Finite Group Databasebeta

← C31×#23903 #21480662

Subgroups — C31×#23903 #21480662

Order 7936.

2096 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3484C211yesmaximal, characteristic, complemented
2C2×C31×#534C211yesmaximal, characteristic, complemented
3C2×C31×#458C211yesmaximal, characteristic, complemented
4C2×C31×B(4,𝔽2)C211yesmaximal, characteristic, complemented
5C31×#2613C212yesmaximal, complemented
6C31×#2022C212yesmaximal, complemented
7C31×#2021C212yesmaximal, complemented
8C31×#1898C212yesmaximal, complemented
9C31×#1890C211yesmaximal, characteristic, complemented
10C31×#1889C211yesmaximal, characteristic, complemented
11C31×#1781C211yesmaximal, characteristic, complemented
12C2×C31×H(5,𝔽2)C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C23×D4×C31C2211yescharacteristic, complemented
15C31×#546—24no—
16D42×C31—24no—
17C31×#535—21no—
18C31×#534—21no—
19C31×#534—24no—
20C31×#534—24no—
21C31×#534C2212yes—
22C31×#525—21no—
23C2×C31×#123—21no—
24C2×C31×#123C2211yescharacteristic
25C2×C31×#123C2211yescharacteristic, complemented
26C2×C31×#123C2212yescomplemented
27C2×C31×#121—21no—
28C2×C31×#121—21no—
29C2×C31×#120—21no—
30C2×C31×#120—21no—
31C2×C31×#120C2211yescharacteristic
32C2×C31×#120C2212yes—
33C2×C31×#120C2211yescharacteristic, complemented
34C2×C31×#120C2212yescomplemented
35C31×#518C2211yescharacteristic
36C22×C22⋊C4×C31C2211yescharacteristic, complemented
37C31×#458—24no—
38C31×B(4,𝔽2)—24no—
39C2×C31×#99C2211yescharacteristic
40C2×C31×#99C2211yescharacteristic
41C2×C31×#99C2212yescomplemented
42C2×C31×#99C2212yescomplemented
43C2×C31×#99C2212yescomplemented
44C31×#394—24no—
45C31×#392—24no—
46C31×#381C2212yescomplemented
47C31×#379C2212yescomplemented
48C31×#379C2212yescomplemented
49C31×#342C2212yescomplemented
50C31×#342C2212yescomplemented
51C25×C31D411yescharacteristic, complemented
52C25×C31C2311yescharacteristic
53C25×C31C2311yescharacteristic
54C31×H(5,𝔽2)—22no—
55C31×H(5,𝔽2)—22no—
56C31×H(5,𝔽2)—42no—
57C2×#41×C31—21no—
58C2×#41×C31—22no—
59C22×D4×C31—21no—
60C22×D4×C31—21no—
61C22×D4×C31—21no—
62C22×D4×C31—22no—
63C22×D4×C31—24no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31—22no—
69C22×D4×C31—22no—
70C22×D4×C31—24no—
71C22×D4×C31—22no—
72C22×D4×C31—22no—
73C22×D4×C31—42no—
74C22×D4×C31—42no—
75C22×D4×C31D411yescharacteristic, complemented
76C22×D4×C31D411yescharacteristic, complemented
77C22×D4×C31D414yescomplemented
78C22×D4×C31C2312yes—
79C22×D4×C31C2311yescharacteristic
80C22×D4×C31C2311yescharacteristic
81C23×C4×C31—21no—
82C23×C4×C31D411yescharacteristic, complemented
83C23×C4×C31C2311yescharacteristic
84C31×#127—22no—
85C31×#124—22no—
86C31×#123—28no—
87C31×#123—22no—
88C31×#123—22no—
89C31×#123—22no—
90C31×#123—22no—
91C31×#123—22no—
92C31×#123—22no—
93C31×#123—24no—
94C31×#123—42no—
95C31×#123D414yescomplemented
96C31×C22⋊Q8—22no—
97C31×#121—28no—
98C31×#121—28no—
99C31×#121—22no—
100C31×#121—24no—
101C31×#121—24no—
102C31×#121—24no—
103C31×#120—28no—
104C31×#120—24no—
105C31×#120—22no—
106C31×#120—22no—
107C31×#120—22no—
108C31×#120—22no—
109C31×#120—24no—
110C31×#120—22no—
111C31×#120—22no—
112C31×#120—22no—
113C31×#120—22no—
114C31×#120—24no—
115C31×#120—42no—
116C31×#120D414yescomplemented
117C4×D4×C31—24no—
118C4×D4×C31—24no—
119C31×#117—21no—
120C2×C4⋊C4×C31—21no—
121C2×C4⋊C4×C31—21no—
122C2×C4⋊C4×C31—22no—
123C2×C22⋊C4×C31—22no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—22no—
131C2×C22⋊C4×C31—22no—
132C2×C22⋊C4×C31—22no—
133C2×C22⋊C4×C31—22no—
134C2×C22⋊C4×C31—24no—
135C2×C22⋊C4×C31—24no—
136C2×C22⋊C4×C31D414yescomplemented
137C2×C22⋊C4×C31C2312yes—
138C2×C22⋊C4×C31C2312yes—
139C2×C22⋊C4×C31C2312yes—
140C2×C22⋊C4×C31C2311yescharacteristic
141C2×C22⋊C4×C31C2311yescharacteristic
142C31×#99—22no—
143C31×#99—22no—
144C31×#99—24no—
145C31×#99—24no—
146C31×#99—42no—
147C31×#95—24no—
148C24×C31—21no—
149C24×C31—21no—
150C24×C31—22no—
151C24×C31—21no—
152C24×C31—22no—
153C24×C31—21no—
154C24×C31—22no—
155C24×C31—22no—
156C24×C31—21no—
157C24×C31—22no—
158C24×C31—41no—
159C24×C31—82no—
160C24×C31—82no—
161C24×C31—82no—
162C24×C31C2×D411yescharacteristic
163C24×C31C2×D412yes—
164C24×C31C2×D411yescharacteristic
165C24×C31C2×D414yes—
166C24×C31C2×D411yescharacteristic
167C24×C31C2×D411yescharacteristic
168C24×C31C2×D412yescomplemented
169C24×C31C2411yescharacteristic
170#41×C31—44no—
171#41×C31—44no—
172#41×C31—42no—
173#41×C31—42no—
174C2×Q8×C31—21no—
175C2×D4×C31—22no—
176C2×D4×C31—22no—
177C2×D4×C31—22no—
178C2×D4×C31—24no—
179C2×D4×C31—24no—
180C2×D4×C31—21no—
181C2×D4×C31—24no—
182C2×D4×C31—22no—
183C2×D4×C31—22no—
184C2×D4×C31—22no—
185C2×D4×C31—22no—
186C2×D4×C31—22no—
187C2×D4×C31—22no—
188C2×D4×C31—22no—
189C2×D4×C31—21no—
190C2×D4×C31—21no—
191C2×D4×C31—22no—
192C2×D4×C31—22no—
193C2×D4×C31—22no—
194C2×D4×C31—22no—
195C2×D4×C31—24no—
196C2×D4×C31—24no—
197C2×D4×C31—24no—
198C2×D4×C31—24no—
199C2×D4×C31—22no—
200C2×D4×C31—41no—
201C2×D4×C31—41no—
202C2×D4×C31—48no—
203C2×D4×C31—48no—
204C2×D4×C31—48no—
205C2×D4×C31—44no—
206C2×D4×C31—44no—
207C2×D4×C31—48no—
208C2×D4×C31—42no—
209C2×D4×C31—42no—
210C2×D4×C31—42no—
211C2×D4×C31—42no—
212C2×D4×C31—42no—
213C2×D4×C31—42no—
214C2×D4×C31—44no—
215C2×D4×C31—84no—
216C2×D4×C31—82no—
217C2×D4×C31—82no—
218C2×D4×C31—84no—
219C2×D4×C31—84no—
220C2×D4×C31C2×D412yes—
221C2×D4×C31C2×D412yes—
222C22×C4×C31—21no—
223C22×C4×C31—22no—
224C22×C4×C31—22no—
225C22×C4×C31—22no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—22no—
231C22×C4×C31—22no—
232C22×C4×C31—24no—
233C22×C4×C31—22no—
234C22×C4×C31—22no—
235C22×C4×C31—22no—
236C22×C4×C31—41no—
237C22×C4×C31—82no—
238C22×C4×C31C2×D412yes—
239C22×C4×C31C2×D411yescharacteristic
240C22×C4×C31C2×D411yescharacteristic
241C22×C4×C31C2×D414yes—
242C22×C4×C31C2×D412yescomplemented
243C4⋊C4×C31—24no—
244C4⋊C4×C31—22no—
245C4⋊C4×C31—24no—
246C4⋊C4×C31—24no—
247C4⋊C4×C31—44no—
248C22⋊C4×C31—24no—
249C22⋊C4×C31—22no—
250C22⋊C4×C31—24no—
251C22⋊C4×C31—24no—
252C22⋊C4×C31—24no—
253C22⋊C4×C31—24no—
254C22⋊C4×C31—24no—
255C22⋊C4×C31—24no—
256C22⋊C4×C31—24no—
257C22⋊C4×C31—21no—
258C22⋊C4×C31—21no—
259C22⋊C4×C31—22no—
260C22⋊C4×C31—22no—
261C22⋊C4×C31—24no—
262C22⋊C4×C31—22no—
263C22⋊C4×C31—22no—
264C22⋊C4×C31—22no—
265C22⋊C4×C31—22no—
266C22⋊C4×C31—44no—
267C22⋊C4×C31—44no—
268C22⋊C4×C31—84no—
269C22⋊C4×C31—84no—
270C22⋊C4×C31C2×D412yescomplemented
271C22⋊C4×C31C2×D412yescomplemented
272C42×C31—22no—
273#23903C3111yesmaximal, characteristic, direct product factor, Sylow
274C23×C31—21no—
275C23×C31—21no—
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—24no—
281C23×C31—24no—
282C23×C31—21no—
283C23×C31—22no—
284C23×C31—21no—
285C23×C31—22no—
286C23×C31—24no—
287C23×C31—21no—
288C23×C31—22no—
289C23×C31—22no—
290C23×C31—42no—
291C23×C31—42no—
292C23×C31—42no—
293C23×C31—44no—
294C23×C31—44no—
295C23×C31—44no—
296C23×C31—42no—
297C23×C31—42no—
298C23×C31—44no—
299C23×C31—44no—
300C23×C31—42no—
301C23×C31—42no—
302C23×C31—44no—
303C23×C31—42no—
304C23×C31—44no—
305C23×C31—41no—
306C23×C31—41no—
307C23×C31—42no—
308C23×C31—82no—
309C23×C31—82no—
310C23×C31—82no—
311C23×C31—82no—
312C23×C31—82no—
313C23×C31—84no—
314C23×C31—84no—
315C23×C31—84no—
316C23×C31—82no—
317C23×C31—84no—
318C23×C31#12012yes—
319C23×C31#12012yes—
320C23×C31#12012yes—
321C23×C31C22×D411yescharacteristic
322C23×C31C22×D412yes—
323C23×C31C22×D411yescharacteristic
324C23×C31C22×D411yescharacteristic
325C23×C31H(5,𝔽2)12yes—
326Q8×C31—42no—
327D4×C31—24no—
328D4×C31—24no—
329D4×C31—44no—
330D4×C31—42no—
331D4×C31—44no—
332D4×C31—48no—
333D4×C31—48no—
334D4×C31—44no—
335D4×C31—48no—
336D4×C31—42no—
337D4×C31—42no—
338D4×C31—42no—
339D4×C31—42no—
340D4×C31—42no—
341D4×C31—42no—
342D4×C31—84no—
343D4×C31—84no—
344D4×C31—84no—
345D4×C31—84no—
346D4×C31—88no—
347C2×C4×C31—21no—
348C2×C4×C31—21no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
351C2×C4×C31—21no—
352C2×C4×C31—22no—
353C2×C4×C31—24no—
354C2×C4×C31—22no—
355C2×C4×C31—21no—
356C2×C4×C31—21no—
357C2×C4×C31—22no—
358C2×C4×C31—24no—
359C2×C4×C31—22no—
360C2×C4×C31—44no—
361C2×C4×C31—44no—
362C2×C4×C31—42no—
363C2×C4×C31—42no—
364C2×C4×C31—42no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31—42no—
368C2×C4×C31—44no—
369C2×C4×C31—44no—
370C2×C4×C31—44no—
371C2×C4×C31—42no—
372C2×C4×C31—42no—
373C2×C4×C31—84no—
374C2×C4×C31—82no—
375C2×C4×C31#12012yes—
376#3484C2×C3111yescharacteristic, complemented
377C2×#534C2×C3111yescharacteristic, complemented
378C2×#458C2×C3111yescharacteristic, complemented
379C2×B(4,𝔽2)C2×C3111yescharacteristic, complemented
380#2613C2×C3112yescomplemented
381#2022C2×C3112yescomplemented
382#2021C2×C3112yescomplemented
383#1898C2×C3112yescomplemented
384#1890C2×C3111yescharacteristic, complemented
385#1889C2×C3111yescharacteristic, complemented
386#1781C2×C3111yescharacteristic, complemented
387C22×C31—24no—
388C22×C31—22no—
389C22×C31—22no—
390C22×C31—22no—
391C22×C31—22no—
392C22×C31—22no—
393C22×C31—24no—
394C22×C31—22no—
395C22×C31—41no—
396C22×C31—41no—
397C22×C31—42no—
398C22×C31—42no—
399C22×C31—42no—
400C22×C31—42no—
401C22×C31—42no—
402C22×C31—42no—
403C22×C31—42no—
404C22×C31—42no—
405C22×C31—42no—
406C22×C31—44no—
407C22×C31—44no—
408C22×C31—42no—
409C22×C31—42no—
410C22×C31—42no—
411C22×C31—41no—
412C22×C31—44no—
413C22×C31—42no—
414C22×C31—84no—
415C22×C31—84no—
416C22×C31—81no—
417C22×C31—82no—
418C22×C31—82no—
419C22×C31—81no—
420C22×C31—84no—
421C22×C31—82no—
422C22×C31—88no—
423C22×C31—82no—
424C22×C31—162no—
425C22×C31C2×#12011yescharacteristic
426C22×C31C2×#12011yescharacteristic
427C22×C31#53411yescharacteristic
428C22×C31D4212yes—
429C22×C31D4212yes—
430C4×C31—22no—
431C4×C31—42no—
432C4×C31—42no—
433C4×C31—41no—
434C4×C31—42no—
435C4×C31—42no—
436C4×C31—44no—
437C4×C31—82no—
438C4×C31—82no—
439C2×H(5,𝔽2)C22×C3111yescharacteristic
440C23×D4C22×C3111yescharacteristic
441C23×D4C22×C3111yescharacteristic, complemented
442#546—24no—
443D42—24no—
444#535—21no—
445#534—21no—
446#534—24no—
447#534—24no—
448#534C22×C3112yes—
449#525—21no—
450C2×#123—21no—
451C2×#123C22×C3111yescharacteristic
452C2×#123C22×C3111yescharacteristic, complemented
453C2×#123C22×C3112yescomplemented
454C2×#121—21no—
455C2×#121—21no—
456C2×#120—21no—
457C2×#120—21no—
458C2×#120C22×C3111yescharacteristic
459C2×#120C22×C3112yes—
460C2×#120C22×C3111yescharacteristic, complemented
461C2×#120C22×C3112yescomplemented
462#518C22×C3111yescharacteristic
463C22×C22⋊C4C22×C3111yescharacteristic, complemented
464#458—24no—
465B(4,𝔽2)—24no—
466C2×#99C22×C3111yescharacteristic
467C2×#99C22×C3111yescharacteristic
468C2×#99C22×C3112yescomplemented
469C2×#99C22×C3112yescomplemented
470C2×#99C22×C3112yescomplemented
471#394—24no—
472#392—24no—
473#381C22×C3112yescomplemented
474#379C22×C3112yescomplemented
475#379C22×C3112yescomplemented
476#342C22×C3112yescomplemented
477#342C22×C3112yescomplemented
478C2×C31—21no—
479C2×C31—22no—
480C2×C31—22no—
481C2×C31—21no—
482C2×C31—42no—
483C2×C31—42no—
484C2×C31—42no—
485C2×C31—82no—
486C2×C31—81no—
487C2×C31—82no—
488C2×C31#240311yescharacteristic
489C2×C31#302612yes—
490C25D4×C3111yescharacteristic, complemented
491C25C23×C3111yescharacteristic
492C25C23×C3111yescharacteristic
493H(5,𝔽2)—22no—
494H(5,𝔽2)—22no—
495H(5,𝔽2)—42no—
496C2×#41—21no—
497C2×#41—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—24no—
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—24no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—42no—
513C22×D4—42no—
514C22×D4D4×C3111yescharacteristic, complemented
515C22×D4D4×C3111yescharacteristic, complemented
516C22×D4D4×C3114yescomplemented
517C22×D4C23×C3112yes—
518C22×D4C23×C3111yescharacteristic
519C22×D4C23×C3111yescharacteristic
520C23×C4—21no—
521C23×C4D4×C3111yescharacteristic, complemented
522C23×C4C23×C3111yescharacteristic
523#127—22no—
524#124—22no—
525#123—28no—
526#123—22no—
527#123—22no—
528#123—22no—
529#123—22no—
530#123—22no—
531#123—22no—
532#123—24no—
533#123—42no—
534#123D4×C3114yescomplemented
535C22⋊Q8—22no—
536#121—28no—
537#121—28no—
538#121—22no—
539#121—24no—
540#121—24no—
541#121—24no—
542#120—28no—
543#120—24no—
544#120—22no—
545#120—22no—
546#120—22no—
547#120—22no—
548#120—24no—
549#120—22no—
550#120—22no—
551#120—22no—
552#120—22no—
553#120—24no—
554#120—42no—
555#120D4×C3114yescomplemented
556C4×D4—24no—
557C4×D4—24no—
558#117—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4D4×C3114yescomplemented
576C2×C22⋊C4C23×C3112yes—
577C2×C22⋊C4C23×C3112yes—
578C2×C22⋊C4C23×C3112yes—
579C2×C22⋊C4C23×C3111yescharacteristic
580C2×C22⋊C4C23×C3111yescharacteristic
581#99—22no—
582#99—22no—
583#99—24no—
584#99—24no—
585#99—42no—
586#95—24no—
587C31#2390311yescharacteristic, direct product factor, Sylow
588C24—21no—
589C24—21no—
590C24—22no—
591C24—21no—
592C24—22no—
593C24—21no—
594C24—22no—
595C24—22no—
596C24—21no—
597C24—22no—
598C24—41no—
599C24—82no—
600C24—82no—
601C24—82no—
602C24C2×D4×C3111yescharacteristic
603C24C2×D4×C3112yes—
604C24C2×D4×C3111yescharacteristic
605C24C2×D4×C3114yes—
606C24C2×D4×C3111yescharacteristic
607C24C2×D4×C3111yescharacteristic
608C24C2×D4×C3112yescomplemented
609C24C24×C3111yescharacteristic
610#41—44no—
611#41—44no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—24no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—22no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—48no—
643C2×D4—48no—
644C2×D4—48no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—48no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—44no—
655C2×D4—84no—
656C2×D4—82no—
657C2×D4—82no—
658C2×D4—84no—
659C2×D4—84no—
660C2×D4C2×D4×C3112yes—
661C2×D4C2×D4×C3112yes—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—24no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—41no—
677C22×C4—82no—
678C22×C4C2×D4×C3112yes—
679C22×C4C2×D4×C3111yescharacteristic
680C22×C4C2×D4×C3111yescharacteristic
681C22×C4C2×D4×C3114yes—
682C22×C4C2×D4×C3112yescomplemented
683C4⋊C4—24no—
684C4⋊C4—22no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—44no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—24no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—84no—
709C22⋊C4—84no—
710C22⋊C4C2×D4×C3112yescomplemented
711C22⋊C4C2×D4×C3112yescomplemented
712C42—22no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—24no—
720C23—24no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—22no—
725C23—24no—
726C23—21no—
727C23—22no—
728C23—22no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—42no—
736C23—42no—
737C23—44no—
738C23—44no—
739C23—42no—
740C23—42no—
741C23—44no—
742C23—42no—
743C23—44no—
744C23—41no—
745C23—41no—
746C23—42no—
747C23—82no—
748C23—82no—
749C23—82no—
750C23—82no—
751C23—82no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—82no—
756C23—84no—
757C23C31×#12012yes—
758C23C31×#12012yes—
759C23C31×#12012yes—
760C23C22×D4×C3111yescharacteristic
761C23C22×D4×C3112yes—
762C23C22×D4×C3111yescharacteristic
763C23C22×D4×C3111yescharacteristic
764C23C31×H(5,𝔽2)12yes—
765Q8—42no—
766D4—24no—
767D4—24no—
768D4—44no—
769D4—42no—
770D4—44no—
771D4—48no—
772D4—48no—
773D4—44no—
774D4—48no—
775D4—42no—
776D4—42no—
777D4—42no—
778D4—42no—
779D4—42no—
780D4—42no—
781D4—84no—
782D4—84no—
783D4—84no—
784D4—84no—
785D4—88no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—84no—
813C2×C4—82no—
814C2×C4C31×#12012yes—
815C22—24no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—24no—
822C22—22no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—41no—
840C22—44no—
841C22—42no—
842C22—84no—
843C22—84no—
844C22—81no—
845C22—82no—
846C22—81no—
847C22—82no—
848C22—84no—
849C22—82no—
850C22—88no—
851C22—82no—
852C22—162no—
853C22C2×C31×#12011yescharacteristic
854C22C2×C31×#12011yescharacteristic
855C22C31×#53411yescharacteristic
856C22D42×C3112yes—
857C22D42×C3112yes—
858C4—22no—
859C4—42no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—42no—
864C4—44no—
865C4—82no—
866C4—82no—
867C2—21no—
868C2—22no—
869C2—22no—
870C2—21no—
871C2—42no—
872C2—42no—
873C2—42no—
874C2—82no—
875C2—81no—
876C2—82no—
877C2C31×#240311yescharacteristic
878C2C31×#302612yes—
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3484C2semidirect
2. C2×C31×#534C2semidirect
3. C2×C31×#458C2semidirect
4. C2×C31×B(4,𝔽2)C2semidirect
5. C31×#2613C2semidirect
6. C31×#2022C2semidirect
7. C31×#2021C2semidirect
8. C31×#1898C2semidirect
9. C31×#1890C2semidirect
10. C31×#1889C2semidirect
11. C31×#1781C2semidirect
14. C23×D4×C31C22semidirect
25. C2×C31×#123C22semidirect
26. C2×C31×#123C22semidirect
33. C2×C31×#120C22semidirect
34. C2×C31×#120C22semidirect
36. C22×C22⋊C4×C31C22semidirect
41. C2×C31×#99C22semidirect
42. C2×C31×#99C22semidirect
43. C2×C31×#99C22semidirect
46. C31×#381C22semidirect
47. C31×#379C22semidirect
48. C31×#379C22semidirect
49. C31×#342C22semidirect
50. C31×#342C22semidirect
51. C25×C31D4semidirect
75. C22×D4×C31D4semidirect
76. C22×D4×C31D4semidirect
77. C22×D4×C31D4semidirect
82. C23×C4×C31D4semidirect
95. C31×#123D4semidirect
116. C31×#120D4semidirect
136. C2×C22⋊C4×C31D4semidirect
168. C24×C31C2×D4semidirect
242. C22×C4×C31C2×D4semidirect
270. C22⋊C4×C31C2×D4semidirect
271. C22⋊C4×C31C2×D4semidirect
273. #23903C31direct (N × H)
376. #3484C2×C31semidirect
377. C2×#534C2×C31semidirect
378. C2×#458C2×C31semidirect
379. C2×B(4,𝔽2)C2×C31semidirect
380. #2613C2×C31semidirect
381. #2022C2×C31semidirect
382. #2021C2×C31semidirect
383. #1898C2×C31semidirect
384. #1890C2×C31semidirect
385. #1889C2×C31semidirect
386. #1781C2×C31semidirect
441. C23×D4C22×C31semidirect
452. C2×#123C22×C31semidirect
453. C2×#123C22×C31semidirect
460. C2×#120C22×C31semidirect
461. C2×#120C22×C31semidirect
463. C22×C22⋊C4C22×C31semidirect
468. C2×#99C22×C31semidirect
469. C2×#99C22×C31semidirect
470. C2×#99C22×C31semidirect
473. #381C22×C31semidirect
474. #379C22×C31semidirect
475. #379C22×C31semidirect
476. #342C22×C31semidirect
477. #342C22×C31semidirect
490. C25D4×C31semidirect
514. C22×D4D4×C31semidirect
515. C22×D4D4×C31semidirect
516. C22×D4D4×C31semidirect
521. C23×C4D4×C31semidirect
534. #123D4×C31semidirect
555. #120D4×C31semidirect
575. C2×C22⋊C4D4×C31semidirect
587. C31#23903direct (N × H)
608. C24C2×D4×C31semidirect
682. C22×C4C2×D4×C31semidirect
710. C22⋊C4C2×D4×C31semidirect
711. C22⋊C4C2×D4×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#34842
C2×C31×#5342
C2×C31×#4582
C2×C31×B(4,𝔽2)2
C31×#26132
C31×#20222
C31×#20212
C31×#18982
C31×#18902
C31×#18892
C31×#17812
#2390331