Finite Group Databasebeta

← C31×#23857 #21480616

Subgroups — C31×#23857 #21480616

Order 7936.

1852 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#135C211yesmaximal, characteristic, complemented
2C2×C31×#550C211yesmaximal, characteristic, complemented
3C2×C31×#452C211yesmaximal, characteristic, complemented
4C2×C31×#449C211yesmaximal, characteristic, complemented
5C2×C31×#449C211yesmaximal, characteristic, complemented
6C31×#2407C211yesmaximal, characteristic, complemented
7C31×#2014C211yesmaximal, characteristic, complemented
8C31×#2011C211yesmaximal, characteristic, complemented
9C31×#2000C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1893C211yesmaximal, characteristic, complemented
12C31×#1880C211yesmaximal, characteristic, complemented
13C31×#1878C211yesmaximal, characteristic, complemented
14C31×#1869C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C22×#41×C31C2211yescharacteristic
19C2×C31×#135—24no—
20C2×C31×#135—24no—
21C2×C31×#135—24no—
22C22×Q16×C31C2211yescharacteristic
23C22×SD16×C31C2211yescharacteristic
24C22×SD16×C31C2211yescharacteristic
25C22×SD16×C31C2211yescharacteristic
26C22×D8×C31C2211yescharacteristic
27C22×D8×C31C2211yescharacteristic
28C23×C8×C31C2211yescharacteristic
29C31×#550—24no—
30C31×#550—24no—
31C2×C31×#127—21no—
32C2×C31×#127C2211yescharacteristic
33C2×C31×C22⋊Q8C2211yescharacteristic
34C2×C31×#121—21no—
35C2×C31×#121—21no—
36C2×C31×#121C2211yescharacteristic
37C2×C31×#121C2211yescharacteristic
38C2×C31×#121C2211yescharacteristic
39C2×C4×Q8×C31C2211yescharacteristic
40C2×C4×D4×C31—21no—
41C2×C4×D4×C31C2211yescharacteristic
42C31×#452—24no—
43C31×#449—24no—
44C31×#449—24no—
45C2×C31×#103C2211yescharacteristic
46C2×C31×#103C2211yescharacteristic
47C2×C31×#103C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C2×C31×#102C2211yescharacteristic
50C2×C31×#102C2211yescharacteristic
51C2×C31×#102C2211yescharacteristic
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—22no—
72C2×#41×C31—22no—
73C2×#41×C31—22no—
74C2×#41×C31—22no—
75C2×#41×C31—22no—
76C2×#41×C31—22no—
77C2×#41×C31—22no—
78C2×#41×C31—41no—
79C2×#41×C31—41no—
80C2×#41×C31—41no—
81C2×#41×C31—41no—
82C2×#41×C31—41no—
83C2×#41×C31—41no—
84C2×#41×C31D414yescomplemented
85C22×Q8×C31C2311yescharacteristic
86C22×Q8×C31C2311yescharacteristic
87C22×D4×C31—21no—
88C22×D4×C31—21no—
89C22×D4×C31—21no—
90C22×D4×C31—21no—
91C22×D4×C31—21no—
92C22×D4×C31—21no—
93C22×D4×C31—21no—
94C22×D4×C31—21no—
95C22×D4×C31D411yescharacteristic
96C22×D4×C31C2311yescharacteristic
97C22×D4×C31C2311yescharacteristic
98C22×D4×C31C2311yescharacteristic
99C23×C4×C31—21no—
100C23×C4×C31—21no—
101C23×C4×C31—21no—
102C23×C4×C31C2311yescharacteristic
103C23×C4×C31C2311yescharacteristic
104C31×#135—232no—
105C2×Q16×C31—22no—
106C2×Q16×C31—22no—
107C2×Q16×C31D414yescomplemented
108C2×SD16×C31—22no—
109C2×SD16×C31—22no—
110C2×SD16×C31—22no—
111C2×SD16×C31—22no—
112C2×SD16×C31—22no—
113C2×SD16×C31—22no—
114C2×SD16×C31—22no—
115C2×SD16×C31—41no—
116C2×SD16×C31D414yescomplemented
117C2×D8×C31—22no—
118C2×D8×C31—22no—
119C2×D8×C31—22no—
120C2×D8×C31—22no—
121C2×D8×C31—22no—
122C2×D8×C31—41no—
123C22×C8×C31—22no—
124C22×C8×C31—22no—
125C22×C8×C31—22no—
126C22×C8×C31C2311yescharacteristic
127C22×C8×C31C2311yescharacteristic
128C22×C8×C31C2311yescharacteristic
129C22×C8×C31C2311yescharacteristic
130C31×#127—28no—
131C31×#127—22no—
132C31×#127—22no—
133C31×C22⋊Q8—22no—
134C31×C22⋊Q8—41no—
135C31×#121—28no—
136C31×#121—28no—
137C31×#121—22no—
138C31×#121—22no—
139C31×#121—22no—
140C31×#121—22no—
141C31×#121—41no—
142C31×#121D414yescomplemented
143C4×Q8×C31—22no—
144C4×Q8×C31—22no—
145C4×D4×C31—28no—
146C4×D4×C31—22no—
147C4×D4×C31—22no—
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×#102—22no—
169C31×#102—22no—
170C31×#102—22no—
171C31×#102—41no—
172C31×#102—41no—
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×C31—21no—
181C24×C31—21no—
182C24×C31C2×D411yescharacteristic
183C24×C31C2×D411yescharacteristic
184#41×C31—28no—
185#41×C31—28no—
186#41×C31—44no—
187#41×C31—44no—
188#41×C31—44no—
189#41×C31—44no—
190#41×C31—44no—
191#41×C31—44no—
192#41×C31—44no—
193#41×C31—44no—
194#41×C31—44no—
195#41×C31—44no—
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×C31C2×D412yes—
205C2×Q8×C31C2×D412yes—
206C2×Q8×C31C2×D412yes—
207C2×Q8×C31C2×D412yes—
208C2×D4×C31—24no—
209C2×D4×C31—24no—
210C2×D4×C31—22no—
211C2×D4×C31—24no—
212C2×D4×C31—24no—
213C2×D4×C31—24no—
214C2×D4×C31—24no—
215C2×D4×C31—22no—
216C2×D4×C31—21no—
217C2×D4×C31—21no—
218C2×D4×C31—21no—
219C2×D4×C31—21no—
220C2×D4×C31—21no—
221C2×D4×C31—21no—
222C2×D4×C31—21no—
223C2×D4×C31—21no—
224C2×D4×C31—21no—
225C2×D4×C31—21no—
226C2×D4×C31—21no—
227C2×D4×C31—21no—
228C2×D4×C31—21no—
229C2×D4×C31—21no—
230C2×D4×C31—21no—
231C2×D4×C31—41no—
232C2×D4×C31—42no—
233C2×D4×C31—42no—
234C2×D4×C31—42no—
235C2×D4×C31—42no—
236C2×D4×C31—42no—
237C2×D4×C31—42no—
238C2×D4×C31—42no—
239C2×D4×C31—42no—
240C2×D4×C31—42no—
241C2×D4×C31—42no—
242C2×D4×C31—42no—
243C2×D4×C31—81no—
244C2×D4×C31—81no—
245C2×D4×C31—81no—
246C2×D4×C31—81no—
247C2×D4×C31—81no—
248C2×D4×C31—81no—
249C2×D4×C31—81no—
250C2×D4×C31C2×D412yes—
251C2×D4×C31C2×D412yes—
252C2×D4×C31C2×D412yes—
253C22×C4×C31—21no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
256C22×C4×C31—21no—
257C22×C4×C31—21no—
258C22×C4×C31—24no—
259C22×C4×C31—21no—
260C22×C4×C31—21no—
261C22×C4×C31—24no—
262C22×C4×C31—21no—
263C22×C4×C31—21no—
264C22×C4×C31—21no—
265C22×C4×C31—21no—
266C22×C4×C31—21no—
267C22×C4×C31—21no—
268C22×C4×C31—21no—
269C22×C4×C31—21no—
270C22×C4×C31—42no—
271C22×C4×C31—42no—
272C22×C4×C31—42no—
273C22×C4×C31—42no—
274C22×C4×C31—42no—
275C22×C4×C31—42no—
276C22×C4×C31—42no—
277C22×C4×C31C2×D411yescharacteristic
278C22×C4×C31C2×D411yescharacteristic
279C22×C4×C31C2×D411yescharacteristic
280C22×C4×C31C2×D412yes—
281C22×C4×C31C2×D412yes—
282C22×C4×C31C2×D411yescharacteristic
283C22×C4×C31C2411yescharacteristic
284Q16×C31—28no—
285SD16×C31—28no—
286SD16×C31—28no—
287SD16×C31—44no—
288D8×C31—28no—
289D8×C31—44no—
290C2×C8×C31—28no—
291C2×C8×C31—21no—
292C2×C8×C31—21no—
293C2×C8×C31—21no—
294C2×C8×C31—21no—
295C2×C8×C31—21no—
296C2×C8×C31—21no—
297C2×C8×C31—21no—
298C2×C8×C31—21no—
299C2×C8×C31—21no—
300C2×C8×C31—21no—
301C2×C8×C31C2×D412yes—
302C2×C8×C31C2×D412yes—
303C4⋊C4×C31—24no—
304C4⋊C4×C31—22no—
305C4⋊C4×C31—21no—
306C4⋊C4×C31—21no—
307C4⋊C4×C31—21no—
308C4⋊C4×C31—21no—
309C4⋊C4×C31—21no—
310C4⋊C4×C31—42no—
311C4⋊C4×C31C2×D412yes—
312C22⋊C4×C31—24no—
313C22⋊C4×C31—22no—
314C22⋊C4×C31—24no—
315C22⋊C4×C31—22no—
316C22⋊C4×C31—42no—
317C22⋊C4×C31—42no—
318C22⋊C4×C31—42no—
319C22⋊C4×C31—81no—
320C22⋊C4×C31—81no—
321C42×C31—24no—
322C42×C31—21no—
323C42×C31—21no—
324#23857C3111yesmaximal, characteristic, direct product factor, Sylow
325C23×C31—21no—
326C23×C31—21no—
327C23×C31—21no—
328C23×C31—21no—
329C23×C31—21no—
330C23×C31—21no—
331C23×C31—21no—
332C23×C31—22no—
333C23×C31—22no—
334C23×C31—21no—
335C23×C31—22no—
336C23×C31—21no—
337C23×C31—21no—
338C23×C31—21no—
339C23×C31—21no—
340C23×C31—21no—
341C23×C31—41no—
342C23×C31—41no—
343C23×C31—41no—
344C23×C31—41no—
345C23×C31—41no—
346C23×C31—41no—
347C23×C31—41no—
348C23×C31—41no—
349C23×C31—41no—
350C23×C31—41no—
351C23×C31—41no—
352C23×C31—41no—
353C23×C31—41no—
354C23×C31—41no—
355C23×C31—41no—
356C23×C31—41no—
357C23×C31—41no—
358C23×C31—41no—
359C23×C31#12012yes—
360C23×C31C22×D411yescharacteristic
361Q8×C31—22no—
362Q8×C31—22no—
363Q8×C31—22no—
364Q8×C31—22no—
365Q8×C31—22no—
366Q8×C31—41no—
367Q8×C31—41no—
368Q8×C31#12014yes—
369D4×C31—22no—
370D4×C31—22no—
371D4×C31—22no—
372D4×C31—22no—
373D4×C31—22no—
374D4×C31—22no—
375D4×C31—44no—
376D4×C31—48no—
377D4×C31—48no—
378D4×C31—48no—
379D4×C31—48no—
380D4×C31—41no—
381D4×C31—41no—
382D4×C31—41no—
383D4×C31—41no—
384D4×C31—41no—
385D4×C31—41no—
386D4×C31—84no—
387D4×C31—84no—
388D4×C31—84no—
389D4×C31—84no—
390C2×C4×C31—21no—
391C2×C4×C31—22no—
392C2×C4×C31—21no—
393C2×C4×C31—21no—
394C2×C4×C31—22no—
395C2×C4×C31—22no—
396C2×C4×C31—21no—
397C2×C4×C31—22no—
398C2×C4×C31—22no—
399C2×C4×C31—22no—
400C2×C4×C31—22no—
401C2×C4×C31—21no—
402C2×C4×C31—22no—
403C2×C4×C31—21no—
404C2×C4×C31—21no—
405C2×C4×C31—22no—
406C2×C4×C31—21no—
407C2×C4×C31—21no—
408C2×C4×C31—21no—
409C2×C4×C31—48no—
410C2×C4×C31—48no—
411C2×C4×C31—48no—
412C2×C4×C31—41no—
413C2×C4×C31—41no—
414C2×C4×C31—41no—
415C2×C4×C31—41no—
416C2×C4×C31—41no—
417C2×C4×C31—41no—
418C2×C4×C31—41no—
419C2×C4×C31—41no—
420C2×C4×C31—41no—
421C2×C4×C31—41no—
422C2×C4×C31—41no—
423C2×C4×C31—41no—
424C2×C4×C31—41no—
425C2×C4×C31—41no—
426C2×C4×C31#12012yes—
427C2×C4×C31#13512yescomplemented
428C2×C4×C31C22×D411yescharacteristic
429C2×C4×C31C22×D411yescharacteristic
430C2×C4×C31C22×D411yescharacteristic
431C2×C4×C31C22×D411yescharacteristic
432C2×C4×C31H(5,𝔽2)11yescharacteristic
433C2×C4×C31H(5,𝔽2)11yescharacteristic
434C8×C31—22no—
435C8×C31—22no—
436C8×C31—41no—
437C8×C31—41no—
438C22×#135C2×C3111yescharacteristic, complemented
439C2×#550C2×C3111yescharacteristic, complemented
440C2×#452C2×C3111yescharacteristic, complemented
441C2×#449C2×C3111yescharacteristic, complemented
442C2×#449C2×C3111yescharacteristic, complemented
443#2407C2×C3111yescharacteristic, complemented
444#2014C2×C3111yescharacteristic, complemented
445#2011C2×C3111yescharacteristic, complemented
446#2000C2×C3111yescharacteristic, complemented
447#1999C2×C3111yescharacteristic, complemented
448#1893C2×C3111yescharacteristic, complemented
449#1880C2×C3111yescharacteristic, complemented
450#1878C2×C3111yescharacteristic, complemented
451#1869C2×C3111yescharacteristic, complemented
452#1788C2×C3111yescharacteristic, complemented
453C22×C31—22no—
454C22×C31—22no—
455C22×C31—22no—
456C22×C31—41no—
457C22×C31—41no—
458C22×C31—41no—
459C22×C31—41no—
460C22×C31—42no—
461C22×C31—42no—
462C22×C31—42no—
463C22×C31—41no—
464C22×C31—41no—
465C22×C31—42no—
466C22×C31—42no—
467C22×C31—41no—
468C22×C31—42no—
469C22×C31—42no—
470C22×C31—41no—
471C22×C31—42no—
472C22×C31—41no—
473C22×C31—41no—
474C22×C31—42no—
475C22×C31—41no—
476C22×C31—81no—
477C22×C31—81no—
478C22×C31—81no—
479C22×C31—81no—
480C22×C31—81no—
481C22×C31—81no—
482C22×C31—81no—
483C22×C31—81no—
484C22×C31—81no—
485C22×C31—81no—
486C22×C31—81no—
487C22×C31—81no—
488C22×C31C2×#12011yescharacteristic
489C22×C31D4211yescharacteristic
490C22×C31D4211yescharacteristic
491C22×C31C2×#13511yescharacteristic
492C22×C31#57511yescharacteristic
493C22×C31#57611yescharacteristic
494C22×C31#57711yescharacteristic
495C4×C31—22no—
496C4×C31—24no—
497C4×C31—22no—
498C4×C31—41no—
499C4×C31—42no—
500C4×C31—41no—
501C4×C31—42no—
502C4×C31—81no—
503C4×C31—81no—
504C4×C31C2×#12011yescharacteristic
505C4×C31#53411yescharacteristic
506C4×C31D4211yescharacteristic
507C4×C31D4211yescharacteristic
508C22×#41C22×C3111yescharacteristic
509C22×#41C22×C3111yescharacteristic
510C22×#41C22×C3111yescharacteristic
511C2×#135—24no—
512C2×#135—24no—
513C2×#135—24no—
514C22×Q16C22×C3111yescharacteristic
515C22×SD16C22×C3111yescharacteristic
516C22×SD16C22×C3111yescharacteristic
517C22×SD16C22×C3111yescharacteristic
518C22×D8C22×C3111yescharacteristic
519C22×D8C22×C3111yescharacteristic
520C23×C8C22×C3111yescharacteristic
521#550—24no—
522#550—24no—
523C2×#127—21no—
524C2×#127C22×C3111yescharacteristic
525C2×C22⋊Q8C22×C3111yescharacteristic
526C2×#121—21no—
527C2×#121—21no—
528C2×#121C22×C3111yescharacteristic
529C2×#121C22×C3111yescharacteristic
530C2×#121C22×C3111yescharacteristic
531C2×C4×Q8C22×C3111yescharacteristic
532C2×C4×D4—21no—
533C2×C4×D4C22×C3111yescharacteristic
534#452—24no—
535#449—24no—
536#449—24no—
537C2×#103C22×C3111yescharacteristic
538C2×#103C22×C3111yescharacteristic
539C2×#103C22×C3111yescharacteristic
540C2×#102C22×C3111yescharacteristic
541C2×#102C22×C3111yescharacteristic
542C2×#102C22×C3111yescharacteristic
543C2×#102C22×C3111yescharacteristic
544C2×#102C22×C3111yescharacteristic
545C2×C22⋊C8C22×C3111yescharacteristic
546C2×C22⋊C8C22×C3111yescharacteristic
547C2×C22⋊C8C22×C3111yescharacteristic
548#394—21no—
549#392—21no—
550#391C22×C3111yescharacteristic
551#390C22×C3111yescharacteristic
552#386—21no—
553#385—21no—
554#380C22×C3111yescharacteristic
555#340C22×C3111yescharacteristic
556#340C22×C3111yescharacteristic
557#336C22×C3111yescharacteristic
558#336C22×C3111yescharacteristic
559C2×C31—42no—
560C2×C31—81no—
561C2×C31—82no—
562C2×C31—82no—
563C2×C31—82no—
564C2×C31#240311yescharacteristic
565C2×C31#300211yescharacteristic
566C2×C31#301211yescharacteristic
567C2×C31#326811yescharacteristic
568C2×C31#327111yescharacteristic
569C2×C31#328411yescharacteristic
570C2×C31#328711yescharacteristic
571C2×#41—22no—
572C2×#41—22no—
573C2×#41—22no—
574C2×#41—22no—
575C2×#41—22no—
576C2×#41—22no—
577C2×#41—22no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—41no—
583C2×#41—41no—
584C2×#41—41no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41D4×C3114yescomplemented
589C22×Q8C23×C3111yescharacteristic
590C22×Q8C23×C3111yescharacteristic
591C22×D4—21no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4D4×C3111yescharacteristic
600C22×D4C23×C3111yescharacteristic
601C22×D4C23×C3111yescharacteristic
602C22×D4C23×C3111yescharacteristic
603C23×C4—21no—
604C23×C4—21no—
605C23×C4—21no—
606C23×C4C23×C3111yescharacteristic
607C23×C4C23×C3111yescharacteristic
608#135—232no—
609C2×Q16—22no—
610C2×Q16—22no—
611C2×Q16D4×C3114yescomplemented
612C2×SD16—22no—
613C2×SD16—22no—
614C2×SD16—22no—
615C2×SD16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—41no—
620C2×SD16D4×C3114yescomplemented
621C2×D8—22no—
622C2×D8—22no—
623C2×D8—22no—
624C2×D8—22no—
625C2×D8—22no—
626C2×D8—41no—
627C22×C8—22no—
628C22×C8—22no—
629C22×C8—22no—
630C22×C8C23×C3111yescharacteristic
631C22×C8C23×C3111yescharacteristic
632C22×C8C23×C3111yescharacteristic
633C22×C8C23×C3111yescharacteristic
634#127—28no—
635#127—22no—
636#127—22no—
637C22⋊Q8—22no—
638C22⋊Q8—41no—
639#121—28no—
640#121—28no—
641#121—22no—
642#121—22no—
643#121—22no—
644#121—22no—
645#121—41no—
646#121D4×C3114yescomplemented
647C4×Q8—22no—
648C4×Q8—22no—
649C4×D4—28no—
650C4×D4—22no—
651C4×D4—22no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4D4×C3111yescharacteristic
655C2×C4⋊C4C23×C3111yescharacteristic
656C2×C4⋊C4C23×C3111yescharacteristic
657C2×C4⋊C4C23×C3111yescharacteristic
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4D4×C3111yescharacteristic
666C2×C22⋊C4D4×C3111yescharacteristic
667C2×C42—21no—
668C2×C42C23×C3111yescharacteristic
669#103—22no—
670#103—22no—
671#103—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—41no—
676#102—41no—
677C22⋊C8—22no—
678C22⋊C8—22no—
679C22⋊C8—22no—
680#95—21no—
681#95—21no—
682#95—21no—
683C31#2385711yescharacteristic, direct product factor, Sylow
684C24—21no—
685C24—21no—
686C24—21no—
687C24C2×D4×C3111yescharacteristic
688C24C2×D4×C3111yescharacteristic
689#41—28no—
690#41—28no—
691#41—44no—
692#41—44no—
693#41—44no—
694#41—44no—
695#41—44no—
696#41—44no—
697#41—44no—
698#41—44no—
699#41—44no—
700#41—44no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8C2×D4×C3112yes—
710C2×Q8C2×D4×C3112yes—
711C2×Q8C2×D4×C3112yes—
712C2×Q8C2×D4×C3112yes—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—22no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—22no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4C2×D4×C3112yes—
756C2×D4C2×D4×C3112yes—
757C2×D4C2×D4×C3112yes—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—24no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4C2×D4×C3111yescharacteristic
783C22×C4C2×D4×C3111yescharacteristic
784C22×C4C2×D4×C3111yescharacteristic
785C22×C4C2×D4×C3112yes—
786C22×C4C2×D4×C3112yes—
787C22×C4C2×D4×C3111yescharacteristic
788C22×C4C24×C3111yescharacteristic
789Q16—28no—
790SD16—28no—
791SD16—28no—
792SD16—44no—
793D8—28no—
794D8—44no—
795C2×C8—28no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8C2×D4×C3112yes—
807C2×C8C2×D4×C3112yes—
808C4⋊C4—24no—
809C4⋊C4—22no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—42no—
816C4⋊C4C2×D4×C3112yes—
817C22⋊C4—24no—
818C22⋊C4—22no—
819C22⋊C4—24no—
820C22⋊C4—22no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—42no—
824C22⋊C4—81no—
825C22⋊C4—81no—
826C42—24no—
827C42—21no—
828C42—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—22no—
837C23—22no—
838C23—21no—
839C23—22no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23C31×#12012yes—
864C23C22×D4×C3111yescharacteristic
865Q8—22no—
866Q8—22no—
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—41no—
871Q8—41no—
872Q8C31×#12014yes—
873D4—22no—
874D4—22no—
875D4—22no—
876D4—22no—
877D4—22no—
878D4—22no—
879D4—44no—
880D4—48no—
881D4—48no—
882D4—48no—
883D4—48no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—84no—
891D4—84no—
892D4—84no—
893D4—84no—
894C2×C4—21no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—48no—
914C2×C4—48no—
915C2×C4—48no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4C31×#12012yes—
931C2×C4C31×#13512yescomplemented
932C2×C4C22×D4×C3111yescharacteristic
933C2×C4C22×D4×C3111yescharacteristic
934C2×C4C22×D4×C3111yescharacteristic
935C2×C4C22×D4×C3111yescharacteristic
936C2×C4C31×H(5,𝔽2)11yescharacteristic
937C2×C4C31×H(5,𝔽2)11yescharacteristic
938C8—22no—
939C8—22no—
940C8—41no—
941C8—41no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—41no—
953C22—41no—
954C22—42no—
955C22—42no—
956C22—41no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22C2×C31×#12011yescharacteristic
978C22D42×C3111yescharacteristic
979C22D42×C3111yescharacteristic
980C22C2×C31×#13511yescharacteristic
981C22C31×#57511yescharacteristic
982C22C31×#57611yescharacteristic
983C22C31×#57711yescharacteristic
984C4—22no—
985C4—24no—
986C4—22no—
987C4—41no—
988C4—42no—
989C4—41no—
990C4—42no—
991C4—81no—
992C4—81no—
993C4C2×C31×#12011yescharacteristic
994C4C31×#53411yescharacteristic
995C4D42×C3111yescharacteristic
996C4D42×C3111yescharacteristic
997C2—42no—
998C2—81no—
999C2—82no—
1000C2—82no—
1001C2—82no—
1002C2C31×#240311yescharacteristic
1003C2C31×#300211yescharacteristic
1004C2C31×#301211yescharacteristic
1005C2C31×#326811yescharacteristic
1006C2C31×#327111yescharacteristic
1007C2C31×#328411yescharacteristic
1008C2C31×#328711yescharacteristic
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. C22×C31×#135C2semidirect
2. C2×C31×#550C2semidirect
3. C2×C31×#452C2semidirect
4. C2×C31×#449C2semidirect
5. C2×C31×#449C2semidirect
6. C31×#2407C2semidirect
7. C31×#2014C2semidirect
8. C31×#2011C2semidirect
9. C31×#2000C2semidirect
10. C31×#1999C2semidirect
11. C31×#1893C2semidirect
12. C31×#1880C2semidirect
13. C31×#1878C2semidirect
14. C31×#1869C2semidirect
15. C31×#1788C2semidirect
84. C2×#41×C31D4semidirect
107. C2×Q16×C31D4semidirect
116. C2×SD16×C31D4semidirect
142. C31×#121D4semidirect
324. #23857C31direct (N × H)
427. C2×C4×C31#135semidirect
438. C22×#135C2×C31semidirect
439. C2×#550C2×C31semidirect
440. C2×#452C2×C31semidirect
441. C2×#449C2×C31semidirect
442. C2×#449C2×C31semidirect
443. #2407C2×C31semidirect
444. #2014C2×C31semidirect
445. #2011C2×C31semidirect
446. #2000C2×C31semidirect
447. #1999C2×C31semidirect
448. #1893C2×C31semidirect
449. #1880C2×C31semidirect
450. #1878C2×C31semidirect
451. #1869C2×C31semidirect
452. #1788C2×C31semidirect
588. C2×#41D4×C31semidirect
611. C2×Q16D4×C31semidirect
620. C2×SD16D4×C31semidirect
646. #121D4×C31semidirect
683. C31#23857direct (N × H)
931. C2×C4C31×#135semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1352
C2×C31×#5502
C2×C31×#4522
C2×C31×#4492
C31×#24072
C31×#20142
C31×#20112
C31×#20002
C31×#19992
C31×#18932
C31×#18802
C31×#18782
C31×#18692
C31×#17882
#2385731