Finite Group Databasebeta

← C31×#14759 #21471518

Subgroups — C31×#14759 #21471518

Order 7936.

2414 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C31×#393C211yesmaximal, characteristic, complemented
3C2×C31×#386C211yesmaximal, characteristic
4C2×C31×#386C212yesmaximal
5C22×C31×#95C211yesmaximal, characteristic, complemented
6C31×#1446C211yesmaximal, characteristic, complemented
7C31×#1442C212yesmaximal, complemented
8C31×#1442C211yesmaximal, characteristic, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1439C212yesmaximal, complemented
11C31×C22⋊#95C212yesmaximal, complemented
12C23×Q8×C31C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C24×C4×C31C2212yes—
15C24×C4×C31C2211yescharacteristic
16C2×C31×C22⋊Q8—24no—
17C2×C31×C22⋊Q8—28no—
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2211yescharacteristic
26C31×#393—24no—
27C31×#386—24no—
28C31×#386—28no—
29C2×C31×#95—24no—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2212yes—
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2211yescharacteristic
41C25×C31C2311yescharacteristic
42C25×C31C2311yescharacteristic
43C22×Q8×C31—24no—
44C22×Q8×C31—22no—
45C22×Q8×C31—22no—
46C22×Q8×C31—22no—
47C22×Q8×C31—42no—
48C22×D4×C31—22no—
49C22×D4×C31—24no—
50C22×D4×C31—24no—
51C22×D4×C31—22no—
52C22×D4×C31Q814yescomplemented
53C23×C4×C31—24no—
54C23×C4×C31—24no—
55C23×C4×C31—24no—
56C23×C4×C31—22no—
57C23×C4×C31—24no—
58C23×C4×C31—22no—
59C23×C4×C31—24no—
60C23×C4×C31—24no—
61C23×C4×C31—42no—
62C23×C4×C31—42no—
63C23×C4×C31—42no—
64C23×C4×C31D414yes—
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2312yes—
68C23×C4×C31C2312yes—
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2312yes—
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2312yes—
73C23×C4×C31C2311yescharacteristic
74C31×C22⋊Q8—232no—
75C2×C4⋊C4×C31—24no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—24no—
78C2×C4⋊C4×C31—24no—
79C2×C4⋊C4×C31—24no—
80C2×C22⋊C4×C31—24no—
81C2×C22⋊C4×C31—24no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—24no—
84C2×C22⋊C4×C31—24no—
85C2×C22⋊C4×C31—24no—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—24no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—42no—
93C2×C22⋊C4×C31—42no—
94C2×C22⋊C4×C31—42no—
95C2×C22⋊C4×C31D418yes—
96C31×#95—24no—
97C31×#95—22no—
98C31×#95—24no—
99C31×#95—24no—
100C31×#95—22no—
101C31×#95—22no—
102C31×#95—24no—
103C31×#95—24no—
104C31×#95—42no—
105C31×#95—42no—
106C31×#95D414yescomplemented
107C24×C31—21no—
108C24×C31—21no—
109C24×C31—22no—
110C24×C31—22no—
111C24×C31—21no—
112C24×C31—21no—
113C24×C31—21no—
114C24×C31—21no—
115C24×C31—22no—
116C24×C31—21no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31—21no—
120C24×C31—22no—
121C24×C31—21no—
122C24×C31—21no—
123C24×C31C2×D412yes—
124C24×C31C2×D414yes—
125C24×C31C2×Q812yes—
126C24×C31C2×Q812yes—
127C24×C31#4114yes—
128C24×C31#4112yes—
129C24×C31C2411yescharacteristic
130C2×Q8×C31—28no—
131C2×Q8×C31—48no—
132C2×Q8×C31—48no—
133C2×Q8×C31—44no—
134C2×Q8×C31—44no—
135C2×D4×C31—28no—
136C2×D4×C31—216no—
137C2×D4×C31—44no—
138C2×D4×C31—44no—
139C2×D4×C31—48no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—216no—
143C22×C4×C31—28no—
144C22×C4×C31—21no—
145C22×C4×C31—22no—
146C22×C4×C31—21no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—21no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—21no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—28no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—22no—
181C22×C4×C31—21no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—21no—
185C22×C4×C31—22no—
186C22×C4×C31—21no—
187C22×C4×C31—44no—
188C22×C4×C31—48no—
189C22×C4×C31—48no—
190C22×C4×C31—48no—
191C22×C4×C31—48no—
192C22×C4×C31—48no—
193C22×C4×C31—48no—
194C22×C4×C31—48no—
195C22×C4×C31—48no—
196C22×C4×C31C2×D414yes—
197C22×C4×C31C2×D414yes—
198C22×C4×C31C2×D414yes—
199C22×C4×C31C2×D412yes—
200C22×C4×C31C2×D412yes—
201C22×C4×C31C2×D412yes—
202C22×C4×C31C2×Q812yes—
203C22×C4×C31#4114yes—
204C22×C4×C31#4112yes—
205C4⋊C4×C31—28no—
206C4⋊C4×C31—216no—
207C22⋊C4×C31—216no—
208C22⋊C4×C31—48no—
209C22⋊C4×C31—48no—
210C22⋊C4×C31—44no—
211C22⋊C4×C31—44no—
212C22⋊C4×C31—44no—
213#14759C3111yesmaximal, characteristic, direct product factor, Sylow
214C23×C31—22no—
215C23×C31—24no—
216C23×C31—24no—
217C23×C31—22no—
218C23×C31—22no—
219C23×C31—22no—
220C23×C31—24no—
221C23×C31—24no—
222C23×C31—24no—
223C23×C31—22no—
224C23×C31—24no—
225C23×C31—24no—
226C23×C31—24no—
227C23×C31—22no—
228C23×C31—24no—
229C23×C31—22no—
230C23×C31—24no—
231C23×C31—22no—
232C23×C31—22no—
233C23×C31—24no—
234C23×C31—22no—
235C23×C31—24no—
236C23×C31—22no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31—42no—
240C23×C31—41no—
241C23×C31—42no—
242C23×C31—42no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31—42no—
247C23×C31—42no—
248C23×C31—42no—
249C23×C31—42no—
250C23×C31—41no—
251C23×C31—42no—
252C23×C31—42no—
253C23×C31—42no—
254C23×C31—41no—
255C23×C31#12014yes—
256C23×C31C22⋊Q814yes—
257C23×C31C22⋊Q818yes—
258C23×C31#12414yes—
259C23×C31#12418yes—
260C23×C31C22×D411yescharacteristic
261C23×C31C22×D412yes—
262C23×C31C22×D411yescharacteristic
263C23×C31C22×Q811yescharacteristic
264C23×C31C2×#4111yescharacteristic
265C23×C31C2×#4112yes—
266C23×C31C2×#4111yescharacteristic
267C23×C31C2×#4112yes—
268C23×C31H(5,𝔽2)12yes—
269C23×C31H(5,𝔽2)11yescharacteristic
270C23×C312−1+411yescharacteristic
271Q8×C31—416no—
272D4×C31—416no—
273C2×C4×C31—22no—
274C2×C4×C31—22no—
275C2×C4×C31—24no—
276C2×C4×C31—24no—
277C2×C4×C31—24no—
278C2×C4×C31—24no—
279C2×C4×C31—22no—
280C2×C4×C31—22no—
281C2×C4×C31—22no—
282C2×C4×C31—24no—
283C2×C4×C31—24no—
284C2×C4×C31—24no—
285C2×C4×C31—22no—
286C2×C4×C31—24no—
287C2×C4×C31—24no—
288C2×C4×C31—24no—
289C2×C4×C31—24no—
290C2×C4×C31—24no—
291C2×C4×C31—24no—
292C2×C4×C31—24no—
293C2×C4×C31—24no—
294C2×C4×C31—416no—
295C2×C4×C31—432no—
296C2×C4×C31—41no—
297C2×C4×C31—42no—
298C2×C4×C31—42no—
299C2×C4×C31—42no—
300C2×C4×C31—41no—
301C2×C4×C31—42no—
302C2×C4×C31—42no—
303C2×C4×C31—42no—
304C2×C4×C31—42no—
305C2×C4×C31—42no—
306C2×C4×C31—42no—
307C2×C4×C31—42no—
308C2×C4×C31—42no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—42no—
312C2×C4×C31—42no—
313C2×C4×C31—42no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—41no—
318C2×C4×C31—42no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—42no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31#12114yes—
328C22×C22⋊Q8C2×C3111yescharacteristic, complemented
329C2×#393C2×C3111yescharacteristic, complemented
330C2×#386C2×C3111yescharacteristic
331C2×#386C2×C3112yes—
332C22×#95C2×C3111yescharacteristic, complemented
333#1446C2×C3111yescharacteristic, complemented
334#1442C2×C3112yescomplemented
335#1442C2×C3111yescharacteristic, complemented
336#1439C2×C3111yescharacteristic, complemented
337#1439C2×C3112yescomplemented
338C22⋊#95C2×C3112yescomplemented
339C22×C31—24no—
340C22×C31—24no—
341C22×C31—24no—
342C22×C31—24no—
343C22×C31—24no—
344C22×C31—24no—
345C22×C31—28no—
346C22×C31—28no—
347C22×C31—28no—
348C22×C31—28no—
349C22×C31—42no—
350C22×C31—42no—
351C22×C31—42no—
352C22×C31—44no—
353C22×C31—44no—
354C22×C31—81no—
355C22×C31—81no—
356C22×C31—81no—
357C22×C31—81no—
358C22×C31—82no—
359C22×C31—82no—
360C22×C31#39318yescomplemented
361C22×C31C2×#12011yescharacteristic
362C22×C31C2×#12111yescharacteristic
363C22×C31C2×C22⋊Q811yescharacteristic
364C22×C31C2×C22⋊Q812yes—
365C22×C31#52512yes—
366C22×C31C2×#12411yescharacteristic
367C22×C31C2×#12412yes—
368C22×C31#52912yes—
369C22×C31#53211yescharacteristic
370C22×C31#53411yescharacteristic
371C22×C31#53711yescharacteristic
372C22×C31#53812yes—
373C22×C31#53912yes—
374C22×C31D4212yes—
375C22×C31#54612yes—
376C22×C31#54611yescharacteristic
377C22×C31#54612yes—
378C22×C31#54712yes—
379C22×C31D4×Q811yescharacteristic
380C22×C31#55112yes—
381C22×C31#55211yescharacteristic
382C22×C31#55412yes—
383C22×C31#55411yescharacteristic
384C4×C31—24no—
385C4×C31—42no—
386C4×C31—42no—
387C4×C31—44no—
388C4×C31—44no—
389C4×C31—44no—
390C4×C31—44no—
391C4×C31—81no—
392C4×C31—81no—
393C23×Q8C22×C3111yescharacteristic
394C23×D4C22×C3111yescharacteristic
395C24×C4C22×C3112yes—
396C24×C4C22×C3111yescharacteristic
397C2×C22⋊Q8—24no—
398C2×C22⋊Q8—28no—
399C22×C4⋊C4C22×C3111yescharacteristic
400C22×C4⋊C4C22×C3112yes—
401C22×C22⋊C4C22×C3111yescharacteristic
402C22×C22⋊C4C22×C3111yescharacteristic
403C22×C22⋊C4C22×C3112yes—
404C22×C22⋊C4C22×C3112yes—
405C22×C22⋊C4C22×C3112yes—
406C22×C22⋊C4C22×C3111yescharacteristic
407#393—24no—
408#386—24no—
409#386—28no—
410C2×#95—24no—
411C2×#95C22×C3112yes—
412C2×#95C22×C3112yes—
413C2×#95C22×C3112yes—
414C2×#95C22×C3111yescharacteristic
415C2×#95C22×C3111yescharacteristic
416C2×#95C22×C3112yes—
417C2×#95C22×C3111yescharacteristic
418C2×#95C22×C3112yes—
419C2×#95C22×C3112yes—
420C2×#95C22×C3112yes—
421C2×#95C22×C3111yescharacteristic
422C2×C31—28no—
423C2×C31—82no—
424C2×C31C2×#39311yescharacteristic
425C2×C31#241011yescharacteristic
426C2×C31#241711yescharacteristic
427C2×C31#243011yescharacteristic
428C2×C31#244912yes—
429C2×C31#245012yes—
430C2×C31#247212yes—
431C2×C31#248812yes—
432C2×C31#256411yescharacteristic
433C2×C31#263911yescharacteristic
434C2×C31#285011yescharacteristic
435C25C23×C3111yescharacteristic
436C25C23×C3111yescharacteristic
437C22×Q8—24no—
438C22×Q8—22no—
439C22×Q8—22no—
440C22×Q8—22no—
441C22×Q8—42no—
442C22×D4—22no—
443C22×D4—24no—
444C22×D4—24no—
445C22×D4—22no—
446C22×D4Q8×C3114yescomplemented
447C23×C4—24no—
448C23×C4—24no—
449C23×C4—24no—
450C23×C4—22no—
451C23×C4—24no—
452C23×C4—22no—
453C23×C4—24no—
454C23×C4—24no—
455C23×C4—42no—
456C23×C4—42no—
457C23×C4—42no—
458C23×C4D4×C3114yes—
459C23×C4C23×C3111yescharacteristic
460C23×C4C23×C3111yescharacteristic
461C23×C4C23×C3112yes—
462C23×C4C23×C3112yes—
463C23×C4C23×C3111yescharacteristic
464C23×C4C23×C3112yes—
465C23×C4C23×C3111yescharacteristic
466C23×C4C23×C3112yes—
467C23×C4C23×C3111yescharacteristic
468C22⋊Q8—232no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4D4×C3118yes—
490#95—24no—
491#95—22no—
492#95—24no—
493#95—24no—
494#95—22no—
495#95—22no—
496#95—24no—
497#95—24no—
498#95—42no—
499#95—42no—
500#95D4×C3114yescomplemented
501C31#1475911yescharacteristic, direct product factor, Sylow
502C24—21no—
503C24—21no—
504C24—22no—
505C24—22no—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—22no—
511C24—21no—
512C24—22no—
513C24—22no—
514C24—21no—
515C24—22no—
516C24—21no—
517C24—21no—
518C24C2×D4×C3112yes—
519C24C2×D4×C3114yes—
520C24C2×Q8×C3112yes—
521C24C2×Q8×C3112yes—
522C24#41×C3114yes—
523C24#41×C3112yes—
524C24C24×C3111yescharacteristic
525C2×Q8—28no—
526C2×Q8—48no—
527C2×Q8—48no—
528C2×Q8—44no—
529C2×Q8—44no—
530C2×D4—28no—
531C2×D4—216no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—48no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—216no—
538C22×C4—28no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—28no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—44no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4C2×D4×C3114yes—
592C22×C4C2×D4×C3114yes—
593C22×C4C2×D4×C3114yes—
594C22×C4C2×D4×C3112yes—
595C22×C4C2×D4×C3112yes—
596C22×C4C2×D4×C3112yes—
597C22×C4C2×Q8×C3112yes—
598C22×C4#41×C3114yes—
599C22×C4#41×C3112yes—
600C4⋊C4—28no—
601C4⋊C4—216no—
602C22⋊C4—216no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—22no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—22no—
622C23—24no—
623C23—22no—
624C23—24no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—22no—
629C23—24no—
630C23—22no—
631C23—41no—
632C23—41no—
633C23—42no—
634C23—41no—
635C23—42no—
636C23—42no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—41no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—41no—
649C23C31×#12014yes—
650C23C31×C22⋊Q814yes—
651C23C31×C22⋊Q818yes—
652C23C31×#12414yes—
653C23C31×#12418yes—
654C23C22×D4×C3111yescharacteristic
655C23C22×D4×C3112yes—
656C23C22×D4×C3111yescharacteristic
657C23C22×Q8×C3111yescharacteristic
658C23C2×#41×C3111yescharacteristic
659C23C2×#41×C3112yes—
660C23C2×#41×C3111yescharacteristic
661C23C2×#41×C3112yes—
662C23C31×H(5,𝔽2)12yes—
663C23C31×H(5,𝔽2)11yescharacteristic
664C23C31×2−1+411yescharacteristic
665Q8—416no—
666D4—416no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—416no—
689C2×C4—432no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4C31×#12114yes—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—28no—
729C22—28no—
730C22—28no—
731C22—28no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—44no—
736C22—44no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—82no—
742C22—82no—
743C22C31×#39318yescomplemented
744C22C2×C31×#12011yescharacteristic
745C22C2×C31×#12111yescharacteristic
746C22C2×C31×C22⋊Q811yescharacteristic
747C22C2×C31×C22⋊Q812yes—
748C22C31×#52512yes—
749C22C2×C31×#12411yescharacteristic
750C22C2×C31×#12412yes—
751C22C31×#52912yes—
752C22C31×#53211yescharacteristic
753C22C31×#53411yescharacteristic
754C22C31×#53711yescharacteristic
755C22C31×#53812yes—
756C22C31×#53912yes—
757C22D42×C3112yes—
758C22C31×#54612yes—
759C22C31×#54611yescharacteristic
760C22C31×#54612yes—
761C22C31×#54712yes—
762C22D4×Q8×C3111yescharacteristic
763C22C31×#55112yes—
764C22C31×#55211yescharacteristic
765C22C31×#55412yes—
766C22C31×#55411yescharacteristic
767C4—24no—
768C4—42no—
769C4—42no—
770C4—44no—
771C4—44no—
772C4—44no—
773C4—44no—
774C4—81no—
775C4—81no—
776C2—28no—
777C2—82no—
778C2C2×C31×#39311yescharacteristic
779C2C31×#241011yescharacteristic
780C2C31×#241711yescharacteristic
781C2C31×#243011yescharacteristic
782C2C31×#244912yes—
783C2C31×#245012yes—
784C2C31×#247212yes—
785C2C31×#248812yes—
786C2C31×#256411yescharacteristic
787C2C31×#263911yescharacteristic
788C2C31×#285011yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×C22⋊Q8C2semidirect
2. C2×C31×#393C2semidirect
5. C22×C31×#95C2semidirect
6. C31×#1446C2semidirect
7. C31×#1442C2semidirect
8. C31×#1442C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
11. C31×C22⋊#95C2semidirect
52. C22×D4×C31Q8semidirect
106. C31×#95D4semidirect
213. #14759C31direct (N × H)
328. C22×C22⋊Q8C2×C31semidirect
329. C2×#393C2×C31semidirect
332. C22×#95C2×C31semidirect
333. #1446C2×C31semidirect
334. #1442C2×C31semidirect
335. #1442C2×C31semidirect
336. #1439C2×C31semidirect
337. #1439C2×C31semidirect
338. C22⋊#95C2×C31semidirect
360. C22×C31#393semidirect
446. C22×D4Q8×C31semidirect
500. #95D4×C31semidirect
501. C31#14759direct (N × H)
743. C22C31×#393semidirect

Maximal subgroups

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

subgroupindex
C22×C31×C22⋊Q82
C2×C31×#3932
C2×C31×#3862
C22×C31×#952
C31×#14462
C31×#14422
C31×#14392
C31×C22⋊#952
#1475931