Finite Group Databasebeta

← C31×#11017 #21467776

Subgroups — C31×#11017 #21467776

Order 7936.

1358 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#137C211yesmaximal, characteristic
2C22×C31×#104C211yesmaximal, characteristic
3C2×C31×#419C211yesmaximal, characteristic, complemented
4C31×#2311C211yesmaximal, characteristic
5C2×C31×#391C211yesmaximal, characteristic, complemented
6C2×C31×#343C211yesmaximal, characteristic, complemented
7C2×C31×#339C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C23×Q8×C31C2211yescharacteristic
10C2×C31×#137—22no—
11C2×C31×#137—22no—
12C2×C31×#137—22no—
13C2×C31×#137—22no—
14C2×C31×#137—22no—
15C2×C31×#137C414yescomplemented
16C22×Q16×C31—21no—
17C22×SD16×C31—21no—
18C22×M16×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic
20C2×C31×#117C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C42×C31C2211yescharacteristic
23C2×C31×#104—22no—
24C2×C31×#104—22no—
25C2×C31×#104—22no—
26C31×#419—22no—
27C31×#419—22no—
28C2×C31×#103—22no—
29C31×#391—21no—
30C31×#391—22no—
31C31×#391—22no—
32C31×#390—21no—
33C31×#386—22no—
34C31×#380—22no—
35C2×C31×#95—22no—
36C31×#343—22no—
37C31×#339—22no—
38C2×#41×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×C31C2×C412yes—
49C2×#41×C31D412yes—
50C22×Q8×C31—21no—
51C22×Q8×C31—21no—
52C22×Q8×C31—21no—
53C22×Q8×C31—21no—
54C22×Q8×C31—21no—
55C22×Q8×C31—21no—
56C22×Q8×C31—21no—
57C22×Q8×C31—21no—
58C22×Q8×C31—21no—
59C22×Q8×C31—21no—
60C22×Q8×C31—21no—
61C22×Q8×C31C2×C412yes—
62C22×Q8×C31D411yescharacteristic
63C22×Q8×C31D412yes—
64C22×Q8×C31D412yes—
65C22×D4×C31—21no—
66C22×D4×C31D411yescharacteristic
67C23×C4×C31—21no—
68C23×C4×C31—21no—
69C23×C4×C31—21no—
70C23×C4×C31D412yes—
71C23×C4×C31C2311yescharacteristic
72C31×#137—28no—
73C31×#137—28no—
74C31×#137—28no—
75C31×#137—28no—
76C2×Q16×C31—24no—
77C2×Q16×C31—24no—
78C2×Q16×C31—24no—
79C2×SD16×C31—24no—
80C2×SD16×C31—24no—
81C2×SD16×C31—24no—
82C2×M16×C31—21no—
83C2×M16×C31—21no—
84C2×M16×C31—21no—
85C2×M16×C31—21no—
86C2×M16×C31—21no—
87C2×M16×C31—21no—
88C2×M16×C31—21no—
89C2×M16×C31—21no—
90C2×M16×C31C2×C412yes—
91C2×M16×C31D412yes—
92C2×M16×C31D412yes—
93C2×M16×C31D412yes—
94C22×C8×C31—21no—
95C22×C8×C31—21no—
96C31×#117—21no—
97C31×#117—21no—
98C31×#117—21no—
99C31×#117—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31D412yes—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—24no—
109C2×C42×C31—21no—
110C2×C42×C31—21no—
111C2×C42×C31—21no—
112C2×C42×C31—21no—
113C2×C42×C31—21no—
114C2×C42×C31—21no—
115C2×C42×C31D412yes—
116C31×#104—28no—
117C31×#103—28no—
118C31×#95—28no—
119C31×#95—24no—
120C24×C31—21no—
121C24×C31C2×D411yescharacteristic
122#41×C31—22no—
123#41×C31—22no—
124#41×C31—22no—
125#41×C31—22no—
126#41×C31—22no—
127#41×C31—22no—
128#41×C31—22no—
129#41×C31—22no—
130#41×C31—41no—
131#41×C31—41no—
132#41×C31—41no—
133#41×C31—41no—
134#41×C31—41no—
135#41×C31—41no—
136#41×C31—41no—
137#41×C31—41no—
138C2×Q8×C31—22no—
139C2×Q8×C31—22no—
140C2×Q8×C31—22no—
141C2×Q8×C31—21no—
142C2×Q8×C31—22no—
143C2×Q8×C31—22no—
144C2×Q8×C31—22no—
145C2×Q8×C31—22no—
146C2×Q8×C31—22no—
147C2×Q8×C31—22no—
148C2×Q8×C31—22no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31—22no—
152C2×Q8×C31—22no—
153C2×Q8×C31—22no—
154C2×Q8×C31—22no—
155C2×Q8×C31—21no—
156C2×Q8×C31—21no—
157C2×Q8×C31—22no—
158C2×Q8×C31—41no—
159C2×Q8×C31—41no—
160C2×Q8×C31—41no—
161C2×Q8×C31—41no—
162C2×Q8×C31—41no—
163C2×Q8×C31—41no—
164C2×Q8×C31—41no—
165C2×Q8×C31—41no—
166C2×Q8×C31—41no—
167C2×Q8×C31—41no—
168C2×Q8×C31—41no—
169C2×Q8×C31—41no—
170C2×Q8×C31C22⋊C412yes—
171C2×Q8×C31C22⋊C414yescomplemented
172C2×D4×C31—22no—
173C2×D4×C31—22no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—41no—
180C2×D4×C31—41no—
181C2×D4×C31—41no—
182C2×D4×C31—41no—
183C2×D4×C31C22⋊C412yes—
184C22×C4×C31—24no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—21no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—42no—
197C22×C4×C31—41no—
198C22×C4×C31—41no—
199C22×C4×C31—41no—
200C22×C4×C31—41no—
201C22×C4×C31—41no—
202C22×C4×C31—41no—
203C22×C4×C31—41no—
204C22×C4×C31—41no—
205C22×C4×C31—41no—
206C22×C4×C31—41no—
207C22×C4×C31—44no—
208C22×C4×C31C22×C411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31#4111yescharacteristic
219C22×C4×C31#4111yescharacteristic
220C22×C4×C31#4111yescharacteristic
221C22×C4×C31#4111yescharacteristic
222Q16×C31—216no—
223SD16×C31—216no—
224M16×C31—22no—
225M16×C31—22no—
226M16×C31—22no—
227M16×C31—22no—
228M16×C31—22no—
229M16×C31—41no—
230M16×C31—41no—
231M16×C31C22⋊C414yescomplemented
232C2×C8×C31—22no—
233C2×C8×C31—22no—
234C2×C8×C31—22no—
235C2×C8×C31—22no—
236C2×C8×C31—41no—
237C2×C8×C31—41no—
238C4⋊C4×C31—22no—
239C4⋊C4×C31—22no—
240C4⋊C4×C31—41no—
241C4⋊C4×C31—41no—
242C4⋊C4×C31—41no—
243C4⋊C4×C31—41no—
244C22⋊C4×C31—41no—
245C22⋊C4×C31—41no—
246C22⋊C4×C31—84no—
247C42×C31—22no—
248C42×C31—22no—
249C42×C31—41no—
250C42×C31—41no—
251C42×C31—41no—
252C42×C31—41no—
253#11017C3111yesmaximal, characteristic, direct product factor, Sylow
254C23×C31—22no—
255C23×C31—22no—
256C23×C31—22no—
257C23×C31—41no—
258C23×C31—41no—
259C23×C31—42no—
260C23×C31—42no—
261C23×C31C4×D411yescharacteristic
262C23×C31#12011yescharacteristic
263C23×C31#12011yescharacteristic
264C23×C31#12111yescharacteristic
265C23×C31#12111yescharacteristic
266C23×C31#12111yescharacteristic
267C23×C31#12711yescharacteristic
268Q8×C31—24no—
269Q8×C31—22no—
270Q8×C31—24no—
271Q8×C31—22no—
272Q8×C31—42no—
273Q8×C31—42no—
274Q8×C31—42no—
275Q8×C31—42no—
276Q8×C31—42no—
277Q8×C31—42no—
278Q8×C31—41no—
279Q8×C31—41no—
280D4×C31—22no—
281D4×C31—22no—
282D4×C31—42no—
283D4×C31—42no—
284D4×C31—42no—
285D4×C31—42no—
286D4×C31—41no—
287D4×C31—41no—
288C2×C4×C31—24no—
289C2×C4×C31—22no—
290C2×C4×C31—24no—
291C2×C4×C31—44no—
292C2×C4×C31—42no—
293C2×C4×C31—44no—
294C2×C4×C31—42no—
295C2×C4×C31—42no—
296C2×C4×C31—42no—
297C2×C4×C31—41no—
298C2×C4×C31—41no—
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—44no—
308C2×C4×C31—42no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—44no—
312C2×C4×C31—42no—
313C2×C4×C31—82no—
314C2×C4×C31C2×C22⋊C411yescharacteristic
315C2×C4×C31C2×C22⋊C411yescharacteristic
316C2×C4×C31C2×C22⋊C411yescharacteristic
317C2×C4×C31C4×D411yescharacteristic
318C2×C4×C31C4×D411yescharacteristic
319C2×C4×C31C4×D411yescharacteristic
320C2×C4×C31#12011yescharacteristic
321C2×C4×C31#12011yescharacteristic
322C2×C4×C31#12011yescharacteristic
323C2×C4×C31#12011yescharacteristic
324C2×C4×C31#12011yescharacteristic
325C2×C4×C31#12011yescharacteristic
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#12111yescharacteristic
335C2×C4×C31#12311yescharacteristic
336C2×C4×C31#12311yescharacteristic
337C2×C4×C31#12311yescharacteristic
338C2×C4×C31#12311yescharacteristic
339C2×C4×C31#12411yescharacteristic
340C2×C4×C31#12411yescharacteristic
341C2×C4×C31#12711yescharacteristic
342C8×C31—24no—
343C8×C31—42no—
344C22×#137C2×C3111yescharacteristic
345C22×#104C2×C3111yescharacteristic
346C2×#419C2×C3111yescharacteristic, complemented
347#2311C2×C3111yescharacteristic
348C2×#391C2×C3111yescharacteristic, complemented
349C2×#343C2×C3111yescharacteristic, complemented
350C2×#339C2×C3111yescharacteristic, complemented
351C22×C31—22no—
352C22×C31—22no—
353C22×C31—21no—
354C22×C31—21no—
355C22×C31—21no—
356C22×C31—21no—
357C22×C31—22no—
358C22×C31—22no—
359C22×C31—44no—
360C22×C31—42no—
361C22×C31—81no—
362C22×C31—81no—
363C22×C31—82no—
364C22×C31#38611yescharacteristic
365C22×C31#38611yescharacteristic
366C22×C31#39011yescharacteristic
367C22×C31#39211yescharacteristic
368C22×C31#39211yescharacteristic
369C22×C31#39211yescharacteristic
370C22×C31#39411yescharacteristic
371C22×C31#45512yes—
372C22×C31#45612yes—
373C4×C31—44no—
374C4×C31—42no—
375C4×C31—44no—
376C4×C31—82no—
377C4×C31—82no—
378C4×C31#37911yescharacteristic
379C4×C31#38611yescharacteristic
380C4×C31#38611yescharacteristic
381C4×C31#39011yescharacteristic
382C4×C31#39211yescharacteristic
383C4×C31#39411yescharacteristic
384C4×C31#39411yescharacteristic
385C4×C31#39411yescharacteristic
386C22×#41C22×C3111yescharacteristic
387C23×Q8C22×C3111yescharacteristic
388C2×#137—22no—
389C2×#137—22no—
390C2×#137—22no—
391C2×#137—22no—
392C2×#137—22no—
393C2×#137C4×C3114yescomplemented
394C22×Q16—21no—
395C22×SD16—21no—
396C22×M16C22×C3111yescharacteristic
397C22×M16C22×C3111yescharacteristic
398C2×#117C22×C3111yescharacteristic
399C22×C4⋊C4C22×C3111yescharacteristic
400C22×C42C22×C3111yescharacteristic
401C2×#104—22no—
402C2×#104—22no—
403C2×#104—22no—
404#419—22no—
405#419—22no—
406C2×#103—22no—
407#391—21no—
408#391—22no—
409#391—22no—
410#390—21no—
411#386—22no—
412#380—22no—
413C2×#95—22no—
414#343—22no—
415#339—22no—
416C2×C31—21no—
417C2×C31—21no—
418C2×C31—21no—
419C2×C31—21no—
420C2×C31—82no—
421C2×C31#143811yescharacteristic
422C2×C31#188212yes—
423C2×C31#200411yescharacteristic
424C2×C31#200511yescharacteristic
425C2×C31#200712yes—
426C2×#41—21no—
427C2×#41—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×#41C2×C4×C3112yes—
437C2×#41D4×C3112yes—
438C22×Q8—21no—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8—21no—
446C22×Q8—21no—
447C22×Q8—21no—
448C22×Q8—21no—
449C22×Q8C2×C4×C3112yes—
450C22×Q8D4×C3111yescharacteristic
451C22×Q8D4×C3112yes—
452C22×Q8D4×C3112yes—
453C22×D4—21no—
454C22×D4D4×C3111yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—21no—
458C23×C4D4×C3112yes—
459C23×C4C23×C3111yescharacteristic
460#137—28no—
461#137—28no—
462#137—28no—
463#137—28no—
464C2×Q16—24no—
465C2×Q16—24no—
466C2×Q16—24no—
467C2×SD16—24no—
468C2×SD16—24no—
469C2×SD16—24no—
470C2×M16—21no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—21no—
475C2×M16—21no—
476C2×M16—21no—
477C2×M16—21no—
478C2×M16C2×C4×C3112yes—
479C2×M16D4×C3112yes—
480C2×M16D4×C3112yes—
481C2×M16D4×C3112yes—
482C22×C8—21no—
483C22×C8—21no—
484#117—21no—
485#117—21no—
486#117—21no—
487#117—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4D4×C3112yes—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—24no—
497C2×C42—21no—
498C2×C42—21no—
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—21no—
502C2×C42—21no—
503C2×C42D4×C3112yes—
504#104—28no—
505#103—28no—
506#95—28no—
507#95—24no—
508C31#1101711yescharacteristic, direct product factor, Sylow
509C24—21no—
510C24C2×D4×C3111yescharacteristic
511#41—22no—
512#41—22no—
513#41—22no—
514#41—22no—
515#41—22no—
516#41—22no—
517#41—22no—
518#41—22no—
519#41—41no—
520#41—41no—
521#41—41no—
522#41—41no—
523#41—41no—
524#41—41no—
525#41—41no—
526#41—41no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—21no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—41no—
548C2×Q8—41no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8C22⋊C4×C3112yes—
560C2×Q8C22⋊C4×C3114yescomplemented
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4C22⋊C4×C3112yes—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—42no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—44no—
597C22×C4C22×C4×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×C4C2×D4×C3111yescharacteristic
605C22×C4C2×D4×C3111yescharacteristic
606C22×C4C2×D4×C3111yescharacteristic
607C22×C4#41×C3111yescharacteristic
608C22×C4#41×C3111yescharacteristic
609C22×C4#41×C3111yescharacteristic
610C22×C4#41×C3111yescharacteristic
611Q16—216no—
612SD16—216no—
613M16—22no—
614M16—22no—
615M16—22no—
616M16—22no—
617M16—22no—
618M16—41no—
619M16—41no—
620M16C22⋊C4×C3114yescomplemented
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—41no—
626C2×C8—41no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—41no—
630C4⋊C4—41no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C22⋊C4—41no—
634C22⋊C4—41no—
635C22⋊C4—84no—
636C42—22no—
637C42—22no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—42no—
646C23—42no—
647C23—41no—
648C23—41no—
649C23C4×D4×C3111yescharacteristic
650C23C31×#12011yescharacteristic
651C23C31×#12011yescharacteristic
652C23C31×#12111yescharacteristic
653C23C31×#12111yescharacteristic
654C23C31×#12111yescharacteristic
655C23C31×#12711yescharacteristic
656Q8—24no—
657Q8—22no—
658Q8—24no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—42no—
666Q8—41no—
667Q8—41no—
668D4—22no—
669D4—22no—
670D4—42no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—41no—
675D4—41no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—44no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
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—44no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—82no—
702C2×C4C2×C22⋊C4×C3111yescharacteristic
703C2×C4C2×C22⋊C4×C3111yescharacteristic
704C2×C4C2×C22⋊C4×C3111yescharacteristic
705C2×C4C4×D4×C3111yescharacteristic
706C2×C4C4×D4×C3111yescharacteristic
707C2×C4C4×D4×C3111yescharacteristic
708C2×C4C31×#12011yescharacteristic
709C2×C4C31×#12011yescharacteristic
710C2×C4C31×#12011yescharacteristic
711C2×C4C31×#12011yescharacteristic
712C2×C4C31×#12011yescharacteristic
713C2×C4C31×#12011yescharacteristic
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×#12411yescharacteristic
729C2×C4C31×#12711yescharacteristic
730C8—24no—
731C8—42no—
732C22—22no—
733C22—22no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—22no—
739C22—22no—
740C22—44no—
741C22—42no—
742C22—81no—
743C22—81no—
744C22—82no—
745C22C31×#38611yescharacteristic
746C22C31×#38611yescharacteristic
747C22C31×#39011yescharacteristic
748C22C31×#39211yescharacteristic
749C22C31×#39211yescharacteristic
750C22C31×#39211yescharacteristic
751C22C31×#39411yescharacteristic
752C22C31×#45512yes—
753C22C31×#45612yes—
754C4—44no—
755C4—42no—
756C4—44no—
757C4—82no—
758C4—82no—
759C4C31×#37911yescharacteristic
760C4C31×#38611yescharacteristic
761C4C31×#38611yescharacteristic
762C4C31×#39011yescharacteristic
763C4C31×#39211yescharacteristic
764C4C31×#39411yescharacteristic
765C4C31×#39411yescharacteristic
766C4C31×#39411yescharacteristic
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—82no—
772C2C31×#143811yescharacteristic
773C2C31×#188212yes—
774C2C31×#200411yescharacteristic
775C2C31×#200511yescharacteristic
776C2C31×#200712yes—
subgroupG/H
center, socleC23×C31#120
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×#41×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#419C2semidirect
5. C2×C31×#391C2semidirect
6. C2×C31×#343C2semidirect
7. C2×C31×#339C2semidirect
15. C2×C31×#137C4semidirect
171. C2×Q8×C31C22⋊C4semidirect
231. M16×C31C22⋊C4semidirect
253. #11017C31direct (N × H)
346. C2×#419C2×C31semidirect
348. C2×#391C2×C31semidirect
349. C2×#343C2×C31semidirect
350. C2×#339C2×C31semidirect
393. C2×#137C4×C31semidirect
508. C31#11017direct (N × H)
560. C2×Q8C22⋊C4×C31semidirect
620. M16C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1372
C22×C31×#1042
C2×C31×#4192
C31×#23112
C2×C31×#3912
C2×C31×#3432
C2×C31×#3392
#1101731