Finite Group Databasebeta

← C31×#25554 #21482313

Subgroups — C31×#25554 #21482313

Order 7936.

1236 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#555C211yesmaximal, characteristic, complemented
2C2×C31×#482C211yesmaximal, characteristic, complemented
3C2×C31×#469C211yesmaximal, characteristic, complemented
4C31×#2416C211yesmaximal, characteristic, complemented
5C31×#2058C211yesmaximal, characteristic, complemented
6C31×#2034C211yesmaximal, characteristic, complemented
7C31×#2023C211yesmaximal, characteristic, complemented
8C31×#1999C211yesmaximal, characteristic, complemented
9C31×#1879C211yesmaximal, characteristic, complemented
10C31×#1875C211yesmaximal, characteristic, complemented
11C31×#1874C211yesmaximal, characteristic, complemented
12C31×#1870C211yesmaximal, characteristic, complemented
13C31×#1862C211yesmaximal, characteristic, complemented
14C31×#1854C211yesmaximal, characteristic, complemented
15C31×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C31C2211yescharacteristic
17C22×M16×C31C2211yescharacteristic
18C31×#555—24no—
19C31×#555—24no—
20C2×C31×C4⋊Q8C2211yescharacteristic
21C2×C31×#124—21no—
22C2×C31×#124—21no—
23C2×C31×#121—21no—
24C2×C31×#121—21no—
25C2×C31×#121C2211yescharacteristic
26C2×C31×#121C2211yescharacteristic
27C2×C31×#121C2211yescharacteristic
28C2×C31×#121C2211yescharacteristic
29C2×C4×D4×C31C2211yescharacteristic
30C2×C4×D4×C31C2211yescharacteristic
31C2×C31×#117—21no—
32C2×C31×#117C2211yescharacteristic
33C2×C31×#117C2211yescharacteristic
34C22×C4⋊C4×C31C2211yescharacteristic
35C31×#482—24no—
36C31×#469—24no—
37C2×C31×#107C2211yescharacteristic
38C2×C31×#106C2211yescharacteristic
39C2×C31×#106C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×C22⋊C8C2211yescharacteristic
49C31×#396—21no—
50C31×#394—21no—
51C31×#390C2211yescharacteristic
52C31×#389C2211yescharacteristic
53C31×#386—21no—
54C31×#380C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31D411yescharacteristic
69C22×D4×C31C2311yescharacteristic
70C22×D4×C31C2311yescharacteristic
71C23×C4×C31—21no—
72C23×C4×C31—21no—
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C2×D8×C31—22no—
76C2×D8×C31—22no—
77C2×D8×C31—41no—
78C2×M16×C31—22no—
79C2×M16×C31—22no—
80C2×M16×C31—41no—
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C31×C4⋊Q8—22no—
86C31×C4⋊Q8—22no—
87C31×#124—28no—
88C31×#124—28no—
89C31×#121—28no—
90C31×#121—22no—
91C31×#121—22no—
92C31×#121—22no—
93C31×#121—22no—
94C31×#121—22no—
95C31×#121—22no—
96C31×#121—41no—
97C31×#121—44no—
98C31×#121D414yescomplemented
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31—22no—
102C4×D4×C31—22no—
103C31×#117—28no—
104C31×#117—22no—
105C31×#117—22no—
106C31×#117—22no—
107C31×#117D414yescomplemented
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—22no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—41no—
113C2×C4⋊C4×C31D411yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C4⋊C4×C31C2311yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
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×C31D411yescharacteristic
131C2×C22⋊C4×C31D411yescharacteristic
132C2×C42×C31—21no—
133C2×C42×C31—21no—
134C2×C42×C31C2311yescharacteristic
135C31×#107—22no—
136C31×#106—22no—
137C31×#106—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—41no—
144C31×C22⋊C8—22no—
145C31×C22⋊C8—22no—
146C31×C22⋊C8—41no—
147C31×#95—21no—
148C31×#95—21no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31C2×D411yescharacteristic
152C24×C31C2×D411yescharacteristic
153C2×Q8×C31—24no—
154C2×Q8×C31—81no—
155C2×Q8×C31—81no—
156C2×D4×C31—22no—
157C2×D4×C31—24no—
158C2×D4×C31—24no—
159C2×D4×C31—22no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—41no—
172C2×D4×C31—42no—
173C2×D4×C31—42no—
174C2×D4×C31—42no—
175C2×D4×C31—42no—
176C2×D4×C31—42no—
177C2×D4×C31—81no—
178C2×D4×C31—81no—
179C2×D4×C31—81no—
180C2×D4×C31—81no—
181C2×D4×C31—81no—
182C2×D4×C31C2×D412yes—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—24no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—42no—
201C22×C4×C31—42no—
202C22×C4×C31—42no—
203C22×C4×C31—42no—
204C22×C4×C31—81no—
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D412yes—
209C22×C4×C31C2×D412yes—
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2411yescharacteristic
212D8×C31—44no—
213M16×C31—44no—
214C2×C8×C31—21no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31—21no—
218C2×C8×C31—21no—
219C2×C8×C31—21no—
220C2×C8×C31—21no—
221C2×C8×C31—21no—
222C2×C8×C31—21no—
223C2×C8×C31—21no—
224C2×C8×C31—21no—
225C2×C8×C31#4112yes—
226C4⋊C4×C31—24no—
227C4⋊C4×C31—22no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—42no—
237C4⋊C4×C31—42no—
238C4⋊C4×C31C2×D412yes—
239C4⋊C4×C31C2×D412yes—
240C4⋊C4×C31C2×D412yes—
241C4⋊C4×C31#4112yes—
242C22⋊C4×C31—24no—
243C22⋊C4×C31—24no—
244C22⋊C4×C31—24no—
245C22⋊C4×C31—24no—
246C22⋊C4×C31—22no—
247C22⋊C4×C31—24no—
248C22⋊C4×C31—22no—
249C22⋊C4×C31—42no—
250C22⋊C4×C31—42no—
251C22⋊C4×C31—42no—
252C22⋊C4×C31—42no—
253C22⋊C4×C31—81no—
254C42×C31—24no—
255C42×C31—24no—
256C42×C31—21no—
257C42×C31—21no—
258#25554C3111yesmaximal, characteristic, direct product factor, Sylow
259C23×C31—21no—
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—21no—
265C23×C31—21no—
266C23×C31—22no—
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—21no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31#12012yes—
287C23×C31C22×D411yescharacteristic
288Q8×C31—84no—
289D4×C31—22no—
290D4×C31—22no—
291D4×C31—44no—
292D4×C31—41no—
293D4×C31—41no—
294D4×C31—41no—
295D4×C31—41no—
296D4×C31—41no—
297D4×C31—41no—
298D4×C31—84no—
299D4×C31—84no—
300D4×C31—84no—
301D4×C31—84no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—21no—
311C2×C4×C31—22no—
312C2×C4×C31—21no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—21no—
316C2×C4×C31—22no—
317C2×C4×C31—21no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—48no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—84no—
340C2×C4×C31#12012yes—
341C2×C4×C31AGL(1,ℤ/8)12yes—
342C2×C4×C31C22×D411yescharacteristic
343C2×C4×C31C22×D411yescharacteristic
344C2×C4×C31C2×#4111yescharacteristic
345C2×C4×C31C2×#4111yescharacteristic
346C2×C4×C31H(5,𝔽2)11yescharacteristic
347C2×C4×C312−1+411yescharacteristic
348C8×C31—22no—
349C8×C31—41no—
350C8×C31—41no—
351C8×C31—41no—
352C2×#555C2×C3111yescharacteristic, complemented
353C2×#482C2×C3111yescharacteristic, complemented
354C2×#469C2×C3111yescharacteristic, complemented
355#2416C2×C3111yescharacteristic, complemented
356#2058C2×C3111yescharacteristic, complemented
357#2034C2×C3111yescharacteristic, complemented
358#2023C2×C3111yescharacteristic, complemented
359#1999C2×C3111yescharacteristic, complemented
360#1879C2×C3111yescharacteristic, complemented
361#1875C2×C3111yescharacteristic, complemented
362#1874C2×C3111yescharacteristic, complemented
363#1870C2×C3111yescharacteristic, complemented
364#1862C2×C3111yescharacteristic, complemented
365#1854C2×C3111yescharacteristic, complemented
366#1736C2×C3111yescharacteristic, complemented
367C22×C31—22no—
368C22×C31—22no—
369C22×C31—22no—
370C22×C31—41no—
371C22×C31—41no—
372C22×C31—41no—
373C22×C31—41no—
374C22×C31—41no—
375C22×C31—41no—
376C22×C31—41no—
377C22×C31—42no—
378C22×C31—42no—
379C22×C31—41no—
380C22×C31—41no—
381C22×C31—42no—
382C22×C31—41no—
383C22×C31—41no—
384C22×C31—81no—
385C22×C31—81no—
386C22×C31—81no—
387C22×C31—81no—
388C22×C31—81no—
389C22×C31—81no—
390C22×C31—81no—
391C22×C31—81no—
392C22×C31—81no—
393C22×C31—81no—
394C22×C31—81no—
395C22×C31C2×#12011yescharacteristic
396C22×C31#54611yescharacteristic
397C22×C31#54711yescharacteristic
398C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
399C22×C31#57511yescharacteristic
400C22×C31#57611yescharacteristic
401C22×C31#57711yescharacteristic
402C4×C31—22no—
403C4×C31—22no—
404C4×C31—41no—
405C4×C31—42no—
406C4×C31—41no—
407C4×C31—42no—
408C4×C31—42no—
409C4×C31—42no—
410C4×C31—81no—
411C4×C31—81no—
412C4×C31#53211yescharacteristic
413C4×C31#53711yescharacteristic
414C4×C31#54611yescharacteristic
415C4×C31#54711yescharacteristic
416C22×D8C22×C3111yescharacteristic
417C22×M16C22×C3111yescharacteristic
418#555—24no—
419#555—24no—
420C2×C4⋊Q8C22×C3111yescharacteristic
421C2×#124—21no—
422C2×#124—21no—
423C2×#121—21no—
424C2×#121—21no—
425C2×#121C22×C3111yescharacteristic
426C2×#121C22×C3111yescharacteristic
427C2×#121C22×C3111yescharacteristic
428C2×#121C22×C3111yescharacteristic
429C2×C4×D4C22×C3111yescharacteristic
430C2×C4×D4C22×C3111yescharacteristic
431C2×#117—21no—
432C2×#117C22×C3111yescharacteristic
433C2×#117C22×C3111yescharacteristic
434C22×C4⋊C4C22×C3111yescharacteristic
435#482—24no—
436#469—24no—
437C2×#107C22×C3111yescharacteristic
438C2×#106C22×C3111yescharacteristic
439C2×#106C22×C3111yescharacteristic
440C2×#102C22×C3111yescharacteristic
441C2×#102C22×C3111yescharacteristic
442C2×#102C22×C3111yescharacteristic
443C2×#102C22×C3111yescharacteristic
444C2×#102C22×C3111yescharacteristic
445C2×#102C22×C3111yescharacteristic
446C2×C22⋊C8C22×C3111yescharacteristic
447C2×C22⋊C8C22×C3111yescharacteristic
448C2×C22⋊C8C22×C3111yescharacteristic
449#396—21no—
450#394—21no—
451#390C22×C3111yescharacteristic
452#389C22×C3111yescharacteristic
453#386—21no—
454#380C22×C3111yescharacteristic
455#340C22×C3111yescharacteristic
456#340C22×C3111yescharacteristic
457#340C22×C3111yescharacteristic
458#340C22×C3111yescharacteristic
459#340C22×C3111yescharacteristic
460#340C22×C3111yescharacteristic
461#336C22×C3111yescharacteristic
462#336C22×C3111yescharacteristic
463C2×C31—42no—
464C2×C31—81no—
465C2×C31—82no—
466C2×C31—161no—
467C2×C31#243011yescharacteristic
468C2×C31#300611yescharacteristic
469C2×C31#301211yescharacteristic
470C2×C31#332111yescharacteristic
471C2×C31#332511yescharacteristic
472C2×C31#334711yescharacteristic
473C2×C31#335411yescharacteristic
474C22×Q8—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4D4×C3111yescharacteristic
480C22×D4C23×C3111yescharacteristic
481C22×D4C23×C3111yescharacteristic
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C3111yescharacteristic
485C23×C4C23×C3111yescharacteristic
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—41no—
489C2×M16—22no—
490C2×M16—22no—
491C2×M16—41no—
492C22×C8C23×C3111yescharacteristic
493C22×C8C23×C3111yescharacteristic
494C22×C8C23×C3111yescharacteristic
495C22×C8C23×C3111yescharacteristic
496C4⋊Q8—22no—
497C4⋊Q8—22no—
498#124—28no—
499#124—28no—
500#121—28no—
501#121—22no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—41no—
508#121—44no—
509#121D4×C3114yescomplemented
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514#117—28no—
515#117—22no—
516#117—22no—
517#117—22no—
518#117D4×C3114yescomplemented
519C2×C4⋊C4—21no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—41no—
524C2×C4⋊C4D4×C3111yescharacteristic
525C2×C4⋊C4C23×C3111yescharacteristic
526C2×C4⋊C4C23×C3111yescharacteristic
527C2×C4⋊C4C23×C3111yescharacteristic
528C2×C4⋊C4C23×C3111yescharacteristic
529C2×C4⋊C4C23×C3111yescharacteristic
530C2×C4⋊C4C23×C3111yescharacteristic
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4D4×C3111yescharacteristic
542C2×C22⋊C4D4×C3111yescharacteristic
543C2×C42—21no—
544C2×C42—21no—
545C2×C42C23×C3111yescharacteristic
546#107—22no—
547#106—22no—
548#106—22no—
549#102—22no—
550#102—22no—
551#102—22no—
552#102—22no—
553#102—22no—
554#102—41no—
555C22⋊C8—22no—
556C22⋊C8—22no—
557C22⋊C8—41no—
558#95—21no—
559#95—21no—
560C31#2555411yescharacteristic, direct product factor, Sylow
561C24—21no—
562C24—21no—
563C24C2×D4×C3111yescharacteristic
564C24C2×D4×C3111yescharacteristic
565C2×Q8—24no—
566C2×Q8—81no—
567C2×Q8—81no—
568C2×D4—22no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4C2×D4×C3112yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—81no—
617C22×C4C2×D4×C3111yescharacteristic
618C22×C4C2×D4×C3111yescharacteristic
619C22×C4C2×D4×C3111yescharacteristic
620C22×C4C2×D4×C3112yes—
621C22×C4C2×D4×C3112yes—
622C22×C4C2×D4×C3111yescharacteristic
623C22×C4C24×C3111yescharacteristic
624D8—44no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8#41×C3112yes—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4C2×D4×C3112yes—
651C4⋊C4C2×D4×C3112yes—
652C4⋊C4C2×D4×C3112yes—
653C4⋊C4#41×C3112yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—24no—
660C22⋊C4—22no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—81no—
666C42—24no—
667C42—24no—
668C42—21no—
669C42—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23C31×#12012yes—
698C23C22×D4×C3111yescharacteristic
699Q8—84no—
700D4—22no—
701D4—22no—
702D4—44no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—84no—
711D4—84no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—48no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—84no—
751C2×C4C31×#12012yes—
752C2×C4C31×AGL(1,ℤ/8)12yes—
753C2×C4C22×D4×C3111yescharacteristic
754C2×C4C22×D4×C3111yescharacteristic
755C2×C4C2×#41×C3111yescharacteristic
756C2×C4C2×#41×C3111yescharacteristic
757C2×C4C31×H(5,𝔽2)11yescharacteristic
758C2×C4C31×2−1+411yescharacteristic
759C8—22no—
760C8—41no—
761C8—41no—
762C8—41no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—41no—
776C22—41no—
777C22—42no—
778C22—41no—
779C22—41no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C2×C31×#12011yescharacteristic
792C22C31×#54611yescharacteristic
793C22C31×#54711yescharacteristic
794C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
795C22C31×#57511yescharacteristic
796C22C31×#57611yescharacteristic
797C22C31×#57711yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—81no—
807C4—81no—
808C4C31×#53211yescharacteristic
809C4C31×#53711yescharacteristic
810C4C31×#54611yescharacteristic
811C4C31×#54711yescharacteristic
812C2—42no—
813C2—81no—
814C2—82no—
815C2—161no—
816C2C31×#243011yescharacteristic
817C2C31×#300611yescharacteristic
818C2C31×#301211yescharacteristic
819C2C31×#332111yescharacteristic
820C2C31×#332511yescharacteristic
821C2C31×#334711yescharacteristic
822C2C31×#335411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
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
1. C2×C31×#555C2semidirect
2. C2×C31×#482C2semidirect
3. C2×C31×#469C2semidirect
4. C31×#2416C2semidirect
5. C31×#2058C2semidirect
6. C31×#2034C2semidirect
7. C31×#2023C2semidirect
8. C31×#1999C2semidirect
9. C31×#1879C2semidirect
10. C31×#1875C2semidirect
11. C31×#1874C2semidirect
12. C31×#1870C2semidirect
13. C31×#1862C2semidirect
14. C31×#1854C2semidirect
15. C31×#1736C2semidirect
98. C31×#121D4semidirect
107. C31×#117D4semidirect
258. #25554C31direct (N × H)
352. C2×#555C2×C31semidirect
353. C2×#482C2×C31semidirect
354. C2×#469C2×C31semidirect
355. #2416C2×C31semidirect
356. #2058C2×C31semidirect
357. #2034C2×C31semidirect
358. #2023C2×C31semidirect
359. #1999C2×C31semidirect
360. #1879C2×C31semidirect
361. #1875C2×C31semidirect
362. #1874C2×C31semidirect
363. #1870C2×C31semidirect
364. #1862C2×C31semidirect
365. #1854C2×C31semidirect
366. #1736C2×C31semidirect
509. #121D4×C31semidirect
518. #117D4×C31semidirect
560. C31#25554direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5552
C2×C31×#4822
C2×C31×#4692
C31×#24162
C31×#20582
C31×#20342
C31×#20232
C31×#19992
C31×#18792
C31×#18752
C31×#18742
C31×#18702
C31×#18622
C31×#18542
C31×#17362
#2555431