Finite Group Databasebeta

← C31×#12753 #21469512

Subgroups — C31×#12753 #21469512

Order 7936.

936 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3532C211yesmaximal, characteristic
2C31×#2127C211yesmaximal, characteristic, complemented
3C31×#2121C211yesmaximal, characteristic, complemented
4C2×C31×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
5C31×#1913C211yesmaximal, characteristic, complemented
6C31×#1911C211yesmaximal, characteristic, complemented
7C31×#1889C211yesmaximal, characteristic, complemented
8C31×H(3,𝔽4)C411yescharacteristic, complemented
9C31×#560—21no—
10C31×#560C411yescharacteristic, complemented
11C31×#551—21no—
12C31×#551C411yescharacteristic, complemented
13C31×#546—21no—
14C31×#546—21no—
15C31×#546—21no—
16D42×C31—21no—
17D42×C31C411yescharacteristic, complemented
18C31×#538—21no—
19C31×#538—21no—
20C31×#538—21no—
21C31×#535—21no—
22C31×#535C2211yescharacteristic
23C31×#534—21no—
24C31×#534C2211yescharacteristic
25C2×C31×#120—21no—
26C2×C31×#120C2211yescharacteristic
27C31×#518C2211yescharacteristic, complemented
28C31×#421—21no—
29C2×C31×#100C2211yescharacteristic, complemented
30C2×C31×#99—21no—
31C2×C31×#99C2211yescharacteristic, complemented
32C2×C31×#99C2211yescharacteristic, complemented
33C31×#379—21no—
34C31×#354—21no—
35C31×#353—21no—
36C31×#352—21no—
37C31×AΣL(1,𝔽16)—21no—
38C31×AΣL(1,𝔽16)—21no—
39C31×AΣL(1,𝔽16)—21no—
40C31×#342—21no—
41C31×#342—21no—
42C31×H(3,ℤ/4)—21no—
43C25×C31D411yescharacteristic
44C2×#41×C31—21no—
45C2×#41×C31D411yescharacteristic
46C22×D4×C31—21no—
47C22×D4×C31—21no—
48C22×D4×C31—21no—
49C22×D4×C31—21no—
50C22×D4×C31—21no—
51C22×D4×C31D411yescharacteristic
52C22×D4×C31C2311yescharacteristic
53C2×M16×C31—21no—
54C31×#127—21no—
55C31×#127C2×C411yescharacteristic
56C31×#127D411yescharacteristic
57C31×#126—21no—
58C31×#126—21no—
59C31×#126—21no—
60C31×#126—21no—
61C31×#124—21no—
62C31×#124—21no—
63C31×#124—21no—
64C31×#124—21no—
65C31×#124—21no—
66C31×#124C2×C411yescharacteristic
67C31×#124D411yescharacteristic
68C31×#123—21no—
69C31×#123—21no—
70C31×#123—21no—
71C31×#123—21no—
72C31×#123—21no—
73C31×#123—21no—
74C31×#123—21no—
75C31×#123—21no—
76C31×#123C2×C411yescharacteristic
77C31×#123D411yescharacteristic
78C31×C22⋊Q8—21no—
79C31×C22⋊Q8—21no—
80C31×C22⋊Q8—21no—
81C31×#121—21no—
82C31×#121—21no—
83C31×#121—21no—
84C31×#121—21no—
85C31×#121—21no—
86C31×#121—21no—
87C31×#121—21no—
88C31×#121—21no—
89C31×#121—21no—
90C31×#121—21no—
91C31×#121—21no—
92C31×#121—21no—
93C31×#121—21no—
94C31×#121—21no—
95C31×#121—21no—
96C31×#120—21no—
97C31×#120—21no—
98C31×#120—21no—
99C31×#120—21no—
100C31×#120—21no—
101C31×#120—21no—
102C31×#120—21no—
103C31×#120—21no—
104C31×#120—21no—
105C31×#120—21no—
106C31×#120—21no—
107C31×#120—21no—
108C31×#120—21no—
109C31×#120—21no—
110C31×#120C2×C411yescharacteristic
111C31×#120C2×C411yescharacteristic
112C31×#120C2×C411yescharacteristic
113C31×#120D411yescharacteristic
114C31×#120D411yescharacteristic
115C31×#120D411yescharacteristic
116C4×D4×C31—21no—
117C4×D4×C31—21no—
118C4×D4×C31—21no—
119C4×D4×C31—21no—
120C4×D4×C31—21no—
121C4×D4×C31—21no—
122C4×D4×C31—42no—
123C31×#117—21no—
124C31×#117—21no—
125C31×#117D411yescharacteristic
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31—42no—
136C2×C22⋊C4×C31D411yescharacteristic
137C2×C22⋊C4×C31D411yescharacteristic
138C31×#104—42no—
139C31×#100—21no—
140C31×#100—21no—
141C31×#99—21no—
142C31×#99—21no—
143C31×#99—21no—
144C31×#99—21no—
145C31×#99—42no—
146C24×C31—21no—
147C24×C31—21no—
148C24×C31—21no—
149C24×C31—41no—
150C24×C31—41no—
151C24×C31—82no—
152C24×C31C22⋊C411yescharacteristic
153C24×C31C22⋊C411yescharacteristic
154C24×C31C22⋊C411yescharacteristic, complemented
155C24×C31C2×D411yescharacteristic
156C24×C31C2×D411yescharacteristic
157#41×C31—41no—
158#41×C31—41no—
159#41×C31—82no—
160C2×Q8×C31—21no—
161C2×Q8×C31C22⋊C411yescharacteristic, complemented
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—41no—
183C2×D4×C31—41no—
184C2×D4×C31—41no—
185C2×D4×C31—41no—
186C2×D4×C31—82no—
187C2×D4×C31—82no—
188C2×D4×C31—82no—
189C2×D4×C31—82no—
190C2×D4×C31—81no—
191C2×D4×C31—81no—
192C2×D4×C31C22⋊C411yescharacteristic, complemented
193C2×D4×C31C22×C411yescharacteristic
194C2×D4×C31C2×D411yescharacteristic
195C2×D4×C31C2×D411yescharacteristic
196C2×D4×C31C2×D411yescharacteristic
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—22no—
206C22×C4×C31—41no—
207C22×C4×C31—41no—
208C22×C4×C31—41no—
209C22×C4×C31C22⋊C411yescharacteristic, complemented
210C22×C4×C31C2×D411yescharacteristic
211M16×C31—41no—
212M16×C31—41no—
213C2×C8×C31—41no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—41no—
224C22⋊C4×C31—21no—
225C22⋊C4×C31—21no—
226C22⋊C4×C31—21no—
227C22⋊C4×C31—21no—
228C22⋊C4×C31—21no—
229C22⋊C4×C31—21no—
230C22⋊C4×C31—21no—
231C22⋊C4×C31—21no—
232C22⋊C4×C31—21no—
233C22⋊C4×C31—21no—
234C22⋊C4×C31—21no—
235C22⋊C4×C31—21no—
236C22⋊C4×C31—21no—
237C22⋊C4×C31—21no—
238C22⋊C4×C31—21no—
239C22⋊C4×C31—21no—
240C22⋊C4×C31—21no—
241C22⋊C4×C31—21no—
242C22⋊C4×C31—21no—
243C22⋊C4×C31—21no—
244C22⋊C4×C31—21no—
245C22⋊C4×C31—21no—
246C22⋊C4×C31—21no—
247C22⋊C4×C31—21no—
248C22⋊C4×C31—21no—
249C22⋊C4×C31—22no—
250C22⋊C4×C31—41no—
251C22⋊C4×C31—41no—
252C22⋊C4×C31—41no—
253C22⋊C4×C31—41no—
254C22⋊C4×C31—41no—
255C22⋊C4×C31—41no—
256C22⋊C4×C31—84no—
257C22⋊C4×C31C22⋊C411yescharacteristic
258C22⋊C4×C31C22⋊C411yescharacteristic
259C22⋊C4×C31C22⋊C411yescharacteristic, complemented
260C22⋊C4×C31C22⋊C411yescharacteristic, complemented
261C42×C31—21no—
262C42×C31—21no—
263C42×C31—22no—
264C42×C31C22⋊C411yescharacteristic, complemented
265C42×C31C22⋊C411yescharacteristic, complemented
266#12753C3111yesmaximal, characteristic, direct product factor, Sylow
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—21no—
275C23×C31—42no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—42no—
279C23×C31—42no—
280C23×C31—42no—
281C23×C31—41no—
282C23×C31—44no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—81no—
286C23×C31—81no—
287C23×C31—81no—
288C23×C31—81no—
289C23×C31—81no—
290C23×C31—81no—
291C23×C31—81no—
292C23×C31—81no—
293C23×C31—81no—
294C23×C31—82no—
295C23×C31—82no—
296C23×C31—82no—
297C23×C31C2×C22⋊C411yescharacteristic
298C23×C31C2×C22⋊C411yescharacteristic
299C23×C31#12011yescharacteristic
300C23×C31#12011yescharacteristic
301C23×C31#12011yescharacteristic
302Q8×C31—41no—
303Q8×C31—81no—
304D4×C31—41no—
305D4×C31—41no—
306D4×C31—41no—
307D4×C31—41no—
308D4×C31—41no—
309D4×C31—42no—
310D4×C31—42no—
311D4×C31—42no—
312D4×C31—42no—
313D4×C31—41no—
314D4×C31—41no—
315D4×C31—41no—
316D4×C31—41no—
317D4×C31—81no—
318D4×C31—81no—
319D4×C31—81no—
320D4×C31—81no—
321D4×C31—81no—
322D4×C31—81no—
323D4×C31—81no—
324D4×C31—81no—
325D4×C31—81no—
326D4×C31—81no—
327D4×C31—81no—
328D4×C31—81no—
329D4×C31—81no—
330D4×C31—81no—
331C2×C4×C31—21no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—21no—
339C2×C4×C31—21no—
340C2×C4×C31—21no—
341C2×C4×C31—42no—
342C2×C4×C31—41no—
343C2×C4×C31—42no—
344C2×C4×C31—81no—
345C2×C4×C31—81no—
346C2×C4×C31—81no—
347C2×C4×C31—81no—
348C2×C4×C31—81no—
349C2×C4×C31—81no—
350C2×C4×C31—81no—
351C2×C4×C31—82no—
352C2×C4×C31—81no—
353C2×C4×C31—81no—
354C2×C4×C31—82no—
355C2×C4×C31—161no—
356C2×C4×C31—161no—
357C2×C4×C31C2×C22⋊C411yescharacteristic
358C2×C4×C31#12011yescharacteristic
359C8×C31—81no—
360#3532C2×C3111yescharacteristic
361#2127C2×C3111yescharacteristic, complemented
362#2121C2×C3111yescharacteristic, complemented
363C2×AΣL(1,𝔽16)C2×C3111yescharacteristic, complemented
364#1913C2×C3111yescharacteristic, complemented
365#1911C2×C3111yescharacteristic, complemented
366#1889C2×C3111yescharacteristic, complemented
367C22×C31—22no—
368C22×C31—21no—
369C22×C31—21no—
370C22×C31—21no—
371C22×C31—21no—
372C22×C31—41no—
373C22×C31—41no—
374C22×C31—41no—
375C22×C31—41no—
376C22×C31—41no—
377C22×C31—42no—
378C22×C31—41no—
379C22×C31—41no—
380C22×C31—41no—
381C22×C31—41no—
382C22×C31—41no—
383C22×C31—41no—
384C22×C31—41no—
385C22×C31—42no—
386C22×C31—41no—
387C22×C31—42no—
388C22×C31—41no—
389C22×C31—41no—
390C22×C31—41no—
391C22×C31—81no—
392C22×C31—81no—
393C22×C31—81no—
394C22×C31—82no—
395C22×C31—82no—
396C22×C31—81no—
397C22×C31—84no—
398C22×C31—81no—
399C22×C31—161no—
400C22×C31—162no—
401C22×C31#37911yescharacteristic
402C22×C31B(4,𝔽2)11yescharacteristic
403C22×C31#45811yescharacteristic
404C4×C31—21no—
405C4×C31—21no—
406C4×C31—41no—
407C4×C31—41no—
408C4×C31—41no—
409C4×C31—41no—
410C4×C31—41no—
411C4×C31—41no—
412C4×C31—41no—
413C4×C31—41no—
414C4×C31—82no—
415C4×C31—161no—
416C4×C31—161no—
417H(3,𝔽4)C4×C3111yescharacteristic, complemented
418#560—21no—
419#560C4×C3111yescharacteristic, complemented
420#551—21no—
421#551C4×C3111yescharacteristic, complemented
422#546—21no—
423#546—21no—
424#546—21no—
425D42—21no—
426D42C4×C3111yescharacteristic, complemented
427#538—21no—
428#538—21no—
429#538—21no—
430#535—21no—
431#535C22×C3111yescharacteristic
432#534—21no—
433#534C22×C3111yescharacteristic
434C2×#120—21no—
435C2×#120C22×C3111yescharacteristic
436#518C22×C3111yescharacteristic, complemented
437#421—21no—
438C2×#100C22×C3111yescharacteristic, complemented
439C2×#99—21no—
440C2×#99C22×C3111yescharacteristic, complemented
441C2×#99C22×C3111yescharacteristic, complemented
442#379—21no—
443#354—21no—
444#353—21no—
445#352—21no—
446AΣL(1,𝔽16)—21no—
447AΣL(1,𝔽16)—21no—
448AΣL(1,𝔽16)—21no—
449#342—21no—
450#342—21no—
451H(3,ℤ/4)—21no—
452C2×C31—21no—
453C2×C31—21no—
454C2×C31—21no—
455C2×C31—41no—
456C2×C31—41no—
457C2×C31—41no—
458C2×C31—42no—
459C2×C31—41no—
460C2×C31—81no—
461C2×C31—81no—
462C2×C31—81no—
463C2×C31#179011yescharacteristic
464C25D4×C3111yescharacteristic
465C2×#41—21no—
466C2×#41D4×C3111yescharacteristic
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4D4×C3111yescharacteristic
473C22×D4C23×C3111yescharacteristic
474C2×M16—21no—
475#127—21no—
476#127C2×C4×C3111yescharacteristic
477#127D4×C3111yescharacteristic
478#126—21no—
479#126—21no—
480#126—21no—
481#126—21no—
482#124—21no—
483#124—21no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124C2×C4×C3111yescharacteristic
488#124D4×C3111yescharacteristic
489#123—21no—
490#123—21no—
491#123—21no—
492#123—21no—
493#123—21no—
494#123—21no—
495#123—21no—
496#123—21no—
497#123C2×C4×C3111yescharacteristic
498#123D4×C3111yescharacteristic
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502#121—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#120—21no—
518#120—21no—
519#120—21no—
520#120—21no—
521#120—21no—
522#120—21no—
523#120—21no—
524#120—21no—
525#120—21no—
526#120—21no—
527#120—21no—
528#120—21no—
529#120—21no—
530#120—21no—
531#120C2×C4×C3111yescharacteristic
532#120C2×C4×C3111yescharacteristic
533#120C2×C4×C3111yescharacteristic
534#120D4×C3111yescharacteristic
535#120D4×C3111yescharacteristic
536#120D4×C3111yescharacteristic
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—42no—
544#117—21no—
545#117—21no—
546#117D4×C3111yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4D4×C3111yescharacteristic
558C2×C22⋊C4D4×C3111yescharacteristic
559#104—42no—
560#100—21no—
561#100—21no—
562#99—21no—
563#99—21no—
564#99—21no—
565#99—21no—
566#99—42no—
567C31#1275311yescharacteristic, direct product factor, Sylow
568C24—21no—
569C24—21no—
570C24—21no—
571C24—41no—
572C24—41no—
573C24—82no—
574C24C22⋊C4×C3111yescharacteristic
575C24C22⋊C4×C3111yescharacteristic
576C24C22⋊C4×C3111yescharacteristic, complemented
577C24C2×D4×C3111yescharacteristic
578C24C2×D4×C3111yescharacteristic
579#41—41no—
580#41—41no—
581#41—82no—
582C2×Q8—21no—
583C2×Q8C22⋊C4×C3111yescharacteristic, complemented
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—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—82no—
609C2×D4—82no—
610C2×D4—82no—
611C2×D4—82no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4C22⋊C4×C3111yescharacteristic, complemented
615C2×D4C22×C4×C3111yescharacteristic
616C2×D4C2×D4×C3111yescharacteristic
617C2×D4C2×D4×C3111yescharacteristic
618C2×D4C2×D4×C3111yescharacteristic
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4C22⋊C4×C3111yescharacteristic, complemented
632C22×C4C2×D4×C3111yescharacteristic
633M16—41no—
634M16—41no—
635C2×C8—41no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—41no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—84no—
679C22⋊C4C22⋊C4×C3111yescharacteristic
680C22⋊C4C22⋊C4×C3111yescharacteristic
681C22⋊C4C22⋊C4×C3111yescharacteristic, complemented
682C22⋊C4C22⋊C4×C3111yescharacteristic, complemented
683C42—21no—
684C42—21no—
685C42—22no—
686C42C22⋊C4×C3111yescharacteristic, complemented
687C42C22⋊C4×C3111yescharacteristic, complemented
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—41no—
703C23—44no—
704C23—41no—
705C23—41no—
706C23—81no—
707C23—81no—
708C23—81no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—82no—
716C23—82no—
717C23—82no—
718C23C2×C22⋊C4×C3111yescharacteristic
719C23C2×C22⋊C4×C3111yescharacteristic
720C23C31×#12011yescharacteristic
721C23C31×#12011yescharacteristic
722C23C31×#12011yescharacteristic
723Q8—41no—
724Q8—81no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—42no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—81no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—82no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—82no—
776C2×C4—161no—
777C2×C4—161no—
778C2×C4C2×C22⋊C4×C3111yescharacteristic
779C2×C4C31×#12011yescharacteristic
780C8—81no—
781C22—22no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—82no—
809C22—82no—
810C22—81no—
811C22—84no—
812C22—81no—
813C22—161no—
814C22—162no—
815C22C31×#37911yescharacteristic
816C22C31×B(4,𝔽2)11yescharacteristic
817C22C31×#45811yescharacteristic
818C4—21no—
819C4—21no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—82no—
829C4—161no—
830C4—161no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—41no—
835C2—41no—
836C2—41no—
837C2—42no—
838C2—41no—
839C2—81no—
840C2—81no—
841C2—81no—
842C2C31×#179011yescharacteristic
subgroupG/H
center, socleC2×C31#1790
commutatorC2×D4C22×C4×C31
Frattini, cosocleC22×D4C23×C31
prime radicalC31×#3532C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C23×C31 ◁ C22×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2127C2semidirect
3. C31×#2121C2semidirect
4. C2×C31×AΣL(1,𝔽16)C2semidirect
5. C31×#1913C2semidirect
6. C31×#1911C2semidirect
7. C31×#1889C2semidirect
8. C31×H(3,𝔽4)C4semidirect
10. C31×#560C4semidirect
12. C31×#551C4semidirect
17. D42×C31C4semidirect
27. C31×#518C22semidirect
29. C2×C31×#100C22semidirect
31. C2×C31×#99C22semidirect
32. C2×C31×#99C22semidirect
154. C24×C31C22⋊C4semidirect
161. C2×Q8×C31C22⋊C4semidirect
192. C2×D4×C31C22⋊C4semidirect
209. C22×C4×C31C22⋊C4semidirect
259. C22⋊C4×C31C22⋊C4semidirect
260. C22⋊C4×C31C22⋊C4semidirect
264. C42×C31C22⋊C4semidirect
265. C42×C31C22⋊C4semidirect
266. #12753C31direct (N × H)
361. #2127C2×C31semidirect
362. #2121C2×C31semidirect
363. C2×AΣL(1,𝔽16)C2×C31semidirect
364. #1913C2×C31semidirect
365. #1911C2×C31semidirect
366. #1889C2×C31semidirect
417. H(3,𝔽4)C4×C31semidirect
419. #560C4×C31semidirect
421. #551C4×C31semidirect
426. D42C4×C31semidirect
436. #518C22×C31semidirect
438. C2×#100C22×C31semidirect
440. C2×#99C22×C31semidirect
441. C2×#99C22×C31semidirect
567. C31#12753direct (N × H)
576. C24C22⋊C4×C31semidirect
583. C2×Q8C22⋊C4×C31semidirect
614. C2×D4C22⋊C4×C31semidirect
631. C22×C4C22⋊C4×C31semidirect
681. C22⋊C4C22⋊C4×C31semidirect
682. C22⋊C4C22⋊C4×C31semidirect
686. C42C22⋊C4×C31semidirect
687. C42C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#35322
C31×#21272
C31×#21212
C2×C31×AΣL(1,𝔽16)2
C31×#19132
C31×#19112
C31×#18892
#1275331