Finite Group Databasebeta

← C31×#11014 #21467773

Subgroups — C31×#11014 #21467773

Order 7936.

1370 conjugacy classes of subgroups.

The subgroup lattice has 764 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×#421C211yesmaximal, characteristic, complemented
3C2×C31×#418C211yesmaximal, characteristic, complemented
4C22×C31×#100C211yesmaximal, characteristic, complemented
5C31×#2879C211yesmaximal, characteristic, complemented
6C2×C31×#344C211yesmaximal, characteristic, complemented
7C2×C31×#338C211yesmaximal, 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)—22no—
16C22×SD16×C31C412yescomplemented
17C22×D8×C31C412yescomplemented
18C22×M16×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C22×M16×C31C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C31×#421—22no—
24C31×#421—22no—
25C2×C31×#104—22no—
26C31×#418—22no—
27C31×#418—22no—
28C2×C31×#102—22no—
29C2×C31×#100—22no—
30C2×C31×#100—22no—
31C2×C31×#100—22no—
32C31×#408—22no—
33C31×#408—22no—
34C31×#407—22no—
35C31×#344—22no—
36C31×#338—22no—
37C25×C31—21no—
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×C31D412yes—
49C2×#41×C31D412yes—
50C22×Q8×C31C2×C411yescharacteristic
51C22×D4×C31—21no—
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×C31C2×C411yescharacteristic
64C22×D4×C31C2×C412yes—
65C22×D4×C31D412yes—
66C22×D4×C31D412yes—
67C23×C4×C31—21no—
68C23×C4×C31C2311yescharacteristic
69C31×AGL(1,ℤ/8)—28no—
70C31×AGL(1,ℤ/8)—28no—
71C31×AGL(1,ℤ/8)—28no—
72C31×AGL(1,ℤ/8)—28no—
73C2×SD16×C31—24no—
74C2×SD16×C31—24no—
75C2×SD16×C31—24no—
76C2×D8×C31—24no—
77C2×D8×C31—24no—
78C2×D8×C31—24no—
79C2×M16×C31—21no—
80C2×M16×C31—21no—
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×C31—21no—
95C2×M16×C31—21no—
96C2×M16×C31—21no—
97C2×M16×C31—21no—
98C2×M16×C31—21no—
99C2×M16×C31D412yes—
100C2×M16×C31D412yes—
101C2×M16×C31D412yes—
102C2×M16×C31D412yes—
103C22×C8×C31—21no—
104C22×C8×C31—21no—
105C22×C8×C31C2×C412yes—
106C22×C8×C31D412yes—
107C31×#117—21no—
108C31×#117—21no—
109C31×#117—21no—
110C31×#117D412yes—
111C2×C4⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C42×C31—21no—
114C31×#104—28no—
115C31×#102—28no—
116C31×#100—28no—
117C31×C22⋊C8—28no—
118C24×C31—21no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31—22no—
122C24×C31—41no—
123C24×C31—41no—
124C24×C31—41no—
125C24×C31—41no—
126C24×C31—84no—
127C24×C31#4111yescharacteristic
128#41×C31—22no—
129#41×C31—22no—
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—41no—
137#41×C31—41no—
138#41×C31—41no—
139#41×C31—41no—
140#41×C31—41no—
141#41×C31—41no—
142#41×C31—41no—
143#41×C31—41no—
144C2×Q8×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31C22⋊C412yes—
150C2×D4×C31—22no—
151C2×D4×C31—22no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—22no—
155C2×D4×C31—22no—
156C2×D4×C31—22no—
157C2×D4×C31—22no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—22no—
161C2×D4×C31—21no—
162C2×D4×C31—22no—
163C2×D4×C31—22no—
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—41no—
173C2×D4×C31—41no—
174C2×D4×C31—41no—
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×C31C22⋊C412yes—
189C2×D4×C31C22⋊C414yes—
190C22×C4×C31—21no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—41no—
194C22×C4×C31—41no—
195C22×C4×C31—41no—
196C22×C4×C31—41no—
197C22×C4×C31—41no—
198C22×C4×C31C22×C411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31#4111yescharacteristic
210C22×C4×C31#4111yescharacteristic
211C22×C4×C31#4111yescharacteristic
212SD16×C31—216no—
213D8×C31—216no—
214M16×C31—22no—
215M16×C31—22no—
216M16×C31—22no—
217M16×C31—22no—
218M16×C31—22no—
219M16×C31—22no—
220M16×C31—22no—
221M16×C31—22no—
222M16×C31—41no—
223M16×C31—41no—
224M16×C31—41no—
225M16×C31—41no—
226M16×C31—41no—
227M16×C31—41no—
228M16×C31—41no—
229M16×C31—41no—
230C2×C8×C31—22no—
231C2×C8×C31—22no—
232C2×C8×C31—22no—
233C2×C8×C31—22no—
234C2×C8×C31—22no—
235C2×C8×C31—22no—
236C2×C8×C31—22no—
237C2×C8×C31—41no—
238C2×C8×C31—41no—
239C2×C8×C31—41no—
240C2×C8×C31—41no—
241C2×C8×C31C22⋊C414yes—
242C4⋊C4×C31—22no—
243C4⋊C4×C31—41no—
244C22⋊C4×C31—22no—
245C22⋊C4×C31—41no—
246C42×C31—22no—
247C42×C31—41no—
248#11014C3111yesmaximal, characteristic, direct product factor, Sylow
249C23×C31—22no—
250C23×C31—24no—
251C23×C31—42no—
252C23×C31—41no—
253C23×C31—42no—
254C23×C31—41no—
255C23×C31—42no—
256C23×C31—42no—
257C23×C31—42no—
258C23×C31—42no—
259C23×C31—42no—
260C23×C31—82no—
261C23×C31—84no—
262C23×C31—84no—
263C23×C31—84no—
264C23×C31—84no—
265C23×C31—84no—
266C23×C31—84no—
267C23×C31—84no—
268C23×C31C4×D411yescharacteristic
269C23×C31#12111yescharacteristic
270C23×C31#12111yescharacteristic
271C23×C31#12111yescharacteristic
272C23×C31#12311yescharacteristic
273C23×C31#12311yescharacteristic
274C23×C31#12411yescharacteristic
275Q8×C31—22no—
276Q8×C31—22no—
277Q8×C31—41no—
278Q8×C31—41no—
279D4×C31—22no—
280D4×C31—24no—
281D4×C31—24no—
282D4×C31—22no—
283D4×C31—42no—
284D4×C31—42no—
285D4×C31—42no—
286D4×C31—42no—
287D4×C31—42no—
288D4×C31—41no—
289D4×C31—42no—
290D4×C31—41no—
291D4×C31—42no—
292D4×C31—42no—
293D4×C31—42no—
294D4×C31—42no—
295C2×C4×C31—22no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—42no—
299C2×C4×C31—42no—
300C2×C4×C31—42no—
301C2×C4×C31—42no—
302C2×C4×C31—42no—
303C2×C4×C31—82no—
304C2×C4×C31C2×C22⋊C411yescharacteristic
305C2×C4×C31C2×C22⋊C411yescharacteristic
306C2×C4×C31C2×C22⋊C411yescharacteristic
307C2×C4×C31C4×D411yescharacteristic
308C2×C4×C31C4×D411yescharacteristic
309C2×C4×C31C4×D411yescharacteristic
310C2×C4×C31#12011yescharacteristic
311C2×C4×C31#12011yescharacteristic
312C2×C4×C31#12011yescharacteristic
313C2×C4×C31#12011yescharacteristic
314C2×C4×C31#12011yescharacteristic
315C2×C4×C31#12011yescharacteristic
316C2×C4×C31#12011yescharacteristic
317C2×C4×C31#12011yescharacteristic
318C2×C4×C31#12111yescharacteristic
319C2×C4×C31#12111yescharacteristic
320C2×C4×C31#12111yescharacteristic
321C2×C4×C31#12111yescharacteristic
322C2×C4×C31#12111yescharacteristic
323C2×C4×C31#12111yescharacteristic
324C2×C4×C31#12111yescharacteristic
325C2×C4×C31#12111yescharacteristic
326C2×C4×C31#12111yescharacteristic
327C2×C4×C31#12311yescharacteristic
328C2×C4×C31#12311yescharacteristic
329C2×C4×C31#12411yescharacteristic
330C2×C4×C31#12711yescharacteristic
331C2×C4×C31#12711yescharacteristic
332C8×C31—24no—
333C8×C31—42no—
334C8×C31—42no—
335C8×C31—42no—
336C22×AGL(1,ℤ/8)C2×C3111yescharacteristic
337C2×#421C2×C3111yescharacteristic, complemented
338C2×#418C2×C3111yescharacteristic, complemented
339C22×#100C2×C3111yescharacteristic, complemented
340#2879C2×C3111yescharacteristic, complemented
341C2×#344C2×C3111yescharacteristic, complemented
342C2×#338C2×C3111yescharacteristic, complemented
343C22×C31—22no—
344C22×C31—22no—
345C22×C31—22no—
346C22×C31—41no—
347C22×C31—41no—
348C22×C31—41no—
349C22×C31—41no—
350C22×C31—44no—
351C22×C31—42no—
352C22×C31—44no—
353C22×C31—84no—
354C22×C31—82no—
355C22×C31—82no—
356C22×C31—84no—
357C22×C31—84no—
358C22×C31—84no—
359C22×C31—84no—
360C22×C31—84no—
361C22×C31—84no—
362C22×C31#38611yescharacteristic
363C22×C31#38611yescharacteristic
364C22×C31#39011yescharacteristic
365C22×C31#39211yescharacteristic
366C22×C31#39411yescharacteristic
367C22×C31#39411yescharacteristic
368C22×C31#39411yescharacteristic
369C4×C31—42no—
370C4×C31—82no—
371C4×C31#37911yescharacteristic
372C4×C31#38611yescharacteristic
373C4×C31#38611yescharacteristic
374C4×C31#39011yescharacteristic
375C4×C31#39211yescharacteristic
376C4×C31#39211yescharacteristic
377C4×C31#39211yescharacteristic
378C4×C31#39411yescharacteristic
379C22×#41C22×C3111yescharacteristic
380C23×D4C22×C3111yescharacteristic
381C2×AGL(1,ℤ/8)—22no—
382C2×AGL(1,ℤ/8)—22no—
383C2×AGL(1,ℤ/8)—22no—
384C2×AGL(1,ℤ/8)—22no—
385C2×AGL(1,ℤ/8)—22no—
386C2×AGL(1,ℤ/8)—22no—
387C22×SD16C4×C3112yescomplemented
388C22×D8C4×C3112yescomplemented
389C22×M16C22×C3111yescharacteristic
390C22×M16C22×C3111yescharacteristic
391C22×M16C22×C3111yescharacteristic
392C22×M16C22×C3111yescharacteristic
393C2×#117C22×C3111yescharacteristic
394#421—22no—
395#421—22no—
396C2×#104—22no—
397#418—22no—
398#418—22no—
399C2×#102—22no—
400C2×#100—22no—
401C2×#100—22no—
402C2×#100—22no—
403#408—22no—
404#408—22no—
405#407—22no—
406#344—22no—
407#338—22no—
408C2×C31—21no—
409C2×C31—21no—
410C2×C31—21no—
411C2×C31—21no—
412C2×C31—21no—
413C2×C31—21no—
414C2×C31—82no—
415C2×C31—84no—
416C2×C31#143811yescharacteristic
417C2×C31#190312yes—
418C25—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41D4×C3112yes—
430C2×#41D4×C3112yes—
431C22×Q8C2×C4×C3111yescharacteristic
432C22×D4—21no—
433C22×D4—21no—
434C22×D4—21no—
435C22×D4—21no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—21no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4C2×C4×C3111yescharacteristic
445C22×D4C2×C4×C3112yes—
446C22×D4D4×C3112yes—
447C22×D4D4×C3112yes—
448C23×C4—21no—
449C23×C4C23×C3111yescharacteristic
450AGL(1,ℤ/8)—28no—
451AGL(1,ℤ/8)—28no—
452AGL(1,ℤ/8)—28no—
453AGL(1,ℤ/8)—28no—
454C2×SD16—24no—
455C2×SD16—24no—
456C2×SD16—24no—
457C2×D8—24no—
458C2×D8—24no—
459C2×D8—24no—
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×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—21no—
475C2×M16—21no—
476C2×M16—21no—
477C2×M16—21no—
478C2×M16—21no—
479C2×M16—21no—
480C2×M16D4×C3112yes—
481C2×M16D4×C3112yes—
482C2×M16D4×C3112yes—
483C2×M16D4×C3112yes—
484C22×C8—21no—
485C22×C8—21no—
486C22×C8C2×C4×C3112yes—
487C22×C8D4×C3112yes—
488#117—21no—
489#117—21no—
490#117—21no—
491#117D4×C3112yes—
492C2×C4⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C42—21no—
495#104—28no—
496#102—28no—
497#100—28no—
498C22⋊C8—28no—
499C31#1101411yescharacteristic, direct product factor, Sylow
500C24—21no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—41no—
505C24—41no—
506C24—41no—
507C24—41no—
508C24—84no—
509C24#41×C3111yescharacteristic
510#41—22no—
511#41—22no—
512#41—22no—
513#41—22no—
514#41—22no—
515#41—22no—
516#41—22no—
517#41—22no—
518#41—41no—
519#41—41no—
520#41—41no—
521#41—41no—
522#41—41no—
523#41—41no—
524#41—41no—
525#41—41no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8C22⋊C4×C3112yes—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—21no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4C22⋊C4×C3112yes—
571C2×D4C22⋊C4×C3114yes—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4C22×C4×C3111yescharacteristic
581C22×C4C2×D4×C3111yescharacteristic
582C22×C4C2×D4×C3111yescharacteristic
583C22×C4C2×D4×C3111yescharacteristic
584C22×C4C2×D4×C3111yescharacteristic
585C22×C4C2×D4×C3111yescharacteristic
586C22×C4C2×D4×C3111yescharacteristic
587C22×C4C2×D4×C3111yescharacteristic
588C22×C4C2×D4×C3111yescharacteristic
589C22×C4C2×D4×C3111yescharacteristic
590C22×C4C2×D4×C3111yescharacteristic
591C22×C4#41×C3111yescharacteristic
592C22×C4#41×C3111yescharacteristic
593C22×C4#41×C3111yescharacteristic
594SD16—216no—
595D8—216no—
596M16—22no—
597M16—22no—
598M16—22no—
599M16—22no—
600M16—22no—
601M16—22no—
602M16—22no—
603M16—22no—
604M16—41no—
605M16—41no—
606M16—41no—
607M16—41no—
608M16—41no—
609M16—41no—
610M16—41no—
611M16—41no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8C22⋊C4×C3114yes—
624C4⋊C4—22no—
625C4⋊C4—41no—
626C22⋊C4—22no—
627C22⋊C4—41no—
628C42—22no—
629C42—41no—
630C23—22no—
631C23—24no—
632C23—42no—
633C23—41no—
634C23—42no—
635C23—41no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—82no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23C4×D4×C3111yescharacteristic
650C23C31×#12111yescharacteristic
651C23C31×#12111yescharacteristic
652C23C31×#12111yescharacteristic
653C23C31×#12311yescharacteristic
654C23C31×#12311yescharacteristic
655C23C31×#12411yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—41no—
659Q8—41no—
660D4—22no—
661D4—24no—
662D4—24no—
663D4—22no—
664D4—42no—
665D4—42no—
666D4—42no—
667D4—42no—
668D4—42no—
669D4—41no—
670D4—42no—
671D4—41no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—42no—
676C2×C4—22no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—82no—
685C2×C4C2×C22⋊C4×C3111yescharacteristic
686C2×C4C2×C22⋊C4×C3111yescharacteristic
687C2×C4C2×C22⋊C4×C3111yescharacteristic
688C2×C4C4×D4×C3111yescharacteristic
689C2×C4C4×D4×C3111yescharacteristic
690C2×C4C4×D4×C3111yescharacteristic
691C2×C4C31×#12011yescharacteristic
692C2×C4C31×#12011yescharacteristic
693C2×C4C31×#12011yescharacteristic
694C2×C4C31×#12011yescharacteristic
695C2×C4C31×#12011yescharacteristic
696C2×C4C31×#12011yescharacteristic
697C2×C4C31×#12011yescharacteristic
698C2×C4C31×#12011yescharacteristic
699C2×C4C31×#12111yescharacteristic
700C2×C4C31×#12111yescharacteristic
701C2×C4C31×#12111yescharacteristic
702C2×C4C31×#12111yescharacteristic
703C2×C4C31×#12111yescharacteristic
704C2×C4C31×#12111yescharacteristic
705C2×C4C31×#12111yescharacteristic
706C2×C4C31×#12111yescharacteristic
707C2×C4C31×#12111yescharacteristic
708C2×C4C31×#12311yescharacteristic
709C2×C4C31×#12311yescharacteristic
710C2×C4C31×#12411yescharacteristic
711C2×C4C31×#12711yescharacteristic
712C2×C4C31×#12711yescharacteristic
713C8—24no—
714C8—42no—
715C8—42no—
716C8—42no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—44no—
725C22—42no—
726C22—44no—
727C22—84no—
728C22—84no—
729C22—84no—
730C22—84no—
731C22—84no—
732C22—84no—
733C22—82no—
734C22—82no—
735C22—84no—
736C22C31×#38611yescharacteristic
737C22C31×#38611yescharacteristic
738C22C31×#39011yescharacteristic
739C22C31×#39211yescharacteristic
740C22C31×#39411yescharacteristic
741C22C31×#39411yescharacteristic
742C22C31×#39411yescharacteristic
743C4—42no—
744C4—82no—
745C4C31×#37911yescharacteristic
746C4C31×#38611yescharacteristic
747C4C31×#38611yescharacteristic
748C4C31×#39011yescharacteristic
749C4C31×#39211yescharacteristic
750C4C31×#39211yescharacteristic
751C4C31×#39211yescharacteristic
752C4C31×#39411yescharacteristic
753C2—21no—
754C2—21no—
755C2—21no—
756C2—21no—
757C2—21no—
758C2—21no—
759C2—82no—
760C2—84no—
761C2C31×#143811yescharacteristic
762C2C31×#190312yes—
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×C31×AGL(1,ℤ/8)C2
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. C2×C31×#418C2semidirect
4. C22×C31×#100C2semidirect
5. C31×#2879C2semidirect
6. C2×C31×#344C2semidirect
7. C2×C31×#338C2semidirect
16. C22×SD16×C31C4semidirect
17. C22×D8×C31C4semidirect
248. #11014C31direct (N × H)
337. C2×#421C2×C31semidirect
338. C2×#418C2×C31semidirect
339. C22×#100C2×C31semidirect
340. #2879C2×C31semidirect
341. C2×#344C2×C31semidirect
342. C2×#338C2×C31semidirect
387. C22×SD16C4×C31semidirect
388. C22×D8C4×C31semidirect
499. C31#11014direct (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×#4212
C2×C31×#4182
C22×C31×#1002
C31×#28792
C2×C31×#3442
C2×C31×#3382
#1101431