Finite Group Databasebeta

← C31×#16261 #21473020

Subgroups — C31×#16261 #21473020

Order 7936.

2402 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic
2C2×C31×#396C212yesmaximal, complemented
3C2×C31×#394C211yesmaximal, characteristic, complemented
4C2×C31×#394C212yesmaximal, complemented
5C2×C31×#385C211yesmaximal, characteristic, complemented
6C2×C31×#380C211yesmaximal, characteristic, complemented
7C31×#1444C211yesmaximal, characteristic, complemented
8C31×#1441C211yesmaximal, characteristic, complemented
9C31×#1439C212yesmaximal, complemented
10C31×#1438C211yesmaximal, characteristic, complemented
11C31×#1438C212yesmaximal, complemented
12C23×D4×C31C2212yes—
13C23×D4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C2×C31×#121—24no—
16C2×C31×#121—28no—
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2212yes—
21C22×C4⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2212yes—
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2212yes—
30C31×#396—28no—
31C31×#394—28no—
32C31×#394—24no—
33C31×#385—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×C31C2312yes—
43C25×C31C2311yescharacteristic
44C22×D4×C31—24no—
45C22×D4×C31—24no—
46C22×D4×C31—24no—
47C22×D4×C31—24no—
48C22×D4×C31—24no—
49C22×D4×C31—24no—
50C22×D4×C31—22no—
51C22×D4×C31—22no—
52C22×D4×C31—22no—
53C22×D4×C31—42no—
54C22×D4×C31—42no—
55C22×D4×C31—42no—
56C23×C4×C31—24no—
57C23×C4×C31—22no—
58C23×C4×C31—22no—
59C23×C4×C31—42no—
60C23×C4×C31D414yes—
61C23×C4×C31C2311yescharacteristic
62C23×C4×C31C2312yes—
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2312yes—
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2312yes—
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C31×#121—232no—
71C2×C4⋊C4×C31—24no—
72C2×C4⋊C4×C31—22no—
73C2×C4⋊C4×C31—24no—
74C2×C4⋊C4×C31—24no—
75C2×C4⋊C4×C31—24no—
76C2×C4⋊C4×C31—24no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—24no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—42no—
83C2×C4⋊C4×C31—42no—
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31—24no—
87C2×C22⋊C4×C31—24no—
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—24no—
96C2×C22⋊C4×C31—24no—
97C2×C22⋊C4×C31—42no—
98C2×C22⋊C4×C31—42no—
99C2×C22⋊C4×C31—42no—
100C2×C22⋊C4×C31—42no—
101C2×C22⋊C4×C31—42no—
102C2×C22⋊C4×C31—42no—
103C2×C22⋊C4×C31—42no—
104C2×C22⋊C4×C31—42no—
105C2×C22⋊C4×C31D418yes—
106C2×C22⋊C4×C31D414yescomplemented
107C31×#95—24no—
108C31×#95—22no—
109C31×#95—22no—
110C31×#95—22no—
111C31×#95—24no—
112C31×#95—42no—
113C31×#95D414yescomplemented
114C24×C31—21no—
115C24×C31—22no—
116C24×C31—21no—
117C24×C31—21no—
118C24×C31—22no—
119C24×C31—22no—
120C24×C31—22no—
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×C31C2×D414yes—
137C24×C31C2×D412yes—
138C24×C31C2×D412yes—
139C24×C31#4112yes—
140C24×C31C2411yescharacteristic
141C2×D4×C31—28no—
142C2×D4×C31—216no—
143C2×D4×C31—48no—
144C2×D4×C31—48no—
145C2×D4×C31—48no—
146C2×D4×C31—48no—
147C2×D4×C31—44no—
148C2×D4×C31—48no—
149C2×D4×C31—48no—
150C2×D4×C31—48no—
151C2×D4×C31—48no—
152C2×D4×C31—44no—
153C22×C4×C31—21no—
154C22×C4×C31—22no—
155C22×C4×C31—21no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—22no—
161C22×C4×C31—21no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—21no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—21no—
180C22×C4×C31—28no—
181C22×C4×C31—28no—
182C22×C4×C31—21no—
183C22×C4×C31—22no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—21no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—21no—
199C22×C4×C31—44no—
200C22×C4×C31—48no—
201C22×C4×C31—48no—
202C22×C4×C31C2×D412yes—
203C22×C4×C31C2×D414yes—
204C22×C4×C31C2×D414yes—
205C22×C4×C31C2×D412yes—
206C22×C4×C31C2×D412yes—
207C22×C4×C31C2×D414yes—
208C22×C4×C31C2×D412yes—
209C22×C4×C31C2×D412yes—
210C22×C4×C31#4112yes—
211C4⋊C4×C31—28no—
212C4⋊C4×C31—48no—
213C4⋊C4×C31—48no—
214C4⋊C4×C31—44no—
215C4⋊C4×C31—44no—
216C22⋊C4×C31—28no—
217C22⋊C4×C31—216no—
218C22⋊C4×C31—48no—
219C22⋊C4×C31—48no—
220C22⋊C4×C31—48no—
221C22⋊C4×C31—48no—
222C22⋊C4×C31—44no—
223C22⋊C4×C31—48no—
224#16261C3111yesmaximal, characteristic, direct product factor, Sylow
225C23×C31—22no—
226C23×C31—22no—
227C23×C31—22no—
228C23×C31—22no—
229C23×C31—22no—
230C23×C31—24no—
231C23×C31—22no—
232C23×C31—24no—
233C23×C31—22no—
234C23×C31—24no—
235C23×C31—24no—
236C23×C31—22no—
237C23×C31—22no—
238C23×C31—22no—
239C23×C31—24no—
240C23×C31—24no—
241C23×C31—24no—
242C23×C31—24no—
243C23×C31—24no—
244C23×C31—24no—
245C23×C31—24no—
246C23×C31—42no—
247C23×C31—42no—
248C23×C31—42no—
249C23×C31—42no—
250C23×C31—42no—
251C23×C31—42no—
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#12114yes—
283C23×C31C22×D411yescharacteristic
284C23×C31C22×D412yes—
285C23×C31C22×D411yescharacteristic
286C23×C31C22×D411yescharacteristic
287C23×C31C2×#4111yescharacteristic
288C23×C31C2×#4111yescharacteristic
289C23×C31H(5,𝔽2)12yes—
290C23×C31H(5,𝔽2)12yes—
291C23×C31H(5,𝔽2)11yescharacteristic
292C23×C312−1+412yes—
293C23×C312−1+411yescharacteristic
294D4×C31—416no—
295D4×C31—432no—
296C2×C4×C31—22no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
299C2×C4×C31—22no—
300C2×C4×C31—24no—
301C2×C4×C31—24no—
302C2×C4×C31—24no—
303C2×C4×C31—24no—
304C2×C4×C31—24no—
305C2×C4×C31—22no—
306C2×C4×C31—22no—
307C2×C4×C31—24no—
308C2×C4×C31—22no—
309C2×C4×C31—24no—
310C2×C4×C31—24no—
311C2×C4×C31—24no—
312C2×C4×C31—24no—
313C2×C4×C31—24no—
314C2×C4×C31—22no—
315C2×C4×C31—416no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—42no—
319C2×C4×C31—41no—
320C2×C4×C31—42no—
321C2×C4×C31—41no—
322C2×C4×C31—42no—
323C2×C4×C31—42no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—42no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—42no—
337C2×C4×C31—42no—
338C2×C4×C31—42no—
339C2×C4×C31—41no—
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#12014yes—
349C2×C4×C31#12114yes—
350C22×#121C2×C3111yescharacteristic
351C2×#396C2×C3112yescomplemented
352C2×#394C2×C3111yescharacteristic, complemented
353C2×#394C2×C3112yescomplemented
354C2×#385C2×C3111yescharacteristic, complemented
355C2×#380C2×C3111yescharacteristic, complemented
356#1444C2×C3111yescharacteristic, complemented
357#1441C2×C3111yescharacteristic, complemented
358#1439C2×C3112yescomplemented
359#1438C2×C3111yescharacteristic, complemented
360#1438C2×C3112yescomplemented
361C22×C31—24no—
362C22×C31—24no—
363C22×C31—24no—
364C22×C31—42no—
365C22×C31—42no—
366C22×C31—42no—
367C22×C31—44no—
368C22×C31—44no—
369C22×C31—44no—
370C22×C31—44no—
371C22×C31—42no—
372C22×C31—44no—
373C22×C31—44no—
374C22×C31—44no—
375C22×C31—44no—
376C22×C31—44no—
377C22×C31—44no—
378C22×C31—44no—
379C22×C31—82no—
380C22×C31—82no—
381C22×C31—82no—
382C22×C31—82no—
383C22×C31—82no—
384C22×C31—82no—
385C22×C31—82no—
386C22×C31—82no—
387C22×C31C2×#12011yescharacteristic
388C22×C31C2×#12111yescharacteristic
389C22×C31C2×#12111yescharacteristic
390C22×C31#53411yescharacteristic
391C22×C31#53511yescharacteristic
392C22×C31#53611yescharacteristic
393C22×C31#53612yes—
394C22×C31#53711yescharacteristic
395C22×C31#53712yes—
396C22×C31#53712yes—
397C22×C31#53712yes—
398C22×C31#53912yes—
399C22×C31#54212yes—
400C22×C31D4212yes—
401C22×C31D4212yes—
402C22×C31D4211yescharacteristic
403C22×C31#54612yes—
404C22×C31#54612yes—
405C22×C31#54711yescharacteristic
406C22×C31#54811yescharacteristic
407C22×C31#55311yescharacteristic
408C22×C31#56012yes—
409C22×C31#56212yes—
410C4×C31—24no—
411C4×C31—24no—
412C4×C31—42no—
413C4×C31—44no—
414C4×C31—42no—
415C4×C31—44no—
416C4×C31—81no—
417C4×C31—82no—
418C4×C31—81no—
419C23×D4C22×C3112yes—
420C23×D4C22×C3111yescharacteristic
421C24×C4C22×C3111yescharacteristic
422C2×#121—24no—
423C2×#121—28no—
424C22×C4⋊C4C22×C3111yescharacteristic
425C22×C4⋊C4C22×C3111yescharacteristic
426C22×C4⋊C4C22×C3111yescharacteristic
427C22×C4⋊C4C22×C3112yes—
428C22×C4⋊C4C22×C3112yes—
429C22×C22⋊C4C22×C3112yes—
430C22×C22⋊C4C22×C3112yes—
431C22×C22⋊C4C22×C3112yes—
432C22×C22⋊C4C22×C3112yes—
433C22×C22⋊C4C22×C3112yes—
434C22×C22⋊C4C22×C3111yescharacteristic
435C22×C22⋊C4C22×C3111yescharacteristic
436C22×C22⋊C4C22×C3112yes—
437#396—28no—
438#394—28no—
439#394—24no—
440#385—24no—
441#380—24no—
442C2×#95C22×C3112yes—
443C2×#95C22×C3112yes—
444C2×#95C22×C3111yescharacteristic
445C2×#95C22×C3111yescharacteristic
446C2×#95C22×C3111yescharacteristic
447C2×#95C22×C3112yes—
448C2×#95C22×C3111yescharacteristic
449C2×C31—44no—
450C2×C31—84no—
451C2×C31#240811yescharacteristic
452C2×C31#241011yescharacteristic
453C2×C31#241611yescharacteristic
454C2×C31#261611yescharacteristic
455C2×C31#261811yescharacteristic
456C2×C31#262011yescharacteristic
457C2×C31#267212yes—
458C2×C31#267512yes—
459C2×C31#268112yes—
460C2×C31#269112yes—
461C2×C31#281311yescharacteristic
462C25C23×C3112yes—
463C25C23×C3111yescharacteristic
464C22×D4—24no—
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—42no—
474C22×D4—42no—
475C22×D4—42no—
476C23×C4—24no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—42no—
480C23×C4D4×C3114yes—
481C23×C4C23×C3111yescharacteristic
482C23×C4C23×C3112yes—
483C23×C4C23×C3111yescharacteristic
484C23×C4C23×C3111yescharacteristic
485C23×C4C23×C3112yes—
486C23×C4C23×C3111yescharacteristic
487C23×C4C23×C3112yes—
488C23×C4C23×C3111yescharacteristic
489C23×C4C23×C3111yescharacteristic
490#121—232no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—42no—
503C2×C4⋊C4—42no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—22no—
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—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4D4×C3118yes—
526C2×C22⋊C4D4×C3114yescomplemented
527#95—22no—
528#95—22no—
529#95—22no—
530#95—24no—
531#95—24no—
532#95—42no—
533#95D4×C3114yescomplemented
534C31#1626111yescharacteristic, direct product factor, Sylow
535C24—21no—
536C24—22no—
537C24—21no—
538C24—21no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—21no—
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—
559C24C2×D4×C3112yes—
560C24#41×C3112yes—
561C24C24×C3111yescharacteristic
562C2×D4—28no—
563C2×D4—216no—
564C2×D4—48no—
565C2×D4—48no—
566C2×D4—48no—
567C2×D4—48no—
568C2×D4—44no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—48no—
572C2×D4—48no—
573C2×D4—44no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—21no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—21no—
620C22×C4—44no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4C2×D4×C3112yes—
624C22×C4C2×D4×C3114yes—
625C22×C4C2×D4×C3114yes—
626C22×C4C2×D4×C3112yes—
627C22×C4C2×D4×C3112yes—
628C22×C4C2×D4×C3114yes—
629C22×C4C2×D4×C3112yes—
630C22×C4C2×D4×C3112yes—
631C22×C4#41×C3112yes—
632C4⋊C4—28no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C22⋊C4—28no—
638C22⋊C4—216no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—44no—
644C22⋊C4—48no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—24no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—42no—
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—
701C23—42no—
702C23C31×#12114yes—
703C23C22×D4×C3111yescharacteristic
704C23C22×D4×C3112yes—
705C23C22×D4×C3111yescharacteristic
706C23C22×D4×C3111yescharacteristic
707C23C2×#41×C3111yescharacteristic
708C23C2×#41×C3111yescharacteristic
709C23C31×H(5,𝔽2)12yes—
710C23C31×H(5,𝔽2)12yes—
711C23C31×H(5,𝔽2)11yescharacteristic
712C23C31×2−1+412yes—
713C23C31×2−1+411yescharacteristic
714D4—416no—
715D4—432no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—416no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4C31×#12014yes—
769C2×C4C31×#12114yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—42no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22C2×C31×#12011yescharacteristic
797C22C2×C31×#12111yescharacteristic
798C22C2×C31×#12111yescharacteristic
799C22C31×#53411yescharacteristic
800C22C31×#53511yescharacteristic
801C22C31×#53611yescharacteristic
802C22C31×#53612yes—
803C22C31×#53711yescharacteristic
804C22C31×#53712yes—
805C22C31×#53712yes—
806C22C31×#53712yes—
807C22C31×#53912yes—
808C22C31×#54212yes—
809C22D42×C3112yes—
810C22D42×C3112yes—
811C22D42×C3111yescharacteristic
812C22C31×#54612yes—
813C22C31×#54612yes—
814C22C31×#54711yescharacteristic
815C22C31×#54811yescharacteristic
816C22C31×#55311yescharacteristic
817C22C31×#56012yes—
818C22C31×#56212yes—
819C4—24no—
820C4—24no—
821C4—44no—
822C4—42no—
823C4—42no—
824C4—44no—
825C4—81no—
826C4—82no—
827C4—81no—
828C2—44no—
829C2—84no—
830C2C31×#240811yescharacteristic
831C2C31×#241011yescharacteristic
832C2C31×#241611yescharacteristic
833C2C31×#261611yescharacteristic
834C2C31×#261811yescharacteristic
835C2C31×#262011yescharacteristic
836C2C31×#267212yes—
837C2C31×#267512yes—
838C2C31×#268112yes—
839C2C31×#269112yes—
840C2C31×#281311yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC22×C31×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#396C2semidirect
3. C2×C31×#394C2semidirect
4. C2×C31×#394C2semidirect
5. C2×C31×#385C2semidirect
6. C2×C31×#380C2semidirect
7. C31×#1444C2semidirect
8. C31×#1441C2semidirect
9. C31×#1439C2semidirect
10. C31×#1438C2semidirect
11. C31×#1438C2semidirect
106. C2×C22⋊C4×C31D4semidirect
113. C31×#95D4semidirect
224. #16261C31direct (N × H)
351. C2×#396C2×C31semidirect
352. C2×#394C2×C31semidirect
353. C2×#394C2×C31semidirect
354. C2×#385C2×C31semidirect
355. C2×#380C2×C31semidirect
356. #1444C2×C31semidirect
357. #1441C2×C31semidirect
358. #1439C2×C31semidirect
359. #1438C2×C31semidirect
360. #1438C2×C31semidirect
526. C2×C22⋊C4D4×C31semidirect
533. #95D4×C31semidirect
534. C31#16261direct (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×#3962
C2×C31×#3942
C2×C31×#3852
C2×C31×#3802
C31×#14442
C31×#14412
C31×#14392
C31×#14382
#1626131