Finite Group Databasebeta

← C31×#23569 #21480328

Subgroups — C31×#23569 #21480328

Order 7936.

1272 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#529C211yesmaximal, characteristic, complemented
2C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
3C2×C4×D8×C31C211yesmaximal, characteristic, complemented
4C4×C31×#121C211yesmaximal, characteristic, complemented
5C31×#2059C211yesmaximal, characteristic, complemented
6C31×#2042C211yesmaximal, characteristic, complemented
7C31×#2036C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic, complemented
9C31×#2025C211yesmaximal, characteristic, complemented
10C31×#2012C211yesmaximal, characteristic, complemented
11C31×#2000C211yesmaximal, characteristic, complemented
12C31×#1999C211yesmaximal, characteristic
13C4×C31×#103C211yesmaximal, characteristic, complemented
14C4×C31×#102C211yesmaximal, characteristic, complemented
15C4×C31×C22⋊C8C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C31×#529—24no—
19C31×#529—24no—
20C2×C31×#126—21no—
21C2×C31×#125C2211yescharacteristic
22C2×C31×#124C2211yescharacteristic
23C2×C31×#123—21no—
24C2×C31×C22⋊Q8C2211yescharacteristic
25C2×C31×#121C2211yescharacteristic
26C2×C31×#121C2211yescharacteristic
27C2×C4×Q8×C31C2211yescharacteristic
28C2×C4×D4×C31—21no—
29C2×C4×D4×C31—21no—
30C2×C4×D4×C31C2211yescharacteristic
31C2×C4×D4×C31C2211yescharacteristic
32C2×C31×#117—21no—
33C22×C42×C31C2211yescharacteristic
34C4×SD16×C31—24no—
35C4×D8×C31—24no—
36C2×C31×#107C2211yescharacteristic
37C2×C31×#106C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C4×C8×C31C2211yescharacteristic
49C2×C4×C8×C31C2211yescharacteristic
50C31×#390C2211yescharacteristic
51C31×#389C2211yescharacteristic
52C31×#388—21no—
53C31×#386—21no—
54C31×#380C2211yescharacteristic
55C4×C4⋊C4×C31C2211yescharacteristic
56C4×C22⋊C4×C31—21no—
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31C2311yescharacteristic
67C22×D4×C31C2311yescharacteristic
68C23×C4×C31—21no—
69C23×C4×C31—21no—
70C23×C4×C31D411yescharacteristic
71C23×C4×C31D411yescharacteristic
72C23×C4×C31C2311yescharacteristic
73C2×SD16×C31—22no—
74C2×SD16×C31—22no—
75C2×SD16×C31—22no—
76C2×D8×C31—22no—
77C2×D8×C31—22no—
78C2×D8×C31—22no—
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C31×#126—28no—
84C31×#125—22no—
85C31×#125—22no—
86C31×#124—22no—
87C31×#124—22no—
88C31×#123—28no—
89C31×C22⋊Q8—22no—
90C31×C22⋊Q8—22no—
91C31×#121—22no—
92C31×#121—22no—
93C31×#121—22no—
94C31×#121—22no—
95C4×Q8×C31—22no—
96C4×Q8×C31D414yescomplemented
97C4×D4×C31—28no—
98C4×D4×C31—22no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31—44no—
102C4×D4×C31D414yescomplemented
103C31×#117—28no—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C42×C31—21no—
125C2×C42×C31—22no—
126C2×C42×C31—22no—
127C2×C42×C31—21no—
128C2×C42×C31D411yescharacteristic
129C2×C42×C31D411yescharacteristic
130C2×C42×C31C2311yescharacteristic
131C2×C42×C31C2311yescharacteristic
132C31×#107—22no—
133C31×#106—22no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#103—22no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×C22⋊C8—22no—
143C31×C22⋊C8—22no—
144C4×C8×C31—22no—
145C4×C8×C31—22no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95—21no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31C2×D411yescharacteristic
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31—21no—
157C2×Q8×C31C2×D412yes—
158C2×D4×C31—24no—
159C2×D4×C31—24no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—42no—
171C2×D4×C31—42no—
172C2×D4×C31—42no—
173C2×D4×C31—42no—
174C2×D4×C31C2×D412yes—
175C2×D4×C31#4112yes—
176C22×C4×C31—22no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—22no—
182C22×C4×C31—22no—
183C22×C4×C31—24no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—41no—
195C22×C4×C31—42no—
196C22×C4×C31—42no—
197C22×C4×C31—42no—
198C22×C4×C31—42no—
199C22×C4×C31—42no—
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2411yescharacteristic
206SD16×C31—28no—
207D8×C31—28no—
208C2×C8×C31—21no—
209C2×C8×C31—21no—
210C2×C8×C31—21no—
211C2×C8×C31—21no—
212C2×C8×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31—21no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31—21no—
218C2×C8×C31#4112yes—
219C2×C8×C31#4112yes—
220C4⋊C4×C31—24no—
221C4⋊C4×C31—24no—
222C4⋊C4×C31—24no—
223C4⋊C4×C31—24no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—42no—
232C4⋊C4×C31C2×D412yes—
233C4⋊C4×C31C2×D412yes—
234C4⋊C4×C31#4112yes—
235C22⋊C4×C31—24no—
236C22⋊C4×C31—24no—
237C22⋊C4×C31—24no—
238C22⋊C4×C31—24no—
239C22⋊C4×C31—24no—
240C22⋊C4×C31—24no—
241C22⋊C4×C31—42no—
242C22⋊C4×C31—42no—
243C22⋊C4×C31—42no—
244C22⋊C4×C31—42no—
245C42×C31—22no—
246C42×C31—22no—
247C42×C31—24no—
248C42×C31—21no—
249C42×C31—21no—
250C42×C31—42no—
251C42×C31C2×D412yes—
252C42×C31C2×D412yes—
253#23569C3111yesmaximal, characteristic, direct product factor, Sylow
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—22no—
261C23×C31—22no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31#13512yes—
275C23×C31C22×D411yescharacteristic
276Q8×C31—22no—
277Q8×C31—22no—
278Q8×C31—41no—
279Q8×C31—41no—
280D4×C31—22no—
281D4×C31—22no—
282D4×C31—22no—
283D4×C31—22no—
284D4×C31—48no—
285D4×C31—48no—
286D4×C31—41no—
287D4×C31—41no—
288D4×C31—41no—
289D4×C31—41no—
290C2×C4×C31—21no—
291C2×C4×C31—21no—
292C2×C4×C31—21no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—22no—
296C2×C4×C31—22no—
297C2×C4×C31—22no—
298C2×C4×C31—21no—
299C2×C4×C31—22no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—44no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—44no—
319C2×C4×C31—48no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—84no—
327C2×C4×C31#12012yes—
328C2×C4×C31#12012yes—
329C2×C4×C31#13512yes—
330C2×C4×C31AGL(1,ℤ/8)12yes—
331C2×C4×C31C22×D411yescharacteristic
332C2×C4×C31C22×D411yescharacteristic
333C2×C4×C31C2×#4111yescharacteristic
334C2×C4×C31C2×#4111yescharacteristic
335C2×C4×C31C2×#4111yescharacteristic
336C2×C4×C31C2×#4111yescharacteristic
337C8×C31—22no—
338C8×C31—22no—
339C8×C31—41no—
340C8×C31—41no—
341C2×#529C2×C3111yescharacteristic, complemented
342C2×C4×SD16C2×C3111yescharacteristic, complemented
343C2×C4×D8C2×C3111yescharacteristic, complemented
344C4×#121C2×C3111yescharacteristic, complemented
345#2059C2×C3111yescharacteristic, complemented
346#2042C2×C3111yescharacteristic, complemented
347#2036C2×C3111yescharacteristic, complemented
348#2034C2×C3111yescharacteristic, complemented
349#2025C2×C3111yescharacteristic, complemented
350#2012C2×C3111yescharacteristic, complemented
351#2000C2×C3111yescharacteristic, complemented
352#1999C2×C3111yescharacteristic
353C4×#103C2×C3111yescharacteristic, complemented
354C4×#102C2×C3111yescharacteristic, complemented
355C4×C22⋊C8C2×C3111yescharacteristic, complemented
356C22×C31—22no—
357C22×C31—22no—
358C22×C31—22no—
359C22×C31—41no—
360C22×C31—41no—
361C22×C31—41no—
362C22×C31—41no—
363C22×C31—42no—
364C22×C31—42no—
365C22×C31—42no—
366C22×C31—42no—
367C22×C31—42no—
368C22×C31—42no—
369C22×C31—81no—
370C22×C31—81no—
371C22×C31—81no—
372C22×C31—81no—
373C22×C31—81no—
374C22×C31—81no—
375C22×C31—81no—
376C22×C31—81no—
377C22×C31C2×#12011yescharacteristic
378C22×C31#52511yescharacteristic
379C22×C31#53211yescharacteristic
380C22×C31C2×#13511yescharacteristic
381C22×C31C2×#13511yescharacteristic
382C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C31#57511yescharacteristic
384C4×C31—22no—
385C4×C31—42no—
386C4×C31—41no—
387C4×C31—42no—
388C4×C31—41no—
389C4×C31—42no—
390C4×C31—41no—
391C4×C31—42no—
392C4×C31—81no—
393C4×C31—81no—
394C4×C31#44914yes—
395C4×C31#52511yescharacteristic
396C4×C31#52511yescharacteristic
397C4×C31#53211yescharacteristic
398C4×C31#53211yescharacteristic
399C22×SD16C22×C3111yescharacteristic
400C22×D8C22×C3111yescharacteristic
401#529—24no—
402#529—24no—
403C2×#126—21no—
404C2×#125C22×C3111yescharacteristic
405C2×#124C22×C3111yescharacteristic
406C2×#123—21no—
407C2×C22⋊Q8C22×C3111yescharacteristic
408C2×#121C22×C3111yescharacteristic
409C2×#121C22×C3111yescharacteristic
410C2×C4×Q8C22×C3111yescharacteristic
411C2×C4×D4—21no—
412C2×C4×D4—21no—
413C2×C4×D4C22×C3111yescharacteristic
414C2×C4×D4C22×C3111yescharacteristic
415C2×#117—21no—
416C22×C42C22×C3111yescharacteristic
417C4×SD16—24no—
418C4×D8—24no—
419C2×#107C22×C3111yescharacteristic
420C2×#106C22×C3111yescharacteristic
421C2×#103C22×C3111yescharacteristic
422C2×#103C22×C3111yescharacteristic
423C2×#103C22×C3111yescharacteristic
424C2×#102C22×C3111yescharacteristic
425C2×#102C22×C3111yescharacteristic
426C2×#102C22×C3111yescharacteristic
427C2×#102C22×C3111yescharacteristic
428C2×#102C22×C3111yescharacteristic
429C2×C22⋊C8C22×C3111yescharacteristic
430C2×C22⋊C8C22×C3111yescharacteristic
431C2×C4×C8C22×C3111yescharacteristic
432C2×C4×C8C22×C3111yescharacteristic
433#390C22×C3111yescharacteristic
434#389C22×C3111yescharacteristic
435#388—21no—
436#386—21no—
437#380C22×C3111yescharacteristic
438C4×C4⋊C4C22×C3111yescharacteristic
439C4×C22⋊C4—21no—
440#340C22×C3111yescharacteristic
441#340C22×C3111yescharacteristic
442#340C22×C3111yescharacteristic
443#340C22×C3111yescharacteristic
444#336C22×C3111yescharacteristic
445#336C22×C3111yescharacteristic
446C2×C31—42no—
447C2×C31—82no—
448C2×C31—82no—
449C2×C31#238811yescharacteristic
450C2×C31C2×#44911yescharacteristic
451C2×C31#300211yescharacteristic
452C2×C31#310211yescharacteristic
453C2×C31#310511yescharacteristic
454C2×C31#316811yescharacteristic
455C2×C31#317111yescharacteristic
456C22×Q8C23×C3111yescharacteristic
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C23×C3111yescharacteristic
460C22×D4C23×C3111yescharacteristic
461C23×C4—21no—
462C23×C4—21no—
463C23×C4D4×C3111yescharacteristic
464C23×C4D4×C3111yescharacteristic
465C23×C4C23×C3111yescharacteristic
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—22no—
469C2×D8—22no—
470C2×D8—22no—
471C2×D8—22no—
472C22×C8C23×C3111yescharacteristic
473C22×C8C23×C3111yescharacteristic
474C22×C8C23×C3111yescharacteristic
475C22×C8C23×C3111yescharacteristic
476#126—28no—
477#125—22no—
478#125—22no—
479#124—22no—
480#124—22no—
481#123—28no—
482C22⋊Q8—22no—
483C22⋊Q8—22no—
484#121—22no—
485#121—22no—
486#121—22no—
487#121—22no—
488C4×Q8—22no—
489C4×Q8D4×C3114yescomplemented
490C4×D4—28no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—44no—
495C4×D4D4×C3114yescomplemented
496#117—28no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4C23×C3111yescharacteristic
503C2×C4⋊C4C23×C3111yescharacteristic
504C2×C4⋊C4C23×C3111yescharacteristic
505C2×C4⋊C4C23×C3111yescharacteristic
506C2×C4⋊C4C23×C3111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C42—21no—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—21no—
521C2×C42D4×C3111yescharacteristic
522C2×C42D4×C3111yescharacteristic
523C2×C42C23×C3111yescharacteristic
524C2×C42C23×C3111yescharacteristic
525#107—22no—
526#106—22no—
527#103—22no—
528#103—22no—
529#103—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—22no—
534#102—22no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C4×C8—22no—
538C4×C8—22no—
539#95—21no—
540#95—21no—
541#95—21no—
542C31#2356911yescharacteristic, direct product factor, Sylow
543C24—21no—
544C24—21no—
545C24C2×D4×C3111yescharacteristic
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8C2×D4×C3112yes—
552C2×D4—24no—
553C2×D4—24no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4C2×D4×C3112yes—
569C2×D4#41×C3112yes—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—41no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4C2×D4×C3111yescharacteristic
595C22×C4C2×D4×C3111yescharacteristic
596C22×C4C2×D4×C3111yescharacteristic
597C22×C4C2×D4×C3111yescharacteristic
598C22×C4C2×D4×C3111yescharacteristic
599C22×C4C24×C3111yescharacteristic
600SD16—28no—
601D8—28no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8#41×C3112yes—
613C2×C8#41×C3112yes—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—42no—
626C4⋊C4C2×D4×C3112yes—
627C4⋊C4C2×D4×C3112yes—
628C4⋊C4#41×C3112yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C42—22no—
640C42—22no—
641C42—24no—
642C42—21no—
643C42—21no—
644C42—42no—
645C42C2×D4×C3112yes—
646C42C2×D4×C3112yes—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23C31×#13512yes—
668C23C22×D4×C3111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—41no—
672Q8—41no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—22no—
677D4—48no—
678D4—48no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—44no—
708C2×C4—48no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—84no—
720C2×C4C31×#12012yes—
721C2×C4C31×#12012yes—
722C2×C4C31×#13512yes—
723C2×C4C31×AGL(1,ℤ/8)12yes—
724C2×C4C22×D4×C3111yescharacteristic
725C2×C4C22×D4×C3111yescharacteristic
726C2×C4C2×#41×C3111yescharacteristic
727C2×C4C2×#41×C3111yescharacteristic
728C2×C4C2×#41×C3111yescharacteristic
729C2×C4C2×#41×C3111yescharacteristic
730C8—22no—
731C8—22no—
732C8—41no—
733C8—41no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22C2×C31×#12011yescharacteristic
756C22C31×#52511yescharacteristic
757C22C31×#53211yescharacteristic
758C22C2×C31×#13511yescharacteristic
759C22C2×C31×#13511yescharacteristic
760C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
761C22C31×#57511yescharacteristic
762C4—22no—
763C4—42no—
764C4—41no—
765C4—42no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—81no—
771C4—81no—
772C4C31×#44914yes—
773C4C31×#52511yescharacteristic
774C4C31×#52511yescharacteristic
775C4C31×#53211yescharacteristic
776C4C31×#53211yescharacteristic
777C2—42no—
778C2—82no—
779C2—82no—
780C2C31×#238811yescharacteristic
781C2C2×C31×#44911yescharacteristic
782C2C31×#300211yescharacteristic
783C2C31×#310211yescharacteristic
784C2C31×#310511yescharacteristic
785C2C31×#316811yescharacteristic
786C2C31×#317111yescharacteristic
subgroupG/H
centerC22×C4×C31C2×D4
commutator, Frattini, cosocleC22×C4C24×C31
socleC23×C31C22×D4
prime radicalC31×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×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×SD16×C31C2semidirect
3. C2×C4×D8×C31C2semidirect
4. C4×C31×#121C2semidirect
5. C31×#2059C2semidirect
6. C31×#2042C2semidirect
7. C31×#2036C2semidirect
8. C31×#2034C2semidirect
9. C31×#2025C2semidirect
10. C31×#2012C2semidirect
11. C31×#2000C2semidirect
13. C4×C31×#103C2semidirect
14. C4×C31×#102C2semidirect
15. C4×C31×C22⋊C8C2semidirect
96. C4×Q8×C31D4semidirect
102. C4×D4×C31D4semidirect
253. #23569C31direct (N × H)
341. C2×#529C2×C31semidirect
342. C2×C4×SD16C2×C31semidirect
343. C2×C4×D8C2×C31semidirect
344. C4×#121C2×C31semidirect
345. #2059C2×C31semidirect
346. #2042C2×C31semidirect
347. #2036C2×C31semidirect
348. #2034C2×C31semidirect
349. #2025C2×C31semidirect
350. #2012C2×C31semidirect
351. #2000C2×C31semidirect
353. C4×#103C2×C31semidirect
354. C4×#102C2×C31semidirect
355. C4×C22⋊C8C2×C31semidirect
489. C4×Q8D4×C31semidirect
495. C4×D4D4×C31semidirect
542. C31#23569direct (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×SD16×C312
C2×C4×D8×C312
C4×C31×#1212
C31×#20592
C31×#20422
C31×#20362
C31×#20342
C31×#20252
C31×#20122
C31×#20002
C31×#19992
C4×C31×#1032
C4×C31×#1022
C4×C31×C22⋊C82
#2356931