Finite Group Databasebeta

← C31×#16298 #21473057

Subgroups — C31×#16298 #21473057

Order 7936.

2830 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#399C211yesmaximal, characteristic, complemented
2C2×C31×#396C212yesmaximal, complemented
3C2×C31×#379C211yesmaximal, characteristic
4C2×C31×#379C212yesmaximal
5C31×#1439C212yesmaximal, complemented
6C31×#1439C212yesmaximal, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1439C212yesmaximal, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C26×C31C2211yescharacteristic
11C22×C4⋊C4×C31C2211yescharacteristic, complemented
12C22×C4⋊C4×C31C2212yescomplemented
13C22×C4⋊C4×C31C2212yescomplemented
14C22×C4⋊C4×C31C2211yescharacteristic, complemented
15C22×C22⋊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×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2211yescharacteristic
25C31×#399—24no—
26C31×#396—28no—
27C31×#379—28no—
28C31×#379—24no—
29C2×C31×#95C2212yescomplemented
30C2×C31×#95C2211yescharacteristic, complemented
31C2×C31×#95C2212yescomplemented
32C2×C31×#95C2212yescomplemented
33C2×C31×#95C2211yescharacteristic, complemented
34C2×C31×#95C2212yescomplemented
35C25×C31—24no—
36C25×C31—22no—
37C25×C31—22no—
38C25×C31—24no—
39C25×C31—41no—
40C25×C31—42no—
41C25×C31—42no—
42C25×C31—41no—
43C25×C31—41no—
44C25×C31—41no—
45C25×C31Q814yes—
46C25×C31C2312yes—
47C25×C31C2311yescharacteristic
48C23×C4×C31C2312yes—
49C23×C4×C31C2312yes—
50C23×C4×C31C2312yes—
51C23×C4×C31C2311yescharacteristic
52C23×C4×C31C2312yes—
53C23×C4×C31C2312yes—
54C23×C4×C31C2311yescharacteristic
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31—24no—
57C2×C4⋊C4×C31—24no—
58C2×C4⋊C4×C31—24no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—41no—
61C2×C4⋊C4×C31—42no—
62C2×C4⋊C4×C31—42no—
63C2×C4⋊C4×C31—42no—
64C2×C4⋊C4×C31—41no—
65C2×C4⋊C4×C31—41no—
66C2×C22⋊C4×C31—24no—
67C2×C22⋊C4×C31—24no—
68C2×C22⋊C4×C31—24no—
69C2×C22⋊C4×C31—24no—
70C2×C22⋊C4×C31—22no—
71C2×C22⋊C4×C31—24no—
72C2×C22⋊C4×C31—24no—
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—42no—
81C2×C22⋊C4×C31—41no—
82C2×C22⋊C4×C31—42no—
83C2×C22⋊C4×C31—41no—
84C2×C22⋊C4×C31—42no—
85C2×C22⋊C4×C31—42no—
86C2×C22⋊C4×C31—42no—
87C2×C22⋊C4×C31—42no—
88C2×C22⋊C4×C31—42no—
89C2×C22⋊C4×C31—42no—
90C2×C22⋊C4×C31—41no—
91C2×C22⋊C4×C31—42no—
92C2×C22⋊C4×C31—42no—
93C2×C22⋊C4×C31—41no—
94C2×C22⋊C4×C31D418yes—
95C2×C22⋊C4×C31D414yes—
96C31×#95—24no—
97C31×#95—22no—
98C31×#95—42no—
99C31×#95—41no—
100C31×#95—42no—
101C31×#95—42no—
102C24×C31—22no—
103C24×C31—22no—
104C24×C31—22no—
105C24×C31—22no—
106C24×C31—22no—
107C24×C31—22no—
108C24×C31—22no—
109C24×C31—21no—
110C24×C31—21no—
111C24×C31—22no—
112C24×C31—21no—
113C24×C31—22no—
114C24×C31—22no—
115C24×C31—21no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31—22no—
122C24×C31—216no—
123C24×C31—28no—
124C24×C31—44no—
125C24×C31—48no—
126C24×C31—44no—
127C24×C31—44no—
128C24×C31—48no—
129C24×C31—48no—
130C24×C31—48no—
131C24×C31—48no—
132C24×C31—48no—
133C24×C31—44no—
134C24×C31—48no—
135C24×C31—44no—
136C24×C31—48no—
137C24×C31—44no—
138C24×C31—44no—
139C24×C31—48no—
140C24×C31—44no—
141C24×C31—48no—
142C24×C31—44no—
143C24×C31—44no—
144C24×C31—48no—
145C24×C31C2×D414yes—
146C24×C31C2×D412yes—
147C24×C31C2×Q814yes—
148C24×C31C2×Q812yes—
149C24×C31#4112yes—
150C24×C31#4114yes—
151C24×C31C2411yescharacteristic
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—21no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—21no—
164C22×C4×C31—22no—
165C22×C4×C31—21no—
166C22×C4×C31—22no—
167C22×C4×C31—21no—
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—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—22no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31C2×D412yes—
194C22×C4×C31C2×D414yes—
195C22×C4×C31C2×D414yes—
196C22×C4×C31C2×D412yes—
197C4⋊C4×C31—44no—
198C4⋊C4×C31—48no—
199C4⋊C4×C31—48no—
200C4⋊C4×C31—44no—
201C22⋊C4×C31—48no—
202C22⋊C4×C31—44no—
203C22⋊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—44no—
211#16298C3111yesmaximal, characteristic, direct product factor, Sylow
212C23×C31—24no—
213C23×C31—24no—
214C23×C31—24no—
215C23×C31—24no—
216C23×C31—22no—
217C23×C31—24no—
218C23×C31—22no—
219C23×C31—22no—
220C23×C31—24no—
221C23×C31—22no—
222C23×C31—24no—
223C23×C31—22no—
224C23×C31—24no—
225C23×C31—24no—
226C23×C31—22no—
227C23×C31—24no—
228C23×C31—24no—
229C23×C31—24no—
230C23×C31—24no—
231C23×C31—24no—
232C23×C31—24no—
233C23×C31—24no—
234C23×C31—24no—
235C23×C31—24no—
236C23×C31—24no—
237C23×C31—24no—
238C23×C31—24no—
239C23×C31—24no—
240C23×C31—24no—
241C23×C31—24no—
242C23×C31—416no—
243C23×C31—432no—
244C23×C31—432no—
245C23×C31—416no—
246C23×C31—416no—
247C23×C31—416no—
248C23×C31—416no—
249C23×C31—432no—
250C23×C31—432no—
251C23×C31—416no—
252C23×C31—416no—
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—41no—
266C23×C31—42no—
267C23×C31—42no—
268C23×C31—42no—
269C23×C31—42no—
270C23×C31—42no—
271C23×C31—41no—
272C23×C31—42no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—42no—
276C23×C31—42no—
277C23×C31—42no—
278C23×C31—42no—
279C23×C31C22⋊Q818yes—
280C23×C31C22⋊Q814yes—
281C23×C31C22×D412yes—
282C23×C31C22×D411yescharacteristic
283C23×C31C22×Q811yescharacteristic
284C23×C31C2×#4111yescharacteristic
285C23×C31C2×#4112yes—
286C23×C31H(5,𝔽2)11yescharacteristic
287C23×C31H(5,𝔽2)11yescharacteristic
288C23×C31H(5,𝔽2)11yescharacteristic
289C23×C31H(5,𝔽2)12yes—
290C23×C31H(5,𝔽2)12yes—
291C23×C31H(5,𝔽2)11yescharacteristic
292C2×C4×C31—24no—
293C2×C4×C31—22no—
294C2×C4×C31—24no—
295C2×C4×C31—22no—
296C2×C4×C31—24no—
297C2×C4×C31—24no—
298C2×C4×C31—24no—
299C2×C4×C31—24no—
300C2×C4×C31—24no—
301C2×C4×C31—24no—
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—41no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—41no—
312C2×C4×C31—42no—
313C2×C4×C31—41no—
314C2×C4×C31—42no—
315C2×C4×C31—41no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31—42no—
322C2×C4×C31—42no—
323C2×C4×C31—42no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—42no—
331C2×C4×C31—42no—
332C2×C4×C31—42no—
333C2×C4×C31—42no—
334C2×C4×C31—42no—
335C2×C4×C31—42no—
336C2×C4×C31—42no—
337C2×#399C2×C3111yescharacteristic, complemented
338C2×#396C2×C3112yescomplemented
339C2×#379C2×C3111yescharacteristic
340C2×#379C2×C3112yes—
341#1439C2×C3112yescomplemented
342#1439C2×C3112yescomplemented
343#1439C2×C3112yescomplemented
344#1439C2×C3112yescomplemented
345#1439C2×C3111yescharacteristic, complemented
346C22×C31—28no—
347C22×C31—24no—
348C22×C31—28no—
349C22×C31—28no—
350C22×C31—28no—
351C22×C31—464no—
352C22×C31—44no—
353C22×C31—42no—
354C22×C31—44no—
355C22×C31—44no—
356C22×C31—44no—
357C22×C31—44no—
358C22×C31—42no—
359C22×C31—42no—
360C22×C31—44no—
361C22×C31—44no—
362C22×C31—44no—
363C22×C31—44no—
364C22×C31—44no—
365C22×C31—44no—
366C22×C31—44no—
367C22×C31—42no—
368C22×C31—44no—
369C22×C31—42no—
370C22×C31—44no—
371C22×C31—42no—
372C22×C31—44no—
373C22×C31C2×C22⋊Q812yes—
374C22×C31C2×C22⋊Q811yescharacteristic
375C22×C31#53412yes—
376C22×C31#53411yescharacteristic
377C22×C31#53512yes—
378C22×C31#53511yescharacteristic
379C22×C31#53811yescharacteristic
380C22×C31#53812yes—
381C22×C31#53811yescharacteristic
382C22×C31#53812yes—
383C22×C31#54311yescharacteristic
384C22×C31#54312yes—
385C22×C31#54311yescharacteristic
386C22×C31D4211yescharacteristic
387C22×C31D4212yes—
388C22×C31#54612yes—
389C22×C31#54612yes—
390C22×C31#54612yes—
391C22×C31#55112yes—
392C22×C31#55111yescharacteristic
393C22×C31#56011yescharacteristic
394C22×C31#56011yescharacteristic
395C22×C31#56012yes—
396C4×C31—44no—
397C4×C31—42no—
398C4×C31—44no—
399C4×C31—42no—
400C4×C31—82no—
401C4×C31—82no—
402C4×C31—82no—
403C26C22×C3111yescharacteristic
404C22×C4⋊C4C22×C3111yescharacteristic, complemented
405C22×C4⋊C4C22×C3112yescomplemented
406C22×C4⋊C4C22×C3112yescomplemented
407C22×C4⋊C4C22×C3111yescharacteristic, complemented
408C22×C22⋊C4C22×C3112yes—
409C22×C22⋊C4C22×C3112yes—
410C22×C22⋊C4C22×C3112yes—
411C22×C22⋊C4C22×C3112yes—
412C22×C22⋊C4C22×C3112yes—
413C22×C22⋊C4C22×C3112yes—
414C22×C22⋊C4C22×C3112yes—
415C22×C22⋊C4C22×C3111yescharacteristic
416C22×C22⋊C4C22×C3112yes—
417C22×C22⋊C4C22×C3111yescharacteristic
418#399—24no—
419#396—28no—
420#379—28no—
421#379—24no—
422C2×#95C22×C3112yescomplemented
423C2×#95C22×C3111yescharacteristic, complemented
424C2×#95C22×C3112yescomplemented
425C2×#95C22×C3112yescomplemented
426C2×#95C22×C3111yescharacteristic, complemented
427C2×#95C22×C3112yescomplemented
428C2×C31—48no—
429C2×C31—44no—
430C2×C31#243711yescharacteristic
431C2×C31#243712yes—
432C2×C31#262612yes—
433C2×C31#262611yescharacteristic
434C2×C31#266811yescharacteristic
435C2×C31#266911yescharacteristic
436C2×C31#267812yes—
437C2×C31#268512yes—
438C2×C31#269711yescharacteristic
439C2×C31#273511yescharacteristic
440C2×C31#284211yescharacteristic
441C25—24no—
442C25—22no—
443C25—22no—
444C25—24no—
445C25—41no—
446C25—42no—
447C25—42no—
448C25—41no—
449C25—41no—
450C25—41no—
451C25Q8×C3114yes—
452C25C23×C3112yes—
453C25C23×C3111yescharacteristic
454C23×C4C23×C3112yes—
455C23×C4C23×C3112yes—
456C23×C4C23×C3112yes—
457C23×C4C23×C3111yescharacteristic
458C23×C4C23×C3112yes—
459C23×C4C23×C3112yes—
460C23×C4C23×C3111yescharacteristic
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—41no—
471C2×C4⋊C4—41no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—41no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—41no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—41no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—41no—
500C2×C22⋊C4D4×C3118yes—
501C2×C22⋊C4D4×C3114yes—
502#95—24no—
503#95—22no—
504#95—42no—
505#95—41no—
506#95—42no—
507#95—42no—
508C31#1629811yescharacteristic, direct product factor, Sylow
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—21no—
517C24—21no—
518C24—22no—
519C24—21no—
520C24—22no—
521C24—22no—
522C24—21no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—216no—
530C24—28no—
531C24—44no—
532C24—48no—
533C24—44no—
534C24—44no—
535C24—48no—
536C24—48no—
537C24—48no—
538C24—48no—
539C24—48no—
540C24—44no—
541C24—48no—
542C24—44no—
543C24—48no—
544C24—44no—
545C24—44no—
546C24—48no—
547C24—44no—
548C24—48no—
549C24—44no—
550C24—44no—
551C24—48no—
552C24C2×D4×C3114yes—
553C24C2×D4×C3112yes—
554C24C2×Q8×C3114yes—
555C24C2×Q8×C3112yes—
556C24#41×C3112yes—
557C24#41×C3114yes—
558C24C24×C3111yescharacteristic
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
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×C4C2×D4×C3112yes—
601C22×C4C2×D4×C3114yes—
602C22×C4C2×D4×C3114yes—
603C22×C4C2×D4×C3112yes—
604C4⋊C4—44no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—44no—
608C22⋊C4—48no—
609C22⋊C4—44no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—44no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—22no—
623C23—24no—
624C23—22no—
625C23—22no—
626C23—24no—
627C23—22no—
628C23—24no—
629C23—22no—
630C23—24no—
631C23—24no—
632C23—22no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—416no—
649C23—432no—
650C23—432no—
651C23—416no—
652C23—416no—
653C23—416no—
654C23—416no—
655C23—432no—
656C23—432no—
657C23—416no—
658C23—416no—
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—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—41no—
678C23—42no—
679C23—41no—
680C23—41no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23C31×C22⋊Q818yes—
686C23C31×C22⋊Q814yes—
687C23C22×D4×C3112yes—
688C23C22×D4×C3111yescharacteristic
689C23C22×Q8×C3111yescharacteristic
690C23C2×#41×C3111yescharacteristic
691C23C2×#41×C3112yes—
692C23C31×H(5,𝔽2)11yescharacteristic
693C23C31×H(5,𝔽2)11yescharacteristic
694C23C31×H(5,𝔽2)11yescharacteristic
695C23C31×H(5,𝔽2)12yes—
696C23C31×H(5,𝔽2)12yes—
697C23C31×H(5,𝔽2)11yescharacteristic
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
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—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C22—28no—
744C22—24no—
745C22—28no—
746C22—28no—
747C22—28no—
748C22—464no—
749C22—44no—
750C22—42no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—42no—
756C22—42no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—42no—
765C22—44no—
766C22—42no—
767C22—44no—
768C22—42no—
769C22—44no—
770C22C2×C31×C22⋊Q812yes—
771C22C2×C31×C22⋊Q811yescharacteristic
772C22C31×#53412yes—
773C22C31×#53411yescharacteristic
774C22C31×#53512yes—
775C22C31×#53511yescharacteristic
776C22C31×#53811yescharacteristic
777C22C31×#53812yes—
778C22C31×#53811yescharacteristic
779C22C31×#53812yes—
780C22C31×#54311yescharacteristic
781C22C31×#54312yes—
782C22C31×#54311yescharacteristic
783C22D42×C3111yescharacteristic
784C22D42×C3112yes—
785C22C31×#54612yes—
786C22C31×#54612yes—
787C22C31×#54612yes—
788C22C31×#55112yes—
789C22C31×#55111yescharacteristic
790C22C31×#56011yescharacteristic
791C22C31×#56011yescharacteristic
792C22C31×#56012yes—
793C4—44no—
794C4—42no—
795C4—44no—
796C4—42no—
797C4—82no—
798C4—82no—
799C4—82no—
800C2—48no—
801C2—44no—
802C2C31×#243711yescharacteristic
803C2C31×#243712yes—
804C2C31×#262612yes—
805C2C31×#262611yescharacteristic
806C2C31×#266811yescharacteristic
807C2C31×#266911yescharacteristic
808C2C31×#267812yes—
809C2C31×#268512yes—
810C2C31×#269711yescharacteristic
811C2C31×#273511yescharacteristic
812C2C31×#284211yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC26×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#399C2semidirect
2. C2×C31×#396C2semidirect
5. C31×#1439C2semidirect
6. C31×#1439C2semidirect
7. C31×#1439C2semidirect
8. C31×#1439C2semidirect
9. C31×#1439C2semidirect
11. C22×C4⋊C4×C31C22semidirect
12. C22×C4⋊C4×C31C22semidirect
13. C22×C4⋊C4×C31C22semidirect
14. C22×C4⋊C4×C31C22semidirect
29. C2×C31×#95C22semidirect
30. C2×C31×#95C22semidirect
31. C2×C31×#95C22semidirect
32. C2×C31×#95C22semidirect
33. C2×C31×#95C22semidirect
34. C2×C31×#95C22semidirect
211. #16298C31direct (N × H)
337. C2×#399C2×C31semidirect
338. C2×#396C2×C31semidirect
341. #1439C2×C31semidirect
342. #1439C2×C31semidirect
343. #1439C2×C31semidirect
344. #1439C2×C31semidirect
345. #1439C2×C31semidirect
404. C22×C4⋊C4C22×C31semidirect
405. C22×C4⋊C4C22×C31semidirect
406. C22×C4⋊C4C22×C31semidirect
407. C22×C4⋊C4C22×C31semidirect
422. C2×#95C22×C31semidirect
423. C2×#95C22×C31semidirect
424. C2×#95C22×C31semidirect
425. C2×#95C22×C31semidirect
426. C2×#95C22×C31semidirect
427. C2×#95C22×C31semidirect
508. C31#16298direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3992
C2×C31×#3962
C2×C31×#3792
C31×#14392
#1629831