Finite Group Databasebeta

← C31×#11019 #21467778

Subgroups — C31×#11019 #21467778

Order 7936.

1338 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#575C211yesmaximal, characteristic
2C2×C31×#421C211yesmaximal, characteristic, complemented
3C22×C31×#104C211yesmaximal, characteristic, complemented
4C2×C31×#410C211yesmaximal, characteristic, complemented
5C31×#2297C211yesmaximal, characteristic, complemented
6C2×C31×#344C211yesmaximal, characteristic, complemented
7C2×C31×#339C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C22×#41×C31C2211yescharacteristic
10C31×#575—22no—
11C31×#575—22no—
12C31×#575—22no—
13C31×#575—22no—
14C2×C31×#137—21no—
15C2×C31×#137C412yescomplemented
16C2×C31×AGL(1,ℤ/8)—21no—
17C2×C31×AGL(1,ℤ/8)C412yescomplemented
18C2×C31×#135—22no—
19C22×M16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C22×C42×C31C2211yescharacteristic
24C31×#421—22no—
25C31×#421—22no—
26C2×C31×#104—22no—
27C2×C31×#104—22no—
28C2×C31×#104—22no—
29C2×C31×#104—22no—
30C31×#410—22no—
31C31×#410—22no—
32C2×C31×#99—22no—
33C31×#391—21no—
34C31×#390—21no—
35C31×#386—22no—
36C4×C22⋊C4×C31—22no—
37C31×#344—22no—
38C31×#339—22no—
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×C31—21no—
50C2×#41×C31—21no—
51C2×#41×C31—21no—
52C2×#41×C31—21no—
53C2×#41×C31—21no—
54C2×#41×C31—21no—
55C2×#41×C31—21no—
56C2×#41×C31—21no—
57C2×#41×C31—21no—
58C2×#41×C31—21no—
59C2×#41×C31C2×C412yes—
60C2×#41×C31D412yes—
61C2×#41×C31D412yes—
62C2×#41×C31D412yes—
63C22×Q8×C31C2×C411yescharacteristic
64C22×Q8×C31D411yescharacteristic
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31C2×C411yescharacteristic
68C22×D4×C31D411yescharacteristic
69C23×C4×C31—21no—
70C23×C4×C31—21no—
71C23×C4×C31—21no—
72C23×C4×C31C2311yescharacteristic
73C31×#137—24no—
74C31×#137—24no—
75C31×#137—24no—
76C31×#137—24no—
77C31×AGL(1,ℤ/8)—24no—
78C31×AGL(1,ℤ/8)—24no—
79C31×AGL(1,ℤ/8)—24no—
80C31×AGL(1,ℤ/8)—24no—
81C31×#135—28no—
82C31×#135—28no—
83C2×Q16×C31—22no—
84C2×SD16×C31—22no—
85C2×SD16×C31—22no—
86C2×D8×C31—22no—
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×C31C2×C412yes—
96C2×M16×C31D412yes—
97C2×M16×C31D412yes—
98C2×M16×C31D412yes—
99C22×C8×C31—21no—
100C22×C8×C31—21no—
101C31×#117—21no—
102C31×#117—21no—
103C31×#117—21no—
104C31×#117—21no—
105C31×#117—21no—
106C31×#117—21no—
107C31×#117—21no—
108C31×#117D412yes—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—24no—
113C2×C22⋊C4×C31D412yes—
114C2×C42×C31—21no—
115C2×C42×C31—21no—
116C2×C42×C31—21no—
117C2×C42×C31—21no—
118C2×C42×C31—21no—
119C2×C42×C31—21no—
120C2×C42×C31—21no—
121C2×C42×C31D412yes—
122C31×#104—28no—
123C31×#104—28no—
124C31×#99—28no—
125C31×#95—24no—
126C24×C31—21no—
127C24×C31—21no—
128C24×C31C2×D411yescharacteristic
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—22no—
137#41×C31—22no—
138#41×C31—22no—
139#41×C31—22no—
140#41×C31—22no—
141#41×C31—22no—
142#41×C31—22no—
143#41×C31—22no—
144#41×C31—22no—
145#41×C31—41no—
146#41×C31—41no—
147#41×C31—41no—
148#41×C31—41no—
149#41×C31—41no—
150#41×C31—41no—
151#41×C31—41no—
152#41×C31—41no—
153#41×C31—41no—
154#41×C31—41no—
155#41×C31—41no—
156#41×C31—41no—
157#41×C31—41no—
158#41×C31—41no—
159#41×C31—41no—
160#41×C31—41no—
161C2×Q8×C31—21no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31—21no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31C22⋊C412yes—
172C2×Q8×C31C22⋊C412yescomplemented
173C2×D4×C31—22no—
174C2×D4×C31—22no—
175C2×D4×C31—22no—
176C2×D4×C31—22no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—21no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—41no—
188C2×D4×C31—41no—
189C2×D4×C31—41no—
190C2×D4×C31—41no—
191C2×D4×C31—41no—
192C2×D4×C31—41no—
193C2×D4×C31—41no—
194C2×D4×C31—41no—
195C2×D4×C31C22⋊C412yes—
196C2×D4×C31C22⋊C412yescomplemented
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—22no—
202C22×C4×C31—22no—
203C22×C4×C31—22no—
204C22×C4×C31—22no—
205C22×C4×C31—44no—
206C22×C4×C31—41no—
207C22×C4×C31—41no—
208C22×C4×C31—41no—
209C22×C4×C31—41no—
210C22×C4×C31—41no—
211C22×C4×C31—41no—
212C22×C4×C31—41no—
213C22×C4×C31—41no—
214C22×C4×C31—41no—
215C22×C4×C31—41no—
216C22×C4×C31—41no—
217C22×C4×C31C22×C411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219C22×C4×C31C2×D411yescharacteristic
220C22×C4×C31C2×D411yescharacteristic
221C22×C4×C31C2×D411yescharacteristic
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31C2×D411yescharacteristic
224C22×C4×C31C2×D411yescharacteristic
225C22×C4×C31C2×D411yescharacteristic
226C22×C4×C31C2×D411yescharacteristic
227C22×C4×C31#4111yescharacteristic
228C22×C4×C31#4111yescharacteristic
229C22×C4×C31#4111yescharacteristic
230C22×C4×C31#4111yescharacteristic
231Q16×C31—28no—
232SD16×C31—28no—
233SD16×C31—28no—
234D8×C31—28no—
235M16×C31—22no—
236M16×C31—22no—
237M16×C31—22no—
238M16×C31—22no—
239M16×C31—22no—
240M16×C31—41no—
241M16×C31—41no—
242M16×C31C22⋊C414yescomplemented
243C2×C8×C31—22no—
244C2×C8×C31—22no—
245C2×C8×C31—22no—
246C2×C8×C31—22no—
247C2×C8×C31—41no—
248C2×C8×C31—41no—
249C4⋊C4×C31—22no—
250C4⋊C4×C31—41no—
251C4⋊C4×C31—41no—
252C4⋊C4×C31—41no—
253C22⋊C4×C31—22no—
254C22⋊C4×C31—22no—
255C22⋊C4×C31—22no—
256C22⋊C4×C31—48no—
257C22⋊C4×C31—41no—
258C42×C31—22no—
259C42×C31—22no—
260C42×C31—22no—
261C42×C31—41no—
262C42×C31—41no—
263C42×C31—41no—
264C42×C31—41no—
265C42×C31—41no—
266#11019C3111yesmaximal, characteristic, direct product factor, Sylow
267C23×C31—22no—
268C23×C31—22no—
269C23×C31—42no—
270C23×C31—44no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—82no—
276C23×C31C4×D411yescharacteristic
277C23×C31#12011yescharacteristic
278C23×C31#12011yescharacteristic
279C23×C31#12111yescharacteristic
280C23×C31#12111yescharacteristic
281C23×C31#12111yescharacteristic
282C23×C31#12711yescharacteristic
283Q8×C31—22no—
284Q8×C31—22no—
285Q8×C31—22no—
286Q8×C31—22no—
287Q8×C31—41no—
288Q8×C31—41no—
289Q8×C31—41no—
290Q8×C31—41no—
291D4×C31—22no—
292D4×C31—22no—
293D4×C31—22no—
294D4×C31—22no—
295D4×C31—42no—
296D4×C31—42no—
297D4×C31—42no—
298D4×C31—42no—
299D4×C31—42no—
300D4×C31—42no—
301D4×C31—42no—
302D4×C31—42no—
303D4×C31—41no—
304D4×C31—41no—
305D4×C31—41no—
306D4×C31—41no—
307C2×C4×C31—24no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—42no—
311C2×C4×C31—44no—
312C2×C4×C31—44no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—42no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31—42no—
322C2×C4×C31—42no—
323C2×C4×C31—42no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31—44no—
327C2×C4×C31—42no—
328C2×C4×C31—42no—
329C2×C4×C31—82no—
330C2×C4×C31C2×C22⋊C411yescharacteristic
331C2×C4×C31C2×C22⋊C411yescharacteristic
332C2×C4×C31C2×C22⋊C411yescharacteristic
333C2×C4×C31C4×D411yescharacteristic
334C2×C4×C31C4×D411yescharacteristic
335C2×C4×C31C4×D411yescharacteristic
336C2×C4×C31#12011yescharacteristic
337C2×C4×C31#12011yescharacteristic
338C2×C4×C31#12011yescharacteristic
339C2×C4×C31#12011yescharacteristic
340C2×C4×C31#12011yescharacteristic
341C2×C4×C31#12011yescharacteristic
342C2×C4×C31#12111yescharacteristic
343C2×C4×C31#12111yescharacteristic
344C2×C4×C31#12111yescharacteristic
345C2×C4×C31#12111yescharacteristic
346C2×C4×C31#12111yescharacteristic
347C2×C4×C31#12111yescharacteristic
348C2×C4×C31#12111yescharacteristic
349C2×C4×C31#12111yescharacteristic
350C2×C4×C31#12111yescharacteristic
351C2×C4×C31#12311yescharacteristic
352C2×C4×C31#12311yescharacteristic
353C2×C4×C31#12311yescharacteristic
354C2×C4×C31#12311yescharacteristic
355C2×C4×C31#12411yescharacteristic
356C2×C4×C31#12411yescharacteristic
357C2×C4×C31#12711yescharacteristic
358C8×C31—24no—
359C8×C31—42no—
360C2×#575C2×C3111yescharacteristic
361C2×#421C2×C3111yescharacteristic, complemented
362C22×#104C2×C3111yescharacteristic, complemented
363C2×#410C2×C3111yescharacteristic, complemented
364#2297C2×C3111yescharacteristic, complemented
365C2×#344C2×C3111yescharacteristic, complemented
366C2×#339C2×C3111yescharacteristic, complemented
367C22×C31—22no—
368C22×C31—22no—
369C22×C31—22no—
370C22×C31—41no—
371C22×C31—41no—
372C22×C31—41no—
373C22×C31—41no—
374C22×C31—44no—
375C22×C31—42no—
376C22×C31—42no—
377C22×C31—82no—
378C22×C31—82no—
379C22×C31—82no—
380C22×C31—82no—
381C22×C31—82no—
382C22×C31#38611yescharacteristic
383C22×C31#38611yescharacteristic
384C22×C31#39011yescharacteristic
385C22×C31#39211yescharacteristic
386C22×C31#39211yescharacteristic
387C22×C31#39211yescharacteristic
388C22×C31#39411yescharacteristic
389C4×C31—44no—
390C4×C31—42no—
391C4×C31—42no—
392C4×C31—82no—
393C4×C31—82no—
394C4×C31#37911yescharacteristic
395C4×C31#38611yescharacteristic
396C4×C31#38611yescharacteristic
397C4×C31#39011yescharacteristic
398C4×C31#39211yescharacteristic
399C4×C31#39411yescharacteristic
400C4×C31#39411yescharacteristic
401C4×C31#39411yescharacteristic
402C22×#41C22×C3111yescharacteristic
403C22×#41C22×C3111yescharacteristic
404#575—22no—
405#575—22no—
406#575—22no—
407#575—22no—
408C2×#137—21no—
409C2×#137C4×C3112yescomplemented
410C2×AGL(1,ℤ/8)—21no—
411C2×AGL(1,ℤ/8)C4×C3112yescomplemented
412C2×#135—22no—
413C22×M16C22×C3111yescharacteristic
414C22×M16C22×C3111yescharacteristic
415C2×#117C22×C3111yescharacteristic
416C2×#117C22×C3111yescharacteristic
417C22×C42C22×C3111yescharacteristic
418#421—22no—
419#421—22no—
420C2×#104—22no—
421C2×#104—22no—
422C2×#104—22no—
423C2×#104—22no—
424#410—22no—
425#410—22no—
426C2×#99—22no—
427#391—21no—
428#390—21no—
429#386—22no—
430C4×C22⋊C4—22no—
431#344—22no—
432#339—22no—
433C2×C31—21no—
434C2×C31—21no—
435C2×C31—21no—
436C2×C31—21no—
437C2×C31—21no—
438C2×C31—21no—
439C2×C31—82no—
440C2×C31—82no—
441C2×C31#143811yescharacteristic
442C2×C31#190612yes—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41C2×C4×C3112yes—
464C2×#41D4×C3112yes—
465C2×#41D4×C3112yes—
466C2×#41D4×C3112yes—
467C22×Q8C2×C4×C3111yescharacteristic
468C22×Q8D4×C3111yescharacteristic
469C22×D4—21no—
470C22×D4—21no—
471C22×D4C2×C4×C3111yescharacteristic
472C22×D4D4×C3111yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—21no—
476C23×C4C23×C3111yescharacteristic
477#137—24no—
478#137—24no—
479#137—24no—
480#137—24no—
481AGL(1,ℤ/8)—24no—
482AGL(1,ℤ/8)—24no—
483AGL(1,ℤ/8)—24no—
484AGL(1,ℤ/8)—24no—
485#135—28no—
486#135—28no—
487C2×Q16—22no—
488C2×SD16—22no—
489C2×SD16—22no—
490C2×D8—22no—
491C2×M16—21no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16C2×C4×C3112yes—
500C2×M16D4×C3112yes—
501C2×M16D4×C3112yes—
502C2×M16D4×C3112yes—
503C22×C8—21no—
504C22×C8—21no—
505#117—21no—
506#117—21no—
507#117—21no—
508#117—21no—
509#117—21no—
510#117—21no—
511#117—21no—
512#117D4×C3112yes—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4D4×C3112yes—
518C2×C42—21no—
519C2×C42—21no—
520C2×C42—21no—
521C2×C42—21no—
522C2×C42—21no—
523C2×C42—21no—
524C2×C42—21no—
525C2×C42D4×C3112yes—
526#104—28no—
527#104—28no—
528#99—28no—
529#95—24no—
530C31#1101911yescharacteristic, direct product factor, Sylow
531C24—21no—
532C24—21no—
533C24C2×D4×C3111yescharacteristic
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8C22⋊C4×C3112yes—
577C2×Q8C22⋊C4×C3112yescomplemented
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4C22⋊C4×C3112yes—
601C2×D4C22⋊C4×C3112yescomplemented
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—44no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4C22×C4×C3111yescharacteristic
623C22×C4C2×D4×C3111yescharacteristic
624C22×C4C2×D4×C3111yescharacteristic
625C22×C4C2×D4×C3111yescharacteristic
626C22×C4C2×D4×C3111yescharacteristic
627C22×C4C2×D4×C3111yescharacteristic
628C22×C4C2×D4×C3111yescharacteristic
629C22×C4C2×D4×C3111yescharacteristic
630C22×C4C2×D4×C3111yescharacteristic
631C22×C4C2×D4×C3111yescharacteristic
632C22×C4#41×C3111yescharacteristic
633C22×C4#41×C3111yescharacteristic
634C22×C4#41×C3111yescharacteristic
635C22×C4#41×C3111yescharacteristic
636Q16—28no—
637SD16—28no—
638SD16—28no—
639D8—28no—
640M16—22no—
641M16—22no—
642M16—22no—
643M16—22no—
644M16—22no—
645M16—41no—
646M16—41no—
647M16C22⋊C4×C3114yescomplemented
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—41no—
653C2×C8—41no—
654C4⋊C4—22no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—48no—
662C22⋊C4—41no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—41no—
667C42—41no—
668C42—41no—
669C42—41no—
670C42—41no—
671C23—22no—
672C23—22no—
673C23—42no—
674C23—44no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—82no—
680C23C4×D4×C3111yescharacteristic
681C23C31×#12011yescharacteristic
682C23C31×#12011yescharacteristic
683C23C31×#12111yescharacteristic
684C23C31×#12111yescharacteristic
685C23C31×#12111yescharacteristic
686C23C31×#12711yescharacteristic
687Q8—22no—
688Q8—22no—
689Q8—22no—
690Q8—22no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694Q8—41no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—42no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—82no—
734C2×C4C2×C22⋊C4×C3111yescharacteristic
735C2×C4C2×C22⋊C4×C3111yescharacteristic
736C2×C4C2×C22⋊C4×C3111yescharacteristic
737C2×C4C4×D4×C3111yescharacteristic
738C2×C4C4×D4×C3111yescharacteristic
739C2×C4C4×D4×C3111yescharacteristic
740C2×C4C31×#12011yescharacteristic
741C2×C4C31×#12011yescharacteristic
742C2×C4C31×#12011yescharacteristic
743C2×C4C31×#12011yescharacteristic
744C2×C4C31×#12011yescharacteristic
745C2×C4C31×#12011yescharacteristic
746C2×C4C31×#12111yescharacteristic
747C2×C4C31×#12111yescharacteristic
748C2×C4C31×#12111yescharacteristic
749C2×C4C31×#12111yescharacteristic
750C2×C4C31×#12111yescharacteristic
751C2×C4C31×#12111yescharacteristic
752C2×C4C31×#12111yescharacteristic
753C2×C4C31×#12111yescharacteristic
754C2×C4C31×#12111yescharacteristic
755C2×C4C31×#12311yescharacteristic
756C2×C4C31×#12311yescharacteristic
757C2×C4C31×#12311yescharacteristic
758C2×C4C31×#12311yescharacteristic
759C2×C4C31×#12411yescharacteristic
760C2×C4C31×#12411yescharacteristic
761C2×C4C31×#12711yescharacteristic
762C8—24no—
763C8—42no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—44no—
772C22—42no—
773C22—42no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22C31×#38611yescharacteristic
780C22C31×#38611yescharacteristic
781C22C31×#39011yescharacteristic
782C22C31×#39211yescharacteristic
783C22C31×#39211yescharacteristic
784C22C31×#39211yescharacteristic
785C22C31×#39411yescharacteristic
786C4—44no—
787C4—42no—
788C4—42no—
789C4—82no—
790C4—82no—
791C4C31×#37911yescharacteristic
792C4C31×#38611yescharacteristic
793C4C31×#38611yescharacteristic
794C4C31×#39011yescharacteristic
795C4C31×#39211yescharacteristic
796C4C31×#39411yescharacteristic
797C4C31×#39411yescharacteristic
798C4C31×#39411yescharacteristic
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—82no—
806C2—82no—
807C2C31×#143811yescharacteristic
808C2C31×#190612yes—
subgroupG/H
centerC2×C4×C31#121
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
socleC22×C31#386
prime radicalC2×C31×#575C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#421C2semidirect
3. C22×C31×#104C2semidirect
4. C2×C31×#410C2semidirect
5. C31×#2297C2semidirect
6. C2×C31×#344C2semidirect
7. C2×C31×#339C2semidirect
15. C2×C31×#137C4semidirect
17. C2×C31×AGL(1,ℤ/8)C4semidirect
172. C2×Q8×C31C22⋊C4semidirect
196. C2×D4×C31C22⋊C4semidirect
242. M16×C31C22⋊C4semidirect
266. #11019C31direct (N × H)
361. C2×#421C2×C31semidirect
362. C22×#104C2×C31semidirect
363. C2×#410C2×C31semidirect
364. #2297C2×C31semidirect
365. C2×#344C2×C31semidirect
366. C2×#339C2×C31semidirect
409. C2×#137C4×C31semidirect
411. C2×AGL(1,ℤ/8)C4×C31semidirect
530. C31#11019direct (N × H)
577. C2×Q8C22⋊C4×C31semidirect
601. C2×D4C22⋊C4×C31semidirect
647. M16C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5752
C2×C31×#4212
C22×C31×#1042
C2×C31×#4102
C31×#22972
C2×C31×#3442
C2×C31×#3392
#1101931