Finite Group Databasebeta

← C31×#14725 #21471484

Subgroups — C31×#14725 #21471484

Order 7936.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#120C211yesmaximal, characteristic
2C23×C22⋊C4×C31C211yesmaximal, characteristic, complemented
3C2×C31×#394C212yesmaximal, complemented
4C2×C31×#386C211yesmaximal, characteristic, complemented
5C2×C31×#386C211yesmaximal, characteristic, complemented
6C2×C31×#380C211yesmaximal, characteristic, complemented
7C2×C31×#379C211yesmaximal, characteristic, complemented
8C31×#1440C212yesmaximal, complemented
9C31×#1439C212yesmaximal, complemented
10C31×#1438C212yesmaximal, complemented
11C31×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C31C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C23×D4×C31C2212yes—
15C24×C4×C31C2211yescharacteristic
16C24×C4×C31C2211yescharacteristic
17C2×C31×#120—24no—
18C2×C31×#120—24no—
19C2×C31×#120—24no—
20C22×C4⋊C4×C31C2212yescomplemented
21C22×C22⋊C4×C31—24no—
22C22×C22⋊C4×C31—28no—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2212yes—
30C22×C22⋊C4×C31C2212yes—
31C22×C22⋊C4×C31C2211yescharacteristic, complemented
32C22×C22⋊C4×C31C2212yescomplemented
33C22×C22⋊C4×C31C2211yescharacteristic, complemented
34C31×#394—28no—
35C31×#386—24no—
36C31×#386—24no—
37C31×#380—24no—
38C31×#379—24no—
39C2×C31×#95C2212yescomplemented
40C2×C31×#95C2212yescomplemented
41C2×C31×#95C2211yescharacteristic, complemented
42C2×C31×#95C2212yescomplemented
43C2×C31×#95C2211yescharacteristic, complemented
44C2×C31×#95C2212yescomplemented
45C25×C31—24no—
46C25×C31—22no—
47C25×C31—24no—
48C25×C31—22no—
49C25×C31—22no—
50C25×C31—22no—
51C25×C31—22no—
52C25×C31—22no—
53C25×C31—42no—
54C25×C31—42no—
55C25×C31D414yes—
56C25×C31C2311yescharacteristic
57C25×C31C2312yes—
58C25×C31C2311yescharacteristic
59C22×D4×C31—24no—
60C22×D4×C31—24no—
61C22×D4×C31—22no—
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—42no—
71C22×D4×C31—42no—
72C22×D4×C31D414yes—
73C23×C4×C31—22no—
74C23×C4×C31—22no—
75C23×C4×C31—22no—
76C23×C4×C31—24no—
77C23×C4×C31—24no—
78C23×C4×C31—22no—
79C23×C4×C31—22no—
80C23×C4×C31—42no—
81C23×C4×C31—42no—
82C23×C4×C31D414yescomplemented
83C23×C4×C31C2312yes—
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C23×C4×C31C2312yes—
88C23×C4×C31C2312yes—
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C31×#120—232no—
92C2×C4⋊C4×C31—24no—
93C2×C4⋊C4×C31—24no—
94C2×C4⋊C4×C31—42no—
95C2×C22⋊C4×C31—232no—
96C2×C22⋊C4×C31—24no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—22no—
99C2×C22⋊C4×C31—22no—
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—24no—
107C2×C22⋊C4×C31—22no—
108C2×C22⋊C4×C31—24no—
109C2×C22⋊C4×C31—22no—
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—22no—
112C2×C22⋊C4×C31—22no—
113C2×C22⋊C4×C31—24no—
114C2×C22⋊C4×C31—24no—
115C2×C22⋊C4×C31—24no—
116C2×C22⋊C4×C31—22no—
117C2×C22⋊C4×C31—22no—
118C2×C22⋊C4×C31—22no—
119C2×C22⋊C4×C31—24no—
120C2×C22⋊C4×C31—24no—
121C2×C22⋊C4×C31—42no—
122C2×C22⋊C4×C31—42no—
123C2×C22⋊C4×C31—42no—
124C2×C22⋊C4×C31—42no—
125C2×C22⋊C4×C31D414yes—
126C2×C22⋊C4×C31D418yescomplemented
127C31×#95—24no—
128C31×#95—22no—
129C31×#95—22no—
130C31×#95—24no—
131C31×#95—24no—
132C31×#95—42no—
133C24×C31—22no—
134C24×C31—22no—
135C24×C31—22no—
136C24×C31—22no—
137C24×C31—28no—
138C24×C31—28no—
139C24×C31—216no—
140C24×C31—216no—
141C24×C31—28no—
142C24×C31—22no—
143C24×C31—22no—
144C24×C31—22no—
145C24×C31—22no—
146C24×C31—22no—
147C24×C31—22no—
148C24×C31—22no—
149C24×C31—22no—
150C24×C31—22no—
151C24×C31—22no—
152C24×C31—22no—
153C24×C31—22no—
154C24×C31—28no—
155C24×C31—28no—
156C24×C31—21no—
157C24×C31—22no—
158C24×C31—21no—
159C24×C31—21no—
160C24×C31—21no—
161C24×C31—21no—
162C24×C31—21no—
163C24×C31—22no—
164C24×C31—22no—
165C24×C31—22no—
166C24×C31—48no—
167C24×C31—48no—
168C24×C31—48no—
169C24×C31—48no—
170C24×C31—48no—
171C24×C31—48no—
172C24×C31—48no—
173C24×C31—48no—
174C24×C31—48no—
175C24×C31—44no—
176C24×C31—44no—
177C24×C31—48no—
178C24×C31—44no—
179C24×C31—44no—
180C24×C31—44no—
181C24×C31—44no—
182C24×C31C2×D412yes—
183C24×C31C2×D414yes—
184C24×C31C2×D414yes—
185C24×C31C2×D412yes—
186C24×C31C2×D412yes—
187C24×C31C2×D412yes—
188C24×C31C2×D412yes—
189C24×C31#4114yes—
190C24×C31#4112yes—
191C24×C31#4112yes—
192C24×C31#4112yes—
193C24×C31C2411yescharacteristic
194C2×D4×C31—216no—
195C2×D4×C31—28no—
196C2×D4×C31—28no—
197C2×D4×C31—28no—
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—44no—
205C2×D4×C31—44no—
206C2×D4×C31—44no—
207C2×D4×C31—44no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—22no—
211C22×C4×C31—28no—
212C22×C4×C31—28no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—22no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—22no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—22no—
223C22×C4×C31—22no—
224C22×C4×C31—21no—
225C22×C4×C31—22no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—22no—
230C22×C4×C31—22no—
231C22×C4×C31—22no—
232C22×C4×C31—22no—
233C22×C4×C31—22no—
234C22×C4×C31—22no—
235C22×C4×C31—28no—
236C22×C4×C31—21no—
237C22×C4×C31—22no—
238C22×C4×C31—22no—
239C22×C4×C31—21no—
240C22×C4×C31—22no—
241C22×C4×C31—22no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—22no—
245C22×C4×C31—21no—
246C22×C4×C31—22no—
247C22×C4×C31—21no—
248C22×C4×C31—22no—
249C22×C4×C31—22no—
250C22×C4×C31—22no—
251C22×C4×C31—22no—
252C22×C4×C31—22no—
253C22×C4×C31—44no—
254C22×C4×C31—48no—
255C22×C4×C31—48no—
256C22×C4×C31—48no—
257C22×C4×C31—48no—
258C22×C4×C31—44no—
259C22×C4×C31—44no—
260C22×C4×C31C2×D412yes—
261C22×C4×C31C2×D412yes—
262C22×C4×C31C2×D414yes—
263C22×C4×C31C2×D414yes—
264C22×C4×C31C2×D412yes—
265C22×C4×C31C2×D414yes—
266C4⋊C4×C31—48no—
267C22⋊C4×C31—216no—
268C22⋊C4×C31—216no—
269C22⋊C4×C31—28no—
270C22⋊C4×C31—216no—
271C22⋊C4×C31—48no—
272C22⋊C4×C31—44no—
273C22⋊C4×C31—48no—
274C22⋊C4×C31—44no—
275C22⋊C4×C31—48no—
276C22⋊C4×C31—44no—
277C22⋊C4×C31—44no—
278#14725C3111yesmaximal, characteristic, direct product factor, Sylow
279C23×C31—22no—
280C23×C31—24no—
281C23×C31—22no—
282C23×C31—24no—
283C23×C31—22no—
284C23×C31—24no—
285C23×C31—22no—
286C23×C31—24no—
287C23×C31—24no—
288C23×C31—24no—
289C23×C31—24no—
290C23×C31—24no—
291C23×C31—24no—
292C23×C31—24no—
293C23×C31—24no—
294C23×C31—24no—
295C23×C31—232no—
296C23×C31—24no—
297C23×C31—24no—
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—24no—
307C23×C31—24no—
308C23×C31—24no—
309C23×C31—24no—
310C23×C31—24no—
311C23×C31—24no—
312C23×C31—24no—
313C23×C31—24no—
314C23×C31—22no—
315C23×C31—22no—
316C23×C31—22no—
317C23×C31—24no—
318C23×C31—24no—
319C23×C31—432no—
320C23×C31—432no—
321C23×C31—416no—
322C23×C31—416no—
323C23×C31—416no—
324C23×C31—416no—
325C23×C31—432no—
326C23×C31—432no—
327C23×C31—416no—
328C23×C31—42no—
329C23×C31—42no—
330C23×C31—42no—
331C23×C31—42no—
332C23×C31—42no—
333C23×C31—42no—
334C23×C31—42no—
335C23×C31—42no—
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—416no—
345C23×C31—41no—
346C23×C31—41no—
347C23×C31—41no—
348C23×C31—42no—
349C23×C31—41no—
350C23×C31—42no—
351C23×C31—41no—
352C23×C31—41no—
353C23×C31—41no—
354C23×C31—42no—
355C23×C31—41no—
356C23×C31—42no—
357C23×C31—42no—
358C23×C31—42no—
359C23×C31—42no—
360C23×C31—42no—
361C23×C31—42no—
362C23×C31—42no—
363C23×C31#12014yes—
364C23×C31#12118yes—
365C23×C31#12114yes—
366C23×C31#12114yes—
367C23×C31#12114yes—
368C23×C31#12314yes—
369C23×C31#12314yes—
370C23×C31#12414yes—
371C23×C31C22×D411yescharacteristic
372C23×C31C22×D411yescharacteristic
373C23×C31C22×D411yescharacteristic
374C23×C31C22×D412yes—
375C23×C31C22×D411yescharacteristic
376C23×C31C2×#4111yescharacteristic
377C23×C31C2×#4111yescharacteristic
378C23×C31C2×#4111yescharacteristic
379C23×C31C2×#4112yes—
380C23×C31H(5,𝔽2)12yes—
381C23×C31H(5,𝔽2)12yes—
382D4×C31—432no—
383D4×C31—416no—
384C2×C4×C31—22no—
385C2×C4×C31—22no—
386C2×C4×C31—24no—
387C2×C4×C31—24no—
388C2×C4×C31—24no—
389C2×C4×C31—22no—
390C2×C4×C31—22no—
391C2×C4×C31—24no—
392C2×C4×C31—22no—
393C2×C4×C31—22no—
394C2×C4×C31—22no—
395C2×C4×C31—22no—
396C2×C4×C31—24no—
397C2×C4×C31—24no—
398C2×C4×C31—24no—
399C2×C4×C31—24no—
400C2×C4×C31—416no—
401C2×C4×C31—416no—
402C2×C4×C31—42no—
403C2×C4×C31—41no—
404C2×C4×C31—41no—
405C2×C4×C31—42no—
406C2×C4×C31—41no—
407C2×C4×C31—41no—
408C2×C4×C31—42no—
409C2×C4×C31—42no—
410C2×C4×C31—42no—
411C2×C4×C31—42no—
412C2×C4×C31—42no—
413C2×C4×C31—42no—
414C2×C4×C31—42no—
415C2×C4×C31—42no—
416C2×C4×C31—41no—
417C2×C4×C31—42no—
418C2×C4×C31—41no—
419C2×C4×C31—42no—
420C2×C4×C31—41no—
421C2×C4×C31—42no—
422C2×C4×C31—41no—
423C2×C4×C31—42no—
424C2×C4×C31—42no—
425C2×C4×C31—41no—
426C2×C4×C31—42no—
427C2×C4×C31—41no—
428C2×C4×C31—42no—
429C2×C4×C31—42no—
430C2×C4×C31—42no—
431C2×C4×C31—42no—
432C2×C4×C31—42no—
433C2×C4×C31#12014yescomplemented
434C22×#120C2×C3111yescharacteristic
435C23×C22⋊C4C2×C3111yescharacteristic, complemented
436C2×#394C2×C3112yescomplemented
437C2×#386C2×C3111yescharacteristic, complemented
438C2×#386C2×C3111yescharacteristic, complemented
439C2×#380C2×C3111yescharacteristic, complemented
440C2×#379C2×C3111yescharacteristic, complemented
441#1440C2×C3112yescomplemented
442#1439C2×C3112yescomplemented
443#1438C2×C3112yescomplemented
444C22⋊#95C2×C3111yescharacteristic, complemented
445C22×C31—24no—
446C22×C31—24no—
447C22×C31—24no—
448C22×C31—24no—
449C22×C31—28no—
450C22×C31—24no—
451C22×C31—28no—
452C22×C31—28no—
453C22×C31—28no—
454C22×C31—24no—
455C22×C31—28no—
456C22×C31—28no—
457C22×C31—28no—
458C22×C31—464no—
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—44no—
468C22×C31—44no—
469C22×C31—44no—
470C22×C31—44no—
471C22×C31—42no—
472C22×C31—42no—
473C22×C31—44no—
474C22×C31—44no—
475C22×C31—42no—
476C22×C31—81no—
477C22×C31—81no—
478C22×C31—81no—
479C22×C31—81no—
480C22×C31—82no—
481C22×C31—82no—
482C22×C31#39418yescomplemented
483C22×C31C2×#12011yescharacteristic
484C22×C31C2×#12011yescharacteristic
485C22×C31C2×#12111yescharacteristic
486C22×C31C2×#12112yes—
487C22×C31C2×#12111yescharacteristic
488C22×C31C2×#12111yescharacteristic
489C22×C31C2×#12311yescharacteristic
490C22×C31C2×#12311yescharacteristic
491C22×C31#52511yescharacteristic
492C22×C31#52512yes—
493C22×C31C2×#12411yescharacteristic
494C22×C31#53412yes—
495C22×C31#53411yescharacteristic
496C22×C31#53511yescharacteristic
497C22×C31#53812yes—
498C22×C31D4212yes—
499C22×C31D4212yes—
500C22×C31#54612yes—
501C22×C31#54612yes—
502C22×C31#54612yes—
503C22×C31#54612yes—
504C22×C31#55112yes—
505C22×C31#55112yes—
506C4×C31—24no—
507C4×C31—42no—
508C4×C31—44no—
509C4×C31—42no—
510C4×C31—44no—
511C4×C31—81no—
512C4×C31—81no—
513C4×C31—82no—
514C26C22×C3111yescharacteristic
515C23×D4C22×C3111yescharacteristic
516C23×D4C22×C3112yes—
517C24×C4C22×C3111yescharacteristic
518C24×C4C22×C3111yescharacteristic
519C2×#120—24no—
520C2×#120—24no—
521C2×#120—24no—
522C22×C4⋊C4C22×C3112yescomplemented
523C22×C22⋊C4—24no—
524C22×C22⋊C4—28no—
525C22×C22⋊C4C22×C3112yes—
526C22×C22⋊C4C22×C3112yes—
527C22×C22⋊C4C22×C3112yes—
528C22×C22⋊C4C22×C3111yescharacteristic
529C22×C22⋊C4C22×C3111yescharacteristic
530C22×C22⋊C4C22×C3111yescharacteristic
531C22×C22⋊C4C22×C3112yes—
532C22×C22⋊C4C22×C3112yes—
533C22×C22⋊C4C22×C3111yescharacteristic, complemented
534C22×C22⋊C4C22×C3112yescomplemented
535C22×C22⋊C4C22×C3111yescharacteristic, complemented
536#394—28no—
537#386—24no—
538#386—24no—
539#380—24no—
540#379—24no—
541C2×#95C22×C3112yescomplemented
542C2×#95C22×C3112yescomplemented
543C2×#95C22×C3111yescharacteristic, complemented
544C2×#95C22×C3112yescomplemented
545C2×#95C22×C3111yescharacteristic, complemented
546C2×#95C22×C3112yescomplemented
547C2×C31—28no—
548C2×C31—48no—
549C2×C31—82no—
550C2×C31C2×#39411yescharacteristic
551C2×C31#240811yescharacteristic
552C2×C31#241011yescharacteristic
553C2×C31#241012yes—
554C2×C31#241111yescharacteristic
555C2×C31#241212yes—
556C2×C31#241812yes—
557C2×C31#247212yes—
558C2×C31#253411yescharacteristic
559C2×C31#261711yescharacteristic
560C2×C31#284711yescharacteristic
561C25—24no—
562C25—22no—
563C25—24no—
564C25—22no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—42no—
570C25—42no—
571C25D4×C3114yes—
572C25C23×C3111yescharacteristic
573C25C23×C3112yes—
574C25C23×C3111yescharacteristic
575C22×D4—24no—
576C22×D4—24no—
577C22×D4—22no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—24no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—42no—
587C22×D4—42no—
588C22×D4D4×C3114yes—
589C23×C4—22no—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—24no—
593C23×C4—24no—
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—42no—
597C23×C4—42no—
598C23×C4D4×C3114yescomplemented
599C23×C4C23×C3112yes—
600C23×C4C23×C3111yescharacteristic
601C23×C4C23×C3111yescharacteristic
602C23×C4C23×C3111yescharacteristic
603C23×C4C23×C3112yes—
604C23×C4C23×C3112yes—
605C23×C4C23×C3111yescharacteristic
606C23×C4C23×C3111yescharacteristic
607#120—232no—
608C2×C4⋊C4—24no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—42no—
611C2×C22⋊C4—232no—
612C2×C22⋊C4—24no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—24no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—24no—
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—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—42no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4D4×C3114yes—
642C2×C22⋊C4D4×C3118yescomplemented
643#95—24no—
644#95—22no—
645#95—22no—
646#95—24no—
647#95—24no—
648#95—42no—
649C31#1472511yescharacteristic, direct product factor, Sylow
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—216no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C3112yes—
700C24C2×D4×C3114yes—
701C24C2×D4×C3114yes—
702C24C2×D4×C3112yes—
703C24C2×D4×C3112yes—
704C24C2×D4×C3112yes—
705C24C2×D4×C3112yes—
706C24#41×C3114yes—
707C24#41×C3112yes—
708C24#41×C3112yes—
709C24#41×C3112yes—
710C24C24×C3111yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C3112yes—
778C22×C4C2×D4×C3112yes—
779C22×C4C2×D4×C3114yes—
780C22×C4C2×D4×C3114yes—
781C22×C4C2×D4×C3112yes—
782C22×C4C2×D4×C3114yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—432no—
836C23—432no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—432no—
842C23—432no—
843C23—416no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—416no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—41no—
866C23—42no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23C31×#12014yes—
880C23C31×#12118yes—
881C23C31×#12114yes—
882C23C31×#12114yes—
883C23C31×#12114yes—
884C23C31×#12314yes—
885C23C31×#12314yes—
886C23C31×#12414yes—
887C23C22×D4×C3111yescharacteristic
888C23C22×D4×C3111yescharacteristic
889C23C22×D4×C3111yescharacteristic
890C23C22×D4×C3112yes—
891C23C22×D4×C3111yescharacteristic
892C23C2×#41×C3111yescharacteristic
893C23C2×#41×C3111yescharacteristic
894C23C2×#41×C3111yescharacteristic
895C23C2×#41×C3112yes—
896C23C31×H(5,𝔽2)12yes—
897C23C31×H(5,𝔽2)12yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—41no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4C31×#12014yescomplemented
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—28no—
955C22—24no—
956C22—28no—
957C22—28no—
958C22—28no—
959C22—24no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—44no—
979C22—44no—
980C22—42no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—82no—
986C22—82no—
987C22C31×#39418yescomplemented
988C22C2×C31×#12011yescharacteristic
989C22C2×C31×#12011yescharacteristic
990C22C2×C31×#12111yescharacteristic
991C22C2×C31×#12112yes—
992C22C2×C31×#12111yescharacteristic
993C22C2×C31×#12111yescharacteristic
994C22C2×C31×#12311yescharacteristic
995C22C2×C31×#12311yescharacteristic
996C22C31×#52511yescharacteristic
997C22C31×#52512yes—
998C22C2×C31×#12411yescharacteristic
999C22C31×#53412yes—
1000C22C31×#53411yescharacteristic
1001C22C31×#53511yescharacteristic
1002C22C31×#53812yes—
1003C22D42×C3112yes—
1004C22D42×C3112yes—
1005C22C31×#54612yes—
1006C22C31×#54612yes—
1007C22C31×#54612yes—
1008C22C31×#54612yes—
1009C22C31×#55112yes—
1010C22C31×#55112yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×C31×#39411yescharacteristic
1023C2C31×#240811yescharacteristic
1024C2C31×#241011yescharacteristic
1025C2C31×#241012yes—
1026C2C31×#241111yescharacteristic
1027C2C31×#241212yes—
1028C2C31×#241812yes—
1029C2C31×#247212yes—
1030C2C31×#253411yescharacteristic
1031C2C31×#261711yescharacteristic
1032C2C31×#284711yescharacteristic
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. C23×C22⋊C4×C31C2semidirect
3. C2×C31×#394C2semidirect
4. C2×C31×#386C2semidirect
5. C2×C31×#386C2semidirect
6. C2×C31×#380C2semidirect
7. C2×C31×#379C2semidirect
8. C31×#1440C2semidirect
9. C31×#1439C2semidirect
10. C31×#1438C2semidirect
11. C31×C22⋊#95C2semidirect
20. C22×C4⋊C4×C31C22semidirect
31. C22×C22⋊C4×C31C22semidirect
32. C22×C22⋊C4×C31C22semidirect
33. C22×C22⋊C4×C31C22semidirect
39. C2×C31×#95C22semidirect
40. C2×C31×#95C22semidirect
41. C2×C31×#95C22semidirect
42. C2×C31×#95C22semidirect
43. C2×C31×#95C22semidirect
44. C2×C31×#95C22semidirect
82. C23×C4×C31D4semidirect
126. C2×C22⋊C4×C31D4semidirect
278. #14725C31direct (N × H)
433. C2×C4×C31#120semidirect
435. C23×C22⋊C4C2×C31semidirect
436. C2×#394C2×C31semidirect
437. C2×#386C2×C31semidirect
438. C2×#386C2×C31semidirect
439. C2×#380C2×C31semidirect
440. C2×#379C2×C31semidirect
441. #1440C2×C31semidirect
442. #1439C2×C31semidirect
443. #1438C2×C31semidirect
444. C22⋊#95C2×C31semidirect
482. C22×C31#394semidirect
522. C22×C4⋊C4C22×C31semidirect
533. C22×C22⋊C4C22×C31semidirect
534. C22×C22⋊C4C22×C31semidirect
535. C22×C22⋊C4C22×C31semidirect
541. C2×#95C22×C31semidirect
542. C2×#95C22×C31semidirect
543. C2×#95C22×C31semidirect
544. C2×#95C22×C31semidirect
545. C2×#95C22×C31semidirect
546. C2×#95C22×C31semidirect
598. C23×C4D4×C31semidirect
642. C2×C22⋊C4D4×C31semidirect
649. C31#14725direct (N × H)
949. C2×C4C31×#120semidirect
987. C22C31×#394semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1202
C23×C22⋊C4×C312
C2×C31×#3942
C2×C31×#3862
C2×C31×#3802
C2×C31×#3792
C31×#14402
C31×#14392
C31×#14382
C31×C22⋊#952
#1472531