Finite Group Databasebeta

← C31×#25880 #21482639

Subgroups — C31×#25880 #21482639

Order 7936.

1242 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3500C211yesmaximal, characteristic
2C31×#3141C211yesmaximal, characteristic, complemented
3C31×#3079C211yesmaximal, characteristic, complemented
4C31×#2640C211yesmaximal, characteristic, complemented
5C31×#2038C212yesmaximal, complemented
6C31×#2037C212yesmaximal, complemented
7C31×#1967C211yesmaximal, characteristic, complemented
8C31×#1963C211yesmaximal, characteristic, complemented
9C31×#1793C212yesmaximal, complemented
10C31×#1792C212yesmaximal, complemented
11C31×#1759C211yesmaximal, characteristic, complemented
12C2×C31×2−1+4C2211yescharacteristic
13C2×C31×H(5,𝔽2)C2211yescharacteristic
14C31×#548—21no—
15C31×#548—21no—
16C31×#546—21no—
17C31×#546—21no—
18C31×#546—22no—
19C31×#546—22no—
20C31×#536—21no—
21C31×#536C2211yescharacteristic
22C31×#535—21no—
23C31×#535C2211yescharacteristic
24C31×#532—21no—
25C31×#532C2211yescharacteristic
26C2×C31×C4⋊Q8C2211yescharacteristic, complemented
27C2×C31×#124—21no—
28C2×C31×#124C2211yescharacteristic
29C4×#41×C31C2211yescharacteristic
30C31×#489—21no—
31C31×#489—21no—
32C31×#487—21no—
33C31×#486—21no—
34C31×#477—21no—
35C31×#476—21no—
36C31×#475—21no—
37C31×#474—21no—
38C31×#428C2212yescomplemented
39C31×#423C2211yescharacteristic, complemented
40C2×C31×#104C2212yes—
41C2×C31×#104C2212yes—
42C2×C31×#104C2212yescomplemented
43C31×#417C2212yes—
44C31×#417C2212yes—
45C31×#417C2212yescomplemented
46C2×C31×#101C2212yescomplemented
47C2×C31×#100C2212yes—
48C4×M16×C31C2211yescharacteristic, complemented
49C31×#397—22no—
50C31×#393—22no—
51C31×#391C2212yescomplemented
52C31×#390C2212yes—
53C31×#376C2211yescharacteristic, complemented
54C31×#339C2212yescomplemented
55C31×2−1+4—24no—
56C31×2−1+4—42no—
57C31×H(5,𝔽2)—24no—
58C31×H(5,𝔽2)—42no—
59C2×#41×C31—21no—
60C2×#41×C31—21no—
61C2×#41×C31—21no—
62C2×#41×C31—21no—
63C2×#41×C31—22no—
64C2×#41×C31C2311yescharacteristic
65C2×#41×C31C2311yescharacteristic
66C2×#41×C31C2311yescharacteristic
67C22×Q8×C31—21no—
68C22×Q8×C31—21no—
69C22×Q8×C31—21no—
70C22×Q8×C31C2311yescharacteristic
71C22×D4×C31—22no—
72C22×D4×C31—21no—
73C22×D4×C31—21no—
74C22×D4×C31C2311yescharacteristic
75C2×M16×C31C2312yes—
76C2×M16×C31C2312yes—
77C31×C4⋊Q8—21no—
78C31×C4⋊Q8—21no—
79C31×C4⋊Q8—21no—
80C31×C4⋊Q8—21no—
81C31×C4⋊Q8—21no—
82C31×C4⋊Q8D411yescharacteristic
83C31×#127—21no—
84C31×#127D411yescharacteristic
85C31×#124—22no—
86C31×#124—22no—
87C31×#124—21no—
88C31×#124—21no—
89C31×#124—21no—
90C31×#124—21no—
91C31×#124—21no—
92C31×#124—21no—
93C31×#124D411yescharacteristic
94C31×#124D411yescharacteristic
95C31×#123—22no—
96C31×#123—22no—
97C31×#123—22no—
98C31×C22⋊Q8—22no—
99C31×C22⋊Q8—22no—
100C31×C22⋊Q8—21no—
101C31×C22⋊Q8—21no—
102C31×#121—22no—
103C31×#121—22no—
104C31×#121—22no—
105C31×#121—22no—
106C31×#121—21no—
107C31×#121—21no—
108C31×#121—21no—
109C31×#121—21no—
110C31×#120—22no—
111C31×#120—22no—
112C31×#120—22no—
113C4×Q8×C31D411yescharacteristic
114C4×Q8×C31D411yescharacteristic
115C4×D4×C31—22no—
116C4×D4×C31—22no—
117C4×D4×C31—21no—
118C4×D4×C31—21no—
119C4×D4×C31—21no—
120C4×D4×C31—21no—
121C4×D4×C31D411yescharacteristic
122C4×D4×C31D411yescharacteristic
123C31×#117—21no—
124C31×#117C2311yescharacteristic
125C2×C4⋊C4×C31—21no—
126C2×C4⋊C4×C31C2312yes—
127C2×C22⋊C4×C31—22no—
128C2×C22⋊C4×C31—22no—
129C2×C22⋊C4×C31—24no—
130C2×C22⋊C4×C31D412yes—
131C2×C22⋊C4×C31D412yes—
132C2×C42×C31—21no—
133C2×C42×C31C2312yes—
134C2×C42×C31C2311yescharacteristic
135C31×#107—22no—
136C31×#106—22no—
137C31×C4⋊C8—21no—
138C31×C4⋊C8—21no—
139C31×#104—24no—
140C31×#104—42no—
141C31×#104—42no—
142C31×#103—22no—
143C31×#103—22no—
144C31×#103—22no—
145C31×#102—22no—
146C31×#102—22no—
147C31×#102—22no—
148C31×#101—42no—
149C31×#100—42no—
150C31×#97—21no—
151C4×C8×C31—21no—
152C31×#95—21no—
153C31×#95—24no—
154C31×#95—21no—
155C24×C31—22no—
156C24×C31C2×D412yes—
157#41×C31—22no—
158#41×C31—22no—
159#41×C31—22no—
160#41×C31—22no—
161#41×C31—22no—
162#41×C31—44no—
163#41×C31—48no—
164#41×C31—44no—
165#41×C31—42no—
166#41×C31—42no—
167#41×C31—42no—
168#41×C31—42no—
169#41×C31#4114yes—
170C2×Q8×C31—22no—
171C2×Q8×C31—21no—
172C2×Q8×C31—21no—
173C2×Q8×C31—22no—
174C2×Q8×C31—22no—
175C2×Q8×C31—44no—
176C2×Q8×C31—42no—
177C2×Q8×C31—42no—
178C2×Q8×C31—41no—
179C2×Q8×C31—41no—
180C2×Q8×C31—82no—
181C2×Q8×C31C2×D411yescharacteristic
182C2×Q8×C31C2×D411yescharacteristic
183C2×Q8×C31C2×D411yescharacteristic
184C2×D4×C31—21no—
185C2×D4×C31—22no—
186C2×D4×C31—22no—
187C2×D4×C31—22no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—22no—
191C2×D4×C31—22no—
192C2×D4×C31—21no—
193C2×D4×C31—21no—
194C2×D4×C31—21no—
195C2×D4×C31—21no—
196C2×D4×C31—22no—
197C2×D4×C31—22no—
198C2×D4×C31—44no—
199C2×D4×C31—48no—
200C2×D4×C31—42no—
201C2×D4×C31—42no—
202C2×D4×C31C2×D411yescharacteristic
203C2×D4×C31C2×D411yescharacteristic
204C2×D4×C31C2×D411yescharacteristic
205C22×C4×C31—21no—
206C22×C4×C31—22no—
207C22×C4×C31—22no—
208C22×C4×C31—22no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—22no—
214C22×C4×C31—22no—
215C22×C4×C31C2×D412yes—
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2411yescharacteristic
219M16×C31—22no—
220M16×C31—22no—
221M16×C31—22no—
222M16×C31—22no—
223C2×C8×C31—22no—
224C2×C8×C31—22no—
225C4⋊C4×C31—22no—
226C4⋊C4×C31—22no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—22no—
232C4⋊C4×C31—22no—
233C4⋊C4×C31—41no—
234C4⋊C4×C31—41no—
235C4⋊C4×C31C2×D411yescharacteristic
236C4⋊C4×C31C2×D411yescharacteristic
237C22⋊C4×C31—22no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—22no—
240C22⋊C4×C31—22no—
241C22⋊C4×C31—21no—
242C22⋊C4×C31—21no—
243C22⋊C4×C31—21no—
244C22⋊C4×C31—22no—
245C22⋊C4×C31—22no—
246C22⋊C4×C31—22no—
247C22⋊C4×C31—22no—
248C22⋊C4×C31—21no—
249C22⋊C4×C31—21no—
250C22⋊C4×C31—21no—
251C22⋊C4×C31—21no—
252C22⋊C4×C31—84no—
253C42×C31—21no—
254C42×C31—21no—
255C42×C31—21no—
256C42×C31—22no—
257C42×C31—22no—
258C42×C31C2×D411yescharacteristic
259C42×C31C2×D411yescharacteristic
260C42×C31C2×D411yescharacteristic
261C42×C31C2×D411yescharacteristic
262#25880C3111yesmaximal, characteristic, direct product factor, Sylow
263C23×C31—21no—
264C23×C31—22no—
265C23×C31—21no—
266C23×C31—21no—
267C23×C31—24no—
268C23×C31—44no—
269C23×C31—42no—
270C23×C31—42no—
271C23×C31—82no—
272C23×C31—82no—
273C23×C31C22×D411yescharacteristic
274Q8×C31—21no—
275Q8×C31—22no—
276Q8×C31—22no—
277Q8×C31—44no—
278Q8×C31—41no—
279Q8×C31—41no—
280Q8×C31—42no—
281Q8×C31—82no—
282Q8×C31—82no—
283Q8×C31#12412yes—
284D4×C31—24no—
285D4×C31—21no—
286D4×C31—22no—
287D4×C31—22no—
288D4×C31—44no—
289D4×C31—44no—
290D4×C31—44no—
291D4×C31—42no—
292D4×C31—42no—
293D4×C31—41no—
294D4×C31—41no—
295D4×C31—42no—
296D4×C31—81no—
297D4×C31—81no—
298D4×C31—82no—
299D4×C31—82no—
300D4×C31#12412yes—
301C2×C4×C31—21no—
302C2×C4×C31—24no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—22no—
307C2×C4×C31—21no—
308C2×C4×C31—24no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—44no—
312C2×C4×C31—44no—
313C2×C4×C31—44no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—42no—
319C2×C4×C31—44no—
320C2×C4×C31—42no—
321C2×C4×C31—42no—
322C2×C4×C31—42no—
323C2×C4×C31—81no—
324C2×C4×C31—81no—
325C2×C4×C31#12011yescharacteristic
326C2×C4×C31#12011yescharacteristic
327C2×C4×C31#12011yescharacteristic
328C2×C4×C31#12011yescharacteristic
329C2×C4×C31C22×D411yescharacteristic
330C2×C4×C31C22×D411yescharacteristic
331C2×C4×C31C2×#4112yes—
332C2×C4×C31H(5,𝔽2)12yes—
333C8×C31—42no—
334C8×C31—42no—
335#3500C2×C3111yescharacteristic
336#3141C2×C3111yescharacteristic, complemented
337#3079C2×C3111yescharacteristic, complemented
338#2640C2×C3111yescharacteristic, complemented
339#2038C2×C3112yescomplemented
340#2037C2×C3112yescomplemented
341#1967C2×C3111yescharacteristic, complemented
342#1963C2×C3111yescharacteristic, complemented
343#1793C2×C3112yescomplemented
344#1792C2×C3112yescomplemented
345#1759C2×C3111yescharacteristic, complemented
346C22×C31—21no—
347C22×C31—21no—
348C22×C31—22no—
349C22×C31—41no—
350C22×C31—41no—
351C22×C31—41no—
352C22×C31—41no—
353C22×C31—42no—
354C22×C31—41no—
355C22×C31—42no—
356C22×C31—41no—
357C22×C31—41no—
358C22×C31—42no—
359C22×C31—41no—
360C22×C31—84no—
361C22×C31—164no—
362C22×C31C2×#12011yescharacteristic
363C22×C31#54612yes—
364C4×C31—22no—
365C4×C31—21no—
366C4×C31—21no—
367C4×C31—21no—
368C4×C31—21no—
369C4×C31—42no—
370C4×C31—41no—
371C4×C31—41no—
372C4×C31—41no—
373C4×C31—41no—
374C4×C31—82no—
375C4×C31—82no—
376C4×C31C2×#12411yescharacteristic
377C4×C31#53511yescharacteristic
378C4×C31#54612yes—
379C2×2−1+4C22×C3111yescharacteristic
380C2×H(5,𝔽2)C22×C3111yescharacteristic
381#548—21no—
382#548—21no—
383#546—21no—
384#546—21no—
385#546—22no—
386#546—22no—
387#536—21no—
388#536C22×C3111yescharacteristic
389#535—21no—
390#535C22×C3111yescharacteristic
391#532—21no—
392#532C22×C3111yescharacteristic
393C2×C4⋊Q8C22×C3111yescharacteristic, complemented
394C2×#124—21no—
395C2×#124C22×C3111yescharacteristic
396C4×#41C22×C3111yescharacteristic
397#489—21no—
398#489—21no—
399#487—21no—
400#486—21no—
401#477—21no—
402#476—21no—
403#475—21no—
404#474—21no—
405#428C22×C3112yescomplemented
406#423C22×C3111yescharacteristic, complemented
407C2×#104C22×C3112yes—
408C2×#104C22×C3112yes—
409C2×#104C22×C3112yescomplemented
410#417C22×C3112yes—
411#417C22×C3112yes—
412#417C22×C3112yescomplemented
413C2×#101C22×C3112yescomplemented
414C2×#100C22×C3112yes—
415C4×M16C22×C3111yescharacteristic, complemented
416#397—22no—
417#393—22no—
418#391C22×C3112yescomplemented
419#390C22×C3112yes—
420#376C22×C3111yescharacteristic, complemented
421#339C22×C3112yescomplemented
422C2×C31—22no—
423C2×C31—42no—
424C2×C31—81no—
425C2×C31—82no—
426C2×C31—81no—
427C2×C31#243511yescharacteristic
428C2×C31#302111yescharacteristic
429C2×C31#302211yescharacteristic
4302−1+4—24no—
4312−1+4—42no—
432H(5,𝔽2)—24no—
433H(5,𝔽2)—42no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—22no—
439C2×#41C23×C3111yescharacteristic
440C2×#41C23×C3111yescharacteristic
441C2×#41C23×C3111yescharacteristic
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8C23×C3111yescharacteristic
446C22×D4—22no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4C23×C3111yescharacteristic
450C2×M16C23×C3112yes—
451C2×M16C23×C3112yes—
452C4⋊Q8—21no—
453C4⋊Q8—21no—
454C4⋊Q8—21no—
455C4⋊Q8—21no—
456C4⋊Q8—21no—
457C4⋊Q8D4×C3111yescharacteristic
458#127—21no—
459#127D4×C3111yescharacteristic
460#124—22no—
461#124—22no—
462#124—21no—
463#124—21no—
464#124—21no—
465#124—21no—
466#124—21no—
467#124—21no—
468#124D4×C3111yescharacteristic
469#124D4×C3111yescharacteristic
470#123—22no—
471#123—22no—
472#123—22no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—21no—
482#121—21no—
483#121—21no—
484#121—21no—
485#120—22no—
486#120—22no—
487#120—22no—
488C4×Q8D4×C3111yescharacteristic
489C4×Q8D4×C3111yescharacteristic
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4D4×C3111yescharacteristic
497C4×D4D4×C3111yescharacteristic
498#117—21no—
499#117C23×C3111yescharacteristic
500C2×C4⋊C4—21no—
501C2×C4⋊C4C23×C3112yes—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4D4×C3112yes—
506C2×C22⋊C4D4×C3112yes—
507C2×C42—21no—
508C2×C42C23×C3112yes—
509C2×C42C23×C3111yescharacteristic
510#107—22no—
511#106—22no—
512C4⋊C8—21no—
513C4⋊C8—21no—
514#104—24no—
515#104—42no—
516#104—42no—
517#103—22no—
518#103—22no—
519#103—22no—
520#102—22no—
521#102—22no—
522#102—22no—
523#101—42no—
524#100—42no—
525#97—21no—
526C4×C8—21no—
527#95—21no—
528#95—21no—
529#95—24no—
530C31#2588011yescharacteristic, direct product factor, Sylow
531C24—22no—
532C24C2×D4×C3112yes—
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—44no—
539#41—48no—
540#41—44no—
541#41—42no—
542#41—42no—
543#41—42no—
544#41—42no—
545#41#41×C3114yes—
546C2×Q8—22no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—44no—
552C2×Q8—42no—
553C2×Q8—42no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—82no—
557C2×Q8C2×D4×C3111yescharacteristic
558C2×Q8C2×D4×C3111yescharacteristic
559C2×Q8C2×D4×C3111yescharacteristic
560C2×D4—21no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—44no—
575C2×D4—48no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4C2×D4×C3111yescharacteristic
579C2×D4C2×D4×C3111yescharacteristic
580C2×D4C2×D4×C3111yescharacteristic
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4C2×D4×C3112yes—
592C22×C4C2×D4×C3111yescharacteristic
593C22×C4C2×D4×C3111yescharacteristic
594C22×C4C24×C3111yescharacteristic
595M16—22no—
596M16—22no—
597M16—22no—
598M16—22no—
599C2×C8—22no—
600C2×C8—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—41no—
610C4⋊C4—41no—
611C4⋊C4C2×D4×C3111yescharacteristic
612C4⋊C4C2×D4×C3111yescharacteristic
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—84no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—22no—
633C42—22no—
634C42C2×D4×C3111yescharacteristic
635C42C2×D4×C3111yescharacteristic
636C42C2×D4×C3111yescharacteristic
637C42C2×D4×C3111yescharacteristic
638C23—21no—
639C23—22no—
640C23—21no—
641C23—21no—
642C23—24no—
643C23—44no—
644C23—42no—
645C23—42no—
646C23—82no—
647C23—82no—
648C23C22×D4×C3111yescharacteristic
649Q8—21no—
650Q8—22no—
651Q8—22no—
652Q8—44no—
653Q8—41no—
654Q8—41no—
655Q8—42no—
656Q8—82no—
657Q8—82no—
658Q8C31×#12412yes—
659D4—24no—
660D4—21no—
661D4—22no—
662D4—22no—
663D4—44no—
664D4—44no—
665D4—44no—
666D4—42no—
667D4—42no—
668D4—41no—
669D4—41no—
670D4—42no—
671D4—81no—
672D4—81no—
673D4—82no—
674D4—82no—
675D4C31×#12412yes—
676C2×C4—21no—
677C2×C4—24no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—24no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4C31×#12011yescharacteristic
701C2×C4C31×#12011yescharacteristic
702C2×C4C31×#12011yescharacteristic
703C2×C4C31×#12011yescharacteristic
704C2×C4C22×D4×C3111yescharacteristic
705C2×C4C22×D4×C3111yescharacteristic
706C2×C4C2×#41×C3112yes—
707C2×C4C31×H(5,𝔽2)12yes—
708C8—42no—
709C8—42no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—42no—
718C22—41no—
719C22—42no—
720C22—41no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22—84no—
725C22—164no—
726C22C2×C31×#12011yescharacteristic
727C22C31×#54612yes—
728C4—22no—
729C4—21no—
730C4—21no—
731C4—21no—
732C4—21no—
733C4—42no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—82no—
739C4—82no—
740C4C2×C31×#12411yescharacteristic
741C4C31×#53511yescharacteristic
742C4C31×#54612yes—
743C2—22no—
744C2—42no—
745C2—82no—
746C2—81no—
747C2—81no—
748C2C31×#243511yescharacteristic
749C2C31×#302111yescharacteristic
750C2C31×#302211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3500C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3141C2semidirect
3. C31×#3079C2semidirect
4. C31×#2640C2semidirect
5. C31×#2038C2semidirect
6. C31×#2037C2semidirect
7. C31×#1967C2semidirect
8. C31×#1963C2semidirect
9. C31×#1793C2semidirect
10. C31×#1792C2semidirect
11. C31×#1759C2semidirect
26. C2×C31×C4⋊Q8C22semidirect
38. C31×#428C22semidirect
39. C31×#423C22semidirect
42. C2×C31×#104C22semidirect
45. C31×#417C22semidirect
46. C2×C31×#101C22semidirect
48. C4×M16×C31C22semidirect
51. C31×#391C22semidirect
53. C31×#376C22semidirect
54. C31×#339C22semidirect
262. #25880C31direct (N × H)
336. #3141C2×C31semidirect
337. #3079C2×C31semidirect
338. #2640C2×C31semidirect
339. #2038C2×C31semidirect
340. #2037C2×C31semidirect
341. #1967C2×C31semidirect
342. #1963C2×C31semidirect
343. #1793C2×C31semidirect
344. #1792C2×C31semidirect
345. #1759C2×C31semidirect
393. C2×C4⋊Q8C22×C31semidirect
405. #428C22×C31semidirect
406. #423C22×C31semidirect
409. C2×#104C22×C31semidirect
412. #417C22×C31semidirect
413. C2×#101C22×C31semidirect
415. C4×M16C22×C31semidirect
418. #391C22×C31semidirect
420. #376C22×C31semidirect
421. #339C22×C31semidirect
530. C31#25880direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35002
C31×#31412
C31×#30792
C31×#26402
C31×#20382
C31×#20372
C31×#19672
C31×#19632
C31×#17932
C31×#17922
C31×#17592
#2588031