Finite Group Databasebeta

← C31×#23975 #21480734

Subgroups — C31×#23975 #21480734

Order 7936.

1326 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#553C211yesmaximal, characteristic, complemented
2C2×C31×#449C211yesmaximal, characteristic, complemented
3C2×C31×#417C211yesmaximal, characteristic, complemented
4C31×#2407C211yesmaximal, characteristic, complemented
5C31×#2026C211yesmaximal, characteristic, complemented
6C31×#2025C211yesmaximal, characteristic, complemented
7C31×#2000C211yesmaximal, characteristic, complemented
8C31×#1999C211yesmaximal, characteristic, complemented
9C31×#1895C211yesmaximal, characteristic, complemented
10C31×#1879C211yesmaximal, characteristic, complemented
11C31×#1877C211yesmaximal, characteristic, complemented
12C31×#1875C211yesmaximal, characteristic, complemented
13C31×#1873C211yesmaximal, characteristic, complemented
14C31×#1870C211yesmaximal, characteristic, complemented
15C31×#1823C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic
20C31×#553—24no—
21C31×#553—24no—
22C2×C31×#126—21no—
23C2×C31×#125C2211yescharacteristic
24C2×C31×#123—21no—
25C2×C31×C22⋊Q8C2211yescharacteristic
26C2×C31×#121—21no—
27C2×C31×#121C2211yescharacteristic
28C2×C31×#121C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic
30C2×C4×D4×C31—21no—
31C2×C4×D4×C31C2211yescharacteristic
32C2×C4×D4×C31C2211yescharacteristic
33C2×C31×#117C2211yescharacteristic
34C22×C4⋊C4×C31C2211yescharacteristic
35C31×#449—24no—
36C31×#417—24no—
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C31×#394—21no—
49C31×#392—21no—
50C31×#391C2211yescharacteristic
51C31×#390C2211yescharacteristic
52C31×#386—21no—
53C31×#385—21no—
54C31×#380C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C2×#41×C31—22no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—41no—
68C2×#41×C31—41no—
69C22×Q8×C31C2311yescharacteristic
70C22×D4×C31—21no—
71C22×D4×C31—21no—
72C22×D4×C31—21no—
73C22×D4×C31—21no—
74C22×D4×C31D411yescharacteristic
75C22×D4×C31C2311yescharacteristic
76C22×D4×C31C2311yescharacteristic
77C23×C4×C31—21no—
78C23×C4×C31—21no—
79C23×C4×C31—21no—
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C2×SD16×C31—22no—
83C2×SD16×C31—22no—
84C2×SD16×C31—41no—
85C2×D8×C31—22no—
86C2×D8×C31—22no—
87C2×D8×C31—41no—
88C2×M16×C31—22no—
89C2×M16×C31—41no—
90C2×M16×C31—41no—
91C22×C8×C31C2311yescharacteristic
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C22×C8×C31C2311yescharacteristic
95C31×#126—28no—
96C31×#125—22no—
97C31×#125—22no—
98C31×#123—28no—
99C31×C22⋊Q8—22no—
100C31×C22⋊Q8—41no—
101C31×#121—28no—
102C31×#121—22no—
103C31×#121—22no—
104C31×#121—22no—
105C31×#121—22no—
106C31×#121—41no—
107C31×#121D414yescomplemented
108C4×D4×C31—28no—
109C4×D4×C31—22no—
110C4×D4×C31—22no—
111C4×D4×C31—22no—
112C4×D4×C31—22no—
113C31×#117—22no—
114C31×#117—22no—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31—22no—
117C2×C4⋊C4×C31—21no—
118C2×C4⋊C4×C31—21no—
119C2×C4⋊C4×C31—21no—
120C2×C4⋊C4×C31D411yescharacteristic
121C2×C4⋊C4×C31D414yescomplemented
122C2×C4⋊C4×C31C2311yescharacteristic
123C2×C4⋊C4×C31C2311yescharacteristic
124C2×C4⋊C4×C31C2311yescharacteristic
125C2×C4⋊C4×C31C2311yescharacteristic
126C2×C4⋊C4×C31C2311yescharacteristic
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31—21no—
136C2×C22⋊C4×C31D411yescharacteristic
137C2×C22⋊C4×C31D411yescharacteristic
138C2×C42×C31—21no—
139C2×C42×C31C2311yescharacteristic
140C31×#103—22no—
141C31×#103—22no—
142C31×#103—22no—
143C31×#102—22no—
144C31×#102—22no—
145C31×#102—22no—
146C31×#102—41no—
147C31×#102—41no—
148C31×C22⋊C8—22no—
149C31×C22⋊C8—41no—
150C31×C22⋊C8—41no—
151C31×#95—21no—
152C31×#95—21no—
153C31×#95—21no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31C2×D411yescharacteristic
157C24×C31C2×D411yescharacteristic
158#41×C31—28no—
159#41×C31—44no—
160#41×C31—44no—
161#41×C31—44no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31#4112yes—
168C2×D4×C31—22no—
169C2×D4×C31—24no—
170C2×D4×C31—24no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—41no—
182C2×D4×C31—41no—
183C2×D4×C31—42no—
184C2×D4×C31—42no—
185C2×D4×C31—42no—
186C2×D4×C31—42no—
187C2×D4×C31—42no—
188C2×D4×C31—42no—
189C2×D4×C31—42no—
190C2×D4×C31—81no—
191C2×D4×C31—81no—
192C2×D4×C31—81no—
193C2×D4×C31C2×D412yes—
194C2×D4×C31#4112yes—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—24no—
204C22×C4×C31—24no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—42no—
214C22×C4×C31—42no—
215C22×C4×C31—42no—
216C22×C4×C31—81no—
217C22×C4×C31—81no—
218C22×C4×C31—81no—
219C22×C4×C31—81no—
220C22×C4×C31C2×D411yescharacteristic
221C22×C4×C31C2×D411yescharacteristic
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31C2×D411yescharacteristic
224C22×C4×C31C2×D412yes—
225C22×C4×C31C2×D412yes—
226C22×C4×C31C2411yescharacteristic
227SD16×C31—44no—
228D8×C31—44no—
229M16×C31—44no—
230C2×C8×C31—21no—
231C2×C8×C31—21no—
232C2×C8×C31—21no—
233C2×C8×C31—21no—
234C2×C8×C31—21no—
235C2×C8×C31—21no—
236C2×C8×C31—21no—
237C2×C8×C31—21no—
238C2×C8×C31—21no—
239C2×C8×C31—21no—
240C2×C8×C31—21no—
241C2×C8×C31—21no—
242C4⋊C4×C31—24no—
243C4⋊C4×C31—24no—
244C4⋊C4×C31—24no—
245C4⋊C4×C31—22no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31—21no—
248C4⋊C4×C31—21no—
249C4⋊C4×C31—21no—
250C4⋊C4×C31—21no—
251C4⋊C4×C31—21no—
252C4⋊C4×C31—21no—
253C4⋊C4×C31—42no—
254C4⋊C4×C31C2×D412yes—
255C4⋊C4×C31C2×D412yes—
256C4⋊C4×C31C2×D412yes—
257C22⋊C4×C31—24no—
258C22⋊C4×C31—24no—
259C22⋊C4×C31—24no—
260C22⋊C4×C31—22no—
261C22⋊C4×C31—24no—
262C22⋊C4×C31—22no—
263C22⋊C4×C31—42no—
264C22⋊C4×C31—42no—
265C22⋊C4×C31—42no—
266C22⋊C4×C31—81no—
267C22⋊C4×C31—81no—
268C42×C31—24no—
269C42×C31—21no—
270C42×C31—21no—
271#23975C3111yesmaximal, characteristic, direct product factor, Sylow
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—21no—
275C23×C31—21no—
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—22no—
280C23×C31—21no—
281C23×C31—22no—
282C23×C31—21no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31#12012yes—
300C23×C31C22×D411yescharacteristic
301Q8×C31—22no—
302Q8×C31—22no—
303Q8×C31—41no—
304Q8×C31—41no—
305D4×C31—22no—
306D4×C31—22no—
307D4×C31—22no—
308D4×C31—22no—
309D4×C31—44no—
310D4×C31—48no—
311D4×C31—48no—
312D4×C31—41no—
313D4×C31—41no—
314D4×C31—41no—
315D4×C31—41no—
316D4×C31—84no—
317D4×C31—84no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—22no—
321C2×C4×C31—22no—
322C2×C4×C31—22no—
323C2×C4×C31—22no—
324C2×C4×C31—21no—
325C2×C4×C31—21no—
326C2×C4×C31—22no—
327C2×C4×C31—21no—
328C2×C4×C31—22no—
329C2×C4×C31—22no—
330C2×C4×C31—21no—
331C2×C4×C31—22no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—48no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—84no—
357C2×C4×C31—84no—
358C2×C4×C31#12012yes—
359C2×C4×C31C22×D411yescharacteristic
360C2×C4×C31C22×D411yescharacteristic
361C2×C4×C31C2×#4111yescharacteristic
362C2×C4×C31C2×#4111yescharacteristic
363C2×C4×C31H(5,𝔽2)11yescharacteristic
364C2×C4×C31H(5,𝔽2)11yescharacteristic
365C8×C31—41no—
366C8×C31—41no—
367C8×C31—41no—
368C8×C31—41no—
369C2×#553C2×C3111yescharacteristic, complemented
370C2×#449C2×C3111yescharacteristic, complemented
371C2×#417C2×C3111yescharacteristic, complemented
372#2407C2×C3111yescharacteristic, complemented
373#2026C2×C3111yescharacteristic, complemented
374#2025C2×C3111yescharacteristic, complemented
375#2000C2×C3111yescharacteristic, complemented
376#1999C2×C3111yescharacteristic, complemented
377#1895C2×C3111yescharacteristic, complemented
378#1879C2×C3111yescharacteristic, complemented
379#1877C2×C3111yescharacteristic, complemented
380#1875C2×C3111yescharacteristic, complemented
381#1873C2×C3111yescharacteristic, complemented
382#1870C2×C3111yescharacteristic, complemented
383#1823C2×C3111yescharacteristic, complemented
384C22×C31—22no—
385C22×C31—22no—
386C22×C31—22no—
387C22×C31—41no—
388C22×C31—41no—
389C22×C31—41no—
390C22×C31—41no—
391C22×C31—42no—
392C22×C31—41no—
393C22×C31—42no—
394C22×C31—41no—
395C22×C31—42no—
396C22×C31—42no—
397C22×C31—41no—
398C22×C31—41no—
399C22×C31—42no—
400C22×C31—41no—
401C22×C31—41no—
402C22×C31—42no—
403C22×C31—41no—
404C22×C31—81no—
405C22×C31—81no—
406C22×C31—81no—
407C22×C31—81no—
408C22×C31—81no—
409C22×C31—81no—
410C22×C31—81no—
411C22×C31—81no—
412C22×C31C2×#12011yescharacteristic
413C22×C31#54611yescharacteristic
414C22×C31#54611yescharacteristic
415C22×C31#57511yescharacteristic
416C22×C31#57511yescharacteristic
417C22×C31#57611yescharacteristic
418C22×C31#57711yescharacteristic
419C4×C31—22no—
420C4×C31—41no—
421C4×C31—42no—
422C4×C31—41no—
423C4×C31—42no—
424C4×C31—41no—
425C4×C31—42no—
426C4×C31—42no—
427C4×C31—81no—
428C4×C31—81no—
429C4×C31#52511yescharacteristic
430C4×C31#53511yescharacteristic
431C4×C31#54611yescharacteristic
432C4×C31#54611yescharacteristic
433C22×#41C22×C3111yescharacteristic
434C22×SD16C22×C3111yescharacteristic
435C22×D8C22×C3111yescharacteristic
436C22×M16C22×C3111yescharacteristic
437#553—24no—
438#553—24no—
439C2×#126—21no—
440C2×#125C22×C3111yescharacteristic
441C2×#123—21no—
442C2×C22⋊Q8C22×C3111yescharacteristic
443C2×#121—21no—
444C2×#121C22×C3111yescharacteristic
445C2×#121C22×C3111yescharacteristic
446C2×#121C22×C3111yescharacteristic
447C2×C4×D4—21no—
448C2×C4×D4C22×C3111yescharacteristic
449C2×C4×D4C22×C3111yescharacteristic
450C2×#117C22×C3111yescharacteristic
451C22×C4⋊C4C22×C3111yescharacteristic
452#449—24no—
453#417—24no—
454C2×#103C22×C3111yescharacteristic
455C2×#103C22×C3111yescharacteristic
456C2×#103C22×C3111yescharacteristic
457C2×#102C22×C3111yescharacteristic
458C2×#102C22×C3111yescharacteristic
459C2×#102C22×C3111yescharacteristic
460C2×#102C22×C3111yescharacteristic
461C2×#102C22×C3111yescharacteristic
462C2×C22⋊C8C22×C3111yescharacteristic
463C2×C22⋊C8C22×C3111yescharacteristic
464C2×C22⋊C8C22×C3111yescharacteristic
465#394—21no—
466#392—21no—
467#391C22×C3111yescharacteristic
468#390C22×C3111yescharacteristic
469#386—21no—
470#385—21no—
471#380C22×C3111yescharacteristic
472#340C22×C3111yescharacteristic
473#340C22×C3111yescharacteristic
474#340C22×C3111yescharacteristic
475#340C22×C3111yescharacteristic
476#340C22×C3111yescharacteristic
477#340C22×C3111yescharacteristic
478#336C22×C3111yescharacteristic
479#336C22×C3111yescharacteristic
480C2×C31—42no—
481C2×C31—81no—
482C2×C31—82no—
483C2×C31—82no—
484C2×C31#240411yescharacteristic
485C2×C31#300511yescharacteristic
486C2×C31#301211yescharacteristic
487C2×C31#330711yescharacteristic
488C2×C31#330911yescharacteristic
489C2×C31#332211yescharacteristic
490C2×C31#332611yescharacteristic
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8C23×C3111yescharacteristic
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4D4×C3111yescharacteristic
503C22×D4C23×C3111yescharacteristic
504C22×D4C23×C3111yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C23×C3111yescharacteristic
509C23×C4C23×C3111yescharacteristic
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—41no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—41no—
516C2×M16—22no—
517C2×M16—41no—
518C2×M16—41no—
519C22×C8C23×C3111yescharacteristic
520C22×C8C23×C3111yescharacteristic
521C22×C8C23×C3111yescharacteristic
522C22×C8C23×C3111yescharacteristic
523#126—28no—
524#125—22no—
525#125—22no—
526#123—28no—
527C22⋊Q8—22no—
528C22⋊Q8—41no—
529#121—28no—
530#121—22no—
531#121—22no—
532#121—22no—
533#121—22no—
534#121—41no—
535#121D4×C3114yescomplemented
536C4×D4—28no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541#117—22no—
542#117—22no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4D4×C3111yescharacteristic
549C2×C4⋊C4D4×C3114yescomplemented
550C2×C4⋊C4C23×C3111yescharacteristic
551C2×C4⋊C4C23×C3111yescharacteristic
552C2×C4⋊C4C23×C3111yescharacteristic
553C2×C4⋊C4C23×C3111yescharacteristic
554C2×C4⋊C4C23×C3111yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4D4×C3111yescharacteristic
565C2×C22⋊C4D4×C3111yescharacteristic
566C2×C42—21no—
567C2×C42C23×C3111yescharacteristic
568#103—22no—
569#103—22no—
570#103—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—41no—
575#102—41no—
576C22⋊C8—22no—
577C22⋊C8—41no—
578C22⋊C8—41no—
579#95—21no—
580#95—21no—
581#95—21no—
582C31#2397511yescharacteristic, direct product factor, Sylow
583C24—21no—
584C24—21no—
585C24C2×D4×C3111yescharacteristic
586C24C2×D4×C3111yescharacteristic
587#41—28no—
588#41—44no—
589#41—44no—
590#41—44no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8#41×C3112yes—
597C2×D4—22no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4C2×D4×C3112yes—
623C2×D4#41×C3112yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4—81no—
649C22×C4C2×D4×C3111yescharacteristic
650C22×C4C2×D4×C3111yescharacteristic
651C22×C4C2×D4×C3111yescharacteristic
652C22×C4C2×D4×C3111yescharacteristic
653C22×C4C2×D4×C3112yes—
654C22×C4C2×D4×C3112yes—
655C22×C4C24×C3111yescharacteristic
656SD16—44no—
657D8—44no—
658M16—44no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—22no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—42no—
683C4⋊C4C2×D4×C3112yes—
684C4⋊C4C2×D4×C3112yes—
685C4⋊C4C2×D4×C3112yes—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—22no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—81no—
696C22⋊C4—81no—
697C42—24no—
698C42—21no—
699C42—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23C31×#12012yes—
728C23C22×D4×C3111yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—41no—
732Q8—41no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—44no—
738D4—48no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—84no—
745D4—84no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—48no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4C31×#12012yes—
787C2×C4C22×D4×C3111yescharacteristic
788C2×C4C22×D4×C3111yescharacteristic
789C2×C4C2×#41×C3111yescharacteristic
790C2×C4C2×#41×C3111yescharacteristic
791C2×C4C31×H(5,𝔽2)11yescharacteristic
792C2×C4C31×H(5,𝔽2)11yescharacteristic
793C8—41no—
794C8—41no—
795C8—41no—
796C8—41no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—42no—
810C22—41no—
811C22—41no—
812C22—42no—
813C22—41no—
814C22—41no—
815C22—42no—
816C22—41no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22C2×C31×#12011yescharacteristic
826C22C31×#54611yescharacteristic
827C22C31×#54611yescharacteristic
828C22C31×#57511yescharacteristic
829C22C31×#57511yescharacteristic
830C22C31×#57611yescharacteristic
831C22C31×#57711yescharacteristic
832C4—22no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—42no—
837C4—41no—
838C4—42no—
839C4—42no—
840C4—81no—
841C4—81no—
842C4C31×#52511yescharacteristic
843C4C31×#53511yescharacteristic
844C4C31×#54611yescharacteristic
845C4C31×#54611yescharacteristic
846C2—42no—
847C2—81no—
848C2—82no—
849C2—82no—
850C2C31×#240411yescharacteristic
851C2C31×#300511yescharacteristic
852C2C31×#301211yescharacteristic
853C2C31×#330711yescharacteristic
854C2C31×#330911yescharacteristic
855C2C31×#332211yescharacteristic
856C2C31×#332611yescharacteristic
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×#553C2semidirect
2. C2×C31×#449C2semidirect
3. C2×C31×#417C2semidirect
4. C31×#2407C2semidirect
5. C31×#2026C2semidirect
6. C31×#2025C2semidirect
7. C31×#2000C2semidirect
8. C31×#1999C2semidirect
9. C31×#1895C2semidirect
10. C31×#1879C2semidirect
11. C31×#1877C2semidirect
12. C31×#1875C2semidirect
13. C31×#1873C2semidirect
14. C31×#1870C2semidirect
15. C31×#1823C2semidirect
107. C31×#121D4semidirect
121. C2×C4⋊C4×C31D4semidirect
271. #23975C31direct (N × H)
369. C2×#553C2×C31semidirect
370. C2×#449C2×C31semidirect
371. C2×#417C2×C31semidirect
372. #2407C2×C31semidirect
373. #2026C2×C31semidirect
374. #2025C2×C31semidirect
375. #2000C2×C31semidirect
376. #1999C2×C31semidirect
377. #1895C2×C31semidirect
378. #1879C2×C31semidirect
379. #1877C2×C31semidirect
380. #1875C2×C31semidirect
381. #1873C2×C31semidirect
382. #1870C2×C31semidirect
383. #1823C2×C31semidirect
535. #121D4×C31semidirect
549. C2×C4⋊C4D4×C31semidirect
582. C31#23975direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5532
C2×C31×#4492
C2×C31×#4172
C31×#24072
C31×#20262
C31×#20252
C31×#20002
C31×#19992
C31×#18952
C31×#18792
C31×#18772
C31×#18752
C31×#18732
C31×#18702
C31×#18232
#2397531