Finite Group Databasebeta

← C31×#17083 #21473842

Subgroups — C31×#17083 #21473842

Order 7936.

2430 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#394C212yesmaximal, complemented
2C2×C31×#394C212yesmaximal, complemented
3C2×C31×#392C212yesmaximal, complemented
4C2×C31×#392C212yesmaximal, complemented
5C31×#1442C211yesmaximal, characteristic, complemented
6C31×#1439C212yesmaximal, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1438C211yesmaximal, characteristic, complemented
9C31×#1438C211yesmaximal, characteristic, complemented
10C23×D4×C31C2212yes—
11C23×D4×C31C2212yes—
12C23×D4×C31C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C31×#394—28no—
25C31×#394—28no—
26C31×#392—28no—
27C31×#392—28no—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2211yescharacteristic
35C25×C31C2312yes—
36C25×C31C2312yes—
37C22×D4×C31—24no—
38C22×D4×C31—24no—
39C22×D4×C31—24no—
40C22×D4×C31—24no—
41C22×D4×C31—24no—
42C22×D4×C31—24no—
43C22×D4×C31—24no—
44C22×D4×C31—22no—
45C22×D4×C31—41no—
46C22×D4×C31—41no—
47C22×D4×C31—41no—
48C22×D4×C31—41no—
49C22×D4×C31—42no—
50C22×D4×C31—42no—
51C22×D4×C31—42no—
52C22×D4×C31—42no—
53C22×D4×C31—42no—
54C22×D4×C31—42no—
55C22×D4×C31—42no—
56C22×D4×C31—42no—
57C22×D4×C31—42no—
58C22×D4×C31—42no—
59C22×D4×C31—42no—
60C22×D4×C31D414yescomplemented
61C23×C4×C31C2312yes—
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2312yes—
64C23×C4×C31C2312yes—
65C23×C4×C31C2312yes—
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C2×C4⋊C4×C31—24no—
69C2×C4⋊C4×C31—24no—
70C2×C4⋊C4×C31—41no—
71C2×C4⋊C4×C31—42no—
72C2×C4⋊C4×C31—42no—
73C2×C22⋊C4×C31—24no—
74C2×C22⋊C4×C31—24no—
75C2×C22⋊C4×C31—24no—
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—24no—
86C2×C22⋊C4×C31—42no—
87C2×C22⋊C4×C31—42no—
88C2×C22⋊C4×C31—42no—
89C2×C22⋊C4×C31—42no—
90C2×C22⋊C4×C31—42no—
91C2×C22⋊C4×C31—42no—
92C2×C22⋊C4×C31—42no—
93C2×C22⋊C4×C31—42no—
94C2×C22⋊C4×C31—42no—
95C2×C22⋊C4×C31—42no—
96C2×C22⋊C4×C31D418yescomplemented
97C31×#95—24no—
98C31×#95—24no—
99C31×#95—24no—
100C31×#95—41no—
101C31×#95—41no—
102C31×#95—41no—
103C31×#95D414yescomplemented
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×C31—22no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31—22no—
122C24×C31—22no—
123C24×C31—22no—
124C24×C31—22no—
125C24×C31—22no—
126C24×C31—22no—
127C24×C31—22no—
128C24×C31—22no—
129C24×C31—22no—
130C24×C31—22no—
131C24×C31—22no—
132C24×C31C2×D414yes—
133C24×C31C2×D414yes—
134C24×C31C2411yescharacteristic
135C2×D4×C31—48no—
136C2×D4×C31—44no—
137C2×D4×C31—48no—
138C2×D4×C31—48no—
139C2×D4×C31—48no—
140C2×D4×C31—48no—
141C2×D4×C31—48no—
142C2×D4×C31—48no—
143C2×D4×C31—48no—
144C2×D4×C31—44no—
145C2×D4×C31—48no—
146C2×D4×C31—48no—
147C2×D4×C31—44no—
148C2×D4×C31—48no—
149C2×D4×C31—48no—
150C2×D4×C31—48no—
151C2×D4×C31—48no—
152C2×D4×C31—48no—
153C2×D4×C31—48no—
154C2×D4×C31—44no—
155C2×D4×C31—48no—
156C2×D4×C31—44no—
157C2×D4×C31—48no—
158C2×D4×C31—44no—
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—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
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—22no—
180C22×C4×C31—22no—
181C22×C4×C31—22no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—21no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31C2×D412yes—
197C22×C4×C31C2×D414yes—
198C22×C4×C31C2×D414yes—
199C22×C4×C31C2×D412yes—
200C22×C4×C31C2×D414yes—
201C22×C4×C31#4112yes—
202C4⋊C4×C31—44no—
203C4⋊C4×C31—48no—
204C22⋊C4×C31—48no—
205C22⋊C4×C31—48no—
206C22⋊C4×C31—48no—
207C22⋊C4×C31—48no—
208C22⋊C4×C31—48no—
209C22⋊C4×C31—48no—
210C22⋊C4×C31—48no—
211C22⋊C4×C31—48no—
212#17083C3111yesmaximal, characteristic, direct product factor, Sylow
213C23×C31—24no—
214C23×C31—24no—
215C23×C31—24no—
216C23×C31—24no—
217C23×C31—24no—
218C23×C31—24no—
219C23×C31—24no—
220C23×C31—24no—
221C23×C31—24no—
222C23×C31—24no—
223C23×C31—24no—
224C23×C31—24no—
225C23×C31—24no—
226C23×C31—24no—
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×C31—42no—
251C23×C31—42no—
252C23×C31—42no—
253C23×C31—42no—
254C23×C31—42no—
255C23×C31—42no—
256C23×C31—42no—
257C23×C31—42no—
258C23×C31—42no—
259C23×C31—42no—
260C23×C31—42no—
261C23×C31—42no—
262C23×C31—42no—
263C23×C31—42no—
264C23×C31—42no—
265C23×C31—42no—
266C23×C31—42no—
267C23×C31—42no—
268C23×C31—42no—
269C23×C31—42no—
270C23×C31—42no—
271C23×C31—42no—
272C23×C31—42no—
273C23×C31—42no—
274C23×C31—42no—
275C23×C31—42no—
276C23×C31—42no—
277C23×C31—42no—
278C23×C31—42no—
279C23×C31—42no—
280C23×C31—42no—
281C23×C31—42no—
282C23×C31—42no—
283C23×C31C22×D411yescharacteristic
284C23×C31C22×D412yes—
285C23×C31C22×D411yescharacteristic
286C23×C31C2×#4111yescharacteristic
287C23×C31H(5,𝔽2)11yescharacteristic
288C23×C31H(5,𝔽2)12yes—
289C23×C31H(5,𝔽2)12yes—
290C23×C31H(5,𝔽2)11yescharacteristic
291C23×C31H(5,𝔽2)12yes—
292C23×C31H(5,𝔽2)11yescharacteristic
293C23×C312−1+411yescharacteristic
294D4×C31—432no—
295D4×C31—416no—
296D4×C31—432no—
297D4×C31—416no—
298C2×C4×C31—24no—
299C2×C4×C31—24no—
300C2×C4×C31—24no—
301C2×C4×C31—22no—
302C2×C4×C31—24no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—24no—
306C2×C4×C31—24no—
307C2×C4×C31—24no—
308C2×C4×C31—24no—
309C2×C4×C31—24no—
310C2×C4×C31—24no—
311C2×C4×C31—24no—
312C2×C4×C31—24no—
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×C31—41no—
322C2×C4×C31—42no—
323C2×C4×C31—41no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—41no—
328C2×C4×C31—42no—
329C2×C4×C31—41no—
330C2×C4×C31—42no—
331C2×C4×C31—41no—
332C2×C4×C31—42no—
333C2×C4×C31—41no—
334C2×C4×C31—42no—
335C2×C4×C31—42no—
336C2×C4×C31—42no—
337C2×C4×C31—42no—
338C2×C4×C31—42no—
339C2×C4×C31—42no—
340C2×C4×C31—42no—
341C2×#394C2×C3112yescomplemented
342C2×#394C2×C3112yescomplemented
343C2×#392C2×C3112yescomplemented
344C2×#392C2×C3112yescomplemented
345#1442C2×C3111yescharacteristic, complemented
346#1439C2×C3112yescomplemented
347#1439C2×C3112yescomplemented
348#1438C2×C3111yescharacteristic, complemented
349#1438C2×C3111yescharacteristic, complemented
350C22×C31—44no—
351C22×C31—44no—
352C22×C31—44no—
353C22×C31—44no—
354C22×C31—44no—
355C22×C31—44no—
356C22×C31—44no—
357C22×C31—44no—
358C22×C31—44no—
359C22×C31—44no—
360C22×C31—44no—
361C22×C31—44no—
362C22×C31—44no—
363C22×C31—44no—
364C22×C31—82no—
365C22×C31—82no—
366C22×C31—82no—
367C22×C31—82no—
368C22×C31—82no—
369C22×C31—82no—
370C22×C31—82no—
371C22×C31—82no—
372C22×C31—82no—
373C22×C31—82no—
374C22×C31—82no—
375C22×C31—82no—
376C22×C31—82no—
377C22×C31—82no—
378C22×C31—82no—
379C22×C31—82no—
380C22×C31#53412yes—
381C22×C31#53412yes—
382C22×C31#53411yescharacteristic
383C22×C31#53512yes—
384C22×C31#53512yes—
385C22×C31#53711yescharacteristic
386C22×C31#53712yes—
387C22×C31#53811yescharacteristic
388C22×C31#54012yes—
389C22×C31D4211yescharacteristic
390C22×C31D4212yes—
391C22×C31D4212yes—
392C22×C31D4211yescharacteristic
393C22×C31#54612yes—
394C22×C31#54711yescharacteristic
395C22×C31#55011yescharacteristic
396C22×C31#56012yes—
397C22×C31#56011yescharacteristic
398C22×C31#56012yes—
399C22×C31H(3,𝔽4)11yescharacteristic
400C22×C31H(3,𝔽4)11yescharacteristic
401C22×C31#56212yes—
402C22×C31#56211yescharacteristic
403C4×C31—44no—
404C4×C31—42no—
405C4×C31—44no—
406C4×C31—42no—
407C4×C31—44no—
408C4×C31—42no—
409C4×C31—82no—
410C23×D4C22×C3112yes—
411C23×D4C22×C3112yes—
412C23×D4C22×C3111yescharacteristic
413C23×D4C22×C3111yescharacteristic
414C22×C4⋊C4C22×C3111yescharacteristic
415C22×C4⋊C4C22×C3112yes—
416C22×C22⋊C4C22×C3112yes—
417C22×C22⋊C4C22×C3112yes—
418C22×C22⋊C4C22×C3112yes—
419C22×C22⋊C4C22×C3112yes—
420C22×C22⋊C4C22×C3112yes—
421C22×C22⋊C4C22×C3112yes—
422C22×C22⋊C4C22×C3112yes—
423C22×C22⋊C4C22×C3112yes—
424#394—28no—
425#394—28no—
426#392—28no—
427#392—28no—
428C2×#95C22×C3112yes—
429C2×#95C22×C3112yes—
430C2×#95C22×C3112yes—
431C2×#95C22×C3111yescharacteristic
432C2×#95C22×C3111yescharacteristic
433C2×#95C22×C3111yescharacteristic
434C2×#95C22×C3111yescharacteristic
435C2×C31—84no—
436C2×C31—84no—
437C2×C31#266912yes—
438C2×C31#267011yescharacteristic
439C2×C31#267112yes—
440C2×C31#267312yes—
441C2×C31#267511yescharacteristic
442C2×C31#267911yescharacteristic
443C2×C31#268211yescharacteristic
444C2×C31#281211yescharacteristic
445C2×C31#281312yes—
446C2×C31#281911yescharacteristic
447C2×C31#282811yescharacteristic
448C25C23×C3112yes—
449C25C23×C3112yes—
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—24no—
453C22×D4—24no—
454C22×D4—24no—
455C22×D4—24no—
456C22×D4—24no—
457C22×D4—22no—
458C22×D4—41no—
459C22×D4—41no—
460C22×D4—41no—
461C22×D4—41no—
462C22×D4—42no—
463C22×D4—42no—
464C22×D4—42no—
465C22×D4—42no—
466C22×D4—42no—
467C22×D4—42no—
468C22×D4—42no—
469C22×D4—42no—
470C22×D4—42no—
471C22×D4—42no—
472C22×D4—42no—
473C22×D4D4×C3114yescomplemented
474C23×C4C23×C3112yes—
475C23×C4C23×C3111yescharacteristic
476C23×C4C23×C3112yes—
477C23×C4C23×C3112yes—
478C23×C4C23×C3112yes—
479C23×C4C23×C3111yescharacteristic
480C23×C4C23×C3111yescharacteristic
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—41no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4D4×C3118yescomplemented
510#95—24no—
511#95—24no—
512#95—24no—
513#95—41no—
514#95—41no—
515#95—41no—
516#95D4×C3114yescomplemented
517C31#1708311yescharacteristic, direct product factor, Sylow
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24C2×D4×C3114yes—
547C24C2×D4×C3114yes—
548C24C24×C3111yescharacteristic
549C2×D4—48no—
550C2×D4—44no—
551C2×D4—48no—
552C2×D4—48no—
553C2×D4—48no—
554C2×D4—48no—
555C2×D4—48no—
556C2×D4—48no—
557C2×D4—48no—
558C2×D4—44no—
559C2×D4—48no—
560C2×D4—48no—
561C2×D4—44no—
562C2×D4—48no—
563C2×D4—48no—
564C2×D4—48no—
565C2×D4—48no—
566C2×D4—48no—
567C2×D4—48no—
568C2×D4—44no—
569C2×D4—48no—
570C2×D4—44no—
571C2×D4—48no—
572C2×D4—44no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4C2×D4×C3112yes—
611C22×C4C2×D4×C3114yes—
612C22×C4C2×D4×C3114yes—
613C22×C4C2×D4×C3112yes—
614C22×C4C2×D4×C3114yes—
615C22×C4#41×C3112yes—
616C4⋊C4—44no—
617C4⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23C22×D4×C3111yescharacteristic
697C23C22×D4×C3112yes—
698C23C22×D4×C3111yescharacteristic
699C23C2×#41×C3111yescharacteristic
700C23C31×H(5,𝔽2)11yescharacteristic
701C23C31×H(5,𝔽2)12yes—
702C23C31×H(5,𝔽2)12yes—
703C23C31×H(5,𝔽2)11yescharacteristic
704C23C31×H(5,𝔽2)12yes—
705C23C31×H(5,𝔽2)11yescharacteristic
706C23C31×2−1+411yescharacteristic
707D4—432no—
708D4—416no—
709D4—432no—
710D4—416no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22C31×#53412yes—
785C22C31×#53412yes—
786C22C31×#53411yescharacteristic
787C22C31×#53512yes—
788C22C31×#53512yes—
789C22C31×#53711yescharacteristic
790C22C31×#53712yes—
791C22C31×#53811yescharacteristic
792C22C31×#54012yes—
793C22D42×C3111yescharacteristic
794C22D42×C3112yes—
795C22D42×C3112yes—
796C22D42×C3111yescharacteristic
797C22C31×#54612yes—
798C22C31×#54711yescharacteristic
799C22C31×#55011yescharacteristic
800C22C31×#56012yes—
801C22C31×#56011yescharacteristic
802C22C31×#56012yes—
803C22C31×H(3,𝔽4)11yescharacteristic
804C22C31×H(3,𝔽4)11yescharacteristic
805C22C31×#56212yes—
806C22C31×#56211yescharacteristic
807C4—44no—
808C4—42no—
809C4—44no—
810C4—42no—
811C4—44no—
812C4—42no—
813C4—82no—
814C2—84no—
815C2—84no—
816C2C31×#266912yes—
817C2C31×#267011yescharacteristic
818C2C31×#267112yes—
819C2C31×#267312yes—
820C2C31×#267511yescharacteristic
821C2C31×#267911yescharacteristic
822C2C31×#268211yescharacteristic
823C2C31×#281211yescharacteristic
824C2C31×#281312yes—
825C2C31×#281911yescharacteristic
826C2C31×#282811yescharacteristic
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. C2×C31×#394C2semidirect
2. C2×C31×#394C2semidirect
3. C2×C31×#392C2semidirect
4. C2×C31×#392C2semidirect
5. C31×#1442C2semidirect
6. C31×#1439C2semidirect
7. C31×#1439C2semidirect
8. C31×#1438C2semidirect
9. C31×#1438C2semidirect
60. C22×D4×C31D4semidirect
96. C2×C22⋊C4×C31D4semidirect
103. C31×#95D4semidirect
212. #17083C31direct (N × H)
341. C2×#394C2×C31semidirect
342. C2×#394C2×C31semidirect
343. C2×#392C2×C31semidirect
344. C2×#392C2×C31semidirect
345. #1442C2×C31semidirect
346. #1439C2×C31semidirect
347. #1439C2×C31semidirect
348. #1438C2×C31semidirect
349. #1438C2×C31semidirect
473. C22×D4D4×C31semidirect
509. C2×C22⋊C4D4×C31semidirect
516. #95D4×C31semidirect
517. C31#17083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3942
C2×C31×#3922
C31×#14422
C31×#14392
C31×#14382
#1708331