Finite Group Databasebeta

← C31×#16551 #21473310

Subgroups — C31×#16551 #21473310

Order 7936.

2470 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#394C211yesmaximal, characteristic, complemented
2C2×C31×#394C212yesmaximal, complemented
3C2×C31×#392C212yesmaximal, complemented
4C2×C31×#392C212yesmaximal, complemented
5C2×C31×#390C211yesmaximal, characteristic, complemented
6C31×#1441C211yesmaximal, characteristic, complemented
7C31×#1440C212yesmaximal, complemented
8C31×#1438C212yesmaximal, complemented
9C31×#1437C212yesmaximal, complemented
10C23×D4×C31C2211yescharacteristic
11C23×D4×C31C2212yes—
12C23×D4×C31C2212yes—
13C23×D4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C42×C31C2211yescharacteristic
25C31×#394—24no—
26C31×#394—28no—
27C31×#392—28no—
28C31×#392—28no—
29C31×#390—24no—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2212yes—
35C2×C31×#95C2211yescharacteristic
36C25×C31C2312yes—
37C25×C31C2312yes—
38C22×D4×C31—24no—
39C22×D4×C31—24no—
40C22×D4×C31—24no—
41C22×D4×C31—24no—
42C22×D4×C31—24no—
43C22×D4×C31—22no—
44C22×D4×C31—24no—
45C22×D4×C31—22no—
46C22×D4×C31—22no—
47C22×D4×C31—24no—
48C22×D4×C31—41no—
49C22×D4×C31—41no—
50C22×D4×C31—41no—
51C22×D4×C31—41no—
52C22×D4×C31—42no—
53C22×D4×C31—42no—
54C22×D4×C31—42no—
55C22×D4×C31—42no—
56C22×D4×C31—42no—
57C22×D4×C31—42no—
58C22×D4×C31—42no—
59C22×D4×C31—42no—
60C22×D4×C31—42no—
61C22×D4×C31—41no—
62C22×D4×C31—41no—
63C22×D4×C31D414yescomplemented
64C23×C4×C31C2312yes—
65C23×C4×C31C2312yes—
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C23×C4×C31C2312yes—
69C23×C4×C31C2312yes—
70C23×C4×C31C2311yescharacteristic
71C2×C4⋊C4×C31—24no—
72C2×C4⋊C4×C31—41no—
73C2×C4⋊C4×C31—41no—
74C2×C4⋊C4×C31—41no—
75C2×C4⋊C4×C31D414yescomplemented
76C2×C22⋊C4×C31—24no—
77C2×C22⋊C4×C31—24no—
78C2×C22⋊C4×C31—24no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—24no—
81C2×C22⋊C4×C31—24no—
82C2×C22⋊C4×C31—24no—
83C2×C22⋊C4×C31—24no—
84C2×C22⋊C4×C31—24no—
85C2×C22⋊C4×C31—24no—
86C2×C22⋊C4×C31—24no—
87C2×C22⋊C4×C31—24no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—24no—
91C2×C22⋊C4×C31—42no—
92C2×C22⋊C4×C31—42no—
93C2×C22⋊C4×C31—42no—
94C2×C22⋊C4×C31—42no—
95C2×C22⋊C4×C31—42no—
96C2×C22⋊C4×C31—42no—
97C2×C22⋊C4×C31—42no—
98C2×C22⋊C4×C31—42no—
99C2×C22⋊C4×C31D418yescomplemented
100C2×C42×C31—22no—
101C2×C42×C31—41no—
102C2×C42×C31—41no—
103C31×#95—24no—
104C31×#95—24no—
105C31×#95—24no—
106C31×#95—22no—
107C31×#95—42no—
108C31×#95—41no—
109C24×C31—22no—
110C24×C31—22no—
111C24×C31—22no—
112C24×C31—22no—
113C24×C31—22no—
114C24×C31—22no—
115C24×C31—22no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31—22no—
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×C31C2×D414yes—
138C24×C31C2×D414yes—
139C24×C31C2411yescharacteristic
140C2×D4×C31—28no—
141C2×D4×C31—44no—
142C2×D4×C31—44no—
143C2×D4×C31—48no—
144C2×D4×C31—48no—
145C2×D4×C31—48no—
146C2×D4×C31—48no—
147C2×D4×C31—48no—
148C2×D4×C31—44no—
149C2×D4×C31—44no—
150C2×D4×C31—44no—
151C2×D4×C31—44no—
152C2×D4×C31—48no—
153C2×D4×C31—44no—
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—48no—
162C2×D4×C31—48no—
163C2×D4×C31—44no—
164C2×D4×C31—48no—
165C2×D4×C31—48no—
166C22×C4×C31—21no—
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—22no—
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—22no—
181C22×C4×C31—22no—
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—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
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×C31C2×D414yes—
204C22×C4×C31C2×D412yes—
205C22×C4×C31C2×D414yes—
206C22×C4×C31C2×D412yes—
207C22×C4×C31C2×D412yes—
208C22×C4×C31C2×D412yes—
209C22×C4×C31#4114yes—
210C22×C4×C31#4112yes—
211C4⋊C4×C31—44no—
212C4⋊C4×C31—44no—
213C22⋊C4×C31—48no—
214C22⋊C4×C31—48no—
215C22⋊C4×C31—48no—
216C22⋊C4×C31—48no—
217C22⋊C4×C31—48no—
218C22⋊C4×C31—48no—
219C22⋊C4×C31—48no—
220C22⋊C4×C31—48no—
221C42×C31—44no—
222#16551C3111yesmaximal, characteristic, direct product factor, Sylow
223C23×C31—24no—
224C23×C31—24no—
225C23×C31—24no—
226C23×C31—24no—
227C23×C31—24no—
228C23×C31—24no—
229C23×C31—24no—
230C23×C31—24no—
231C23×C31—24no—
232C23×C31—24no—
233C23×C31—24no—
234C23×C31—24no—
235C23×C31—24no—
236C23×C31—24no—
237C23×C31—42no—
238C23×C31—42no—
239C23×C31—42no—
240C23×C31—42no—
241C23×C31—42no—
242C23×C31—42no—
243C23×C31—42no—
244C23×C31—42no—
245C23×C31—42no—
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—42no—
283C23×C31—42no—
284C23×C31—42no—
285C23×C31—42no—
286C23×C31—42no—
287C23×C31—42no—
288C23×C31—42no—
289C23×C31—42no—
290C23×C31—42no—
291C23×C31—42no—
292C23×C31—42no—
293C23×C31C22×D411yescharacteristic
294C23×C31C22×D411yescharacteristic
295C23×C31C22×D412yes—
296C23×C31C2×#4111yescharacteristic
297C23×C31C2×#4112yes—
298C23×C31H(5,𝔽2)11yescharacteristic
299C23×C31H(5,𝔽2)11yescharacteristic
300C23×C31H(5,𝔽2)11yescharacteristic
301C23×C31H(5,𝔽2)11yescharacteristic
302C23×C31H(5,𝔽2)12yes—
303C23×C31H(5,𝔽2)12yes—
304D4×C31—416no—
305D4×C31—416no—
306D4×C31—432no—
307D4×C31—432no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—22no—
311C2×C4×C31—22no—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—24no—
315C2×C4×C31—24no—
316C2×C4×C31—22no—
317C2×C4×C31—22no—
318C2×C4×C31—24no—
319C2×C4×C31—24no—
320C2×C4×C31—24no—
321C2×C4×C31—24no—
322C2×C4×C31—24no—
323C2×C4×C31—24no—
324C2×C4×C31—24no—
325C2×C4×C31—24no—
326C2×C4×C31—24no—
327C2×C4×C31—42no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—42no—
331C2×C4×C31—42no—
332C2×C4×C31—42no—
333C2×C4×C31—42no—
334C2×C4×C31—42no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—42no—
338C2×C4×C31—42no—
339C2×C4×C31—42no—
340C2×C4×C31—41no—
341C2×C4×C31—42no—
342C2×C4×C31—41no—
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—42no—
350C2×C4×C31—42no—
351C2×C4×C31—42no—
352C2×C4×C31#12114yes—
353C2×#394C2×C3111yescharacteristic, complemented
354C2×#394C2×C3112yescomplemented
355C2×#392C2×C3112yescomplemented
356C2×#392C2×C3112yescomplemented
357C2×#390C2×C3111yescharacteristic, complemented
358#1441C2×C3111yescharacteristic, complemented
359#1440C2×C3112yescomplemented
360#1438C2×C3112yescomplemented
361#1437C2×C3112yescomplemented
362C22×C31—44no—
363C22×C31—44no—
364C22×C31—44no—
365C22×C31—44no—
366C22×C31—44no—
367C22×C31—44no—
368C22×C31—44no—
369C22×C31—44no—
370C22×C31—44no—
371C22×C31—44no—
372C22×C31—44no—
373C22×C31—44no—
374C22×C31—44no—
375C22×C31—44no—
376C22×C31—82no—
377C22×C31—82no—
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×C31—82no—
387C22×C31—82no—
388C22×C31—82no—
389C22×C31—82no—
390C22×C31—82no—
391C22×C31—82no—
392C22×C31C2×#12111yescharacteristic
393C22×C31#53212yes—
394C22×C31#53411yescharacteristic
395C22×C31#53411yescharacteristic
396C22×C31#53411yescharacteristic
397C22×C31#53412yes—
398C22×C31#53511yescharacteristic
399C22×C31#53512yes—
400C22×C31#53811yescharacteristic
401C22×C31#53811yescharacteristic
402C22×C31#53812yes—
403C22×C31#54012yes—
404C22×C31#54012yes—
405C22×C31D4212yes—
406C22×C31D4211yescharacteristic
407C22×C31D4212yes—
408C22×C31#54612yes—
409C22×C31#54612yes—
410C22×C31#55012yes—
411C22×C31#55511yescharacteristic
412C22×C31#56011yescharacteristic
413C22×C31#56012yes—
414C22×C31H(3,𝔽4)11yescharacteristic
415C4×C31—24no—
416C4×C31—42no—
417C4×C31—42no—
418C4×C31—44no—
419C4×C31—44no—
420C4×C31—44no—
421C4×C31—82no—
422C23×D4C22×C3111yescharacteristic
423C23×D4C22×C3112yes—
424C23×D4C22×C3112yes—
425C23×D4C22×C3111yescharacteristic
426C22×C4⋊C4C22×C3111yescharacteristic
427C22×C4⋊C4C22×C3111yescharacteristic
428C22×C22⋊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×C3112yes—
435C22×C22⋊C4C22×C3112yes—
436C22×C42C22×C3111yescharacteristic
437#394—24no—
438#394—28no—
439#392—28no—
440#392—28no—
441#390—24no—
442C2×#95C22×C3112yes—
443C2×#95C22×C3112yes—
444C2×#95C22×C3112yes—
445C2×#95C22×C3111yescharacteristic
446C2×#95C22×C3112yes—
447C2×#95C22×C3111yescharacteristic
448C2×C31—84no—
449C2×C31—84no—
450C2×C31#242812yes—
451C2×C31#255511yescharacteristic
452C2×C31#261711yescharacteristic
453C2×C31#266112yes—
454C2×C31#266911yescharacteristic
455C2×C31#267312yes—
456C2×C31#267812yes—
457C2×C31#267911yescharacteristic
458C2×C31#269911yescharacteristic
459C2×C31#273311yescharacteristic
460C2×C31#282811yescharacteristic
461C25C23×C3112yes—
462C25C23×C3112yes—
463C22×D4—24no—
464C22×D4—24no—
465C22×D4—24no—
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—22no—
469C22×D4—24no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—24no—
473C22×D4—41no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4—41no—
477C22×D4—42no—
478C22×D4—42no—
479C22×D4—42no—
480C22×D4—42no—
481C22×D4—42no—
482C22×D4—42no—
483C22×D4—42no—
484C22×D4—42no—
485C22×D4—42no—
486C22×D4—41no—
487C22×D4—41no—
488C22×D4D4×C3114yescomplemented
489C23×C4C23×C3112yes—
490C23×C4C23×C3111yescharacteristic
491C23×C4C23×C3112yes—
492C23×C4C23×C3111yescharacteristic
493C23×C4C23×C3112yes—
494C23×C4C23×C3112yes—
495C23×C4C23×C3111yescharacteristic
496C2×C4⋊C4—24no—
497C2×C4⋊C4—41no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4D4×C3114yescomplemented
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
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—42no—
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⋊C4D4×C3118yescomplemented
525C2×C42—22no—
526C2×C42—41no—
527C2×C42—41no—
528#95—24no—
529#95—24no—
530#95—24no—
531#95—22no—
532#95—42no—
533#95—41no—
534C31#1655111yescharacteristic, direct product factor, Sylow
535C24—22no—
536C24—22no—
537C24—22no—
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—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24C2×D4×C3114yes—
564C24C2×D4×C3114yes—
565C24C24×C3111yescharacteristic
566C2×D4—28no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—48no—
572C2×D4—48no—
573C2×D4—48no—
574C2×D4—44no—
575C2×D4—44no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—48no—
579C2×D4—44no—
580C2×D4—48no—
581C2×D4—48no—
582C2×D4—44no—
583C2×D4—48no—
584C2×D4—48no—
585C2×D4—48no—
586C2×D4—48no—
587C2×D4—48no—
588C2×D4—48no—
589C2×D4—44no—
590C2×D4—48no—
591C2×D4—48no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
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—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4C2×D4×C3114yes—
630C22×C4C2×D4×C3112yes—
631C22×C4C2×D4×C3114yes—
632C22×C4C2×D4×C3112yes—
633C22×C4C2×D4×C3112yes—
634C22×C4C2×D4×C3112yes—
635C22×C4#41×C3114yes—
636C22×C4#41×C3112yes—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C42—44no—
648C23—24no—
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—42no—
663C23—42no—
664C23—42no—
665C23—42no—
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—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23C22×D4×C3111yescharacteristic
719C23C22×D4×C3111yescharacteristic
720C23C22×D4×C3112yes—
721C23C2×#41×C3111yescharacteristic
722C23C2×#41×C3112yes—
723C23C31×H(5,𝔽2)11yescharacteristic
724C23C31×H(5,𝔽2)11yescharacteristic
725C23C31×H(5,𝔽2)11yescharacteristic
726C23C31×H(5,𝔽2)11yescharacteristic
727C23C31×H(5,𝔽2)12yes—
728C23C31×H(5,𝔽2)12yes—
729D4—416no—
730D4—416no—
731D4—432no—
732D4—432no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
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—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4C31×#12114yes—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22C2×C31×#12111yescharacteristic
809C22C31×#53212yes—
810C22C31×#53411yescharacteristic
811C22C31×#53411yescharacteristic
812C22C31×#53411yescharacteristic
813C22C31×#53412yes—
814C22C31×#53511yescharacteristic
815C22C31×#53512yes—
816C22C31×#53811yescharacteristic
817C22C31×#53811yescharacteristic
818C22C31×#53812yes—
819C22C31×#54012yes—
820C22C31×#54012yes—
821C22D42×C3112yes—
822C22D42×C3111yescharacteristic
823C22D42×C3112yes—
824C22C31×#54612yes—
825C22C31×#54612yes—
826C22C31×#55012yes—
827C22C31×#55511yescharacteristic
828C22C31×#56011yescharacteristic
829C22C31×#56012yes—
830C22C31×H(3,𝔽4)11yescharacteristic
831C4—24no—
832C4—42no—
833C4—42no—
834C4—44no—
835C4—44no—
836C4—44no—
837C4—82no—
838C2—84no—
839C2—84no—
840C2C31×#242812yes—
841C2C31×#255511yescharacteristic
842C2C31×#261711yescharacteristic
843C2C31×#266112yes—
844C2C31×#266911yescharacteristic
845C2C31×#267312yes—
846C2C31×#267812yes—
847C2C31×#267911yescharacteristic
848C2C31×#269911yescharacteristic
849C2C31×#273311yescharacteristic
850C2C31×#282811yescharacteristic
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. C2×C31×#394C2semidirect
2. C2×C31×#394C2semidirect
3. C2×C31×#392C2semidirect
4. C2×C31×#392C2semidirect
5. C2×C31×#390C2semidirect
6. C31×#1441C2semidirect
7. C31×#1440C2semidirect
8. C31×#1438C2semidirect
9. C31×#1437C2semidirect
63. C22×D4×C31D4semidirect
75. C2×C4⋊C4×C31D4semidirect
99. C2×C22⋊C4×C31D4semidirect
222. #16551C31direct (N × H)
353. C2×#394C2×C31semidirect
354. C2×#394C2×C31semidirect
355. C2×#392C2×C31semidirect
356. C2×#392C2×C31semidirect
357. C2×#390C2×C31semidirect
358. #1441C2×C31semidirect
359. #1440C2×C31semidirect
360. #1438C2×C31semidirect
361. #1437C2×C31semidirect
488. C22×D4D4×C31semidirect
500. C2×C4⋊C4D4×C31semidirect
524. C2×C22⋊C4D4×C31semidirect
534. C31#16551direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3942
C2×C31×#3922
C2×C31×#3902
C31×#14412
C31×#14402
C31×#14382
C31×#14372
#1655131