Finite Group Databasebeta

← C31×#24452 #21481211

Subgroups — C31×#24452 #21481211

Order 7936.

1592 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#546C211yesmaximal, characteristic
2C2×C31×#468C211yesmaximal, characteristic, complemented
3C2×C31×#452C211yesmaximal, characteristic, complemented
4C2×C31×#450C211yesmaximal, characteristic, complemented
5C2×C31×#417C211yesmaximal, characteristic, complemented
6C31×#2417C211yesmaximal, characteristic, complemented
7C31×#2042C211yesmaximal, characteristic, complemented
8C31×#2036C211yesmaximal, characteristic, complemented
9C31×#2015C211yesmaximal, characteristic, complemented
10C31×#2001C211yesmaximal, characteristic, complemented
11C31×#1877C211yesmaximal, characteristic, complemented
12C31×#1874C211yesmaximal, characteristic, complemented
13C31×#1870C211yesmaximal, characteristic, complemented
14C31×#1862C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C22×Q16×C31C2211yescharacteristic, complemented
19C22×SD16×C31C2211yescharacteristic
20C22×SD16×C31C2211yescharacteristic
21C22×M16×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
34C22×C4⋊C4×C31C2211yescharacteristic, complemented
35C22×C22⋊C4×C31—21no—
36C31×#468—24no—
37C31×#452—24no—
38C31×#450—24no—
39C2×C31×#107C2211yescharacteristic, complemented
40C31×#417—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×#398—21no—
55C31×#396—21no—
56C31×#391C2211yescharacteristic, complemented
57C31×#389C2211yescharacteristic, complemented
58C31×#386—21no—
59C31×#380—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×C31—21no—
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C2×Q16×C31—22no—
92C2×Q16×C31—41no—
93C2×Q16×C31—41no—
94C2×SD16×C31—22no—
95C2×SD16×C31—22no—
96C2×SD16×C31—22no—
97C2×SD16×C31—22no—
98C2×SD16×C31—22no—
99C2×SD16×C31—41no—
100C2×M16×C31—22no—
101C2×M16×C31—22no—
102C2×M16×C31—41no—
103C22×C8×C31C2311yescharacteristic
104C22×C8×C31C2311yescharacteristic
105C22×C8×C31C2311yescharacteristic
106C22×C8×C31C2311yescharacteristic
107C31×#124—22no—
108C31×#124—22no—
109C31×#123—28no—
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×#121—28no—
117C31×#121—22no—
118C31×#121D414yes—
119C31×#120—28no—
120C4×D4×C31—22no—
121C4×D4×C31—22no—
122C4×D4×C31—22no—
123C4×D4×C31—22no—
124C2×C4⋊C4×C31—21no—
125C2×C4⋊C4×C31—22no—
126C2×C4⋊C4×C31—21no—
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31—21no—
129C2×C4⋊C4×C31—21no—
130C2×C4⋊C4×C31—41no—
131C2×C4⋊C4×C31D411yescharacteristic
132C2×C4⋊C4×C31C2311yescharacteristic
133C2×C4⋊C4×C31C2311yescharacteristic
134C2×C4⋊C4×C31C2311yescharacteristic
135C2×C4⋊C4×C31C2311yescharacteristic
136C2×C22⋊C4×C31—28no—
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×C31D411yescharacteristic
146C2×C22⋊C4×C31D411yescharacteristic
147C2×C42×C31C2311yescharacteristic
148C31×#107—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—42no—
242C22×C4×C31—42no—
243C22×C4×C31—81no—
244C22×C4×C31—81no—
245C22×C4×C31—81no—
246C22×C4×C31C2×D411yescharacteristic
247C22×C4×C31C2×D411yescharacteristic
248C22×C4×C31C2×D411yescharacteristic
249C22×C4×C31C2×D411yescharacteristic
250C22×C4×C31C2×D412yes—
251C22×C4×C31C2×D412yes—
252C22×C4×C31C2411yescharacteristic
253Q16×C31—44no—
254SD16×C31—44no—
255SD16×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×C31—21no—
268C2×C8×C31C2×D412yes—
269C4⋊C4×C31—24no—
270C4⋊C4×C31—22no—
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—42no—
278C4⋊C4×C31—42no—
279C4⋊C4×C31—42no—
280C4⋊C4×C31—81no—
281C4⋊C4×C31C2×D412yes—
282C4⋊C4×C31C2×D412yes—
283C22⋊C4×C31—24no—
284C22⋊C4×C31—24no—
285C22⋊C4×C31—24no—
286C22⋊C4×C31—24no—
287C22⋊C4×C31—22no—
288C22⋊C4×C31—22no—
289C22⋊C4×C31—24no—
290C22⋊C4×C31—42no—
291C22⋊C4×C31—42no—
292C22⋊C4×C31—81no—
293C42×C31—21no—
294C42×C31—21no—
295#24452C3111yesmaximal, characteristic, direct product factor, Sylow
296C23×C31—21no—
297C23×C31—22no—
298C23×C31—21no—
299C23×C31—21no—
300C23×C31—22no—
301C23×C31—21no—
302C23×C31—21no—
303C23×C31—22no—
304C23×C31—21no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—21no—
308C23×C31—21no—
309C23×C31—21no—
310C23×C31—21no—
311C23×C31—22no—
312C23×C31—48no—
313C23×C31—48no—
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—41no—
323C23×C31—41no—
324C23×C31—84no—
325C23×C31—84no—
326C23×C31—84no—
327C23×C31—84no—
328C23×C31—84no—
329C23×C31#12012yes—
330C23×C31#13712yes—
331C23×C31C22×D411yescharacteristic
332Q8×C31—22no—
333Q8×C31—22no—
334Q8×C31—41no—
335Q8×C31—41no—
336Q8×C31—41no—
337Q8×C31—41no—
338Q8×C31—41no—
339Q8×C31—41no—
340D4×C31—22no—
341D4×C31—22no—
342D4×C31—22no—
343D4×C31—22no—
344D4×C31—22no—
345D4×C31—44no—
346D4×C31—48no—
347D4×C31—48no—
348D4×C31—41no—
349D4×C31—41no—
350D4×C31—84no—
351D4×C31#12114yes—
352C2×C4×C31—21no—
353C2×C4×C31—21no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—22no—
357C2×C4×C31—22no—
358C2×C4×C31—21no—
359C2×C4×C31—21no—
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—21no—
367C2×C4×C31—21no—
368C2×C4×C31—21no—
369C2×C4×C31—21no—
370C2×C4×C31—48no—
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—84no—
391C2×C4×C31—84no—
392C2×C4×C31#12012yes—
393C2×C4×C31C22×D411yescharacteristic
394C2×C4×C31C22×D411yescharacteristic
395C2×C4×C31C22×D411yescharacteristic
396C2×C4×C31C2×#4111yescharacteristic
397C2×C4×C31H(5,𝔽2)11yescharacteristic
398C2×C4×C31H(5,𝔽2)11yescharacteristic
399C8×C31—22no—
400C8×C31—41no—
401C8×C31—41no—
402C8×C31—41no—
403C2×#546C2×C3111yescharacteristic
404C2×#468C2×C3111yescharacteristic, complemented
405C2×#452C2×C3111yescharacteristic, complemented
406C2×#450C2×C3111yescharacteristic, complemented
407C2×#417C2×C3111yescharacteristic, complemented
408#2417C2×C3111yescharacteristic, complemented
409#2042C2×C3111yescharacteristic, complemented
410#2036C2×C3111yescharacteristic, complemented
411#2015C2×C3111yescharacteristic, complemented
412#2001C2×C3111yescharacteristic, complemented
413#1877C2×C3111yescharacteristic, complemented
414#1874C2×C3111yescharacteristic, complemented
415#1870C2×C3111yescharacteristic, complemented
416#1862C2×C3111yescharacteristic, complemented
417#1786C2×C3111yescharacteristic, complemented
418C22×C31—22no—
419C22×C31—24no—
420C22×C31—22no—
421C22×C31—22no—
422C22×C31—22no—
423C22×C31—22no—
424C22×C31—22no—
425C22×C31—41no—
426C22×C31—42no—
427C22×C31—41no—
428C22×C31—42no—
429C22×C31—42no—
430C22×C31—41no—
431C22×C31—41no—
432C22×C31—41no—
433C22×C31—42no—
434C22×C31—41no—
435C22×C31—42no—
436C22×C31—41no—
437C22×C31—41no—
438C22×C31—42no—
439C22×C31—42no—
440C22×C31—42no—
441C22×C31—42no—
442C22×C31—816no—
443C22×C31—81no—
444C22×C31—81no—
445C22×C31—81no—
446C22×C31—81no—
447C22×C31C2×#12011yescharacteristic
448C22×C31D4211yescharacteristic
449C22×C31#54611yescharacteristic
450C22×C31C2×#13711yescharacteristic
451C22×C31#57511yescharacteristic
452C22×C31#57611yescharacteristic
453C22×C31#57711yescharacteristic
454C4×C31—22no—
455C4×C31—41no—
456C4×C31—42no—
457C4×C31—41no—
458C4×C31—41no—
459C4×C31—42no—
460C4×C31—42no—
461C4×C31—81no—
462C4×C31—81no—
463C4×C31—81no—
464C4×C31C2×#12111yescharacteristic
465C4×C31#53411yescharacteristic
466C4×C31D4211yescharacteristic
467C4×C31#54611yescharacteristic
468C22×#41C22×C3111yescharacteristic
469C23×D4C22×C3111yescharacteristic
470C22×Q16C22×C3111yescharacteristic, complemented
471C22×SD16C22×C3111yescharacteristic
472C22×SD16C22×C3111yescharacteristic
473C22×M16C22×C3111yescharacteristic, complemented
474#546—24no—
475#546—24no—
476C2×#124C22×C3111yescharacteristic
477C2×#123—21no—
478C2×C22⋊Q8C22×C3111yescharacteristic
479C2×C22⋊Q8C22×C3111yescharacteristic
480C2×C22⋊Q8C22×C3111yescharacteristic, complemented
481C2×#121—21no—
482C2×#121C22×C3111yescharacteristic
483C2×#120—21no—
484C2×C4×D4C22×C3111yescharacteristic
485C2×C4×D4C22×C3111yescharacteristic
486C22×C4⋊C4C22×C3111yescharacteristic, complemented
487C22×C22⋊C4—21no—
488#468—24no—
489#452—24no—
490#450—24no—
491C2×#107C22×C3111yescharacteristic, complemented
492#417—24no—
493C2×#103C22×C3111yescharacteristic, complemented
494C2×#103C22×C3111yescharacteristic, complemented
495C2×#103C22×C3111yescharacteristic, complemented
496C2×#103C22×C3111yescharacteristic, complemented
497C2×#102C22×C3111yescharacteristic
498C2×#102C22×C3111yescharacteristic
499C2×#102C22×C3111yescharacteristic
500C2×#102C22×C3111yescharacteristic
501C2×#102C22×C3111yescharacteristic
502C2×#102C22×C3111yescharacteristic
503C2×C22⋊C8C22×C3111yescharacteristic
504C2×C22⋊C8C22×C3111yescharacteristic
505C2×C22⋊C8C22×C3111yescharacteristic, complemented
506#398—21no—
507#396—21no—
508#391C22×C3111yescharacteristic, complemented
509#389C22×C3111yescharacteristic, complemented
510#386—21no—
511#380—21no—
512#380C22×C3111yescharacteristic
513#340C22×C3111yescharacteristic, complemented
514#340C22×C3111yescharacteristic, complemented
515#336C22×C3111yescharacteristic, complemented
516#336C22×C3111yescharacteristic, complemented
517C2×C31—42no—
518C2×C31—42no—
519C2×C31—44no—
520C2×C31—82no—
521C2×C31#241011yescharacteristic
522C2×C31#300711yescharacteristic
523C2×C31#301211yescharacteristic
524C2×C31#326611yescharacteristic
525C2×C31#327311yescharacteristic
526C2×C31#331411yescharacteristic
527C2×C31#332311yescharacteristic
528C25—21no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—41no—
533C2×#41—41no—
534C2×#41D4×C3114yes—
535C22×Q8C23×C3111yescharacteristic
536C22×Q8C23×C3111yescharacteristic
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—21no—
544C22×D4—41no—
545C22×D4—41no—
546C22×D4D4×C3111yescharacteristic
547C22×D4C23×C3111yescharacteristic
548C22×D4C23×C3111yescharacteristic
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—21no—
552C23×C4C23×C3111yescharacteristic
553C23×C4C23×C3111yescharacteristic
554C2×Q16—22no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—41no—
563C2×M16—22no—
564C2×M16—22no—
565C2×M16—41no—
566C22×C8C23×C3111yescharacteristic
567C22×C8C23×C3111yescharacteristic
568C22×C8C23×C3111yescharacteristic
569C22×C8C23×C3111yescharacteristic
570#124—22no—
571#124—22no—
572#123—28no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—41no—
579#121—28no—
580#121—22no—
581#121D4×C3114yes—
582#120—28no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4D4×C3111yescharacteristic
595C2×C4⋊C4C23×C3111yescharacteristic
596C2×C4⋊C4C23×C3111yescharacteristic
597C2×C4⋊C4C23×C3111yescharacteristic
598C2×C4⋊C4C23×C3111yescharacteristic
599C2×C22⋊C4—28no—
600C2×C22⋊C4—21no—
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⋊C4D4×C3111yescharacteristic
609C2×C22⋊C4D4×C3111yescharacteristic
610C2×C42C23×C3111yescharacteristic
611#107—22no—
612#103—22no—
613#103—22no—
614#103—22no—
615#103—22no—
616#102—22no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102—41no—
621#102D4×C3114yescomplemented
622C22⋊C8—22no—
623C22⋊C8—22no—
624C22⋊C8—41no—
625#95—21no—
626#95—21no—
627#95—21no—
628#95—21no—
629C31#2445211yescharacteristic, direct product factor, Sylow
630C24—21no—
631C24—24no—
632C24—21no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—81no—
638C24—81no—
639C24C2×D4×C3111yescharacteristic
640C24C2×D4×C3111yescharacteristic
641#41—28no—
642#41—44no—
643#41—44no—
644#41—44no—
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×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8C2×D4×C3112yes—
657C2×D4—24no—
658C2×D4—22no—
659C2×D4—24no—
660C2×D4—22no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—41no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—44no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—44no—
679C2×D4—81no—
680C2×D4—81no—
681C2×D4C2×D4×C3112yes—
682C2×D4C2×D4×C3112yes—
683C2×D4C2×D4×C3112yes—
684C2×D4#41×C3112yes—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—81no—
708C22×C4—81no—
709C22×C4—81no—
710C22×C4C2×D4×C3111yescharacteristic
711C22×C4C2×D4×C3111yescharacteristic
712C22×C4C2×D4×C3111yescharacteristic
713C22×C4C2×D4×C3111yescharacteristic
714C22×C4C2×D4×C3112yes—
715C22×C4C2×D4×C3112yes—
716C22×C4C24×C3111yescharacteristic
717Q16—44no—
718SD16—44no—
719SD16—44no—
720M16—44no—
721C2×C8—21no—
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—
733C4⋊C4—24no—
734C4⋊C4—22no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—42no—
742C4⋊C4—42no—
743C4⋊C4—42no—
744C4⋊C4—81no—
745C4⋊C4C2×D4×C3112yes—
746C4⋊C4C2×D4×C3112yes—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—24no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—81no—
757C42—21no—
758C42—21no—
759C23—21no—
760C23—22no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—21no—
765C23—21no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—48no—
776C23—48no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23—84no—
792C23C31×#12012yes—
793C23C31×#13712yes—
794C23C22×D4×C3111yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—44no—
809D4—48no—
810D4—48no—
811D4—41no—
812D4—41no—
813D4—84no—
814D4C31×#12114yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
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—84no—
854C2×C4—84no—
855C2×C4C31×#12012yes—
856C2×C4C22×D4×C3111yescharacteristic
857C2×C4C22×D4×C3111yescharacteristic
858C2×C4C22×D4×C3111yescharacteristic
859C2×C4C2×#41×C3111yescharacteristic
860C2×C4C31×H(5,𝔽2)11yescharacteristic
861C2×C4C31×H(5,𝔽2)11yescharacteristic
862C8—22no—
863C8—41no—
864C8—41no—
865C8—41no—
866C22—22no—
867C22—24no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—41no—
874C22—42no—
875C22—41no—
876C22—42no—
877C22—42no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—42no—
882C22—41no—
883C22—42no—
884C22—41no—
885C22—41no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—816no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22—81no—
895C22C2×C31×#12011yescharacteristic
896C22D42×C3111yescharacteristic
897C22C31×#54611yescharacteristic
898C22C2×C31×#13711yescharacteristic
899C22C31×#57511yescharacteristic
900C22C31×#57611yescharacteristic
901C22C31×#57711yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—42no—
908C4—42no—
909C4—81no—
910C4—81no—
911C4—81no—
912C4C2×C31×#12111yescharacteristic
913C4C31×#53411yescharacteristic
914C4D42×C3111yescharacteristic
915C4C31×#54611yescharacteristic
916C2—42no—
917C2—42no—
918C2—44no—
919C2—82no—
920C2C31×#241011yescharacteristic
921C2C31×#300711yescharacteristic
922C2C31×#301211yescharacteristic
923C2C31×#326611yescharacteristic
924C2C31×#327311yescharacteristic
925C2C31×#331411yescharacteristic
926C2C31×#332311yescharacteristic
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×#468C2semidirect
3. C2×C31×#452C2semidirect
4. C2×C31×#450C2semidirect
5. C2×C31×#417C2semidirect
6. C31×#2417C2semidirect
7. C31×#2042C2semidirect
8. C31×#2036C2semidirect
9. C31×#2015C2semidirect
10. C31×#2001C2semidirect
11. C31×#1877C2semidirect
12. C31×#1874C2semidirect
13. C31×#1870C2semidirect
14. C31×#1862C2semidirect
15. C31×#1786C2semidirect
18. C22×Q16×C31C22semidirect
21. C22×M16×C31C22semidirect
28. C2×C31×C22⋊Q8C22semidirect
34. C22×C4⋊C4×C31C22semidirect
39. C2×C31×#107C22semidirect
41. C2×C31×#103C22semidirect
42. C2×C31×#103C22semidirect
43. C2×C31×#103C22semidirect
44. C2×C31×#103C22semidirect
53. C2×C31×C22⋊C8C22semidirect
56. C31×#391C22semidirect
57. C31×#389C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#336C22semidirect
64. C31×#336C22semidirect
158. C31×#102D4semidirect
295. #24452C31direct (N × H)
404. C2×#468C2×C31semidirect
405. C2×#452C2×C31semidirect
406. C2×#450C2×C31semidirect
407. C2×#417C2×C31semidirect
408. #2417C2×C31semidirect
409. #2042C2×C31semidirect
410. #2036C2×C31semidirect
411. #2015C2×C31semidirect
412. #2001C2×C31semidirect
413. #1877C2×C31semidirect
414. #1874C2×C31semidirect
415. #1870C2×C31semidirect
416. #1862C2×C31semidirect
417. #1786C2×C31semidirect
470. C22×Q16C22×C31semidirect
473. C22×M16C22×C31semidirect
480. C2×C22⋊Q8C22×C31semidirect
486. C22×C4⋊C4C22×C31semidirect
491. C2×#107C22×C31semidirect
493. C2×#103C22×C31semidirect
494. C2×#103C22×C31semidirect
495. C2×#103C22×C31semidirect
496. C2×#103C22×C31semidirect
505. C2×C22⋊C8C22×C31semidirect
508. #391C22×C31semidirect
509. #389C22×C31semidirect
513. #340C22×C31semidirect
514. #340C22×C31semidirect
515. #336C22×C31semidirect
516. #336C22×C31semidirect
621. #102D4×C31semidirect
629. C31#24452direct (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×#4682
C2×C31×#4522
C2×C31×#4502
C2×C31×#4172
C31×#24172
C31×#20422
C31×#20362
C31×#20152
C31×#20012
C31×#18772
C31×#18742
C31×#18702
C31×#18622
C31×#17862
#2445231