Finite Group Databasebeta

← C31×#60750 #21517509

Subgroups — C31×#60750 #21517509

Order 7936.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#525C211yesmaximal, characteristic, complemented
2C22×C31×#121C211yesmaximal, characteristic, complemented
3C31×#3194C214yesmaximal, complemented
4C31×#3193C212yesmaximal, complemented
5C31×#3192C212yesmaximal, complemented
6C31×#3188C214yesmaximal, complemented
7C31×#3187C212yesmaximal, complemented
8C31×#3186C212yesmaximal, complemented
9C31×#3094C212yesmaximal, complemented
10C31×#3092C212yesmaximal, complemented
11C31×#3055C214yesmaximal, complemented
12C31×#3006C212yesmaximal, complemented
13C31×#3003C212yesmaximal, complemented
14C2×C31×#407C211yesmaximal, characteristic, complemented
15C22×#41×C31C2211yescharacteristic, complemented
16C23×D4×C31—21no—
17C23×D4×C31C2211yescharacteristic, complemented
18C24×C4×C31C2211yescharacteristic
19C2×C31×AGL(1,ℤ/8)C2214yescomplemented
20C22×M16×C31C2212yescomplemented
21C31×#525—21no—
22C31×#525—21no—
23C31×#525—21no—
24C31×#525—21no—
25C31×#525C2212yes—
26C31×#525C2212yescomplemented
27C31×#525C2212yescomplemented
28C31×#525C2212yescomplemented
29C2×C31×#123—21no—
30C2×C31×C22⋊Q8C2211yescharacteristic, complemented
31C2×C31×C22⋊Q8C2211yescharacteristic, complemented
32C2×C31×#121—21no—
33C2×C31×#121—21no—
34C2×C31×#121—21no—
35C2×C31×#121—21no—
36C2×C31×#121—21no—
37C2×C31×#121—21no—
38C2×C31×#121C2212yes—
39C2×C31×#121C2212yes—
40C2×C31×#121C2212yes—
41C2×C31×#121C2212yescomplemented
42C2×C31×#121C2212yescomplemented
43C2×C31×#121C2212yescomplemented
44C2×C31×#121C2211yescharacteristic, complemented
45C2×C31×#121C2211yescharacteristic, complemented
46C2×C31×#120—21no—
47C2×C4×D4×C31—21no—
48C2×C4×D4×C31—21no—
49C2×C31×#117C2211yescharacteristic, complemented
50C22×C4⋊C4×C31C2211yescharacteristic, complemented
51C22×C22⋊C4×C31—21no—
52C31×#484C2214yescomplemented
53C31×#483C2214yescomplemented
54C31×#482C2218yescomplemented
55C31×#481C2214yescomplemented
56C31×#481C2214yescomplemented
57C31×#480C2214yescomplemented
58C31×#480C2214yescomplemented
59C31×#469C2218yescomplemented
60C31×#468C2218yescomplemented
61C31×#466C2218yescomplemented
62C31×#465C2218yescomplemented
63C31×#450C2214yescomplemented
64C31×#450C2214yescomplemented
65C31×#449C2218yescomplemented
66C31×#448C2214yescomplemented
67C31×#447C2214yescomplemented
68C31×#447C2214yescomplemented
69C31×#447C2214yescomplemented
70C31×#428C2214yescomplemented
71C31×#418C2214yescomplemented
72C31×#417C2214yescomplemented
73C31×#407C2212yescomplemented
74C31×#407C2212yescomplemented
75C31×#407C2212yescomplemented
76C31×#407C2212yescomplemented
77C2×C31×C22⋊C8C2212yescomplemented
78C2×C31×C22⋊C8C2212yescomplemented
79C25×C31—21no—
80C25×C31D411yescharacteristic
81C2×#41×C31—21no—
82C2×#41×C31—21no—
83C2×#41×C31—44no—
84C2×#41×C31C2312yes—
85C2×#41×C31C2312yescomplemented
86C22×Q8×C31C2311yescharacteristic, complemented
87C22×D4×C31—21no—
88C22×D4×C31—21no—
89C22×D4×C31—21no—
90C22×D4×C31—22no—
91C22×D4×C31—22no—
92C22×D4×C31—22no—
93C22×D4×C31—22no—
94C22×D4×C31—22no—
95C22×D4×C31—22no—
96C22×D4×C31—21no—
97C22×D4×C31—21no—
98C22×D4×C31—21no—
99C22×D4×C31—44no—
100C22×D4×C31—48no—
101C22×D4×C31C2312yes—
102C22×D4×C31C2312yes—
103C22×D4×C31C2312yes—
104C22×D4×C31C2311yescharacteristic, complemented
105C23×C4×C31—21no—
106C23×C4×C31—21no—
107C23×C4×C31—44no—
108C23×C4×C31D411yescharacteristic
109C23×C4×C31D411yescharacteristic
110C23×C4×C31D411yescharacteristic
111C23×C4×C31D411yescharacteristic
112C23×C4×C31D411yescharacteristic
113C23×C4×C31D411yescharacteristic
114C23×C4×C31D411yescharacteristic
115C23×C4×C31C2311yescharacteristic
116C23×C4×C31C2311yescharacteristic
117C23×C4×C31C2311yescharacteristic
118C23×C4×C31C2311yescharacteristic
119C23×C4×C31C2311yescharacteristic
120C23×C4×C31C2311yescharacteristic
121C23×C4×C31C2311yescharacteristic
122C31×AGL(1,ℤ/8)—48no—
123C2×SD16×C31C2318yescomplemented
124C2×D8×C31C2318yescomplemented
125C2×M16×C31—44no—
126C2×M16×C31C2314yes—
127C2×M16×C31C2314yescomplemented
128C22×C8×C31C2314yescomplemented
129C31×#123—22no—
130C31×#123—22no—
131C31×#123—22no—
132C31×#123—22no—
133C31×C22⋊Q8—21no—
134C31×C22⋊Q8—21no—
135C31×C22⋊Q8—21no—
136C31×C22⋊Q8—21no—
137C31×C22⋊Q8C2312yes—
138C31×C22⋊Q8C2312yes—
139C31×C22⋊Q8C2312yescomplemented
140C31×C22⋊Q8C2312yescomplemented
141C31×#121—22no—
142C31×#121—22no—
143C31×#121—22no—
144C31×#121—22no—
145C31×#121—22no—
146C31×#121—22no—
147C31×#121—22no—
148C31×#121—22no—
149C31×#121—22no—
150C31×#121—22no—
151C31×#121—22no—
152C31×#121—22no—
153C31×#121—21no—
154C31×#121—21no—
155C31×#121—21no—
156C31×#121—21no—
157C31×#121C2312yes—
158C31×#121C2312yes—
159C31×#121C2314yes—
160C31×#121C2314yes—
161C31×#121C2314yes—
162C31×#121C2314yes—
163C31×#121C2312yescomplemented
164C31×#121C2312yescomplemented
165C31×#120—22no—
166C31×#120—22no—
167C31×#120—22no—
168C31×#120—22no—
169C4×D4×C31—22no—
170C4×D4×C31—22no—
171C4×D4×C31—22no—
172C4×D4×C31—22no—
173C4×D4×C31—22no—
174C4×D4×C31—22no—
175C4×D4×C31—22no—
176C4×D4×C31—22no—
177C31×#117—21no—
178C31×#117—21no—
179C31×#117C2312yes—
180C31×#117C2312yescomplemented
181C2×C4⋊C4×C31—21no—
182C2×C4⋊C4×C31—21no—
183C2×C4⋊C4×C31—21no—
184C2×C4⋊C4×C31—21no—
185C2×C4⋊C4×C31—21no—
186C2×C4⋊C4×C31C2312yes—
187C2×C4⋊C4×C31C2312yes—
188C2×C4⋊C4×C31C2312yes—
189C2×C4⋊C4×C31C2311yescharacteristic, complemented
190C2×C4⋊C4×C31C2311yescharacteristic, complemented
191C2×C22⋊C4×C31—21no—
192C2×C22⋊C4×C31—21no—
193C2×C22⋊C4×C31—21no—
194C2×C22⋊C4×C31—22no—
195C2×C22⋊C4×C31—22no—
196C2×C22⋊C4×C31—22no—
197C2×C22⋊C4×C31—22no—
198C2×C22⋊C4×C31—22no—
199C2×C22⋊C4×C31—22no—
200C2×C22⋊C4×C31—21no—
201C2×C22⋊C4×C31—21no—
202C2×C42×C31—21no—
203C31×#107C2318yescomplemented
204C31×#106C2318yescomplemented
205C31×#103C2318yescomplemented
206C31×#102C2318yescomplemented
207C31×#102C2318yescomplemented
208C31×#102C2318yescomplemented
209C31×C22⋊C8C2314yes—
210C31×C22⋊C8C2314yes—
211C31×C22⋊C8C2314yescomplemented
212C31×C22⋊C8C2314yescomplemented
213C24×C31—24no—
214C24×C31—21no—
215C24×C31—22no—
216C24×C31—22no—
217C24×C31—22no—
218C24×C31—42no—
219C24×C31—42no—
220C24×C31—44no—
221C24×C31—44no—
222C24×C31—44no—
223C24×C31C2×D411yescharacteristic
224C24×C31C2×D411yescharacteristic
225C24×C31C2×D411yescharacteristic
226C24×C31C2×D411yescharacteristic
227C24×C31C2×D411yescharacteristic
228C24×C31C2×D411yescharacteristic
229C24×C31C2×D411yescharacteristic
230#41×C31—28no—
231#41×C31—44no—
232#41×C31—44no—
233#41×C31—44no—
234C2×Q8×C31—21no—
235C2×Q8×C31—42no—
236C2×Q8×C31C2412yes—
237C2×D4×C31—22no—
238C2×D4×C31—22no—
239C2×D4×C31—22no—
240C2×D4×C31—22no—
241C2×D4×C31—22no—
242C2×D4×C31—22no—
243C2×D4×C31—24no—
244C2×D4×C31—24no—
245C2×D4×C31—24no—
246C2×D4×C31—24no—
247C2×D4×C31—22no—
248C2×D4×C31—22no—
249C2×D4×C31—22no—
250C2×D4×C31—21no—
251C2×D4×C31—28no—
252C2×D4×C31—44no—
253C2×D4×C31—44no—
254C2×D4×C31—42no—
255C2×D4×C31—44no—
256C2×D4×C31—44no—
257C2×D4×C31—44no—
258C2×D4×C31—44no—
259C2×D4×C31—48no—
260C2×D4×C31—48no—
261C2×D4×C31—48no—
262C2×D4×C31—48no—
263C2×D4×C31—48no—
264C2×D4×C31—44no—
265C2×D4×C31—44no—
266C2×D4×C31—48no—
267C2×D4×C31C2414yes—
268C2×D4×C31C2412yes—
269C22×C4×C31—24no—
270C22×C4×C31—24no—
271C22×C4×C31—24no—
272C22×C4×C31—21no—
273C22×C4×C31—21no—
274C22×C4×C31—21no—
275C22×C4×C31—22no—
276C22×C4×C31—22no—
277C22×C4×C31—22no—
278C22×C4×C31—22no—
279C22×C4×C31—22no—
280C22×C4×C31—42no—
281C22×C4×C31—42no—
282C22×C4×C31—42no—
283C22×C4×C31—42no—
284C22×C4×C31—42no—
285C22×C4×C31—42no—
286C22×C4×C31—42no—
287C22×C4×C31—42no—
288C22×C4×C31—42no—
289C22×C4×C31—42no—
290C22×C4×C31—42no—
291C22×C4×C31—44no—
292C22×C4×C31—44no—
293C22×C4×C31C2×D411yescharacteristic
294C22×C4×C31C2×D411yescharacteristic
295C22×C4×C31C2×D411yescharacteristic
296C22×C4×C31C2×D411yescharacteristic
297C22×C4×C31C2×D411yescharacteristic
298C22×C4×C31C2×D411yescharacteristic
299C22×C4×C31C2×D411yescharacteristic
300C22×C4×C31C2×D411yescharacteristic
301C22×C4×C31C2×D411yescharacteristic
302C22×C4×C31C2×D411yescharacteristic
303C22×C4×C31C2×D411yescharacteristic
304C22×C4×C31C2×D411yescharacteristic
305C22×C4×C31C2×D411yescharacteristic
306C22×C4×C31C2×D411yescharacteristic
307C22×C4×C31C2×D411yescharacteristic
308C22×C4×C31C2×D411yescharacteristic
309C22×C4×C31C2×D411yescharacteristic
310C22×C4×C31C2×D411yescharacteristic
311C22×C4×C31C2×D411yescharacteristic
312C22×C4×C31C2×D411yescharacteristic
313C22×C4×C31C2×D411yescharacteristic
314C22×C4×C31C2411yescharacteristic
315C22×C4×C31C2411yescharacteristic
316C22×C4×C31C2411yescharacteristic
317C22×C4×C31C2411yescharacteristic
318C22×C4×C31C2411yescharacteristic
319C22×C4×C31C2411yescharacteristic
320C22×C4×C31C2411yescharacteristic
321SD16×C31—48no—
322D8×C31—48no—
323M16×C31—28no—
324M16×C31—44no—
325C2×C8×C31—44no—
326C2×C8×C31C2418yes—
327C4⋊C4×C31—22no—
328C4⋊C4×C31—22no—
329C4⋊C4×C31—22no—
330C4⋊C4×C31—22no—
331C4⋊C4×C31—22no—
332C4⋊C4×C31—22no—
333C4⋊C4×C31—22no—
334C4⋊C4×C31—21no—
335C4⋊C4×C31—21no—
336C4⋊C4×C31C2412yes—
337C4⋊C4×C31C2412yes—
338C4⋊C4×C31C2414yes—
339C22⋊C4×C31—22no—
340C22⋊C4×C31—22no—
341C22⋊C4×C31—22no—
342C22⋊C4×C31—22no—
343C22⋊C4×C31—22no—
344C22⋊C4×C31—22no—
345C22⋊C4×C31—24no—
346C22⋊C4×C31—24no—
347C22⋊C4×C31—24no—
348C22⋊C4×C31—24no—
349C22⋊C4×C31—22no—
350C22⋊C4×C31—22no—
351C22⋊C4×C31—22no—
352C22⋊C4×C31—22no—
353C42×C31—22no—
354C42×C31—22no—
355#60750C3111yesmaximal, characteristic, direct product factor, Sylow
356C23×C31—22no—
357C23×C31—22no—
358C23×C31—22no—
359C23×C31—22no—
360C23×C31—22no—
361C23×C31—22no—
362C23×C31—22no—
363C23×C31—22no—
364C23×C31—22no—
365C23×C31—22no—
366C23×C31—22no—
367C23×C31—22no—
368C23×C31—22no—
369C23×C31—24no—
370C23×C31—41no—
371C23×C31—41no—
372C23×C31—41no—
373C23×C31—41no—
374C23×C31—41no—
375C23×C31—41no—
376C23×C31—41no—
377C23×C31—41no—
378C23×C31—416no—
379C23×C31—42no—
380C23×C31—44no—
381C23×C31—44no—
382C23×C31—44no—
383C23×C31—44no—
384C23×C31—42no—
385C23×C31—44no—
386C23×C31—44no—
387C23×C31—44no—
388C23×C31—44no—
389C23×C31—42no—
390C23×C31—44no—
391C23×C31—816no—
392C23×C31AGL(1,ℤ/8)14yescomplemented
393C23×C31C22×D411yescharacteristic
394C23×C31C22×D411yescharacteristic
395C23×C31C22×D411yescharacteristic
396C23×C31C22×D411yescharacteristic
397C23×C31C22×D411yescharacteristic
398C23×C31C22×D411yescharacteristic
399C23×C31C22×D411yescharacteristic
400Q8×C31—24no—
401Q8×C31—42no—
402D4×C31—24no—
403D4×C31—28no—
404D4×C31—44no—
405D4×C31—44no—
406D4×C31—42no—
407D4×C31—44no—
408D4×C31—48no—
409D4×C31—48no—
410D4×C31—44no—
411D4×C31—44no—
412D4×C31—44no—
413D4×C31—44no—
414D4×C31—48no—
415D4×C31—48no—
416D4×C31—44no—
417D4×C31—44no—
418C2×C4×C31—22no—
419C2×C4×C31—22no—
420C2×C4×C31—22no—
421C2×C4×C31—22no—
422C2×C4×C31—22no—
423C2×C4×C31—22no—
424C2×C4×C31—22no—
425C2×C4×C31—22no—
426C2×C4×C31—22no—
427C2×C4×C31—22no—
428C2×C4×C31—22no—
429C2×C4×C31—22no—
430C2×C4×C31—22no—
431C2×C4×C31—22no—
432C2×C4×C31—22no—
433C2×C4×C31—22no—
434C2×C4×C31—22no—
435C2×C4×C31—22no—
436C2×C4×C31—24no—
437C2×C4×C31—41no—
438C2×C4×C31—41no—
439C2×C4×C31—41no—
440C2×C4×C31—41no—
441C2×C4×C31—41no—
442C2×C4×C31—41no—
443C2×C4×C31—41no—
444C2×C4×C31—41no—
445C2×C4×C31—41no—
446C2×C4×C31—41no—
447C2×C4×C31—41no—
448C2×C4×C31—41no—
449C2×C4×C31—44no—
450C2×C4×C31—44no—
451C2×C4×C31—44no—
452C2×C4×C31—42no—
453C2×C4×C31—42no—
454C2×C4×C31—44no—
455C2×C4×C31—42no—
456C2×C4×C31—44no—
457C2×C4×C31C22×D411yescharacteristic
458C2×C4×C31C22×D411yescharacteristic
459C2×C4×C31C22×D411yescharacteristic
460C2×C4×C31C22×D411yescharacteristic
461C2×C4×C31C22×D411yescharacteristic
462C2×C4×C31C22×D411yescharacteristic
463C2×C4×C31C22×D411yescharacteristic
464C2×C4×C31H(5,𝔽2)14yes—
465C2×C4×C31C2511yescharacteristic
466C8×C31—28no—
467C2×#525C2×C3111yescharacteristic, complemented
468C22×#121C2×C3111yescharacteristic, complemented
469#3194C2×C3114yescomplemented
470#3193C2×C3112yescomplemented
471#3192C2×C3112yescomplemented
472#3188C2×C3114yescomplemented
473#3187C2×C3112yescomplemented
474#3186C2×C3112yescomplemented
475#3094C2×C3112yescomplemented
476#3092C2×C3112yescomplemented
477#3055C2×C3114yescomplemented
478#3006C2×C3112yescomplemented
479#3003C2×C3112yescomplemented
480C2×#407C2×C3111yescharacteristic, complemented
481C22×C31—28no—
482C22×C31—21no—
483C22×C31—21no—
484C22×C31—21no—
485C22×C31—21no—
486C22×C31—21no—
487C22×C31—21no—
488C22×C31—21no—
489C22×C31—21no—
490C22×C31—21no—
491C22×C31—21no—
492C22×C31—21no—
493C22×C31—21no—
494C22×C31—21no—
495C22×C31—21no—
496C22×C31—21no—
497C22×C31—21no—
498C22×C31—44no—
499C22×C31—44no—
500C22×C31—44no—
501C22×C31—44no—
502C22×C31—44no—
503C22×C31—44no—
504C22×C31—42no—
505C22×C31—44no—
506C22×C31—44no—
507C22×C31—42no—
508C22×C31—42no—
509C22×C31—44no—
510C22×C31—84no—
511C22×C31—88no—
512C22×C31—88no—
513C22×C31—88no—
514C22×C31#53412yes—
515C22×C31C2×AGL(1,ℤ/8)12yes—
516C22×C31C2×AGL(1,ℤ/8)12yes—
517C22×C31C2×AGL(1,ℤ/8)12yes—
518C22×C31#57512yes—
519C22×C31C23×D411yescharacteristic
520C4×C31—21no—
521C4×C31—21no—
522C4×C31—21no—
523C4×C31—21no—
524C4×C31—21no—
525C4×C31—21no—
526C4×C31—42no—
527C4×C31—44no—
528C4×C31—42no—
529C4×C31—42no—
530C4×C31#53412yes—
531C4×C31C2×H(5,𝔽2)12yes—
532C22×#41C22×C3111yescharacteristic, complemented
533C23×D4—21no—
534C23×D4C22×C3111yescharacteristic, complemented
535C24×C4C22×C3111yescharacteristic
536C2×AGL(1,ℤ/8)C22×C3114yescomplemented
537C22×M16C22×C3112yescomplemented
538#525—21no—
539#525—21no—
540#525—21no—
541#525—21no—
542#525C22×C3112yes—
543#525C22×C3112yescomplemented
544#525C22×C3112yescomplemented
545#525C22×C3112yescomplemented
546C2×#123—21no—
547C2×C22⋊Q8C22×C3111yescharacteristic, complemented
548C2×C22⋊Q8C22×C3111yescharacteristic, complemented
549C2×#121—21no—
550C2×#121—21no—
551C2×#121—21no—
552C2×#121—21no—
553C2×#121—21no—
554C2×#121—21no—
555C2×#121C22×C3112yes—
556C2×#121C22×C3112yes—
557C2×#121C22×C3112yes—
558C2×#121C22×C3112yescomplemented
559C2×#121C22×C3112yescomplemented
560C2×#121C22×C3112yescomplemented
561C2×#121C22×C3111yescharacteristic, complemented
562C2×#121C22×C3111yescharacteristic, complemented
563C2×#120—21no—
564C2×C4×D4—21no—
565C2×C4×D4—21no—
566C2×#117C22×C3111yescharacteristic, complemented
567C22×C4⋊C4C22×C3111yescharacteristic, complemented
568C22×C22⋊C4—21no—
569#484C22×C3114yescomplemented
570#483C22×C3114yescomplemented
571#482C22×C3118yescomplemented
572#481C22×C3114yescomplemented
573#481C22×C3114yescomplemented
574#480C22×C3114yescomplemented
575#480C22×C3114yescomplemented
576#469C22×C3118yescomplemented
577#468C22×C3118yescomplemented
578#466C22×C3118yescomplemented
579#465C22×C3118yescomplemented
580#450C22×C3114yescomplemented
581#450C22×C3114yescomplemented
582#449C22×C3118yescomplemented
583#448C22×C3114yescomplemented
584#447C22×C3114yescomplemented
585#447C22×C3114yescomplemented
586#447C22×C3114yescomplemented
587#428C22×C3114yescomplemented
588#418C22×C3114yescomplemented
589#417C22×C3114yescomplemented
590#407C22×C3112yescomplemented
591#407C22×C3112yescomplemented
592#407C22×C3112yescomplemented
593#407C22×C3112yescomplemented
594C2×C22⋊C8C22×C3112yescomplemented
595C2×C22⋊C8C22×C3112yescomplemented
596C2×C31—22no—
597C2×C31—22no—
598C2×C31—22no—
599C2×C31—22no—
600C2×C31—22no—
601C2×C31—41no—
602C2×C31—41no—
603C2×C31—82no—
604C2×C31—84no—
605C2×C31C2×#53411yescharacteristic
606C2×C31C22×AGL(1,ℤ/8)11yescharacteristic
607C2×C31C2×#57511yescharacteristic
608C25—21no—
609C25D4×C3111yescharacteristic
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—44no—
613C2×#41C23×C3112yes—
614C2×#41C23×C3112yescomplemented
615C22×Q8C23×C3111yescharacteristic, complemented
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—22no—
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—22no—
623C22×D4—22no—
624C22×D4—22no—
625C22×D4—21no—
626C22×D4—21no—
627C22×D4—21no—
628C22×D4—44no—
629C22×D4—48no—
630C22×D4C23×C3112yes—
631C22×D4C23×C3112yes—
632C22×D4C23×C3112yes—
633C22×D4C23×C3111yescharacteristic, complemented
634C23×C4—21no—
635C23×C4—21no—
636C23×C4—44no—
637C23×C4D4×C3111yescharacteristic
638C23×C4D4×C3111yescharacteristic
639C23×C4D4×C3111yescharacteristic
640C23×C4D4×C3111yescharacteristic
641C23×C4D4×C3111yescharacteristic
642C23×C4D4×C3111yescharacteristic
643C23×C4D4×C3111yescharacteristic
644C23×C4C23×C3111yescharacteristic
645C23×C4C23×C3111yescharacteristic
646C23×C4C23×C3111yescharacteristic
647C23×C4C23×C3111yescharacteristic
648C23×C4C23×C3111yescharacteristic
649C23×C4C23×C3111yescharacteristic
650C23×C4C23×C3111yescharacteristic
651AGL(1,ℤ/8)—48no—
652C2×SD16C23×C3118yescomplemented
653C2×D8C23×C3118yescomplemented
654C2×M16—44no—
655C2×M16C23×C3114yes—
656C2×M16C23×C3114yescomplemented
657C22×C8C23×C3114yescomplemented
658#123—22no—
659#123—22no—
660#123—22no—
661#123—22no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8C23×C3112yes—
667C22⋊Q8C23×C3112yes—
668C22⋊Q8C23×C3112yescomplemented
669C22⋊Q8C23×C3112yescomplemented
670#121—22no—
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—22no—
680#121—22no—
681#121—22no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—21no—
686#121C23×C3114yes—
687#121C23×C3114yes—
688#121C23×C3114yes—
689#121C23×C3114yes—
690#121C23×C3112yes—
691#121C23×C3112yes—
692#121C23×C3112yescomplemented
693#121C23×C3112yescomplemented
694#120—22no—
695#120—22no—
696#120—22no—
697#120—22no—
698C4×D4—22no—
699C4×D4—22no—
700C4×D4—22no—
701C4×D4—22no—
702C4×D4—22no—
703C4×D4—22no—
704C4×D4—22no—
705C4×D4—22no—
706#117—21no—
707#117—21no—
708#117C23×C3112yes—
709#117C23×C3112yescomplemented
710C2×C4⋊C4—21no—
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—21no—
715C2×C4⋊C4C23×C3112yes—
716C2×C4⋊C4C23×C3112yes—
717C2×C4⋊C4C23×C3112yes—
718C2×C4⋊C4C23×C3111yescharacteristic, complemented
719C2×C4⋊C4C23×C3111yescharacteristic, complemented
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C42—21no—
732#107C23×C3118yescomplemented
733#106C23×C3118yescomplemented
734#103C23×C3118yescomplemented
735#102C23×C3118yescomplemented
736#102C23×C3118yescomplemented
737#102C23×C3118yescomplemented
738C22⋊C8C23×C3114yes—
739C22⋊C8C23×C3114yes—
740C22⋊C8C23×C3114yescomplemented
741C22⋊C8C23×C3114yescomplemented
742C31#6075011yescharacteristic, direct product factor, Sylow
743C24—24no—
744C24—21no—
745C24—22no—
746C24—22no—
747C24—22no—
748C24—42no—
749C24—42no—
750C24—44no—
751C24—44no—
752C24—44no—
753C24C2×D4×C3111yescharacteristic
754C24C2×D4×C3111yescharacteristic
755C24C2×D4×C3111yescharacteristic
756C24C2×D4×C3111yescharacteristic
757C24C2×D4×C3111yescharacteristic
758C24C2×D4×C3111yescharacteristic
759C24C2×D4×C3111yescharacteristic
760#41—28no—
761#41—44no—
762#41—44no—
763#41—44no—
764C2×Q8—21no—
765C2×Q8—42no—
766C2×Q8C24×C3112yes—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—24no—
774C2×D4—24no—
775C2×D4—24no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4—21no—
781C2×D4—28no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—42no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—48no—
792C2×D4—48no—
793C2×D4—48no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—48no—
797C2×D4C24×C3114yes—
798C2×D4C24×C3112yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4C2×D4×C3111yescharacteristic
824C22×C4C2×D4×C3111yescharacteristic
825C22×C4C2×D4×C3111yescharacteristic
826C22×C4C2×D4×C3111yescharacteristic
827C22×C4C2×D4×C3111yescharacteristic
828C22×C4C2×D4×C3111yescharacteristic
829C22×C4C2×D4×C3111yescharacteristic
830C22×C4C2×D4×C3111yescharacteristic
831C22×C4C2×D4×C3111yescharacteristic
832C22×C4C2×D4×C3111yescharacteristic
833C22×C4C2×D4×C3111yescharacteristic
834C22×C4C2×D4×C3111yescharacteristic
835C22×C4C2×D4×C3111yescharacteristic
836C22×C4C2×D4×C3111yescharacteristic
837C22×C4C2×D4×C3111yescharacteristic
838C22×C4C2×D4×C3111yescharacteristic
839C22×C4C2×D4×C3111yescharacteristic
840C22×C4C2×D4×C3111yescharacteristic
841C22×C4C2×D4×C3111yescharacteristic
842C22×C4C2×D4×C3111yescharacteristic
843C22×C4C2×D4×C3111yescharacteristic
844C22×C4C24×C3111yescharacteristic
845C22×C4C24×C3111yescharacteristic
846C22×C4C24×C3111yescharacteristic
847C22×C4C24×C3111yescharacteristic
848C22×C4C24×C3111yescharacteristic
849C22×C4C24×C3111yescharacteristic
850C22×C4C24×C3111yescharacteristic
851SD16—48no—
852D8—48no—
853M16—28no—
854M16—44no—
855C2×C8—44no—
856C2×C8C24×C3118yes—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4C24×C3112yes—
867C4⋊C4C24×C3112yes—
868C4⋊C4C24×C3114yes—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—24no—
876C22⋊C4—24no—
877C22⋊C4—24no—
878C22⋊C4—24no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—22no—
882C22⋊C4—22no—
883C42—22no—
884C42—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—24no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—416no—
908C23—42no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—42no—
914C23—44no—
915C23—44no—
916C23—44no—
917C23—44no—
918C23—42no—
919C23—44no—
920C23—816no—
921C23C31×AGL(1,ℤ/8)14yescomplemented
922C23C22×D4×C3111yescharacteristic
923C23C22×D4×C3111yescharacteristic
924C23C22×D4×C3111yescharacteristic
925C23C22×D4×C3111yescharacteristic
926C23C22×D4×C3111yescharacteristic
927C23C22×D4×C3111yescharacteristic
928C23C22×D4×C3111yescharacteristic
929Q8—24no—
930Q8—42no—
931D4—24no—
932D4—28no—
933D4—44no—
934D4—44no—
935D4—42no—
936D4—44no—
937D4—48no—
938D4—48no—
939D4—44no—
940D4—44no—
941D4—44no—
942D4—44no—
943D4—48no—
944D4—48no—
945D4—44no—
946D4—44no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—44no—
979C2×C4—44no—
980C2×C4—44no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—44no—
984C2×C4—42no—
985C2×C4—44no—
986C2×C4C22×D4×C3111yescharacteristic
987C2×C4C22×D4×C3111yescharacteristic
988C2×C4C22×D4×C3111yescharacteristic
989C2×C4C22×D4×C3111yescharacteristic
990C2×C4C22×D4×C3111yescharacteristic
991C2×C4C22×D4×C3111yescharacteristic
992C2×C4C22×D4×C3111yescharacteristic
993C2×C4C31×H(5,𝔽2)14yes—
994C2×C4C25×C3111yescharacteristic
995C8—28no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—42no—
1020C22—44no—
1021C22—44no—
1022C22—42no—
1023C22—42no—
1024C22—44no—
1025C22—88no—
1026C22—88no—
1027C22—88no—
1028C22—84no—
1029C22C31×#53412yes—
1030C22C2×C31×AGL(1,ℤ/8)12yes—
1031C22C2×C31×AGL(1,ℤ/8)12yes—
1032C22C2×C31×AGL(1,ℤ/8)12yes—
1033C22C31×#57512yes—
1034C22C23×D4×C3111yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—42no—
1042C4—44no—
1043C4—42no—
1044C4—42no—
1045C4C31×#53412yes—
1046C4C2×C31×H(5,𝔽2)12yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—84no—
1055C2—82no—
1056C2C2×C31×#53411yescharacteristic
1057C2C22×C31×AGL(1,ℤ/8)11yescharacteristic
1058C2C2×C31×#57511yescharacteristic
subgroupG/H
center, socleC22×C31C23×D4
commutator, Frattini, cosocleC2×C4C25×C31
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#525C2semidirect
2. C22×C31×#121C2semidirect
3. C31×#3194C2semidirect
4. C31×#3193C2semidirect
5. C31×#3192C2semidirect
6. C31×#3188C2semidirect
7. C31×#3187C2semidirect
8. C31×#3186C2semidirect
9. C31×#3094C2semidirect
10. C31×#3092C2semidirect
11. C31×#3055C2semidirect
12. C31×#3006C2semidirect
13. C31×#3003C2semidirect
14. C2×C31×#407C2semidirect
15. C22×#41×C31C22semidirect
17. C23×D4×C31C22semidirect
19. C2×C31×AGL(1,ℤ/8)C22semidirect
20. C22×M16×C31C22semidirect
26. C31×#525C22semidirect
27. C31×#525C22semidirect
28. C31×#525C22semidirect
30. C2×C31×C22⋊Q8C22semidirect
31. C2×C31×C22⋊Q8C22semidirect
41. C2×C31×#121C22semidirect
42. C2×C31×#121C22semidirect
43. C2×C31×#121C22semidirect
44. C2×C31×#121C22semidirect
45. C2×C31×#121C22semidirect
49. C2×C31×#117C22semidirect
50. C22×C4⋊C4×C31C22semidirect
52. C31×#484C22semidirect
53. C31×#483C22semidirect
54. C31×#482C22semidirect
55. C31×#481C22semidirect
56. C31×#481C22semidirect
57. C31×#480C22semidirect
58. C31×#480C22semidirect
59. C31×#469C22semidirect
60. C31×#468C22semidirect
61. C31×#466C22semidirect
62. C31×#465C22semidirect
63. C31×#450C22semidirect
64. C31×#450C22semidirect
65. C31×#449C22semidirect
66. C31×#448C22semidirect
67. C31×#447C22semidirect
68. C31×#447C22semidirect
69. C31×#447C22semidirect
70. C31×#428C22semidirect
71. C31×#418C22semidirect
72. C31×#417C22semidirect
73. C31×#407C22semidirect
74. C31×#407C22semidirect
75. C31×#407C22semidirect
76. C31×#407C22semidirect
77. C2×C31×C22⋊C8C22semidirect
78. C2×C31×C22⋊C8C22semidirect
85. C2×#41×C31C23semidirect
86. C22×Q8×C31C23semidirect
104. C22×D4×C31C23semidirect
123. C2×SD16×C31C23semidirect
124. C2×D8×C31C23semidirect
127. C2×M16×C31C23semidirect
128. C22×C8×C31C23semidirect
139. C31×C22⋊Q8C23semidirect
140. C31×C22⋊Q8C23semidirect
163. C31×#121C23semidirect
164. C31×#121C23semidirect
180. C31×#117C23semidirect
189. C2×C4⋊C4×C31C23semidirect
190. C2×C4⋊C4×C31C23semidirect
203. C31×#107C23semidirect
204. C31×#106C23semidirect
205. C31×#103C23semidirect
206. C31×#102C23semidirect
207. C31×#102C23semidirect
208. C31×#102C23semidirect
211. C31×C22⋊C8C23semidirect
212. C31×C22⋊C8C23semidirect
355. #60750C31direct (N × H)
392. C23×C31AGL(1,ℤ/8)semidirect
467. C2×#525C2×C31semidirect
468. C22×#121C2×C31semidirect
469. #3194C2×C31semidirect
470. #3193C2×C31semidirect
471. #3192C2×C31semidirect
472. #3188C2×C31semidirect
473. #3187C2×C31semidirect
474. #3186C2×C31semidirect
475. #3094C2×C31semidirect
476. #3092C2×C31semidirect
477. #3055C2×C31semidirect
478. #3006C2×C31semidirect
479. #3003C2×C31semidirect
480. C2×#407C2×C31semidirect
532. C22×#41C22×C31semidirect
534. C23×D4C22×C31semidirect
536. C2×AGL(1,ℤ/8)C22×C31semidirect
537. C22×M16C22×C31semidirect
543. #525C22×C31semidirect
544. #525C22×C31semidirect
545. #525C22×C31semidirect
547. C2×C22⋊Q8C22×C31semidirect
548. C2×C22⋊Q8C22×C31semidirect
558. C2×#121C22×C31semidirect
559. C2×#121C22×C31semidirect
560. C2×#121C22×C31semidirect
561. C2×#121C22×C31semidirect
562. C2×#121C22×C31semidirect
566. C2×#117C22×C31semidirect
567. C22×C4⋊C4C22×C31semidirect
569. #484C22×C31semidirect
570. #483C22×C31semidirect
571. #482C22×C31semidirect
572. #481C22×C31semidirect
573. #481C22×C31semidirect
574. #480C22×C31semidirect
575. #480C22×C31semidirect
576. #469C22×C31semidirect
577. #468C22×C31semidirect
578. #466C22×C31semidirect
579. #465C22×C31semidirect
580. #450C22×C31semidirect
581. #450C22×C31semidirect
582. #449C22×C31semidirect
583. #448C22×C31semidirect
584. #447C22×C31semidirect
585. #447C22×C31semidirect
586. #447C22×C31semidirect
587. #428C22×C31semidirect
588. #418C22×C31semidirect
589. #417C22×C31semidirect
590. #407C22×C31semidirect
591. #407C22×C31semidirect
592. #407C22×C31semidirect
593. #407C22×C31semidirect
594. C2×C22⋊C8C22×C31semidirect
595. C2×C22⋊C8C22×C31semidirect
614. C2×#41C23×C31semidirect
615. C22×Q8C23×C31semidirect
633. C22×D4C23×C31semidirect
652. C2×SD16C23×C31semidirect
653. C2×D8C23×C31semidirect
656. C2×M16C23×C31semidirect
657. C22×C8C23×C31semidirect
668. C22⋊Q8C23×C31semidirect
669. C22⋊Q8C23×C31semidirect
692. #121C23×C31semidirect
693. #121C23×C31semidirect
709. #117C23×C31semidirect
718. C2×C4⋊C4C23×C31semidirect
719. C2×C4⋊C4C23×C31semidirect
732. #107C23×C31semidirect
733. #106C23×C31semidirect
734. #103C23×C31semidirect
735. #102C23×C31semidirect
736. #102C23×C31semidirect
737. #102C23×C31semidirect
740. C22⋊C8C23×C31semidirect
741. C22⋊C8C23×C31semidirect
742. C31#60750direct (N × H)
921. C23C31×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5252
C22×C31×#1212
C31×#31942
C31×#31932
C31×#31922
C31×#31882
C31×#31872
C31×#31862
C31×#30942
C31×#30922
C31×#30552
C31×#30062
C31×#30032
C2×C31×#4072
#6075031