Finite Group Databasebeta

← C31×#60563 #21517322

Subgroups — C31×#60563 #21517322

Order 7936.

2180 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#529C211yesmaximal, characteristic, complemented
2C2×C4×#41×C31C211yesmaximal, characteristic, complemented
3C31×#3117C212yesmaximal, complemented
4C31×#3114C212yesmaximal, complemented
5C31×#3111C214yesmaximal, complemented
6C31×#3108C212yesmaximal, complemented
7C31×#3105C212yesmaximal, complemented
8C31×#3102C214yesmaximal, complemented
9C31×#3095C211yesmaximal, characteristic, complemented
10C31×#3094C211yesmaximal, characteristic, complemented
11C31×#3080C212yesmaximal, complemented
12C31×#3040C212yesmaximal, complemented
13C31×#3007C211yesmaximal, characteristic, complemented
14C31×#3006C211yesmaximal, characteristic
15C4×C31×#137C212yesmaximal, complemented
16C4×C31×AGL(1,ℤ/8)C212yesmaximal, complemented
17C31×#2920C211yesmaximal, characteristic, complemented
18C22×#41×C31C2211yescharacteristic
19C2×C31×#137C2212yes—
20C2×C31×AGL(1,ℤ/8)C2212yes—
21C31×#529—21no—
22C31×#529—21no—
23C31×#529—21no—
24C31×#529—21no—
25C31×#529C2212yes—
26C31×#529C2212yes—
27C31×#529C2212yescomplemented
28C31×#529C2212yescomplemented
29C2×C31×#126—21no—
30C2×C31×#125C2211yescharacteristic, complemented
31C2×C31×#124C2211yescharacteristic, complemented
32C2×C31×#123—21no—
33C2×C31×C22⋊Q8C2211yescharacteristic
34C2×C31×#121C2211yescharacteristic
35C4×#41×C31—21no—
36C4×#41×C31—21no—
37C4×#41×C31—21no—
38C4×#41×C31—21no—
39C4×#41×C31C2212yes—
40C4×#41×C31C2212yes—
41C4×#41×C31C2212yescomplemented
42C4×#41×C31C2212yescomplemented
43C2×C4×Q8×C31C2211yescharacteristic, complemented
44C2×C4×Q8×C31C2211yescharacteristic, complemented
45C2×C4×Q8×C31C2211yescharacteristic, complemented
46C2×C4×D4×C31—21no—
47C2×C4×D4×C31—21no—
48C2×C4×D4×C31—21no—
49C2×C4×D4×C31C2211yescharacteristic, complemented
50C2×C4×D4×C31C2211yescharacteristic, complemented
51C2×C4×D4×C31C2211yescharacteristic, complemented
52C2×C31×#117—21no—
53C2×C31×#117—21no—
54C2×C31×#117C2211yescharacteristic
55C22×C42×C31—21no—
56C22×C42×C31C2211yescharacteristic
57C31×#485C2214yescomplemented
58C31×#484C2212yescomplemented
59C31×#483C2212yescomplemented
60C31×#482C2214yescomplemented
61C31×#481C2212yes—
62C31×#480C2212yes—
63C31×#479C2214yescomplemented
64C31×#479C2214yescomplemented
65C31×#478C2214yescomplemented
66C31×#478C2214yescomplemented
67C31×#464C2214yescomplemented
68C31×#464C2214yescomplemented
69C31×#463C2214yescomplemented
70C31×#463C2214yescomplemented
71C31×#452C2214yescomplemented
72C31×#451C2212yescomplemented
73C31×#450C2212yescomplemented
74C31×#449C2214yes—
75C31×#448C2212yes—
76C31×#447C2212yes—
77C31×#442C2214yescomplemented
78C31×#441C2214yescomplemented
79C31×#440C2214yescomplemented
80C31×#440C2214yescomplemented
81C4×Q16×C31C2214yescomplemented
82C4×SD16×C31C2214yescomplemented
83C4×SD16×C31C2214yescomplemented
84C4×D8×C31C2214yescomplemented
85C31×#432C2212yescomplemented
86C31×#432C2212yescomplemented
87C31×#431C2212yescomplemented
88C31×#431C2212yescomplemented
89C31×#428C2212yescomplemented
90C31×#428C2212yescomplemented
91C31×#423C2212yescomplemented
92C31×#419C2212yescomplemented
93C31×#418C2212yescomplemented
94C31×#417C2212yes—
95C31×#417C2212yes—
96C31×#407C2211yescharacteristic
97C31×#407C2211yescharacteristic
98C4×M16×C31C2212yescomplemented
99C2×#41×C31—28no—
100C2×#41×C31—21no—
101C2×#41×C31—21no—
102C2×#41×C31C2312yes—
103C2×#41×C31C2312yes—
104C22×Q8×C31C2311yescharacteristic
105C22×Q8×C31C2311yescharacteristic
106C22×D4×C31—21no—
107C22×D4×C31—21no—
108C22×D4×C31C2311yescharacteristic
109C22×D4×C31C2311yescharacteristic
110C23×C4×C31—21no—
111C23×C4×C31—21no—
112C23×C4×C31—21no—
113C23×C4×C31—21no—
114C23×C4×C31D411yescharacteristic
115C23×C4×C31D411yescharacteristic
116C23×C4×C31C2311yescharacteristic
117C31×#137—28no—
118C31×AGL(1,ℤ/8)—28no—
119C2×Q16×C31C2314yes—
120C2×SD16×C31C2314yes—
121C2×SD16×C31C2314yes—
122C2×D8×C31C2314yes—
123C2×M16×C31C2312yes—
124C2×M16×C31C2312yes—
125C31×#126—22no—
126C31×#126—22no—
127C31×#126—22no—
128C31×#126—22no—
129C31×#125—21no—
130C31×#125—21no—
131C31×#125C2312yes—
132C31×#125C2312yes—
133C31×#124—21no—
134C31×#124—21no—
135C31×#124C2312yes—
136C31×#124C2312yes—
137C31×#123—22no—
138C31×#123—22no—
139C31×#123—22no—
140C31×#123—22no—
141C31×C22⋊Q8—21no—
142C31×C22⋊Q8—21no—
143C31×C22⋊Q8C2312yes—
144C31×C22⋊Q8C2312yes—
145C31×#121—21no—
146C31×#121—21no—
147C31×#121C2312yes—
148C31×#121C2312yes—
149C4×Q8×C31—21no—
150C4×Q8×C31—21no—
151C4×Q8×C31—21no—
152C4×Q8×C31—21no—
153C4×Q8×C31—21no—
154C4×Q8×C31—21no—
155C4×Q8×C31C2312yes—
156C4×Q8×C31C2312yes—
157C4×Q8×C31C2312yes—
158C4×Q8×C31C2312yes—
159C4×Q8×C31C2312yes—
160C4×Q8×C31C2312yes—
161C4×D4×C31—22no—
162C4×D4×C31—22no—
163C4×D4×C31—22no—
164C4×D4×C31—22no—
165C4×D4×C31—22no—
166C4×D4×C31—22no—
167C4×D4×C31—22no—
168C4×D4×C31—22no—
169C4×D4×C31—22no—
170C4×D4×C31—22no—
171C4×D4×C31—22no—
172C4×D4×C31—22no—
173C4×D4×C31—21no—
174C4×D4×C31—21no—
175C4×D4×C31—21no—
176C4×D4×C31—21no—
177C4×D4×C31—21no—
178C4×D4×C31—21no—
179C4×D4×C31C2312yes—
180C4×D4×C31C2312yes—
181C4×D4×C31C2312yes—
182C4×D4×C31C2312yes—
183C4×D4×C31C2312yes—
184C4×D4×C31C2312yes—
185C31×#117—21no—
186C31×#117—21no—
187C31×#117—22no—
188C31×#117—22no—
189C31×#117—22no—
190C31×#117—22no—
191C31×#117—22no—
192C31×#117—22no—
193C31×#117—22no—
194C31×#117—22no—
195C31×#117C2312yes—
196C31×#117C2312yes—
197C2×C4⋊C4×C31—21no—
198C2×C4⋊C4×C31—21no—
199C2×C4⋊C4×C31—21no—
200C2×C4⋊C4×C31—21no—
201C2×C4⋊C4×C31—21no—
202C2×C4⋊C4×C31—21no—
203C2×C4⋊C4×C31C2311yescharacteristic
204C2×C4⋊C4×C31C2311yescharacteristic
205C2×C4⋊C4×C31C2311yescharacteristic
206C2×C4⋊C4×C31C2311yescharacteristic
207C2×C22⋊C4×C31—21no—
208C2×C22⋊C4×C31—21no—
209C2×C22⋊C4×C31—21no—
210C2×C22⋊C4×C31—21no—
211C2×C22⋊C4×C31—21no—
212C2×C22⋊C4×C31—21no—
213C2×C22⋊C4×C31—21no—
214C2×C22⋊C4×C31—21no—
215C2×C42×C31—21no—
216C2×C42×C31—21no—
217C2×C42×C31—21no—
218C2×C42×C31—21no—
219C2×C42×C31—22no—
220C2×C42×C31—22no—
221C2×C42×C31—22no—
222C2×C42×C31—22no—
223C2×C42×C31D411yescharacteristic
224C2×C42×C31D411yescharacteristic
225C2×C42×C31D411yescharacteristic
226C2×C42×C31D411yescharacteristic
227C2×C42×C31D411yescharacteristic
228C2×C42×C31D411yescharacteristic
229C2×C42×C31C2311yescharacteristic
230C2×C42×C31C2311yescharacteristic
231C2×C42×C31C2311yescharacteristic
232C2×C42×C31C2311yescharacteristic
233C2×C42×C31C2311yescharacteristic
234C2×C42×C31C2311yescharacteristic
235C31×#107C2314yes—
236C31×#107C2314yes—
237C31×#106C2314yes—
238C31×#106C2314yes—
239C31×C4⋊C8C2314yes—
240C31×C4⋊C8C2314yes—
241C31×#103C2314yes—
242C31×#103C2314yes—
243C31×#103C2314yes—
244C31×#103C2314yes—
245C31×#102C2314yes—
246C31×#102C2314yes—
247C31×#102C2314yes—
248C31×#102C2314yes—
249C31×C22⋊C8C2312yes—
250C31×C22⋊C8C2312yes—
251C31×C22⋊C8C2312yes—
252C31×C22⋊C8C2312yes—
253C31×#97C2314yes—
254C4×C8×C31C2314yes—
255C24×C31—21no—
256C24×C31—21no—
257C24×C31C2×D411yescharacteristic
258#41×C31—28no—
259#41×C31—28no—
260#41×C31—24no—
261#41×C31—24no—
262#41×C31—24no—
263#41×C31#4118yes—
264C2×Q8×C31—24no—
265C2×Q8×C31—21no—
266C2×Q8×C31—21no—
267C2×Q8×C31—24no—
268C2×Q8×C31C2412yes—
269C2×Q8×C31C2412yes—
270C2×D4×C31—28no—
271C2×D4×C31—22no—
272C2×D4×C31—22no—
273C2×D4×C31—24no—
274C2×D4×C31—22no—
275C2×D4×C31—22no—
276C2×D4×C31—21no—
277C2×D4×C31—21no—
278C2×D4×C31—24no—
279C2×D4×C31—44no—
280C2×D4×C31C2412yes—
281C2×D4×C31C2412yes—
282C22×C4×C31—28no—
283C22×C4×C31—21no—
284C22×C4×C31—22no—
285C22×C4×C31—22no—
286C22×C4×C31—24no—
287C22×C4×C31—21no—
288C22×C4×C31—21no—
289C22×C4×C31—21no—
290C22×C4×C31—21no—
291C22×C4×C31—21no—
292C22×C4×C31—22no—
293C22×C4×C31—22no—
294C22×C4×C31—22no—
295C22×C4×C31—22no—
296C22×C4×C31—22no—
297C22×C4×C31—22no—
298C22×C4×C31—42no—
299C22×C4×C31—42no—
300C22×C4×C31—44no—
301C22×C4×C31—44no—
302C22×C4×C31—44no—
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×C31C2×D411yescharacteristic
315C22×C4×C31C2×D411yescharacteristic
316C22×C4×C31C2×D411yescharacteristic
317C22×C4×C31C2×D411yescharacteristic
318C22×C4×C31C2411yescharacteristic
319C22×C4×C31C2411yescharacteristic
320C22×C4×C31C2411yescharacteristic
321Q16×C31—28no—
322SD16×C31—28no—
323SD16×C31—28no—
324D8×C31—28no—
325M16×C31—24no—
326M16×C31—24no—
327C2×C8×C31C2414yes—
328C2×C8×C31C2414yes—
329C4⋊C4×C31—22no—
330C4⋊C4×C31—22no—
331C4⋊C4×C31—22no—
332C4⋊C4×C31—22no—
333C4⋊C4×C31—22no—
334C4⋊C4×C31—22no—
335C4⋊C4×C31—22no—
336C4⋊C4×C31—22no—
337C4⋊C4×C31—22no—
338C4⋊C4×C31—22no—
339C4⋊C4×C31—22no—
340C4⋊C4×C31—22no—
341C4⋊C4×C31—21no—
342C4⋊C4×C31—21no—
343C4⋊C4×C31—21no—
344C4⋊C4×C31—21no—
345C4⋊C4×C31C2412yes—
346C4⋊C4×C31C2412yes—
347C4⋊C4×C31C2412yes—
348C4⋊C4×C31C2412yes—
349C22⋊C4×C31—22no—
350C22⋊C4×C31—22no—
351C22⋊C4×C31—22no—
352C22⋊C4×C31—22no—
353C22⋊C4×C31—22no—
354C22⋊C4×C31—22no—
355C22⋊C4×C31—22no—
356C22⋊C4×C31—22no—
357C22⋊C4×C31—22no—
358C22⋊C4×C31—22no—
359C22⋊C4×C31—22no—
360C22⋊C4×C31—22no—
361C22⋊C4×C31—22no—
362C22⋊C4×C31—22no—
363C22⋊C4×C31—22no—
364C22⋊C4×C31—22no—
365C42×C31—22no—
366C42×C31—22no—
367C42×C31—22no—
368C42×C31—22no—
369C42×C31—22no—
370C42×C31—22no—
371C42×C31—22no—
372C42×C31—22no—
373C42×C31C2×D411yescharacteristic
374C42×C31C2×D411yescharacteristic
375C42×C31C2×D411yescharacteristic
376C42×C31C2×D411yescharacteristic
377C42×C31C2×D411yescharacteristic
378C42×C31C2×D411yescharacteristic
379C42×C31C2×D411yescharacteristic
380C42×C31C2×D411yescharacteristic
381C42×C31C2×D411yescharacteristic
382C42×C31C2×D411yescharacteristic
383C42×C31C2×D411yescharacteristic
384C42×C31C2×D411yescharacteristic
385C42×C31C2411yescharacteristic
386C42×C31C2411yescharacteristic
387C42×C31C2411yescharacteristic
388C42×C31C2411yescharacteristic
389#60563C3111yesmaximal, characteristic, direct product factor, Sylow
390C23×C31—24no—
391C23×C31—22no—
392C23×C31—22no—
393C23×C31—22no—
394C23×C31—22no—
395C23×C31—41no—
396C23×C31—42no—
397C23×C31—42no—
398C23×C31—42no—
399C23×C31—42no—
400C23×C31—42no—
401C23×C31C22×D411yescharacteristic
402C23×C31C22×D411yescharacteristic
403C23×C31C22×D411yescharacteristic
404Q8×C31—24no—
405Q8×C31—22no—
406Q8×C31—24no—
407Q8×C31—42no—
408Q8×C31C2×#4114yes—
409D4×C31—28no—
410D4×C31—24no—
411D4×C31—28no—
412D4×C31—22no—
413D4×C31—24no—
414D4×C31—44no—
415D4×C31—44no—
416D4×C31—42no—
417D4×C31C2×#4114yes—
418C2×C4×C31—24no—
419C2×C4×C31—28no—
420C2×C4×C31—22no—
421C2×C4×C31—22no—
422C2×C4×C31—22no—
423C2×C4×C31—22no—
424C2×C4×C31—22no—
425C2×C4×C31—28no—
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—22no—
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—44no—
445C2×C4×C31—44no—
446C2×C4×C31—44no—
447C2×C4×C31—44no—
448C2×C4×C31—42no—
449C2×C4×C31—42no—
450C2×C4×C31—42no—
451C2×C4×C31—42no—
452C2×C4×C31—42no—
453C2×C4×C31—44no—
454C2×C4×C31—44no—
455C2×C4×C31C22×D411yescharacteristic
456C2×C4×C31C22×D411yescharacteristic
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×C31C22×D411yescharacteristic
465C2×C4×C31C22×D411yescharacteristic
466C2×C4×C31C2×#4114yes—
467C2×C4×C31C2511yescharacteristic
468C8×C31—24no—
469C8×C31—24no—
470C2×#529C2×C3111yescharacteristic, complemented
471C2×C4×#41C2×C3111yescharacteristic, complemented
472#3117C2×C3112yescomplemented
473#3114C2×C3112yescomplemented
474#3111C2×C3114yescomplemented
475#3108C2×C3112yescomplemented
476#3105C2×C3112yescomplemented
477#3102C2×C3114yescomplemented
478#3095C2×C3111yescharacteristic, complemented
479#3094C2×C3111yescharacteristic, complemented
480#3080C2×C3112yescomplemented
481#3040C2×C3112yescomplemented
482#3007C2×C3111yescharacteristic, complemented
483#3006C2×C3111yescharacteristic
484C4×#137C2×C3112yescomplemented
485C4×AGL(1,ℤ/8)C2×C3112yescomplemented
486#2920C2×C3111yescharacteristic, complemented
487C22×C31—21no—
488C22×C31—21no—
489C22×C31—21no—
490C22×C31—21no—
491C22×C31—21no—
492C22×C31—24no—
493C22×C31—21no—
494C22×C31—21no—
495C22×C31—44no—
496C22×C31—48no—
497C22×C31—42no—
498C22×C31—42no—
499C22×C31—42no—
500C22×C31—42no—
501C22×C31—42no—
502C22×C31—84no—
503C22×C31#52512yes—
504C22×C31#57512yes—
505C22×C31C23×D411yescharacteristic
506C4×C31—21no—
507C4×C31—24no—
508C4×C31—21no—
509C4×C31—21no—
510C4×C31—21no—
511C4×C31—21no—
512C4×C31—21no—
513C4×C31—21no—
514C4×C31—21no—
515C4×C31—21no—
516C4×C31—42no—
517C4×C31—42no—
518C4×C31—42no—
519C4×C31—42no—
520C4×C31—42no—
521C4×C31#52512yes—
522C4×C31#57512yes—
523C4×C31C22×#4112yes—
524C22×#41C22×C3111yescharacteristic
525C2×#137C22×C3112yes—
526C2×AGL(1,ℤ/8)C22×C3112yes—
527#529—21no—
528#529—21no—
529#529—21no—
530#529—21no—
531#529C22×C3112yes—
532#529C22×C3112yes—
533#529C22×C3112yescomplemented
534#529C22×C3112yescomplemented
535C2×#126—21no—
536C2×#125C22×C3111yescharacteristic, complemented
537C2×#124C22×C3111yescharacteristic, complemented
538C2×#123—21no—
539C2×C22⋊Q8C22×C3111yescharacteristic
540C2×#121C22×C3111yescharacteristic
541C4×#41—21no—
542C4×#41—21no—
543C4×#41—21no—
544C4×#41—21no—
545C4×#41C22×C3112yes—
546C4×#41C22×C3112yes—
547C4×#41C22×C3112yescomplemented
548C4×#41C22×C3112yescomplemented
549C2×C4×Q8C22×C3111yescharacteristic, complemented
550C2×C4×Q8C22×C3111yescharacteristic, complemented
551C2×C4×Q8C22×C3111yescharacteristic, complemented
552C2×C4×D4—21no—
553C2×C4×D4—21no—
554C2×C4×D4—21no—
555C2×C4×D4C22×C3111yescharacteristic, complemented
556C2×C4×D4C22×C3111yescharacteristic, complemented
557C2×C4×D4C22×C3111yescharacteristic, complemented
558C2×#117—21no—
559C2×#117—21no—
560C2×#117C22×C3111yescharacteristic
561C22×C42—21no—
562C22×C42C22×C3111yescharacteristic
563#485C22×C3114yescomplemented
564#484C22×C3112yescomplemented
565#483C22×C3112yescomplemented
566#482C22×C3114yescomplemented
567#481C22×C3112yes—
568#480C22×C3112yes—
569#479C22×C3114yescomplemented
570#479C22×C3114yescomplemented
571#478C22×C3114yescomplemented
572#478C22×C3114yescomplemented
573#464C22×C3114yescomplemented
574#464C22×C3114yescomplemented
575#463C22×C3114yescomplemented
576#463C22×C3114yescomplemented
577#452C22×C3114yescomplemented
578#451C22×C3112yescomplemented
579#450C22×C3112yescomplemented
580#449C22×C3114yes—
581#448C22×C3112yes—
582#447C22×C3112yes—
583#442C22×C3114yescomplemented
584#441C22×C3114yescomplemented
585#440C22×C3114yescomplemented
586#440C22×C3114yescomplemented
587C4×Q16C22×C3114yescomplemented
588C4×SD16C22×C3114yescomplemented
589C4×SD16C22×C3114yescomplemented
590C4×D8C22×C3114yescomplemented
591#432C22×C3112yescomplemented
592#432C22×C3112yescomplemented
593#431C22×C3112yescomplemented
594#431C22×C3112yescomplemented
595#428C22×C3112yescomplemented
596#428C22×C3112yescomplemented
597#423C22×C3112yescomplemented
598#419C22×C3112yescomplemented
599#418C22×C3112yescomplemented
600#417C22×C3112yes—
601#417C22×C3112yes—
602#407C22×C3111yescharacteristic
603#407C22×C3111yescharacteristic
604C4×M16C22×C3112yescomplemented
605C2×C31—22no—
606C2×C31—22no—
607C2×C31—41no—
608C2×C31—44no—
609C2×C31—82no—
610C2×C31C2×#52511yescharacteristic
611C2×C31C2×#57511yescharacteristic
612C2×C31C2×#57511yescharacteristic
613C2×#41—28no—
614C2×#41—21no—
615C2×#41—21no—
616C2×#41C23×C3112yes—
617C2×#41C23×C3112yes—
618C22×Q8C23×C3111yescharacteristic
619C22×Q8C23×C3111yescharacteristic
620C22×D4—21no—
621C22×D4—21no—
622C22×D4C23×C3111yescharacteristic
623C22×D4C23×C3111yescharacteristic
624C23×C4—21no—
625C23×C4—21no—
626C23×C4—21no—
627C23×C4—21no—
628C23×C4D4×C3111yescharacteristic
629C23×C4D4×C3111yescharacteristic
630C23×C4C23×C3111yescharacteristic
631#137—28no—
632AGL(1,ℤ/8)—28no—
633C2×Q16C23×C3114yes—
634C2×SD16C23×C3114yes—
635C2×SD16C23×C3114yes—
636C2×D8C23×C3114yes—
637C2×M16C23×C3112yes—
638C2×M16C23×C3112yes—
639#126—22no—
640#126—22no—
641#126—22no—
642#126—22no—
643#125—21no—
644#125—21no—
645#125C23×C3112yes—
646#125C23×C3112yes—
647#124—21no—
648#124—21no—
649#124C23×C3112yes—
650#124C23×C3112yes—
651#123—22no—
652#123—22no—
653#123—22no—
654#123—22no—
655C22⋊Q8—21no—
656C22⋊Q8—21no—
657C22⋊Q8C23×C3112yes—
658C22⋊Q8C23×C3112yes—
659#121—21no—
660#121—21no—
661#121C23×C3112yes—
662#121C23×C3112yes—
663C4×Q8—21no—
664C4×Q8—21no—
665C4×Q8—21no—
666C4×Q8—21no—
667C4×Q8—21no—
668C4×Q8—21no—
669C4×Q8C23×C3112yes—
670C4×Q8C23×C3112yes—
671C4×Q8C23×C3112yes—
672C4×Q8C23×C3112yes—
673C4×Q8C23×C3112yes—
674C4×Q8C23×C3112yes—
675C4×D4—22no—
676C4×D4—22no—
677C4×D4—22no—
678C4×D4—22no—
679C4×D4—22no—
680C4×D4—22no—
681C4×D4—22no—
682C4×D4—22no—
683C4×D4—22no—
684C4×D4—22no—
685C4×D4—22no—
686C4×D4—22no—
687C4×D4—21no—
688C4×D4—21no—
689C4×D4—21no—
690C4×D4—21no—
691C4×D4—21no—
692C4×D4—21no—
693C4×D4C23×C3112yes—
694C4×D4C23×C3112yes—
695C4×D4C23×C3112yes—
696C4×D4C23×C3112yes—
697C4×D4C23×C3112yes—
698C4×D4C23×C3112yes—
699#117—21no—
700#117—21no—
701#117—22no—
702#117—22no—
703#117—22no—
704#117—22no—
705#117—22no—
706#117—22no—
707#117—22no—
708#117—22no—
709#117C23×C3112yes—
710#117C23×C3112yes—
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—21no—
715C2×C4⋊C4—21no—
716C2×C4⋊C4—21no—
717C2×C4⋊C4C23×C3111yescharacteristic
718C2×C4⋊C4C23×C3111yescharacteristic
719C2×C4⋊C4C23×C3111yescharacteristic
720C2×C4⋊C4C23×C3111yescharacteristic
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—22no—
734C2×C42—22no—
735C2×C42—22no—
736C2×C42—22no—
737C2×C42D4×C3111yescharacteristic
738C2×C42D4×C3111yescharacteristic
739C2×C42D4×C3111yescharacteristic
740C2×C42D4×C3111yescharacteristic
741C2×C42D4×C3111yescharacteristic
742C2×C42D4×C3111yescharacteristic
743C2×C42C23×C3111yescharacteristic
744C2×C42C23×C3111yescharacteristic
745C2×C42C23×C3111yescharacteristic
746C2×C42C23×C3111yescharacteristic
747C2×C42C23×C3111yescharacteristic
748C2×C42C23×C3111yescharacteristic
749#107C23×C3114yes—
750#107C23×C3114yes—
751#106C23×C3114yes—
752#106C23×C3114yes—
753C4⋊C8C23×C3114yes—
754C4⋊C8C23×C3114yes—
755#103C23×C3114yes—
756#103C23×C3114yes—
757#103C23×C3114yes—
758#103C23×C3114yes—
759#102C23×C3114yes—
760#102C23×C3114yes—
761#102C23×C3114yes—
762#102C23×C3114yes—
763C22⋊C8C23×C3112yes—
764C22⋊C8C23×C3112yes—
765C22⋊C8C23×C3112yes—
766C22⋊C8C23×C3112yes—
767#97C23×C3114yes—
768C4×C8C23×C3114yes—
769C31#6056311yescharacteristic, direct product factor, Sylow
770C24—21no—
771C24—21no—
772C24C2×D4×C3111yescharacteristic
773#41—28no—
774#41—28no—
775#41—24no—
776#41—24no—
777#41—24no—
778#41#41×C3118yes—
779C2×Q8—24no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—24no—
783C2×Q8C24×C3112yes—
784C2×Q8C24×C3112yes—
785C2×D4—28no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—24no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—24no—
794C2×D4—44no—
795C2×D4C24×C3112yes—
796C2×D4C24×C3112yes—
797C22×C4—28no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—24no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4C2×D4×C3111yescharacteristic
819C22×C4C2×D4×C3111yescharacteristic
820C22×C4C2×D4×C3111yescharacteristic
821C22×C4C2×D4×C3111yescharacteristic
822C22×C4C2×D4×C3111yescharacteristic
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×C4C24×C3111yescharacteristic
834C22×C4C24×C3111yescharacteristic
835C22×C4C24×C3111yescharacteristic
836Q16—28no—
837SD16—28no—
838SD16—28no—
839D8—28no—
840M16—24no—
841M16—24no—
842C2×C8C24×C3114yes—
843C2×C8C24×C3114yes—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4C24×C3112yes—
861C4⋊C4C24×C3112yes—
862C4⋊C4C24×C3112yes—
863C4⋊C4C24×C3112yes—
864C22⋊C4—22no—
865C22⋊C4—22no—
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C42—22no—
881C42—22no—
882C42—22no—
883C42—22no—
884C42—22no—
885C42—22no—
886C42—22no—
887C42—22no—
888C42C2×D4×C3111yescharacteristic
889C42C2×D4×C3111yescharacteristic
890C42C2×D4×C3111yescharacteristic
891C42C2×D4×C3111yescharacteristic
892C42C2×D4×C3111yescharacteristic
893C42C2×D4×C3111yescharacteristic
894C42C2×D4×C3111yescharacteristic
895C42C2×D4×C3111yescharacteristic
896C42C2×D4×C3111yescharacteristic
897C42C2×D4×C3111yescharacteristic
898C42C2×D4×C3111yescharacteristic
899C42C2×D4×C3111yescharacteristic
900C42C24×C3111yescharacteristic
901C42C24×C3111yescharacteristic
902C42C24×C3111yescharacteristic
903C42C24×C3111yescharacteristic
904C23—24no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—41no—
910C23—42no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—42no—
915C23C22×D4×C3111yescharacteristic
916C23C22×D4×C3111yescharacteristic
917C23C22×D4×C3111yescharacteristic
918Q8—24no—
919Q8—22no—
920Q8—24no—
921Q8—42no—
922Q8C2×#41×C3114yes—
923D4—28no—
924D4—24no—
925D4—28no—
926D4—22no—
927D4—24no—
928D4—44no—
929D4—44no—
930D4—42no—
931D4C2×#41×C3114yes—
932C2×C4—24no—
933C2×C4—28no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—28no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—44no—
959C2×C4—44no—
960C2×C4—44no—
961C2×C4—44no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—44no—
968C2×C4—44no—
969C2×C4C22×D4×C3111yescharacteristic
970C2×C4C22×D4×C3111yescharacteristic
971C2×C4C22×D4×C3111yescharacteristic
972C2×C4C22×D4×C3111yescharacteristic
973C2×C4C22×D4×C3111yescharacteristic
974C2×C4C22×D4×C3111yescharacteristic
975C2×C4C22×D4×C3111yescharacteristic
976C2×C4C22×D4×C3111yescharacteristic
977C2×C4C22×D4×C3111yescharacteristic
978C2×C4C22×D4×C3111yescharacteristic
979C2×C4C22×D4×C3111yescharacteristic
980C2×C4C2×#41×C3114yes—
981C2×C4C25×C3111yescharacteristic
982C8—24no—
983C8—24no—
984C22—21no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—24no—
990C22—21no—
991C22—21no—
992C22—44no—
993C22—48no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—84no—
1000C22C31×#52512yes—
1001C22C31×#57512yes—
1002C22C23×D4×C3111yescharacteristic
1003C4—21no—
1004C4—24no—
1005C4—21no—
1006C4—21no—
1007C4—21no—
1008C4—21no—
1009C4—21no—
1010C4—21no—
1011C4—21no—
1012C4—21no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4C31×#52512yes—
1019C4C31×#57512yes—
1020C4C22×#41×C3112yes—
1021C2—22no—
1022C2—22no—
1023C2—41no—
1024C2—44no—
1025C2—82no—
1026C2C2×C31×#52511yescharacteristic
1027C2C2×C31×#57511yescharacteristic
1028C2C2×C31×#57511yescharacteristic
subgroupG/H
centerC2×C4×C31C22×D4
commutator, Frattini, cosocleC2×C4C25×C31
socleC22×C31C23×D4
prime radicalC31×#3006C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#529C2semidirect
2. C2×C4×#41×C31C2semidirect
3. C31×#3117C2semidirect
4. C31×#3114C2semidirect
5. C31×#3111C2semidirect
6. C31×#3108C2semidirect
7. C31×#3105C2semidirect
8. C31×#3102C2semidirect
9. C31×#3095C2semidirect
10. C31×#3094C2semidirect
11. C31×#3080C2semidirect
12. C31×#3040C2semidirect
13. C31×#3007C2semidirect
15. C4×C31×#137C2semidirect
16. C4×C31×AGL(1,ℤ/8)C2semidirect
17. C31×#2920C2semidirect
27. C31×#529C22semidirect
28. C31×#529C22semidirect
30. C2×C31×#125C22semidirect
31. C2×C31×#124C22semidirect
41. C4×#41×C31C22semidirect
42. C4×#41×C31C22semidirect
43. C2×C4×Q8×C31C22semidirect
44. C2×C4×Q8×C31C22semidirect
45. C2×C4×Q8×C31C22semidirect
49. C2×C4×D4×C31C22semidirect
50. C2×C4×D4×C31C22semidirect
51. C2×C4×D4×C31C22semidirect
57. C31×#485C22semidirect
58. C31×#484C22semidirect
59. C31×#483C22semidirect
60. C31×#482C22semidirect
63. C31×#479C22semidirect
64. C31×#479C22semidirect
65. C31×#478C22semidirect
66. C31×#478C22semidirect
67. C31×#464C22semidirect
68. C31×#464C22semidirect
69. C31×#463C22semidirect
70. C31×#463C22semidirect
71. C31×#452C22semidirect
72. C31×#451C22semidirect
73. C31×#450C22semidirect
77. C31×#442C22semidirect
78. C31×#441C22semidirect
79. C31×#440C22semidirect
80. C31×#440C22semidirect
81. C4×Q16×C31C22semidirect
82. C4×SD16×C31C22semidirect
83. C4×SD16×C31C22semidirect
84. C4×D8×C31C22semidirect
85. C31×#432C22semidirect
86. C31×#432C22semidirect
87. C31×#431C22semidirect
88. C31×#431C22semidirect
89. C31×#428C22semidirect
90. C31×#428C22semidirect
91. C31×#423C22semidirect
92. C31×#419C22semidirect
93. C31×#418C22semidirect
98. C4×M16×C31C22semidirect
389. #60563C31direct (N × H)
470. C2×#529C2×C31semidirect
471. C2×C4×#41C2×C31semidirect
472. #3117C2×C31semidirect
473. #3114C2×C31semidirect
474. #3111C2×C31semidirect
475. #3108C2×C31semidirect
476. #3105C2×C31semidirect
477. #3102C2×C31semidirect
478. #3095C2×C31semidirect
479. #3094C2×C31semidirect
480. #3080C2×C31semidirect
481. #3040C2×C31semidirect
482. #3007C2×C31semidirect
484. C4×#137C2×C31semidirect
485. C4×AGL(1,ℤ/8)C2×C31semidirect
486. #2920C2×C31semidirect
533. #529C22×C31semidirect
534. #529C22×C31semidirect
536. C2×#125C22×C31semidirect
537. C2×#124C22×C31semidirect
547. C4×#41C22×C31semidirect
548. C4×#41C22×C31semidirect
549. C2×C4×Q8C22×C31semidirect
550. C2×C4×Q8C22×C31semidirect
551. C2×C4×Q8C22×C31semidirect
555. C2×C4×D4C22×C31semidirect
556. C2×C4×D4C22×C31semidirect
557. C2×C4×D4C22×C31semidirect
563. #485C22×C31semidirect
564. #484C22×C31semidirect
565. #483C22×C31semidirect
566. #482C22×C31semidirect
569. #479C22×C31semidirect
570. #479C22×C31semidirect
571. #478C22×C31semidirect
572. #478C22×C31semidirect
573. #464C22×C31semidirect
574. #464C22×C31semidirect
575. #463C22×C31semidirect
576. #463C22×C31semidirect
577. #452C22×C31semidirect
578. #451C22×C31semidirect
579. #450C22×C31semidirect
583. #442C22×C31semidirect
584. #441C22×C31semidirect
585. #440C22×C31semidirect
586. #440C22×C31semidirect
587. C4×Q16C22×C31semidirect
588. C4×SD16C22×C31semidirect
589. C4×SD16C22×C31semidirect
590. C4×D8C22×C31semidirect
591. #432C22×C31semidirect
592. #432C22×C31semidirect
593. #431C22×C31semidirect
594. #431C22×C31semidirect
595. #428C22×C31semidirect
596. #428C22×C31semidirect
597. #423C22×C31semidirect
598. #419C22×C31semidirect
599. #418C22×C31semidirect
604. C4×M16C22×C31semidirect
769. C31#60563direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5292
C2×C4×#41×C312
C31×#31172
C31×#31142
C31×#31112
C31×#31082
C31×#31052
C31×#31022
C31×#30952
C31×#30942
C31×#30802
C31×#30402
C31×#30072
C31×#30062
C4×C31×#1372
C4×C31×AGL(1,ℤ/8)2
C31×#29202
#6056331