Finite Group Databasebeta

← C31×#24389 #21481148

Subgroups — C31×#24389 #21481148

Order 7936.

1568 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#525C211yesmaximal, characteristic
2C2×C31×#470C211yesmaximal, characteristic, complemented
3C2×C31×#468C211yesmaximal, characteristic, complemented
4C2×C31×#452C211yesmaximal, characteristic, complemented
5C2×C31×#407C211yesmaximal, characteristic, complemented
6C31×#2848C211yesmaximal, characteristic, complemented
7C31×#2036C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic, complemented
9C31×#2001C211yesmaximal, characteristic, complemented
10C31×#2000C211yesmaximal, characteristic, complemented
11C31×#1895C211yesmaximal, characteristic, complemented
12C31×#1894C211yesmaximal, characteristic, complemented
13C31×#1873C211yesmaximal, characteristic, complemented
14C31×#1854C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C24×C4×C31C2211yescharacteristic
18C22×Q16×C31C2211yescharacteristic, complemented
19C22×SD16×C31C2211yescharacteristic, complemented
20C22×M16×C31C2211yescharacteristic
21C22×M16×C31C2211yescharacteristic
22C31×#525—24no—
23C31×#525—24no—
24C2×C31×#123—21no—
25C2×C31×C22⋊Q8C2211yescharacteristic
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C31×C22⋊Q8C2211yescharacteristic
28C2×C31×C22⋊Q8C2211yescharacteristic
29C2×C31×C22⋊Q8C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C31×#121C2211yescharacteristic
32C2×C31×#120—21no—
33C2×C4×D4×C31—21no—
34C2×C4×D4×C31—21no—
35C2×C31×#117C2211yescharacteristic
36C31×#470—24no—
37C31×#468—24no—
38C31×#452—24no—
39C2×C31×#107C2211yescharacteristic, complemented
40C2×C31×#106C2211yescharacteristic, complemented
41C2×C31×#103C2211yescharacteristic, complemented
42C2×C31×#103C2211yescharacteristic, complemented
43C2×C31×#103C2211yescharacteristic, complemented
44C2×C31×#103C2211yescharacteristic, complemented
45C2×C31×#103C2211yescharacteristic, complemented
46C2×C31×#102C2211yescharacteristic, complemented
47C2×C31×#102C2211yescharacteristic, complemented
48C2×C31×#102C2211yescharacteristic, complemented
49C31×#407—24no—
50C2×C31×C22⋊C8C2211yescharacteristic
51C2×C31×C22⋊C8C2211yescharacteristic
52C2×C31×C22⋊C8C2211yescharacteristic
53C2×C31×C22⋊C8C2211yescharacteristic
54C31×#385—21no—
55C31×#385—21no—
56C31×#385—21no—
57C31×#380C2211yescharacteristic
58C31×#380C2211yescharacteristic
59C31×#380C2211yescharacteristic
60C31×#379—21no—
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C31×#340C2211yescharacteristic, complemented
64C31×#340C2211yescharacteristic, complemented
65C25×C31D411yescharacteristic
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—41no—
71C2×#41×C31—41no—
72C22×Q8×C31C2311yescharacteristic
73C22×Q8×C31C2311yescharacteristic
74C22×D4×C31—21no—
75C22×D4×C31—21no—
76C22×D4×C31—21no—
77C22×D4×C31C2311yescharacteristic
78C23×C4×C31—22no—
79C23×C4×C31—21no—
80C23×C4×C31—22no—
81C23×C4×C31—22no—
82C23×C4×C31—22no—
83C23×C4×C31—41no—
84C23×C4×C31—41no—
85C23×C4×C31D411yescharacteristic
86C23×C4×C31D411yescharacteristic
87C23×C4×C31D411yescharacteristic
88C23×C4×C31C2311yescharacteristic
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C2×Q16×C31—22no—
92C2×Q16×C31—22no—
93C2×Q16×C31—41no—
94C2×SD16×C31—22no—
95C2×SD16×C31—22no—
96C2×SD16×C31—41no—
97C2×M16×C31—22no—
98C2×M16×C31—22no—
99C2×M16×C31—22no—
100C2×M16×C31—22no—
101C2×M16×C31—41no—
102C2×M16×C31—41no—
103C22×C8×C31C2311yescharacteristic
104C22×C8×C31C2311yescharacteristic
105C22×C8×C31C2311yescharacteristic
106C22×C8×C31C2311yescharacteristic
107C31×#123—28no—
108C31×C22⋊Q8—22no—
109C31×C22⋊Q8—22no—
110C31×C22⋊Q8—22no—
111C31×C22⋊Q8—22no—
112C31×C22⋊Q8—22no—
113C31×C22⋊Q8—22no—
114C31×C22⋊Q8—22no—
115C31×C22⋊Q8—41no—
116C31×C22⋊Q8—41no—
117C31×C22⋊Q8D414yes—
118C31×#121—22no—
119C31×#121—22no—
120C31×#121—22no—
121C31×#121D414yes—
122C31×#120—28no—
123C4×D4×C31—28no—
124C4×D4×C31—28no—
125C31×#117—22no—
126C31×#117—22no—
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31—21no—
129C2×C4⋊C4×C31—21no—
130C2×C4⋊C4×C31—21no—
131C2×C4⋊C4×C31—21no—
132C2×C4⋊C4×C31C2311yescharacteristic
133C2×C4⋊C4×C31C2311yescharacteristic
134C2×C4⋊C4×C31C2311yescharacteristic
135C2×C4⋊C4×C31C2311yescharacteristic
136C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
145C2×C22⋊C4×C31—21no—
146C2×C22⋊C4×C31—21no—
147C2×C22⋊C4×C31—21no—
148C2×C42×C31—21no—
149C31×#107—22no—
150C31×#106—22no—
151C31×#103—22no—
152C31×#103—22no—
153C31×#103—22no—
154C31×#103—22no—
155C31×#103—41no—
156C31×#102—22no—
157C31×#102—22no—
158C31×#102—41no—
159C31×C22⋊C8—22no—
160C31×C22⋊C8—22no—
161C31×C22⋊C8—22no—
162C31×C22⋊C8D414yescomplemented
163C31×#95—21no—
164C31×#95—21no—
165C31×#95—21no—
166C24×C31—22no—
167C24×C31—22no—
168C24×C31—22no—
169C24×C31—21no—
170C24×C31—41no—
171C24×C31—41no—
172C24×C31—41no—
173C24×C31—41no—
174C24×C31C2×D411yescharacteristic
175C24×C31C2×D411yescharacteristic
176C24×C31C2×D411yescharacteristic
177#41×C31—44no—
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—24no—
195C2×D4×C31—24no—
196C2×D4×C31—21no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—42no—
202C2×D4×C31—42no—
203C2×D4×C31—42no—
204C2×D4×C31—42no—
205C2×D4×C31—42no—
206C2×D4×C31—42no—
207C2×D4×C31C2×D412yes—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—24no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—22no—
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—21no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—41no—
237C22×C4×C31—41no—
238C22×C4×C31—41no—
239C22×C4×C31—44no—
240C22×C4×C31—44no—
241C22×C4×C31—44no—
242C22×C4×C31—44no—
243C22×C4×C31—42no—
244C22×C4×C31—42no—
245C22×C4×C31C2×D411yescharacteristic
246C22×C4×C31C2×D411yescharacteristic
247C22×C4×C31C2×D412yes—
248C22×C4×C31C2×D412yes—
249C22×C4×C31C2×D411yescharacteristic
250C22×C4×C31C2×D412yes—
251C22×C4×C31#4112yes—
252C22×C4×C31C2411yescharacteristic
253Q16×C31—44no—
254SD16×C31—44no—
255M16×C31—44no—
256M16×C31—44no—
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—21no—
265C2×C8×C31—21no—
266C2×C8×C31—21no—
267C2×C8×C31C2×D412yes—
268C2×C8×C31C2×D412yes—
269C4⋊C4×C31—24no—
270C4⋊C4×C31—24no—
271C4⋊C4×C31—21no—
272C4⋊C4×C31—21no—
273C4⋊C4×C31—21no—
274C4⋊C4×C31—21no—
275C4⋊C4×C31—21no—
276C4⋊C4×C31—21no—
277C4⋊C4×C31—21no—
278C4⋊C4×C31—21no—
279C4⋊C4×C31—42no—
280C4⋊C4×C31—42no—
281C4⋊C4×C31—42no—
282C4⋊C4×C31C2×D412yes—
283C4⋊C4×C31C2×D412yes—
284C22⋊C4×C31—24no—
285C22⋊C4×C31—24no—
286C22⋊C4×C31—24no—
287C22⋊C4×C31—24no—
288C22⋊C4×C31—24no—
289C22⋊C4×C31—42no—
290C22⋊C4×C31—42no—
291C22⋊C4×C31—42no—
292C22⋊C4×C31—42no—
293C22⋊C4×C31—42no—
294C22⋊C4×C31—42no—
295C42×C31—24no—
296#24389C3111yesmaximal, characteristic, direct product factor, Sylow
297C23×C31—21no—
298C23×C31—21no—
299C23×C31—21no—
300C23×C31—21no—
301C23×C31—21no—
302C23×C31—21no—
303C23×C31—21no—
304C23×C31—21no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—21no—
308C23×C31—21no—
309C23×C31—21no—
310C23×C31—21no—
311C23×C31—21no—
312C23×C31—21no—
313C23×C31—21no—
314C23×C31—21no—
315C23×C31—22no—
316C23×C31—44no—
317C23×C31—44no—
318C23×C31—44no—
319C23×C31—44no—
320C23×C31—44no—
321C23×C31—44no—
322C23×C31—44no—
323C23×C31—41no—
324C23×C31—41no—
325C23×C31—41no—
326C23×C31—41no—
327C23×C31—41no—
328C23×C31—41no—
329C23×C31#12012yes—
330C23×C31#12112yes—
331C23×C31#13712yes—
332C23×C31C22×D411yescharacteristic
333Q8×C31—22no—
334Q8×C31—22no—
335Q8×C31—41no—
336Q8×C31—41no—
337Q8×C31—41no—
338Q8×C31—41no—
339Q8×C31—41no—
340Q8×C31—41no—
341D4×C31—22no—
342D4×C31—22no—
343D4×C31—48no—
344D4×C31—48no—
345D4×C31—48no—
346D4×C31—41no—
347D4×C31—41no—
348C2×C4×C31—21no—
349C2×C4×C31—21no—
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—22no—
357C2×C4×C31—22no—
358C2×C4×C31—22no—
359C2×C4×C31—22no—
360C2×C4×C31—22no—
361C2×C4×C31—22no—
362C2×C4×C31—21no—
363C2×C4×C31—22no—
364C2×C4×C31—21no—
365C2×C4×C31—21no—
366C2×C4×C31—44no—
367C2×C4×C31—44no—
368C2×C4×C31—44no—
369C2×C4×C31—48no—
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—41no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—41no—
392C2×C4×C31#12012yes—
393C2×C4×C31#12112yes—
394C2×C4×C31C22×D411yescharacteristic
395C2×C4×C31C22×D411yescharacteristic
396C2×C4×C31C22×D411yescharacteristic
397C2×C4×C31C2×#4111yescharacteristic
398C2×C4×C31H(5,𝔽2)11yescharacteristic
399C2×C4×C31H(5,𝔽2)11yescharacteristic
400C8×C31—22no—
401C8×C31—22no—
402C8×C31—41no—
403C8×C31—41no—
404C2×#525C2×C3111yescharacteristic
405C2×#470C2×C3111yescharacteristic, complemented
406C2×#468C2×C3111yescharacteristic, complemented
407C2×#452C2×C3111yescharacteristic, complemented
408C2×#407C2×C3111yescharacteristic, complemented
409#2848C2×C3111yescharacteristic, complemented
410#2036C2×C3111yescharacteristic, complemented
411#2034C2×C3111yescharacteristic, complemented
412#2001C2×C3111yescharacteristic, complemented
413#2000C2×C3111yescharacteristic, complemented
414#1895C2×C3111yescharacteristic, complemented
415#1894C2×C3111yescharacteristic, complemented
416#1873C2×C3111yescharacteristic, complemented
417#1854C2×C3111yescharacteristic, complemented
418#1788C2×C3111yescharacteristic, complemented
419C22×C31—22no—
420C22×C31—22no—
421C22×C31—22no—
422C22×C31—22no—
423C22×C31—22no—
424C22×C31—22no—
425C22×C31—22no—
426C22×C31—22no—
427C22×C31—22no—
428C22×C31—416no—
429C22×C31—41no—
430C22×C31—41no—
431C22×C31—41no—
432C22×C31—41no—
433C22×C31—41no—
434C22×C31—41no—
435C22×C31—41no—
436C22×C31—41no—
437C22×C31—41no—
438C22×C31—41no—
439C22×C31—41no—
440C22×C31—41no—
441C22×C31—42no—
442C22×C31—42no—
443C22×C31—42no—
444C22×C31—81no—
445C22×C31—81no—
446C22×C31—81no—
447C22×C31—81no—
448C22×C31C2×#12011yescharacteristic
449C22×C31C2×#12111yescharacteristic
450C22×C31#53411yescharacteristic
451C22×C31C2×#13711yescharacteristic
452C22×C31#57511yescharacteristic
453C22×C31#57511yescharacteristic
454C22×C31#57511yescharacteristic
455C4×C31—22no—
456C4×C31—22no—
457C4×C31—41no—
458C4×C31—42no—
459C4×C31—42no—
460C4×C31—42no—
461C4×C31—81no—
462C4×C31—81no—
463C4×C31—81no—
464C4×C31—81no—
465C4×C31D4211yescharacteristic
466C4×C31D4211yescharacteristic
467C4×C31#54611yescharacteristic
468C4×C31#54611yescharacteristic
469C22×#41C22×C3111yescharacteristic
470C24×C4C22×C3111yescharacteristic
471C22×Q16C22×C3111yescharacteristic, complemented
472C22×SD16C22×C3111yescharacteristic, complemented
473C22×M16C22×C3111yescharacteristic
474C22×M16C22×C3111yescharacteristic
475#525—24no—
476#525—24no—
477C2×#123—21no—
478C2×C22⋊Q8C22×C3111yescharacteristic
479C2×C22⋊Q8C22×C3111yescharacteristic
480C2×C22⋊Q8C22×C3111yescharacteristic
481C2×C22⋊Q8C22×C3111yescharacteristic
482C2×C22⋊Q8C22×C3111yescharacteristic
483C2×#121C22×C3111yescharacteristic
484C2×#121C22×C3111yescharacteristic
485C2×#120—21no—
486C2×C4×D4—21no—
487C2×C4×D4—21no—
488C2×#117C22×C3111yescharacteristic
489#470—24no—
490#468—24no—
491#452—24no—
492C2×#107C22×C3111yescharacteristic, complemented
493C2×#106C22×C3111yescharacteristic, complemented
494C2×#103C22×C3111yescharacteristic, complemented
495C2×#103C22×C3111yescharacteristic, complemented
496C2×#103C22×C3111yescharacteristic, complemented
497C2×#103C22×C3111yescharacteristic, complemented
498C2×#103C22×C3111yescharacteristic, complemented
499C2×#102C22×C3111yescharacteristic, complemented
500C2×#102C22×C3111yescharacteristic, complemented
501C2×#102C22×C3111yescharacteristic, complemented
502#407—24no—
503C2×C22⋊C8C22×C3111yescharacteristic
504C2×C22⋊C8C22×C3111yescharacteristic
505C2×C22⋊C8C22×C3111yescharacteristic
506C2×C22⋊C8C22×C3111yescharacteristic
507#385—21no—
508#385—21no—
509#385—21no—
510#380C22×C3111yescharacteristic
511#380C22×C3111yescharacteristic
512#380C22×C3111yescharacteristic
513#379—21no—
514#340C22×C3111yescharacteristic, complemented
515#340C22×C3111yescharacteristic, complemented
516#340C22×C3111yescharacteristic, complemented
517#340C22×C3111yescharacteristic, complemented
518C2×C31—42no—
519C2×C31—42no—
520C2×C31—42no—
521C2×C31—82no—
522C2×C31#241011yescharacteristic
523C2×C31#300511yescharacteristic
524C2×C31#300711yescharacteristic
525C2×C31#305411yescharacteristic
526C2×C31#305611yescharacteristic
527C2×C31#319611yescharacteristic
528C2×C31#319711yescharacteristic
529C25D4×C3111yescharacteristic
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—41no—
535C2×#41—41no—
536C22×Q8C23×C3111yescharacteristic
537C22×Q8C23×C3111yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4C23×C3111yescharacteristic
542C23×C4—21no—
543C23×C4—22no—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—41no—
548C23×C4—41no—
549C23×C4D4×C3111yescharacteristic
550C23×C4D4×C3111yescharacteristic
551C23×C4D4×C3111yescharacteristic
552C23×C4C23×C3111yescharacteristic
553C23×C4C23×C3111yescharacteristic
554C23×C4C23×C3111yescharacteristic
555C2×Q16—22no—
556C2×Q16—22no—
557C2×Q16—41no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—41no—
561C2×M16—22no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—22no—
565C2×M16—41no—
566C2×M16—41no—
567C22×C8C23×C3111yescharacteristic
568C22×C8C23×C3111yescharacteristic
569C22×C8C23×C3111yescharacteristic
570C22×C8C23×C3111yescharacteristic
571#123—28no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8D4×C3114yes—
582#121—22no—
583#121—22no—
584#121—22no—
585#121D4×C3114yes—
586#120—28no—
587C4×D4—28no—
588C4×D4—28no—
589#117—22no—
590#117—22no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4C23×C3111yescharacteristic
597C2×C4⋊C4C23×C3111yescharacteristic
598C2×C4⋊C4C23×C3111yescharacteristic
599C2×C4⋊C4C23×C3111yescharacteristic
600C2×C4⋊C4C23×C3111yescharacteristic
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C42—21no—
613#107—22no—
614#106—22no—
615#103—22no—
616#103—22no—
617#103—22no—
618#103—22no—
619#103—41no—
620#102—22no—
621#102—22no—
622#102—41no—
623C22⋊C8—22no—
624C22⋊C8—22no—
625C22⋊C8—22no—
626C22⋊C8D4×C3114yescomplemented
627#95—21no—
628#95—21no—
629#95—21no—
630C31#2438911yescharacteristic, direct product factor, Sylow
631C24—22no—
632C24—22no—
633C24—22no—
634C24—21no—
635C24—41no—
636C24—41no—
637C24—41no—
638C24—41no—
639C24C2×D4×C3111yescharacteristic
640C24C2×D4×C3111yescharacteristic
641C24C2×D4×C3111yescharacteristic
642#41—44no—
643#41—44no—
644#41—44no—
645#41—44no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8C2×D4×C3112yes—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4C2×D4×C3112yes—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
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—21no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—41no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4C2×D4×C3111yescharacteristic
711C22×C4C2×D4×C3111yescharacteristic
712C22×C4C2×D4×C3112yes—
713C22×C4C2×D4×C3112yes—
714C22×C4C2×D4×C3111yescharacteristic
715C22×C4C2×D4×C3112yes—
716C22×C4#41×C3112yes—
717C22×C4C24×C3111yescharacteristic
718Q16—44no—
719SD16—44no—
720M16—44no—
721M16—44no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8C2×D4×C3112yes—
733C2×C8C2×D4×C3112yes—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—42no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4C2×D4×C3112yes—
748C4⋊C4C2×D4×C3112yes—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C42—24no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23C31×#12012yes—
794C23C31×#12112yes—
795C23C31×#13712yes—
796C23C22×D4×C3111yescharacteristic
797Q8—22no—
798Q8—22no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803Q8—41no—
804Q8—41no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—48no—
810D4—41no—
811D4—41no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—48no—
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—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4C31×#12012yes—
857C2×C4C31×#12112yes—
858C2×C4C22×D4×C3111yescharacteristic
859C2×C4C22×D4×C3111yescharacteristic
860C2×C4C22×D4×C3111yescharacteristic
861C2×C4C2×#41×C3111yescharacteristic
862C2×C4C31×H(5,𝔽2)11yescharacteristic
863C2×C4C31×H(5,𝔽2)11yescharacteristic
864C8—22no—
865C8—22no—
866C8—41no—
867C8—41no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—416no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22C2×C31×#12011yescharacteristic
898C22C2×C31×#12111yescharacteristic
899C22C31×#53411yescharacteristic
900C22C2×C31×#13711yescharacteristic
901C22C31×#57511yescharacteristic
902C22C31×#57511yescharacteristic
903C22C31×#57511yescharacteristic
904C4—22no—
905C4—22no—
906C4—41no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—81no—
911C4—81no—
912C4—81no—
913C4—81no—
914C4D42×C3111yescharacteristic
915C4D42×C3111yescharacteristic
916C4C31×#54611yescharacteristic
917C4C31×#54611yescharacteristic
918C2—42no—
919C2—42no—
920C2—42no—
921C2—82no—
922C2C31×#241011yescharacteristic
923C2C31×#300511yescharacteristic
924C2C31×#300711yescharacteristic
925C2C31×#305411yescharacteristic
926C2C31×#305611yescharacteristic
927C2C31×#319611yescharacteristic
928C2C31×#319711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#470C2semidirect
3. C2×C31×#468C2semidirect
4. C2×C31×#452C2semidirect
5. C2×C31×#407C2semidirect
6. C31×#2848C2semidirect
7. C31×#2036C2semidirect
8. C31×#2034C2semidirect
9. C31×#2001C2semidirect
10. C31×#2000C2semidirect
11. C31×#1895C2semidirect
12. C31×#1894C2semidirect
13. C31×#1873C2semidirect
14. C31×#1854C2semidirect
15. C31×#1788C2semidirect
18. C22×Q16×C31C22semidirect
19. C22×SD16×C31C22semidirect
39. C2×C31×#107C22semidirect
40. C2×C31×#106C22semidirect
41. C2×C31×#103C22semidirect
42. C2×C31×#103C22semidirect
43. C2×C31×#103C22semidirect
44. C2×C31×#103C22semidirect
45. C2×C31×#103C22semidirect
46. C2×C31×#102C22semidirect
47. C2×C31×#102C22semidirect
48. C2×C31×#102C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#340C22semidirect
64. C31×#340C22semidirect
162. C31×C22⋊C8D4semidirect
296. #24389C31direct (N × H)
405. C2×#470C2×C31semidirect
406. C2×#468C2×C31semidirect
407. C2×#452C2×C31semidirect
408. C2×#407C2×C31semidirect
409. #2848C2×C31semidirect
410. #2036C2×C31semidirect
411. #2034C2×C31semidirect
412. #2001C2×C31semidirect
413. #2000C2×C31semidirect
414. #1895C2×C31semidirect
415. #1894C2×C31semidirect
416. #1873C2×C31semidirect
417. #1854C2×C31semidirect
418. #1788C2×C31semidirect
471. C22×Q16C22×C31semidirect
472. C22×SD16C22×C31semidirect
492. C2×#107C22×C31semidirect
493. C2×#106C22×C31semidirect
494. C2×#103C22×C31semidirect
495. C2×#103C22×C31semidirect
496. C2×#103C22×C31semidirect
497. C2×#103C22×C31semidirect
498. C2×#103C22×C31semidirect
499. C2×#102C22×C31semidirect
500. C2×#102C22×C31semidirect
501. C2×#102C22×C31semidirect
514. #340C22×C31semidirect
515. #340C22×C31semidirect
516. #340C22×C31semidirect
517. #340C22×C31semidirect
626. C22⋊C8D4×C31semidirect
630. C31#24389direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5252
C2×C31×#4702
C2×C31×#4682
C2×C31×#4522
C2×C31×#4072
C31×#28482
C31×#20362
C31×#20342
C31×#20012
C31×#20002
C31×#18952
C31×#18942
C31×#18732
C31×#18542
C31×#17882
#2438931