Finite Group Databasebeta

← C31×#14762 #21471521

Subgroups — C31×#14762 #21471521

Order 7936.

2970 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic, complemented
2C2×C31×#394C212yesmaximal, complemented
3C2×C31×#392C211yesmaximal, characteristic, complemented
4C2×C31×#392C212yesmaximal, complemented
5C2×C31×#390C212yesmaximal, complemented
6C2×C31×#386C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
8C31×#1444C211yesmaximal, characteristic, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1438C211yesmaximal, characteristic, complemented
11C31×#1437C212yesmaximal, complemented
12C23×D4×C31C2211yescharacteristic
13C23×D4×C31C2212yes—
14C23×D4×C31C2212yes—
15C23×D4×C31C2211yescharacteristic
16C24×C4×C31C2211yescharacteristic
17C2×C31×#121—24no—
18C2×C31×#121—28no—
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2212yes—
27C22×C22⋊C4×C31C2212yes—
28C22×C22⋊C4×C31C2212yes—
29C22×C22⋊C4×C31C2212yes—
30C22×C42×C31C2212yes—
31C31×#394—28no—
32C31×#392—28no—
33C31×#392—24no—
34C31×#390—28no—
35C31×#386—24no—
36C4×C22⋊C4×C31—24no—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2211yescharacteristic
40C2×C31×#95C2211yescharacteristic
41C2×C31×#95C2211yescharacteristic
42C2×C31×#95C2211yescharacteristic
43C25×C31C2312yes—
44C25×C31C2311yescharacteristic
45C25×C31C2311yescharacteristic
46C22×D4×C31—24no—
47C22×D4×C31—24no—
48C22×D4×C31—24no—
49C22×D4×C31—22no—
50C22×D4×C31—24no—
51C22×D4×C31—24no—
52C22×D4×C31—22no—
53C22×D4×C31—24no—
54C22×D4×C31—24no—
55C22×D4×C31—24no—
56C22×D4×C31—24no—
57C22×D4×C31—22no—
58C22×D4×C31—22no—
59C22×D4×C31—24no—
60C22×D4×C31—24no—
61C22×D4×C31—22no—
62C22×D4×C31—24no—
63C22×D4×C31—22no—
64C22×D4×C31—42no—
65C22×D4×C31—42no—
66C22×D4×C31—42no—
67C22×D4×C31—42no—
68C22×D4×C31—42no—
69C22×D4×C31—42no—
70C23×C4×C31—24no—
71C23×C4×C31—22no—
72C23×C4×C31—22no—
73C23×C4×C31—42no—
74C23×C4×C31D414yescomplemented
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2312yes—
78C23×C4×C31C2312yes—
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2312yes—
82C23×C4×C31C2311yescharacteristic
83C31×#121—232no—
84C2×C4⋊C4×C31—24no—
85C2×C4⋊C4×C31—22no—
86C2×C4⋊C4×C31—24no—
87C2×C4⋊C4×C31—24no—
88C2×C4⋊C4×C31—42no—
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—24no—
91C2×C22⋊C4×C31—24no—
92C2×C22⋊C4×C31—24no—
93C2×C22⋊C4×C31—22no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—24no—
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—22no—
98C2×C22⋊C4×C31—24no—
99C2×C22⋊C4×C31—24no—
100C2×C22⋊C4×C31—24no—
101C2×C22⋊C4×C31—24no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—24no—
104C2×C22⋊C4×C31—24no—
105C2×C22⋊C4×C31—24no—
106C2×C22⋊C4×C31—24no—
107C2×C22⋊C4×C31—22no—
108C2×C22⋊C4×C31—24no—
109C2×C22⋊C4×C31—42no—
110C2×C22⋊C4×C31—42no—
111C2×C22⋊C4×C31—42no—
112C2×C22⋊C4×C31D418yescomplemented
113C2×C22⋊C4×C31D418yescomplemented
114C2×C42×C31—24no—
115C2×C42×C31—24no—
116C2×C42×C31—42no—
117C31×#95—22no—
118C31×#95—22no—
119C31×#95—22no—
120C31×#95—24no—
121C31×#95—24no—
122C31×#95D414yescomplemented
123C24×C31—21no—
124C24×C31—22no—
125C24×C31—22no—
126C24×C31—21no—
127C24×C31—21no—
128C24×C31—21no—
129C24×C31—22no—
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—21no—
140C24×C31—22no—
141C24×C31—22no—
142C24×C31—22no—
143C24×C31—21no—
144C24×C31—22no—
145C24×C31—22no—
146C24×C31—22no—
147C24×C31—21no—
148C24×C31—22no—
149C24×C31—21no—
150C24×C31—22no—
151C24×C31—22no—
152C24×C31—22no—
153C24×C31—22no—
154C24×C31—22no—
155C24×C31—21no—
156C24×C31C2×D414yes—
157C24×C31C2×D414yes—
158C24×C31C2×D412yes—
159C24×C31#4112yes—
160C24×C31C2411yescharacteristic
161C2×D4×C31—28no—
162C2×D4×C31—216no—
163C2×D4×C31—216no—
164C2×D4×C31—28no—
165C2×D4×C31—48no—
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—48no—
173C2×D4×C31—48no—
174C2×D4×C31—44no—
175C2×D4×C31—48no—
176C2×D4×C31—48no—
177C2×D4×C31—48no—
178C2×D4×C31—48no—
179C2×D4×C31—44no—
180C2×D4×C31—48no—
181C2×D4×C31—48no—
182C2×D4×C31—44no—
183C2×D4×C31—44no—
184C2×D4×C31—48no—
185C22×C4×C31—21no—
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—21no—
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—22no—
203C22×C4×C31—22no—
204C22×C4×C31—21no—
205C22×C4×C31—22no—
206C22×C4×C31—22no—
207C22×C4×C31—22no—
208C22×C4×C31—22no—
209C22×C4×C31—22no—
210C22×C4×C31—28no—
211C22×C4×C31—28no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—22no—
215C22×C4×C31—21no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—44no—
223C22×C4×C31—48no—
224C22×C4×C31—48no—
225C22×C4×C31C2×D414yes—
226C22×C4×C31C2×D414yes—
227C22×C4×C31C2×D412yes—
228C22×C4×C31C2×D414yes—
229C22×C4×C31C2×D412yes—
230C22×C4×C31C2×D412yes—
231C22×C4×C31C2×D414yes—
232C22×C4×C31C2×D414yes—
233C22×C4×C31#4112yes—
234C22×C4×C31#4112yes—
235C22×C4×C31#4114yes—
236C4⋊C4×C31—28no—
237C4⋊C4×C31—48no—
238C22⋊C4×C31—216no—
239C22⋊C4×C31—216no—
240C22⋊C4×C31—48no—
241C22⋊C4×C31—48no—
242C22⋊C4×C31—48no—
243C22⋊C4×C31—44no—
244C22⋊C4×C31—44no—
245C22⋊C4×C31—44no—
246C22⋊C4×C31—48no—
247C42×C31—48no—
248#14762C3111yesmaximal, characteristic, direct product factor, Sylow
249C23×C31—22no—
250C23×C31—24no—
251C23×C31—22no—
252C23×C31—22no—
253C23×C31—22no—
254C23×C31—24no—
255C23×C31—22no—
256C23×C31—22no—
257C23×C31—24no—
258C23×C31—24no—
259C23×C31—24no—
260C23×C31—24no—
261C23×C31—24no—
262C23×C31—24no—
263C23×C31—22no—
264C23×C31—24no—
265C23×C31—24no—
266C23×C31—24no—
267C23×C31—24no—
268C23×C31—24no—
269C23×C31—22no—
270C23×C31—24no—
271C23×C31—24no—
272C23×C31—22no—
273C23×C31—42no—
274C23×C31—42no—
275C23×C31—42no—
276C23×C31—42no—
277C23×C31—42no—
278C23×C31—42no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—42no—
286C23×C31—42no—
287C23×C31—42no—
288C23×C31—42no—
289C23×C31—42no—
290C23×C31—42no—
291C23×C31—42no—
292C23×C31—41no—
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—41no—
302C23×C31—42no—
303C23×C31—41no—
304C23×C31—42no—
305C23×C31—42no—
306C23×C31—42no—
307C23×C31—42no—
308C23×C31—42no—
309C23×C31—42no—
310C23×C31—42no—
311C23×C31—42no—
312C23×C31—42no—
313C23×C31—42no—
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—41no—
325C23×C31—42no—
326C23×C31—42no—
327C23×C31—41no—
328C23×C31—42no—
329C23×C31#12714yes—
330C23×C31C22×D411yescharacteristic
331C23×C31C22×D412yes—
332C23×C31C22×D411yescharacteristic
333C23×C31C22×D412yes—
334C23×C31C2×#4112yes—
335C23×C31C2×#4111yescharacteristic
336C23×C31C2×#4111yescharacteristic
337C23×C31C2×#4111yescharacteristic
338C23×C31H(5,𝔽2)12yes—
339C23×C31H(5,𝔽2)11yescharacteristic
340C23×C31H(5,𝔽2)11yescharacteristic
341D4×C31—416no—
342D4×C31—432no—
343D4×C31—432no—
344D4×C31—416no—
345C2×C4×C31—22no—
346C2×C4×C31—22no—
347C2×C4×C31—24no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—24no—
351C2×C4×C31—24no—
352C2×C4×C31—24no—
353C2×C4×C31—24no—
354C2×C4×C31—24no—
355C2×C4×C31—24no—
356C2×C4×C31—24no—
357C2×C4×C31—24no—
358C2×C4×C31—24no—
359C2×C4×C31—24no—
360C2×C4×C31—24no—
361C2×C4×C31—22no—
362C2×C4×C31—24no—
363C2×C4×C31—24no—
364C2×C4×C31—24no—
365C2×C4×C31—24no—
366C2×C4×C31—24no—
367C2×C4×C31—416no—
368C2×C4×C31—42no—
369C2×C4×C31—41no—
370C2×C4×C31—42no—
371C2×C4×C31—41no—
372C2×C4×C31—42no—
373C2×C4×C31—42no—
374C2×C4×C31—42no—
375C2×C4×C31—42no—
376C2×C4×C31—42no—
377C2×C4×C31—42no—
378C2×C4×C31—42no—
379C2×C4×C31—41no—
380C2×C4×C31—41no—
381C2×C4×C31—42no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—42no—
386C2×C4×C31—41no—
387C2×C4×C31—42no—
388C2×C4×C31—42no—
389C2×C4×C31#12014yes—
390C2×C4×C31#12114yes—
391C2×C4×C31#12118yescomplemented
392C22×#121C2×C3111yescharacteristic, complemented
393C2×#394C2×C3112yescomplemented
394C2×#392C2×C3111yescharacteristic, complemented
395C2×#392C2×C3112yescomplemented
396C2×#390C2×C3112yescomplemented
397C2×#386C2×C3111yescharacteristic, complemented
398C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
399#1444C2×C3111yescharacteristic, complemented
400#1439C2×C3111yescharacteristic, complemented
401#1438C2×C3111yescharacteristic, complemented
402#1437C2×C3112yescomplemented
403C22×C31—24no—
404C22×C31—24no—
405C22×C31—24no—
406C22×C31—42no—
407C22×C31—42no—
408C22×C31—42no—
409C22×C31—42no—
410C22×C31—44no—
411C22×C31—44no—
412C22×C31—44no—
413C22×C31—44no—
414C22×C31—44no—
415C22×C31—42no—
416C22×C31—44no—
417C22×C31—42no—
418C22×C31—44no—
419C22×C31—44no—
420C22×C31—44no—
421C22×C31—44no—
422C22×C31—44no—
423C22×C31—44no—
424C22×C31—42no—
425C22×C31—44no—
426C22×C31—82no—
427C22×C31—81no—
428C22×C31—82no—
429C22×C31—81no—
430C22×C31—81no—
431C22×C31—82no—
432C22×C31—82no—
433C22×C31—82no—
434C22×C31—82no—
435C22×C31—81no—
436C22×C31—82no—
437C22×C31—82no—
438C22×C31—82no—
439C22×C31—82no—
440C22×C31C2×#12011yescharacteristic
441C22×C31C2×#12111yescharacteristic
442C22×C31C2×#12112yes—
443C22×C31#52511yescharacteristic
444C22×C31#52512yes—
445C22×C31C2×#12711yescharacteristic
446C22×C31#53211yescharacteristic
447C22×C31#53212yes—
448C22×C31#53212yes—
449C22×C31#53411yescharacteristic
450C22×C31#53511yescharacteristic
451C22×C31#53812yes—
452C22×C31#54012yes—
453C22×C31D4212yes—
454C22×C31D4212yes—
455C22×C31D4212yes—
456C22×C31#54612yes—
457C22×C31#54611yescharacteristic
458C22×C31#54612yes—
459C22×C31#54612yes—
460C22×C31#55011yescharacteristic
461C22×C31#55311yescharacteristic
462C22×C31#55511yescharacteristic
463C4×C31—24no—
464C4×C31—24no—
465C4×C31—28no—
466C4×C31—44no—
467C4×C31—44no—
468C4×C31—42no—
469C4×C31—81no—
470C4×C31—81no—
471C23×D4C22×C3111yescharacteristic
472C23×D4C22×C3112yes—
473C23×D4C22×C3112yes—
474C23×D4C22×C3111yescharacteristic
475C24×C4C22×C3111yescharacteristic
476C2×#121—24no—
477C2×#121—28no—
478C22×C4⋊C4C22×C3111yescharacteristic
479C22×C4⋊C4C22×C3112yes—
480C22×C22⋊C4C22×C3112yes—
481C22×C22⋊C4C22×C3111yescharacteristic
482C22×C22⋊C4C22×C3111yescharacteristic
483C22×C22⋊C4C22×C3111yescharacteristic
484C22×C22⋊C4C22×C3112yes—
485C22×C22⋊C4C22×C3112yes—
486C22×C22⋊C4C22×C3112yes—
487C22×C22⋊C4C22×C3112yes—
488C22×C22⋊C4C22×C3112yes—
489C22×C42C22×C3112yes—
490#394—28no—
491#392—28no—
492#392—24no—
493#390—28no—
494#386—24no—
495C4×C22⋊C4—24no—
496C2×#95C22×C3112yes—
497C2×#95C22×C3112yes—
498C2×#95C22×C3111yescharacteristic
499C2×#95C22×C3111yescharacteristic
500C2×#95C22×C3111yescharacteristic
501C2×#95C22×C3111yescharacteristic
502C2×C31—44no—
503C2×C31—84no—
504C2×C31—82no—
505C2×C31#238811yescharacteristic
506C2×C31#241011yescharacteristic
507C2×C31#241411yescharacteristic
508C2×C31#242412yes—
509C2×C31#242812yes—
510C2×C31#243311yescharacteristic
511C2×C31#246412yes—
512C2×C31#253911yescharacteristic
513C2×C31#255512yes—
514C2×C31#266111yescharacteristic
515C2×C31#285611yescharacteristic
516C25C23×C3112yes—
517C25C23×C3111yescharacteristic
518C25C23×C3111yescharacteristic
519C22×D4—24no—
520C22×D4—24no—
521C22×D4—24no—
522C22×D4—22no—
523C22×D4—24no—
524C22×D4—24no—
525C22×D4—22no—
526C22×D4—24no—
527C22×D4—24no—
528C22×D4—24no—
529C22×D4—24no—
530C22×D4—22no—
531C22×D4—22no—
532C22×D4—24no—
533C22×D4—24no—
534C22×D4—22no—
535C22×D4—24no—
536C22×D4—22no—
537C22×D4—42no—
538C22×D4—42no—
539C22×D4—42no—
540C22×D4—42no—
541C22×D4—42no—
542C22×D4—42no—
543C23×C4—24no—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—42no—
547C23×C4D4×C3114yescomplemented
548C23×C4C23×C3111yescharacteristic
549C23×C4C23×C3111yescharacteristic
550C23×C4C23×C3112yes—
551C23×C4C23×C3112yes—
552C23×C4C23×C3111yescharacteristic
553C23×C4C23×C3111yescharacteristic
554C23×C4C23×C3112yes—
555C23×C4C23×C3111yescharacteristic
556#121—232no—
557C2×C4⋊C4—24no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—24no—
560C2×C4⋊C4—24no—
561C2×C4⋊C4—42no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—24no—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—24no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—24no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4D4×C3118yescomplemented
586C2×C22⋊C4D4×C3118yescomplemented
587C2×C42—24no—
588C2×C42—24no—
589C2×C42—42no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—24no—
594#95—24no—
595#95D4×C3114yescomplemented
596C31#1476211yescharacteristic, direct product factor, Sylow
597C24—21no—
598C24—22no—
599C24—22no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—22no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—21no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—21no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—21no—
622C24—22no—
623C24—21no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—21no—
630C24C2×D4×C3114yes—
631C24C2×D4×C3114yes—
632C24C2×D4×C3112yes—
633C24#41×C3112yes—
634C24C24×C3111yescharacteristic
635C2×D4—28no—
636C2×D4—216no—
637C2×D4—216no—
638C2×D4—28no—
639C2×D4—48no—
640C2×D4—48no—
641C2×D4—48no—
642C2×D4—48no—
643C2×D4—48no—
644C2×D4—48no—
645C2×D4—48no—
646C2×D4—48no—
647C2×D4—48no—
648C2×D4—44no—
649C2×D4—48no—
650C2×D4—48no—
651C2×D4—48no—
652C2×D4—48no—
653C2×D4—44no—
654C2×D4—48no—
655C2×D4—48no—
656C2×D4—44no—
657C2×D4—44no—
658C2×D4—48no—
659C22×C4—21no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—21no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—28no—
685C22×C4—28no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—21no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—44no—
697C22×C4—48no—
698C22×C4—48no—
699C22×C4C2×D4×C3114yes—
700C22×C4C2×D4×C3114yes—
701C22×C4C2×D4×C3112yes—
702C22×C4C2×D4×C3114yes—
703C22×C4C2×D4×C3112yes—
704C22×C4C2×D4×C3112yes—
705C22×C4C2×D4×C3114yes—
706C22×C4C2×D4×C3114yes—
707C22×C4#41×C3112yes—
708C22×C4#41×C3112yes—
709C22×C4#41×C3114yes—
710C4⋊C4—28no—
711C4⋊C4—48no—
712C22⋊C4—216no—
713C22⋊C4—216no—
714C22⋊C4—48no—
715C22⋊C4—48no—
716C22⋊C4—48no—
717C22⋊C4—44no—
718C22⋊C4—44no—
719C22⋊C4—44no—
720C22⋊C4—48no—
721C42—48no—
722C23—22no—
723C23—24no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—24no—
728C23—22no—
729C23—22no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—22no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—22no—
743C23—24no—
744C23—24no—
745C23—22no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—41no—
766C23—41no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—41no—
775C23—42no—
776C23—41no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—41no—
798C23—42no—
799C23—42no—
800C23—41no—
801C23—42no—
802C23C31×#12714yes—
803C23C22×D4×C3111yescharacteristic
804C23C22×D4×C3112yes—
805C23C22×D4×C3111yescharacteristic
806C23C22×D4×C3112yes—
807C23C2×#41×C3112yes—
808C23C2×#41×C3111yescharacteristic
809C23C2×#41×C3111yescharacteristic
810C23C2×#41×C3111yescharacteristic
811C23C31×H(5,𝔽2)12yes—
812C23C31×H(5,𝔽2)11yescharacteristic
813C23C31×H(5,𝔽2)11yescharacteristic
814D4—416no—
815D4—432no—
816D4—432no—
817D4—416no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—416no—
841C2×C4—42no—
842C2×C4—41no—
843C2×C4—42no—
844C2×C4—41no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—42no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4C31×#12014yes—
863C2×C4C31×#12114yes—
864C2×C4C31×#12118yescomplemented
865C22—24no—
866C22—24no—
867C22—24no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—44no—
876C22—44no—
877C22—42no—
878C22—44no—
879C22—42no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—42no—
887C22—44no—
888C22—82no—
889C22—81no—
890C22—82no—
891C22—81no—
892C22—81no—
893C22—82no—
894C22—82no—
895C22—82no—
896C22—82no—
897C22—81no—
898C22—82no—
899C22—82no—
900C22—82no—
901C22—82no—
902C22C2×C31×#12011yescharacteristic
903C22C2×C31×#12111yescharacteristic
904C22C2×C31×#12112yes—
905C22C31×#52511yescharacteristic
906C22C31×#52512yes—
907C22C2×C31×#12711yescharacteristic
908C22C31×#53211yescharacteristic
909C22C31×#53212yes—
910C22C31×#53212yes—
911C22C31×#53411yescharacteristic
912C22C31×#53511yescharacteristic
913C22C31×#53812yes—
914C22C31×#54012yes—
915C22D42×C3112yes—
916C22D42×C3112yes—
917C22D42×C3112yes—
918C22C31×#54612yes—
919C22C31×#54611yescharacteristic
920C22C31×#54612yes—
921C22C31×#54612yes—
922C22C31×#55011yescharacteristic
923C22C31×#55311yescharacteristic
924C22C31×#55511yescharacteristic
925C4—24no—
926C4—24no—
927C4—28no—
928C4—44no—
929C4—44no—
930C4—42no—
931C4—81no—
932C4—81no—
933C2—44no—
934C2—84no—
935C2—82no—
936C2C31×#238811yescharacteristic
937C2C31×#241011yescharacteristic
938C2C31×#241411yescharacteristic
939C2C31×#242412yes—
940C2C31×#242812yes—
941C2C31×#243311yescharacteristic
942C2C31×#246412yes—
943C2C31×#253911yescharacteristic
944C2C31×#255512yes—
945C2C31×#266111yescharacteristic
946C2C31×#285611yescharacteristic
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×#394C2semidirect
3. C2×C31×#392C2semidirect
4. C2×C31×#392C2semidirect
5. C2×C31×#390C2semidirect
6. C2×C31×#386C2semidirect
7. C2×C4×C22⋊C4×C31C2semidirect
8. C31×#1444C2semidirect
9. C31×#1439C2semidirect
10. C31×#1438C2semidirect
11. C31×#1437C2semidirect
74. C23×C4×C31D4semidirect
112. C2×C22⋊C4×C31D4semidirect
113. C2×C22⋊C4×C31D4semidirect
122. C31×#95D4semidirect
248. #14762C31direct (N × H)
391. C2×C4×C31#121semidirect
392. C22×#121C2×C31semidirect
393. C2×#394C2×C31semidirect
394. C2×#392C2×C31semidirect
395. C2×#392C2×C31semidirect
396. C2×#390C2×C31semidirect
397. C2×#386C2×C31semidirect
398. C2×C4×C22⋊C4C2×C31semidirect
399. #1444C2×C31semidirect
400. #1439C2×C31semidirect
401. #1438C2×C31semidirect
402. #1437C2×C31semidirect
547. C23×C4D4×C31semidirect
585. C2×C22⋊C4D4×C31semidirect
586. C2×C22⋊C4D4×C31semidirect
595. #95D4×C31semidirect
596. C31#14762direct (N × H)
864. C2×C4C31×#121semidirect

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×#3942
C2×C31×#3922
C2×C31×#3902
C2×C31×#3862
C2×C4×C22⋊C4×C312
C31×#14442
C31×#14392
C31×#14382
C31×#14372
#1476231