Finite Group Databasebeta

← C31×#23996 #21480755

Subgroups — C31×#23996 #21480755

Order 7936.

1396 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3490C211yesmaximal, characteristic, complemented
2C31×#3026C211yesmaximal, characteristic, complemented
3C2×C31×B(4,𝔽2)C211yesmaximal, characteristic, complemented
4C31×#2883C211yesmaximal, characteristic, complemented
5C31×#2032C212yesmaximal, complemented
6C31×#2021C212yesmaximal, complemented
7C31×#1913C212yesmaximal, complemented
8C31×#1913C211yesmaximal, characteristic, complemented
9C31×#1898C212yesmaximal, complemented
10C31×#1889C211yesmaximal, characteristic, complemented
11C31×#1828C211yesmaximal, characteristic, complemented
12C2×C31×H(5,𝔽2)C2211yescharacteristic
13C31×#551—22no—
14C31×#551—22no—
15C31×#546—22no—
16C31×#546—22no—
17C31×#543C2211yescharacteristic, complemented
18C31×#538—22no—
19C31×#534C2212yes—
20C31×#534C2211yescharacteristic
21C31×#525—22no—
22C2×C31×#120C2212yes—
23C2×C31×#120C2211yescharacteristic
24C2×C31×#120C2211yescharacteristic, complemented
25C31×#518C2211yescharacteristic
26C31×#518C2211yescharacteristic
27C31×#518C2211yescharacteristic, complemented
28C22×C22⋊C4×C31C2211yescharacteristic, complemented
29C31×#458—22no—
30C31×B(4,𝔽2)—22no—
31C31×B(4,𝔽2)—22no—
32C31×B(4,𝔽2)—22no—
33C31×#410—22no—
34C2×C31×#99—22no—
35C2×C31×#99C2211yescharacteristic
36C2×C31×#99C2211yescharacteristic
37C2×C31×#99C2212yes—
38C2×C31×#99C2212yes—
39C2×C31×#99C2212yes—
40C2×C31×#99C2212yes—
41C2×C31×#99C2212yescomplemented
42C31×#379C2212yescomplemented
43C31×#342C2212yescomplemented
44C31×#342C2212yescomplemented
45C31×#342C2212yescomplemented
46C31×#342C2212yescomplemented
47C25×C31C2311yescharacteristic
48C31×H(5,𝔽2)—22no—
49C31×H(5,𝔽2)—22no—
50C31×H(5,𝔽2)—42no—
51C2×#41×C31—22no—
52C2×#41×C31—21no—
53C2×#41×C31—22no—
54C22×D4×C31—21no—
55C22×D4×C31—22no—
56C22×D4×C31—21no—
57C22×D4×C31—21no—
58C22×D4×C31—22no—
59C22×D4×C31C2311yescharacteristic
60C22×D4×C31C2311yescharacteristic
61C22×D4×C31C2312yes—
62C23×C4×C31—21no—
63C31×#126—22no—
64C31×#126—22no—
65C31×#124—22no—
66C31×#124—22no—
67C31×#123—22no—
68C31×#123—22no—
69C31×#123—22no—
70C31×#123—22no—
71C31×#123—21no—
72C31×#123—22no—
73C31×#123—22no—
74C31×#123D412yescomplemented
75C31×C22⋊Q8—22no—
76C31×C22⋊Q8—22no—
77C31×C22⋊Q8—22no—
78C31×C22⋊Q8—22no—
79C31×#121—22no—
80C31×#121—22no—
81C31×#121—22no—
82C31×#121—22no—
83C31×#121—42no—
84C31×#120—21no—
85C31×#120—21no—
86C31×#120—21no—
87C31×#120—22no—
88C31×#120—22no—
89C31×#120—22no—
90C31×#120—22no—
91C31×#120—22no—
92C31×#120—22no—
93C31×#120—42no—
94C31×#120D412yescomplemented
95C31×#120D412yescomplemented
96C31×#120D412yescomplemented
97C4×D4×C31—22no—
98C4×D4×C31—22no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31—22no—
102C4×D4×C31—22no—
103C4×D4×C31—42no—
104C31×#117—22no—
105C31×#117—21no—
106C31×#117—21no—
107C31×#117D412yescomplemented
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—22no—
113C2×C22⋊C4×C31—22no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—22no—
116C2×C22⋊C4×C31—42no—
117C2×C22⋊C4×C31D412yescomplemented
118C2×C22⋊C4×C31C2312yes—
119C2×C22⋊C4×C31C2312yes—
120C2×C22⋊C4×C31C2312yes—
121C2×C22⋊C4×C31C2311yescharacteristic
122C2×C22⋊C4×C31C2311yescharacteristic
123C2×C22⋊C4×C31C2311yescharacteristic
124C2×C22⋊C4×C31C2311yescharacteristic
125C31×#99—22no—
126C31×#99—22no—
127C31×#99—24no—
128C31×#99—24no—
129C31×#99—24no—
130C31×#99—24no—
131C31×#99—42no—
132C24×C31—21no—
133C24×C31—21no—
134C24×C31—21no—
135C24×C31—22no—
136C24×C31—22no—
137C24×C31—82no—
138C24×C31C2×D411yescharacteristic
139C24×C31C2×D411yescharacteristic
140C24×C31C2×D411yescharacteristic
141C24×C31C2×D411yescharacteristic
142C24×C31#4112yescomplemented
143C24×C31C2411yescharacteristic
144#41×C31—44no—
145#41×C31—44no—
146#41×C31—42no—
147#41×C31—42no—
148#41×C31—84no—
149C2×Q8×C31—21no—
150C2×Q8×C31—22no—
151C2×D4×C31—22no—
152C2×D4×C31—22no—
153C2×D4×C31—22no—
154C2×D4×C31—21no—
155C2×D4×C31—22no—
156C2×D4×C31—22no—
157C2×D4×C31—22no—
158C2×D4×C31—22no—
159C2×D4×C31—22no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—22no—
163C2×D4×C31—22no—
164C2×D4×C31—22no—
165C2×D4×C31—22no—
166C2×D4×C31—22no—
167C2×D4×C31—22no—
168C2×D4×C31—22no—
169C2×D4×C31—22no—
170C2×D4×C31—44no—
171C2×D4×C31—44no—
172C2×D4×C31—42no—
173C2×D4×C31—42no—
174C2×D4×C31—42no—
175C2×D4×C31—42no—
176C2×D4×C31—42no—
177C2×D4×C31—82no—
178C2×D4×C31—82no—
179C2×D4×C31—84no—
180C2×D4×C31C2×D412yes—
181C2×D4×C31C2×D412yes—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—21no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—41no—
196C22×C4×C31—82no—
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31#4112yescomplemented
200C4⋊C4×C31—22no—
201C4⋊C4×C31—22no—
202C4⋊C4×C31—22no—
203C4⋊C4×C31—22no—
204C4⋊C4×C31—22no—
205C4⋊C4×C31—22no—
206C4⋊C4×C31—42no—
207C4⋊C4×C31—41no—
208C22⋊C4×C31—22no—
209C22⋊C4×C31—22no—
210C22⋊C4×C31—22no—
211C22⋊C4×C31—22no—
212C22⋊C4×C31—22no—
213C22⋊C4×C31—22no—
214C22⋊C4×C31—22no—
215C22⋊C4×C31—21no—
216C22⋊C4×C31—21no—
217C22⋊C4×C31—21no—
218C22⋊C4×C31—21no—
219C22⋊C4×C31—22no—
220C22⋊C4×C31—22no—
221C22⋊C4×C31—22no—
222C22⋊C4×C31—22no—
223C22⋊C4×C31—22no—
224C22⋊C4×C31—22no—
225C22⋊C4×C31—22no—
226C22⋊C4×C31—22no—
227C22⋊C4×C31—22no—
228C22⋊C4×C31—42no—
229C22⋊C4×C31—42no—
230C22⋊C4×C31—42no—
231C22⋊C4×C31—42no—
232C22⋊C4×C31—41no—
233C22⋊C4×C31—84no—
234C22⋊C4×C31C2×D412yes—
235C22⋊C4×C31C2×D412yes—
236C22⋊C4×C31C2×D412yes—
237C22⋊C4×C31C2×D412yes—
238C42×C31—22no—
239C42×C31—22no—
240C42×C31—41no—
241#23996C3111yesmaximal, characteristic, direct product factor, Sylow
242C23×C31—21no—
243C23×C31—22no—
244C23×C31—21no—
245C23×C31—21no—
246C23×C31—21no—
247C23×C31—21no—
248C23×C31—22no—
249C23×C31—22no—
250C23×C31—22no—
251C23×C31—22no—
252C23×C31—22no—
253C23×C31—42no—
254C23×C31—44no—
255C23×C31—42no—
256C23×C31—42no—
257C23×C31—44no—
258C23×C31—42no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—42no—
262C23×C31—81no—
263C23×C31—81no—
264C23×C31—81no—
265C23×C31—81no—
266C23×C31—82no—
267C23×C31—81no—
268C23×C31—81no—
269C23×C31—82no—
270C23×C31—82no—
271C23×C31—161no—
272C23×C31#12012yes—
273C23×C31C22×D411yescharacteristic
274C23×C31C22×D411yescharacteristic
275C23×C31C22×D411yescharacteristic
276C23×C31C2×#4112yes—
277C23×C31H(5,𝔽2)12yes—
278Q8×C31—42no—
279Q8×C31—82no—
280D4×C31—24no—
281D4×C31—24no—
282D4×C31—42no—
283D4×C31—44no—
284D4×C31—44no—
285D4×C31—44no—
286D4×C31—42no—
287D4×C31—41no—
288D4×C31—41no—
289D4×C31—42no—
290D4×C31—42no—
291D4×C31—42no—
292D4×C31—42no—
293D4×C31—82no—
294D4×C31—82no—
295D4×C31—82no—
296D4×C31—84no—
297D4×C31—84no—
298D4×C31—162no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—22no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—44no—
311C2×C4×C31—44no—
312C2×C4×C31—42no—
313C2×C4×C31—42no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—81no—
317C2×C4×C31—82no—
318C2×C4×C31—81no—
319C2×C4×C31—81no—
320C2×C4×C31—81no—
321C2×C4×C31—82no—
322C2×C4×C31—82no—
323C2×C4×C31—82no—
324C2×C4×C31—82no—
325C2×C4×C31—82no—
326C2×C4×C31—161no—
327C2×C4×C31#12012yes—
328#3490C2×C3111yescharacteristic, complemented
329#3026C2×C3111yescharacteristic, complemented
330C2×B(4,𝔽2)C2×C3111yescharacteristic, complemented
331#2883C2×C3111yescharacteristic, complemented
332#2032C2×C3112yescomplemented
333#2021C2×C3112yescomplemented
334#1913C2×C3111yescharacteristic, complemented
335#1913C2×C3112yescomplemented
336#1898C2×C3112yescomplemented
337#1889C2×C3111yescharacteristic, complemented
338#1828C2×C3111yescharacteristic, complemented
339C22×C31—22no—
340C22×C31—24no—
341C22×C31—22no—
342C22×C31—41no—
343C22×C31—42no—
344C22×C31—41no—
345C22×C31—41no—
346C22×C31—42no—
347C22×C31—42no—
348C22×C31—41no—
349C22×C31—42no—
350C22×C31—42no—
351C22×C31—41no—
352C22×C31—41no—
353C22×C31—42no—
354C22×C31—42no—
355C22×C31—41no—
356C22×C31—42no—
357C22×C31—41no—
358C22×C31—41no—
359C22×C31—81no—
360C22×C31—81no—
361C22×C31—82no—
362C22×C31—84no—
363C22×C31—82no—
364C22×C31—82no—
365C22×C31—82no—
366C22×C31—82no—
367C22×C31—82no—
368C22×C31—162no—
369C22×C31C2×#12011yescharacteristic
370C22×C31#52511yescharacteristic
371C22×C31#53511yescharacteristic
372C22×C31#54612yes—
373C22×C31#54612yes—
374C4×C31—22no—
375C4×C31—42no—
376C4×C31—42no—
377C4×C31—42no—
378C4×C31—42no—
379C4×C31—42no—
380C4×C31—41no—
381C4×C31—82no—
382C4×C31—82no—
383C4×C31—82no—
384C2×H(5,𝔽2)C22×C3111yescharacteristic
385#551—22no—
386#551—22no—
387#546—22no—
388#546—22no—
389#543C22×C3111yescharacteristic, complemented
390#538—22no—
391#534C22×C3112yes—
392#534C22×C3111yescharacteristic
393#525—22no—
394C2×#120C22×C3112yes—
395C2×#120C22×C3111yescharacteristic
396C2×#120C22×C3111yescharacteristic, complemented
397#518C22×C3111yescharacteristic
398#518C22×C3111yescharacteristic
399#518C22×C3111yescharacteristic, complemented
400C22×C22⋊C4C22×C3111yescharacteristic, complemented
401#458—22no—
402B(4,𝔽2)—22no—
403B(4,𝔽2)—22no—
404B(4,𝔽2)—22no—
405#410—22no—
406C2×#99—22no—
407C2×#99C22×C3111yescharacteristic
408C2×#99C22×C3111yescharacteristic
409C2×#99C22×C3112yes—
410C2×#99C22×C3112yes—
411C2×#99C22×C3112yes—
412C2×#99C22×C3112yes—
413C2×#99C22×C3112yescomplemented
414#379C22×C3112yescomplemented
415#342C22×C3112yescomplemented
416#342C22×C3112yescomplemented
417#342C22×C3112yescomplemented
418#342C22×C3112yescomplemented
419C2×C31—21no—
420C2×C31—21no—
421C2×C31—22no—
422C2×C31—22no—
423C2×C31—21no—
424C2×C31—42no—
425C2×C31—42no—
426C2×C31—81no—
427C2×C31—81no—
428C2×C31—82no—
429C2×C31#240411yescharacteristic
430C25C23×C3111yescharacteristic
431H(5,𝔽2)—22no—
432H(5,𝔽2)—22no—
433H(5,𝔽2)—42no—
434C2×#41—22no—
435C2×#41—21no—
436C2×#41—22no—
437C22×D4—21no—
438C22×D4—22no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4—22no—
442C22×D4C23×C3111yescharacteristic
443C22×D4C23×C3111yescharacteristic
444C22×D4C23×C3112yes—
445C23×C4—21no—
446#126—22no—
447#126—22no—
448#124—22no—
449#124—22no—
450#123—22no—
451#123—22no—
452#123—22no—
453#123—22no—
454#123—21no—
455#123—22no—
456#123—22no—
457#123D4×C3112yescomplemented
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462#121—22no—
463#121—22no—
464#121—22no—
465#121—22no—
466#121—42no—
467#120—21no—
468#120—21no—
469#120—21no—
470#120—22no—
471#120—22no—
472#120—22no—
473#120—22no—
474#120—22no—
475#120—22no—
476#120—42no—
477#120D4×C3112yescomplemented
478#120D4×C3112yescomplemented
479#120D4×C3112yescomplemented
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—42no—
487#117—22no—
488#117—21no—
489#117—21no—
490#117D4×C3112yescomplemented
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4D4×C3112yescomplemented
501C2×C22⋊C4C23×C3112yes—
502C2×C22⋊C4C23×C3112yes—
503C2×C22⋊C4C23×C3112yes—
504C2×C22⋊C4C23×C3111yescharacteristic
505C2×C22⋊C4C23×C3111yescharacteristic
506C2×C22⋊C4C23×C3111yescharacteristic
507C2×C22⋊C4C23×C3111yescharacteristic
508#99—22no—
509#99—22no—
510#99—24no—
511#99—24no—
512#99—24no—
513#99—24no—
514#99—42no—
515C31#2399611yescharacteristic, direct product factor, Sylow
516C24—21no—
517C24—21no—
518C24—21no—
519C24—22no—
520C24—22no—
521C24—82no—
522C24C2×D4×C3111yescharacteristic
523C24C2×D4×C3111yescharacteristic
524C24C2×D4×C3111yescharacteristic
525C24C2×D4×C3111yescharacteristic
526C24#41×C3112yescomplemented
527C24C24×C3111yescharacteristic
528#41—44no—
529#41—44no—
530#41—42no—
531#41—42no—
532#41—84no—
533C2×Q8—21no—
534C2×Q8—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—82no—
562C2×D4—82no—
563C2×D4—84no—
564C2×D4C2×D4×C3112yes—
565C2×D4C2×D4×C3112yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—41no—
580C22×C4—82no—
581C22×C4C2×D4×C3111yescharacteristic
582C22×C4C2×D4×C3111yescharacteristic
583C22×C4#41×C3112yescomplemented
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—42no—
591C4⋊C4—41no—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—41no—
617C22⋊C4—84no—
618C22⋊C4C2×D4×C3112yes—
619C22⋊C4C2×D4×C3112yes—
620C22⋊C4C2×D4×C3112yes—
621C22⋊C4C2×D4×C3112yes—
622C42—22no—
623C42—22no—
624C42—41no—
625C23—21no—
626C23—22no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—42no—
637C23—44no—
638C23—42no—
639C23—42no—
640C23—44no—
641C23—42no—
642C23—41no—
643C23—41no—
644C23—42no—
645C23—81no—
646C23—81no—
647C23—81no—
648C23—81no—
649C23—82no—
650C23—81no—
651C23—81no—
652C23—82no—
653C23—82no—
654C23—161no—
655C23C31×#12012yes—
656C23C22×D4×C3111yescharacteristic
657C23C22×D4×C3111yescharacteristic
658C23C22×D4×C3111yescharacteristic
659C23C2×#41×C3112yes—
660C23C31×H(5,𝔽2)12yes—
661Q8—42no—
662Q8—82no—
663D4—24no—
664D4—24no—
665D4—42no—
666D4—44no—
667D4—44no—
668D4—44no—
669D4—42no—
670D4—41no—
671D4—41no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—42no—
676D4—82no—
677D4—82no—
678D4—82no—
679D4—84no—
680D4—84no—
681D4—162no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—81no—
700C2×C4—82no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—82no—
709C2×C4—161no—
710C2×C4C31×#12012yes—
711C22—22no—
712C22—24no—
713C22—22no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—41no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—41no—
725C22—42no—
726C22—42no—
727C22—41no—
728C22—42no—
729C22—41no—
730C22—41no—
731C22—81no—
732C22—81no—
733C22—82no—
734C22—84no—
735C22—82no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—162no—
741C22C2×C31×#12011yescharacteristic
742C22C31×#52511yescharacteristic
743C22C31×#53511yescharacteristic
744C22C31×#54612yes—
745C22C31×#54612yes—
746C4—22no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—41no—
753C4—82no—
754C4—82no—
755C4—82no—
756C2—21no—
757C2—21no—
758C2—22no—
759C2—22no—
760C2—21no—
761C2—42no—
762C2—42no—
763C2—81no—
764C2—81no—
765C2—82no—
766C2C31×#240411yescharacteristic
subgroupG/H
center, socleC2×C31#2404
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3490C2semidirect
2. C31×#3026C2semidirect
3. C2×C31×B(4,𝔽2)C2semidirect
4. C31×#2883C2semidirect
5. C31×#2032C2semidirect
6. C31×#2021C2semidirect
7. C31×#1913C2semidirect
8. C31×#1913C2semidirect
9. C31×#1898C2semidirect
10. C31×#1889C2semidirect
11. C31×#1828C2semidirect
17. C31×#543C22semidirect
24. C2×C31×#120C22semidirect
27. C31×#518C22semidirect
28. C22×C22⋊C4×C31C22semidirect
41. C2×C31×#99C22semidirect
42. C31×#379C22semidirect
43. C31×#342C22semidirect
44. C31×#342C22semidirect
45. C31×#342C22semidirect
46. C31×#342C22semidirect
74. C31×#123D4semidirect
94. C31×#120D4semidirect
95. C31×#120D4semidirect
96. C31×#120D4semidirect
107. C31×#117D4semidirect
117. C2×C22⋊C4×C31D4semidirect
142. C24×C31#41semidirect
199. C22×C4×C31#41semidirect
241. #23996C31direct (N × H)
328. #3490C2×C31semidirect
329. #3026C2×C31semidirect
330. C2×B(4,𝔽2)C2×C31semidirect
331. #2883C2×C31semidirect
332. #2032C2×C31semidirect
333. #2021C2×C31semidirect
334. #1913C2×C31semidirect
335. #1913C2×C31semidirect
336. #1898C2×C31semidirect
337. #1889C2×C31semidirect
338. #1828C2×C31semidirect
389. #543C22×C31semidirect
396. C2×#120C22×C31semidirect
399. #518C22×C31semidirect
400. C22×C22⋊C4C22×C31semidirect
413. C2×#99C22×C31semidirect
414. #379C22×C31semidirect
415. #342C22×C31semidirect
416. #342C22×C31semidirect
417. #342C22×C31semidirect
418. #342C22×C31semidirect
457. #123D4×C31semidirect
477. #120D4×C31semidirect
478. #120D4×C31semidirect
479. #120D4×C31semidirect
490. #117D4×C31semidirect
500. C2×C22⋊C4D4×C31semidirect
515. C31#23996direct (N × H)
526. C24#41×C31semidirect
583. C22×C4#41×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#34902
C31×#30262
C2×C31×B(4,𝔽2)2
C31×#28832
C31×#20322
C31×#20212
C31×#19132
C31×#18982
C31×#18892
C31×#18282
#2399631