
315C23×C31—42no—
316C23×C31—42no—
317C23×C31—42no—
318C23×C31—42no—
319C23×C31—42no—
320C23×C31—42no—
321C23×C31#12014yes—
322C23×C31C22×D411yescharacteristic
323C23×C31C22×D412yes—
324C23×C31C22×D411yescharacteristic
325C23×C31C2×#4111yescharacteristic
326C23×C31C2×#4111yescharacteristic
327C23×C31C2×#4111yescharacteristic
328C23×C31H(5,𝔽2)12yes—
329C23×C31H(5,𝔽2)11yescharacteristic
330C23×C31H(5,𝔽2)11yescharacteristic
331C23×C31H(5,𝔽2)12yes—
332C23×C31H(5,𝔽2)12yes—
333D4×C31—416no—
334D4×C31—432no—
335D4×C31—416no—
336D4×C31—432no—
337C2×C4×C31—22no—
338C2×C4×C31—22no—
339C2×C4×C31—24no—
340C2×C4×C31—24no—
341C2×C4×C31—22no—
342C2×C4×C31—24no—
343C2×C4×C31—22no—
344C2×C4×C31—22no—
345C2×C4×C31—22no—
346C2×C4×C31—24no—
347C2×C4×C31—24no—
348C2×C4×C31—24no—
349C2×C4×C31—24no—
350C2×C4×C31—24no—
351C2×C4×C31—24no—
352C2×C4×C31—416no—
353C2×C4×C31—41no—
354C2×C4×C31—42no—
355C2×C4×C31—42no—
356C2×C4×C31—42no—
357C2×C4×C31—42no—
358C2×C4×C31—42no—
359C2×C4×C31—41no—
360C2×C4×C31—42no—
361C2×C4×C31—42no—
362C2×C4×C31—42no—
363C2×C4×C31—42no—
364C2×C4×C31—42no—
365C2×C4×C31—42no—
366C2×C4×C31—41no—
367C2×C4×C31—42no—
368C2×C4×C31—41no—
369C2×C4×C31—41no—
370C2×C4×C31—42no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—42no—
374C2×C4×C31—41no—
375C2×C4×C31—42no—
376C2×C4×C31—42no—
377C2×C4×C31—42no—
378C2×C4×C31—42no—
379C2×C4×C31—42no—
380C2×C4×C31—42no—
381C2×C4×C31—42no—
382C2×C4×C31—42no—
383C2×C4×C31#12114yes—
384C22×#121C2×C3111yescharacteristic, complemented
385C2×#392C2×C3111yescharacteristic, complemented
386C2×#392C2×C3112yescomplemented
387C2×#386C2×C3111yescharacteristic, complemented
388C2×#381C2×C3111yescharacteristic, complemented
389#1442C2×C3111yescharacteristic, complemented
390#1440C2×C3112yescomplemented
391#1439C2×C3111yescharacteristic, complemented
392#1438C2×C3112yescomplemented
393#1438C2×C3111yescharacteristic, complemented
394#1438C2×C3112yescomplemented
395C22×C31—24no—
396C22×C31—24no—
397C22×C31—24no—
398C22×C31—42no—
399C22×C31—42no—
400C22×C31—42no—
401C22×C31—44no—
402C22×C31—44no—
403C22×C31—44no—
404C22×C31—44no—
405C22×C31—42no—
406C22×C31—44no—
407C22×C31—42no—
408C22×C31—42no—
409C22×C31—44no—
410C22×C31—44no—
411C22×C31—42no—
412C22×C31—44no—
413C22×C31—44no—
414C22×C31—44no—
415C22×C31—44no—
416C22×C31—44no—
417C22×C31—44no—
418C22×C31—81no—
419C22×C31—81no—
420C22×C31—82no—
421C22×C31—82no—
422C22×C31—81no—
423C22×C31—82no—
424C22×C31—82no—
425C22×C31—82no—
426C22×C31—82no—
427C22×C31—82no—
428C22×C31—82no—
429C22×C31—82no—
430C22×C31—81no—
431C22×C31—82no—
432C22×C31C2×#12011yescharacteristic
433C22×C31C2×#12111yescharacteristic
434C22×C31#52511yescharacteristic
435C22×C31#53412yes—
436C22×C31#53412yes—
437C22×C31#53411yescharacteristic
438C22×C31#53511yescharacteristic
439C22×C31#53511yescharacteristic
440C22×C31#53511yescharacteristic
441C22×C31#53512yes—
442C22×C31#53812yes—
443C22×C31#54012yes—
444C22×C31#54012yes—
445C22×C31D4212yes—
446C22×C31#54612yes—
447C22×C31#54612yes—
448C22×C31#54612yes—
449C22×C31#54611yescharacteristic
450C22×C31#55011yescharacteristic
451C22×C31#55311yescharacteristic
452C22×C31#55511yescharacteristic
453C22×C31#56012yes—
454C22×C31#56012yes—
455C4×C31—24no—
456C4×C31—44no—
457C4×C31—42no—
458C4×C31—42no—
459C4×C31—44no—
460C4×C31—81no—
461C4×C31—82no—
462C4×C31—81no—
463C23×D4C22×C3111yescharacteristic
464C23×D4C22×C3111yescharacteristic
465C23×D4C22×C3112yes—
466C23×D4C22×C3112yes—
467C24×C4C22×C3111yescharacteristic
468C2×#121—28no—
469C2×#121—24no—
470C22×C4⋊C4C22×C3111yescharacteristic
471C22×C22⋊C4C22×C3111yescharacteristic
472C22×C22⋊C4C22×C3112yes—
473C22×C22⋊C4C22×C3112yes—
474C22×C22⋊C4C22×C3112yes—
475C22×C22⋊C4C22×C3112yes—
476C22×C22⋊C4C22×C3112yes—
477C22×C22⋊C4C22×C3111yescharacteristic
478C22×C22⋊C4C22×C3111yescharacteristic
479C22×C22⋊C4C22×C3112yes—
480#392—28no—
481#392—24no—
482#386—24no—
483#381—24no—
484C2×#95C22×C3112yes—
485C2×#95C22×C3111yescharacteristic
486C2×#95C22×C3112yes—
487C2×#95C22×C3111yescharacteristic
488C2×#95C22×C3111yescharacteristic
489C2×#95C22×C3112yes—
490C2×#95C22×C3112yes—
491C2×#95C22×C3111yescharacteristic
492C2×C31—44no—
493C2×C31—84no—
494C2×C31—82no—
495C2×C31#240411yescharacteristic
496C2×C31#241011yescharacteristic
497C2×C31#241411yescharacteristic
498C2×C31#261311yescharacteristic
499C2×C31#261911yescharacteristic
500C2×C31#263511yescharacteristic
501C2×C31#267312yes—
502C2×C31#267812yes—
503C2×C31#268812yes—
504C2×C31#269912yes—
505C2×C31#281511yescharacteristic
506C25C23×C3112yes—
507C25C23×C3111yescharacteristic
508C25C23×C3111yescharacteristic
509C22×D4—24no—
510C22×D4—24no—
511C22×D4—24no—
512C22×D4—22no—
513C22×D4—22no—
514C22×D4—24no—
515C22×D4—24no—
516C22×D4—24no—
517C22×D4—22no—
518C22×D4—24no—
519C22×D4—22no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—42no—
523C22×D4—42no—
524C22×D4—42no—
525C22×D4—42no—
526C22×D4—42no—
527C22×D4—42no—
528C22×D4—42no—
529C22×D4—42no—
530C22×D4—42no—
531C22×D4—42no—
532C22×D4D4×C3118yescomplemented
533C23×C4—24no—
534C23×C4—22no—
535C23×C4—22no—
536C23×C4—42no—
537C23×C4D4×C3114yescomplemented
538C23×C4C23×C3112yes—
539C23×C4C23×C3111yescharacteristic
540C23×C4C23×C3111yescharacteristic
541C23×C4C23×C3111yescharacteristic
542C23×C4C23×C3112yes—
543C23×C4C23×C3112yes—
544C23×C4C23×C3111yescharacteristic
545C23×C4C23×C3111yescharacteristic
546#121—232no—
547C2×C4⋊C4—24no—
548C2×C4⋊C4—22no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574#95—24no—
575#95—22no—
576#95—22no—
577#95—22no—
578#95—24no—
579#95—42no—
580#95—42no—
581#95D4×C3114yescomplemented
582C31#1625811yescharacteristic, direct product factor, Sylow
583C24—21no—
584C24—21no—
585C24—21no—
586C24—21no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—21no—
591C24—21no—
592C24—21no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—22no—
599C24—21no—
600C24—21no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—21no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—21no—
615C24—22no—
616C24C2×D4×C3114yes—
617C24C2×D4×C3114yes—
618C24C2×D4×C3112yes—
619C24#41×C3112yes—
620C24C24×C3111yescharacteristic
621C2×D4—28no—
622C2×D4—28no—
623C2×D4—216no—
624C2×D4—48no—
625C2×D4—48no—
626C2×D4—48no—
627C2×D4—48no—
628C2×D4—48no—
629C2×D4—48no—
630C2×D4—48no—
631C2×D4—44no—
632C2×D4—48no—
633C2×D4—48no—
634C2×D4—48no—
635C2×D4—48no—
636C2×D4—48no—
637C2×D4—48no—
638C2×D4—44no—
639C2×D4—48no—
640C2×D4—48no—
641C2×D4—48no—
642C2×D4—48no—
643C2×D4—44no—
644C2×D4—44no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—28no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—28no—
669C22×C4—22no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—22no—
686C22×C4—44no—
687C22×C4—48no—
688C22×C4—48no—
689C22×C4C2×D4×C3114yes—
690C22×C4C2×D4×C3112yes—
691C22×C4C2×D4×C3114yes—
692C22×C4C2×D4×C3112yes—
693C22×C4C2×D4×C3112yes—
694C22×C4#41×C3112yes—
695C22×C4#41×C3112yes—
696C4⋊C4—28no—
697C22⋊C4—216no—
698C22⋊C4—48no—
699C22⋊C4—48no—
700C22⋊C4—44no—
701C22⋊C4—48no—
702C22⋊C4—48no—
703C22⋊C4—44no—
704C22⋊C4—48no—
705C22⋊C4—44no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—24no—
710C23—24no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—22no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—22no—
727C23—24no—
728C23—24no—
729C23—22no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—42no—
739C23—42no—
740C23—41no—
741C23—41no—
742C23—42no—
743C23—42no—
744C23—41no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—41no—
754C23—42no—
755C23—42no—
756C23—41no—
757C23—42no—
758C23—41no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—41no—
776C23—42no—
777C23—42no—
778C23—41no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23C31×#12014yes—
787C23C22×D4×C3111yescharacteristic
788C23C22×D4×C3112yes—
789C23C22×D4×C3111yescharacteristic
790C23C2×#41×C3111yescharacteristic
791C23C2×#41×C3111yescharacteristic
792C23C2×#41×C3111yescharacteristic
793C23C31×H(5,𝔽2)12yes—
794C23C31×H(5,𝔽2)11yescharacteristic
795C23C31×H(5,𝔽2)11yescharacteristic
796C23C31×H(5,𝔽2)12yes—
797C23C31×H(5,𝔽2)12yes—
798D4—416no—
799D4—432no—
800D4—416no—
801D4—432no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—416no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4C31×#12114yes—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—42no—
860C22—44no—
861C22—42no—
862C22—42no—
863C22—44no—
864C22—44no—
865C22—42no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—81no—
873C22—81no—
874C22—82no—
875C22—82no—
876C22—81no—
877C22—82no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22—82no—
883C22—82no—
884C22—81no—
885C22—82no—
886C22C2×C31×#12011yescharacteristic
887C22C2×C31×#12111yescharacteristic
888C22C31×#52511yescharacteristic
889C22C31×#53412yes—
890C22C31×#53412yes—
891C22C31×#53411yescharacteristic
892C22C31×#53511yescharacteristic
893C22C31×#53511yescharacteristic
894C22C31×#53511yescharacteristic
895C22C31×#53512yes—
896C22C31×#53812yes—
897C22C31×#54012yes—
898C22C31×#54012yes—
899C22D42×C3112yes—
900C22C31×#54612yes—
901C22C31×#54612yes—
902C22C31×#54612yes—
903C22C31×#54611yescharacteristic
904C22C31×#55011yescharacteristic
905C22C31×#55311yescharacteristic
906C22C31×#55511yescharacteristic
907C22C31×#56012yes—
908C22C31×#56012yes—
909C4—24no—
910C4—44no—
911C4—42no—
912C4—42no—
913C4—44no—
914C4—81no—
915C4—82no—
916C4—81no—
917C2—44no—
918C2—84no—
919C2—82no—
920C2C31×#240411yescharacteristic
921C2C31×#241011yescharacteristic
922C2C31×#241411yescharacteristic
923C2C31×#261311yescharacteristic
924C2C31×#261911yescharacteristic
925C2C31×#263511yescharacteristic
926C2C31×#267312yes—
927C2C31×#267812yes—
928C2C31×#268812yes—
929C2C31×#269912yes—
930C2C31×#281511yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#121C2semidirect
2. C2×C31×#392C2semidirect
3. C2×C31×#392C2semidirect
4. C2×C31×#386C2semidirect
5. C2×C31×#381C2semidirect
6. C31×#1442C2semidirect
7. C31×#1440C2semidirect
8. C31×#1439C2semidirect
9. C31×#1438C2semidirect
10. C31×#1438C2semidirect
11. C31×#1438C2semidirect
67. C22×D4×C31D4semidirect
72. C23×C4×C31D4semidirect
116. C31×#95D4semidirect
240. #16258C31direct (N × H)
384. C22×#121C2×C31semidirect
385. C2×#392C2×C31semidirect
386. C2×#392C2×C31semidirect
387. C2×#386C2×C31semidirect
388. C2×#381C2×C31semidirect
389. #1442C2×C31semidirect
390. #1440C2×C31semidirect
391. #1439C2×C31semidirect
392. #1438C2×C31semidirect
393. #1438C2×C31semidirect
394. #1438C2×C31semidirect
532. C22×D4D4×C31semidirect
537. C23×C4D4×C31semidirect
581. #95D4×C31semidirect
582. C31#16258direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C2×C31×#3922
C2×C31×#3862
C2×C31×#3812
C31×#14422
C31×#14402
C31×#14392
C31×#14382
#1625831