Finite Group Databasebeta

← C31×#12754 #21469513

Subgroups — C31×#12754 #21469513

Order 7936.

782 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3533C211yesmaximal, characteristic
2C31×#2127C211yesmaximal, characteristic, complemented
3C31×#2121C211yesmaximal, characteristic, complemented
4C2×C31×#352C211yesmaximal, characteristic, complemented
5C31×#1913C211yesmaximal, characteristic, complemented
6C31×#1911C211yesmaximal, characteristic, complemented
7C31×#1890C211yesmaximal, characteristic, complemented
8C31×#563C411yescharacteristic, complemented
9C31×#562—21no—
10C31×#560C411yescharacteristic, complemented
11C31×#559C411yescharacteristic, complemented
12C31×#553—21no—
13C31×#552—21no—
14C31×#551—21no—
15C31×#551C411yescharacteristic, complemented
16C31×#547—21no—
17C31×#546—21no—
18C31×#542—21no—
19C31×#540—21no—
20C31×#539—21no—
21C31×#538—21no—
22C31×#538—21no—
23C31×#535C2211yescharacteristic
24C31×#534C2211yescharacteristic
25C31×#525—21no—
26C2×C31×#123C2211yescharacteristic
27C31×#518C2211yescharacteristic
28C31×#421—21no—
29C2×C31×#100C2211yescharacteristic
30C2×C31×#99—21no—
31C2×C31×#99C2211yescharacteristic
32C2×C31×#99C2211yescharacteristic
33C31×#381—21no—
34C31×#354—21no—
35C31×#353—21no—
36C31×#352—21no—
37C31×#352—21no—
38C31×#352—21no—
39C31×AΣL(1,𝔽16)—21no—
40C31×#342—21no—
41C31×#342—21no—
42C31×H(3,ℤ/4)—21no—
43C2×#41×C31—21no—
44C2×#41×C31D411yescharacteristic
45C22×D4×C31D411yescharacteristic
46C22×D4×C31C2311yescharacteristic
47C23×C4×C31D411yescharacteristic
48C2×M16×C31—21no—
49C31×C4⋊Q8—21no—
50C31×#127C2×C411yescharacteristic
51C31×#127D411yescharacteristic
52C31×#126—21no—
53C31×#126—21no—
54C31×#126—21no—
55C31×#126—21no—
56C31×#126—21no—
57C31×#126—21no—
58C31×#125—21no—
59C31×#125—21no—
60C31×#125—21no—
61C31×#124—21no—
62C31×#124—21no—
63C31×#124—21no—
64C31×#124—21no—
65C31×#124C2×C411yescharacteristic
66C31×#124D411yescharacteristic
67C31×#123—21no—
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×#123—21no—
77C31×#123—21no—
78C31×#123—21no—
79C31×#123C2×C411yescharacteristic
80C31×#123C2×C411yescharacteristic
81C31×#123C2×C411yescharacteristic
82C31×#123D411yescharacteristic
83C31×#123D411yescharacteristic
84C31×#123D411yescharacteristic
85C31×C22⋊Q8—21no—
86C31×C22⋊Q8—21no—
87C31×C22⋊Q8—21no—
88C31×C22⋊Q8—21no—
89C31×C22⋊Q8—21no—
90C31×C22⋊Q8—21no—
91C31×C22⋊Q8—21no—
92C31×C22⋊Q8—21no—
93C31×#121—21no—
94C31×#121—21no—
95C31×#121—21no—
96C31×#121—21no—
97C31×#121—21no—
98C31×#121—21no—
99C31×#121—21no—
100C31×#121—21no—
101C31×#121—21no—
102C31×#121—21no—
103C31×#121—21no—
104C31×#121—21no—
105C31×#120—21no—
106C31×#120—21no—
107C31×#120—21no—
108C31×#120—21no—
109C31×#120C2×C411yescharacteristic
110C31×#120D411yescharacteristic
111C4×Q8×C31—21no—
112C4×D4×C31—21no—
113C4×D4×C31—21no—
114C4×D4×C31—21no—
115C4×D4×C31—21no—
116C4×D4×C31—21no—
117C4×D4×C31—21no—
118C4×D4×C31—21no—
119C4×D4×C31—21no—
120C4×D4×C31—21no—
121C4×D4×C31—42no—
122C31×#117—21no—
123C31×#117—21no—
124C31×#117—21no—
125C31×#117—21no—
126C31×#117D411yescharacteristic
127C2×C4⋊C4×C31—21no—
128C2×C4⋊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×C31D411yescharacteristic
136C2×C22⋊C4×C31D411yescharacteristic
137C31×#104—42no—
138C31×#100—21no—
139C31×#100—21no—
140C31×#99—21no—
141C31×#99—21no—
142C31×#99—21no—
143C31×#99—21no—
144C31×#99—42no—
145C31×#95—42no—
146C24×C31C22⋊C411yescharacteristic
147C24×C31C2×D411yescharacteristic
148C24×C31C2×D411yescharacteristic
149#41×C31—41no—
150#41×C31—41no—
151#41×C31—81no—
152#41×C31—81no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31C22⋊C411yescharacteristic
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—41no—
168C2×D4×C31—41no—
169C2×D4×C31—41no—
170C2×D4×C31—41no—
171C2×D4×C31C22⋊C411yescharacteristic
172C2×D4×C31C22×C411yescharacteristic
173C2×D4×C31C2×D411yescharacteristic
174C2×D4×C31C2×D411yescharacteristic
175C2×D4×C31C2×D411yescharacteristic
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—22no—
186C22×C4×C31—41no—
187C22×C4×C31—41no—
188C22×C4×C31—41no—
189C22×C4×C31—41no—
190C22×C4×C31—41no—
191C22×C4×C31C22⋊C411yescharacteristic
192C22×C4×C31C22⋊C411yescharacteristic
193C22×C4×C31C22⋊C411yescharacteristic
194C22×C4×C31C2×D411yescharacteristic
195M16×C31—41no—
196M16×C31—41no—
197C2×C8×C31—41no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—41no—
218C22⋊C4×C31—21no—
219C22⋊C4×C31—21no—
220C22⋊C4×C31—21no—
221C22⋊C4×C31—21no—
222C22⋊C4×C31—21no—
223C22⋊C4×C31—21no—
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—22no—
242C22⋊C4×C31—41no—
243C22⋊C4×C31—41no—
244C22⋊C4×C31—41no—
245C22⋊C4×C31—41no—
246C22⋊C4×C31—41no—
247C22⋊C4×C31—41no—
248C22⋊C4×C31C22⋊C411yescharacteristic
249C22⋊C4×C31C22⋊C411yescharacteristic
250C22⋊C4×C31C22⋊C411yescharacteristic
251C22⋊C4×C31C22⋊C411yescharacteristic
252C42×C31—21no—
253C42×C31—21no—
254C42×C31—21no—
255C42×C31—21no—
256C42×C31—22no—
257C42×C31C22⋊C411yescharacteristic
258C42×C31C22⋊C411yescharacteristic
259#12754C3111yesmaximal, characteristic, direct product factor, Sylow
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—21no—
265C23×C31—21no—
266C23×C31—41no—
267C23×C31—81no—
268C23×C31—81no—
269C23×C31—81no—
270C23×C31C2×C22⋊C411yescharacteristic
271C23×C31C2×C22⋊C411yescharacteristic
272C23×C31#12011yescharacteristic
273C23×C31#12011yescharacteristic
274C23×C31#12011yescharacteristic
275Q8×C31—41no—
276Q8×C31—81no—
277Q8×C31—81no—
278D4×C31—41no—
279D4×C31—41no—
280D4×C31—41no—
281D4×C31—41no—
282D4×C31—41no—
283D4×C31—41no—
284D4×C31—41no—
285D4×C31—41no—
286D4×C31—41no—
287D4×C31—81no—
288D4×C31—81no—
289D4×C31—81no—
290D4×C31—81no—
291D4×C31—81no—
292D4×C31—81no—
293D4×C31—81no—
294D4×C31—81no—
295D4×C31—81no—
296C2×C4×C31—21no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—42no—
314C2×C4×C31—81no—
315C2×C4×C31—81no—
316C2×C4×C31—81no—
317C2×C4×C31—81no—
318C2×C4×C31—81no—
319C2×C4×C31—81no—
320C2×C4×C31—81no—
321C2×C4×C31—81no—
322C2×C4×C31—82no—
323C2×C4×C31—81no—
324C2×C4×C31—81no—
325C2×C4×C31—82no—
326C2×C4×C31—161no—
327C2×C4×C31—161no—
328C2×C4×C31C2×C22⋊C411yescharacteristic
329C2×C4×C31#12011yescharacteristic
330C8×C31—81no—
331#3533C2×C3111yescharacteristic
332#2127C2×C3111yescharacteristic, complemented
333#2121C2×C3111yescharacteristic, complemented
334C2×#352C2×C3111yescharacteristic, complemented
335#1913C2×C3111yescharacteristic, complemented
336#1911C2×C3111yescharacteristic, complemented
337#1890C2×C3111yescharacteristic, complemented
338C22×C31—21no—
339C22×C31—21no—
340C22×C31—21no—
341C22×C31—21no—
342C22×C31—41no—
343C22×C31—41no—
344C22×C31—41no—
345C22×C31—41no—
346C22×C31—41no—
347C22×C31—42no—
348C22×C31—41no—
349C22×C31—41no—
350C22×C31—41no—
351C22×C31—41no—
352C22×C31—41no—
353C22×C31—41no—
354C22×C31—81no—
355C22×C31—81no—
356C22×C31—81no—
357C22×C31—161no—
358C22×C31#37911yescharacteristic
359C22×C31B(4,𝔽2)11yescharacteristic
360C22×C31#45811yescharacteristic
361C4×C31—21no—
362C4×C31—21no—
363C4×C31—41no—
364C4×C31—41no—
365C4×C31—41no—
366C4×C31—41no—
367C4×C31—41no—
368C4×C31—41no—
369C4×C31—41no—
370C4×C31—41no—
371C4×C31—41no—
372C4×C31—41no—
373C4×C31—82no—
374C4×C31—161no—
375C4×C31—161no—
376#563C4×C3111yescharacteristic, complemented
377#562—21no—
378#560C4×C3111yescharacteristic, complemented
379#559C4×C3111yescharacteristic, complemented
380#553—21no—
381#552—21no—
382#551—21no—
383#551C4×C3111yescharacteristic, complemented
384#547—21no—
385#546—21no—
386#542—21no—
387#540—21no—
388#539—21no—
389#538—21no—
390#538—21no—
391#535C22×C3111yescharacteristic
392#534C22×C3111yescharacteristic
393#525—21no—
394C2×#123C22×C3111yescharacteristic
395#518C22×C3111yescharacteristic
396#421—21no—
397C2×#100C22×C3111yescharacteristic
398C2×#99—21no—
399C2×#99C22×C3111yescharacteristic
400C2×#99C22×C3111yescharacteristic
401#381—21no—
402#354—21no—
403#353—21no—
404#352—21no—
405#352—21no—
406#352—21no—
407AΣL(1,𝔽16)—21no—
408#342—21no—
409#342—21no—
410H(3,ℤ/4)—21no—
411C2×C31—21no—
412C2×C31—21no—
413C2×C31—21no—
414C2×C31—41no—
415C2×C31—41no—
416C2×C31—41no—
417C2×C31—41no—
418C2×C31—81no—
419C2×C31—81no—
420C2×C31#179011yescharacteristic
421C2×#41—21no—
422C2×#41D4×C3111yescharacteristic
423C22×D4D4×C3111yescharacteristic
424C22×D4C23×C3111yescharacteristic
425C23×C4D4×C3111yescharacteristic
426C2×M16—21no—
427C4⋊Q8—21no—
428#127C2×C4×C3111yescharacteristic
429#127D4×C3111yescharacteristic
430#126—21no—
431#126—21no—
432#126—21no—
433#126—21no—
434#126—21no—
435#126—21no—
436#125—21no—
437#125—21no—
438#125—21no—
439#124—21no—
440#124—21no—
441#124—21no—
442#124—21no—
443#124C2×C4×C3111yescharacteristic
444#124D4×C3111yescharacteristic
445#123—21no—
446#123—21no—
447#123—21no—
448#123—21no—
449#123—21no—
450#123—21no—
451#123—21no—
452#123—21no—
453#123—21no—
454#123—21no—
455#123—21no—
456#123—21no—
457#123C2×C4×C3111yescharacteristic
458#123C2×C4×C3111yescharacteristic
459#123C2×C4×C3111yescharacteristic
460#123D4×C3111yescharacteristic
461#123D4×C3111yescharacteristic
462#123D4×C3111yescharacteristic
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8—21no—
471#121—21no—
472#121—21no—
473#121—21no—
474#121—21no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#120—21no—
484#120—21no—
485#120—21no—
486#120—21no—
487#120C2×C4×C3111yescharacteristic
488#120D4×C3111yescharacteristic
489C4×Q8—21no—
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—42no—
500#117—21no—
501#117—21no—
502#117—21no—
503#117—21no—
504#117D4×C3111yescharacteristic
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4D4×C3111yescharacteristic
514C2×C22⋊C4D4×C3111yescharacteristic
515#104—42no—
516#100—21no—
517#100—21no—
518#99—21no—
519#99—21no—
520#99—21no—
521#99—21no—
522#99—42no—
523#95—42no—
524C31#1275411yescharacteristic, direct product factor, Sylow
525C24C22⋊C4×C3111yescharacteristic
526C24C2×D4×C3111yescharacteristic
527C24C2×D4×C3111yescharacteristic
528#41—41no—
529#41—41no—
530#41—81no—
531#41—81no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8C22⋊C4×C3111yescharacteristic
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4C22⋊C4×C3111yescharacteristic
551C2×D4C22×C4×C3111yescharacteristic
552C2×D4C2×D4×C3111yescharacteristic
553C2×D4C2×D4×C3111yescharacteristic
554C2×D4C2×D4×C3111yescharacteristic
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4C22⋊C4×C3111yescharacteristic
571C22×C4C22⋊C4×C3111yescharacteristic
572C22×C4C22⋊C4×C3111yescharacteristic
573C22×C4C2×D4×C3111yescharacteristic
574M16—41no—
575M16—41no—
576C2×C8—41no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—41no—
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—41no—
622C22⋊C4—41no—
623C22⋊C4—41no—
624C22⋊C4—41no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4C22⋊C4×C3111yescharacteristic
628C22⋊C4C22⋊C4×C3111yescharacteristic
629C22⋊C4C22⋊C4×C3111yescharacteristic
630C22⋊C4C22⋊C4×C3111yescharacteristic
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—22no—
636C42C22⋊C4×C3111yescharacteristic
637C42C22⋊C4×C3111yescharacteristic
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—41no—
645C23—81no—
646C23—81no—
647C23—81no—
648C23C2×C22⋊C4×C3111yescharacteristic
649C23C2×C22⋊C4×C3111yescharacteristic
650C23C31×#12011yescharacteristic
651C23C31×#12011yescharacteristic
652C23C31×#12011yescharacteristic
653Q8—41no—
654Q8—81no—
655Q8—81no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4—81no—
667D4—81no—
668D4—81no—
669D4—81no—
670D4—81no—
671D4—81no—
672D4—81no—
673D4—81no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—82no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—82no—
704C2×C4—161no—
705C2×C4—161no—
706C2×C4C2×C22⋊C4×C3111yescharacteristic
707C2×C4C31×#12011yescharacteristic
708C8—81no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—161no—
729C22C31×#37911yescharacteristic
730C22C31×B(4,𝔽2)11yescharacteristic
731C22C31×#45811yescharacteristic
732C4—21no—
733C4—21no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—82no—
745C4—161no—
746C4—161no—
747C2—21no—
748C2—21no—
749C2—21no—
750C2—41no—
751C2—41no—
752C2—41no—
753C2—41no—
754C2—81no—
755C2—81no—
756C2C31×#179011yescharacteristic
subgroupG/H
center, socleC2×C31#1790
commutatorC2×D4C22×C4×C31
Frattini, cosocleC22×D4C23×C31
prime radicalC31×#3533C2
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×#352C2semidirect
5. C31×#1913C2semidirect
6. C31×#1911C2semidirect
7. C31×#1890C2semidirect
8. C31×#563C4semidirect
10. C31×#560C4semidirect
11. C31×#559C4semidirect
15. C31×#551C4semidirect
259. #12754C31direct (N × H)
332. #2127C2×C31semidirect
333. #2121C2×C31semidirect
334. C2×#352C2×C31semidirect
335. #1913C2×C31semidirect
336. #1911C2×C31semidirect
337. #1890C2×C31semidirect
376. #563C4×C31semidirect
378. #560C4×C31semidirect
379. #559C4×C31semidirect
383. #551C4×C31semidirect
524. C31#12754direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35332
C31×#21272
C31×#21212
C2×C31×#3522
C31×#19132
C31×#19112
C31×#18902
#1275431