Finite Group Databasebeta

← C31×#21458 #21478217

Subgroups — C31×#21458 #21478217

Order 7936.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#518C211yesmaximal, characteristic, complemented
2C2×C31×#447C211yesmaximal, characteristic
3C2×C31×#442C211yesmaximal, characteristic, complemented
4C2×C4×D8×C31C211yesmaximal, characteristic, complemented
5C31×#2324C211yesmaximal, characteristic, complemented
6C31×#1879C211yesmaximal, characteristic, complemented
7C31×#1879C211yesmaximal, characteristic, complemented
8C31×#1875C211yesmaximal, characteristic, complemented
9C31×#1864C211yesmaximal, characteristic, complemented
10C31×#1862C211yesmaximal, characteristic, complemented
11C31×#1854C211yesmaximal, characteristic, complemented
12C31×#1786C211yesmaximal, characteristic, complemented
13C31×#1762C211yesmaximal, characteristic, complemented
14C4×C31×#102C211yesmaximal, characteristic, complemented
15C31×#1750C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C2×C31×#121C2211yescharacteristic
20C31×#518—24no—
21C31×#518—24no—
22C2×C4×D4×C31—21no—
23C2×C4×D4×C31—21no—
24C2×C4×D4×C31C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C2×C4×D4×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C2×C4×D4×C31C2211yescharacteristic, complemented
29C2×C31×#117C2211yescharacteristic
30C2×C31×#117C2211yescharacteristic
31C22×C22⋊C4×C31—21no—
32C22×C22⋊C4×C31—21no—
33C31×#447C418yescomplemented
34C31×#442—24no—
35C4×D8×C31—24no—
36C2×C31×#107C2211yescharacteristic, complemented
37C2×C31×#106C2211yescharacteristic, complemented
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic, complemented
45C2×C31×#102C2211yescharacteristic, complemented
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×#97C2211yescharacteristic, complemented
49C2×C4×C8×C31C2211yescharacteristic, complemented
50C31×#390—21no—
51C31×#390C2211yescharacteristic, complemented
52C31×#389C2211yescharacteristic, complemented
53C31×#388—21no—
54C31×#386—21no—
55C31×#385—21no—
56C31×#380C2211yescharacteristic
57C4×C4⋊C4×C31C2211yescharacteristic, complemented
58C31×#340C2211yescharacteristic, complemented
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#340C2211yescharacteristic, complemented
62C31×#336C2211yescharacteristic, complemented
63C31×#336C2211yescharacteristic, complemented
64C25×C31—21no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—21no—
70C22×D4×C31—21no—
71C22×D4×C31—22no—
72C22×D4×C31C2×C414yescomplemented
73C22×D4×C31C2311yescharacteristic
74C22×D4×C31C2311yescharacteristic
75C22×D4×C31C2311yescharacteristic
76C23×C4×C31—21no—
77C23×C4×C31—21no—
78C23×C4×C31—21no—
79C23×C4×C31—21no—
80C23×C4×C31—21no—
81C23×C4×C31C2311yescharacteristic
82C2×D8×C31—22no—
83C2×D8×C31—22no—
84C2×D8×C31—22no—
85C2×D8×C31—22no—
86C2×D8×C31C2×C414yescomplemented
87C2×D8×C31C2×C414yescomplemented
88C22×C8×C31C2311yescharacteristic
89C22×C8×C31C2311yescharacteristic
90C22×C8×C31C2311yescharacteristic
91C22×C8×C31C2311yescharacteristic
92C31×#121—22no—
93C31×#121C2×C414yescomplemented
94C4×D4×C31—28no—
95C4×D4×C31—28no—
96C4×D4×C31—22no—
97C4×D4×C31—22no—
98C4×D4×C31—22no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31—22no—
102C4×D4×C31—22no—
103C4×D4×C31—22no—
104C4×D4×C31D414yescomplemented
105C4×D4×C31D414yescomplemented
106C31×#117—22no—
107C31×#117—22no—
108C31×#117—22no—
109C31×#117—22no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31D411yescharacteristic
112C2×C4⋊C4×C31D411yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C22⋊C4×C31—28no—
119C2×C22⋊C4×C31—28no—
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
135C2×C42×C31C2311yescharacteristic
136C31×#107—22no—
137C31×#106—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—22no—
144C31×#102C2×C414yescomplemented
145C31×#102C2×C414yescomplemented
146C31×C22⋊C8—22no—
147C31×C22⋊C8C2×C414yescomplemented
148C31×#97—22no—
149C4×C8×C31—22no—
150C31×#95—21no—
151C31×#95—21no—
152C31×#95—21no—
153C24×C31—24no—
154C24×C31—24no—
155C24×C31—21no—
156C24×C31—21no—
157C24×C31—24no—
158C24×C31—21no—
159C24×C31—81no—
160C24×C31—81no—
161C24×C31—81no—
162C24×C31—81no—
163C24×C31C2×D411yescharacteristic
164C2×D4×C31—24no—
165C2×D4×C31—24no—
166C2×D4×C31—28no—
167C2×D4×C31—28no—
168C2×D4×C31—28no—
169C2×D4×C31—28no—
170C2×D4×C31—24no—
171C2×D4×C31—24no—
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—21no—
182C2×D4×C31—21no—
183C2×D4×C31—81no—
184C2×D4×C31—81no—
185C2×D4×C31C22×C412yes—
186C2×D4×C31C22×C412yes—
187C2×D4×C31C22×C412yes—
188C2×D4×C31C2×D412yes—
189C2×D4×C31C2×D412yes—
190C2×D4×C31#4112yes—
191C2×D4×C31#4112yes—
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—24no—
200C22×C4×C31—24no—
201C22×C4×C31—24no—
202C22×C4×C31—24no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—42no—
206C22×C4×C31—81no—
207C22×C4×C31—81no—
208C22×C4×C31—81no—
209C22×C4×C31—81no—
210C22×C4×C31—81no—
211C22×C4×C31—81no—
212C22×C4×C31—81no—
213C22×C4×C31—81no—
214C22×C4×C31—81no—
215C22×C4×C31—81no—
216C22×C4×C31C22×C412yes—
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219C22×C4×C31C2×D411yescharacteristic
220C22×C4×C31C2×D411yescharacteristic
221C22×C4×C31C2×D411yescharacteristic
222C22×C4×C31#4112yes—
223C22×C4×C31C2411yescharacteristic
224D8×C31—28no—
225D8×C31—28no—
226C2×C8×C31—21no—
227C2×C8×C31—21no—
228C2×C8×C31—21no—
229C2×C8×C31—21no—
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×C31C22×C412yes—
237C2×C8×C31C22×C412yes—
238C4⋊C4×C31—22no—
239C4⋊C4×C31—22no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—21no—
243C4⋊C4×C31—21no—
244C4⋊C4×C31—21no—
245C4⋊C4×C31—21no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31—81no—
248C4⋊C4×C31C22×C412yes—
249C4⋊C4×C31C2×D412yes—
250C4⋊C4×C31C2×D412yes—
251C22⋊C4×C31—24no—
252C22⋊C4×C31—24no—
253C22⋊C4×C31—24no—
254C22⋊C4×C31—24no—
255C22⋊C4×C31—22no—
256C22⋊C4×C31—22no—
257C22⋊C4×C31—24no—
258C22⋊C4×C31—24no—
259C22⋊C4×C31—42no—
260C22⋊C4×C31—81no—
261C22⋊C4×C31—81no—
262C22⋊C4×C31—81no—
263C42×C31—24no—
264C42×C31—21no—
265C42×C31—21no—
266C42×C31—81no—
267C42×C31C2×D412yes—
268C42×C31C2×D412yes—
269#21458C3111yesmaximal, characteristic, direct product factor, Sylow
270C23×C31—216no—
271C23×C31—22no—
272C23×C31—22no—
273C23×C31—21no—
274C23×C31—22no—
275C23×C31—22no—
276C23×C31—21no—
277C23×C31—22no—
278C23×C31—22no—
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—21no—
282C23×C31—21no—
283C23×C31—22no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31—41no—
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—84no—
299C23×C31—84no—
300C23×C31—84no—
301C23×C31—84no—
302C23×C31—84no—
303C23×C31—84no—
304C23×C31C4×D412yes—
305C23×C31C22×D411yescharacteristic
306D4×C31—216no—
307D4×C31—22no—
308D4×C31—22no—
309D4×C31—22no—
310D4×C31—22no—
311D4×C31—22no—
312D4×C31—22no—
313D4×C31—22no—
314D4×C31—22no—
315D4×C31—41no—
316D4×C31—41no—
317D4×C31—84no—
318D4×C31C4×D414yes—
319D4×C31C4×D414yes—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—21no—
324C2×C4×C31—21no—
325C2×C4×C31—21no—
326C2×C4×C31—22no—
327C2×C4×C31—22no—
328C2×C4×C31—22no—
329C2×C4×C31—22no—
330C2×C4×C31—22no—
331C2×C4×C31—21no—
332C2×C4×C31—21no—
333C2×C4×C31—22no—
334C2×C4×C31—22no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—21no—
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—84no—
352C2×C4×C31—84no—
353C2×C4×C31—84no—
354C2×C4×C31—84no—
355C2×C4×C31—84no—
356C2×C4×C31C4×D412yes—
357C2×C4×C31#12012yes—
358C2×C4×C31#12012yes—
359C2×C4×C31C23×C411yescharacteristic
360C2×C4×C31C22×D411yescharacteristic
361C2×C4×C31C22×D411yescharacteristic
362C2×C4×C31C2×#4111yescharacteristic
363C2×C4×C31C2×#4111yescharacteristic
364C2×C4×C31C2×#4111yescharacteristic
365C8×C31—22no—
366C8×C31—22no—
367C8×C31—41no—
368C8×C31—41no—
369C2×#518C2×C3111yescharacteristic, complemented
370C2×#447C2×C3111yescharacteristic
371C2×#442C2×C3111yescharacteristic, complemented
372C2×C4×D8C2×C3111yescharacteristic, complemented
373#2324C2×C3111yescharacteristic, complemented
374#1879C2×C3111yescharacteristic, complemented
375#1879C2×C3111yescharacteristic, complemented
376#1875C2×C3111yescharacteristic, complemented
377#1864C2×C3111yescharacteristic, complemented
378#1862C2×C3111yescharacteristic, complemented
379#1854C2×C3111yescharacteristic, complemented
380#1786C2×C3111yescharacteristic, complemented
381#1762C2×C3111yescharacteristic, complemented
382C4×#102C2×C3111yescharacteristic, complemented
383#1750C2×C3111yescharacteristic, complemented
384C22×C31—22no—
385C22×C31—22no—
386C22×C31—22no—
387C22×C31—24no—
388C22×C31—24no—
389C22×C31—41no—
390C22×C31—42no—
391C22×C31—42no—
392C22×C31—41no—
393C22×C31—42no—
394C22×C31—42no—
395C22×C31—42no—
396C22×C31—42no—
397C22×C31—42no—
398C22×C31—42no—
399C22×C31—42no—
400C22×C31—42no—
401C22×C31—41no—
402C22×C31—42no—
403C22×C31—42no—
404C22×C31—41no—
405C22×C31—42no—
406C22×C31—42no—
407C22×C31—42no—
408C22×C31—816no—
409C22×C31—81no—
410C22×C31—81no—
411C22×C31—81no—
412C22×C31—81no—
413C22×C31C2×C4×D411yescharacteristic
414C22×C31C2×#12011yescharacteristic
415C22×C31#52511yescharacteristic
416C22×C31#57611yescharacteristic
417C22×C31#57611yescharacteristic
418C22×C31#57611yescharacteristic
419C22×C31#57711yescharacteristic
420C4×C31—22no—
421C4×C31—22no—
422C4×C31—22no—
423C4×C31—42no—
424C4×C31—41no—
425C4×C31—42no—
426C4×C31—41no—
427C4×C31—42no—
428C4×C31—81no—
429C4×C31—81no—
430C4×C31C2×C4×D411yescharacteristic
431C4×C31C2×C4×D411yescharacteristic
432C4×C31#52511yescharacteristic
433C4×C31#52511yescharacteristic
434C23×D4C22×C3111yescharacteristic
435C22×D8C22×C3111yescharacteristic
436C22×D8C22×C3111yescharacteristic
437C2×#121C22×C3111yescharacteristic
438#518—24no—
439#518—24no—
440C2×C4×D4—21no—
441C2×C4×D4—21no—
442C2×C4×D4C22×C3111yescharacteristic
443C2×C4×D4C22×C3111yescharacteristic
444C2×C4×D4C22×C3111yescharacteristic
445C2×C4×D4C22×C3111yescharacteristic
446C2×C4×D4C22×C3111yescharacteristic, complemented
447C2×#117C22×C3111yescharacteristic
448C2×#117C22×C3111yescharacteristic
449C22×C22⋊C4—21no—
450C22×C22⋊C4—21no—
451#447C4×C3118yescomplemented
452#442—24no—
453C4×D8—24no—
454C2×#107C22×C3111yescharacteristic, complemented
455C2×#106C22×C3111yescharacteristic, complemented
456C2×#102C22×C3111yescharacteristic
457C2×#102C22×C3111yescharacteristic
458C2×#102C22×C3111yescharacteristic
459C2×#102C22×C3111yescharacteristic
460C2×#102C22×C3111yescharacteristic
461C2×#102C22×C3111yescharacteristic
462C2×#102C22×C3111yescharacteristic, complemented
463C2×#102C22×C3111yescharacteristic, complemented
464C2×C22⋊C8C22×C3111yescharacteristic
465C2×C22⋊C8C22×C3111yescharacteristic
466C2×#97C22×C3111yescharacteristic, complemented
467C2×C4×C8C22×C3111yescharacteristic, complemented
468#390—21no—
469#390C22×C3111yescharacteristic, complemented
470#389C22×C3111yescharacteristic, complemented
471#388—21no—
472#386—21no—
473#385—21no—
474#380C22×C3111yescharacteristic
475C4×C4⋊C4C22×C3111yescharacteristic, complemented
476#340C22×C3111yescharacteristic, complemented
477#340C22×C3111yescharacteristic, complemented
478#340C22×C3111yescharacteristic, complemented
479#340C22×C3111yescharacteristic, complemented
480#336C22×C3111yescharacteristic, complemented
481#336C22×C3111yescharacteristic, complemented
482C2×C31—42no—
483C2×C31—44no—
484C2×C31—44no—
485C2×C31—82no—
486C2×C31C4×#12011yescharacteristic
487C2×C31#294611yescharacteristic
488C2×C31#294811yescharacteristic
489C2×C31#300811yescharacteristic
490C2×C31#301211yescharacteristic
491C2×C31#311811yescharacteristic
492C2×C31#312211yescharacteristic
493C25—21no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—22no—
501C22×D4C2×C4×C3114yescomplemented
502C22×D4C23×C3111yescharacteristic
503C22×D4C23×C3111yescharacteristic
504C22×D4C23×C3111yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C23×C3111yescharacteristic
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8C2×C4×C3114yescomplemented
516C2×D8C2×C4×C3114yescomplemented
517C22×C8C23×C3111yescharacteristic
518C22×C8C23×C3111yescharacteristic
519C22×C8C23×C3111yescharacteristic
520C22×C8C23×C3111yescharacteristic
521#121—22no—
522#121C2×C4×C3114yescomplemented
523C4×D4—28no—
524C4×D4—28no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4D4×C3114yescomplemented
534C4×D4D4×C3114yescomplemented
535#117—22no—
536#117—22no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4D4×C3111yescharacteristic
541C2×C4⋊C4D4×C3111yescharacteristic
542C2×C4⋊C4C23×C3111yescharacteristic
543C2×C4⋊C4C23×C3111yescharacteristic
544C2×C4⋊C4C23×C3111yescharacteristic
545C2×C4⋊C4C23×C3111yescharacteristic
546C2×C4⋊C4C23×C3111yescharacteristic
547C2×C22⋊C4—28no—
548C2×C22⋊C4—28no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C3111yescharacteristic
560C2×C22⋊C4D4×C3111yescharacteristic
561C2×C42—21no—
562C2×C42—21no—
563C2×C42C23×C3111yescharacteristic
564C2×C42C23×C3111yescharacteristic
565#107—22no—
566#106—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102C2×C4×C3114yescomplemented
574#102C2×C4×C3114yescomplemented
575C22⋊C8—22no—
576C22⋊C8C2×C4×C3114yescomplemented
577#97—22no—
578C4×C8—22no—
579#95—21no—
580#95—21no—
581#95—21no—
582C31#2145811yescharacteristic, direct product factor, Sylow
583C24—24no—
584C24—24no—
585C24—21no—
586C24—21no—
587C24—24no—
588C24—21no—
589C24—81no—
590C24—81no—
591C24—81no—
592C24—81no—
593C24C2×D4×C3111yescharacteristic
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—28no—
600C2×D4—24no—
601C2×D4—24no—
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—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C22×C4×C3112yes—
616C2×D4C22×C4×C3112yes—
617C2×D4C22×C4×C3112yes—
618C2×D4C2×D4×C3112yes—
619C2×D4C2×D4×C3112yes—
620C2×D4#41×C3112yes—
621C2×D4#41×C3112yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4—81no—
642C22×C4—81no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C22×C4×C3112yes—
647C22×C4C2×D4×C3111yescharacteristic
648C22×C4C2×D4×C3111yescharacteristic
649C22×C4C2×D4×C3111yescharacteristic
650C22×C4C2×D4×C3111yescharacteristic
651C22×C4C2×D4×C3111yescharacteristic
652C22×C4#41×C3112yes—
653C22×C4C24×C3111yescharacteristic
654D8—28no—
655D8—28no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C22×C4×C3112yes—
667C2×C8C22×C4×C3112yes—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—81no—
678C4⋊C4C22×C4×C3112yes—
679C4⋊C4C2×D4×C3112yes—
680C4⋊C4C2×D4×C3112yes—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—42no—
690C22⋊C4—81no—
691C22⋊C4—81no—
692C22⋊C4—81no—
693C42—24no—
694C42—21no—
695C42—21no—
696C42—81no—
697C42C2×D4×C3112yes—
698C42C2×D4×C3112yes—
699C23—216no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—84no—
728C23—84no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23C4×D4×C3112yes—
734C23C22×D4×C3111yescharacteristic
735D4—216no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—22no—
743D4—22no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4C4×D4×C3114yes—
748D4C4×D4×C3114yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
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—84no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4C4×D4×C3112yes—
786C2×C4C31×#12012yes—
787C2×C4C31×#12012yes—
788C2×C4C23×C4×C3111yescharacteristic
789C2×C4C22×D4×C3111yescharacteristic
790C2×C4C22×D4×C3111yescharacteristic
791C2×C4C2×#41×C3111yescharacteristic
792C2×C4C2×#41×C3111yescharacteristic
793C2×C4C2×#41×C3111yescharacteristic
794C8—22no—
795C8—22no—
796C8—41no—
797C8—41no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—24no—
802C22—24no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—41no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—816no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22C2×C4×D4×C3111yescharacteristic
828C22C2×C31×#12011yescharacteristic
829C22C31×#52511yescharacteristic
830C22C31×#57611yescharacteristic
831C22C31×#57611yescharacteristic
832C22C31×#57611yescharacteristic
833C22C31×#57711yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—42no—
838C4—41no—
839C4—42no—
840C4—41no—
841C4—42no—
842C4—81no—
843C4—81no—
844C4C2×C4×D4×C3111yescharacteristic
845C4C2×C4×D4×C3111yescharacteristic
846C4C31×#52511yescharacteristic
847C4C31×#52511yescharacteristic
848C2—42no—
849C2—44no—
850C2—44no—
851C2—82no—
852C2C4×C31×#12011yescharacteristic
853C2C31×#294611yescharacteristic
854C2C31×#294811yescharacteristic
855C2C31×#300811yescharacteristic
856C2C31×#301211yescharacteristic
857C2C31×#311811yescharacteristic
858C2C31×#312211yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#447C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C31×#518C2semidirect
3. C2×C31×#442C2semidirect
4. C2×C4×D8×C31C2semidirect
5. C31×#2324C2semidirect
6. C31×#1879C2semidirect
7. C31×#1879C2semidirect
8. C31×#1875C2semidirect
9. C31×#1864C2semidirect
10. C31×#1862C2semidirect
11. C31×#1854C2semidirect
12. C31×#1786C2semidirect
13. C31×#1762C2semidirect
14. C4×C31×#102C2semidirect
15. C31×#1750C2semidirect
28. C2×C4×D4×C31C22semidirect
33. C31×#447C4semidirect
36. C2×C31×#107C22semidirect
37. C2×C31×#106C22semidirect
44. C2×C31×#102C22semidirect
45. C2×C31×#102C22semidirect
48. C2×C31×#97C22semidirect
49. C2×C4×C8×C31C22semidirect
51. C31×#390C22semidirect
52. C31×#389C22semidirect
57. C4×C4⋊C4×C31C22semidirect
58. C31×#340C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#340C22semidirect
62. C31×#336C22semidirect
63. C31×#336C22semidirect
72. C22×D4×C31C2×C4semidirect
86. C2×D8×C31C2×C4semidirect
87. C2×D8×C31C2×C4semidirect
93. C31×#121C2×C4semidirect
104. C4×D4×C31D4semidirect
105. C4×D4×C31D4semidirect
144. C31×#102C2×C4semidirect
145. C31×#102C2×C4semidirect
147. C31×C22⋊C8C2×C4semidirect
269. #21458C31direct (N × H)
369. C2×#518C2×C31semidirect
371. C2×#442C2×C31semidirect
372. C2×C4×D8C2×C31semidirect
373. #2324C2×C31semidirect
374. #1879C2×C31semidirect
375. #1879C2×C31semidirect
376. #1875C2×C31semidirect
377. #1864C2×C31semidirect
378. #1862C2×C31semidirect
379. #1854C2×C31semidirect
380. #1786C2×C31semidirect
381. #1762C2×C31semidirect
382. C4×#102C2×C31semidirect
383. #1750C2×C31semidirect
446. C2×C4×D4C22×C31semidirect
451. #447C4×C31semidirect
454. C2×#107C22×C31semidirect
455. C2×#106C22×C31semidirect
462. C2×#102C22×C31semidirect
463. C2×#102C22×C31semidirect
466. C2×#97C22×C31semidirect
467. C2×C4×C8C22×C31semidirect
469. #390C22×C31semidirect
470. #389C22×C31semidirect
475. C4×C4⋊C4C22×C31semidirect
476. #340C22×C31semidirect
477. #340C22×C31semidirect
478. #340C22×C31semidirect
479. #340C22×C31semidirect
480. #336C22×C31semidirect
481. #336C22×C31semidirect
501. C22×D4C2×C4×C31semidirect
515. C2×D8C2×C4×C31semidirect
516. C2×D8C2×C4×C31semidirect
522. #121C2×C4×C31semidirect
533. C4×D4D4×C31semidirect
534. C4×D4D4×C31semidirect
573. #102C2×C4×C31semidirect
574. #102C2×C4×C31semidirect
576. C22⋊C8C2×C4×C31semidirect
582. C31#21458direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5182
C2×C31×#4472
C2×C31×#4422
C2×C4×D8×C312
C31×#23242
C31×#18792
C31×#18752
C31×#18642
C31×#18622
C31×#18542
C31×#17862
C31×#17622
C4×C31×#1022
C31×#17502
#2145831