Finite Group Databasebeta

← C31×#11036 #21467795

Subgroups — C31×#11036 #21467795

Order 7936.

1310 conjugacy classes of subgroups.

The subgroup lattice has 834 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
3C2×C31×#417C211yesmaximal, characteristic, complemented
4C2×C31×#410C211yesmaximal, characteristic, complemented
5C31×#2311C211yesmaximal, characteristic, complemented
6C2×C31×#344C211yesmaximal, characteristic, complemented
7C31×#1736C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C22×#41×C31C2211yescharacteristic
10C31×#575—22no—
11C31×#575—22no—
12C31×#575—22no—
13C31×#575C414yescomplemented
14C2×C31×#137—21no—
15C2×C31×#137—21no—
16C2×C31×AGL(1,ℤ/8)—21no—
17C2×C31×AGL(1,ℤ/8)—21no—
18C2×C31×#135—22no—
19C22×M16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C31×#421—22no—
25C31×#421—22no—
26C2×C31×#104—22no—
27C31×#417—22no—
28C31×#417—22no—
29C2×C31×#103—21no—
30C2×C31×#102—21no—
31C31×#410—22no—
32C31×#410—22no—
33C2×C31×#99—22no—
34C31×#391—21no—
35C31×#390—21no—
36C31×#386—22no—
37C31×#380—22no—
38C31×#344—22no—
39C31×#340—22no—
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×C31—21no—
60C2×#41×C31C2×C412yes—
61C2×#41×C31C2×C412yes—
62C2×#41×C31D412yes—
63C2×#41×C31D412yes—
64C22×Q8×C31D411yescharacteristic
65C22×Q8×C31D411yescharacteristic
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31D411yescharacteristic
69C22×D4×C31D411yescharacteristic
70C23×C4×C31—21no—
71C23×C4×C31—21no—
72C23×C4×C31—21no—
73C23×C4×C31C2311yescharacteristic
74C31×#137—24no—
75C31×#137—24no—
76C31×#137—24no—
77C31×#137—24no—
78C31×AGL(1,ℤ/8)—24no—
79C31×AGL(1,ℤ/8)—24no—
80C31×AGL(1,ℤ/8)—24no—
81C31×AGL(1,ℤ/8)—24no—
82C31×#135—28no—
83C31×#135—28no—
84C2×Q16×C31—22no—
85C2×SD16×C31—22no—
86C2×SD16×C31—22no—
87C2×D8×C31—22no—
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×C31C2×C412yes—
98C2×M16×C31D412yes—
99C2×M16×C31D412yes—
100C22×C8×C31—21no—
101C22×C8×C31D412yes—
102C31×#117—21no—
103C31×#117—21no—
104C31×#117—21no—
105C31×#117—21no—
106C31×#117—21no—
107C31×#117—21no—
108C31×#117—21no—
109C31×#117D412yes—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31—21no—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31—21no—
117C2×C4⋊C4×C31D412yes—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—24no—
120C2×C22⋊C4×C31D412yes—
121C2×C42×C31—21no—
122C2×C42×C31—21no—
123C31×#104—28no—
124C31×#103—24no—
125C31×#102—24no—
126C31×#99—28no—
127C31×#95—24no—
128C24×C31—21no—
129C24×C31—21no—
130C24×C31C2×D411yescharacteristic
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—22no—
146#41×C31—22no—
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—
161#41×C31—41no—
162#41×C31—41no—
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×C31—21no—
172C2×Q8×C31—21no—
173C2×Q8×C31C22⋊C412yes—
174C2×Q8×C31C22⋊C412yescomplemented
175C2×D4×C31—22no—
176C2×D4×C31—22no—
177C2×D4×C31—22no—
178C2×D4×C31—22no—
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—21no—
188C2×D4×C31—21no—
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×C31—41no—
196C2×D4×C31—41no—
197C2×D4×C31C22⋊C412yes—
198C2×D4×C31C22⋊C412yescomplemented
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—22no—
202C22×C4×C31—22no—
203C22×C4×C31—22no—
204C22×C4×C31—22no—
205C22×C4×C31—22no—
206C22×C4×C31—22no—
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×C31—41no—
218C22×C4×C31—82no—
219C22×C4×C31C22×C411yescharacteristic
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×C31C2×D411yescharacteristic
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31#4111yescharacteristic
230C22×C4×C31#4111yescharacteristic
231C22×C4×C31#4111yescharacteristic
232C22×C4×C31#4111yescharacteristic
233Q16×C31—28no—
234SD16×C31—28no—
235SD16×C31—28no—
236D8×C31—28no—
237M16×C31—22no—
238M16×C31—22no—
239M16×C31—22no—
240M16×C31—22no—
241M16×C31—22no—
242M16×C31—22no—
243M16×C31—41no—
244M16×C31—41no—
245C2×C8×C31—22no—
246C2×C8×C31—22no—
247C2×C8×C31—22no—
248C2×C8×C31—41no—
249C2×C8×C31—41no—
250C2×C8×C31C22⋊C414yescomplemented
251C4⋊C4×C31—22no—
252C4⋊C4×C31—22no—
253C4⋊C4×C31—22no—
254C4⋊C4×C31—41no—
255C4⋊C4×C31—41no—
256C4⋊C4×C31—41no—
257C4⋊C4×C31—41no—
258C4⋊C4×C31—41no—
259C22⋊C4×C31—22no—
260C22⋊C4×C31—22no—
261C22⋊C4×C31—22no—
262C22⋊C4×C31—41no—
263C22⋊C4×C31—84no—
264C42×C31—22no—
265C42×C31—41no—
266C42×C31—41no—
267C42×C31—41no—
268#11036C3111yesmaximal, characteristic, direct product factor, Sylow
269C23×C31—22no—
270C23×C31—22no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—42no—
274C23×C31—42no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—81no—
280C23×C31—81no—
281C23×C31C4×D411yescharacteristic
282C23×C31#12011yescharacteristic
283C23×C31#12011yescharacteristic
284C23×C31#12111yescharacteristic
285C23×C31#12111yescharacteristic
286C23×C31#12111yescharacteristic
287C23×C31#12711yescharacteristic
288Q8×C31—22no—
289Q8×C31—22no—
290Q8×C31—22no—
291Q8×C31—22no—
292Q8×C31—41no—
293Q8×C31—41no—
294Q8×C31—41no—
295Q8×C31—41no—
296D4×C31—22no—
297D4×C31—22no—
298D4×C31—22no—
299D4×C31—22no—
300D4×C31—42no—
301D4×C31—42no—
302D4×C31—42no—
303D4×C31—42no—
304D4×C31—42no—
305D4×C31—42no—
306D4×C31—42no—
307D4×C31—42no—
308D4×C31—41no—
309D4×C31—41no—
310D4×C31—41no—
311D4×C31—41no—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
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—42no—
327C2×C4×C31—44no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—42no—
331C2×C4×C31—42no—
332C2×C4×C31—81no—
333C2×C4×C31—81no—
334C2×C4×C31—82no—
335C2×C4×C31—82no—
336C2×C4×C31C2×C22⋊C411yescharacteristic
337C2×C4×C31C2×C22⋊C411yescharacteristic
338C2×C4×C31C2×C22⋊C411yescharacteristic
339C2×C4×C31C4×D411yescharacteristic
340C2×C4×C31C4×D411yescharacteristic
341C2×C4×C31C4×D411yescharacteristic
342C2×C4×C31#12011yescharacteristic
343C2×C4×C31#12011yescharacteristic
344C2×C4×C31#12011yescharacteristic
345C2×C4×C31#12011yescharacteristic
346C2×C4×C31#12011yescharacteristic
347C2×C4×C31#12011yescharacteristic
348C2×C4×C31#12111yescharacteristic
349C2×C4×C31#12111yescharacteristic
350C2×C4×C31#12111yescharacteristic
351C2×C4×C31#12111yescharacteristic
352C2×C4×C31#12111yescharacteristic
353C2×C4×C31#12111yescharacteristic
354C2×C4×C31#12111yescharacteristic
355C2×C4×C31#12111yescharacteristic
356C2×C4×C31#12111yescharacteristic
357C2×C4×C31#12311yescharacteristic
358C2×C4×C31#12311yescharacteristic
359C2×C4×C31#12311yescharacteristic
360C2×C4×C31#12311yescharacteristic
361C2×C4×C31#12411yescharacteristic
362C2×C4×C31#12411yescharacteristic
363C2×C4×C31#12711yescharacteristic
364C8×C31—24no—
365C8×C31—42no—
366C2×#575C2×C3111yescharacteristic
367C2×#421C2×C3111yescharacteristic, complemented
368C2×#417C2×C3111yescharacteristic, complemented
369C2×#410C2×C3111yescharacteristic, complemented
370#2311C2×C3111yescharacteristic, complemented
371C2×#344C2×C3111yescharacteristic, complemented
372#1736C2×C3111yescharacteristic, complemented
373C22×C31—21no—
374C22×C31—21no—
375C22×C31—21no—
376C22×C31—21no—
377C22×C31—21no—
378C22×C31—21no—
379C22×C31—41no—
380C22×C31—41no—
381C22×C31—41no—
382C22×C31—41no—
383C22×C31—44no—
384C22×C31—42no—
385C22×C31—42no—
386C22×C31—82no—
387C22×C31—82no—
388C22×C31—82no—
389C22×C31—81no—
390C22×C31—81no—
391C22×C31—81no—
392C22×C31—81no—
393C22×C31#38611yescharacteristic
394C22×C31#38611yescharacteristic
395C22×C31#39011yescharacteristic
396C22×C31#39211yescharacteristic
397C22×C31#39211yescharacteristic
398C22×C31#39211yescharacteristic
399C22×C31#39411yescharacteristic
400C4×C31—42no—
401C4×C31—42no—
402C4×C31—82no—
403C4×C31—82no—
404C4×C31—82no—
405C4×C31#37911yescharacteristic
406C4×C31#38611yescharacteristic
407C4×C31#38611yescharacteristic
408C4×C31#39011yescharacteristic
409C4×C31#39211yescharacteristic
410C4×C31#39411yescharacteristic
411C4×C31#39411yescharacteristic
412C4×C31#39411yescharacteristic
413C22×#41C22×C3111yescharacteristic
414C22×#41C22×C3111yescharacteristic
415#575—22no—
416#575—22no—
417#575—22no—
418#575C4×C3114yescomplemented
419C2×#137—21no—
420C2×#137—21no—
421C2×AGL(1,ℤ/8)—21no—
422C2×AGL(1,ℤ/8)—21no—
423C2×#135—22no—
424C22×M16C22×C3111yescharacteristic
425C22×M16C22×C3111yescharacteristic
426C2×#117C22×C3111yescharacteristic
427C2×#117C22×C3111yescharacteristic
428C22×C4⋊C4C22×C3111yescharacteristic
429#421—22no—
430#421—22no—
431C2×#104—22no—
432#417—22no—
433#417—22no—
434C2×#103—21no—
435C2×#102—21no—
436#410—22no—
437#410—22no—
438C2×#99—22no—
439#391—21no—
440#390—21no—
441#386—22no—
442#380—22no—
443#344—22no—
444#340—22no—
445C2×C31—21no—
446C2×C31—21no—
447C2×C31—21no—
448C2×C31—21no—
449C2×C31—21no—
450C2×C31—21no—
451C2×C31—82no—
452C2×C31—82no—
453C2×C31#143811yescharacteristic
454C2×C31#200811yescharacteristic
455C2×C31#200911yescharacteristic
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C2×#41C2×C4×C3112yes—
477C2×#41C2×C4×C3112yes—
478C2×#41D4×C3112yes—
479C2×#41D4×C3112yes—
480C22×Q8D4×C3111yescharacteristic
481C22×Q8D4×C3111yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4D4×C3111yescharacteristic
485C22×D4D4×C3111yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4C23×C3111yescharacteristic
490#137—24no—
491#137—24no—
492#137—24no—
493#137—24no—
494AGL(1,ℤ/8)—24no—
495AGL(1,ℤ/8)—24no—
496AGL(1,ℤ/8)—24no—
497AGL(1,ℤ/8)—24no—
498#135—28no—
499#135—28no—
500C2×Q16—22no—
501C2×SD16—22no—
502C2×SD16—22no—
503C2×D8—22no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16—21no—
508C2×M16—21no—
509C2×M16—21no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16C2×C4×C3112yes—
514C2×M16D4×C3112yes—
515C2×M16D4×C3112yes—
516C22×C8—21no—
517C22×C8D4×C3112yes—
518#117—21no—
519#117—21no—
520#117—21no—
521#117—21no—
522#117—21no—
523#117—21no—
524#117—21no—
525#117D4×C3112yes—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4D4×C3112yes—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4D4×C3112yes—
537C2×C42—21no—
538C2×C42—21no—
539#104—28no—
540#103—24no—
541#102—24no—
542#99—28no—
543#95—24no—
544C31#1103611yescharacteristic, direct product factor, Sylow
545C24—21no—
546C24—21no—
547C24C2×D4×C3111yescharacteristic
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575#41—41no—
576#41—41no—
577#41—41no—
578#41—41no—
579#41—41no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8C22⋊C4×C3112yes—
591C2×Q8C22⋊C4×C3112yescomplemented
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4C22⋊C4×C3112yes—
615C2×D4C22⋊C4×C3112yescomplemented
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—82no—
636C22×C4C22×C4×C3111yescharacteristic
637C22×C4C2×D4×C3111yescharacteristic
638C22×C4C2×D4×C3111yescharacteristic
639C22×C4C2×D4×C3111yescharacteristic
640C22×C4C2×D4×C3111yescharacteristic
641C22×C4C2×D4×C3111yescharacteristic
642C22×C4C2×D4×C3111yescharacteristic
643C22×C4C2×D4×C3111yescharacteristic
644C22×C4C2×D4×C3111yescharacteristic
645C22×C4C2×D4×C3111yescharacteristic
646C22×C4#41×C3111yescharacteristic
647C22×C4#41×C3111yescharacteristic
648C22×C4#41×C3111yescharacteristic
649C22×C4#41×C3111yescharacteristic
650Q16—28no—
651SD16—28no—
652SD16—28no—
653D8—28no—
654M16—22no—
655M16—22no—
656M16—22no—
657M16—22no—
658M16—22no—
659M16—22no—
660M16—41no—
661M16—41no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—41no—
666C2×C8—41no—
667C2×C8C22⋊C4×C3114yescomplemented
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—41no—
672C4⋊C4—41no—
673C4⋊C4—41no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—41no—
680C22⋊C4—84no—
681C42—22no—
682C42—41no—
683C42—41no—
684C42—41no—
685C23—22no—
686C23—22no—
687C23—41no—
688C23—41no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—81no—
696C23—81no—
697C23C4×D4×C3111yescharacteristic
698C23C31×#12011yescharacteristic
699C23C31×#12011yescharacteristic
700C23C31×#12111yescharacteristic
701C23C31×#12111yescharacteristic
702C23C31×#12111yescharacteristic
703C23C31×#12711yescharacteristic
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—22no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711Q8—41no—
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—42no—
717D4—42no—
718D4—42no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—82no—
751C2×C4—82no—
752C2×C4C2×C22⋊C4×C3111yescharacteristic
753C2×C4C2×C22⋊C4×C3111yescharacteristic
754C2×C4C2×C22⋊C4×C3111yescharacteristic
755C2×C4C4×D4×C3111yescharacteristic
756C2×C4C4×D4×C3111yescharacteristic
757C2×C4C4×D4×C3111yescharacteristic
758C2×C4C31×#12011yescharacteristic
759C2×C4C31×#12011yescharacteristic
760C2×C4C31×#12011yescharacteristic
761C2×C4C31×#12011yescharacteristic
762C2×C4C31×#12011yescharacteristic
763C2×C4C31×#12011yescharacteristic
764C2×C4C31×#12111yescharacteristic
765C2×C4C31×#12111yescharacteristic
766C2×C4C31×#12111yescharacteristic
767C2×C4C31×#12111yescharacteristic
768C2×C4C31×#12111yescharacteristic
769C2×C4C31×#12111yescharacteristic
770C2×C4C31×#12111yescharacteristic
771C2×C4C31×#12111yescharacteristic
772C2×C4C31×#12111yescharacteristic
773C2×C4C31×#12311yescharacteristic
774C2×C4C31×#12311yescharacteristic
775C2×C4C31×#12311yescharacteristic
776C2×C4C31×#12311yescharacteristic
777C2×C4C31×#12411yescharacteristic
778C2×C4C31×#12411yescharacteristic
779C2×C4C31×#12711yescharacteristic
780C8—24no—
781C8—42no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—44no—
793C22—42no—
794C22—42no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22C31×#38611yescharacteristic
803C22C31×#38611yescharacteristic
804C22C31×#39011yescharacteristic
805C22C31×#39211yescharacteristic
806C22C31×#39211yescharacteristic
807C22C31×#39211yescharacteristic
808C22C31×#39411yescharacteristic
809C4—42no—
810C4—42no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4C31×#37911yescharacteristic
815C4C31×#38611yescharacteristic
816C4C31×#38611yescharacteristic
817C4C31×#39011yescharacteristic
818C4C31×#39211yescharacteristic
819C4C31×#39411yescharacteristic
820C4C31×#39411yescharacteristic
821C4C31×#39411yescharacteristic
822C2—21no—
823C2—21no—
824C2—21no—
825C2—21no—
826C2—21no—
827C2—21no—
828C2—82no—
829C2—82no—
830C2C31×#143811yescharacteristic
831C2C31×#200811yescharacteristic
832C2C31×#200911yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#575C2
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×#417C2semidirect
4. C2×C31×#410C2semidirect
5. C31×#2311C2semidirect
6. C2×C31×#344C2semidirect
7. C31×#1736C2semidirect
13. C31×#575C4semidirect
174. C2×Q8×C31C22⋊C4semidirect
198. C2×D4×C31C22⋊C4semidirect
250. C2×C8×C31C22⋊C4semidirect
268. #11036C31direct (N × H)
367. C2×#421C2×C31semidirect
368. C2×#417C2×C31semidirect
369. C2×#410C2×C31semidirect
370. #2311C2×C31semidirect
371. C2×#344C2×C31semidirect
372. #1736C2×C31semidirect
418. #575C4×C31semidirect
544. C31#11036direct (N × H)
591. C2×Q8C22⋊C4×C31semidirect
615. C2×D4C22⋊C4×C31semidirect
667. C2×C8C22⋊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
C2×C31×#4172
C2×C31×#4102
C31×#23112
C2×C31×#3442
C31×#17362
#1103631