Finite Group Databasebeta

← C31×#24284 #21481043

Subgroups — C31×#24284 #21481043

Order 7936.

1432 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C2×C31×#472C211yesmaximal, characteristic, complemented
3C2×C31×#471C211yesmaximal, characteristic, complemented
4C31×#3005C211yesmaximal, characteristic, complemented
5C31×#3003C211yesmaximal, characteristic, complemented
6C31×#2930C211yesmaximal, characteristic, complemented
7C31×#2046C211yesmaximal, characteristic, complemented
8C31×#2045C211yesmaximal, characteristic, complemented
9C31×#2019C211yesmaximal, characteristic, complemented
10C31×#2018C211yesmaximal, characteristic, complemented
11C31×#1978C211yesmaximal, characteristic, complemented
12C31×#1977C211yesmaximal, characteristic, complemented
13C31×#1811C211yesmaximal, characteristic, complemented
14C31×#1785C211yesmaximal, characteristic, complemented
15C31×#1783C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C2×C31×#137C2211yescharacteristic, complemented
19C2×C31×AGL(1,ℤ/8)—24no—
20C2×C31×AGL(1,ℤ/8)—24no—
21C2×C31×AGL(1,ℤ/8)—22no—
22C2×C31×AGL(1,ℤ/8)—22no—
23C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
24C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
25C2×C31×AGL(1,ℤ/8)C2211yescharacteristic, complemented
26C22×SD16×C31C2211yescharacteristic
27C22×SD16×C31C2211yescharacteristic
28C22×D8×C31C2211yescharacteristic
29C22×D8×C31C2211yescharacteristic
30C2×C31×#131C2211yescharacteristic, complemented
31C22×M16×C31C2211yescharacteristic
32C31×#525C2211yescharacteristic
33C31×#472—24no—
34C31×#471—24no—
35C31×#452—22no—
36C31×#450—22no—
37C31×#449—22no—
38C31×#447—22no—
39C31×#436—22no—
40C31×#435—22no—
41C2×C31×#108C2211yescharacteristic, complemented
42C2×C31×#108C2211yescharacteristic, complemented
43C31×#424C2211yescharacteristic, complemented
44C31×#419C2211yescharacteristic, complemented
45C31×#418C2211yescharacteristic
46C31×#418C2211yescharacteristic
47C31×#418C2211yescharacteristic, complemented
48C2×C31×#101C2211yescharacteristic, complemented
49C2×C31×#101C2211yescharacteristic, complemented
50C2×C31×#100C2211yescharacteristic
51C2×C31×#100C2211yescharacteristic
52C2×C31×#100C2211yescharacteristic
53C2×C31×#100C2211yescharacteristic
54C2×C31×#100C2211yescharacteristic, complemented
55C2×C31×#100C2211yescharacteristic, complemented
56C31×#408C2211yescharacteristic, complemented
57C31×#407C2211yescharacteristic
58C31×#407C2211yescharacteristic
59C31×#407C2211yescharacteristic
60C31×#405C2211yescharacteristic, complemented
61C31×#341C2211yescharacteristic, complemented
62C31×#341C2211yescharacteristic, complemented
63C25×C31—21no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—41no—
69C2×#41×C31—41no—
70C2×#41×C31C2311yescharacteristic
71C22×Q8×C31C2311yescharacteristic
72C22×D4×C31—22no—
73C22×D4×C31—22no—
74C22×D4×C31—21no—
75C22×D4×C31—22no—
76C22×D4×C31—22no—
77C22×D4×C31—21no—
78C22×D4×C31—41no—
79C22×D4×C31—41no—
80C22×D4×C31C2311yescharacteristic
81C22×D4×C31C2311yescharacteristic
82C22×D4×C31C2311yescharacteristic
83C23×C4×C31—21no—
84C23×C4×C31C2311yescharacteristic
85C31×#137—22no—
86C31×#137—41no—
87C31×AGL(1,ℤ/8)—216no—
88C31×AGL(1,ℤ/8)—216no—
89C31×AGL(1,ℤ/8)—22no—
90C31×AGL(1,ℤ/8)—22no—
91C31×AGL(1,ℤ/8)—22no—
92C31×AGL(1,ℤ/8)—41no—
93C31×AGL(1,ℤ/8)—41no—
94C31×AGL(1,ℤ/8)—41no—
95C2×Q16×C31—21no—
96C2×SD16×C31—22no—
97C2×SD16×C31—22no—
98C2×SD16×C31—21no—
99C2×SD16×C31—21no—
100C2×SD16×C31—21no—
101C2×SD16×C31—21no—
102C2×SD16×C31—22no—
103C2×SD16×C31—21no—
104C2×SD16×C31—21no—
105C2×SD16×C31—22no—
106C2×SD16×C31D414yescomplemented
107C2×D8×C31—22no—
108C2×D8×C31—22no—
109C2×D8×C31—21no—
110C2×D8×C31—21no—
111C2×D8×C31—21no—
112C2×D8×C31—22no—
113C2×D8×C31—21no—
114C2×D8×C31—21no—
115C2×D8×C31—22no—
116C2×D8×C31D414yescomplemented
117C31×#131—22no—
118C31×#131—22no—
119C2×M16×C31—22no—
120C2×M16×C31—22no—
121C2×M16×C31—21no—
122C2×M16×C31D412yes—
123C2×M16×C31D412yes—
124C2×M16×C31C2311yescharacteristic
125C2×M16×C31C2311yescharacteristic
126C2×M16×C31C2311yescharacteristic
127C2×M16×C31C2311yescharacteristic
128C2×M16×C31C2311yescharacteristic
129C2×M16×C31C2311yescharacteristic
130C22×C8×C31—21no—
131C22×C8×C31C2311yescharacteristic
132C22×C8×C31C2311yescharacteristic
133C31×#123—21no—
134C31×C22⋊Q8D412yes—
135C31×#121D412yes—
136C31×#120—21no—
137C4×D4×C31—22no—
138C31×#117C2311yescharacteristic
139C31×#108—22no—
140C31×#108—22no—
141C31×C4⋊C8—22no—
142C31×#103—22no—
143C31×#102—22no—
144C31×#102—22no—
145C31×#102—22no—
146C31×#101—22no—
147C31×#101—41no—
148C31×#100—22no—
149C31×#100—22no—
150C31×#100—22no—
151C31×#100—41no—
152C31×#100—41no—
153C31×#100—41no—
154C31×C22⋊C8—22no—
155C31×C22⋊C8—22no—
156C31×C22⋊C8—22no—
157C31×C22⋊C8—22no—
158C31×#97—21no—
159C4×C8×C31—21no—
160C24×C31—21no—
161C24×C31—21no—
162C24×C31—21no—
163C24×C31—42no—
164C24×C31—42no—
165C24×C31—42no—
166C24×C31—84no—
167C24×C31#4111yescharacteristic
168#41×C31—28no—
169#41×C31—21no—
170#41×C31—21no—
171#41×C31—21no—
172#41×C31—21no—
173#41×C31—44no—
174#41×C31—44no—
175#41×C31—44no—
176C2×Q8×C31—21no—
177C2×Q8×C31—21no—
178C2×Q8×C31—21no—
179C2×Q8×C31—21no—
180C2×Q8×C31—21no—
181C2×Q8×C31C2×D412yes—
182C2×Q8×C31C2×D411yescharacteristic
183C2×D4×C31—28no—
184C2×D4×C31—21no—
185C2×D4×C31—22no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—21no—
193C2×D4×C31—21no—
194C2×D4×C31—21no—
195C2×D4×C31—21no—
196C2×D4×C31—21no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—44no—
202C2×D4×C31—44no—
203C2×D4×C31—42no—
204C2×D4×C31—42no—
205C2×D4×C31—42no—
206C2×D4×C31—44no—
207C2×D4×C31—42no—
208C2×D4×C31—42no—
209C2×D4×C31—42no—
210C2×D4×C31C2×D412yes—
211C2×D4×C31C2×D412yes—
212C2×D4×C31C2×D412yes—
213C2×D4×C31C2×D411yescharacteristic
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—42no—
221C22×C4×C31—42no—
222C22×C4×C31—42no—
223C22×C4×C31C2×D412yes—
224C22×C4×C31C2×D412yes—
225C22×C4×C31#4111yescharacteristic
226C22×C4×C31C2411yescharacteristic
227Q16×C31—42no—
228SD16×C31—28no—
229SD16×C31—24no—
230SD16×C31—24no—
231SD16×C31—42no—
232SD16×C31—42no—
233SD16×C31—42no—
234SD16×C31—42no—
235D8×C31—28no—
236D8×C31—24no—
237D8×C31—24no—
238D8×C31—42no—
239D8×C31—42no—
240D8×C31—42no—
241M16×C31—24no—
242M16×C31—24no—
243M16×C31—21no—
244M16×C31—21no—
245M16×C31—21no—
246M16×C31—21no—
247M16×C31—21no—
248M16×C31—21no—
249M16×C31—21no—
250M16×C31—21no—
251M16×C31—21no—
252M16×C31—21no—
253M16×C31—21no—
254M16×C31—21no—
255M16×C31—42no—
256C2×C8×C31—21no—
257C2×C8×C31—21no—
258C2×C8×C31—21no—
259C2×C8×C31—21no—
260C2×C8×C31—21no—
261C2×C8×C31—21no—
262C2×C8×C31—21no—
263C2×C8×C31—21no—
264C2×C8×C31—42no—
265C2×C8×C31C2×D412yes—
266C2×C8×C31C2×D411yescharacteristic
267C2×C8×C31C2×D411yescharacteristic
268C2×C8×C31C2×D412yes—
269C2×C8×C31C2×D412yes—
270C4⋊C4×C31—22no—
271C4⋊C4×C31C2×D412yes—
272C22⋊C4×C31—22no—
273C22⋊C4×C31—21no—
274C22⋊C4×C31—22no—
275C42×C31—21no—
276#24284C3111yesmaximal, characteristic, direct product factor, Sylow
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—22no—
281C23×C31—22no—
282C23×C31—22no—
283C23×C31—42no—
284C23×C31—48no—
285C23×C31—41no—
286C23×C31—41no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—82no—
292C23×C31—82no—
293C23×C31—82no—
294C23×C31—84no—
295C23×C31—84no—
296C23×C31—88no—
297C23×C31—88no—
298C23×C31#12112yes—
299C23×C31C2×#4111yescharacteristic
300Q8×C31—22no—
301Q8×C31—21no—
302Q8×C31—21no—
303Q8×C31—22no—
304Q8×C31—41no—
305Q8×C31—41no—
306D4×C31—22no—
307D4×C31—22no—
308D4×C31—22no—
309D4×C31—21no—
310D4×C31—21no—
311D4×C31—22no—
312D4×C31—22no—
313D4×C31—22no—
314D4×C31—48no—
315D4×C31—48no—
316D4×C31—41no—
317D4×C31—41no—
318D4×C31—41no—
319D4×C31—41no—
320D4×C31—41no—
321D4×C31—41no—
322D4×C31—41no—
323D4×C31—41no—
324D4×C31—82no—
325C2×C4×C31—21no—
326C2×C4×C31—21no—
327C2×C4×C31—22no—
328C2×C4×C31—22no—
329C2×C4×C31—22no—
330C2×C4×C31—22no—
331C2×C4×C31—22no—
332C2×C4×C31—21no—
333C2×C4×C31—22no—
334C2×C4×C31—48no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31#12112yes—
340C2×C4×C31C22×D411yescharacteristic
341C2×C4×C31C22×D411yescharacteristic
342C2×C4×C31C22×D411yescharacteristic
343C2×C4×C31C22×D411yescharacteristic
344C2×C4×C31H(5,𝔽2)11yescharacteristic
345C2×C4×C31H(5,𝔽2)11yescharacteristic
346C8×C31—22no—
347C8×C31—41no—
348C8×C31—41no—
349C8×C31—41no—
350C8×C31—41no—
351C8×C31—41no—
352C8×C31—41no—
353C8×C31#12012yes—
354C8×C31#12012yes—
355C22×AGL(1,ℤ/8)C2×C3111yescharacteristic, complemented
356C2×#472C2×C3111yescharacteristic, complemented
357C2×#471C2×C3111yescharacteristic, complemented
358#3005C2×C3111yescharacteristic, complemented
359#3003C2×C3111yescharacteristic, complemented
360#2930C2×C3111yescharacteristic, complemented
361#2046C2×C3111yescharacteristic, complemented
362#2045C2×C3111yescharacteristic, complemented
363#2019C2×C3111yescharacteristic, complemented
364#2018C2×C3111yescharacteristic, complemented
365#1978C2×C3111yescharacteristic, complemented
366#1977C2×C3111yescharacteristic, complemented
367#1811C2×C3111yescharacteristic, complemented
368#1785C2×C3111yescharacteristic, complemented
369#1783C2×C3111yescharacteristic, complemented
370C22×C31—22no—
371C22×C31—22no—
372C22×C31—22no—
373C22×C31—22no—
374C22×C31—42no—
375C22×C31—42no—
376C22×C31—42no—
377C22×C31—41no—
378C22×C31—42no—
379C22×C31—42no—
380C22×C31—42no—
381C22×C31—82no—
382C22×C31—82no—
383C22×C31—82no—
384C22×C31—82no—
385C22×C31—82no—
386C22×C31—82no—
387C22×C31—816no—
388C22×C31—82no—
389C22×C31—82no—
390C22×C31—82no—
391C22×C31C2×#12111yescharacteristic
392C22×C31#54611yescharacteristic
393C22×C31#54611yescharacteristic
394C4×C31—22no—
395C4×C31—42no—
396C4×C31—41no—
397C4×C31—42no—
398C4×C31C2×#12011yescharacteristic
399C4×C31#53511yescharacteristic
400C4×C31D4211yescharacteristic
401C4×C31D4211yescharacteristic
402C22×#41C22×C3111yescharacteristic
403C23×D4C22×C3111yescharacteristic
404C2×#137C22×C3111yescharacteristic, complemented
405C2×AGL(1,ℤ/8)—24no—
406C2×AGL(1,ℤ/8)—24no—
407C2×AGL(1,ℤ/8)—22no—
408C2×AGL(1,ℤ/8)—22no—
409C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
410C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
411C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
412C22×SD16C22×C3111yescharacteristic
413C22×SD16C22×C3111yescharacteristic
414C22×D8C22×C3111yescharacteristic
415C22×D8C22×C3111yescharacteristic
416C2×#131C22×C3111yescharacteristic, complemented
417C22×M16C22×C3111yescharacteristic
418#525C22×C3111yescharacteristic
419#472—24no—
420#471—24no—
421#452—22no—
422#450—22no—
423#449—22no—
424#447—22no—
425#436—22no—
426#435—22no—
427C2×#108C22×C3111yescharacteristic, complemented
428C2×#108C22×C3111yescharacteristic, complemented
429#424C22×C3111yescharacteristic, complemented
430#419C22×C3111yescharacteristic, complemented
431#418C22×C3111yescharacteristic
432#418C22×C3111yescharacteristic
433#418C22×C3111yescharacteristic, complemented
434C2×#101C22×C3111yescharacteristic, complemented
435C2×#101C22×C3111yescharacteristic, complemented
436C2×#100C22×C3111yescharacteristic
437C2×#100C22×C3111yescharacteristic
438C2×#100C22×C3111yescharacteristic
439C2×#100C22×C3111yescharacteristic
440C2×#100C22×C3111yescharacteristic, complemented
441C2×#100C22×C3111yescharacteristic, complemented
442#408C22×C3111yescharacteristic, complemented
443#407C22×C3111yescharacteristic
444#407C22×C3111yescharacteristic
445#407C22×C3111yescharacteristic
446#405C22×C3111yescharacteristic, complemented
447#341C22×C3111yescharacteristic, complemented
448#341C22×C3111yescharacteristic, complemented
449C2×C31—21no—
450C2×C31—21no—
451C2×C31—42no—
452C2×C31—81no—
453C2×C31—82no—
454C2×C31—82no—
455C2×C31—82no—
456C2×C31#240811yescharacteristic
457C2×C31#306812yes—
458C25—21no—
459C2×#41—22no—
460C2×#41—22no—
461C2×#41—22no—
462C2×#41—22no—
463C2×#41—41no—
464C2×#41—41no—
465C2×#41C23×C3111yescharacteristic
466C22×Q8C23×C3111yescharacteristic
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—21no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—21no—
473C22×D4—41no—
474C22×D4—41no—
475C22×D4C23×C3111yescharacteristic
476C22×D4C23×C3111yescharacteristic
477C22×D4C23×C3111yescharacteristic
478C23×C4—21no—
479C23×C4C23×C3111yescharacteristic
480#137—22no—
481#137—41no—
482AGL(1,ℤ/8)—216no—
483AGL(1,ℤ/8)—216no—
484AGL(1,ℤ/8)—22no—
485AGL(1,ℤ/8)—22no—
486AGL(1,ℤ/8)—22no—
487AGL(1,ℤ/8)—41no—
488AGL(1,ℤ/8)—41no—
489AGL(1,ℤ/8)—41no—
490C2×Q16—21no—
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—21no—
494C2×SD16—21no—
495C2×SD16—21no—
496C2×SD16—21no—
497C2×SD16—22no—
498C2×SD16—21no—
499C2×SD16—21no—
500C2×SD16—22no—
501C2×SD16D4×C3114yescomplemented
502C2×D8—22no—
503C2×D8—22no—
504C2×D8—21no—
505C2×D8—21no—
506C2×D8—21no—
507C2×D8—22no—
508C2×D8—21no—
509C2×D8—21no—
510C2×D8—22no—
511C2×D8D4×C3114yescomplemented
512#131—22no—
513#131—22no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—21no—
517C2×M16D4×C3112yes—
518C2×M16D4×C3112yes—
519C2×M16C23×C3111yescharacteristic
520C2×M16C23×C3111yescharacteristic
521C2×M16C23×C3111yescharacteristic
522C2×M16C23×C3111yescharacteristic
523C2×M16C23×C3111yescharacteristic
524C2×M16C23×C3111yescharacteristic
525C22×C8—21no—
526C22×C8C23×C3111yescharacteristic
527C22×C8C23×C3111yescharacteristic
528#123—21no—
529C22⋊Q8D4×C3112yes—
530#121D4×C3112yes—
531#120—21no—
532C4×D4—22no—
533#117C23×C3111yescharacteristic
534#108—22no—
535#108—22no—
536C4⋊C8—22no—
537#103—22no—
538#102—22no—
539#102—22no—
540#102—22no—
541#101—22no—
542#101—41no—
543#100—22no—
544#100—22no—
545#100—22no—
546#100—41no—
547#100—41no—
548#100—41no—
549C22⋊C8—22no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553#97—21no—
554C4×C8—21no—
555C31#2428411yescharacteristic, direct product factor, Sylow
556C24—21no—
557C24—21no—
558C24—21no—
559C24—42no—
560C24—42no—
561C24—42no—
562C24—84no—
563C24#41×C3111yescharacteristic
564#41—28no—
565#41—21no—
566#41—21no—
567#41—21no—
568#41—21no—
569#41—44no—
570#41—44no—
571#41—44no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C3112yes—
578C2×Q8C2×D4×C3111yescharacteristic
579C2×D4—28no—
580C2×D4—21no—
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—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—44no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4C2×D4×C3112yes—
607C2×D4C2×D4×C3112yes—
608C2×D4C2×D4×C3112yes—
609C2×D4C2×D4×C3111yescharacteristic
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4C2×D4×C3112yes—
620C22×C4C2×D4×C3112yes—
621C22×C4#41×C3111yescharacteristic
622C22×C4C24×C3111yescharacteristic
623Q16—42no—
624SD16—28no—
625SD16—24no—
626SD16—24no—
627SD16—42no—
628SD16—42no—
629SD16—42no—
630SD16—42no—
631D8—28no—
632D8—24no—
633D8—24no—
634D8—42no—
635D8—42no—
636D8—42no—
637M16—24no—
638M16—24no—
639M16—21no—
640M16—21no—
641M16—21no—
642M16—21no—
643M16—21no—
644M16—21no—
645M16—21no—
646M16—21no—
647M16—21no—
648M16—21no—
649M16—21no—
650M16—21no—
651M16—42no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—42no—
661C2×C8C2×D4×C3112yes—
662C2×C8C2×D4×C3111yescharacteristic
663C2×C8C2×D4×C3111yescharacteristic
664C2×C8C2×D4×C3112yes—
665C2×C8C2×D4×C3112yes—
666C4⋊C4—22no—
667C4⋊C4C2×D4×C3112yes—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—22no—
671C42—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—42no—
679C23—48no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—82no—
687C23—82no—
688C23—82no—
689C23—84no—
690C23—84no—
691C23—88no—
692C23—88no—
693C23C31×#12112yes—
694C23C2×#41×C3111yescharacteristic
695Q8—22no—
696Q8—21no—
697Q8—21no—
698Q8—22no—
699Q8—41no—
700Q8—41no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—21no—
705D4—21no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—48no—
710D4—48no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—82no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—48no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4C31×#12112yes—
735C2×C4C22×D4×C3111yescharacteristic
736C2×C4C22×D4×C3111yescharacteristic
737C2×C4C22×D4×C3111yescharacteristic
738C2×C4C22×D4×C3111yescharacteristic
739C2×C4C31×H(5,𝔽2)11yescharacteristic
740C2×C4C31×H(5,𝔽2)11yescharacteristic
741C8—22no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—41no—
747C8—41no—
748C8C31×#12012yes—
749C8C31×#12012yes—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—816no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22C2×C31×#12111yescharacteristic
772C22C31×#54611yescharacteristic
773C22C31×#54611yescharacteristic
774C4—22no—
775C4—42no—
776C4—41no—
777C4—42no—
778C4C2×C31×#12011yescharacteristic
779C4C31×#53511yescharacteristic
780C4D42×C3111yescharacteristic
781C4D42×C3111yescharacteristic
782C2—21no—
783C2—21no—
784C2—42no—
785C2—81no—
786C2—82no—
787C2—82no—
788C2—82no—
789C2C31×#240811yescharacteristic
790C2C31×#306812yes—
subgroupG/H
center, socleC22×C31C2×#121
commutator, Frattini, cosocleC22×C4C24×C31
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
1. C22×C31×AGL(1,ℤ/8)C2semidirect
2. C2×C31×#472C2semidirect
3. C2×C31×#471C2semidirect
4. C31×#3005C2semidirect
5. C31×#3003C2semidirect
6. C31×#2930C2semidirect
7. C31×#2046C2semidirect
8. C31×#2045C2semidirect
9. C31×#2019C2semidirect
10. C31×#2018C2semidirect
11. C31×#1978C2semidirect
12. C31×#1977C2semidirect
13. C31×#1811C2semidirect
14. C31×#1785C2semidirect
15. C31×#1783C2semidirect
18. C2×C31×#137C22semidirect
25. C2×C31×AGL(1,ℤ/8)C22semidirect
30. C2×C31×#131C22semidirect
41. C2×C31×#108C22semidirect
42. C2×C31×#108C22semidirect
43. C31×#424C22semidirect
44. C31×#419C22semidirect
47. C31×#418C22semidirect
48. C2×C31×#101C22semidirect
49. C2×C31×#101C22semidirect
54. C2×C31×#100C22semidirect
55. C2×C31×#100C22semidirect
56. C31×#408C22semidirect
60. C31×#405C22semidirect
61. C31×#341C22semidirect
62. C31×#341C22semidirect
106. C2×SD16×C31D4semidirect
116. C2×D8×C31D4semidirect
276. #24284C31direct (N × H)
355. C22×AGL(1,ℤ/8)C2×C31semidirect
356. C2×#472C2×C31semidirect
357. C2×#471C2×C31semidirect
358. #3005C2×C31semidirect
359. #3003C2×C31semidirect
360. #2930C2×C31semidirect
361. #2046C2×C31semidirect
362. #2045C2×C31semidirect
363. #2019C2×C31semidirect
364. #2018C2×C31semidirect
365. #1978C2×C31semidirect
366. #1977C2×C31semidirect
367. #1811C2×C31semidirect
368. #1785C2×C31semidirect
369. #1783C2×C31semidirect
404. C2×#137C22×C31semidirect
411. C2×AGL(1,ℤ/8)C22×C31semidirect
416. C2×#131C22×C31semidirect
427. C2×#108C22×C31semidirect
428. C2×#108C22×C31semidirect
429. #424C22×C31semidirect
430. #419C22×C31semidirect
433. #418C22×C31semidirect
434. C2×#101C22×C31semidirect
435. C2×#101C22×C31semidirect
440. C2×#100C22×C31semidirect
441. C2×#100C22×C31semidirect
442. #408C22×C31semidirect
446. #405C22×C31semidirect
447. #341C22×C31semidirect
448. #341C22×C31semidirect
501. C2×SD16D4×C31semidirect
511. C2×D8D4×C31semidirect
555. C31#24284direct (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×#4722
C2×C31×#4712
C31×#30052
C31×#30032
C31×#29302
C31×#20462
C31×#20452
C31×#20192
C31×#20182
C31×#19782
C31×#19772
C31×#18112
C31×#17852
C31×#17832
#2428431