Finite Group Databasebeta

← C31×#16250 #21473009

Subgroups — C31×#16250 #21473009

Order 7936.

2894 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#123C211yesmaximal, characteristic, complemented
2C22×C31×#121C211yesmaximal, characteristic, complemented
3C2×C31×#394C211yesmaximal, characteristic, complemented
4C2×C31×#392C212yesmaximal, complemented
5C2×C31×#392C211yesmaximal, characteristic, complemented
6C31×#1441C211yesmaximal, characteristic, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1439C211yesmaximal, characteristic, complemented
9C31×#1438C212yesmaximal, complemented
10C31×#1438C212yesmaximal, complemented
11C31×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C23×D4×C31C2212yes—
15C23×D4×C31C2212yes—
16C24×C4×C31C2211yescharacteristic
17C2×C31×#123—24no—
18C2×C31×#123—24no—
19C2×C31×#123—24no—
20C2×C31×#121—28no—
21C2×C31×#121—24no—
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2212yes—
29C22×C22⋊C4×C31C2212yes—
30C22×C22⋊C4×C31C2212yes—
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2212yes—
33C22×C22⋊C4×C31C2212yes—
34C31×#394—24no—
35C31×#392—28no—
36C31×#392—24no—
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2212yes—
39C2×C31×#95C2211yescharacteristic
40C2×C31×#95C2212yes—
41C2×C31×#95C2212yes—
42C2×C31×#95C2212yes—
43C25×C31C2311yescharacteristic
44C25×C31C2312yes—
45C25×C31C2311yescharacteristic
46C22×D4×C31—24no—
47C22×D4×C31—24no—
48C22×D4×C31—24no—
49C22×D4×C31—22no—
50C22×D4×C31—22no—
51C22×D4×C31—24no—
52C22×D4×C31—24no—
53C22×D4×C31—24no—
54C22×D4×C31—22no—
55C22×D4×C31—22no—
56C22×D4×C31—22no—
57C22×D4×C31—22no—
58C22×D4×C31—24no—
59C22×D4×C31—42no—
60C22×D4×C31—42no—
61C22×D4×C31—42no—
62C22×D4×C31—42no—
63C22×D4×C31—42no—
64C22×D4×C31—42no—
65C22×D4×C31—42no—
66C22×D4×C31—42no—
67C22×D4×C31—42no—
68C22×D4×C31—42no—
69C22×D4×C31D418yescomplemented
70C23×C4×C31—24no—
71C23×C4×C31—22no—
72C23×C4×C31—22no—
73C23×C4×C31—42no—
74C23×C4×C31D414yescomplemented
75C23×C4×C31C2312yes—
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2312yes—
81C23×C4×C31C2312yes—
82C23×C4×C31C2311yescharacteristic
83C31×#123—232no—
84C31×#121—232no—
85C2×C4⋊C4×C31—24no—
86C2×C4⋊C4×C31—22no—
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—22no—
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31D414yescomplemented
93C2×C22⋊C4×C31—24no—
94C2×C22⋊C4×C31—22no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—24no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—22no—
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—24no—
105C2×C22⋊C4×C31—24no—
106C2×C22⋊C4×C31—24no—
107C2×C22⋊C4×C31—24no—
108C2×C22⋊C4×C31—24no—
109C2×C22⋊C4×C31—24no—
110C2×C22⋊C4×C31—24no—
111C2×C22⋊C4×C31—24no—
112C2×C22⋊C4×C31—42no—
113C2×C22⋊C4×C31—42no—
114C2×C22⋊C4×C31—42no—
115C2×C22⋊C4×C31—42no—
116C2×C22⋊C4×C31—42no—
117C2×C22⋊C4×C31—42no—
118C2×C22⋊C4×C31—42no—
119C2×C22⋊C4×C31D414yescomplemented
120C31×#95—24no—
121C31×#95—22no—
122C31×#95—22no—
123C31×#95—42no—
124C31×#95—42no—
125C31×#95—42no—
126C24×C31—21no—
127C24×C31—21no—
128C24×C31—22no—
129C24×C31—21no—
130C24×C31—22no—
131C24×C31—21no—
132C24×C31—21no—
133C24×C31—22no—
134C24×C31—21no—
135C24×C31—21no—
136C24×C31—21no—
137C24×C31—22no—
138C24×C31—22no—
139C24×C31—22no—
140C24×C31—22no—
141C24×C31—22no—
142C24×C31—22no—
143C24×C31—22no—
144C24×C31—22no—
145C24×C31—21no—
146C24×C31—22no—
147C24×C31—22no—
148C24×C31—22no—
149C24×C31—22no—
150C24×C31—22no—
151C24×C31—22no—
152C24×C31—22no—
153C24×C31—21no—
154C24×C31—21no—
155C24×C31—22no—
156C24×C31—22no—
157C24×C31—21no—
158C24×C31—22no—
159C24×C31C2×D414yes—
160C24×C31C2×D412yes—
161C24×C31C2×D414yes—
162C24×C31C2×D412yes—
163C24×C31C2411yescharacteristic
164C2×D4×C31—28no—
165C2×D4×C31—28no—
166C2×D4×C31—216no—
167C2×D4×C31—48no—
168C2×D4×C31—48no—
169C2×D4×C31—48no—
170C2×D4×C31—48no—
171C2×D4×C31—48no—
172C2×D4×C31—48no—
173C2×D4×C31—48no—
174C2×D4×C31—44no—
175C2×D4×C31—48no—
176C2×D4×C31—48no—
177C2×D4×C31—48no—
178C2×D4×C31—44no—
179C2×D4×C31—48no—
180C2×D4×C31—48no—
181C2×D4×C31—48no—
182C2×D4×C31—48no—
183C2×D4×C31—48no—
184C2×D4×C31—48no—
185C2×D4×C31—48no—
186C2×D4×C31—44no—
187C2×D4×C31—44no—
188C22×C4×C31—22no—
189C22×C4×C31—22no—
190C22×C4×C31—28no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—22no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—22no—
202C22×C4×C31—22no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—22no—
206C22×C4×C31—21no—
207C22×C4×C31—22no—
208C22×C4×C31—22no—
209C22×C4×C31—22no—
210C22×C4×C31—22no—
211C22×C4×C31—22no—
212C22×C4×C31—22no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—22no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—22no—
220C22×C4×C31—21no—
221C22×C4×C31—28no—
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—22no—
229C22×C4×C31—44no—
230C22×C4×C31—48no—
231C22×C4×C31—48no—
232C22×C4×C31C2×D414yes—
233C22×C4×C31C2×D412yes—
234C22×C4×C31C2×D412yes—
235C22×C4×C31C2×D412yes—
236C22×C4×C31C2×D412yes—
237C22×C4×C31C2×D412yes—
238C22×C4×C31C2×D412yes—
239C22×C4×C31C2×D412yes—
240C22×C4×C31#4114yes—
241C4⋊C4×C31—28no—
242C4⋊C4×C31—28no—
243C4⋊C4×C31—28no—
244C22⋊C4×C31—216no—
245C22⋊C4×C31—28no—
246C22⋊C4×C31—28no—
247C22⋊C4×C31—28no—
248C22⋊C4×C31—48no—
249C22⋊C4×C31—48no—
250C22⋊C4×C31—48no—
251C22⋊C4×C31—48no—
252C22⋊C4×C31—48no—
253#16250C3111yesmaximal, characteristic, direct product factor, Sylow
254C23×C31—22no—
255C23×C31—22no—
256C23×C31—22no—
257C23×C31—24no—
258C23×C31—24no—
259C23×C31—22no—
260C23×C31—22no—
261C23×C31—22no—
262C23×C31—24no—
263C23×C31—24no—
264C23×C31—24no—
265C23×C31—24no—
266C23×C31—22no—
267C23×C31—24no—
268C23×C31—24no—
269C23×C31—24no—
270C23×C31—22no—
271C23×C31—22no—
272C23×C31—24no—
273C23×C31—24no—
274C23×C31—24no—
275C23×C31—24no—
276C23×C31—24no—
277C23×C31—24no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—42no—
283C23×C31—42no—
284C23×C31—42no—
285C23×C31—42no—
286C23×C31—42no—
287C23×C31—42no—
288C23×C31—41no—
289C23×C31—42no—
290C23×C31—42no—
291C23×C31—41no—
292C23×C31—42no—
293C23×C31—42no—
294C23×C31—42no—
295C23×C31—42no—
296C23×C31—41no—
297C23×C31—42no—
298C23×C31—42no—
299C23×C31—42no—
300C23×C31—42no—
301C23×C31—42no—
302C23×C31—41no—
303C23×C31—41no—
304C23×C31—41no—
305C23×C31—41no—
306C23×C31—41no—
307C23×C31—42no—
308C23×C31—42no—
309C23×C31—42no—
310C23×C31—42no—
311C23×C31—42no—
312C23×C31—42no—
313C23×C31—42no—
314C23×C31—42no—
315C23×C31—42no—
316C23×C31—42no—
317C23×C31—42no—
318C23×C31—42no—
319C23×C31—42no—
320C23×C31—42no—
321C23×C31—42no—
322C23×C31—42no—
323C23×C31—42no—
324C23×C31—42no—
325C23×C31—42no—
326C23×C31—42no—
327C23×C31—42no—
328C23×C31—42no—
329C23×C31—42no—
330C23×C31—42no—
331C23×C31—42no—
332C23×C31—42no—
333C23×C31—42no—
334C23×C31#12014yes—
335C23×C31C22×D411yescharacteristic
336C23×C31C22×D412yes—
337C23×C31C22×D411yescharacteristic
338C23×C31C22×D411yescharacteristic
339C23×C31C2×#4112yes—
340C23×C31H(5,𝔽2)11yescharacteristic
341C23×C31H(5,𝔽2)11yescharacteristic
342C23×C31H(5,𝔽2)12yes—
343C23×C31H(5,𝔽2)12yes—
344C23×C31H(5,𝔽2)11yescharacteristic
345C23×C312−1+411yescharacteristic
346D4×C31—416no—
347D4×C31—432no—
348D4×C31—416no—
349D4×C31—432no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—24no—
353C2×C4×C31—24no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—22no—
357C2×C4×C31—22no—
358C2×C4×C31—24no—
359C2×C4×C31—22no—
360C2×C4×C31—24no—
361C2×C4×C31—22no—
362C2×C4×C31—24no—
363C2×C4×C31—22no—
364C2×C4×C31—22no—
365C2×C4×C31—24no—
366C2×C4×C31—24no—
367C2×C4×C31—24no—
368C2×C4×C31—24no—
369C2×C4×C31—24no—
370C2×C4×C31—416no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—42no—
374C2×C4×C31—42no—
375C2×C4×C31—41no—
376C2×C4×C31—42no—
377C2×C4×C31—41no—
378C2×C4×C31—41no—
379C2×C4×C31—41no—
380C2×C4×C31—42no—
381C2×C4×C31—42no—
382C2×C4×C31—42no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—42no—
386C2×C4×C31—42no—
387C2×C4×C31—42no—
388C2×C4×C31—42no—
389C2×C4×C31—42no—
390C2×C4×C31—42no—
391C2×C4×C31—42no—
392C2×C4×C31—42no—
393C2×C4×C31—42no—
394C2×C4×C31—42no—
395C2×C4×C31—42no—
396C2×C4×C31—42no—
397C2×C4×C31—42no—
398C2×C4×C31#12014yes—
399C22×#123C2×C3111yescharacteristic, complemented
400C22×#121C2×C3111yescharacteristic, complemented
401C2×#394C2×C3111yescharacteristic, complemented
402C2×#392C2×C3112yescomplemented
403C2×#392C2×C3111yescharacteristic, complemented
404#1441C2×C3111yescharacteristic, complemented
405#1439C2×C3112yescomplemented
406#1439C2×C3111yescharacteristic, complemented
407#1438C2×C3112yescomplemented
408#1438C2×C3112yescomplemented
409C22⋊#95C2×C3111yescharacteristic, complemented
410C22×C31—24no—
411C22×C31—24no—
412C22×C31—24no—
413C22×C31—42no—
414C22×C31—42no—
415C22×C31—44no—
416C22×C31—44no—
417C22×C31—44no—
418C22×C31—44no—
419C22×C31—42no—
420C22×C31—42no—
421C22×C31—44no—
422C22×C31—42no—
423C22×C31—44no—
424C22×C31—42no—
425C22×C31—44no—
426C22×C31—44no—
427C22×C31—44no—
428C22×C31—44no—
429C22×C31—44no—
430C22×C31—44no—
431C22×C31—44no—
432C22×C31—42no—
433C22×C31—81no—
434C22×C31—82no—
435C22×C31—82no—
436C22×C31—81no—
437C22×C31—82no—
438C22×C31—82no—
439C22×C31—82no—
440C22×C31—82no—
441C22×C31—82no—
442C22×C31—82no—
443C22×C31—81no—
444C22×C31—82no—
445C22×C31—82no—
446C22×C31—81no—
447C22×C31C2×#12011yescharacteristic
448C22×C31C2×#12011yescharacteristic
449C22×C31#53211yescharacteristic
450C22×C31#53412yes—
451C22×C31#53412yes—
452C22×C31#53411yescharacteristic
453C22×C31#53511yescharacteristic
454C22×C31#53511yescharacteristic
455C22×C31#53511yescharacteristic
456C22×C31#53511yescharacteristic
457C22×C31#53711yescharacteristic
458C22×C31#53711yescharacteristic
459C22×C31#53711yescharacteristic
460C22×C31#53812yes—
461C22×C31#54012yes—
462C22×C31D4212yes—
463C22×C31D4212yes—
464C22×C31#54612yes—
465C22×C31#54612yes—
466C22×C31#54712yes—
467C22×C31#55012yes—
468C22×C31#56012yes—
469C22×C31#56212yes—
470C4×C31—24no—
471C4×C31—44no—
472C4×C31—42no—
473C4×C31—42no—
474C4×C31—42no—
475C4×C31—44no—
476C4×C31—42no—
477C4×C31—82no—
478C23×D4C22×C3111yescharacteristic
479C23×D4C22×C3111yescharacteristic
480C23×D4C22×C3112yes—
481C23×D4C22×C3112yes—
482C24×C4C22×C3111yescharacteristic
483C2×#123—24no—
484C2×#123—24no—
485C2×#123—24no—
486C2×#121—28no—
487C2×#121—24no—
488C22×C4⋊C4C22×C3111yescharacteristic
489C22×C4⋊C4C22×C3111yescharacteristic
490C22×C4⋊C4C22×C3111yescharacteristic
491C22×C22⋊C4C22×C3112yes—
492C22×C22⋊C4C22×C3111yescharacteristic
493C22×C22⋊C4C22×C3111yescharacteristic
494C22×C22⋊C4C22×C3112yes—
495C22×C22⋊C4C22×C3112yes—
496C22×C22⋊C4C22×C3112yes—
497C22×C22⋊C4C22×C3111yescharacteristic
498C22×C22⋊C4C22×C3112yes—
499C22×C22⋊C4C22×C3112yes—
500#394—24no—
501#392—28no—
502#392—24no—
503C2×#95C22×C3111yescharacteristic
504C2×#95C22×C3112yes—
505C2×#95C22×C3111yescharacteristic
506C2×#95C22×C3112yes—
507C2×#95C22×C3112yes—
508C2×#95C22×C3112yes—
509C2×C31—44no—
510C2×C31—84no—
511C2×C31—82no—
512C2×C31#240311yescharacteristic
513C2×C31#243011yescharacteristic
514C2×C31#243111yescharacteristic
515C2×C31#261311yescharacteristic
516C2×C31#261511yescharacteristic
517C2×C31#266111yescharacteristic
518C2×C31#267112yes—
519C2×C31#267312yes—
520C2×C31#267812yes—
521C2×C31#268212yes—
522C2×C31#281311yescharacteristic
523C25C23×C3111yescharacteristic
524C25C23×C3112yes—
525C25C23×C3111yescharacteristic
526C22×D4—24no—
527C22×D4—24no—
528C22×D4—24no—
529C22×D4—22no—
530C22×D4—22no—
531C22×D4—24no—
532C22×D4—24no—
533C22×D4—24no—
534C22×D4—22no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—24no—
539C22×D4—42no—
540C22×D4—42no—
541C22×D4—42no—
542C22×D4—42no—
543C22×D4—42no—
544C22×D4—42no—
545C22×D4—42no—
546C22×D4—42no—
547C22×D4—42no—
548C22×D4—42no—
549C22×D4D4×C3118yescomplemented
550C23×C4—24no—
551C23×C4—22no—
552C23×C4—22no—
553C23×C4—42no—
554C23×C4D4×C3114yescomplemented
555C23×C4C23×C3112yes—
556C23×C4C23×C3111yescharacteristic
557C23×C4C23×C3111yescharacteristic
558C23×C4C23×C3111yescharacteristic
559C23×C4C23×C3111yescharacteristic
560C23×C4C23×C3112yes—
561C23×C4C23×C3112yes—
562C23×C4C23×C3111yescharacteristic
563#123—232no—
564#121—232no—
565C2×C4⋊C4—24no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4D4×C3114yescomplemented
573C2×C22⋊C4—24no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—24no—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—24no—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4—42no—
597C2×C22⋊C4—42no—
598C2×C22⋊C4—42no—
599C2×C22⋊C4D4×C3114yescomplemented
600#95—24no—
601#95—22no—
602#95—22no—
603#95—42no—
604#95—42no—
605#95—42no—
606C31#1625011yescharacteristic, direct product factor, Sylow
607C24—21no—
608C24—21no—
609C24—22no—
610C24—21no—
611C24—22no—
612C24—21no—
613C24—21no—
614C24—22no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—21no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—21no—
635C24—21no—
636C24—22no—
637C24—22no—
638C24—21no—
639C24—22no—
640C24C2×D4×C3114yes—
641C24C2×D4×C3112yes—
642C24C2×D4×C3114yes—
643C24C2×D4×C3112yes—
644C24C24×C3111yescharacteristic
645C2×D4—28no—
646C2×D4—28no—
647C2×D4—216no—
648C2×D4—48no—
649C2×D4—48no—
650C2×D4—48no—
651C2×D4—48no—
652C2×D4—48no—
653C2×D4—48no—
654C2×D4—48no—
655C2×D4—44no—
656C2×D4—48no—
657C2×D4—48no—
658C2×D4—48no—
659C2×D4—44no—
660C2×D4—48no—
661C2×D4—48no—
662C2×D4—48no—
663C2×D4—48no—
664C2×D4—48no—
665C2×D4—48no—
666C2×D4—48no—
667C2×D4—44no—
668C2×D4—44no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—28no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—21no—
702C22×C4—28no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—44no—
711C22×C4—48no—
712C22×C4—48no—
713C22×C4C2×D4×C3114yes—
714C22×C4C2×D4×C3112yes—
715C22×C4C2×D4×C3112yes—
716C22×C4C2×D4×C3112yes—
717C22×C4C2×D4×C3112yes—
718C22×C4C2×D4×C3112yes—
719C22×C4C2×D4×C3112yes—
720C22×C4C2×D4×C3112yes—
721C22×C4#41×C3114yes—
722C4⋊C4—28no—
723C4⋊C4—28no—
724C4⋊C4—28no—
725C22⋊C4—216no—
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—28no—
729C22⋊C4—48no—
730C22⋊C4—48no—
731C22⋊C4—48no—
732C22⋊C4—48no—
733C22⋊C4—48no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—24no—
738C23—24no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—22no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—22no—
751C23—22no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—41no—
769C23—42no—
770C23—42no—
771C23—41no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—41no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23C31×#12014yes—
815C23C22×D4×C3111yescharacteristic
816C23C22×D4×C3112yes—
817C23C22×D4×C3111yescharacteristic
818C23C22×D4×C3111yescharacteristic
819C23C2×#41×C3112yes—
820C23C31×H(5,𝔽2)11yescharacteristic
821C23C31×H(5,𝔽2)11yescharacteristic
822C23C31×H(5,𝔽2)12yes—
823C23C31×H(5,𝔽2)12yes—
824C23C31×H(5,𝔽2)11yescharacteristic
825C23C31×2−1+411yescharacteristic
826D4—416no—
827D4—432no—
828D4—416no—
829D4—432no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—24no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—416no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4C31×#12014yes—
879C22—24no—
880C22—24no—
881C22—24no—
882C22—42no—
883C22—42no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—42no—
889C22—42no—
890C22—44no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—44no—
895C22—44no—
896C22—44no—
897C22—44no—
898C22—44no—
899C22—44no—
900C22—44no—
901C22—42no—
902C22—81no—
903C22—82no—
904C22—82no—
905C22—81no—
906C22—82no—
907C22—82no—
908C22—82no—
909C22—82no—
910C22—82no—
911C22—82no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—81no—
916C22C2×C31×#12011yescharacteristic
917C22C2×C31×#12011yescharacteristic
918C22C31×#53211yescharacteristic
919C22C31×#53412yes—
920C22C31×#53412yes—
921C22C31×#53411yescharacteristic
922C22C31×#53511yescharacteristic
923C22C31×#53511yescharacteristic
924C22C31×#53511yescharacteristic
925C22C31×#53511yescharacteristic
926C22C31×#53711yescharacteristic
927C22C31×#53711yescharacteristic
928C22C31×#53711yescharacteristic
929C22C31×#53812yes—
930C22C31×#54012yes—
931C22D42×C3112yes—
932C22D42×C3112yes—
933C22C31×#54612yes—
934C22C31×#54612yes—
935C22C31×#54712yes—
936C22C31×#55012yes—
937C22C31×#56012yes—
938C22C31×#56212yes—
939C4—24no—
940C4—44no—
941C4—42no—
942C4—42no—
943C4—42no—
944C4—44no—
945C4—42no—
946C4—82no—
947C2—44no—
948C2—84no—
949C2—82no—
950C2C31×#240311yescharacteristic
951C2C31×#243011yescharacteristic
952C2C31×#243111yescharacteristic
953C2C31×#261311yescharacteristic
954C2C31×#261511yescharacteristic
955C2C31×#266111yescharacteristic
956C2C31×#267112yes—
957C2C31×#267312yes—
958C2C31×#267812yes—
959C2C31×#268212yes—
960C2C31×#281311yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#123C2semidirect
2. C22×C31×#121C2semidirect
3. C2×C31×#394C2semidirect
4. C2×C31×#392C2semidirect
5. C2×C31×#392C2semidirect
6. C31×#1441C2semidirect
7. C31×#1439C2semidirect
8. C31×#1439C2semidirect
9. C31×#1438C2semidirect
10. C31×#1438C2semidirect
11. C31×C22⋊#95C2semidirect
69. C22×D4×C31D4semidirect
74. C23×C4×C31D4semidirect
92. C2×C4⋊C4×C31D4semidirect
119. C2×C22⋊C4×C31D4semidirect
253. #16250C31direct (N × H)
399. C22×#123C2×C31semidirect
400. C22×#121C2×C31semidirect
401. C2×#394C2×C31semidirect
402. C2×#392C2×C31semidirect
403. C2×#392C2×C31semidirect
404. #1441C2×C31semidirect
405. #1439C2×C31semidirect
406. #1439C2×C31semidirect
407. #1438C2×C31semidirect
408. #1438C2×C31semidirect
409. C22⋊#95C2×C31semidirect
549. C22×D4D4×C31semidirect
554. C23×C4D4×C31semidirect
572. C2×C4⋊C4D4×C31semidirect
599. C2×C22⋊C4D4×C31semidirect
606. C31#16250direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1232
C22×C31×#1212
C2×C31×#3942
C2×C31×#3922
C31×#14412
C31×#14392
C31×#14382
C31×C22⋊#952
#1625031