Finite Group Databasebeta

← C31×#15310 #21472069

Subgroups — C31×#15310 #21472069

Order 7936.

3562 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#127C211yesmaximal, characteristic, complemented
2C22×C31×#121C211yesmaximal, characteristic, complemented
3C2×C31×#394C211yesmaximal, characteristic, complemented
4C2×C31×#392C212yesmaximal, complemented
5C2×C31×#392C212yesmaximal, complemented
6C2×C31×#392C211yesmaximal, characteristic, complemented
7C2×C31×#386C212yesmaximal, complemented
8C31×#1438C212yesmaximal, complemented
9C31×#1438C211yesmaximal, characteristic, complemented
10C31×#1437C211yesmaximal, characteristic, complemented
11C31×#1436C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C23×D4×C31C2211yescharacteristic
15C23×D4×C31C2212yes—
16C23×D4×C31C2212yes—
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2212yes—
19C24×C4×C31C2211yescharacteristic
20C2×C31×#127—24no—
21C2×C31×#127—28no—
22C2×C31×#121—24no—
23C2×C31×#121—24no—
24C2×C31×#121—24no—
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2212yes—
27C22×C22⋊C4×C31C2212yes—
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2212yes—
30C22×C22⋊C4×C31C2212yes—
31C22×C22⋊C4×C31C2212yes—
32C22×C22⋊C4×C31C2211yescharacteristic
33C22×C22⋊C4×C31C2212yes—
34C22×C42×C31C2211yescharacteristic
35C31×#394—24no—
36C31×#392—28no—
37C31×#392—24no—
38C31×#392—28no—
39C31×#386—28no—
40C2×C31×#95C2212yes—
41C2×C31×#95C2211yescharacteristic
42C2×C31×#95C2211yescharacteristic
43C2×C31×#95C2212yes—
44C2×C31×#95C2212yes—
45C25×C31C2312yes—
46C25×C31C2311yescharacteristic
47C25×C31C2311yescharacteristic
48C25×C31C2311yescharacteristic
49C22×D4×C31—22no—
50C22×D4×C31—22no—
51C22×D4×C31—22no—
52C22×D4×C31—22no—
53C22×D4×C31—24no—
54C22×D4×C31—24no—
55C22×D4×C31—24no—
56C22×D4×C31—24no—
57C22×D4×C31—24no—
58C22×D4×C31—24no—
59C22×D4×C31—24no—
60C22×D4×C31—24no—
61C22×D4×C31—24no—
62C22×D4×C31—22no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—24no—
68C22×D4×C31—24no—
69C22×D4×C31—24no—
70C22×D4×C31—22no—
71C22×D4×C31—24no—
72C22×D4×C31—24no—
73C22×D4×C31—22no—
74C22×D4×C31—24no—
75C22×D4×C31—24no—
76C22×D4×C31—42no—
77C22×D4×C31—42no—
78C22×D4×C31—42no—
79C22×D4×C31—42no—
80C22×D4×C31—42no—
81C22×D4×C31—42no—
82C22×D4×C31—42no—
83C22×D4×C31—42no—
84C22×D4×C31—42no—
85C22×D4×C31—42no—
86C22×D4×C31—42no—
87C22×D4×C31—42no—
88C22×D4×C31D414yescomplemented
89C22×D4×C31D418yescomplemented
90C23×C4×C31—22no—
91C23×C4×C31—22no—
92C23×C4×C31—22no—
93C23×C4×C31—24no—
94C23×C4×C31—42no—
95C23×C4×C31C2312yes—
96C23×C4×C31C2311yescharacteristic
97C23×C4×C31C2311yescharacteristic
98C23×C4×C31C2312yes—
99C23×C4×C31C2311yescharacteristic
100C23×C4×C31C2311yescharacteristic
101C23×C4×C31C2312yes—
102C31×#127—232no—
103C31×#121—232no—
104C2×C4⋊C4×C31—22no—
105C2×C4⋊C4×C31—22no—
106C2×C4⋊C4×C31D414yescomplemented
107C2×C22⋊C4×C31—22no—
108C2×C22⋊C4×C31—22no—
109C2×C22⋊C4×C31—22no—
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—22no—
112C2×C22⋊C4×C31—24no—
113C2×C22⋊C4×C31—24no—
114C2×C22⋊C4×C31—24no—
115C2×C22⋊C4×C31—24no—
116C2×C22⋊C4×C31—24no—
117C2×C22⋊C4×C31—24no—
118C2×C22⋊C4×C31—24no—
119C2×C22⋊C4×C31—24no—
120C2×C22⋊C4×C31—24no—
121C2×C22⋊C4×C31—24no—
122C2×C22⋊C4×C31—24no—
123C2×C22⋊C4×C31—24no—
124C2×C22⋊C4×C31—24no—
125C2×C22⋊C4×C31—42no—
126C2×C22⋊C4×C31—42no—
127C2×C22⋊C4×C31—42no—
128C2×C22⋊C4×C31—42no—
129C2×C22⋊C4×C31—42no—
130C2×C22⋊C4×C31D414yescomplemented
131C2×C42×C31—22no—
132C2×C42×C31—24no—
133C31×#95—24no—
134C31×#95—22no—
135C31×#95—24no—
136C31×#95—22no—
137C31×#95D418yescomplemented
138C24×C31—22no—
139C24×C31—21no—
140C24×C31—21no—
141C24×C31—22no—
142C24×C31—22no—
143C24×C31—22no—
144C24×C31—22no—
145C24×C31—22no—
146C24×C31—22no—
147C24×C31—21no—
148C24×C31—21no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31—22no—
152C24×C31—22no—
153C24×C31—22no—
154C24×C31—22no—
155C24×C31—22no—
156C24×C31—22no—
157C24×C31—22no—
158C24×C31—22no—
159C24×C31—22no—
160C24×C31—22no—
161C24×C31—22no—
162C24×C31—22no—
163C24×C31—22no—
164C24×C31—22no—
165C24×C31—22no—
166C24×C31—22no—
167C24×C31—22no—
168C24×C31—22no—
169C24×C31—22no—
170C24×C31—22no—
171C24×C31—22no—
172C24×C31—22no—
173C24×C31—22no—
174C24×C31—22no—
175C24×C31C2×D412yes—
176C24×C31C2×D414yes—
177C24×C31C2×D412yes—
178C24×C31C2×D414yes—
179C24×C31C2×D412yes—
180C24×C31C2411yescharacteristic
181C2×D4×C31—28no—
182C2×D4×C31—28no—
183C2×D4×C31—28no—
184C2×D4×C31—216no—
185C2×D4×C31—28no—
186C2×D4×C31—216no—
187C2×D4×C31—28no—
188C2×D4×C31—216no—
189C2×D4×C31—44no—
190C2×D4×C31—48no—
191C2×D4×C31—48no—
192C2×D4×C31—48no—
193C2×D4×C31—48no—
194C2×D4×C31—48no—
195C2×D4×C31—48no—
196C2×D4×C31—48no—
197C2×D4×C31—48no—
198C2×D4×C31—48no—
199C2×D4×C31—48no—
200C2×D4×C31—48no—
201C2×D4×C31—48no—
202C2×D4×C31—48no—
203C2×D4×C31—48no—
204C2×D4×C31—48no—
205C2×D4×C31—48no—
206C2×D4×C31—48no—
207C2×D4×C31—48no—
208C2×D4×C31—44no—
209C2×D4×C31—48no—
210C2×D4×C31—44no—
211C2×D4×C31—48no—
212C2×D4×C31—48no—
213C2×D4×C31—48no—
214C2×D4×C31—44no—
215C2×D4×C31—48no—
216C2×D4×C31—48no—
217C2×D4×C31—48no—
218C2×D4×C31—44no—
219C2×D4×C31—44no—
220C2×D4×C31—48no—
221C2×D4×C31—44no—
222C22×C4×C31—22no—
223C22×C4×C31—22no—
224C22×C4×C31—22no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—22no—
228C22×C4×C31—22no—
229C22×C4×C31—22no—
230C22×C4×C31—22no—
231C22×C4×C31—28no—
232C22×C4×C31—22no—
233C22×C4×C31—22no—
234C22×C4×C31—22no—
235C22×C4×C31—22no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—21no—
240C22×C4×C31—22no—
241C22×C4×C31—22no—
242C22×C4×C31—22no—
243C22×C4×C31—22no—
244C22×C4×C31—22no—
245C22×C4×C31—22no—
246C22×C4×C31—22no—
247C22×C4×C31—22no—
248C22×C4×C31—22no—
249C22×C4×C31—22no—
250C22×C4×C31—22no—
251C22×C4×C31—22no—
252C22×C4×C31—22no—
253C22×C4×C31—48no—
254C22×C4×C31—48no—
255C22×C4×C31—44no—
256C22×C4×C31—44no—
257C22×C4×C31C2×D414yes—
258C22×C4×C31C2×D412yes—
259C22×C4×C31C2×D412yes—
260C22×C4×C31C2×D412yes—
261C22×C4×C31C2×D412yes—
262C22×C4×C31C2×D412yes—
263C22×C4×C31C2×D414yes—
264C22×C4×C31C2×D414yes—
265C22×C4×C31C2×D414yes—
266C22×C4×C31C2×D412yes—
267C22×C4×C31#4114yes—
268C4⋊C4×C31—28no—
269C22⋊C4×C31—28no—
270C22⋊C4×C31—28no—
271C22⋊C4×C31—48no—
272C22⋊C4×C31—48no—
273C22⋊C4×C31—48no—
274C22⋊C4×C31—48no—
275C22⋊C4×C31—48no—
276C22⋊C4×C31—48no—
277C42×C31—28no—
278#15310C3111yesmaximal, characteristic, direct product factor, Sylow
279C23×C31—22no—
280C23×C31—24no—
281C23×C31—22no—
282C23×C31—24no—
283C23×C31—24no—
284C23×C31—24no—
285C23×C31—24no—
286C23×C31—24no—
287C23×C31—24no—
288C23×C31—24no—
289C23×C31—22no—
290C23×C31—22no—
291C23×C31—22no—
292C23×C31—24no—
293C23×C31—24no—
294C23×C31—22no—
295C23×C31—24no—
296C23×C31—22no—
297C23×C31—22no—
298C23×C31—24no—
299C23×C31—24no—
300C23×C31—24no—
301C23×C31—24no—
302C23×C31—24no—
303C23×C31—24no—
304C23×C31—24no—
305C23×C31—24no—
306C23×C31—41no—
307C23×C31—41no—
308C23×C31—41no—
309C23×C31—41no—
310C23×C31—42no—
311C23×C31—42no—
312C23×C31—42no—
313C23×C31—42no—
314C23×C31—42no—
315C23×C31—42no—
316C23×C31—41no—
317C23×C31—42no—
318C23×C31—42no—
319C23×C31—42no—
320C23×C31—42no—
321C23×C31—42no—
322C23×C31—41no—
323C23×C31—41no—
324C23×C31—42no—
325C23×C31—41no—
326C23×C31—42no—
327C23×C31—41no—
328C23×C31—42no—
329C23×C31—42no—
330C23×C31—42no—
331C23×C31—42no—
332C23×C31—42no—
333C23×C31—42no—
334C23×C31—42no—
335C23×C31—41no—
336C23×C31—41no—
337C23×C31—42no—
338C23×C31—41no—
339C23×C31—42no—
340C23×C31—42no—
341C23×C31—42no—
342C23×C31—42no—
343C23×C31—42no—
344C23×C31—42no—
345C23×C31—42no—
346C23×C31—42no—
347C23×C31—42no—
348C23×C31—42no—
349C23×C31—42no—
350C23×C31—42no—
351C23×C31—42no—
352C23×C31—42no—
353C23×C31—42no—
354C23×C31—42no—
355C23×C31—42no—
356C23×C31—42no—
357C23×C31—42no—
358C23×C31—42no—
359C23×C31—42no—
360C23×C31—42no—
361C23×C31—42no—
362C23×C31—42no—
363C23×C31—42no—
364C23×C31—42no—
365C23×C31—42no—
366C23×C31—42no—
367C23×C31—42no—
368C23×C31—42no—
369C23×C31—42no—
370C23×C31—42no—
371C23×C31—42no—
372C23×C31—42no—
373C23×C31—42no—
374C23×C31—42no—
375C23×C31—42no—
376C23×C31#12014yes—
377C23×C31C22×D411yescharacteristic
378C23×C31C22×D412yes—
379C23×C31C22×D411yescharacteristic
380C23×C31C22×D411yescharacteristic
381C23×C31C22×D412yes—
382C23×C31C2×#4112yes—
383C23×C31H(5,𝔽2)12yes—
384C23×C31H(5,𝔽2)12yes—
385C23×C31H(5,𝔽2)12yes—
386D4×C31—416no—
387D4×C31—432no—
388D4×C31—416no—
389D4×C31—432no—
390D4×C31—416no—
391D4×C31—416no—
392D4×C31—432no—
393C2×C4×C31—22no—
394C2×C4×C31—24no—
395C2×C4×C31—22no—
396C2×C4×C31—22no—
397C2×C4×C31—24no—
398C2×C4×C31—22no—
399C2×C4×C31—24no—
400C2×C4×C31—24no—
401C2×C4×C31—24no—
402C2×C4×C31—24no—
403C2×C4×C31—24no—
404C2×C4×C31—24no—
405C2×C4×C31—24no—
406C2×C4×C31—24no—
407C2×C4×C31—22no—
408C2×C4×C31—22no—
409C2×C4×C31—24no—
410C2×C4×C31—24no—
411C2×C4×C31—24no—
412C2×C4×C31—24no—
413C2×C4×C31—24no—
414C2×C4×C31—416no—
415C2×C4×C31—41no—
416C2×C4×C31—41no—
417C2×C4×C31—41no—
418C2×C4×C31—42no—
419C2×C4×C31—41no—
420C2×C4×C31—42no—
421C2×C4×C31—42no—
422C2×C4×C31—42no—
423C2×C4×C31—42no—
424C2×C4×C31—42no—
425C2×C4×C31—42no—
426C2×C4×C31—42no—
427C2×C4×C31—42no—
428C2×C4×C31—42no—
429C2×C4×C31—42no—
430C2×C4×C31—42no—
431C2×C4×C31—42no—
432C2×C4×C31#12014yes—
433C2×C4×C31#12118yescomplemented
434C2×C4×C31#12714yescomplemented
435C22×#127C2×C3111yescharacteristic, complemented
436C22×#121C2×C3111yescharacteristic, complemented
437C2×#394C2×C3111yescharacteristic, complemented
438C2×#392C2×C3112yescomplemented
439C2×#392C2×C3112yescomplemented
440C2×#392C2×C3111yescharacteristic, complemented
441C2×#386C2×C3112yescomplemented
442#1438C2×C3112yescomplemented
443#1438C2×C3111yescharacteristic, complemented
444#1437C2×C3111yescharacteristic, complemented
445#1436C2×C3111yescharacteristic, complemented
446C22×C31—24no—
447C22×C31—28no—
448C22×C31—44no—
449C22×C31—44no—
450C22×C31—44no—
451C22×C31—44no—
452C22×C31—42no—
453C22×C31—42no—
454C22×C31—44no—
455C22×C31—42no—
456C22×C31—44no—
457C22×C31—42no—
458C22×C31—44no—
459C22×C31—44no—
460C22×C31—44no—
461C22×C31—44no—
462C22×C31—44no—
463C22×C31—44no—
464C22×C31—44no—
465C22×C31—44no—
466C22×C31—44no—
467C22×C31—42no—
468C22×C31—42no—
469C22×C31—42no—
470C22×C31—42no—
471C22×C31—44no—
472C22×C31—82no—
473C22×C31—82no—
474C22×C31—82no—
475C22×C31—82no—
476C22×C31—82no—
477C22×C31—82no—
478C22×C31—82no—
479C22×C31—82no—
480C22×C31—82no—
481C22×C31—82no—
482C22×C31—82no—
483C22×C31—82no—
484C22×C31—82no—
485C22×C31—82no—
486C22×C31—82no—
487C22×C31—82no—
488C22×C31C2×#12011yescharacteristic
489C22×C31C2×#12011yescharacteristic
490C22×C31C2×#12112yes—
491C22×C31C2×#12711yescharacteristic
492C22×C31#53211yescharacteristic
493C22×C31#53411yescharacteristic
494C22×C31#53412yes—
495C22×C31#53511yescharacteristic
496C22×C31#53512yes—
497C22×C31#53511yescharacteristic
498C22×C31#54012yes—
499C22×C31D4212yes—
500C22×C31D4212yes—
501C22×C31D4212yes—
502C22×C31D4212yes—
503C22×C31D4212yes—
504C22×C31#54612yes—
505C22×C31#54612yes—
506C22×C31#55012yes—
507C22×C31#55012yes—
508C22×C31#56012yes—
509C4×C31—24no—
510C4×C31—28no—
511C4×C31—24no—
512C4×C31—42no—
513C4×C31—44no—
514C4×C31—42no—
515C4×C31—82no—
516C23×D4C22×C3111yescharacteristic
517C23×D4C22×C3111yescharacteristic
518C23×D4C22×C3111yescharacteristic
519C23×D4C22×C3112yes—
520C23×D4C22×C3112yes—
521C23×D4C22×C3111yescharacteristic
522C23×D4C22×C3112yes—
523C24×C4C22×C3111yescharacteristic
524C2×#127—24no—
525C2×#127—28no—
526C2×#121—24no—
527C2×#121—24no—
528C2×#121—24no—
529C22×C4⋊C4C22×C3111yescharacteristic
530C22×C22⋊C4C22×C3112yes—
531C22×C22⋊C4C22×C3112yes—
532C22×C22⋊C4C22×C3111yescharacteristic
533C22×C22⋊C4C22×C3112yes—
534C22×C22⋊C4C22×C3112yes—
535C22×C22⋊C4C22×C3112yes—
536C22×C22⋊C4C22×C3111yescharacteristic
537C22×C22⋊C4C22×C3112yes—
538C22×C42C22×C3111yescharacteristic
539#394—24no—
540#392—28no—
541#392—24no—
542#392—28no—
543#386—28no—
544C2×#95C22×C3112yes—
545C2×#95C22×C3111yescharacteristic
546C2×#95C22×C3111yescharacteristic
547C2×#95C22×C3112yes—
548C2×#95C22×C3112yes—
549C2×C31—44no—
550C2×C31—84no—
551C2×C31—82no—
552C2×C31—82no—
553C2×C31#240311yescharacteristic
554C2×C31#241012yes—
555C2×C31#242812yes—
556C2×C31#243111yescharacteristic
557C2×C31#243311yescharacteristic
558C2×C31#254112yes—
559C2×C31#266912yes—
560C2×C31#267312yes—
561C2×C31#267312yes—
562C25C23×C3112yes—
563C25C23×C3111yescharacteristic
564C25C23×C3111yescharacteristic
565C25C23×C3111yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—22no—
569C22×D4—22no—
570C22×D4—24no—
571C22×D4—24no—
572C22×D4—24no—
573C22×D4—24no—
574C22×D4—24no—
575C22×D4—24no—
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—24no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—22no—
588C22×D4—24no—
589C22×D4—24no—
590C22×D4—22no—
591C22×D4—24no—
592C22×D4—24no—
593C22×D4—42no—
594C22×D4—42no—
595C22×D4—42no—
596C22×D4—42no—
597C22×D4—42no—
598C22×D4—42no—
599C22×D4—42no—
600C22×D4—42no—
601C22×D4—42no—
602C22×D4—42no—
603C22×D4—42no—
604C22×D4—42no—
605C22×D4D4×C3114yescomplemented
606C22×D4D4×C3118yescomplemented
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—22no—
610C23×C4—24no—
611C23×C4—42no—
612C23×C4C23×C3112yes—
613C23×C4C23×C3111yescharacteristic
614C23×C4C23×C3111yescharacteristic
615C23×C4C23×C3112yes—
616C23×C4C23×C3111yescharacteristic
617C23×C4C23×C3111yescharacteristic
618C23×C4C23×C3112yes—
619#127—232no—
620#121—232no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4D4×C3114yescomplemented
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—42no—
643C2×C22⋊C4—42no—
644C2×C22⋊C4—42no—
645C2×C22⋊C4—42no—
646C2×C22⋊C4—42no—
647C2×C22⋊C4D4×C3114yescomplemented
648C2×C42—22no—
649C2×C42—24no—
650#95—24no—
651#95—22no—
652#95—24no—
653#95—22no—
654#95D4×C3118yescomplemented
655C31#1531011yescharacteristic, direct product factor, Sylow
656C24—22no—
657C24—21no—
658C24—21no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24C2×D4×C3112yes—
694C24C2×D4×C3114yes—
695C24C2×D4×C3112yes—
696C24C2×D4×C3114yes—
697C24C2×D4×C3112yes—
698C24C24×C3111yescharacteristic
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—216no—
703C2×D4—28no—
704C2×D4—216no—
705C2×D4—28no—
706C2×D4—216no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—44no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—44no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—48no—
739C2×D4—44no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—28no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4C2×D4×C3114yes—
776C22×C4C2×D4×C3112yes—
777C22×C4C2×D4×C3112yes—
778C22×C4C2×D4×C3112yes—
779C22×C4C2×D4×C3112yes—
780C22×C4C2×D4×C3112yes—
781C22×C4C2×D4×C3114yes—
782C22×C4C2×D4×C3114yes—
783C22×C4C2×D4×C3114yes—
784C22×C4C2×D4×C3112yes—
785C22×C4#41×C3114yes—
786C4⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C42—28no—
796C23—22no—
797C23—24no—
798C23—22no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—24no—
810C23—24no—
811C23—22no—
812C23—24no—
813C23—22no—
814C23—22no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—41no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—41no—
840C23—41no—
841C23—42no—
842C23—41no—
843C23—42no—
844C23—41no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23—42no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23C31×#12014yes—
894C23C22×D4×C3111yescharacteristic
895C23C22×D4×C3112yes—
896C23C22×D4×C3111yescharacteristic
897C23C22×D4×C3111yescharacteristic
898C23C22×D4×C3112yes—
899C23C2×#41×C3112yes—
900C23C31×H(5,𝔽2)12yes—
901C23C31×H(5,𝔽2)12yes—
902C23C31×H(5,𝔽2)12yes—
903D4—416no—
904D4—432no—
905D4—416no—
906D4—432no—
907D4—416no—
908D4—416no—
909D4—432no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—416no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4C31×#12014yes—
950C2×C4C31×#12118yescomplemented
951C2×C4C31×#12714yescomplemented
952C22—24no—
953C22—28no—
954C22—44no—
955C22—44no—
956C22—44no—
957C22—44no—
958C22—42no—
959C22—42no—
960C22—44no—
961C22—42no—
962C22—44no—
963C22—42no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—44no—
978C22—82no—
979C22—82no—
980C22—82no—
981C22—82no—
982C22—82no—
983C22—82no—
984C22—82no—
985C22—82no—
986C22—82no—
987C22—82no—
988C22—82no—
989C22—82no—
990C22—82no—
991C22—82no—
992C22—82no—
993C22—82no—
994C22C2×C31×#12011yescharacteristic
995C22C2×C31×#12011yescharacteristic
996C22C2×C31×#12112yes—
997C22C2×C31×#12711yescharacteristic
998C22C31×#53211yescharacteristic
999C22C31×#53411yescharacteristic
1000C22C31×#53412yes—
1001C22C31×#53511yescharacteristic
1002C22C31×#53512yes—
1003C22C31×#53511yescharacteristic
1004C22C31×#54012yes—
1005C22D42×C3112yes—
1006C22D42×C3112yes—
1007C22D42×C3112yes—
1008C22D42×C3112yes—
1009C22D42×C3112yes—
1010C22C31×#54612yes—
1011C22C31×#54612yes—
1012C22C31×#55012yes—
1013C22C31×#55012yes—
1014C22C31×#56012yes—
1015C4—24no—
1016C4—28no—
1017C4—24no—
1018C4—42no—
1019C4—44no—
1020C4—42no—
1021C4—82no—
1022C2—44no—
1023C2—84no—
1024C2—82no—
1025C2—82no—
1026C2C31×#240311yescharacteristic
1027C2C31×#241012yes—
1028C2C31×#242812yes—
1029C2C31×#243111yescharacteristic
1030C2C31×#243311yescharacteristic
1031C2C31×#254112yes—
1032C2C31×#266912yes—
1033C2C31×#267312yes—
1034C2C31×#267312yes—
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×#127C2semidirect
2. C22×C31×#121C2semidirect
3. C2×C31×#394C2semidirect
4. C2×C31×#392C2semidirect
5. C2×C31×#392C2semidirect
6. C2×C31×#392C2semidirect
7. C2×C31×#386C2semidirect
8. C31×#1438C2semidirect
9. C31×#1438C2semidirect
10. C31×#1437C2semidirect
11. C31×#1436C2semidirect
88. C22×D4×C31D4semidirect
89. C22×D4×C31D4semidirect
106. C2×C4⋊C4×C31D4semidirect
130. C2×C22⋊C4×C31D4semidirect
137. C31×#95D4semidirect
278. #15310C31direct (N × H)
433. C2×C4×C31#121semidirect
434. C2×C4×C31#127semidirect
435. C22×#127C2×C31semidirect
436. C22×#121C2×C31semidirect
437. C2×#394C2×C31semidirect
438. C2×#392C2×C31semidirect
439. C2×#392C2×C31semidirect
440. C2×#392C2×C31semidirect
441. C2×#386C2×C31semidirect
442. #1438C2×C31semidirect
443. #1438C2×C31semidirect
444. #1437C2×C31semidirect
445. #1436C2×C31semidirect
605. C22×D4D4×C31semidirect
606. C22×D4D4×C31semidirect
623. C2×C4⋊C4D4×C31semidirect
647. C2×C22⋊C4D4×C31semidirect
654. #95D4×C31semidirect
655. C31#15310direct (N × H)
950. C2×C4C31×#121semidirect
951. C2×C4C31×#127semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1272
C22×C31×#1212
C2×C31×#3942
C2×C31×#3922
C2×C31×#3862
C31×#14382
C31×#14372
C31×#14362
#1531031