Finite Group Databasebeta

← C31×#16260 #21473019

Subgroups — C31×#16260 #21473019

Order 7936.

2790 conjugacy classes of subgroups.

The subgroup lattice has 940 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×#386C211yesmaximal, characteristic, complemented
6C2×C31×#380C211yesmaximal, characteristic, complemented
7C31×#1442C211yesmaximal, characteristic, complemented
8C31×#1439C211yesmaximal, characteristic, complemented
9C31×#1439C212yesmaximal, complemented
10C31×#1438C212yesmaximal, complemented
11C31×#1438C211yesmaximal, characteristic, complemented
12C23×D4×C31C2212yes—
13C23×D4×C31C2211yescharacteristic
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×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2212yes—
27C22×C22⋊C4×C31C2212yes—
28C22×C22⋊C4×C31C2212yes—
29C22×C22⋊C4×C31C2211yescharacteristic
30C31×#394—28no—
31C31×#392—28no—
32C31×#392—24no—
33C31×#386—24no—
34C31×#380—24no—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2211yescharacteristic
39C2×C31×#95C2211yescharacteristic
40C2×C31×#95C2212yes—
41C2×C31×#95C2211yescharacteristic
42C25×C31C2311yescharacteristic
43C25×C31C2312yes—
44C25×C31C2311yescharacteristic
45C22×D4×C31—24no—
46C22×D4×C31—24no—
47C22×D4×C31—24no—
48C22×D4×C31—22no—
49C22×D4×C31—22no—
50C22×D4×C31—24no—
51C22×D4×C31—24no—
52C22×D4×C31—24no—
53C22×D4×C31—24no—
54C22×D4×C31—24no—
55C22×D4×C31—22no—
56C22×D4×C31—24no—
57C22×D4×C31—22no—
58C22×D4×C31—22no—
59C22×D4×C31—42no—
60C22×D4×C31—42no—
61C22×D4×C31—42no—
62C22×D4×C31—42no—
63C22×D4×C31—42no—
64C22×D4×C31—42no—
65C22×D4×C31—42no—
66C22×D4×C31—42no—
67C22×D4×C31—42no—
68C22×D4×C31D414yescomplemented
69C23×C4×C31—24no—
70C23×C4×C31—22no—
71C23×C4×C31—22no—
72C23×C4×C31—42no—
73C23×C4×C31D414yescomplemented
74C23×C4×C31C2312yes—
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2312yes—
78C23×C4×C31C2312yes—
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C31×#121—232no—
83C2×C4⋊C4×C31—24no—
84C2×C4⋊C4×C31—22no—
85C2×C4⋊C4×C31—24no—
86C2×C4⋊C4×C31—24no—
87C2×C4⋊C4×C31—42no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—24no—
92C2×C22⋊C4×C31—24no—
93C2×C22⋊C4×C31—24no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—24no—
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—24no—
101C2×C22⋊C4×C31—24no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—42no—
104C2×C22⋊C4×C31—42no—
105C2×C22⋊C4×C31—42no—
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×C31D418yescomplemented
113C31×#95—22no—
114C31×#95—22no—
115C31×#95—22no—
116C31×#95—24no—
117C31×#95—24no—
118C31×#95—42no—
119C31×#95D414yescomplemented
120C24×C31—21no—
121C24×C31—22no—
122C24×C31—21no—
123C24×C31—21no—
124C24×C31—22no—
125C24×C31—22no—
126C24×C31—22no—
127C24×C31—21no—
128C24×C31—21no—
129C24×C31—22no—
130C24×C31—22no—
131C24×C31—22no—
132C24×C31—21no—
133C24×C31—22no—
134C24×C31—22no—
135C24×C31—21no—
136C24×C31—21no—
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—22no—
147C24×C31—22no—
148C24×C31—21no—
149C24×C31—22no—
150C24×C31—22no—
151C24×C31—21no—
152C24×C31C2×D412yes—
153C24×C31C2×D414yes—
154C24×C31C2×D412yes—
155C24×C31C2×D412yes—
156C24×C31#4112yes—
157C24×C31C2411yescharacteristic
158C2×D4×C31—28no—
159C2×D4×C31—216no—
160C2×D4×C31—28no—
161C2×D4×C31—48no—
162C2×D4×C31—48no—
163C2×D4×C31—48no—
164C2×D4×C31—48no—
165C2×D4×C31—48no—
166C2×D4×C31—48no—
167C2×D4×C31—48no—
168C2×D4×C31—44no—
169C2×D4×C31—48no—
170C2×D4×C31—48no—
171C2×D4×C31—48no—
172C2×D4×C31—48no—
173C2×D4×C31—44no—
174C2×D4×C31—48no—
175C2×D4×C31—44no—
176C2×D4×C31—48no—
177C2×D4×C31—48no—
178C2×D4×C31—48no—
179C2×D4×C31—48no—
180C2×D4×C31—48no—
181C2×D4×C31—44no—
182C22×C4×C31—21no—
183C22×C4×C31—22no—
184C22×C4×C31—21no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—21no—
188C22×C4×C31—22no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—21no—
194C22×C4×C31—22no—
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—28no—
204C22×C4×C31—28no—
205C22×C4×C31—21no—
206C22×C4×C31—22no—
207C22×C4×C31—21no—
208C22×C4×C31—22no—
209C22×C4×C31—21no—
210C22×C4×C31—22no—
211C22×C4×C31—22no—
212C22×C4×C31—21no—
213C22×C4×C31—22no—
214C22×C4×C31—22no—
215C22×C4×C31—22no—
216C22×C4×C31—22no—
217C22×C4×C31—21no—
218C22×C4×C31—22no—
219C22×C4×C31—22no—
220C22×C4×C31—22no—
221C22×C4×C31—21no—
222C22×C4×C31—44no—
223C22×C4×C31—48no—
224C22×C4×C31—48no—
225C22×C4×C31C2×D412yes—
226C22×C4×C31C2×D414yes—
227C22×C4×C31C2×D414yes—
228C22×C4×C31C2×D412yes—
229C22×C4×C31C2×D414yes—
230C22×C4×C31C2×D412yes—
231C22×C4×C31C2×D412yes—
232C22×C4×C31#4112yes—
233C4⋊C4×C31—28no—
234C4⋊C4×C31—48no—
235C22⋊C4×C31—216no—
236C22⋊C4×C31—48no—
237C22⋊C4×C31—48no—
238C22⋊C4×C31—48no—
239C22⋊C4×C31—48no—
240C22⋊C4×C31—44no—
241C22⋊C4×C31—48no—
242C22⋊C4×C31—44no—
243C22⋊C4×C31—44no—
244#16260C3111yesmaximal, characteristic, direct product factor, Sylow
245C23×C31—22no—
246C23×C31—22no—
247C23×C31—22no—
248C23×C31—24no—
249C23×C31—22no—
250C23×C31—22no—
251C23×C31—22no—
252C23×C31—24no—
253C23×C31—22no—
254C23×C31—24no—
255C23×C31—24no—
256C23×C31—22no—
257C23×C31—22no—
258C23×C31—22no—
259C23×C31—24no—
260C23×C31—22no—
261C23×C31—24no—
262C23×C31—24no—
263C23×C31—24no—
264C23×C31—24no—
265C23×C31—24no—
266C23×C31—24no—
267C23×C31—22no—
268C23×C31—24no—
269C23×C31—24no—
270C23×C31—22no—
271C23×C31—42no—
272C23×C31—42no—
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—42no—
282C23×C31—42no—
283C23×C31—42no—
284C23×C31—41no—
285C23×C31—42no—
286C23×C31—42no—
287C23×C31—42no—
288C23×C31—41no—
289C23×C31—42no—
290C23×C31—42no—
291C23×C31—42no—
292C23×C31—42no—
293C23×C31—42no—
294C23×C31—42no—
295C23×C31—41no—
296C23×C31—42no—
297C23×C31—42no—
298C23×C31—42no—
299C23×C31—41no—
300C23×C31—42no—
301C23×C31—42no—
302C23×C31—42no—
303C23×C31—42no—
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—41no—
316C23×C31—42no—
317C23×C31—41no—
318C23×C31—42no—
319C23×C31—42no—
320C23×C31—42no—
321C23×C31—42no—
322C23×C31—42no—
323C23×C31—42no—
324C23×C31—42no—
325C23×C31#12114yes—
326C23×C31C22×D411yescharacteristic
327C23×C31C22×D412yes—
328C23×C31C22×D411yescharacteristic
329C23×C31C22×D411yescharacteristic
330C23×C31C2×#4111yescharacteristic
331C23×C31C2×#4111yescharacteristic
332C23×C31H(5,𝔽2)12yes—
333C23×C31H(5,𝔽2)12yes—
334C23×C31H(5,𝔽2)11yescharacteristic
335C23×C31H(5,𝔽2)12yes—
336C23×C312−1+411yescharacteristic
337D4×C31—416no—
338D4×C31—416no—
339D4×C31—432no—
340D4×C31—432no—
341C2×C4×C31—22no—
342C2×C4×C31—22no—
343C2×C4×C31—22no—
344C2×C4×C31—22no—
345C2×C4×C31—24no—
346C2×C4×C31—24no—
347C2×C4×C31—24no—
348C2×C4×C31—24no—
349C2×C4×C31—24no—
350C2×C4×C31—22no—
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—416no—
358C2×C4×C31—42no—
359C2×C4×C31—41no—
360C2×C4×C31—42no—
361C2×C4×C31—41no—
362C2×C4×C31—42no—
363C2×C4×C31—42no—
364C2×C4×C31—42no—
365C2×C4×C31—42no—
366C2×C4×C31—42no—
367C2×C4×C31—42no—
368C2×C4×C31—42no—
369C2×C4×C31—41no—
370C2×C4×C31—41no—
371C2×C4×C31—42no—
372C2×C4×C31—41no—
373C2×C4×C31—42no—
374C2×C4×C31—41no—
375C2×C4×C31—42no—
376C2×C4×C31—42no—
377C2×C4×C31—41no—
378C2×C4×C31—42no—
379C2×C4×C31—42no—
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#12014yes—
387C2×C4×C31#12114yes—
388C22×#121C2×C3111yescharacteristic, complemented
389C2×#394C2×C3112yescomplemented
390C2×#392C2×C3111yescharacteristic, complemented
391C2×#392C2×C3112yescomplemented
392C2×#386C2×C3111yescharacteristic, complemented
393C2×#380C2×C3111yescharacteristic, complemented
394#1442C2×C3111yescharacteristic, complemented
395#1439C2×C3111yescharacteristic, complemented
396#1439C2×C3112yescomplemented
397#1438C2×C3112yescomplemented
398#1438C2×C3111yescharacteristic, complemented
399C22×C31—24no—
400C22×C31—24no—
401C22×C31—24no—
402C22×C31—42no—
403C22×C31—42no—
404C22×C31—42no—
405C22×C31—44no—
406C22×C31—44no—
407C22×C31—44no—
408C22×C31—44no—
409C22×C31—42no—
410C22×C31—44no—
411C22×C31—42no—
412C22×C31—44no—
413C22×C31—42no—
414C22×C31—44no—
415C22×C31—44no—
416C22×C31—44no—
417C22×C31—44no—
418C22×C31—44no—
419C22×C31—42no—
420C22×C31—44no—
421C22×C31—44no—
422C22×C31—81no—
423C22×C31—82no—
424C22×C31—81no—
425C22×C31—82no—
426C22×C31—81no—
427C22×C31—82no—
428C22×C31—82no—
429C22×C31—82no—
430C22×C31—82no—
431C22×C31—82no—
432C22×C31—82no—
433C22×C31—82no—
434C22×C31—82no—
435C22×C31—81no—
436C22×C31C2×#12011yescharacteristic
437C22×C31C2×#12111yescharacteristic
438C22×C31C2×#12111yescharacteristic
439C22×C31#53411yescharacteristic
440C22×C31#53412yes—
441C22×C31#53511yescharacteristic
442C22×C31#53512yes—
443C22×C31#53511yescharacteristic
444C22×C31#53512yes—
445C22×C31#53712yes—
446C22×C31#53711yescharacteristic
447C22×C31#53812yes—
448C22×C31#54012yes—
449C22×C31D4212yes—
450C22×C31D4212yes—
451C22×C31D4211yescharacteristic
452C22×C31#54612yes—
453C22×C31#54612yes—
454C22×C31#54711yescharacteristic
455C22×C31#54811yescharacteristic
456C22×C31#55311yescharacteristic
457C22×C31#56012yes—
458C22×C31#56212yes—
459C4×C31—24no—
460C4×C31—24no—
461C4×C31—42no—
462C4×C31—44no—
463C4×C31—44no—
464C4×C31—81no—
465C4×C31—81no—
466C4×C31—82no—
467C23×D4C22×C3112yes—
468C23×D4C22×C3111yescharacteristic
469C23×D4C22×C3112yes—
470C23×D4C22×C3111yescharacteristic
471C24×C4C22×C3111yescharacteristic
472C2×#121—24no—
473C2×#121—28no—
474C22×C4⋊C4C22×C3111yescharacteristic
475C22×C4⋊C4C22×C3112yes—
476C22×C22⋊C4C22×C3111yescharacteristic
477C22×C22⋊C4C22×C3111yescharacteristic
478C22×C22⋊C4C22×C3112yes—
479C22×C22⋊C4C22×C3112yes—
480C22×C22⋊C4C22×C3112yes—
481C22×C22⋊C4C22×C3112yes—
482C22×C22⋊C4C22×C3112yes—
483C22×C22⋊C4C22×C3112yes—
484C22×C22⋊C4C22×C3111yescharacteristic
485#394—28no—
486#392—28no—
487#392—24no—
488#386—24no—
489#380—24no—
490C2×#95C22×C3112yes—
491C2×#95C22×C3112yes—
492C2×#95C22×C3111yescharacteristic
493C2×#95C22×C3111yescharacteristic
494C2×#95C22×C3111yescharacteristic
495C2×#95C22×C3112yes—
496C2×#95C22×C3111yescharacteristic
497C2×C31—44no—
498C2×C31—84no—
499C2×C31—82no—
500C2×C31#240811yescharacteristic
501C2×C31#241011yescharacteristic
502C2×C31#241611yescharacteristic
503C2×C31#261511yescharacteristic
504C2×C31#261711yescharacteristic
505C2×C31#261911yescharacteristic
506C2×C31#266912yes—
507C2×C31#267112yes—
508C2×C31#267612yes—
509C2×C31#270312yes—
510C2×C31#281311yescharacteristic
511C25C23×C3111yescharacteristic
512C25C23×C3112yes—
513C25C23×C3111yescharacteristic
514C22×D4—24no—
515C22×D4—24no—
516C22×D4—24no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—24no—
520C22×D4—24no—
521C22×D4—24no—
522C22×D4—24no—
523C22×D4—24no—
524C22×D4—22no—
525C22×D4—24no—
526C22×D4—22no—
527C22×D4—22no—
528C22×D4—42no—
529C22×D4—42no—
530C22×D4—42no—
531C22×D4—42no—
532C22×D4—42no—
533C22×D4—42no—
534C22×D4—42no—
535C22×D4—42no—
536C22×D4—42no—
537C22×D4D4×C3114yescomplemented
538C23×C4—24no—
539C23×C4—22no—
540C23×C4—22no—
541C23×C4—42no—
542C23×C4D4×C3114yescomplemented
543C23×C4C23×C3112yes—
544C23×C4C23×C3111yescharacteristic
545C23×C4C23×C3111yescharacteristic
546C23×C4C23×C3112yes—
547C23×C4C23×C3112yes—
548C23×C4C23×C3111yescharacteristic
549C23×C4C23×C3111yescharacteristic
550C23×C4C23×C3111yescharacteristic
551#121—232no—
552C2×C4⋊C4—24no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—24no—
556C2×C4⋊C4—42no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4D4×C3118yescomplemented
582#95—22no—
583#95—22no—
584#95—22no—
585#95—24no—
586#95—24no—
587#95—42no—
588#95D4×C3114yescomplemented
589C31#1626011yescharacteristic, direct product factor, Sylow
590C24—21no—
591C24—22no—
592C24—21no—
593C24—21no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—21no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—21no—
603C24—22no—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—21no—
619C24—22no—
620C24—22no—
621C24—21no—
622C24C2×D4×C3112yes—
623C24C2×D4×C3114yes—
624C24C2×D4×C3112yes—
625C24C2×D4×C3112yes—
626C24#41×C3112yes—
627C24C24×C3111yescharacteristic
628C2×D4—28no—
629C2×D4—216no—
630C2×D4—28no—
631C2×D4—48no—
632C2×D4—48no—
633C2×D4—48no—
634C2×D4—48no—
635C2×D4—48no—
636C2×D4—48no—
637C2×D4—48no—
638C2×D4—44no—
639C2×D4—48no—
640C2×D4—48no—
641C2×D4—48no—
642C2×D4—48no—
643C2×D4—44no—
644C2×D4—48no—
645C2×D4—44no—
646C2×D4—48no—
647C2×D4—48no—
648C2×D4—48no—
649C2×D4—48no—
650C2×D4—48no—
651C2×D4—44no—
652C22×C4—21no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—21no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—21no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—21no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—22no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—21no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—44no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C2×D4×C3112yes—
696C22×C4C2×D4×C3114yes—
697C22×C4C2×D4×C3114yes—
698C22×C4C2×D4×C3112yes—
699C22×C4C2×D4×C3114yes—
700C22×C4C2×D4×C3112yes—
701C22×C4C2×D4×C3112yes—
702C22×C4#41×C3112yes—
703C4⋊C4—28no—
704C4⋊C4—48no—
705C22⋊C4—216no—
706C22⋊C4—48no—
707C22⋊C4—48no—
708C22⋊C4—48no—
709C22⋊C4—48no—
710C22⋊C4—44no—
711C22⋊C4—48no—
712C22⋊C4—44no—
713C22⋊C4—44no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—24no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—22no—
723C23—24no—
724C23—24no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—24no—
729C23—22no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—22no—
737C23—24no—
738C23—24no—
739C23—22no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—41no—
749C23—41no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—41no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—41no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—41no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—41no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—41no—
785C23—42no—
786C23—41no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23C31×#12114yes—
795C23C22×D4×C3111yescharacteristic
796C23C22×D4×C3112yes—
797C23C22×D4×C3111yescharacteristic
798C23C22×D4×C3111yescharacteristic
799C23C2×#41×C3111yescharacteristic
800C23C2×#41×C3111yescharacteristic
801C23C31×H(5,𝔽2)12yes—
802C23C31×H(5,𝔽2)12yes—
803C23C31×H(5,𝔽2)11yescharacteristic
804C23C31×H(5,𝔽2)12yes—
805C23C31×2−1+411yescharacteristic
806D4—416no—
807D4—416no—
808D4—432no—
809D4—432no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—22no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—416no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—41no—
842C2×C4—42no—
843C2×C4—41no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—41no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4C31×#12014yes—
856C2×C4C31×#12114yes—
857C22—24no—
858C22—24no—
859C22—24no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—44no—
864C22—44no—
865C22—44no—
866C22—44no—
867C22—42no—
868C22—44no—
869C22—42no—
870C22—44no—
871C22—42no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—44no—
876C22—44no—
877C22—42no—
878C22—44no—
879C22—44no—
880C22—81no—
881C22—82no—
882C22—81no—
883C22—82no—
884C22—81no—
885C22—82no—
886C22—82no—
887C22—82no—
888C22—82no—
889C22—82no—
890C22—82no—
891C22—82no—
892C22—82no—
893C22—81no—
894C22C2×C31×#12011yescharacteristic
895C22C2×C31×#12111yescharacteristic
896C22C2×C31×#12111yescharacteristic
897C22C31×#53411yescharacteristic
898C22C31×#53412yes—
899C22C31×#53511yescharacteristic
900C22C31×#53512yes—
901C22C31×#53511yescharacteristic
902C22C31×#53512yes—
903C22C31×#53712yes—
904C22C31×#53711yescharacteristic
905C22C31×#53812yes—
906C22C31×#54012yes—
907C22D42×C3112yes—
908C22D42×C3112yes—
909C22D42×C3111yescharacteristic
910C22C31×#54612yes—
911C22C31×#54612yes—
912C22C31×#54711yescharacteristic
913C22C31×#54811yescharacteristic
914C22C31×#55311yescharacteristic
915C22C31×#56012yes—
916C22C31×#56212yes—
917C4—24no—
918C4—24no—
919C4—42no—
920C4—44no—
921C4—44no—
922C4—81no—
923C4—81no—
924C4—82no—
925C2—44no—
926C2—84no—
927C2—82no—
928C2C31×#240811yescharacteristic
929C2C31×#241011yescharacteristic
930C2C31×#241611yescharacteristic
931C2C31×#261511yescharacteristic
932C2C31×#261711yescharacteristic
933C2C31×#261911yescharacteristic
934C2C31×#266912yes—
935C2C31×#267112yes—
936C2C31×#267612yes—
937C2C31×#270312yes—
938C2C31×#281311yescharacteristic
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×#386C2semidirect
6. C2×C31×#380C2semidirect
7. C31×#1442C2semidirect
8. C31×#1439C2semidirect
9. C31×#1439C2semidirect
10. C31×#1438C2semidirect
11. C31×#1438C2semidirect
68. C22×D4×C31D4semidirect
73. C23×C4×C31D4semidirect
112. C2×C22⋊C4×C31D4semidirect
119. C31×#95D4semidirect
244. #16260C31direct (N × H)
388. C22×#121C2×C31semidirect
389. C2×#394C2×C31semidirect
390. C2×#392C2×C31semidirect
391. C2×#392C2×C31semidirect
392. C2×#386C2×C31semidirect
393. C2×#380C2×C31semidirect
394. #1442C2×C31semidirect
395. #1439C2×C31semidirect
396. #1439C2×C31semidirect
397. #1438C2×C31semidirect
398. #1438C2×C31semidirect
537. C22×D4D4×C31semidirect
542. C23×C4D4×C31semidirect
581. C2×C22⋊C4D4×C31semidirect
588. #95D4×C31semidirect
589. C31#16260direct (N × H)

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×#3862
C2×C31×#3802
C31×#14422
C31×#14392
C31×#14382
#1626031