Finite Group Databasebeta

← C31×#24436 #21481195

Subgroups — C31×#24436 #21481195

Order 7936.

1582 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#546C211yesmaximal, characteristic
2C2×C31×#465C211yesmaximal, characteristic, complemented
3C2×C31×#452C211yesmaximal, characteristic, complemented
4C2×C31×#450C211yesmaximal, characteristic, complemented
5C2×C31×#416C211yesmaximal, characteristic, complemented
6C31×#2415C211yesmaximal, characteristic, complemented
7C31×#2042C211yesmaximal, characteristic, complemented
8C31×#2035C211yesmaximal, characteristic, complemented
9C31×#2015C211yesmaximal, characteristic, complemented
10C31×#2001C211yesmaximal, characteristic, complemented
11C31×#1877C211yesmaximal, characteristic, complemented
12C31×#1875C211yesmaximal, characteristic, complemented
13C31×#1869C211yesmaximal, characteristic, complemented
14C31×#1864C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C22×Q16×C31C2211yescharacteristic, complemented
19C22×SD16×C31C2211yescharacteristic
20C22×SD16×C31C2211yescharacteristic
21C23×C8×C31C2211yescharacteristic, complemented
22C31×#546—24no—
23C31×#546—24no—
24C2×C31×#124C2211yescharacteristic
25C2×C31×#123—21no—
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C31×C22⋊Q8C2211yescharacteristic
28C2×C31×C22⋊Q8C2211yescharacteristic, complemented
29C2×C31×#121—21no—
30C2×C31×#121C2211yescharacteristic
31C2×C31×#120—21no—
32C2×C4×D4×C31C2211yescharacteristic
33C2×C4×D4×C31C2211yescharacteristic
34C2×C31×#117C2211yescharacteristic, complemented
35C22×C22⋊C4×C31—21no—
36C31×#465—24no—
37C31×#452—24no—
38C31×#450—24no—
39C2×C31×#106C2211yescharacteristic, complemented
40C31×#416—24no—
41C2×C31×#103C2211yescharacteristic, complemented
42C2×C31×#103C2211yescharacteristic, complemented
43C2×C31×#103C2211yescharacteristic, complemented
44C2×C31×#103C2211yescharacteristic, complemented
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×#102C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C2×C31×#102C2211yescharacteristic
50C2×C31×#102C2211yescharacteristic
51C2×C31×C22⋊C8C2211yescharacteristic
52C2×C31×C22⋊C8C2211yescharacteristic
53C2×C31×C22⋊C8C2211yescharacteristic, complemented
54C31×#397—21no—
55C31×#394—21no—
56C31×#391C2211yescharacteristic, complemented
57C31×#389—21no—
58C31×#389C2211yescharacteristic, complemented
59C31×#388—21no—
60C31×#380C2211yescharacteristic
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C31×#336C2211yescharacteristic, complemented
64C31×#336C2211yescharacteristic, complemented
65C25×C31—21no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—41no—
70C2×#41×C31—41no—
71C2×#41×C31D414yes—
72C22×Q8×C31C2311yescharacteristic
73C22×Q8×C31C2311yescharacteristic
74C22×D4×C31—21no—
75C22×D4×C31—21no—
76C22×D4×C31—22no—
77C22×D4×C31—22no—
78C22×D4×C31—22no—
79C22×D4×C31—22no—
80C22×D4×C31—21no—
81C22×D4×C31—41no—
82C22×D4×C31—41no—
83C22×D4×C31D411yescharacteristic
84C22×D4×C31C2311yescharacteristic
85C22×D4×C31C2311yescharacteristic
86C23×C4×C31—21no—
87C23×C4×C31—21no—
88C23×C4×C31C2311yescharacteristic
89C23×C4×C31C2311yescharacteristic
90C2×Q16×C31—22no—
91C2×Q16×C31—41no—
92C2×Q16×C31—41no—
93C2×SD16×C31—22no—
94C2×SD16×C31—22no—
95C2×SD16×C31—22no—
96C2×SD16×C31—22no—
97C2×SD16×C31—22no—
98C2×SD16×C31—41no—
99C22×C8×C31—22no—
100C22×C8×C31—22no—
101C22×C8×C31—41no—
102C22×C8×C31C2311yescharacteristic
103C22×C8×C31C2311yescharacteristic
104C22×C8×C31C2311yescharacteristic
105C22×C8×C31C2311yescharacteristic
106C31×#124—22no—
107C31×#124—22no—
108C31×#123—28no—
109C31×C22⋊Q8—22no—
110C31×C22⋊Q8—22no—
111C31×C22⋊Q8—22no—
112C31×C22⋊Q8—22no—
113C31×C22⋊Q8—22no—
114C31×C22⋊Q8—41no—
115C31×#121—28no—
116C31×#121—22no—
117C31×#121D414yes—
118C31×#120—28no—
119C4×D4×C31—22no—
120C4×D4×C31—22no—
121C4×D4×C31—22no—
122C4×D4×C31—22no—
123C31×#117—22no—
124C31×#117—41no—
125C2×C4⋊C4×C31—21no—
126C2×C4⋊C4×C31—21no—
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31—21no—
129C2×C4⋊C4×C31D411yescharacteristic
130C2×C4⋊C4×C31C2311yescharacteristic
131C2×C4⋊C4×C31C2311yescharacteristic
132C2×C4⋊C4×C31C2311yescharacteristic
133C2×C4⋊C4×C31C2311yescharacteristic
134C2×C22⋊C4×C31—28no—
135C2×C22⋊C4×C31—21no—
136C2×C22⋊C4×C31—21no—
137C2×C22⋊C4×C31—21no—
138C2×C22⋊C4×C31—21no—
139C2×C22⋊C4×C31—21no—
140C2×C22⋊C4×C31—21no—
141C2×C22⋊C4×C31—21no—
142C2×C22⋊C4×C31—21no—
143C2×C22⋊C4×C31—21no—
144C2×C22⋊C4×C31D411yescharacteristic
145C2×C22⋊C4×C31D411yescharacteristic
146C2×C42×C31—21no—
147C2×C42×C31C2311yescharacteristic
148C31×#106—22no—
149C31×#103—22no—
150C31×#103—22no—
151C31×#103—22no—
152C31×#103—22no—
153C31×#102—22no—
154C31×#102—22no—
155C31×#102—22no—
156C31×#102—22no—
157C31×#102—41no—
158C31×#102D414yescomplemented
159C31×C22⋊C8—22no—
160C31×C22⋊C8—22no—
161C31×C22⋊C8—41no—
162C31×#95—21no—
163C31×#95—21no—
164C31×#95—21no—
165C31×#95—21no—
166C24×C31—21no—
167C24×C31—24no—
168C24×C31—21no—
169C24×C31—42no—
170C24×C31—42no—
171C24×C31—42no—
172C24×C31—42no—
173C24×C31—81no—
174C24×C31—81no—
175C24×C31C2×D411yescharacteristic
176C24×C31C2×D411yescharacteristic
177#41×C31—28no—
178#41×C31—44no—
179#41×C31—44no—
180#41×C31—44no—
181C2×Q8×C31—21no—
182C2×Q8×C31—21no—
183C2×Q8×C31—21no—
184C2×Q8×C31—21no—
185C2×Q8×C31—21no—
186C2×Q8×C31—21no—
187C2×Q8×C31—21no—
188C2×Q8×C31—21no—
189C2×Q8×C31—21no—
190C2×Q8×C31—21no—
191C2×Q8×C31—21no—
192C2×Q8×C31C2×D412yes—
193C2×D4×C31—24no—
194C2×D4×C31—22no—
195C2×D4×C31—24no—
196C2×D4×C31—22no—
197C2×D4×C31—24no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—41no—
207C2×D4×C31—42no—
208C2×D4×C31—42no—
209C2×D4×C31—44no—
210C2×D4×C31—44no—
211C2×D4×C31—44no—
212C2×D4×C31—42no—
213C2×D4×C31—42no—
214C2×D4×C31—44no—
215C2×D4×C31—81no—
216C2×D4×C31—81no—
217C2×D4×C31C2×D412yes—
218C2×D4×C31C2×D412yes—
219C2×D4×C31C2×D412yes—
220C2×D4×C31#4112yes—
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—24no—
229C22×C4×C31—24no—
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—42no—
240C22×C4×C31—42no—
241C22×C4×C31—81no—
242C22×C4×C31—81no—
243C22×C4×C31C2×D411yescharacteristic
244C22×C4×C31C2×D411yescharacteristic
245C22×C4×C31C2×D411yescharacteristic
246C22×C4×C31C2×D411yescharacteristic
247C22×C4×C31C2×D412yes—
248C22×C4×C31C2×D412yes—
249C22×C4×C31C2411yescharacteristic
250Q16×C31—44no—
251SD16×C31—44no—
252SD16×C31—44no—
253C2×C8×C31—21no—
254C2×C8×C31—21no—
255C2×C8×C31—21no—
256C2×C8×C31—21no—
257C2×C8×C31—21no—
258C2×C8×C31—21no—
259C2×C8×C31—21no—
260C2×C8×C31—21no—
261C2×C8×C31—21no—
262C2×C8×C31—21no—
263C2×C8×C31—21no—
264C2×C8×C31—44no—
265C2×C8×C31C2×D412yes—
266C4⋊C4×C31—24no—
267C4⋊C4×C31—22no—
268C4⋊C4×C31—21no—
269C4⋊C4×C31—21no—
270C4⋊C4×C31—21no—
271C4⋊C4×C31—21no—
272C4⋊C4×C31—21no—
273C4⋊C4×C31—21no—
274C4⋊C4×C31—42no—
275C4⋊C4×C31—42no—
276C4⋊C4×C31—42no—
277C4⋊C4×C31C2×D412yes—
278C4⋊C4×C31C2×D412yes—
279C22⋊C4×C31—24no—
280C22⋊C4×C31—24no—
281C22⋊C4×C31—24no—
282C22⋊C4×C31—24no—
283C22⋊C4×C31—22no—
284C22⋊C4×C31—22no—
285C22⋊C4×C31—24no—
286C22⋊C4×C31—42no—
287C22⋊C4×C31—42no—
288C22⋊C4×C31—42no—
289C22⋊C4×C31—42no—
290C42×C31—21no—
291C42×C31—21no—
292C42×C31—42no—
293#24436C3111yesmaximal, characteristic, direct product factor, Sylow
294C23×C31—21no—
295C23×C31—22no—
296C23×C31—21no—
297C23×C31—21no—
298C23×C31—22no—
299C23×C31—21no—
300C23×C31—21no—
301C23×C31—22no—
302C23×C31—21no—
303C23×C31—21no—
304C23×C31—21no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—21no—
308C23×C31—21no—
309C23×C31—22no—
310C23×C31—48no—
311C23×C31—48no—
312C23×C31—41no—
313C23×C31—41no—
314C23×C31—41no—
315C23×C31—41no—
316C23×C31—41no—
317C23×C31—41no—
318C23×C31—41no—
319C23×C31—41no—
320C23×C31—41no—
321C23×C31—41no—
322C23×C31—84no—
323C23×C31—84no—
324C23×C31—84no—
325C23×C31—84no—
326C23×C31—84no—
327C23×C31#12012yes—
328C23×C31#13512yes—
329C23×C31C22×D411yescharacteristic
330Q8×C31—22no—
331Q8×C31—22no—
332Q8×C31—41no—
333Q8×C31—41no—
334Q8×C31—41no—
335Q8×C31—41no—
336Q8×C31—41no—
337Q8×C31—41no—
338D4×C31—22no—
339D4×C31—22no—
340D4×C31—22no—
341D4×C31—22no—
342D4×C31—22no—
343D4×C31—44no—
344D4×C31—48no—
345D4×C31—48no—
346D4×C31—41no—
347D4×C31—41no—
348D4×C31—84no—
349D4×C31#12114yes—
350C2×C4×C31—21no—
351C2×C4×C31—21no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—21no—
357C2×C4×C31—21no—
358C2×C4×C31—22no—
359C2×C4×C31—22no—
360C2×C4×C31—21no—
361C2×C4×C31—22no—
362C2×C4×C31—21no—
363C2×C4×C31—21no—
364C2×C4×C31—21no—
365C2×C4×C31—21no—
366C2×C4×C31—21no—
367C2×C4×C31—21no—
368C2×C4×C31—48no—
369C2×C4×C31—41no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—41no—
374C2×C4×C31—41no—
375C2×C4×C31—41no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—41no—
379C2×C4×C31—41no—
380C2×C4×C31—41no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—84no—
389C2×C4×C31#12012yes—
390C2×C4×C31C22×D411yescharacteristic
391C2×C4×C31C22×D411yescharacteristic
392C2×C4×C31C22×D411yescharacteristic
393C2×C4×C31C2×#4111yescharacteristic
394C2×C4×C31H(5,𝔽2)11yescharacteristic
395C2×C4×C31H(5,𝔽2)11yescharacteristic
396C8×C31—22no—
397C8×C31—41no—
398C8×C31—41no—
399C8×C31—41no—
400C2×#546C2×C3111yescharacteristic
401C2×#465C2×C3111yescharacteristic, complemented
402C2×#452C2×C3111yescharacteristic, complemented
403C2×#450C2×C3111yescharacteristic, complemented
404C2×#416C2×C3111yescharacteristic, complemented
405#2415C2×C3111yescharacteristic, complemented
406#2042C2×C3111yescharacteristic, complemented
407#2035C2×C3111yescharacteristic, complemented
408#2015C2×C3111yescharacteristic, complemented
409#2001C2×C3111yescharacteristic, complemented
410#1877C2×C3111yescharacteristic, complemented
411#1875C2×C3111yescharacteristic, complemented
412#1869C2×C3111yescharacteristic, complemented
413#1864C2×C3111yescharacteristic, complemented
414#1786C2×C3111yescharacteristic, complemented
415C22×C31—22no—
416C22×C31—24no—
417C22×C31—22no—
418C22×C31—22no—
419C22×C31—22no—
420C22×C31—22no—
421C22×C31—22no—
422C22×C31—41no—
423C22×C31—42no—
424C22×C31—42no—
425C22×C31—41no—
426C22×C31—41no—
427C22×C31—41no—
428C22×C31—42no—
429C22×C31—41no—
430C22×C31—42no—
431C22×C31—41no—
432C22×C31—42no—
433C22×C31—41no—
434C22×C31—41no—
435C22×C31—42no—
436C22×C31—42no—
437C22×C31—42no—
438C22×C31—42no—
439C22×C31—816no—
440C22×C31—81no—
441C22×C31—81no—
442C22×C31—81no—
443C22×C31—81no—
444C22×C31C2×#12011yescharacteristic
445C22×C31D4211yescharacteristic
446C22×C31#54611yescharacteristic
447C22×C31C2×#13511yescharacteristic
448C22×C31#57511yescharacteristic
449C22×C31#57711yescharacteristic
450C22×C31#57711yescharacteristic
451C4×C31—22no—
452C4×C31—41no—
453C4×C31—42no—
454C4×C31—41no—
455C4×C31—41no—
456C4×C31—42no—
457C4×C31—42no—
458C4×C31—81no—
459C4×C31—81no—
460C4×C31—81no—
461C4×C31C2×#12111yescharacteristic
462C4×C31#53411yescharacteristic
463C4×C31D4211yescharacteristic
464C4×C31#54611yescharacteristic
465C22×#41C22×C3111yescharacteristic
466C23×D4C22×C3111yescharacteristic
467C22×Q16C22×C3111yescharacteristic, complemented
468C22×SD16C22×C3111yescharacteristic
469C22×SD16C22×C3111yescharacteristic
470C23×C8C22×C3111yescharacteristic, complemented
471#546—24no—
472#546—24no—
473C2×#124C22×C3111yescharacteristic
474C2×#123—21no—
475C2×C22⋊Q8C22×C3111yescharacteristic
476C2×C22⋊Q8C22×C3111yescharacteristic
477C2×C22⋊Q8C22×C3111yescharacteristic, complemented
478C2×#121—21no—
479C2×#121C22×C3111yescharacteristic
480C2×#120—21no—
481C2×C4×D4C22×C3111yescharacteristic
482C2×C4×D4C22×C3111yescharacteristic
483C2×#117C22×C3111yescharacteristic, complemented
484C22×C22⋊C4—21no—
485#465—24no—
486#452—24no—
487#450—24no—
488C2×#106C22×C3111yescharacteristic, complemented
489#416—24no—
490C2×#103C22×C3111yescharacteristic, complemented
491C2×#103C22×C3111yescharacteristic, complemented
492C2×#103C22×C3111yescharacteristic, complemented
493C2×#103C22×C3111yescharacteristic, complemented
494C2×#102C22×C3111yescharacteristic
495C2×#102C22×C3111yescharacteristic
496C2×#102C22×C3111yescharacteristic
497C2×#102C22×C3111yescharacteristic
498C2×#102C22×C3111yescharacteristic
499C2×#102C22×C3111yescharacteristic
500C2×C22⋊C8C22×C3111yescharacteristic
501C2×C22⋊C8C22×C3111yescharacteristic
502C2×C22⋊C8C22×C3111yescharacteristic, complemented
503#397—21no—
504#394—21no—
505#391C22×C3111yescharacteristic, complemented
506#389—21no—
507#389C22×C3111yescharacteristic, complemented
508#388—21no—
509#380C22×C3111yescharacteristic
510#340C22×C3111yescharacteristic, complemented
511#340C22×C3111yescharacteristic, complemented
512#336C22×C3111yescharacteristic, complemented
513#336C22×C3111yescharacteristic, complemented
514C2×C31—42no—
515C2×C31—42no—
516C2×C31—44no—
517C2×C31—82no—
518C2×C31#241011yescharacteristic
519C2×C31#300211yescharacteristic
520C2×C31#300911yescharacteristic
521C2×C31#326711yescharacteristic
522C2×C31#328211yescharacteristic
523C2×C31#329611yescharacteristic
524C2×C31#331111yescharacteristic
525C25—21no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—41no—
530C2×#41—41no—
531C2×#41D4×C3114yes—
532C22×Q8C23×C3111yescharacteristic
533C22×Q8C23×C3111yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—41no—
542C22×D4—41no—
543C22×D4D4×C3111yescharacteristic
544C22×D4C23×C3111yescharacteristic
545C22×D4C23×C3111yescharacteristic
546C23×C4—21no—
547C23×C4—21no—
548C23×C4C23×C3111yescharacteristic
549C23×C4C23×C3111yescharacteristic
550C2×Q16—22no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—41no—
559C22×C8—22no—
560C22×C8—22no—
561C22×C8—41no—
562C22×C8C23×C3111yescharacteristic
563C22×C8C23×C3111yescharacteristic
564C22×C8C23×C3111yescharacteristic
565C22×C8C23×C3111yescharacteristic
566#124—22no—
567#124—22no—
568#123—28no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—41no—
575#121—28no—
576#121—22no—
577#121D4×C3114yes—
578#120—28no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583#117—22no—
584#117—41no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4D4×C3111yescharacteristic
590C2×C4⋊C4C23×C3111yescharacteristic
591C2×C4⋊C4C23×C3111yescharacteristic
592C2×C4⋊C4C23×C3111yescharacteristic
593C2×C4⋊C4C23×C3111yescharacteristic
594C2×C22⋊C4—28no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4D4×C3111yescharacteristic
605C2×C22⋊C4D4×C3111yescharacteristic
606C2×C42—21no—
607C2×C42C23×C3111yescharacteristic
608#106—22no—
609#103—22no—
610#103—22no—
611#103—22no—
612#103—22no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—41no—
618#102D4×C3114yescomplemented
619C22⋊C8—22no—
620C22⋊C8—22no—
621C22⋊C8—41no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626C31#2443611yescharacteristic, direct product factor, Sylow
627C24—21no—
628C24—24no—
629C24—21no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—42no—
634C24—81no—
635C24—81no—
636C24C2×D4×C3111yescharacteristic
637C24C2×D4×C3111yescharacteristic
638#41—28no—
639#41—44no—
640#41—44no—
641#41—44no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8C2×D4×C3112yes—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—44no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4C2×D4×C3112yes—
679C2×D4C2×D4×C3112yes—
680C2×D4C2×D4×C3112yes—
681C2×D4#41×C3112yes—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—81no—
703C22×C4—81no—
704C22×C4C2×D4×C3111yescharacteristic
705C22×C4C2×D4×C3111yescharacteristic
706C22×C4C2×D4×C3111yescharacteristic
707C22×C4C2×D4×C3111yescharacteristic
708C22×C4C2×D4×C3112yes—
709C22×C4C2×D4×C3112yes—
710C22×C4C24×C3111yescharacteristic
711Q16—44no—
712SD16—44no—
713SD16—44no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—44no—
726C2×C8C2×D4×C3112yes—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4C2×D4×C3112yes—
739C4⋊C4C2×D4×C3112yes—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—24no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C42—21no—
752C42—21no—
753C42—42no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—48no—
771C23—48no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—84no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23—84no—
787C23C31×#12012yes—
788C23C31×#13512yes—
789C23C22×D4×C3111yescharacteristic
790Q8—22no—
791Q8—22no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796Q8—41no—
797Q8—41no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—44no—
804D4—48no—
805D4—48no—
806D4—41no—
807D4—41no—
808D4—84no—
809D4C31×#12114yes—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—48no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—84no—
849C2×C4C31×#12012yes—
850C2×C4C22×D4×C3111yescharacteristic
851C2×C4C22×D4×C3111yescharacteristic
852C2×C4C22×D4×C3111yescharacteristic
853C2×C4C2×#41×C3111yescharacteristic
854C2×C4C31×H(5,𝔽2)11yescharacteristic
855C2×C4C31×H(5,𝔽2)11yescharacteristic
856C8—22no—
857C8—41no—
858C8—41no—
859C8—41no—
860C22—22no—
861C22—24no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—41no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—42no—
874C22—41no—
875C22—42no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—41no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—816no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22C2×C31×#12011yescharacteristic
890C22D42×C3111yescharacteristic
891C22C31×#54611yescharacteristic
892C22C2×C31×#13511yescharacteristic
893C22C31×#57511yescharacteristic
894C22C31×#57711yescharacteristic
895C22C31×#57711yescharacteristic
896C4—22no—
897C4—41no—
898C4—42no—
899C4—41no—
900C4—41no—
901C4—42no—
902C4—42no—
903C4—81no—
904C4—81no—
905C4—81no—
906C4C2×C31×#12111yescharacteristic
907C4C31×#53411yescharacteristic
908C4D42×C3111yescharacteristic
909C4C31×#54611yescharacteristic
910C2—42no—
911C2—42no—
912C2—44no—
913C2—82no—
914C2C31×#241011yescharacteristic
915C2C31×#300211yescharacteristic
916C2C31×#300911yescharacteristic
917C2C31×#326711yescharacteristic
918C2C31×#328211yescharacteristic
919C2C31×#329611yescharacteristic
920C2C31×#331111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#546C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#465C2semidirect
3. C2×C31×#452C2semidirect
4. C2×C31×#450C2semidirect
5. C2×C31×#416C2semidirect
6. C31×#2415C2semidirect
7. C31×#2042C2semidirect
8. C31×#2035C2semidirect
9. C31×#2015C2semidirect
10. C31×#2001C2semidirect
11. C31×#1877C2semidirect
12. C31×#1875C2semidirect
13. C31×#1869C2semidirect
14. C31×#1864C2semidirect
15. C31×#1786C2semidirect
18. C22×Q16×C31C22semidirect
21. C23×C8×C31C22semidirect
28. C2×C31×C22⋊Q8C22semidirect
34. C2×C31×#117C22semidirect
39. C2×C31×#106C22semidirect
41. C2×C31×#103C22semidirect
42. C2×C31×#103C22semidirect
43. C2×C31×#103C22semidirect
44. C2×C31×#103C22semidirect
53. C2×C31×C22⋊C8C22semidirect
56. C31×#391C22semidirect
58. C31×#389C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#336C22semidirect
64. C31×#336C22semidirect
158. C31×#102D4semidirect
293. #24436C31direct (N × H)
401. C2×#465C2×C31semidirect
402. C2×#452C2×C31semidirect
403. C2×#450C2×C31semidirect
404. C2×#416C2×C31semidirect
405. #2415C2×C31semidirect
406. #2042C2×C31semidirect
407. #2035C2×C31semidirect
408. #2015C2×C31semidirect
409. #2001C2×C31semidirect
410. #1877C2×C31semidirect
411. #1875C2×C31semidirect
412. #1869C2×C31semidirect
413. #1864C2×C31semidirect
414. #1786C2×C31semidirect
467. C22×Q16C22×C31semidirect
470. C23×C8C22×C31semidirect
477. C2×C22⋊Q8C22×C31semidirect
483. C2×#117C22×C31semidirect
488. C2×#106C22×C31semidirect
490. C2×#103C22×C31semidirect
491. C2×#103C22×C31semidirect
492. C2×#103C22×C31semidirect
493. C2×#103C22×C31semidirect
502. C2×C22⋊C8C22×C31semidirect
505. #391C22×C31semidirect
507. #389C22×C31semidirect
510. #340C22×C31semidirect
511. #340C22×C31semidirect
512. #336C22×C31semidirect
513. #336C22×C31semidirect
618. #102D4×C31semidirect
626. C31#24436direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5462
C2×C31×#4652
C2×C31×#4522
C2×C31×#4502
C2×C31×#4162
C31×#24152
C31×#20422
C31×#20352
C31×#20152
C31×#20012
C31×#18772
C31×#18752
C31×#18692
C31×#18642
C31×#17862
#2443631