Finite Group Databasebeta

← C31×#11020 #21467779

Subgroups — C31×#11020 #21467779

Order 7936.

1406 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C2×C31×#417C211yesmaximal, characteristic, complemented
3C22×C31×#102C211yesmaximal, characteristic, complemented
4C22×C31×#100C211yesmaximal, characteristic, complemented
5C2×C31×#408C211yesmaximal, characteristic, complemented
6C2×C31×#343C211yesmaximal, characteristic, complemented
7C2×C31×#341C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C23×D4×C31C2211yescharacteristic
10C2×C31×AGL(1,ℤ/8)—22no—
11C2×C31×AGL(1,ℤ/8)—22no—
12C2×C31×AGL(1,ℤ/8)—22no—
13C2×C31×AGL(1,ℤ/8)—22no—
14C2×C31×AGL(1,ℤ/8)—22no—
15C2×C31×AGL(1,ℤ/8)C414yescomplemented
16C22×SD16×C31—21no—
17C22×D8×C31—21no—
18C22×M16×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C23×C8×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C31×#417—22no—
24C31×#417—22no—
25C2×C31×#103—21no—
26C2×C31×#102—22no—
27C2×C31×#102—21no—
28C2×C31×#102—22no—
29C2×C31×#102—22no—
30C2×C31×#100—22no—
31C2×C31×#100—22no—
32C2×C31×#100—22no—
33C31×#408—22no—
34C31×#408—22no—
35C2×C31×C22⋊C8—22no—
36C31×#343—22no—
37C31×#341—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—21no—
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×C31C2×C412yes—
65C22×D4×C31D412yes—
66C22×D4×C31D411yescharacteristic
67C22×D4×C31D412yes—
68C23×C4×C31—21no—
69C23×C4×C31—21no—
70C23×C4×C31C2311yescharacteristic
71C31×AGL(1,ℤ/8)—28no—
72C31×AGL(1,ℤ/8)—28no—
73C31×AGL(1,ℤ/8)—28no—
74C31×AGL(1,ℤ/8)—28no—
75C2×SD16×C31—24no—
76C2×SD16×C31—24no—
77C2×SD16×C31—24no—
78C2×D8×C31—24no—
79C2×D8×C31—24no—
80C2×D8×C31—24no—
81C2×M16×C31—21no—
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×C31—21no—
91C2×M16×C31—21no—
92C2×M16×C31—21no—
93C2×M16×C31—21no—
94C2×M16×C31C2×C412yes—
95C2×M16×C31D412yes—
96C2×M16×C31D412yes—
97C2×M16×C31D412yes—
98C2×M16×C31D412yes—
99C22×C8×C31—21no—
100C22×C8×C31—21no—
101C22×C8×C31—21no—
102C22×C8×C31—21no—
103C22×C8×C31—21no—
104C22×C8×C31—21no—
105C22×C8×C31—21no—
106C22×C8×C31—21no—
107C22×C8×C31—21no—
108C22×C8×C31D412yes—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31D412yes—
115C31×#103—24no—
116C31×#102—28no—
117C31×#102—24no—
118C31×#100—28no—
119C31×C22⋊C8—28no—
120C24×C31—21no—
121C24×C31—22no—
122C24×C31—22no—
123C24×C31—22no—
124C24×C31—41no—
125C24×C31—41no—
126C24×C31—41no—
127C24×C31—41no—
128C24×C31—82no—
129C24×C31—82no—
130C24×C31#4111yescharacteristic
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—22no—
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—
146#41×C31—41no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31C22⋊C412yes—
153C2×D4×C31—22no—
154C2×D4×C31—22no—
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—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—22no—
165C2×D4×C31—22no—
166C2×D4×C31—22no—
167C2×D4×C31—22no—
168C2×D4×C31—22no—
169C2×D4×C31—22no—
170C2×D4×C31—22no—
171C2×D4×C31—22no—
172C2×D4×C31—21no—
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×C31C22⋊C412yes—
192C2×D4×C31C22⋊C414yes—
193C22×C4×C31—21no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
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—82no—
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×C31C2×D411yescharacteristic
215C22×C4×C31#4111yescharacteristic
216C22×C4×C31#4111yescharacteristic
217C22×C4×C31#4111yescharacteristic
218SD16×C31—216no—
219D8×C31—216no—
220M16×C31—22no—
221M16×C31—22no—
222M16×C31—22no—
223M16×C31—22no—
224M16×C31—22no—
225M16×C31—22no—
226M16×C31—22no—
227M16×C31—41no—
228M16×C31—41no—
229M16×C31—41no—
230M16×C31—41no—
231M16×C31C22⋊C414yes—
232C2×C8×C31—22no—
233C2×C8×C31—22no—
234C2×C8×C31—22no—
235C2×C8×C31—22no—
236C2×C8×C31—22no—
237C2×C8×C31—22no—
238C2×C8×C31—22no—
239C2×C8×C31—22no—
240C2×C8×C31—41no—
241C2×C8×C31—41no—
242C2×C8×C31—41no—
243C2×C8×C31—41no—
244C2×C8×C31—41no—
245C2×C8×C31—41no—
246C2×C8×C31—41no—
247C2×C8×C31—41no—
248C4⋊C4×C31—22no—
249C4⋊C4×C31—22no—
250C4⋊C4×C31—41no—
251C4⋊C4×C31—41no—
252#11020C3111yesmaximal, characteristic, direct product factor, Sylow
253C23×C31—22no—
254C23×C31—22no—
255C23×C31—22no—
256C23×C31—24no—
257C23×C31—42no—
258C23×C31—42no—
259C23×C31—41no—
260C23×C31—42no—
261C23×C31—41no—
262C23×C31—42no—
263C23×C31—42no—
264C23×C31—42no—
265C23×C31—42no—
266C23×C31—42no—
267C23×C31—84no—
268C23×C31—84no—
269C23×C31—82no—
270C23×C31—82no—
271C23×C31—84no—
272C23×C31—84no—
273C23×C31—82no—
274C23×C31—82no—
275C23×C31—82no—
276C23×C31—82no—
277C23×C31C4×D411yescharacteristic
278C23×C31#12111yescharacteristic
279C23×C31#12111yescharacteristic
280C23×C31#12111yescharacteristic
281C23×C31#12311yescharacteristic
282C23×C31#12311yescharacteristic
283C23×C31#12411yescharacteristic
284Q8×C31—22no—
285Q8×C31—22no—
286Q8×C31—41no—
287Q8×C31—41no—
288D4×C31—22no—
289D4×C31—24no—
290D4×C31—24no—
291D4×C31—22no—
292D4×C31—42no—
293D4×C31—42no—
294D4×C31—42no—
295D4×C31—42no—
296D4×C31—42no—
297D4×C31—42no—
298D4×C31—42no—
299D4×C31—42no—
300D4×C31—42no—
301D4×C31—41no—
302D4×C31—42no—
303D4×C31—41no—
304C2×C4×C31—22no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
307C2×C4×C31—42no—
308C2×C4×C31—42no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—42no—
312C2×C4×C31—82no—
313C2×C4×C31—82no—
314C2×C4×C31—82no—
315C2×C4×C31C2×C22⋊C411yescharacteristic
316C2×C4×C31C2×C22⋊C411yescharacteristic
317C2×C4×C31C2×C22⋊C411yescharacteristic
318C2×C4×C31C4×D411yescharacteristic
319C2×C4×C31C4×D411yescharacteristic
320C2×C4×C31C4×D411yescharacteristic
321C2×C4×C31#12011yescharacteristic
322C2×C4×C31#12011yescharacteristic
323C2×C4×C31#12011yescharacteristic
324C2×C4×C31#12011yescharacteristic
325C2×C4×C31#12011yescharacteristic
326C2×C4×C31#12011yescharacteristic
327C2×C4×C31#12011yescharacteristic
328C2×C4×C31#12011yescharacteristic
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#12111yescharacteristic
336C2×C4×C31#12111yescharacteristic
337C2×C4×C31#12111yescharacteristic
338C2×C4×C31#12311yescharacteristic
339C2×C4×C31#12311yescharacteristic
340C2×C4×C31#12411yescharacteristic
341C2×C4×C31#12711yescharacteristic
342C2×C4×C31#12711yescharacteristic
343C8×C31—24no—
344C8×C31—42no—
345C8×C31—42no—
346C8×C31—42no—
347C22×AGL(1,ℤ/8)C2×C3111yescharacteristic
348C2×#417C2×C3111yescharacteristic, complemented
349C22×#102C2×C3111yescharacteristic, complemented
350C22×#100C2×C3111yescharacteristic, complemented
351C2×#408C2×C3111yescharacteristic, complemented
352C2×#343C2×C3111yescharacteristic, complemented
353C2×#341C2×C3111yescharacteristic, complemented
354C22×C31—22no—
355C22×C31—22no—
356C22×C31—22no—
357C22×C31—22no—
358C22×C31—21no—
359C22×C31—21no—
360C22×C31—21no—
361C22×C31—21no—
362C22×C31—44no—
363C22×C31—42no—
364C22×C31—44no—
365C22×C31—84no—
366C22×C31—84no—
367C22×C31—84no—
368C22×C31—84no—
369C22×C31—82no—
370C22×C31—84no—
371C22×C31—84no—
372C22×C31—81no—
373C22×C31—82no—
374C22×C31—81no—
375C22×C31—82no—
376C22×C31#38611yescharacteristic
377C22×C31#38611yescharacteristic
378C22×C31#39011yescharacteristic
379C22×C31#39211yescharacteristic
380C22×C31#39411yescharacteristic
381C22×C31#39411yescharacteristic
382C22×C31#39411yescharacteristic
383C22×C31#47112yes—
384C22×C31#47212yes—
385C4×C31—42no—
386C4×C31—82no—
387C4×C31#37911yescharacteristic
388C4×C31#38611yescharacteristic
389C4×C31#38611yescharacteristic
390C4×C31#39011yescharacteristic
391C4×C31#39211yescharacteristic
392C4×C31#39211yescharacteristic
393C4×C31#39211yescharacteristic
394C4×C31#39411yescharacteristic
395C22×#41C22×C3111yescharacteristic
396C23×D4C22×C3111yescharacteristic
397C2×AGL(1,ℤ/8)—22no—
398C2×AGL(1,ℤ/8)—22no—
399C2×AGL(1,ℤ/8)—22no—
400C2×AGL(1,ℤ/8)—22no—
401C2×AGL(1,ℤ/8)—22no—
402C2×AGL(1,ℤ/8)C4×C3114yescomplemented
403C22×SD16—21no—
404C22×D8—21no—
405C22×M16C22×C3111yescharacteristic
406C22×M16C22×C3111yescharacteristic
407C22×M16C22×C3111yescharacteristic
408C23×C8C22×C3111yescharacteristic
409C22×C4⋊C4C22×C3111yescharacteristic
410#417—22no—
411#417—22no—
412C2×#103—21no—
413C2×#102—22no—
414C2×#102—21no—
415C2×#102—22no—
416C2×#102—22no—
417C2×#100—22no—
418C2×#100—22no—
419C2×#100—22no—
420#408—22no—
421#408—22no—
422C2×C22⋊C8—22no—
423#343—22no—
424#341—22no—
425C2×C31—21no—
426C2×C31—21no—
427C2×C31—21no—
428C2×C31—21no—
429C2×C31—82no—
430C2×C31—84no—
431C2×C31#143811yescharacteristic
432C2×C31#190712yes—
433C2×C31#201811yescharacteristic
434C2×C31#201911yescharacteristic
435C2×C31#205112yes—
436C25—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41C2×C4×C3112yes—
448C2×#41D4×C3112yes—
449C22×Q8D4×C3111yescharacteristic
450C22×D4—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4C2×C4×C3112yes—
463C22×D4D4×C3111yescharacteristic
464C22×D4D4×C3112yes—
465C22×D4D4×C3112yes—
466C23×C4—21no—
467C23×C4—21no—
468C23×C4C23×C3111yescharacteristic
469AGL(1,ℤ/8)—28no—
470AGL(1,ℤ/8)—28no—
471AGL(1,ℤ/8)—28no—
472AGL(1,ℤ/8)—28no—
473C2×SD16—24no—
474C2×SD16—24no—
475C2×SD16—24no—
476C2×D8—24no—
477C2×D8—24no—
478C2×D8—24no—
479C2×M16—21no—
480C2×M16—21no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—21no—
485C2×M16—21no—
486C2×M16—21no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—21no—
492C2×M16C2×C4×C3112yes—
493C2×M16D4×C3112yes—
494C2×M16D4×C3112yes—
495C2×M16D4×C3112yes—
496C2×M16D4×C3112yes—
497C22×C8—21no—
498C22×C8—21no—
499C22×C8—21no—
500C22×C8—21no—
501C22×C8—21no—
502C22×C8—21no—
503C22×C8—21no—
504C22×C8—21no—
505C22×C8—21no—
506C22×C8D4×C3112yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4D4×C3112yes—
513#103—24no—
514#102—28no—
515#102—24no—
516#100—28no—
517C22⋊C8—28no—
518C31#1102011yescharacteristic, direct product factor, Sylow
519C24—21no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—41no—
524C24—41no—
525C24—41no—
526C24—41no—
527C24—82no—
528C24—82no—
529C24#41×C3111yescharacteristic
530#41—22no—
531#41—22no—
532#41—22no—
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—41no—
539#41—41no—
540#41—41no—
541#41—41no—
542#41—41no—
543#41—41no—
544#41—41no—
545#41—41no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8C22⋊C4×C3112yes—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4C22⋊C4×C3112yes—
591C2×D4C22⋊C4×C3114yes—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—82no—
603C22×C4C22×C4×C3111yescharacteristic
604C22×C4C2×D4×C3111yescharacteristic
605C22×C4C2×D4×C3111yescharacteristic
606C22×C4C2×D4×C3111yescharacteristic
607C22×C4C2×D4×C3111yescharacteristic
608C22×C4C2×D4×C3111yescharacteristic
609C22×C4C2×D4×C3111yescharacteristic
610C22×C4C2×D4×C3111yescharacteristic
611C22×C4C2×D4×C3111yescharacteristic
612C22×C4C2×D4×C3111yescharacteristic
613C22×C4C2×D4×C3111yescharacteristic
614C22×C4#41×C3111yescharacteristic
615C22×C4#41×C3111yescharacteristic
616C22×C4#41×C3111yescharacteristic
617SD16—216no—
618D8—216no—
619M16—22no—
620M16—22no—
621M16—22no—
622M16—22no—
623M16—22no—
624M16—22no—
625M16—22no—
626M16—41no—
627M16—41no—
628M16—41no—
629M16—41no—
630M16C22⋊C4×C3114yes—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—41no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—41no—
660C23—42no—
661C23—41no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—84no—
666C23—84no—
667C23—82no—
668C23—82no—
669C23—84no—
670C23—84no—
671C23—82no—
672C23—82no—
673C23—82no—
674C23—82no—
675C23C4×D4×C3111yescharacteristic
676C23C31×#12111yescharacteristic
677C23C31×#12111yescharacteristic
678C23C31×#12111yescharacteristic
679C23C31×#12311yescharacteristic
680C23C31×#12311yescharacteristic
681C23C31×#12411yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—41no—
685Q8—41no—
686D4—22no—
687D4—24no—
688D4—24no—
689D4—22no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—41no—
700D4—42no—
701D4—41no—
702C2×C4—22no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—82no—
711C2×C4—82no—
712C2×C4—82no—
713C2×C4C2×C22⋊C4×C3111yescharacteristic
714C2×C4C2×C22⋊C4×C3111yescharacteristic
715C2×C4C2×C22⋊C4×C3111yescharacteristic
716C2×C4C4×D4×C3111yescharacteristic
717C2×C4C4×D4×C3111yescharacteristic
718C2×C4C4×D4×C3111yescharacteristic
719C2×C4C31×#12011yescharacteristic
720C2×C4C31×#12011yescharacteristic
721C2×C4C31×#12011yescharacteristic
722C2×C4C31×#12011yescharacteristic
723C2×C4C31×#12011yescharacteristic
724C2×C4C31×#12011yescharacteristic
725C2×C4C31×#12011yescharacteristic
726C2×C4C31×#12011yescharacteristic
727C2×C4C31×#12111yescharacteristic
728C2×C4C31×#12111yescharacteristic
729C2×C4C31×#12111yescharacteristic
730C2×C4C31×#12111yescharacteristic
731C2×C4C31×#12111yescharacteristic
732C2×C4C31×#12111yescharacteristic
733C2×C4C31×#12111yescharacteristic
734C2×C4C31×#12111yescharacteristic
735C2×C4C31×#12111yescharacteristic
736C2×C4C31×#12311yescharacteristic
737C2×C4C31×#12311yescharacteristic
738C2×C4C31×#12411yescharacteristic
739C2×C4C31×#12711yescharacteristic
740C2×C4C31×#12711yescharacteristic
741C8—24no—
742C8—42no—
743C8—42no—
744C8—42no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—44no—
754C22—42no—
755C22—44no—
756C22—84no—
757C22—84no—
758C22—84no—
759C22—84no—
760C22—82no—
761C22—84no—
762C22—84no—
763C22—81no—
764C22—82no—
765C22—81no—
766C22—82no—
767C22C31×#38611yescharacteristic
768C22C31×#38611yescharacteristic
769C22C31×#39011yescharacteristic
770C22C31×#39211yescharacteristic
771C22C31×#39411yescharacteristic
772C22C31×#39411yescharacteristic
773C22C31×#39411yescharacteristic
774C22C31×#47112yes—
775C22C31×#47212yes—
776C4—42no—
777C4—82no—
778C4C31×#37911yescharacteristic
779C4C31×#38611yescharacteristic
780C4C31×#38611yescharacteristic
781C4C31×#39011yescharacteristic
782C4C31×#39211yescharacteristic
783C4C31×#39211yescharacteristic
784C4C31×#39211yescharacteristic
785C4C31×#39411yescharacteristic
786C2—21no—
787C2—21no—
788C2—21no—
789C2—21no—
790C2—82no—
791C2—84no—
792C2C31×#143811yescharacteristic
793C2C31×#190712yes—
794C2C31×#201811yescharacteristic
795C2C31×#201911yescharacteristic
796C2C31×#205112yes—
subgroupG/H
center, socleC23×C31#121
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×C31×AGL(1,ℤ/8)C2
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
2. C2×C31×#417C2semidirect
3. C22×C31×#102C2semidirect
4. C22×C31×#100C2semidirect
5. C2×C31×#408C2semidirect
6. C2×C31×#343C2semidirect
7. C2×C31×#341C2semidirect
15. C2×C31×AGL(1,ℤ/8)C4semidirect
252. #11020C31direct (N × H)
348. C2×#417C2×C31semidirect
349. C22×#102C2×C31semidirect
350. C22×#100C2×C31semidirect
351. C2×#408C2×C31semidirect
352. C2×#343C2×C31semidirect
353. C2×#341C2×C31semidirect
402. C2×AGL(1,ℤ/8)C4×C31semidirect
518. C31#11020direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×AGL(1,ℤ/8)2
C2×C31×#4172
C22×C31×#1022
C22×C31×#1002
C2×C31×#4082
C2×C31×#3432
C2×C31×#3412
#1102031