Finite Group Databasebeta

← C31×#14417 #21471176

Subgroups — C31×#14417 #21471176

Order 7936.

2602 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic
2C2×C31×#386C212yesmaximal, complemented
3C2×C31×#386C212yesmaximal, complemented
4C31×#1445C212yesmaximal, complemented
5C31×#1440C212yesmaximal, complemented
6C31×#1438C212yesmaximal, complemented
7C31×C22⋊#95C211yesmaximal, characteristic, complemented
8C31×C22⋊#95C212yesmaximal, complemented
9C31×C22⋊#95C211yesmaximal, characteristic, complemented
10C23×D4×C31C2212yes—
11C23×D4×C31C2211yescharacteristic
12C24×C4×C31C2212yes—
13C24×C4×C31C2211yescharacteristic
14C2×C31×#121—28no—
15C2×C31×#121C418yescomplemented
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2211yescharacteristic
24C31×#386—28no—
25C31×#386—28no—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
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—41no—
42C22×D4×C31—42no—
43C22×D4×C31—41no—
44C22×D4×C31—42no—
45C22×D4×C31—42no—
46C22×D4×C31C2×C414yes—
47C22×D4×C31C2×C418yescomplemented
48C22×D4×C31D418yes—
49C23×C4×C31—24no—
50C23×C4×C31—24no—
51C23×C4×C31—24no—
52C23×C4×C31—24no—
53C23×C4×C31—41no—
54C23×C4×C31—41no—
55C23×C4×C31—42no—
56C23×C4×C31—42no—
57C23×C4×C31—42no—
58C23×C4×C31—42no—
59C23×C4×C31—42no—
60C23×C4×C31C2×C414yescomplemented
61C23×C4×C31C2312yes—
62C23×C4×C31C2312yes—
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2312yes—
65C23×C4×C31C2312yes—
66C23×C4×C31C2312yes—
67C23×C4×C31C2311yescharacteristic
68C31×#121—232no—
69C2×C4⋊C4×C31—24no—
70C2×C4⋊C4×C31C2×C414yescomplemented
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—24no—
77C2×C22⋊C4×C31—22no—
78C2×C22⋊C4×C31—24no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—24no—
81C2×C22⋊C4×C31—41no—
82C2×C22⋊C4×C31—41no—
83C2×C22⋊C4×C31—42no—
84C2×C22⋊C4×C31—42no—
85C2×C22⋊C4×C31—42no—
86C2×C22⋊C4×C31—42no—
87C2×C22⋊C4×C31—42no—
88C2×C22⋊C4×C31—41no—
89C2×C22⋊C4×C31—41no—
90C2×C22⋊C4×C31C2×C418yescomplemented
91C2×C22⋊C4×C31D414yescomplemented
92C31×#95—24no—
93C31×#95—24no—
94C31×#95—24no—
95C31×#95—24no—
96C31×#95—41no—
97C31×#95—42no—
98C31×#95—42no—
99C31×#95—41no—
100C31×#95—42no—
101C24×C31—22no—
102C24×C31—22no—
103C24×C31—22no—
104C24×C31—22no—
105C24×C31—22no—
106C24×C31—22no—
107C24×C31—21no—
108C24×C31—21no—
109C24×C31—21no—
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—21no—
120C24×C31—22no—
121C24×C31C22×C414yes—
122C24×C31C22×C412yes—
123C24×C31C2×D414yes—
124C24×C31C2×D414yes—
125C24×C31C2×D412yes—
126C24×C31#4112yes—
127C24×C31C2411yescharacteristic
128C2×D4×C31—216no—
129C2×D4×C31—216no—
130C2×D4×C31—44no—
131C2×D4×C31—44no—
132C2×D4×C31—48no—
133C2×D4×C31—48no—
134C2×D4×C31—48no—
135C2×D4×C31—48no—
136C2×D4×C31—48no—
137C2×D4×C31—48no—
138C2×D4×C31—48no—
139C2×D4×C31C22⋊C4116yescomplemented
140C22×C4×C31—21no—
141C22×C4×C31—21no—
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—21no—
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—22no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—28no—
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—22no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—44no—
181C22×C4×C31—44no—
182C22×C4×C31—48no—
183C22×C4×C31—48no—
184C22×C4×C31—48no—
185C22×C4×C31—48no—
186C22×C4×C31—48no—
187C22×C4×C31—48no—
188C22×C4×C31—48no—
189C22×C4×C31—48no—
190C22×C4×C31—48no—
191C22×C4×C31C22×C412yes—
192C22×C4×C31C22×C414yes—
193C22×C4×C31C22×C412yes—
194C22×C4×C31C2×D414yes—
195C22×C4×C31C2×D414yes—
196C22×C4×C31#4114yes—
197C4⋊C4×C31—28no—
198C22⋊C4×C31—216no—
199C22⋊C4×C31—44no—
200C22⋊C4×C31—48no—
201C22⋊C4×C31—48no—
202C22⋊C4×C31—48no—
203C22⋊C4×C31—48no—
204C22⋊C4×C31—44no—
205#14417C3111yesmaximal, characteristic, direct product factor, Sylow
206C23×C31—22no—
207C23×C31—24no—
208C23×C31—24no—
209C23×C31—22no—
210C23×C31—22no—
211C23×C31—22no—
212C23×C31—22no—
213C23×C31—24no—
214C23×C31—24no—
215C23×C31—24no—
216C23×C31—22no—
217C23×C31—24no—
218C23×C31—24no—
219C23×C31—22no—
220C23×C31—24no—
221C23×C31—24no—
222C23×C31—24no—
223C23×C31—22no—
224C23×C31—22no—
225C23×C31—22no—
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—24no—
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×C31C2×C22⋊C418yes—
263C23×C31C4×D414yes—
264C23×C31C23×C411yescharacteristic
265C23×C31C22×D412yes—
266C23×C31C22×D411yescharacteristic
267C23×C31C2×#4111yescharacteristic
268C23×C31C2×#4112yes—
269C23×C31H(5,𝔽2)11yescharacteristic
270C23×C31H(5,𝔽2)11yescharacteristic
271C23×C31H(5,𝔽2)12yes—
272C23×C31H(5,𝔽2)12yes—
273C23×C31H(5,𝔽2)11yescharacteristic
274C23×C312−1+411yescharacteristic
275D4×C31—416no—
276D4×C31—432no—
277C2×C4×C31—22no—
278C2×C4×C31—22no—
279C2×C4×C31—24no—
280C2×C4×C31—24no—
281C2×C4×C31—22no—
282C2×C4×C31—24no—
283C2×C4×C31—24no—
284C2×C4×C31—22no—
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—416no—
294C2×C4×C31—432no—
295C2×C4×C31—42no—
296C2×C4×C31—42no—
297C2×C4×C31—42no—
298C2×C4×C31—42no—
299C2×C4×C31—42no—
300C2×C4×C31—42no—
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—42no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31—42no—
322C2×C4×C31—42no—
323C2×C4×C31C2×C22⋊C414yes—
324C22×#121C2×C3111yescharacteristic
325C2×#386C2×C3112yescomplemented
326C2×#386C2×C3112yescomplemented
327#1445C2×C3112yescomplemented
328#1440C2×C3112yescomplemented
329#1438C2×C3112yescomplemented
330C22⋊#95C2×C3111yescharacteristic, complemented
331C22⋊#95C2×C3112yescomplemented
332C22⋊#95C2×C3111yescharacteristic, complemented
333C22×C31—28no—
334C22×C31—24no—
335C22×C31—24no—
336C22×C31—28no—
337C22×C31—28no—
338C22×C31—24no—
339C22×C31—42no—
340C22×C31—44no—
341C22×C31—42no—
342C22×C31—44no—
343C22×C31—42no—
344C22×C31—44no—
345C22×C31—42no—
346C22×C31—44no—
347C22×C31—44no—
348C22×C31—44no—
349C22×C31—44no—
350C22×C31—44no—
351C22×C31—44no—
352C22×C31—44no—
353C22×C31—44no—
354C22×C31—44no—
355C22×C31—44no—
356C22×C31—44no—
357C22×C31—44no—
358C22×C31—44no—
359C22×C31C22×C22⋊C411yescharacteristic
360C22×C31C2×C4×D411yescharacteristic
361C22×C31C4×#4111yescharacteristic
362C22×C31#51811yescharacteristic
363C22×C31#51811yescharacteristic
364C22×C31#51811yescharacteristic
365C22×C31#52011yescharacteristic
366C22×C31#53412yes—
367C22×C31#53412yes—
368C22×C31#53411yescharacteristic
369C22×C31#53711yescharacteristic
370C22×C31#53811yescharacteristic
371C22×C31#53812yes—
372C22×C31#53911yescharacteristic
373C22×C31#54012yes—
374C22×C31D4212yes—
375C22×C31#54612yes—
376C22×C31#54612yes—
377C22×C31#54612yes—
378C22×C31#54712yes—
379C22×C31#55312yes—
380C22×C31#56012yes—
381C22×C31#56212yes—
382C4×C31—24no—
383C4×C31—42no—
384C4×C31—44no—
385C4×C31—44no—
386C4×C31—44no—
387C4×C31—82no—
388C4×C31—82no—
389C23×D4C22×C3112yes—
390C23×D4C22×C3111yescharacteristic
391C24×C4C22×C3112yes—
392C24×C4C22×C3111yescharacteristic
393C2×#121—28no—
394C2×#121C4×C3118yescomplemented
395C22×C4⋊C4C22×C3111yescharacteristic
396C22×C22⋊C4C22×C3112yes—
397C22×C22⋊C4C22×C3112yes—
398C22×C22⋊C4C22×C3112yes—
399C22×C22⋊C4C22×C3112yes—
400C22×C22⋊C4C22×C3111yescharacteristic
401C22×C22⋊C4C22×C3112yes—
402C22×C22⋊C4C22×C3111yescharacteristic
403#386—28no—
404#386—28no—
405C2×#95C22×C3112yes—
406C2×#95C22×C3112yes—
407C2×#95C22×C3112yes—
408C2×#95C22×C3112yes—
409C2×#95C22×C3111yescharacteristic
410C2×#95C22×C3112yes—
411C2×#95C22×C3112yes—
412C2×#95C22×C3111yescharacteristic
413C2×#95C22×C3112yes—
414C2×C31—48no—
415C2×C31—44no—
416C2×C31#230811yescharacteristic
417C2×C31#232511yescharacteristic
418C2×C31#233311yescharacteristic
419C2×C31D4×C22⋊C411yescharacteristic
420C2×C31#233911yescharacteristic
421C2×C31#236411yescharacteristic
422C2×C31#237711yescharacteristic
423C2×C31#266812yes—
424C2×C31#267112yes—
425C2×C31#268812yes—
426C2×C31#270812yes—
427C25C23×C3112yes—
428C25C23×C3111yescharacteristic
429C22×D4—24no—
430C22×D4—24no—
431C22×D4—24no—
432C22×D4—24no—
433C22×D4—41no—
434C22×D4—42no—
435C22×D4—41no—
436C22×D4—42no—
437C22×D4—42no—
438C22×D4C2×C4×C3114yes—
439C22×D4C2×C4×C3118yescomplemented
440C22×D4D4×C3118yes—
441C23×C4—24no—
442C23×C4—24no—
443C23×C4—24no—
444C23×C4—24no—
445C23×C4—41no—
446C23×C4—41no—
447C23×C4—42no—
448C23×C4—42no—
449C23×C4—42no—
450C23×C4—42no—
451C23×C4—42no—
452C23×C4C2×C4×C3114yescomplemented
453C23×C4C23×C3112yes—
454C23×C4C23×C3112yes—
455C23×C4C23×C3111yescharacteristic
456C23×C4C23×C3112yes—
457C23×C4C23×C3112yes—
458C23×C4C23×C3112yes—
459C23×C4C23×C3111yescharacteristic
460#121—232no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4C2×C4×C3114yescomplemented
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—41no—
474C2×C22⋊C4—41no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—41no—
481C2×C22⋊C4—41no—
482C2×C22⋊C4C2×C4×C3118yescomplemented
483C2×C22⋊C4D4×C3114yescomplemented
484#95—24no—
485#95—24no—
486#95—24no—
487#95—24no—
488#95—41no—
489#95—42no—
490#95—42no—
491#95—41no—
492#95—42no—
493C31#1441711yescharacteristic, direct product factor, Sylow
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—21no—
513C24—22no—
514C24C22×C4×C3114yes—
515C24C22×C4×C3112yes—
516C24C2×D4×C3114yes—
517C24C2×D4×C3114yes—
518C24C2×D4×C3112yes—
519C24#41×C3112yes—
520C24C24×C3111yescharacteristic
521C2×D4—216no—
522C2×D4—216no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—48no—
526C2×D4—48no—
527C2×D4—48no—
528C2×D4—48no—
529C2×D4—48no—
530C2×D4—48no—
531C2×D4—48no—
532C2×D4C22⋊C4×C31116yescomplemented
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—28no—
559C22×C4—22no—
560C22×C4—22no—
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—22no—
572C22×C4—22no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4C22×C4×C3112yes—
585C22×C4C22×C4×C3114yes—
586C22×C4C22×C4×C3112yes—
587C22×C4C2×D4×C3114yes—
588C22×C4C2×D4×C3114yes—
589C22×C4#41×C3114yes—
590C4⋊C4—28no—
591C22⋊C4—216no—
592C22⋊C4—44no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—44no—
598C23—22no—
599C23—24no—
600C23—24no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
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—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23C2×C22⋊C4×C3118yes—
655C23C4×D4×C3114yes—
656C23C23×C4×C3111yescharacteristic
657C23C22×D4×C3112yes—
658C23C22×D4×C3111yescharacteristic
659C23C2×#41×C3111yescharacteristic
660C23C2×#41×C3112yes—
661C23C31×H(5,𝔽2)11yescharacteristic
662C23C31×H(5,𝔽2)11yescharacteristic
663C23C31×H(5,𝔽2)12yes—
664C23C31×H(5,𝔽2)12yes—
665C23C31×H(5,𝔽2)11yescharacteristic
666C23C31×2−1+411yescharacteristic
667D4—416no—
668D4—432no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—416no—
686C2×C4—432no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
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—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4C2×C22⋊C4×C3114yes—
716C22—28no—
717C22—24no—
718C22—24no—
719C22—28no—
720C22—28no—
721C22—24no—
722C22—42no—
723C22—44no—
724C22—42no—
725C22—44no—
726C22—42no—
727C22—44no—
728C22—42no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—44no—
735C22—44no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22C22×C22⋊C4×C3111yescharacteristic
743C22C2×C4×D4×C3111yescharacteristic
744C22C4×#41×C3111yescharacteristic
745C22C31×#51811yescharacteristic
746C22C31×#51811yescharacteristic
747C22C31×#51811yescharacteristic
748C22C31×#52011yescharacteristic
749C22C31×#53412yes—
750C22C31×#53412yes—
751C22C31×#53411yescharacteristic
752C22C31×#53711yescharacteristic
753C22C31×#53811yescharacteristic
754C22C31×#53812yes—
755C22C31×#53911yescharacteristic
756C22C31×#54012yes—
757C22D42×C3112yes—
758C22C31×#54612yes—
759C22C31×#54612yes—
760C22C31×#54612yes—
761C22C31×#54712yes—
762C22C31×#55312yes—
763C22C31×#56012yes—
764C22C31×#56212yes—
765C4—24no—
766C4—42no—
767C4—44no—
768C4—44no—
769C4—44no—
770C4—82no—
771C4—82no—
772C2—48no—
773C2—44no—
774C2C31×#230811yescharacteristic
775C2C31×#232511yescharacteristic
776C2C31×#233311yescharacteristic
777C2D4×C22⋊C4×C3111yescharacteristic
778C2C31×#233911yescharacteristic
779C2C31×#236411yescharacteristic
780C2C31×#237711yescharacteristic
781C2C31×#266812yes—
782C2C31×#267112yes—
783C2C31×#268812yes—
784C2C31×#270812yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC22×C31×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#386C2semidirect
3. C2×C31×#386C2semidirect
4. C31×#1445C2semidirect
5. C31×#1440C2semidirect
6. C31×#1438C2semidirect
7. C31×C22⋊#95C2semidirect
8. C31×C22⋊#95C2semidirect
9. C31×C22⋊#95C2semidirect
15. C2×C31×#121C4semidirect
47. C22×D4×C31C2×C4semidirect
60. C23×C4×C31C2×C4semidirect
70. C2×C4⋊C4×C31C2×C4semidirect
90. C2×C22⋊C4×C31C2×C4semidirect
91. C2×C22⋊C4×C31D4semidirect
139. C2×D4×C31C22⋊C4semidirect
205. #14417C31direct (N × H)
325. C2×#386C2×C31semidirect
326. C2×#386C2×C31semidirect
327. #1445C2×C31semidirect
328. #1440C2×C31semidirect
329. #1438C2×C31semidirect
330. C22⋊#95C2×C31semidirect
331. C22⋊#95C2×C31semidirect
332. C22⋊#95C2×C31semidirect
394. C2×#121C4×C31semidirect
439. C22×D4C2×C4×C31semidirect
452. C23×C4C2×C4×C31semidirect
462. C2×C4⋊C4C2×C4×C31semidirect
482. C2×C22⋊C4C2×C4×C31semidirect
483. C2×C22⋊C4D4×C31semidirect
493. C31#14417direct (N × H)
532. C2×D4C22⋊C4×C31semidirect

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×#3862
C31×#14452
C31×#14402
C31×#14382
C31×C22⋊#952
#1441731