Finite Group Databasebeta

← C31×#23868 #21480627

Subgroups — C31×#23868 #21480627

Order 7936.

1756 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#137C211yesmaximal, characteristic, complemented
2C2×D4×Q8×C31C211yesmaximal, characteristic, complemented
3C2×C31×#452C211yesmaximal, characteristic, complemented
4C2×C31×#451C211yesmaximal, characteristic, complemented
5C2×C31×#448C211yesmaximal, characteristic, complemented
6C31×#2407C211yesmaximal, characteristic
7C31×#2016C211yesmaximal, characteristic, complemented
8C31×#2013C211yesmaximal, characteristic, complemented
9C31×#2001C211yesmaximal, characteristic, complemented
10C31×#2000C211yesmaximal, characteristic, complemented
11C31×#1894C211yesmaximal, characteristic, complemented
12C31×#1880C211yesmaximal, characteristic, complemented
13C31×#1878C211yesmaximal, characteristic, complemented
14C31×#1870C211yesmaximal, characteristic, complemented
15C31×#1787C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×Q8×C31C2211yescharacteristic
18C23×Q8×C31C2211yescharacteristic
19C2×C31×#137—24no—
20C2×C31×#137—24no—
21C2×C31×#137—24no—
22C22×Q16×C31C2211yescharacteristic
23C22×Q16×C31C2211yescharacteristic
24C22×Q16×C31C2211yescharacteristic
25C22×SD16×C31C2211yescharacteristic
26C22×SD16×C31C2211yescharacteristic
27C22×SD16×C31C2211yescharacteristic
28C22×M16×C31C2211yescharacteristic
29D4×Q8×C31—24no—
30D4×Q8×C31—24no—
31C2×C31×C4⋊Q8—21no—
32C2×C31×C4⋊Q8C2211yescharacteristic
33C2×C31×C22⋊Q8—21no—
34C2×C31×C22⋊Q8—21no—
35C2×C31×C22⋊Q8C2211yescharacteristic
36C2×C31×C22⋊Q8C2211yescharacteristic
37C2×C31×C22⋊Q8C2211yescharacteristic
38C2×C31×#121C2211yescharacteristic
39C2×C4×Q8×C31C2211yescharacteristic
40C2×C4×D4×C31—21no—
41C2×C4×D4×C31C2211yescharacteristic
42C31×#452—24no—
43C31×#451—24no—
44C31×#448—24no—
45C2×C31×#103C2211yescharacteristic
46C2×C31×#103C2211yescharacteristic
47C2×C31×#103C2211yescharacteristic
48C2×C31×#103C2211yescharacteristic
49C2×C31×#103C2211yescharacteristic
50C2×C31×#103C2211yescharacteristic
51C2×C31×#103C2211yescharacteristic
52C2×C31×#102C2211yescharacteristic
53C2×C31×C22⋊C8C2211yescharacteristic
54C2×C31×C22⋊C8C2211yescharacteristic
55C2×C31×C22⋊C8C2211yescharacteristic
56C31×#394—21no—
57C31×#392—21no—
58C31×#391C2211yescharacteristic
59C31×#390C2211yescharacteristic
60C31×#386—21no—
61C31×#385—21no—
62C31×#380C2211yescharacteristic
63C31×#340C2211yescharacteristic
64C31×#340C2211yescharacteristic
65C31×#336C2211yescharacteristic
66C31×#336C2211yescharacteristic
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—22no—
71C2×#41×C31—41no—
72C2×#41×C31—41no—
73C22×Q8×C31—22no—
74C22×Q8×C31—22no—
75C22×Q8×C31—21no—
76C22×Q8×C31—21no—
77C22×Q8×C31—22no—
78C22×Q8×C31—22no—
79C22×Q8×C31—22no—
80C22×Q8×C31—22no—
81C22×Q8×C31—22no—
82C22×Q8×C31—41no—
83C22×Q8×C31—41no—
84C22×Q8×C31—41no—
85C22×Q8×C31—41no—
86C22×Q8×C31D414yescomplemented
87C22×Q8×C31C2311yescharacteristic
88C22×Q8×C31C2311yescharacteristic
89C22×Q8×C31C2311yescharacteristic
90C22×Q8×C31C2311yescharacteristic
91C22×D4×C31—21no—
92C22×D4×C31—21no—
93C22×D4×C31D411yescharacteristic
94C22×D4×C31C2311yescharacteristic
95C23×C4×C31—21no—
96C23×C4×C31—21no—
97C23×C4×C31—21no—
98C23×C4×C31C2311yescharacteristic
99C23×C4×C31C2311yescharacteristic
100C31×#137—232no—
101C2×Q16×C31—22no—
102C2×Q16×C31—22no—
103C2×Q16×C31—22no—
104C2×Q16×C31—22no—
105C2×Q16×C31—22no—
106C2×Q16×C31—22no—
107C2×Q16×C31—22no—
108C2×Q16×C31—41no—
109C2×Q16×C31D414yescomplemented
110C2×SD16×C31—22no—
111C2×SD16×C31—22no—
112C2×SD16×C31—22no—
113C2×SD16×C31—22no—
114C2×SD16×C31—22no—
115C2×SD16×C31—22no—
116C2×SD16×C31—22no—
117C2×SD16×C31—41no—
118C2×SD16×C31D414yescomplemented
119C2×M16×C31—22no—
120C2×M16×C31—22no—
121C2×M16×C31—22no—
122C22×C8×C31C2311yescharacteristic
123C22×C8×C31C2311yescharacteristic
124C22×C8×C31C2311yescharacteristic
125C22×C8×C31C2311yescharacteristic
126C31×C4⋊Q8—28no—
127C31×C4⋊Q8—22no—
128C31×C4⋊Q8—22no—
129C31×C22⋊Q8—28no—
130C31×C22⋊Q8—28no—
131C31×C22⋊Q8—22no—
132C31×C22⋊Q8—22no—
133C31×C22⋊Q8—22no—
134C31×C22⋊Q8—22no—
135C31×C22⋊Q8—41no—
136C31×C22⋊Q8D414yescomplemented
137C31×#121—22no—
138C31×#121—41no—
139C4×Q8×C31—22no—
140C4×Q8×C31—22no—
141C4×D4×C31—28no—
142C4×D4×C31—22no—
143C4×D4×C31—22no—
144C2×C4⋊C4×C31—21no—
145C2×C4⋊C4×C31—21no—
146C2×C4⋊C4×C31—21no—
147C2×C4⋊C4×C31—21no—
148C2×C4⋊C4×C31—21no—
149C2×C4⋊C4×C31—21no—
150C2×C4⋊C4×C31D411yescharacteristic
151C2×C4⋊C4×C31C2311yescharacteristic
152C2×C4⋊C4×C31C2311yescharacteristic
153C2×C4⋊C4×C31C2311yescharacteristic
154C2×C22⋊C4×C31—21no—
155C2×C22⋊C4×C31—21no—
156C2×C22⋊C4×C31—21no—
157C2×C22⋊C4×C31—21no—
158C2×C22⋊C4×C31—21no—
159C2×C22⋊C4×C31—21no—
160C2×C22⋊C4×C31—21no—
161C2×C22⋊C4×C31D411yescharacteristic
162C2×C22⋊C4×C31D411yescharacteristic
163C2×C42×C31—21no—
164C2×C42×C31C2311yescharacteristic
165C31×#103—22no—
166C31×#103—22no—
167C31×#103—22no—
168C31×#103—22no—
169C31×#103—22no—
170C31×#103—41no—
171C31×#103—41no—
172C31×#102—22no—
173C31×C22⋊C8—22no—
174C31×C22⋊C8—22no—
175C31×C22⋊C8—22no—
176C31×#95—21no—
177C31×#95—21no—
178C31×#95—21no—
179C24×C31—21no—
180C24×C31C2×D411yescharacteristic
181C24×C31C2×D411yescharacteristic
182#41×C31—28no—
183#41×C31—44no—
184#41×C31—44no—
185#41×C31—44no—
186C2×Q8×C31—24no—
187C2×Q8×C31—24no—
188C2×Q8×C31—21no—
189C2×Q8×C31—21no—
190C2×Q8×C31—21no—
191C2×Q8×C31—21no—
192C2×Q8×C31—21no—
193C2×Q8×C31—21no—
194C2×Q8×C31—28no—
195C2×Q8×C31—21no—
196C2×Q8×C31—21no—
197C2×Q8×C31—21no—
198C2×Q8×C31—21no—
199C2×Q8×C31—21no—
200C2×Q8×C31—21no—
201C2×Q8×C31—21no—
202C2×Q8×C31—21no—
203C2×Q8×C31—21no—
204C2×Q8×C31—21no—
205C2×Q8×C31—21no—
206C2×Q8×C31—21no—
207C2×Q8×C31—42no—
208C2×Q8×C31—42no—
209C2×Q8×C31—42no—
210C2×Q8×C31—42no—
211C2×Q8×C31—44no—
212C2×Q8×C31—44no—
213C2×Q8×C31—44no—
214C2×Q8×C31—44no—
215C2×Q8×C31—44no—
216C2×Q8×C31—44no—
217C2×Q8×C31—44no—
218C2×Q8×C31C2×D412yes—
219C2×Q8×C31C2×D412yes—
220C2×Q8×C31C2×D412yes—
221C2×Q8×C31C2×D412yes—
222C2×Q8×C31C2×D412yes—
223C2×Q8×C31C2×D412yes—
224C2×D4×C31—22no—
225C2×D4×C31—22no—
226C2×D4×C31—22no—
227C2×D4×C31—21no—
228C2×D4×C31—21no—
229C2×D4×C31—21no—
230C2×D4×C31—21no—
231C2×D4×C31—21no—
232C2×D4×C31—42no—
233C2×D4×C31—42no—
234C2×D4×C31—42no—
235C2×D4×C31—42no—
236C2×D4×C31—42no—
237C2×D4×C31—81no—
238C2×D4×C31C2×D412yes—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—24no—
245C22×C4×C31—24no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—21no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
256C22×C4×C31—21no—
257C22×C4×C31—21no—
258C22×C4×C31—42no—
259C22×C4×C31—42no—
260C22×C4×C31—42no—
261C22×C4×C31—42no—
262C22×C4×C31—42no—
263C22×C4×C31—42no—
264C22×C4×C31—42no—
265C22×C4×C31C2×D411yescharacteristic
266C22×C4×C31C2×D411yescharacteristic
267C22×C4×C31C2×D411yescharacteristic
268C22×C4×C31C2×D412yes—
269C22×C4×C31C2×D412yes—
270C22×C4×C31C2×D411yescharacteristic
271C22×C4×C31C2411yescharacteristic
272Q16×C31—28no—
273Q16×C31—28no—
274Q16×C31—44no—
275SD16×C31—28no—
276SD16×C31—28no—
277SD16×C31—44no—
278M16×C31—28no—
279C2×C8×C31—21no—
280C2×C8×C31—21no—
281C2×C8×C31—21no—
282C2×C8×C31—21no—
283C2×C8×C31—21no—
284C2×C8×C31—21no—
285C2×C8×C31—21no—
286C2×C8×C31—21no—
287C2×C8×C31—21no—
288C2×C8×C31—21no—
289C2×C8×C31C2×D412yes—
290C2×C8×C31C2×D412yes—
291C4⋊C4×C31—24no—
292C4⋊C4×C31—24no—
293C4⋊C4×C31—24no—
294C4⋊C4×C31—24no—
295C4⋊C4×C31—24no—
296C4⋊C4×C31—22no—
297C4⋊C4×C31—21no—
298C4⋊C4×C31—21no—
299C4⋊C4×C31—21no—
300C4⋊C4×C31—21no—
301C4⋊C4×C31—21no—
302C4⋊C4×C31—42no—
303C4⋊C4×C31C2×D412yes—
304C22⋊C4×C31—24no—
305C22⋊C4×C31—24no—
306C22⋊C4×C31—22no—
307C22⋊C4×C31—22no—
308C22⋊C4×C31—42no—
309C22⋊C4×C31—42no—
310C22⋊C4×C31—42no—
311C22⋊C4×C31—81no—
312C22⋊C4×C31—81no—
313C42×C31—24no—
314C42×C31—21no—
315C42×C31—21no—
316#23868C3111yesmaximal, characteristic, direct product factor, Sylow
317C23×C31—21no—
318C23×C31—21no—
319C23×C31—21no—
320C23×C31—21no—
321C23×C31—21no—
322C23×C31—21no—
323C23×C31—21no—
324C23×C31—21no—
325C23×C31—21no—
326C23×C31—21no—
327C23×C31—21no—
328C23×C31—21no—
329C23×C31—22no—
330C23×C31—41no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—41no—
334C23×C31—41no—
335C23×C31—41no—
336C23×C31#12012yes—
337C23×C31#13712yescomplemented
338C23×C31C22×D411yescharacteristic
339Q8×C31—22no—
340Q8×C31—22no—
341Q8×C31—22no—
342Q8×C31—22no—
343Q8×C31—22no—
344Q8×C31—22no—
345Q8×C31—22no—
346Q8×C31—22no—
347Q8×C31—22no—
348Q8×C31—48no—
349Q8×C31—48no—
350Q8×C31—41no—
351Q8×C31—41no—
352Q8×C31—41no—
353Q8×C31—41no—
354Q8×C31—41no—
355Q8×C31—41no—
356Q8×C31#12014yes—
357D4×C31—28no—
358D4×C31—22no—
359D4×C31—22no—
360D4×C31—48no—
361D4×C31—41no—
362D4×C31—41no—
363D4×C31—84no—
364C2×C4×C31—21no—
365C2×C4×C31—22no—
366C2×C4×C31—21no—
367C2×C4×C31—21no—
368C2×C4×C31—22no—
369C2×C4×C31—22no—
370C2×C4×C31—21no—
371C2×C4×C31—22no—
372C2×C4×C31—22no—
373C2×C4×C31—22no—
374C2×C4×C31—22no—
375C2×C4×C31—21no—
376C2×C4×C31—22no—
377C2×C4×C31—22no—
378C2×C4×C31—22no—
379C2×C4×C31—21no—
380C2×C4×C31—21no—
381C2×C4×C31—22no—
382C2×C4×C31—21no—
383C2×C4×C31—21no—
384C2×C4×C31—21no—
385C2×C4×C31—48no—
386C2×C4×C31—48no—
387C2×C4×C31—48no—
388C2×C4×C31—41no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—41no—
392C2×C4×C31—41no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31—41no—
397C2×C4×C31—41no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402C2×C4×C31—41no—
403C2×C4×C31—41no—
404C2×C4×C31—41no—
405C2×C4×C31—41no—
406C2×C4×C31#12012yes—
407C2×C4×C31#13712yescomplemented
408C2×C4×C31C22×D411yescharacteristic
409C2×C4×C31C22×D411yescharacteristic
410C2×C4×C31C22×D411yescharacteristic
411C2×C4×C31C22×D411yescharacteristic
412C2×C4×C31H(5,𝔽2)11yescharacteristic
413C2×C4×C31H(5,𝔽2)11yescharacteristic
414C8×C31—22no—
415C8×C31—22no—
416C8×C31—41no—
417C8×C31—41no—
418C22×#137C2×C3111yescharacteristic, complemented
419C2×D4×Q8C2×C3111yescharacteristic, complemented
420C2×#452C2×C3111yescharacteristic, complemented
421C2×#451C2×C3111yescharacteristic, complemented
422C2×#448C2×C3111yescharacteristic, complemented
423#2407C2×C3111yescharacteristic
424#2016C2×C3111yescharacteristic, complemented
425#2013C2×C3111yescharacteristic, complemented
426#2001C2×C3111yescharacteristic, complemented
427#2000C2×C3111yescharacteristic, complemented
428#1894C2×C3111yescharacteristic, complemented
429#1880C2×C3111yescharacteristic, complemented
430#1878C2×C3111yescharacteristic, complemented
431#1870C2×C3111yescharacteristic, complemented
432#1787C2×C3111yescharacteristic, complemented
433C22×C31—22no—
434C22×C31—22no—
435C22×C31—22no—
436C22×C31—22no—
437C22×C31—22no—
438C22×C31—22no—
439C22×C31—41no—
440C22×C31—41no—
441C22×C31—41no—
442C22×C31—41no—
443C22×C31—41no—
444C22×C31—41no—
445C22×C31—41no—
446C22×C31—41no—
447C22×C31—42no—
448C22×C31—42no—
449C22×C31—42no—
450C22×C31—81no—
451C22×C31—81no—
452C22×C31—81no—
453C22×C31—81no—
454C22×C31C2×#12011yescharacteristic
455C22×C31D4211yescharacteristic
456C22×C31D4211yescharacteristic
457C22×C31C2×#13711yescharacteristic
458C22×C31C2×#13711yescharacteristic
459C22×C31#57711yescharacteristic
460C22×C31#57811yescharacteristic
461C4×C31—22no—
462C4×C31—24no—
463C4×C31—22no—
464C4×C31—41no—
465C4×C31—42no—
466C4×C31—42no—
467C4×C31—42no—
468C4×C31—41no—
469C4×C31—42no—
470C4×C31—81no—
471C4×C31—81no—
472C4×C31C2×#12011yescharacteristic
473C4×C31#53411yescharacteristic
474C4×C31D4211yescharacteristic
475C4×C31D4211yescharacteristic
476C22×#41C22×C3111yescharacteristic
477C23×Q8C22×C3111yescharacteristic
478C23×Q8C22×C3111yescharacteristic
479C2×#137—24no—
480C2×#137—24no—
481C2×#137—24no—
482C22×Q16C22×C3111yescharacteristic
483C22×Q16C22×C3111yescharacteristic
484C22×Q16C22×C3111yescharacteristic
485C22×SD16C22×C3111yescharacteristic
486C22×SD16C22×C3111yescharacteristic
487C22×SD16C22×C3111yescharacteristic
488C22×M16C22×C3111yescharacteristic
489D4×Q8—24no—
490D4×Q8—24no—
491C2×C4⋊Q8—21no—
492C2×C4⋊Q8C22×C3111yescharacteristic
493C2×C22⋊Q8—21no—
494C2×C22⋊Q8—21no—
495C2×C22⋊Q8C22×C3111yescharacteristic
496C2×C22⋊Q8C22×C3111yescharacteristic
497C2×C22⋊Q8C22×C3111yescharacteristic
498C2×#121C22×C3111yescharacteristic
499C2×C4×Q8C22×C3111yescharacteristic
500C2×C4×D4—21no—
501C2×C4×D4C22×C3111yescharacteristic
502#452—24no—
503#451—24no—
504#448—24no—
505C2×#103C22×C3111yescharacteristic
506C2×#103C22×C3111yescharacteristic
507C2×#103C22×C3111yescharacteristic
508C2×#103C22×C3111yescharacteristic
509C2×#103C22×C3111yescharacteristic
510C2×#103C22×C3111yescharacteristic
511C2×#103C22×C3111yescharacteristic
512C2×#102C22×C3111yescharacteristic
513C2×C22⋊C8C22×C3111yescharacteristic
514C2×C22⋊C8C22×C3111yescharacteristic
515C2×C22⋊C8C22×C3111yescharacteristic
516#394—21no—
517#392—21no—
518#391C22×C3111yescharacteristic
519#390C22×C3111yescharacteristic
520#386—21no—
521#385—21no—
522#380C22×C3111yescharacteristic
523#340C22×C3111yescharacteristic
524#340C22×C3111yescharacteristic
525#336C22×C3111yescharacteristic
526#336C22×C3111yescharacteristic
527C2×C31—42no—
528C2×C31—42no—
529C2×C31—82no—
530C2×C31#240311yescharacteristic
531C2×C31#300411yescharacteristic
532C2×C31#301311yescharacteristic
533C2×C31#326611yescharacteristic
534C2×C31#327011yescharacteristic
535C2×C31#327611yescharacteristic
536C2×C31#327811yescharacteristic
537C2×#41—22no—
538C2×#41—22no—
539C2×#41—22no—
540C2×#41—22no—
541C2×#41—41no—
542C2×#41—41no—
543C22×Q8—22no—
544C22×Q8—22no—
545C22×Q8—21no—
546C22×Q8—21no—
547C22×Q8—22no—
548C22×Q8—22no—
549C22×Q8—22no—
550C22×Q8—22no—
551C22×Q8—22no—
552C22×Q8—41no—
553C22×Q8—41no—
554C22×Q8—41no—
555C22×Q8—41no—
556C22×Q8D4×C3114yescomplemented
557C22×Q8C23×C3111yescharacteristic
558C22×Q8C23×C3111yescharacteristic
559C22×Q8C23×C3111yescharacteristic
560C22×Q8C23×C3111yescharacteristic
561C22×D4—21no—
562C22×D4—21no—
563C22×D4D4×C3111yescharacteristic
564C22×D4C23×C3111yescharacteristic
565C23×C4—21no—
566C23×C4—21no—
567C23×C4—21no—
568C23×C4C23×C3111yescharacteristic
569C23×C4C23×C3111yescharacteristic
570#137—232no—
571C2×Q16—22no—
572C2×Q16—22no—
573C2×Q16—22no—
574C2×Q16—22no—
575C2×Q16—22no—
576C2×Q16—22no—
577C2×Q16—22no—
578C2×Q16—41no—
579C2×Q16D4×C3114yescomplemented
580C2×SD16—22no—
581C2×SD16—22no—
582C2×SD16—22no—
583C2×SD16—22no—
584C2×SD16—22no—
585C2×SD16—22no—
586C2×SD16—22no—
587C2×SD16—41no—
588C2×SD16D4×C3114yescomplemented
589C2×M16—22no—
590C2×M16—22no—
591C2×M16—22no—
592C22×C8C23×C3111yescharacteristic
593C22×C8C23×C3111yescharacteristic
594C22×C8C23×C3111yescharacteristic
595C22×C8C23×C3111yescharacteristic
596C4⋊Q8—28no—
597C4⋊Q8—22no—
598C4⋊Q8—22no—
599C22⋊Q8—28no—
600C22⋊Q8—28no—
601C22⋊Q8—22no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—41no—
606C22⋊Q8D4×C3114yescomplemented
607#121—22no—
608#121—41no—
609C4×Q8—22no—
610C4×Q8—22no—
611C4×D4—28no—
612C4×D4—22no—
613C4×D4—22no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4D4×C3111yescharacteristic
621C2×C4⋊C4C23×C3111yescharacteristic
622C2×C4⋊C4C23×C3111yescharacteristic
623C2×C4⋊C4C23×C3111yescharacteristic
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4D4×C3111yescharacteristic
632C2×C22⋊C4D4×C3111yescharacteristic
633C2×C42—21no—
634C2×C42C23×C3111yescharacteristic
635#103—22no—
636#103—22no—
637#103—22no—
638#103—22no—
639#103—22no—
640#103—41no—
641#103—41no—
642#102—22no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645C22⋊C8—22no—
646#95—21no—
647#95—21no—
648#95—21no—
649C31#2386811yescharacteristic, direct product factor, Sylow
650C24—21no—
651C24C2×D4×C3111yescharacteristic
652C24C2×D4×C3111yescharacteristic
653#41—28no—
654#41—44no—
655#41—44no—
656#41—44no—
657C2×Q8—24no—
658C2×Q8—24no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—28no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—42no—
679C2×Q8—42no—
680C2×Q8—42no—
681C2×Q8—42no—
682C2×Q8—44no—
683C2×Q8—44no—
684C2×Q8—44no—
685C2×Q8—44no—
686C2×Q8—44no—
687C2×Q8—44no—
688C2×Q8—44no—
689C2×Q8C2×D4×C3112yes—
690C2×Q8C2×D4×C3112yes—
691C2×Q8C2×D4×C3112yes—
692C2×Q8C2×D4×C3112yes—
693C2×Q8C2×D4×C3112yes—
694C2×Q8C2×D4×C3112yes—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—42no—
707C2×D4—42no—
708C2×D4—81no—
709C2×D4C2×D4×C3112yes—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4C2×D4×C3111yescharacteristic
737C22×C4C2×D4×C3111yescharacteristic
738C22×C4C2×D4×C3111yescharacteristic
739C22×C4C2×D4×C3112yes—
740C22×C4C2×D4×C3112yes—
741C22×C4C2×D4×C3111yescharacteristic
742C22×C4C24×C3111yescharacteristic
743Q16—28no—
744Q16—28no—
745Q16—44no—
746SD16—28no—
747SD16—28no—
748SD16—44no—
749M16—28no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8C2×D4×C3112yes—
761C2×C8C2×D4×C3112yes—
762C4⋊C4—24no—
763C4⋊C4—24no—
764C4⋊C4—24no—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—22no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—42no—
774C4⋊C4C2×D4×C3112yes—
775C22⋊C4—24no—
776C22⋊C4—24no—
777C22⋊C4—22no—
778C22⋊C4—22no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C22⋊C4—81no—
783C22⋊C4—81no—
784C42—24no—
785C42—21no—
786C42—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—22no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23C31×#12012yes—
807C23C31×#13712yescomplemented
808C23C22×D4×C3111yescharacteristic
809Q8—22no—
810Q8—22no—
811Q8—22no—
812Q8—22no—
813Q8—22no—
814Q8—22no—
815Q8—22no—
816Q8—22no—
817Q8—22no—
818Q8—48no—
819Q8—48no—
820Q8—41no—
821Q8—41no—
822Q8—41no—
823Q8—41no—
824Q8—41no—
825Q8—41no—
826Q8C31×#12014yes—
827D4—28no—
828D4—22no—
829D4—22no—
830D4—48no—
831D4—41no—
832D4—41no—
833D4—84no—
834C2×C4—21no—
835C2×C4—22no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—48no—
856C2×C4—48no—
857C2×C4—48no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4C31×#12012yes—
877C2×C4C31×#13712yescomplemented
878C2×C4C22×D4×C3111yescharacteristic
879C2×C4C22×D4×C3111yescharacteristic
880C2×C4C22×D4×C3111yescharacteristic
881C2×C4C22×D4×C3111yescharacteristic
882C2×C4C31×H(5,𝔽2)11yescharacteristic
883C2×C4C31×H(5,𝔽2)11yescharacteristic
884C8—22no—
885C8—22no—
886C8—41no—
887C8—41no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22C2×C31×#12011yescharacteristic
910C22D42×C3111yescharacteristic
911C22D42×C3111yescharacteristic
912C22C2×C31×#13711yescharacteristic
913C22C2×C31×#13711yescharacteristic
914C22C31×#57711yescharacteristic
915C22C31×#57811yescharacteristic
916C4—22no—
917C4—24no—
918C4—22no—
919C4—41no—
920C4—42no—
921C4—42no—
922C4—42no—
923C4—41no—
924C4—42no—
925C4—81no—
926C4—81no—
927C4C2×C31×#12011yescharacteristic
928C4C31×#53411yescharacteristic
929C4D42×C3111yescharacteristic
930C4D42×C3111yescharacteristic
931C2—42no—
932C2—42no—
933C2—82no—
934C2C31×#240311yescharacteristic
935C2C31×#300411yescharacteristic
936C2C31×#301311yescharacteristic
937C2C31×#326611yescharacteristic
938C2C31×#327011yescharacteristic
939C2C31×#327611yescharacteristic
940C2C31×#327811yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2407C2
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. C22×C31×#137C2semidirect
2. C2×D4×Q8×C31C2semidirect
3. C2×C31×#452C2semidirect
4. C2×C31×#451C2semidirect
5. C2×C31×#448C2semidirect
7. C31×#2016C2semidirect
8. C31×#2013C2semidirect
9. C31×#2001C2semidirect
10. C31×#2000C2semidirect
11. C31×#1894C2semidirect
12. C31×#1880C2semidirect
13. C31×#1878C2semidirect
14. C31×#1870C2semidirect
15. C31×#1787C2semidirect
86. C22×Q8×C31D4semidirect
109. C2×Q16×C31D4semidirect
118. C2×SD16×C31D4semidirect
136. C31×C22⋊Q8D4semidirect
316. #23868C31direct (N × H)
337. C23×C31#137semidirect
407. C2×C4×C31#137semidirect
418. C22×#137C2×C31semidirect
419. C2×D4×Q8C2×C31semidirect
420. C2×#452C2×C31semidirect
421. C2×#451C2×C31semidirect
422. C2×#448C2×C31semidirect
424. #2016C2×C31semidirect
425. #2013C2×C31semidirect
426. #2001C2×C31semidirect
427. #2000C2×C31semidirect
428. #1894C2×C31semidirect
429. #1880C2×C31semidirect
430. #1878C2×C31semidirect
431. #1870C2×C31semidirect
432. #1787C2×C31semidirect
556. C22×Q8D4×C31semidirect
579. C2×Q16D4×C31semidirect
588. C2×SD16D4×C31semidirect
606. C22⋊Q8D4×C31semidirect
649. C31#23868direct (N × H)
807. C23C31×#137semidirect
877. C2×C4C31×#137semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1372
C2×D4×Q8×C312
C2×C31×#4522
C2×C31×#4512
C2×C31×#4482
C31×#24072
C31×#20162
C31×#20132
C31×#20012
C31×#20002
C31×#18942
C31×#18802
C31×#18782
C31×#18702
C31×#17872
#2386831