Finite Group Databasebeta

← C31×#14521 #21471280

Subgroups — C31×#14521 #21471280

Order 7936.

2282 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#392C211yesmaximal, characteristic
2C2×C31×#390C212yesmaximal, complemented
3C2×C31×#388C212yesmaximal, complemented
4C2×C31×#386C212yesmaximal, complemented
5C31×#1439C211yesmaximal, characteristic, complemented
6C31×#1439C212yesmaximal, complemented
7C31×#1438C212yesmaximal, complemented
8C31×#1436C212yesmaximal, complemented
9C31×C22⋊#95C211yesmaximal, characteristic, complemented
10C23×D4×C31C2212yes—
11C23×D4×C31C2211yescharacteristic
12C24×C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2212yes—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C42×C31C2212yes—
24C31×#392C418yescomplemented
25C31×#390—28no—
26C31×#388—28no—
27C31×#386—28no—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2212yes—
35C25×C31C2312yes—
36C25×C31C2311yescharacteristic
37C22×D4×C31—24no—
38C22×D4×C31—24no—
39C22×D4×C31—24no—
40C22×D4×C31—24no—
41C22×D4×C31—42no—
42C22×D4×C31—42no—
43C22×D4×C31—42no—
44C22×D4×C31—42no—
45C22×D4×C31—41no—
46C22×D4×C31—41no—
47C22×D4×C31C2×C418yes—
48C22×D4×C31C2×C414yescomplemented
49C23×C4×C31—22no—
50C23×C4×C31—24no—
51C23×C4×C31—42no—
52C23×C4×C31—41no—
53C23×C4×C31—41no—
54C23×C4×C31C2312yes—
55C23×C4×C31C2311yescharacteristic
56C23×C4×C31C2311yescharacteristic
57C23×C4×C31C2312yes—
58C23×C4×C31C2312yes—
59C23×C4×C31C2312yes—
60C23×C4×C31C2312yes—
61C2×C4⋊C4×C31—24no—
62C2×C4⋊C4×C31—24no—
63C2×C4⋊C4×C31—24no—
64C2×C4⋊C4×C31—42no—
65C2×C4⋊C4×C31—41no—
66C2×C22⋊C4×C31—24no—
67C2×C22⋊C4×C31—24no—
68C2×C22⋊C4×C31—24no—
69C2×C22⋊C4×C31—24no—
70C2×C22⋊C4×C31—24no—
71C2×C22⋊C4×C31—24no—
72C2×C22⋊C4×C31—24no—
73C2×C22⋊C4×C31—24no—
74C2×C22⋊C4×C31—24no—
75C2×C22⋊C4×C31—24no—
76C2×C22⋊C4×C31—41no—
77C2×C22⋊C4×C31—41no—
78C2×C22⋊C4×C31—41no—
79C2×C22⋊C4×C31—41no—
80C2×C22⋊C4×C31—42no—
81C2×C22⋊C4×C31—42no—
82C2×C22⋊C4×C31—42no—
83C2×C22⋊C4×C31—42no—
84C2×C22⋊C4×C31—42no—
85C2×C22⋊C4×C31—42no—
86C2×C22⋊C4×C31—42no—
87C2×C22⋊C4×C31C2×C414yes—
88C2×C22⋊C4×C31C2×C418yescomplemented
89C2×C22⋊C4×C31D414yescomplemented
90C2×C42×C31—24no—
91C2×C42×C31—24no—
92C2×C42×C31—42no—
93C31×#95—24no—
94C31×#95—24no—
95C31×#95—42no—
96C31×#95—41no—
97C31×#95—42no—
98C31×#95C2×C414yescomplemented
99C31×#95D418yescomplemented
100C24×C31—22no—
101C24×C31—22no—
102C24×C31—21no—
103C24×C31—21no—
104C24×C31—21no—
105C24×C31—22no—
106C24×C31—22no—
107C24×C31—21no—
108C24×C31—22no—
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×C31C22×C414yes—
123C24×C31C22×C412yes—
124C24×C31C2×D412yes—
125C24×C31#4112yes—
126C24×C31C2411yescharacteristic
127C2×D4×C31—216no—
128C2×D4×C31—216no—
129C2×D4×C31—48no—
130C2×D4×C31—44no—
131C2×D4×C31—48no—
132C2×D4×C31—48no—
133C2×D4×C31—48no—
134C2×D4×C31—48no—
135C2×D4×C31—48no—
136C2×D4×C31—48no—
137C2×D4×C31—44no—
138C2×D4×C31—44no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—21no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31—22no—
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—21no—
167C22×C4×C31—21no—
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—44no—
177C22×C4×C31—48no—
178C22×C4×C31—48no—
179C22×C4×C31—44no—
180C22×C4×C31—44no—
181C22×C4×C31C22×C412yes—
182C22×C4×C31C22×C412yes—
183C22×C4×C31C22×C414yes—
184C22×C4×C31C2×D414yes—
185C22×C4×C31C2×D414yes—
186C22×C4×C31C2×D414yes—
187C22×C4×C31C2×D414yes—
188C22×C4×C31#4114yes—
189C4⋊C4×C31—48no—
190C4⋊C4×C31—44no—
191C22⋊C4×C31—216no—
192C22⋊C4×C31—44no—
193C22⋊C4×C31—44no—
194C22⋊C4×C31—48no—
195C22⋊C4×C31—48no—
196C22⋊C4×C31—48no—
197C22⋊C4×C31—48no—
198C22⋊C4×C31—48no—
199C42×C31—48no—
200#14521C3111yesmaximal, characteristic, direct product factor, Sylow
201C23×C31—24no—
202C23×C31—22no—
203C23×C31—24no—
204C23×C31—22no—
205C23×C31—22no—
206C23×C31—22no—
207C23×C31—22no—
208C23×C31—22no—
209C23×C31—24no—
210C23×C31—24no—
211C23×C31—24no—
212C23×C31—24no—
213C23×C31—24no—
214C23×C31—24no—
215C23×C31—24no—
216C23×C31—24no—
217C23×C31—24no—
218C23×C31—24no—
219C23×C31—24no—
220C23×C31—42no—
221C23×C31—42no—
222C23×C31—42no—
223C23×C31—42no—
224C23×C31—41no—
225C23×C31—42no—
226C23×C31—41no—
227C23×C31—42no—
228C23×C31—41no—
229C23×C31—41no—
230C23×C31—42no—
231C23×C31—42no—
232C23×C31—42no—
233C23×C31—42no—
234C23×C31—42no—
235C23×C31—42no—
236C23×C31—42no—
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×C31C4×D414yes—
259C23×C31C23×C411yescharacteristic
260C23×C31C22×D411yescharacteristic
261C23×C31C22×D412yes—
262C23×C31C2×#4111yescharacteristic
263C23×C31C2×#4112yes—
264C23×C31H(5,𝔽2)11yescharacteristic
265C23×C31H(5,𝔽2)12yes—
266C23×C31H(5,𝔽2)11yescharacteristic
267C23×C31H(5,𝔽2)12yes—
268C23×C31H(5,𝔽2)11yescharacteristic
269C23×C312−1+411yescharacteristic
270D4×C31—432no—
271D4×C31—416no—
272C2×C4×C31—24no—
273C2×C4×C31—24no—
274C2×C4×C31—24no—
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—24no—
282C2×C4×C31—24no—
283C2×C4×C31—24no—
284C2×C4×C31—24no—
285C2×C4×C31—24no—
286C2×C4×C31—24no—
287C2×C4×C31—24no—
288C2×C4×C31—24no—
289C2×C4×C31—24no—
290C2×C4×C31—24no—
291C2×C4×C31—416no—
292C2×C4×C31—42no—
293C2×C4×C31—42no—
294C2×C4×C31—42no—
295C2×C4×C31—42no—
296C2×C4×C31—42no—
297C2×C4×C31—42no—
298C2×C4×C31—42no—
299C2×C4×C31—41no—
300C2×C4×C31—42no—
301C2×C4×C31—42no—
302C2×C4×C31—42no—
303C2×C4×C31—41no—
304C2×C4×C31—42no—
305C2×C4×C31—42no—
306C2×C4×C31—42no—
307C2×C4×C31—41no—
308C2×C4×C31—42no—
309C2×C4×C31—41no—
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×C31C4×D418yes—
318C2×#392C2×C3111yescharacteristic
319C2×#390C2×C3112yescomplemented
320C2×#388C2×C3112yescomplemented
321C2×#386C2×C3112yescomplemented
322#1439C2×C3111yescharacteristic, complemented
323#1439C2×C3112yescomplemented
324#1438C2×C3112yescomplemented
325#1436C2×C3112yescomplemented
326C22⋊#95C2×C3111yescharacteristic, complemented
327C22×C31—24no—
328C22×C31—28no—
329C22×C31—44no—
330C22×C31—42no—
331C22×C31—42no—
332C22×C31—42no—
333C22×C31—44no—
334C22×C31—42no—
335C22×C31—44no—
336C22×C31—42no—
337C22×C31—42no—
338C22×C31—44no—
339C22×C31—44no—
340C22×C31—44no—
341C22×C31—44no—
342C22×C31—44no—
343C22×C31—44no—
344C22×C31—44no—
345C22×C31—82no—
346C22×C31—82no—
347C22×C31—82no—
348C22×C31—82no—
349C22×C31—82no—
350C22×C31—82no—
351C22×C31—82no—
352C22×C31—82no—
353C22×C31C2×C4×D412yes—
354C22×C31C2×C4×D411yescharacteristic
355C22×C31#51812yes—
356C22×C31#51811yescharacteristic
357C22×C31#52011yescharacteristic
358C22×C31#53411yescharacteristic
359C22×C31#53512yes—
360C22×C31#53712yes—
361C22×C31#53711yescharacteristic
362C22×C31#53811yescharacteristic
363C22×C31#53911yescharacteristic
364C22×C31#54012yes—
365C22×C31#54212yes—
366C22×C31D4212yes—
367C22×C31D4211yescharacteristic
368C22×C31#54612yes—
369C22×C31#54612yes—
370C22×C31#55012yes—
371C22×C31#55112yes—
372C22×C31#55911yescharacteristic
373C22×C31#56012yes—
374C22×C31#56011yescharacteristic
375C22×C31H(3,𝔽4)11yescharacteristic
376C4×C31—28no—
377C4×C31—42no—
378C4×C31—42no—
379C4×C31—44no—
380C4×C31—44no—
381C4×C31—44no—
382C4×C31—82no—
383C23×D4C22×C3112yes—
384C23×D4C22×C3111yescharacteristic
385C24×C4C22×C3111yescharacteristic
386C22×C4⋊C4C22×C3112yes—
387C22×C4⋊C4C22×C3111yescharacteristic
388C22×C22⋊C4C22×C3112yes—
389C22×C22⋊C4C22×C3112yes—
390C22×C22⋊C4C22×C3112yes—
391C22×C22⋊C4C22×C3112yes—
392C22×C22⋊C4C22×C3112yes—
393C22×C22⋊C4C22×C3112yes—
394C22×C22⋊C4C22×C3111yescharacteristic
395C22×C22⋊C4C22×C3111yescharacteristic
396C22×C42C22×C3112yes—
397#392C4×C3118yescomplemented
398#390—28no—
399#388—28no—
400#386—28no—
401C2×#95C22×C3112yes—
402C2×#95C22×C3112yes—
403C2×#95C22×C3112yes—
404C2×#95C22×C3112yes—
405C2×#95C22×C3111yescharacteristic
406C2×#95C22×C3111yescharacteristic
407C2×#95C22×C3112yes—
408C2×C31—44no—
409C2×C31—84no—
410C2×C31#232412yes—
411C2×C31#232511yescharacteristic
412C2×C31#235812yes—
413C2×C31#236611yescharacteristic
414C2×C31#237511yescharacteristic
415C2×C31#267011yescharacteristic
416C2×C31#267312yes—
417C2×C31#267511yescharacteristic
418C2×C31#270512yes—
419C2×C31#271211yescharacteristic
420C2×C31#275211yescharacteristic
421C25C23×C3112yes—
422C25C23×C3111yescharacteristic
423C22×D4—24no—
424C22×D4—24no—
425C22×D4—24no—
426C22×D4—24no—
427C22×D4—42no—
428C22×D4—42no—
429C22×D4—42no—
430C22×D4—42no—
431C22×D4—41no—
432C22×D4—41no—
433C22×D4C2×C4×C3118yes—
434C22×D4C2×C4×C3114yescomplemented
435C23×C4—22no—
436C23×C4—24no—
437C23×C4—42no—
438C23×C4—41no—
439C23×C4—41no—
440C23×C4C23×C3112yes—
441C23×C4C23×C3111yescharacteristic
442C23×C4C23×C3111yescharacteristic
443C23×C4C23×C3112yes—
444C23×C4C23×C3112yes—
445C23×C4C23×C3112yes—
446C23×C4C23×C3112yes—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—41no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—41no—
463C2×C22⋊C4—41no—
464C2×C22⋊C4—41no—
465C2×C22⋊C4—41no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—42no—
471C2×C22⋊C4—42no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4C2×C4×C3114yes—
474C2×C22⋊C4C2×C4×C3118yescomplemented
475C2×C22⋊C4D4×C3114yescomplemented
476C2×C42—24no—
477C2×C42—24no—
478C2×C42—42no—
479#95—24no—
480#95—24no—
481#95—42no—
482#95—41no—
483#95—42no—
484#95C2×C4×C3114yescomplemented
485#95D4×C3118yescomplemented
486C31#1452111yescharacteristic, direct product factor, Sylow
487C24—22no—
488C24—22no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—22no—
493C24—22no—
494C24—21no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24C22×C4×C3114yes—
510C24C22×C4×C3112yes—
511C24C2×D4×C3112yes—
512C24#41×C3112yes—
513C24C24×C3111yescharacteristic
514C2×D4—216no—
515C2×D4—216no—
516C2×D4—48no—
517C2×D4—44no—
518C2×D4—48no—
519C2×D4—48no—
520C2×D4—48no—
521C2×D4—48no—
522C2×D4—48no—
523C2×D4—48no—
524C2×D4—44no—
525C2×D4—44no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—44no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4C22×C4×C3112yes—
569C22×C4C22×C4×C3112yes—
570C22×C4C22×C4×C3114yes—
571C22×C4C2×D4×C3114yes—
572C22×C4C2×D4×C3114yes—
573C22×C4C2×D4×C3114yes—
574C22×C4C2×D4×C3114yes—
575C22×C4#41×C3114yes—
576C4⋊C4—48no—
577C4⋊C4—44no—
578C22⋊C4—216no—
579C22⋊C4—44no—
580C22⋊C4—44no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C42—48no—
587C23—24no—
588C23—22no—
589C23—24no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—41no—
611C23—42no—
612C23—41no—
613C23—42no—
614C23—41no—
615C23—41no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23C4×D4×C3114yes—
645C23C23×C4×C3111yescharacteristic
646C23C22×D4×C3111yescharacteristic
647C23C22×D4×C3112yes—
648C23C2×#41×C3111yescharacteristic
649C23C2×#41×C3112yes—
650C23C31×H(5,𝔽2)11yescharacteristic
651C23C31×H(5,𝔽2)12yes—
652C23C31×H(5,𝔽2)11yescharacteristic
653C23C31×H(5,𝔽2)12yes—
654C23C31×H(5,𝔽2)11yescharacteristic
655C23C31×2−1+411yescharacteristic
656D4—432no—
657D4—416no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—416no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4C4×D4×C3118yes—
704C22—24no—
705C22—28no—
706C22—44no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—44no—
711C22—42no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—44no—
716C22—44no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—44no—
721C22—44no—
722C22—82no—
723C22—82no—
724C22—82no—
725C22—82no—
726C22—82no—
727C22—82no—
728C22—82no—
729C22—82no—
730C22C2×C4×D4×C3112yes—
731C22C2×C4×D4×C3111yescharacteristic
732C22C31×#51812yes—
733C22C31×#51811yescharacteristic
734C22C31×#52011yescharacteristic
735C22C31×#53411yescharacteristic
736C22C31×#53512yes—
737C22C31×#53712yes—
738C22C31×#53711yescharacteristic
739C22C31×#53811yescharacteristic
740C22C31×#53911yescharacteristic
741C22C31×#54012yes—
742C22C31×#54212yes—
743C22D42×C3112yes—
744C22D42×C3111yescharacteristic
745C22C31×#54612yes—
746C22C31×#54612yes—
747C22C31×#55012yes—
748C22C31×#55112yes—
749C22C31×#55911yescharacteristic
750C22C31×#56012yes—
751C22C31×#56011yescharacteristic
752C22C31×H(3,𝔽4)11yescharacteristic
753C4—28no—
754C4—42no—
755C4—42no—
756C4—44no—
757C4—44no—
758C4—44no—
759C4—82no—
760C2—44no—
761C2—84no—
762C2C31×#232412yes—
763C2C31×#232511yescharacteristic
764C2C31×#235812yes—
765C2C31×#236611yescharacteristic
766C2C31×#237511yescharacteristic
767C2C31×#267011yescharacteristic
768C2C31×#267312yes—
769C2C31×#267511yescharacteristic
770C2C31×#270512yes—
771C2C31×#271211yescharacteristic
772C2C31×#275211yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC2×C31×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#390C2semidirect
3. C2×C31×#388C2semidirect
4. C2×C31×#386C2semidirect
5. C31×#1439C2semidirect
6. C31×#1439C2semidirect
7. C31×#1438C2semidirect
8. C31×#1436C2semidirect
9. C31×C22⋊#95C2semidirect
24. C31×#392C4semidirect
48. C22×D4×C31C2×C4semidirect
88. C2×C22⋊C4×C31C2×C4semidirect
89. C2×C22⋊C4×C31D4semidirect
98. C31×#95C2×C4semidirect
99. C31×#95D4semidirect
200. #14521C31direct (N × H)
319. C2×#390C2×C31semidirect
320. C2×#388C2×C31semidirect
321. C2×#386C2×C31semidirect
322. #1439C2×C31semidirect
323. #1439C2×C31semidirect
324. #1438C2×C31semidirect
325. #1436C2×C31semidirect
326. C22⋊#95C2×C31semidirect
397. #392C4×C31semidirect
434. C22×D4C2×C4×C31semidirect
474. C2×C22⋊C4C2×C4×C31semidirect
475. C2×C22⋊C4D4×C31semidirect
484. #95C2×C4×C31semidirect
485. #95D4×C31semidirect
486. C31#14521direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3922
C2×C31×#3902
C2×C31×#3882
C2×C31×#3862
C31×#14392
C31×#14382
C31×#14362
C31×C22⋊#952
#1452131