Finite Group Databasebeta

← C31×#15283 #21472042

Subgroups — C31×#15283 #21472042

Order 7936.

3494 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#120C211yesmaximal, characteristic
2C2×C31×#399C211yesmaximal, characteristic, complemented
3C2×C31×#397C211yesmaximal, characteristic, complemented
4C2×C31×#394C212yesmaximal, complemented
5C2×C31×#390C211yesmaximal, characteristic, complemented
6C2×C31×#379C212yesmaximal, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1438C212yesmaximal, complemented
9C31×#1438C211yesmaximal, characteristic, complemented
10C31×#1437C211yesmaximal, characteristic, complemented
11C31×#1437C211yesmaximal, characteristic, complemented
12C26×C31C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C23×D4×C31C2211yescharacteristic
15C23×D4×C31C2211yescharacteristic
16C2×C31×#120—24no—
17C2×C31×#120—24no—
18C2×C31×#120—24no—
19C22×C4⋊C4×C31C2211yescharacteristic, complemented
20C22×C4⋊C4×C31C2212yescomplemented
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2212yes—
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2212yes—
30C22×C22⋊C4×C31C2212yescomplemented
31C22×C22⋊C4×C31C2212yescomplemented
32C22×C42×C31C2211yescharacteristic, complemented
33C31×#399—24no—
34C31×#397—24no—
35C31×#394—28no—
36C31×#390—24no—
37C31×#379—28no—
38C2×C31×#95C2212yescomplemented
39C2×C31×#95C2211yescharacteristic, complemented
40C2×C31×#95C2212yescomplemented
41C2×C31×#95C2211yescharacteristic, complemented
42C2×C31×#95C2212yescomplemented
43C25×C31—22no—
44C25×C31—22no—
45C25×C31—22no—
46C25×C31—24no—
47C25×C31—24no—
48C25×C31—24no—
49C25×C31—42no—
50C25×C31—42no—
51C25×C31—42no—
52C25×C31C2311yescharacteristic
53C25×C31C2311yescharacteristic
54C25×C31C2311yescharacteristic
55C25×C31C2311yescharacteristic
56C22×D4×C31—22no—
57C22×D4×C31—22no—
58C22×D4×C31—22no—
59C22×D4×C31—22no—
60C22×D4×C31—24no—
61C22×D4×C31—24no—
62C22×D4×C31—24no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—42no—
68C22×D4×C31—42no—
69C22×D4×C31—42no—
70C22×D4×C31D414yes—
71C23×C4×C31C2312yes—
72C23×C4×C31C2312yes—
73C23×C4×C31C2312yes—
74C23×C4×C31C2312yes—
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C31×#120—232no—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31—24no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—24no—
84C2×C4⋊C4×C31—42no—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—24no—
93C2×C22⋊C4×C31—24no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—24no—
96C2×C22⋊C4×C31—24no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—24no—
99C2×C22⋊C4×C31—24no—
100C2×C22⋊C4×C31—24no—
101C2×C22⋊C4×C31—24no—
102C2×C22⋊C4×C31—24no—
103C2×C22⋊C4×C31—24no—
104C2×C22⋊C4×C31—24no—
105C2×C22⋊C4×C31—24no—
106C2×C22⋊C4×C31—42no—
107C2×C22⋊C4×C31—42no—
108C2×C22⋊C4×C31—42no—
109C2×C22⋊C4×C31—42no—
110C2×C22⋊C4×C31—42no—
111C2×C22⋊C4×C31—42no—
112C2×C22⋊C4×C31—42no—
113C2×C22⋊C4×C31—42no—
114C2×C22⋊C4×C31—42no—
115C2×C22⋊C4×C31D414yes—
116C2×C22⋊C4×C31D414yes—
117C2×C22⋊C4×C31D418yescomplemented
118C2×C42×C31—22no—
119C2×C42×C31—42no—
120C31×#95—22no—
121C31×#95—24no—
122C31×#95—22no—
123C31×#95—24no—
124C31×#95—42no—
125C24×C31—22no—
126C24×C31—22no—
127C24×C31—21no—
128C24×C31—21no—
129C24×C31—21no—
130C24×C31—21no—
131C24×C31—21no—
132C24×C31—21no—
133C24×C31—22no—
134C24×C31—22no—
135C24×C31—22no—
136C24×C31—22no—
137C24×C31—22no—
138C24×C31—22no—
139C24×C31—22no—
140C24×C31—22no—
141C24×C31—22no—
142C24×C31—22no—
143C24×C31—22no—
144C24×C31—22no—
145C24×C31—22no—
146C24×C31—28no—
147C24×C31—216no—
148C24×C31—22no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31—22no—
152C24×C31—22no—
153C24×C31—22no—
154C24×C31—22no—
155C24×C31—22no—
156C24×C31—48no—
157C24×C31—48no—
158C24×C31—48no—
159C24×C31—48no—
160C24×C31—48no—
161C24×C31—48no—
162C24×C31—48no—
163C24×C31—48no—
164C24×C31—48no—
165C24×C31—48no—
166C24×C31—44no—
167C24×C31—44no—
168C24×C31—44no—
169C24×C31—48no—
170C24×C31—48no—
171C24×C31—48no—
172C24×C31—44no—
173C24×C31—44no—
174C24×C31—44no—
175C24×C31C2×D412yes—
176C24×C31C2×D412yes—
177C24×C31C2×D412yes—
178C24×C31C2×D412yes—
179C24×C31C2×D414yes—
180C24×C31#4114yes—
181C24×C31#4114yes—
182C24×C31C2411yescharacteristic
183C2×D4×C31—28no—
184C2×D4×C31—28no—
185C2×D4×C31—28no—
186C2×D4×C31—28no—
187C2×D4×C31—44no—
188C2×D4×C31—48no—
189C2×D4×C31—48no—
190C2×D4×C31—48no—
191C2×D4×C31—48no—
192C2×D4×C31—48no—
193C2×D4×C31—48no—
194C2×D4×C31—44no—
195C2×D4×C31—44no—
196C2×D4×C31—44no—
197C2×D4×C31—44no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—22no—
202C22×C4×C31—22no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—22no—
208C22×C4×C31—22no—
209C22×C4×C31—22no—
210C22×C4×C31—22no—
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—22no—
219C22×C4×C31—22no—
220C22×C4×C31—22no—
221C22×C4×C31—22no—
222C22×C4×C31—22no—
223C22×C4×C31—22no—
224C22×C4×C31—22no—
225C22×C4×C31—22no—
226C22×C4×C31—22no—
227C22×C4×C31—22no—
228C22×C4×C31—22no—
229C22×C4×C31—22no—
230C22×C4×C31—22no—
231C22×C4×C31—22no—
232C22×C4×C31—22no—
233C22×C4×C31—22no—
234C22×C4×C31C2×D412yes—
235C22×C4×C31C2×D414yes—
236C22×C4×C31C2×D414yes—
237C22×C4×C31C2×D412yes—
238C22×C4×C31C2×D412yes—
239C22×C4×C31C2×D412yes—
240C22×C4×C31C2×D412yes—
241C4⋊C4×C31—48no—
242C4⋊C4×C31—44no—
243C22⋊C4×C31—28no—
244C22⋊C4×C31—28no—
245C22⋊C4×C31—28no—
246C22⋊C4×C31—48no—
247C22⋊C4×C31—48no—
248C22⋊C4×C31—48no—
249C22⋊C4×C31—48no—
250C22⋊C4×C31—48no—
251C22⋊C4×C31—48no—
252C22⋊C4×C31—48no—
253C22⋊C4×C31—48no—
254C42×C31—44no—
255#15283C3111yesmaximal, characteristic, direct product factor, Sylow
256C23×C31—22no—
257C23×C31—22no—
258C23×C31—22no—
259C23×C31—24no—
260C23×C31—24no—
261C23×C31—24no—
262C23×C31—24no—
263C23×C31—22no—
264C23×C31—22no—
265C23×C31—22no—
266C23×C31—24no—
267C23×C31—24no—
268C23×C31—24no—
269C23×C31—24no—
270C23×C31—24no—
271C23×C31—24no—
272C23×C31—24no—
273C23×C31—24no—
274C23×C31—24no—
275C23×C31—24no—
276C23×C31—24no—
277C23×C31—24no—
278C23×C31—24no—
279C23×C31—24no—
280C23×C31—24no—
281C23×C31—24no—
282C23×C31—24no—
283C23×C31—24no—
284C23×C31—24no—
285C23×C31—24no—
286C23×C31—22no—
287C23×C31—22no—
288C23×C31—22no—
289C23×C31—24no—
290C23×C31—24no—
291C23×C31—416no—
292C23×C31—432no—
293C23×C31—416no—
294C23×C31—416no—
295C23×C31—432no—
296C23×C31—432no—
297C23×C31—432no—
298C23×C31—432no—
299C23×C31—432no—
300C23×C31—41no—
301C23×C31—41no—
302C23×C31—41no—
303C23×C31—41no—
304C23×C31—41no—
305C23×C31—41no—
306C23×C31—41no—
307C23×C31—41no—
308C23×C31—42no—
309C23×C31—42no—
310C23×C31—41no—
311C23×C31—41no—
312C23×C31—41no—
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—42no—
322C23×C31—42no—
323C23×C31—42no—
324C23×C31—42no—
325C23×C31—42no—
326C23×C31—42no—
327C23×C31—42no—
328C23×C31—42no—
329C23×C31—42no—
330C23×C31—42no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—42no—
334C23×C31—41no—
335C23×C31—41no—
336C23×C31—42no—
337C23×C31—42no—
338C23×C31—42no—
339C23×C31—42no—
340C23×C31—42no—
341C23×C31—42no—
342C23×C31—42no—
343C23×C31—42no—
344C23×C31—42no—
345C23×C31—42no—
346C23×C31#12314yes—
347C23×C31#12414yes—
348C23×C31#12714yes—
349C23×C31C22×D411yescharacteristic
350C23×C31C22×D411yescharacteristic
351C23×C31C22×D411yescharacteristic
352C23×C31C22×D412yes—
353C23×C31C2×#4112yes—
354C23×C31C2×#4112yes—
355C23×C31H(5,𝔽2)12yes—
356C23×C31H(5,𝔽2)12yes—
357C23×C31H(5,𝔽2)12yes—
358D4×C31—416no—
359D4×C31—416no—
360D4×C31—416no—
361C2×C4×C31—22no—
362C2×C4×C31—22no—
363C2×C4×C31—24no—
364C2×C4×C31—24no—
365C2×C4×C31—22no—
366C2×C4×C31—22no—
367C2×C4×C31—24no—
368C2×C4×C31—24no—
369C2×C4×C31—24no—
370C2×C4×C31—24no—
371C2×C4×C31—24no—
372C2×C4×C31—24no—
373C2×C4×C31—24no—
374C2×C4×C31—24no—
375C2×C4×C31—41no—
376C2×C4×C31—41no—
377C2×C4×C31—42no—
378C2×C4×C31—42no—
379C2×C4×C31—41no—
380C2×C4×C31—41no—
381C2×C4×C31—42no—
382C2×C4×C31—42no—
383C2×C4×C31—42no—
384C2×C4×C31—42no—
385C2×C4×C31—42no—
386C2×C4×C31—42no—
387C2×C4×C31—42no—
388C2×C4×C31—42no—
389C2×C4×C31—42no—
390C2×C4×C31—42no—
391C2×C4×C31—42no—
392C2×C4×C31—42no—
393C2×C4×C31—42no—
394C2×C4×C31—42no—
395C2×C4×C31—42no—
396C2×C4×C31—42no—
397C2×C4×C31—42no—
398C2×C4×C31—42no—
399C2×C4×C31—42no—
400C2×C4×C31—42no—
401C2×C4×C31—42no—
402C2×C4×C31—42no—
403C2×C4×C31#12014yes—
404C22×#120C2×C3111yescharacteristic
405C2×#399C2×C3111yescharacteristic, complemented
406C2×#397C2×C3111yescharacteristic, complemented
407C2×#394C2×C3112yescomplemented
408C2×#390C2×C3111yescharacteristic, complemented
409C2×#379C2×C3112yescomplemented
410#1439C2×C3112yescomplemented
411#1438C2×C3112yescomplemented
412#1438C2×C3111yescharacteristic, complemented
413#1437C2×C3111yescharacteristic, complemented
414#1437C2×C3111yescharacteristic, complemented
415C22×C31—24no—
416C22×C31—28no—
417C22×C31—24no—
418C22×C31—24no—
419C22×C31—28no—
420C22×C31—28no—
421C22×C31—464no—
422C22×C31—42no—
423C22×C31—42no—
424C22×C31—44no—
425C22×C31—44no—
426C22×C31—44no—
427C22×C31—44no—
428C22×C31—44no—
429C22×C31—44no—
430C22×C31—44no—
431C22×C31—44no—
432C22×C31—44no—
433C22×C31—44no—
434C22×C31—44no—
435C22×C31—42no—
436C22×C31—42no—
437C22×C31—42no—
438C22×C31—42no—
439C22×C31—44no—
440C22×C31—44no—
441C22×C31—44no—
442C22×C31—44no—
443C22×C31—42no—
444C22×C31—44no—
445C22×C31—44no—
446C22×C31—42no—
447C22×C31—42no—
448C22×C31—82no—
449C22×C31—82no—
450C22×C31—82no—
451C22×C31—82no—
452C22×C31C2×#12011yescharacteristic
453C22×C31C2×#12311yescharacteristic
454C22×C31#52512yes—
455C22×C31C2×#12411yescharacteristic
456C22×C31C2×#12711yescharacteristic
457C22×C31#53411yescharacteristic
458C22×C31#53412yes—
459C22×C31#53511yescharacteristic
460C22×C31#53511yescharacteristic
461C22×C31#53812yes—
462C22×C31#53812yes—
463C22×C31D4212yes—
464C22×C31D4212yes—
465C22×C31#54612yes—
466C22×C31#54612yes—
467C22×C31#54612yes—
468C22×C31#54612yes—
469C22×C31#54612yes—
470C22×C31#54612yes—
471C22×C31#55112yes—
472C22×C31#56012yes—
473C4×C31—24no—
474C4×C31—44no—
475C4×C31—44no—
476C4×C31—42no—
477C4×C31—42no—
478C4×C31—82no—
479C4×C31—82no—
480C26C22×C3111yescharacteristic
481C23×D4C22×C3111yescharacteristic
482C23×D4C22×C3111yescharacteristic
483C23×D4C22×C3111yescharacteristic
484C2×#120—24no—
485C2×#120—24no—
486C2×#120—24no—
487C22×C4⋊C4C22×C3111yescharacteristic, complemented
488C22×C4⋊C4C22×C3112yescomplemented
489C22×C22⋊C4C22×C3112yes—
490C22×C22⋊C4C22×C3111yescharacteristic
491C22×C22⋊C4C22×C3112yes—
492C22×C22⋊C4C22×C3112yes—
493C22×C22⋊C4C22×C3112yes—
494C22×C22⋊C4C22×C3112yes—
495C22×C22⋊C4C22×C3111yescharacteristic
496C22×C22⋊C4C22×C3111yescharacteristic
497C22×C22⋊C4C22×C3112yes—
498C22×C22⋊C4C22×C3112yescomplemented
499C22×C22⋊C4C22×C3112yescomplemented
500C22×C42C22×C3111yescharacteristic, complemented
501#399—24no—
502#397—24no—
503#394—28no—
504#390—24no—
505#379—28no—
506C2×#95C22×C3112yescomplemented
507C2×#95C22×C3111yescharacteristic, complemented
508C2×#95C22×C3112yescomplemented
509C2×#95C22×C3111yescharacteristic, complemented
510C2×#95C22×C3112yescomplemented
511C2×C31—44no—
512C2×C31—44no—
513C2×C31—44no—
514C2×C31—82no—
515C2×C31#240511yescharacteristic
516C2×C31#241812yes—
517C2×C31#243311yescharacteristic
518C2×C31#243511yescharacteristic
519C2×C31#247212yes—
520C2×C31#253912yes—
521C2×C31#266812yes—
522C2×C31#267812yes—
523C2×C31#268512yes—
524C25—22no—
525C25—22no—
526C25—22no—
527C25—24no—
528C25—24no—
529C25—24no—
530C25—42no—
531C25—42no—
532C25—42no—
533C25C23×C3111yescharacteristic
534C25C23×C3111yescharacteristic
535C25C23×C3111yescharacteristic
536C25C23×C3111yescharacteristic
537C22×D4—22no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—24no—
542C22×D4—24no—
543C22×D4—24no—
544C22×D4—22no—
545C22×D4—22no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—42no—
549C22×D4—42no—
550C22×D4—42no—
551C22×D4D4×C3114yes—
552C23×C4C23×C3112yes—
553C23×C4C23×C3112yes—
554C23×C4C23×C3112yes—
555C23×C4C23×C3112yes—
556C23×C4C23×C3111yescharacteristic
557C23×C4C23×C3111yescharacteristic
558C23×C4C23×C3111yescharacteristic
559#120—232no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—24no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—42no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—24no—
580C2×C22⋊C4—24no—
581C2×C22⋊C4—24no—
582C2×C22⋊C4—24no—
583C2×C22⋊C4—24no—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—42no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—42no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4D4×C3114yes—
597C2×C22⋊C4D4×C3114yes—
598C2×C22⋊C4D4×C3118yescomplemented
599C2×C42—22no—
600C2×C42—42no—
601#95—24no—
602#95—22no—
603#95—24no—
604#95—22no—
605#95—42no—
606C31#1528311yescharacteristic, direct product factor, Sylow
607C24—22no—
608C24—22no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—28no—
629C24—216no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—48no—
639C24—48no—
640C24—48no—
641C24—48no—
642C24—48no—
643C24—48no—
644C24—48no—
645C24—48no—
646C24—48no—
647C24—48no—
648C24—44no—
649C24—44no—
650C24—44no—
651C24—48no—
652C24—48no—
653C24—48no—
654C24—44no—
655C24—44no—
656C24—44no—
657C24C2×D4×C3112yes—
658C24C2×D4×C3112yes—
659C24C2×D4×C3112yes—
660C24C2×D4×C3112yes—
661C24C2×D4×C3114yes—
662C24#41×C3114yes—
663C24#41×C3114yes—
664C24C24×C3111yescharacteristic
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—44no—
670C2×D4—48no—
671C2×D4—48no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4C2×D4×C3112yes—
717C22×C4C2×D4×C3114yes—
718C22×C4C2×D4×C3114yes—
719C22×C4C2×D4×C3112yes—
720C22×C4C2×D4×C3112yes—
721C22×C4C2×D4×C3112yes—
722C22×C4C2×D4×C3112yes—
723C4⋊C4—48no—
724C4⋊C4—44no—
725C22⋊C4—28no—
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—48no—
729C22⋊C4—48no—
730C22⋊C4—48no—
731C22⋊C4—48no—
732C22⋊C4—48no—
733C22⋊C4—48no—
734C22⋊C4—48no—
735C22⋊C4—48no—
736C42—44no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—24no—
764C23—24no—
765C23—24no—
766C23—24no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—24no—
771C23—24no—
772C23—416no—
773C23—432no—
774C23—416no—
775C23—416no—
776C23—432no—
777C23—432no—
778C23—432no—
779C23—432no—
780C23—432no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—42no—
790C23—42no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—41no—
813C23—41no—
814C23—42no—
815C23—41no—
816C23—41no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23C31×#12314yes—
828C23C31×#12414yes—
829C23C31×#12714yes—
830C23C22×D4×C3111yescharacteristic
831C23C22×D4×C3111yescharacteristic
832C23C22×D4×C3111yescharacteristic
833C23C22×D4×C3112yes—
834C23C2×#41×C3112yes—
835C23C2×#41×C3112yes—
836C23C31×H(5,𝔽2)12yes—
837C23C31×H(5,𝔽2)12yes—
838C23C31×H(5,𝔽2)12yes—
839D4—416no—
840D4—416no—
841D4—416no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4C31×#12014yes—
885C22—24no—
886C22—28no—
887C22—24no—
888C22—24no—
889C22—28no—
890C22—28no—
891C22—464no—
892C22—42no—
893C22—42no—
894C22—44no—
895C22—44no—
896C22—44no—
897C22—44no—
898C22—44no—
899C22—44no—
900C22—44no—
901C22—44no—
902C22—44no—
903C22—44no—
904C22—44no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—44no—
910C22—44no—
911C22—44no—
912C22—44no—
913C22—42no—
914C22—44no—
915C22—44no—
916C22—42no—
917C22—42no—
918C22—82no—
919C22—82no—
920C22—82no—
921C22—82no—
922C22C2×C31×#12011yescharacteristic
923C22C2×C31×#12311yescharacteristic
924C22C31×#52512yes—
925C22C2×C31×#12411yescharacteristic
926C22C2×C31×#12711yescharacteristic
927C22C31×#53411yescharacteristic
928C22C31×#53412yes—
929C22C31×#53511yescharacteristic
930C22C31×#53511yescharacteristic
931C22C31×#53812yes—
932C22C31×#53812yes—
933C22D42×C3112yes—
934C22D42×C3112yes—
935C22C31×#54612yes—
936C22C31×#54612yes—
937C22C31×#54612yes—
938C22C31×#54612yes—
939C22C31×#54612yes—
940C22C31×#54612yes—
941C22C31×#55112yes—
942C22C31×#56012yes—
943C4—24no—
944C4—44no—
945C4—44no—
946C4—42no—
947C4—42no—
948C4—82no—
949C4—82no—
950C2—44no—
951C2—44no—
952C2—44no—
953C2—82no—
954C2C31×#240511yescharacteristic
955C2C31×#241812yes—
956C2C31×#243311yescharacteristic
957C2C31×#243511yescharacteristic
958C2C31×#247212yes—
959C2C31×#253912yes—
960C2C31×#266812yes—
961C2C31×#267812yes—
962C2C31×#268512yes—
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC22×C31×#120C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#399C2semidirect
3. C2×C31×#397C2semidirect
4. C2×C31×#394C2semidirect
5. C2×C31×#390C2semidirect
6. C2×C31×#379C2semidirect
7. C31×#1439C2semidirect
8. C31×#1438C2semidirect
9. C31×#1438C2semidirect
10. C31×#1437C2semidirect
11. C31×#1437C2semidirect
19. C22×C4⋊C4×C31C22semidirect
20. C22×C4⋊C4×C31C22semidirect
30. C22×C22⋊C4×C31C22semidirect
31. C22×C22⋊C4×C31C22semidirect
32. C22×C42×C31C22semidirect
38. C2×C31×#95C22semidirect
39. C2×C31×#95C22semidirect
40. C2×C31×#95C22semidirect
41. C2×C31×#95C22semidirect
42. C2×C31×#95C22semidirect
117. C2×C22⋊C4×C31D4semidirect
255. #15283C31direct (N × H)
405. C2×#399C2×C31semidirect
406. C2×#397C2×C31semidirect
407. C2×#394C2×C31semidirect
408. C2×#390C2×C31semidirect
409. C2×#379C2×C31semidirect
410. #1439C2×C31semidirect
411. #1438C2×C31semidirect
412. #1438C2×C31semidirect
413. #1437C2×C31semidirect
414. #1437C2×C31semidirect
487. C22×C4⋊C4C22×C31semidirect
488. C22×C4⋊C4C22×C31semidirect
498. C22×C22⋊C4C22×C31semidirect
499. C22×C22⋊C4C22×C31semidirect
500. C22×C42C22×C31semidirect
506. C2×#95C22×C31semidirect
507. C2×#95C22×C31semidirect
508. C2×#95C22×C31semidirect
509. C2×#95C22×C31semidirect
510. C2×#95C22×C31semidirect
598. C2×C22⋊C4D4×C31semidirect
606. C31#15283direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1202
C2×C31×#3992
C2×C31×#3972
C2×C31×#3942
C2×C31×#3902
C2×C31×#3792
C31×#14392
C31×#14382
C31×#14372
#1528331