Finite Group Databasebeta

← C31×#15264 #21472023

Subgroups — C31×#15264 #21472023

Order 7936.

2618 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#124C211yesmaximal, characteristic, complemented
2C22×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C31×#394C211yesmaximal, characteristic, complemented
4C2×C31×#392C211yesmaximal, characteristic
5C2×C31×#386C212yesmaximal, complemented
6C31×#1446C211yesmaximal, characteristic, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1439C212yesmaximal, complemented
9C31×#1438C212yesmaximal, complemented
10C31×#1437C211yesmaximal, characteristic, complemented
11C31×#1436C211yesmaximal, characteristic, complemented
12C23×Q8×C31C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C23×D4×C31C2212yes—
15C24×C4×C31C2211yescharacteristic
16C2×C31×#124—24no—
17C2×C31×#124—28no—
18C2×C31×C22⋊Q8—24no—
19C2×C31×C22⋊Q8—24no—
20C2×C31×C22⋊Q8—24no—
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C4⋊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×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2212yes—
31C22×C22⋊C4×C31C2212yes—
32C22×C42×C31C2211yescharacteristic
33C31×#394—24no—
34C31×#392—24no—
35C31×#386—28no—
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2212yes—
41C2×C31×#95C2212yes—
42C2×C31×#95C2212yes—
43C25×C31C2312yes—
44C25×C31C2311yescharacteristic
45C22×Q8×C31—22no—
46C22×Q8×C31—22no—
47C22×Q8×C31—24no—
48C22×Q8×C31—42no—
49C22×Q8×C31D414yescomplemented
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—22no—
57C22×D4×C31—22no—
58C22×D4×C31—24no—
59C22×D4×C31—42no—
60C22×D4×C31—42no—
61C22×D4×C31—42no—
62C23×C4×C31—22no—
63C23×C4×C31—22no—
64C23×C4×C31—22no—
65C23×C4×C31—24no—
66C23×C4×C31—42no—
67C23×C4×C31C2312yes—
68C23×C4×C31C2312yes—
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2311yescharacteristic
73C23×C4×C31C2312yes—
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C31×#124—232no—
77C31×C22⋊Q8—232no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31—22no—
85C2×C4⋊C4×C31—22no—
86C2×C4⋊C4×C31D414yescomplemented
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—24no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—24no—
96C2×C22⋊C4×C31—24no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—24no—
99C2×C22⋊C4×C31—24no—
100C2×C22⋊C4×C31—24no—
101C2×C22⋊C4×C31—24no—
102C2×C22⋊C4×C31—24no—
103C2×C22⋊C4×C31—24no—
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×C31D414yes—
110C2×C22⋊C4×C31D418yescomplemented
111C2×C42×C31—24no—
112C2×C42×C31—22no—
113C31×#95—24no—
114C31×#95—24no—
115C31×#95—22no—
116C31×#95—22no—
117C31×#95—24no—
118C31×#95—42no—
119C31×#95—42no—
120C24×C31—21no—
121C24×C31—21no—
122C24×C31—22no—
123C24×C31—22no—
124C24×C31—22no—
125C24×C31—22no—
126C24×C31—22no—
127C24×C31—22no—
128C24×C31—22no—
129C24×C31—22no—
130C24×C31—22no—
131C24×C31—22no—
132C24×C31—22no—
133C24×C31—22no—
134C24×C31—22no—
135C24×C31—22no—
136C24×C31—22no—
137C24×C31—22no—
138C24×C31—22no—
139C24×C31—22no—
140C24×C31—22no—
141C24×C31C2×D414yes—
142C24×C31C2×D412yes—
143C24×C31#4114yes—
144C24×C31C2411yescharacteristic
145C2×Q8×C31—28no—
146C2×Q8×C31—28no—
147C2×Q8×C31—44no—
148C2×Q8×C31—48no—
149C2×Q8×C31—48no—
150C2×D4×C31—28no—
151C2×D4×C31—216no—
152C2×D4×C31—48no—
153C2×D4×C31—48no—
154C2×D4×C31—48no—
155C2×D4×C31—48no—
156C2×D4×C31—44no—
157C2×D4×C31—48no—
158C2×D4×C31—48no—
159C2×D4×C31—48no—
160C2×D4×C31—48no—
161C2×D4×C31—44no—
162C22×C4×C31—22no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—28no—
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—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—22no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
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—48no—
204C22×C4×C31—48no—
205C22×C4×C31—44no—
206C22×C4×C31—44no—
207C22×C4×C31C2×D414yes—
208C22×C4×C31C2×D412yes—
209C22×C4×C31C2×D412yes—
210C22×C4×C31C2×D412yes—
211C22×C4×C31C2×D412yes—
212C22×C4×C31C2×D414yes—
213C22×C4×C31C2×D412yes—
214C22×C4×C31C2×D412yes—
215C22×C4×C31C2×D412yes—
216C22×C4×C31C2×D412yes—
217C22×C4×C31#4114yes—
218C4⋊C4×C31—28no—
219C4⋊C4×C31—28no—
220C4⋊C4×C31—28no—
221C22⋊C4×C31—28no—
222C22⋊C4×C31—216no—
223C22⋊C4×C31—28no—
224C22⋊C4×C31—216no—
225C22⋊C4×C31—48no—
226C22⋊C4×C31—48no—
227C22⋊C4×C31—48no—
228C22⋊C4×C31—48no—
229C42×C31—28no—
230#15264C3111yesmaximal, characteristic, direct product factor, Sylow
231C23×C31—22no—
232C23×C31—24no—
233C23×C31—22no—
234C23×C31—24no—
235C23×C31—24no—
236C23×C31—24no—
237C23×C31—24no—
238C23×C31—24no—
239C23×C31—24no—
240C23×C31—24no—
241C23×C31—24no—
242C23×C31—24no—
243C23×C31—24no—
244C23×C31—24no—
245C23×C31—24no—
246C23×C31—24no—
247C23×C31—24no—
248C23×C31—41no—
249C23×C31—41no—
250C23×C31—41no—
251C23×C31—41no—
252C23×C31—42no—
253C23×C31—42no—
254C23×C31—42no—
255C23×C31—42no—
256C23×C31—42no—
257C23×C31—42no—
258C23×C31—42no—
259C23×C31—42no—
260C23×C31—42no—
261C23×C31—42no—
262C23×C31—42no—
263C23×C31—42no—
264C23×C31—42no—
265C23×C31—42no—
266C23×C31—42no—
267C23×C31—42no—
268C23×C31—42no—
269C23×C31—42no—
270C23×C31—42no—
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—42no—
280C23×C31—42no—
281C23×C31—42no—
282C23×C31—42no—
283C23×C31—42no—
284C23×C31—42no—
285C23×C31—42no—
286C23×C31#12414yescomplemented
287C23×C31C22×D411yescharacteristic
288C23×C31C22×D412yes—
289C23×C31C22×D411yescharacteristic
290C23×C31C22×D411yescharacteristic
291C23×C31C2×#4112yes—
292C23×C31C2×#4112yes—
293C23×C31H(5,𝔽2)12yes—
294C23×C31H(5,𝔽2)12yes—
295C23×C312−1+412yes—
296Q8×C31—416no—
297D4×C31—416no—
298D4×C31—432no—
299C2×C4×C31—22no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—22no—
303C2×C4×C31—24no—
304C2×C4×C31—24no—
305C2×C4×C31—24no—
306C2×C4×C31—24no—
307C2×C4×C31—24no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—22no—
311C2×C4×C31—22no—
312C2×C4×C31—22no—
313C2×C4×C31—24no—
314C2×C4×C31—22no—
315C2×C4×C31—22no—
316C2×C4×C31—22no—
317C2×C4×C31—24no—
318C2×C4×C31—24no—
319C2×C4×C31—24no—
320C2×C4×C31—24no—
321C2×C4×C31—24no—
322C2×C4×C31—24no—
323C2×C4×C31—416no—
324C2×C4×C31—41no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—42no—
331C2×C4×C31—42no—
332C2×C4×C31—42no—
333C2×C4×C31—42no—
334C2×C4×C31—42no—
335C2×C4×C31—42no—
336C2×C4×C31—42no—
337C2×C4×C31—42no—
338C2×C4×C31—42no—
339C2×C4×C31—42no—
340C2×C4×C31—42no—
341C2×C4×C31—42no—
342C2×C4×C31—42no—
343C2×C4×C31—42no—
344C2×C4×C31—42no—
345C2×C4×C31—42no—
346C2×C4×C31—42no—
347C2×C4×C31—42no—
348C2×C4×C31—42no—
349C2×C4×C31#12014yes—
350C2×C4×C31#12014yes—
351C22×#124C2×C3111yescharacteristic, complemented
352C22×C22⋊Q8C2×C3111yescharacteristic, complemented
353C2×#394C2×C3111yescharacteristic, complemented
354C2×#392C2×C3111yescharacteristic
355C2×#386C2×C3112yescomplemented
356#1446C2×C3111yescharacteristic, complemented
357#1439C2×C3112yescomplemented
358#1439C2×C3112yescomplemented
359#1438C2×C3112yescomplemented
360#1437C2×C3111yescharacteristic, complemented
361#1436C2×C3111yescharacteristic, complemented
362C22×C31—24no—
363C22×C31—28no—
364C22×C31—42no—
365C22×C31—44no—
366C22×C31—44no—
367C22×C31—44no—
368C22×C31—42no—
369C22×C31—44no—
370C22×C31—44no—
371C22×C31—44no—
372C22×C31—44no—
373C22×C31—44no—
374C22×C31—44no—
375C22×C31—44no—
376C22×C31—44no—
377C22×C31—44no—
378C22×C31—82no—
379C22×C31—82no—
380C22×C31—82no—
381C22×C31—82no—
382C22×C31—82no—
383C22×C31—82no—
384C22×C31—82no—
385C22×C31—82no—
386C22×C31C2×#12011yescharacteristic
387C22×C31C2×#12011yescharacteristic
388C22×C31#52512yes—
389C22×C31C2×#12411yescharacteristic
390C22×C31#53211yescharacteristic
391C22×C31#53411yescharacteristic
392C22×C31#53511yescharacteristic
393C22×C31#53611yescharacteristic
394C22×C31#53712yes—
395C22×C31#53812yes—
396C22×C31#54212yes—
397C22×C31D4212yes—
398C22×C31D4212yes—
399C22×C31#54612yes—
400C22×C31#54612yes—
401C22×C31#54712yes—
402C22×C31#54812yes—
403C22×C31#54812yes—
404C22×C31#55012yes—
405C22×C31#55112yes—
406C22×C31#56212yes—
407C4×C31—24no—
408C4×C31—24no—
409C4×C31—42no—
410C4×C31—42no—
411C4×C31—44no—
412C4×C31—42no—
413C4×C31—42no—
414C4×C31—44no—
415C4×C31—82no—
416C23×Q8C22×C3111yescharacteristic
417C23×D4C22×C3111yescharacteristic
418C23×D4C22×C3112yes—
419C24×C4C22×C3111yescharacteristic
420C2×#124—24no—
421C2×#124—28no—
422C2×C22⋊Q8—24no—
423C2×C22⋊Q8—24no—
424C2×C22⋊Q8—24no—
425C22×C4⋊C4C22×C3111yescharacteristic
426C22×C4⋊C4C22×C3111yescharacteristic
427C22×C4⋊C4C22×C3111yescharacteristic
428C22×C22⋊C4C22×C3111yescharacteristic
429C22×C22⋊C4C22×C3112yes—
430C22×C22⋊C4C22×C3112yes—
431C22×C22⋊C4C22×C3112yes—
432C22×C22⋊C4C22×C3112yes—
433C22×C22⋊C4C22×C3111yescharacteristic
434C22×C22⋊C4C22×C3112yes—
435C22×C22⋊C4C22×C3112yes—
436C22×C42C22×C3111yescharacteristic
437#394—24no—
438#392—24no—
439#386—28no—
440C2×#95C22×C3111yescharacteristic
441C2×#95C22×C3111yescharacteristic
442C2×#95C22×C3112yes—
443C2×#95C22×C3112yes—
444C2×#95C22×C3112yes—
445C2×#95C22×C3112yes—
446C2×#95C22×C3112yes—
447C2×C31—44no—
448C2×C31—84no—
449C2×C31#240311yescharacteristic
450C2×C31#240712yes—
451C2×C31#243111yescharacteristic
452C2×C31#243611yescharacteristic
453C2×C31#246112yes—
454C2×C31#247212yes—
455C2×C31#267212yes—
456C2×C31#267612yes—
457C2×C31#273012yes—
458C25C23×C3112yes—
459C25C23×C3111yescharacteristic
460C22×Q8—22no—
461C22×Q8—22no—
462C22×Q8—24no—
463C22×Q8—42no—
464C22×Q8D4×C3114yescomplemented
465C22×D4—24no—
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—24no—
474C22×D4—42no—
475C22×D4—42no—
476C22×D4—42no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—24no—
481C23×C4—42no—
482C23×C4C23×C3112yes—
483C23×C4C23×C3111yescharacteristic
484C23×C4C23×C3111yescharacteristic
485C23×C4C23×C3111yescharacteristic
486C23×C4C23×C3112yes—
487C23×C4C23×C3111yescharacteristic
488C23×C4C23×C3112yes—
489C23×C4C23×C3111yescharacteristic
490C23×C4C23×C3111yescharacteristic
491#124—232no—
492C22⋊Q8—232no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4D4×C3114yescomplemented
502C2×C22⋊C4—22no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4D4×C3114yes—
525C2×C22⋊C4D4×C3118yescomplemented
526C2×C42—24no—
527C2×C42—22no—
528#95—24no—
529#95—24no—
530#95—22no—
531#95—22no—
532#95—24no—
533#95—42no—
534#95—42no—
535C31#1526411yescharacteristic, direct product factor, Sylow
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24C2×D4×C3114yes—
558C24C2×D4×C3112yes—
559C24#41×C3114yes—
560C24C24×C3111yescharacteristic
561C2×Q8—28no—
562C2×Q8—28no—
563C2×Q8—44no—
564C2×Q8—48no—
565C2×Q8—48no—
566C2×D4—28no—
567C2×D4—216no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—48no—
572C2×D4—44no—
573C2×D4—48no—
574C2×D4—48no—
575C2×D4—48no—
576C2×D4—48no—
577C2×D4—44no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—28no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4C2×D4×C3114yes—
624C22×C4C2×D4×C3112yes—
625C22×C4C2×D4×C3112yes—
626C22×C4C2×D4×C3112yes—
627C22×C4C2×D4×C3112yes—
628C22×C4C2×D4×C3114yes—
629C22×C4C2×D4×C3112yes—
630C22×C4C2×D4×C3112yes—
631C22×C4C2×D4×C3112yes—
632C22×C4C2×D4×C3112yes—
633C22×C4#41×C3114yes—
634C4⋊C4—28no—
635C4⋊C4—28no—
636C4⋊C4—28no—
637C22⋊C4—28no—
638C22⋊C4—216no—
639C22⋊C4—28no—
640C22⋊C4—216no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C42—28no—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23C31×#12414yescomplemented
702C23C22×D4×C3111yescharacteristic
703C23C22×D4×C3112yes—
704C23C22×D4×C3111yescharacteristic
705C23C22×D4×C3111yescharacteristic
706C23C2×#41×C3112yes—
707C23C2×#41×C3112yes—
708C23C31×H(5,𝔽2)12yes—
709C23C31×H(5,𝔽2)12yes—
710C23C31×2−1+412yes—
711Q8—416no—
712D4—416no—
713D4—432no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—416no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4C31×#12014yes—
765C2×C4C31×#12014yes—
766C22—24no—
767C22—28no—
768C22—42no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—42no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22C2×C31×#12011yescharacteristic
791C22C2×C31×#12011yescharacteristic
792C22C31×#52512yes—
793C22C2×C31×#12411yescharacteristic
794C22C31×#53211yescharacteristic
795C22C31×#53411yescharacteristic
796C22C31×#53511yescharacteristic
797C22C31×#53611yescharacteristic
798C22C31×#53712yes—
799C22C31×#53812yes—
800C22C31×#54212yes—
801C22D42×C3112yes—
802C22D42×C3112yes—
803C22C31×#54612yes—
804C22C31×#54612yes—
805C22C31×#54712yes—
806C22C31×#54812yes—
807C22C31×#54812yes—
808C22C31×#55012yes—
809C22C31×#55112yes—
810C22C31×#56212yes—
811C4—24no—
812C4—24no—
813C4—42no—
814C4—42no—
815C4—44no—
816C4—42no—
817C4—42no—
818C4—44no—
819C4—82no—
820C2—44no—
821C2—84no—
822C2C31×#240311yescharacteristic
823C2C31×#240712yes—
824C2C31×#243111yescharacteristic
825C2C31×#243611yescharacteristic
826C2C31×#246112yes—
827C2C31×#247212yes—
828C2C31×#267212yes—
829C2C31×#267612yes—
830C2C31×#273012yes—
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC2×C31×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#124C2semidirect
2. C22×C31×C22⋊Q8C2semidirect
3. C2×C31×#394C2semidirect
5. C2×C31×#386C2semidirect
6. C31×#1446C2semidirect
7. C31×#1439C2semidirect
8. C31×#1439C2semidirect
9. C31×#1438C2semidirect
10. C31×#1437C2semidirect
11. C31×#1436C2semidirect
49. C22×Q8×C31D4semidirect
86. C2×C4⋊C4×C31D4semidirect
110. C2×C22⋊C4×C31D4semidirect
230. #15264C31direct (N × H)
286. C23×C31#124semidirect
351. C22×#124C2×C31semidirect
352. C22×C22⋊Q8C2×C31semidirect
353. C2×#394C2×C31semidirect
355. C2×#386C2×C31semidirect
356. #1446C2×C31semidirect
357. #1439C2×C31semidirect
358. #1439C2×C31semidirect
359. #1438C2×C31semidirect
360. #1437C2×C31semidirect
361. #1436C2×C31semidirect
464. C22×Q8D4×C31semidirect
501. C2×C4⋊C4D4×C31semidirect
525. C2×C22⋊C4D4×C31semidirect
535. C31#15264direct (N × H)
701. C23C31×#124semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1242
C22×C31×C22⋊Q82
C2×C31×#3942
C2×C31×#3922
C2×C31×#3862
C31×#14462
C31×#14392
C31×#14382
C31×#14372
C31×#14362
#1526431