Finite Group Databasebeta

← C31×#11004 #21467763

Subgroups — C31×#11004 #21467763

Order 7936.

1462 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#535C211yesmaximal, characteristic
2C2×C31×#421C211yesmaximal, characteristic, complemented
3C31×#2896C211yesmaximal, characteristic, complemented
4C2×C31×#418C211yesmaximal, characteristic, complemented
5C2×C31×#418C211yesmaximal, characteristic, complemented
6C2×C31×#344C211yesmaximal, characteristic, complemented
7C31×#1740C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C23×D4×C31C2211yescharacteristic
10C22×M16×C31C2211yescharacteristic
11C22×M16×C31C2211yescharacteristic
12C31×#535—22no—
13C31×#535—22no—
14C31×#535—22no—
15C31×#535C414yescomplemented
16C2×C31×#127—21no—
17C2×C31×#124—21no—
18C2×C31×#121—22no—
19C2×C31×#120—22no—
20C2×C31×#117C2211yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C31×#421—22no—
24C31×#421—22no—
25C2×C31×#104—22no—
26C31×#419—21no—
27C31×#418—22no—
28C31×#418—22no—
29C31×#418—21no—
30C31×#418—22no—
31C31×#418—22no—
32C31×#417—22no—
33C31×#416—22no—
34C2×C31×#102—22no—
35C2×C31×#102—22no—
36C31×#344—22no—
37C31×#342—22no—
38C25×C31—21no—
39C2×#41×C31—21no—
40C2×#41×C31—21no—
41C2×#41×C31—21no—
42C2×#41×C31—21no—
43C2×#41×C31—21no—
44C2×#41×C31—21no—
45C2×#41×C31—21no—
46C2×#41×C31—21no—
47C2×#41×C31—21no—
48C2×#41×C31—21no—
49C2×#41×C31C2×C412yes—
50C2×#41×C31D412yes—
51C22×Q8×C31D411yescharacteristic
52C22×D4×C31—21no—
53C22×D4×C31—24no—
54C22×D4×C31—21no—
55C22×D4×C31—21no—
56C22×D4×C31—21no—
57C22×D4×C31—21no—
58C22×D4×C31—21no—
59C22×D4×C31—21no—
60C22×D4×C31—21no—
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31C2×C412yes—
66C22×D4×C31D412yes—
67C22×D4×C31D411yescharacteristic
68C22×D4×C31D412yes—
69C23×C4×C31—21no—
70C23×C4×C31C2311yescharacteristic
71C2×M16×C31—21no—
72C2×M16×C31—21no—
73C2×M16×C31—21no—
74C2×M16×C31—21no—
75C2×M16×C31—21no—
76C2×M16×C31—21no—
77C2×M16×C31—21no—
78C2×M16×C31—21no—
79C2×M16×C31—21no—
80C2×M16×C31—21no—
81C2×M16×C31—21no—
82C2×M16×C31D412yescomplemented
83C22×C8×C31—21no—
84C22×C8×C31D412yescomplemented
85C31×#127—24no—
86C31×#127—24no—
87C31×#124—24no—
88C31×#124—24no—
89C31×#121—28no—
90C31×#121—28no—
91C31×#120—28no—
92C31×#120—28no—
93C31×#117—21no—
94C31×#117—21no—
95C31×#117—21no—
96C31×#117—21no—
97C31×#117—21no—
98C31×#117—21no—
99C31×#117—21no—
100C31×#117—21no—
101C31×#117—21no—
102C31×#117C2×C412yes—
103C31×#117D412yes—
104C31×#117D412yescomplemented
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31D412yescomplemented
108C2×C22⋊C4×C31—24no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31D412yes—
112C2×C42×C31—21no—
113C2×C42×C31—21no—
114C2×C42×C31—21no—
115C31×#104—28no—
116C31×#103—24no—
117C31×#102—28no—
118C31×#102—28no—
119C31×#102—24no—
120C24×C31—22no—
121C24×C31—21no—
122C24×C31—22no—
123C24×C31—22no—
124C24×C31—41no—
125C24×C31—41no—
126C24×C31—41no—
127C24×C31—41no—
128C24×C31—84no—
129C24×C31C2×D411yescharacteristic
130#41×C31—22no—
131#41×C31—22no—
132#41×C31—22no—
133#41×C31—22no—
134#41×C31—22no—
135#41×C31—22no—
136#41×C31—22no—
137#41×C31—22no—
138#41×C31—41no—
139#41×C31—41no—
140#41×C31—41no—
141#41×C31—41no—
142#41×C31—41no—
143#41×C31—41no—
144#41×C31—41no—
145#41×C31—41no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31C22⋊C412yes—
152C2×D4×C31—22no—
153C2×D4×C31—22no—
154C2×D4×C31—216no—
155C2×D4×C31—22no—
156C2×D4×C31—22no—
157C2×D4×C31—22no—
158C2×D4×C31—22no—
159C2×D4×C31—22no—
160C2×D4×C31—22no—
161C2×D4×C31—22no—
162C2×D4×C31—21no—
163C2×D4×C31—22no—
164C2×D4×C31—22no—
165C2×D4×C31—21no—
166C2×D4×C31—22no—
167C2×D4×C31—22no—
168C2×D4×C31—22no—
169C2×D4×C31—22no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—22no—
173C2×D4×C31—22no—
174C2×D4×C31—21no—
175C2×D4×C31—41no—
176C2×D4×C31—41no—
177C2×D4×C31—41no—
178C2×D4×C31—41no—
179C2×D4×C31—41no—
180C2×D4×C31—41no—
181C2×D4×C31—41no—
182C2×D4×C31—41no—
183C2×D4×C31—41no—
184C2×D4×C31—41no—
185C2×D4×C31—41no—
186C2×D4×C31—41no—
187C2×D4×C31—41no—
188C2×D4×C31—41no—
189C2×D4×C31—41no—
190C2×D4×C31—41no—
191C2×D4×C31—88no—
192C2×D4×C31C22⋊C414yes—
193C2×D4×C31C22⋊C412yes—
194C22×C4×C31—22no—
195C22×C4×C31—21no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—41no—
200C22×C4×C31—41no—
201C22×C4×C31—41no—
202C22×C4×C31—41no—
203C22×C4×C31—41no—
204C22×C4×C31C22×C411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31#4111yescharacteristic
215C22×C4×C31#4111yescharacteristic
216C22×C4×C31#4111yescharacteristic
217C22×C4×C31#4111yescharacteristic
218M16×C31—22no—
219M16×C31—22no—
220M16×C31—41no—
221M16×C31—41no—
222M16×C31—41no—
223M16×C31—41no—
224M16×C31—41no—
225M16×C31—41no—
226C2×C8×C31—22no—
227C2×C8×C31—22no—
228C2×C8×C31—22no—
229C2×C8×C31—22no—
230C2×C8×C31—41no—
231C2×C8×C31—41no—
232C4⋊C4×C31—22no—
233C4⋊C4×C31—22no—
234C4⋊C4×C31—22no—
235C4⋊C4×C31—22no—
236C4⋊C4×C31—22no—
237C4⋊C4×C31—41no—
238C22⋊C4×C31—216no—
239C22⋊C4×C31—22no—
240C22⋊C4×C31—22no—
241C22⋊C4×C31—41no—
242C22⋊C4×C31—41no—
243C22⋊C4×C31—41no—
244C22⋊C4×C31C22⋊C414yes—
245C42×C31—22no—
246C42×C31—22no—
247C42×C31—22no—
248C42×C31—41no—
249C42×C31—41no—
250C42×C31—41no—
251#11004C3111yesmaximal, characteristic, direct product factor, Sylow
252C23×C31—24no—
253C23×C31—22no—
254C23×C31—42no—
255C23×C31—44no—
256C23×C31—48no—
257C23×C31—42no—
258C23×C31—42no—
259C23×C31—42no—
260C23×C31—41no—
261C23×C31—42no—
262C23×C31—41no—
263C23×C31—42no—
264C23×C31—42no—
265C23×C31—84no—
266C23×C31—84no—
267C23×C31—84no—
268C23×C31—84no—
269C23×C31—84no—
270C23×C31—84no—
271C23×C31C2×C22⋊C411yescharacteristic
272C23×C31#12011yescharacteristic
273C23×C31#12011yescharacteristic
274C23×C31#12111yescharacteristic
275C23×C31#12111yescharacteristic
276C23×C31#12411yescharacteristic
277C23×C31#12711yescharacteristic
278Q8×C31—22no—
279Q8×C31—22no—
280Q8×C31—41no—
281Q8×C31—41no—
282D4×C31—24no—
283D4×C31—24no—
284D4×C31—22no—
285D4×C31—22no—
286D4×C31—42no—
287D4×C31—42no—
288D4×C31—42no—
289D4×C31—42no—
290D4×C31—42no—
291D4×C31—42no—
292D4×C31—42no—
293D4×C31—42no—
294D4×C31—41no—
295D4×C31—42no—
296D4×C31—42no—
297D4×C31—41no—
298D4×C31—816no—
299C2×C4×C31—24no—
300C2×C4×C31—22no—
301C2×C4×C31—44no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
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—82no—
311C2×C4×C31—82no—
312C2×C4×C31C2×C22⋊C411yescharacteristic
313C2×C4×C31C2×C22⋊C411yescharacteristic
314C2×C4×C31C4×D411yescharacteristic
315C2×C4×C31C4×D411yescharacteristic
316C2×C4×C31C4×D411yescharacteristic
317C2×C4×C31C4×D411yescharacteristic
318C2×C4×C31#12011yescharacteristic
319C2×C4×C31#12011yescharacteristic
320C2×C4×C31#12011yescharacteristic
321C2×C4×C31#12011yescharacteristic
322C2×C4×C31#12011yescharacteristic
323C2×C4×C31#12011yescharacteristic
324C2×C4×C31#12111yescharacteristic
325C2×C4×C31#12111yescharacteristic
326C2×C4×C31#12111yescharacteristic
327C2×C4×C31#12111yescharacteristic
328C2×C4×C31#12111yescharacteristic
329C2×C4×C31#12111yescharacteristic
330C2×C4×C31#12111yescharacteristic
331C2×C4×C31#12111yescharacteristic
332C2×C4×C31#12111yescharacteristic
333C2×C4×C31#12111yescharacteristic
334C2×C4×C31#12311yescharacteristic
335C2×C4×C31#12311yescharacteristic
336C2×C4×C31#12311yescharacteristic
337C2×C4×C31#12311yescharacteristic
338C2×C4×C31#12411yescharacteristic
339C2×C4×C31#12711yescharacteristic
340C8×C31—42no—
341C8×C31—42no—
342C2×#535C2×C3111yescharacteristic
343C2×#421C2×C3111yescharacteristic, complemented
344#2896C2×C3111yescharacteristic, complemented
345C2×#418C2×C3111yescharacteristic, complemented
346C2×#418C2×C3111yescharacteristic, complemented
347C2×#344C2×C3111yescharacteristic, complemented
348#1740C2×C3111yescharacteristic, complemented
349C22×C31—22no—
350C22×C31—22no—
351C22×C31—22no—
352C22×C31—41no—
353C22×C31—41no—
354C22×C31—41no—
355C22×C31—41no—
356C22×C31—44no—
357C22×C31—48no—
358C22×C31—42no—
359C22×C31—44no—
360C22×C31—82no—
361C22×C31—84no—
362C22×C31—84no—
363C22×C31—84no—
364C22×C31—84no—
365C22×C31—84no—
366C22×C31—82no—
367C22×C31—84no—
368C22×C31#37911yescharacteristic
369C22×C31#39011yescharacteristic
370C22×C31#39011yescharacteristic
371C22×C31#39211yescharacteristic
372C22×C31#39211yescharacteristic
373C22×C31#39411yescharacteristic
374C22×C31#39411yescharacteristic
375C4×C31—44no—
376C4×C31—42no—
377C4×C31—82no—
378C4×C31—82no—
379C4×C31#38611yescharacteristic
380C4×C31#38611yescharacteristic
381C4×C31#38611yescharacteristic
382C4×C31#38611yescharacteristic
383C4×C31#39211yescharacteristic
384C4×C31#39211yescharacteristic
385C4×C31#39411yescharacteristic
386C4×C31#39411yescharacteristic
387C22×#41C22×C3111yescharacteristic
388C23×D4C22×C3111yescharacteristic
389C22×M16C22×C3111yescharacteristic
390C22×M16C22×C3111yescharacteristic
391#535—22no—
392#535—22no—
393#535—22no—
394#535C4×C3114yescomplemented
395C2×#127—21no—
396C2×#124—21no—
397C2×#121—22no—
398C2×#120—22no—
399C2×#117C22×C3111yescharacteristic
400C2×#117C22×C3111yescharacteristic
401C2×#117C22×C3111yescharacteristic
402#421—22no—
403#421—22no—
404C2×#104—22no—
405#419—21no—
406#418—22no—
407#418—22no—
408#418—21no—
409#418—22no—
410#418—22no—
411#417—22no—
412#416—22no—
413C2×#102—22no—
414C2×#102—22no—
415#344—22no—
416#342—22no—
417C2×C31—21no—
418C2×C31—21no—
419C2×C31—21no—
420C2×C31—21no—
421C2×C31—21no—
422C2×C31—21no—
423C2×C31—82no—
424C2×C31—84no—
425C2×C31#143811yescharacteristic
426C2×C31#200812yes—
427C25—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41C2×C4×C3112yes—
439C2×#41D4×C3112yes—
440C22×Q8D4×C3111yescharacteristic
441C22×D4—21no—
442C22×D4—24no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4C2×C4×C3112yes—
455C22×D4D4×C3112yes—
456C22×D4D4×C3111yescharacteristic
457C22×D4D4×C3112yes—
458C23×C4—21no—
459C23×C4C23×C3111yescharacteristic
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16D4×C3112yescomplemented
472C22×C8—21no—
473C22×C8D4×C3112yescomplemented
474#127—24no—
475#127—24no—
476#124—24no—
477#124—24no—
478#121—28no—
479#121—28no—
480#120—28no—
481#120—28no—
482#117—21no—
483#117—21no—
484#117—21no—
485#117—21no—
486#117—21no—
487#117—21no—
488#117—21no—
489#117—21no—
490#117—21no—
491#117C2×C4×C3112yes—
492#117D4×C3112yes—
493#117D4×C3112yescomplemented
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4D4×C3112yescomplemented
497C2×C22⋊C4—24no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4D4×C3112yes—
501C2×C42—21no—
502C2×C42—21no—
503C2×C42—21no—
504#104—28no—
505#103—24no—
506#102—28no—
507#102—28no—
508#102—24no—
509C31#1100411yescharacteristic, direct product factor, Sylow
510C24—22no—
511C24—21no—
512C24—22no—
513C24—22no—
514C24—41no—
515C24—41no—
516C24—41no—
517C24—41no—
518C24—84no—
519C24C2×D4×C3111yescharacteristic
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41—22no—
525#41—22no—
526#41—22no—
527#41—22no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—41no—
532#41—41no—
533#41—41no—
534#41—41no—
535#41—41no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8C22⋊C4×C3112yes—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—216no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—88no—
582C2×D4C22⋊C4×C3114yes—
583C2×D4C22⋊C4×C3112yes—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4C22×C4×C3111yescharacteristic
595C22×C4C2×D4×C3111yescharacteristic
596C22×C4C2×D4×C3111yescharacteristic
597C22×C4C2×D4×C3111yescharacteristic
598C22×C4C2×D4×C3111yescharacteristic
599C22×C4C2×D4×C3111yescharacteristic
600C22×C4C2×D4×C3111yescharacteristic
601C22×C4C2×D4×C3111yescharacteristic
602C22×C4C2×D4×C3111yescharacteristic
603C22×C4C2×D4×C3111yescharacteristic
604C22×C4#41×C3111yescharacteristic
605C22×C4#41×C3111yescharacteristic
606C22×C4#41×C3111yescharacteristic
607C22×C4#41×C3111yescharacteristic
608M16—22no—
609M16—22no—
610M16—41no—
611M16—41no—
612M16—41no—
613M16—41no—
614M16—41no—
615M16—41no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—41no—
621C2×C8—41no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—41no—
628C22⋊C4—216no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—41no—
632C22⋊C4—41no—
633C22⋊C4—41no—
634C22⋊C4C22⋊C4×C3114yes—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—41no—
639C42—41no—
640C42—41no—
641C23—24no—
642C23—22no—
643C23—42no—
644C23—44no—
645C23—48no—
646C23—42no—
647C23—42no—
648C23—41no—
649C23—42no—
650C23—42no—
651C23—41no—
652C23—42no—
653C23—42no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23—84no—
660C23C2×C22⋊C4×C3111yescharacteristic
661C23C31×#12011yescharacteristic
662C23C31×#12011yescharacteristic
663C23C31×#12111yescharacteristic
664C23C31×#12111yescharacteristic
665C23C31×#12411yescharacteristic
666C23C31×#12711yescharacteristic
667Q8—22no—
668Q8—22no—
669Q8—41no—
670Q8—41no—
671D4—24no—
672D4—24no—
673D4—22no—
674D4—22no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—42no—
681D4—42no—
682D4—42no—
683D4—41no—
684D4—42no—
685D4—42no—
686D4—41no—
687D4—816no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—44no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4C2×C22⋊C4×C3111yescharacteristic
702C2×C4C2×C22⋊C4×C3111yescharacteristic
703C2×C4C4×D4×C3111yescharacteristic
704C2×C4C4×D4×C3111yescharacteristic
705C2×C4C4×D4×C3111yescharacteristic
706C2×C4C4×D4×C3111yescharacteristic
707C2×C4C31×#12011yescharacteristic
708C2×C4C31×#12011yescharacteristic
709C2×C4C31×#12011yescharacteristic
710C2×C4C31×#12011yescharacteristic
711C2×C4C31×#12011yescharacteristic
712C2×C4C31×#12011yescharacteristic
713C2×C4C31×#12111yescharacteristic
714C2×C4C31×#12111yescharacteristic
715C2×C4C31×#12111yescharacteristic
716C2×C4C31×#12111yescharacteristic
717C2×C4C31×#12111yescharacteristic
718C2×C4C31×#12111yescharacteristic
719C2×C4C31×#12111yescharacteristic
720C2×C4C31×#12111yescharacteristic
721C2×C4C31×#12111yescharacteristic
722C2×C4C31×#12111yescharacteristic
723C2×C4C31×#12311yescharacteristic
724C2×C4C31×#12311yescharacteristic
725C2×C4C31×#12311yescharacteristic
726C2×C4C31×#12311yescharacteristic
727C2×C4C31×#12411yescharacteristic
728C2×C4C31×#12711yescharacteristic
729C8—42no—
730C8—42no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—44no—
739C22—48no—
740C22—42no—
741C22—44no—
742C22—84no—
743C22—82no—
744C22—84no—
745C22—84no—
746C22—84no—
747C22—84no—
748C22—84no—
749C22—82no—
750C22C31×#37911yescharacteristic
751C22C31×#39011yescharacteristic
752C22C31×#39011yescharacteristic
753C22C31×#39211yescharacteristic
754C22C31×#39211yescharacteristic
755C22C31×#39411yescharacteristic
756C22C31×#39411yescharacteristic
757C4—44no—
758C4—42no—
759C4—82no—
760C4—82no—
761C4C31×#38611yescharacteristic
762C4C31×#38611yescharacteristic
763C4C31×#38611yescharacteristic
764C4C31×#38611yescharacteristic
765C4C31×#39211yescharacteristic
766C4C31×#39211yescharacteristic
767C4C31×#39411yescharacteristic
768C4C31×#39411yescharacteristic
769C2—21no—
770C2—21no—
771C2—21no—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—84no—
776C2—82no—
777C2C31×#143811yescharacteristic
778C2C31×#200812yes—
subgroupG/H
center, socleC22×C31#392
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#421C2semidirect
3. C31×#2896C2semidirect
4. C2×C31×#418C2semidirect
5. C2×C31×#418C2semidirect
6. C2×C31×#344C2semidirect
7. C31×#1740C2semidirect
15. C31×#535C4semidirect
82. C2×M16×C31D4semidirect
84. C22×C8×C31D4semidirect
104. C31×#117D4semidirect
107. C2×C4⋊C4×C31D4semidirect
251. #11004C31direct (N × H)
343. C2×#421C2×C31semidirect
344. #2896C2×C31semidirect
345. C2×#418C2×C31semidirect
346. C2×#418C2×C31semidirect
347. C2×#344C2×C31semidirect
348. #1740C2×C31semidirect
394. #535C4×C31semidirect
471. C2×M16D4×C31semidirect
473. C22×C8D4×C31semidirect
493. #117D4×C31semidirect
496. C2×C4⋊C4D4×C31semidirect
509. C31#11004direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5352
C2×C31×#4212
C31×#28962
C2×C31×#4182
C2×C31×#3442
C31×#17402
#1100431