Finite Group Databasebeta

← C31×#24347 #21481106

Subgroups — C31×#24347 #21481106

Order 7936.

1140 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#554C211yesmaximal, characteristic, complemented
2C2×C31×#478C211yesmaximal, characteristic, complemented
3C2×C31×#442C211yesmaximal, characteristic
4C31×#2538C211yesmaximal, characteristic, complemented
5C31×#2059C211yesmaximal, characteristic, complemented
6C31×#2058C211yesmaximal, characteristic, complemented
7C31×#2025C211yesmaximal, characteristic, complemented
8C31×#2023C211yesmaximal, characteristic, complemented
9C31×#1992C211yesmaximal, characteristic, complemented
10C31×#1985C211yesmaximal, characteristic, complemented
11C31×#1879C211yesmaximal, characteristic
12C31×#1879C211yesmaximal, characteristic
13C31×#1864C211yesmaximal, characteristic, complemented
14C31×#1862C211yesmaximal, characteristic, complemented
15C31×#1802C211yesmaximal, characteristic, complemented
16C22×D8×C31C2211yescharacteristic
17C31×#554—24no—
18C31×#554—24no—
19C2×C31×C4⋊Q8C2211yescharacteristic
20C2×C31×#125C2211yescharacteristic
21C2×C31×#125C2211yescharacteristic
22C2×C31×C22⋊Q8—21no—
23C2×C31×C22⋊Q8—21no—
24C2×C31×C22⋊Q8—21no—
25C2×C31×C22⋊Q8—21no—
26C2×C4×Q8×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C2×C4×D4×C31C2211yescharacteristic
29C2×C4×D4×C31C2211yescharacteristic
30C2×C4×D4×C31C2211yescharacteristic
31C22×C4⋊C4×C31—21no—
32C31×#478—24no—
33C31×#442—24no—
34C2×C31×#107C2211yescharacteristic
35C2×C31×#106C2211yescharacteristic
36C2×C31×#106C2211yescharacteristic
37C2×C31×C4⋊C8C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#97C2211yescharacteristic
45C31×#396—21no—
46C31×#396—21no—
47C31×#390C2211yescharacteristic
48C31×#390C2211yescharacteristic
49C31×#389C2211yescharacteristic
50C31×#389C2211yescharacteristic
51C31×#384C2211yescharacteristic
52C31×#380—21no—
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31—21no—
64C22×Q8×C31D411yescharacteristic
65C22×D4×C31C2311yescharacteristic
66C22×D4×C31C2311yescharacteristic
67C23×C4×C31—21no—
68C23×C4×C31—21no—
69C23×C4×C31—21no—
70C23×C4×C31—21no—
71C2×D8×C31—22no—
72C2×D8×C31—22no—
73C2×D8×C31Q814yescomplemented
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C31×C4⋊Q8—22no—
79C31×C4⋊Q8—22no—
80C31×#125—22no—
81C31×#125—22no—
82C31×#125—22no—
83C31×#125D414yes—
84C31×C22⋊Q8—28no—
85C31×C22⋊Q8—28no—
86C31×C22⋊Q8—28no—
87C31×C22⋊Q8—44no—
88C4×Q8×C31—22no—
89C4×Q8×C31—22no—
90C4×D4×C31—22no—
91C4×D4×C31—22no—
92C4×D4×C31—22no—
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C4×D4×C31—22no—
96C4×D4×C31—22no—
97C4×D4×C31D414yes—
98C2×C4⋊C4×C31—28no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31D411yescharacteristic
109C2×C4⋊C4×C31D411yescharacteristic
110C2×C4⋊C4×C31D411yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
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×C22⋊C4×C31—21no—
125C2×C42×C31C2311yescharacteristic
126C2×C42×C31C2311yescharacteristic
127C2×C42×C31C2311yescharacteristic
128C31×#107—22no—
129C31×#106—22no—
130C31×#106—22no—
131C31×C4⋊C8—22no—
132C31×#102—22no—
133C31×#102—22no—
134C31×#102—22no—
135C31×#102—22no—
136C31×#102—22no—
137C31×#102—22no—
138C31×#97—22no—
139C31×#95—21no—
140C31×#95—21no—
141C24×C31—21no—
142C24×C31—21no—
143C2×Q8×C31—24no—
144C2×Q8×C31—22no—
145C2×Q8×C31—22no—
146C2×Q8×C31—41no—
147C2×Q8×C31—81no—
148C2×Q8×C31—81no—
149C2×D4×C31—21no—
150C2×D4×C31—21no—
151C2×D4×C31—21no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31C2×D412yes—
158C2×D4×C31C2×Q812yes—
159C2×D4×C31C2×Q812yes—
160C2×D4×C31#4112yes—
161C22×C4×C31—24no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—24no—
166C22×C4×C31—24no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—42no—
171C22×C4×C31—42no—
172C22×C4×C31—42no—
173C22×C4×C31—42no—
174C22×C4×C31—42no—
175C22×C4×C31—81no—
176C22×C4×C31—81no—
177C22×C4×C31—81no—
178C22×C4×C31—81no—
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2×D411yescharacteristic
182C22×C4×C31C2×D411yescharacteristic
183C22×C4×C31C2×D411yescharacteristic
184C22×C4×C31C2×D411yescharacteristic
185C22×C4×C31C2411yescharacteristic
186D8×C31—28no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31—21no—
194C2×C8×C31—21no—
195C2×C8×C31—21no—
196C2×C8×C31—21no—
197C2×C8×C31—21no—
198C2×C8×C31C2×Q812yes—
199C4⋊C4×C31—24no—
200C4⋊C4×C31—24no—
201C4⋊C4×C31—24no—
202C4⋊C4×C31—22no—
203C4⋊C4×C31—24no—
204C4⋊C4×C31—24no—
205C4⋊C4×C31—22no—
206C4⋊C4×C31—22no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—42no—
217C4⋊C4×C31—42no—
218C4⋊C4×C31—42no—
219C4⋊C4×C31—81no—
220C4⋊C4×C31C2×D412yes—
221C4⋊C4×C31C2×D412yes—
222C4⋊C4×C31C2×D412yes—
223C22⋊C4×C31—24no—
224C22⋊C4×C31—24no—
225C22⋊C4×C31—24no—
226C22⋊C4×C31—42no—
227C22⋊C4×C31—42no—
228C22⋊C4×C31—42no—
229C22⋊C4×C31—81no—
230C22⋊C4×C31—81no—
231C42×C31—21no—
232C42×C31—21no—
233C42×C31—21no—
234C42×C31—21no—
235C42×C31C2×D412yes—
236C42×C31C2×D412yes—
237#24347C3111yesmaximal, characteristic, direct product factor, Sylow
238C23×C31—22no—
239C23×C31—22no—
240C23×C31—22no—
241C23×C31—22no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31—41no—
250C23×C31—41no—
251C23×C31—41no—
252C23×C31C22×D411yescharacteristic
253Q8×C31—44no—
254Q8×C31—84no—
255D4×C31—22no—
256D4×C31—22no—
257D4×C31—22no—
258D4×C31—22no—
259D4×C31—22no—
260D4×C31—41no—
261D4×C31—41no—
262D4×C31C22⋊Q814yescomplemented
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—21no—
268C2×C4×C31—21no—
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—21no—
272C2×C4×C31—22no—
273C2×C4×C31—22no—
274C2×C4×C31—22no—
275C2×C4×C31—21no—
276C2×C4×C31—21no—
277C2×C4×C31—21no—
278C2×C4×C31—21no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—48no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—84no—
298C2×C4×C31—84no—
299C2×C4×C31—84no—
300C2×C4×C31#12012yes—
301C2×C4×C31#12012yes—
302C2×C4×C31AGL(1,ℤ/8)12yes—
303C2×C4×C31C22×D411yescharacteristic
304C2×C4×C31C22×D411yescharacteristic
305C2×C4×C31C22×Q811yescharacteristic
306C2×C4×C31C2×#4111yescharacteristic
307C2×C4×C312−1+411yescharacteristic
308C2×C4×C312−1+411yescharacteristic
309C8×C31—22no—
310C8×C31—41no—
311C8×C31—41no—
312C8×C31—41no—
313C2×#554C2×C3111yescharacteristic, complemented
314C2×#478C2×C3111yescharacteristic, complemented
315C2×#442C2×C3111yescharacteristic
316#2538C2×C3111yescharacteristic, complemented
317#2059C2×C3111yescharacteristic, complemented
318#2058C2×C3111yescharacteristic, complemented
319#2025C2×C3111yescharacteristic, complemented
320#2023C2×C3111yescharacteristic, complemented
321#1992C2×C3111yescharacteristic, complemented
322#1985C2×C3111yescharacteristic, complemented
323#1879C2×C3111yescharacteristic
324#1879C2×C3111yescharacteristic
325#1864C2×C3111yescharacteristic, complemented
326#1862C2×C3111yescharacteristic, complemented
327#1802C2×C3111yescharacteristic, complemented
328C22×C31—24no—
329C22×C31—42no—
330C22×C31—42no—
331C22×C31—42no—
332C22×C31—42no—
333C22×C31—42no—
334C22×C31—42no—
335C22×C31—42no—
336C22×C31—42no—
337C22×C31—42no—
338C22×C31—81no—
339C22×C31—81no—
340C22×C31—81no—
341C22×C31—81no—
342C22×C31C2×#12011yescharacteristic
343C22×C31#54811yescharacteristic
344C22×C31D4×Q811yescharacteristic
345C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C31#57511yescharacteristic
347C22×C31#57611yescharacteristic
348C22×C31#57711yescharacteristic
349C4×C31—22no—
350C4×C31—22no—
351C4×C31—22no—
352C4×C31—41no—
353C4×C31—42no—
354C4×C31—41no—
355C4×C31—41no—
356C4×C31—42no—
357C4×C31—42no—
358C4×C31—81no—
359C4×C31—81no—
360C4×C31—81no—
361C4×C31C2×C22⋊Q811yescharacteristic
362C4×C31#53611yescharacteristic
363C4×C31#54811yescharacteristic
364C4×C31D4×Q811yescharacteristic
365C22×D8C22×C3111yescharacteristic
366#554—24no—
367#554—24no—
368C2×C4⋊Q8C22×C3111yescharacteristic
369C2×#125C22×C3111yescharacteristic
370C2×#125C22×C3111yescharacteristic
371C2×C22⋊Q8—21no—
372C2×C22⋊Q8—21no—
373C2×C22⋊Q8—21no—
374C2×C22⋊Q8—21no—
375C2×C4×Q8C22×C3111yescharacteristic
376C2×C4×D4C22×C3111yescharacteristic
377C2×C4×D4C22×C3111yescharacteristic
378C2×C4×D4C22×C3111yescharacteristic
379C2×C4×D4C22×C3111yescharacteristic
380C22×C4⋊C4—21no—
381#478—24no—
382#442—24no—
383C2×#107C22×C3111yescharacteristic
384C2×#106C22×C3111yescharacteristic
385C2×#106C22×C3111yescharacteristic
386C2×C4⋊C8C22×C3111yescharacteristic
387C2×#102C22×C3111yescharacteristic
388C2×#102C22×C3111yescharacteristic
389C2×#102C22×C3111yescharacteristic
390C2×#102C22×C3111yescharacteristic
391C2×#102C22×C3111yescharacteristic
392C2×#102C22×C3111yescharacteristic
393C2×#97C22×C3111yescharacteristic
394#396—21no—
395#396—21no—
396#390C22×C3111yescharacteristic
397#390C22×C3111yescharacteristic
398#389C22×C3111yescharacteristic
399#389C22×C3111yescharacteristic
400#384C22×C3111yescharacteristic
401#380—21no—
402#340C22×C3111yescharacteristic
403#340C22×C3111yescharacteristic
404#340C22×C3111yescharacteristic
405#340C22×C3111yescharacteristic
406#340C22×C3111yescharacteristic
407#340C22×C3111yescharacteristic
408#336C22×C3111yescharacteristic
409#336C22×C3111yescharacteristic
410#336C22×C3111yescharacteristic
411#336C22×C3111yescharacteristic
412C2×C31—44no—
413C2×C31—82no—
414C2×C31#240911yescharacteristic
415C2×C31#300611yescharacteristic
416C2×C31#301211yescharacteristic
417C2×C31#336611yescharacteristic
418C2×C31#337611yescharacteristic
419C2×C31#338411yescharacteristic
420C2×C31#338911yescharacteristic
421C22×Q8—21no—
422C22×Q8D4×C3111yescharacteristic
423C22×D4C23×C3111yescharacteristic
424C22×D4C23×C3111yescharacteristic
425C23×C4—21no—
426C23×C4—21no—
427C23×C4—21no—
428C23×C4—21no—
429C2×D8—22no—
430C2×D8—22no—
431C2×D8Q8×C3114yescomplemented
432C22×C8C23×C3111yescharacteristic
433C22×C8C23×C3111yescharacteristic
434C22×C8C23×C3111yescharacteristic
435C22×C8C23×C3111yescharacteristic
436C4⋊Q8—22no—
437C4⋊Q8—22no—
438#125—22no—
439#125—22no—
440#125—22no—
441#125D4×C3114yes—
442C22⋊Q8—28no—
443C22⋊Q8—28no—
444C22⋊Q8—28no—
445C22⋊Q8—44no—
446C4×Q8—22no—
447C4×Q8—22no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—22no—
455C4×D4D4×C3114yes—
456C2×C4⋊C4—28no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4D4×C3111yescharacteristic
467C2×C4⋊C4D4×C3111yescharacteristic
468C2×C4⋊C4D4×C3111yescharacteristic
469C2×C4⋊C4C23×C3111yescharacteristic
470C2×C4⋊C4C23×C3111yescharacteristic
471C2×C4⋊C4C23×C3111yescharacteristic
472C2×C4⋊C4C23×C3111yescharacteristic
473C2×C4⋊C4C23×C3111yescharacteristic
474C2×C4⋊C4C23×C3111yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C42C23×C3111yescharacteristic
484C2×C42C23×C3111yescharacteristic
485C2×C42C23×C3111yescharacteristic
486#107—22no—
487#106—22no—
488#106—22no—
489C4⋊C8—22no—
490#102—22no—
491#102—22no—
492#102—22no—
493#102—22no—
494#102—22no—
495#102—22no—
496#97—22no—
497#95—21no—
498#95—21no—
499C31#2434711yescharacteristic, direct product factor, Sylow
500C24—21no—
501C24—21no—
502C2×Q8—24no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—41no—
506C2×Q8—81no—
507C2×Q8—81no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4C2×D4×C3112yes—
517C2×D4C2×Q8×C3112yes—
518C2×D4C2×Q8×C3112yes—
519C2×D4#41×C3112yes—
520C22×C4—24no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4C2×D4×C3111yescharacteristic
539C22×C4C2×D4×C3111yescharacteristic
540C22×C4C2×D4×C3111yescharacteristic
541C22×C4C2×D4×C3111yescharacteristic
542C22×C4C2×D4×C3111yescharacteristic
543C22×C4C2×D4×C3111yescharacteristic
544C22×C4C24×C3111yescharacteristic
545D8—28no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8C2×Q8×C3112yes—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—22no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—81no—
579C4⋊C4C2×D4×C3112yes—
580C4⋊C4C2×D4×C3112yes—
581C4⋊C4C2×D4×C3112yes—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—24no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42C2×D4×C3112yes—
595C42C2×D4×C3112yes—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23C22×D4×C3111yescharacteristic
611Q8—44no—
612Q8—84no—
613D4—22no—
614D4—22no—
615D4—22no—
616D4—22no—
617D4—22no—
618D4—41no—
619D4—41no—
620D4C31×C22⋊Q814yescomplemented
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—48no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—84no—
656C2×C4—84no—
657C2×C4—84no—
658C2×C4C31×#12012yes—
659C2×C4C31×#12012yes—
660C2×C4C31×AGL(1,ℤ/8)12yes—
661C2×C4C22×D4×C3111yescharacteristic
662C2×C4C22×D4×C3111yescharacteristic
663C2×C4C22×Q8×C3111yescharacteristic
664C2×C4C2×#41×C3111yescharacteristic
665C2×C4C31×2−1+411yescharacteristic
666C2×C4C31×2−1+411yescharacteristic
667C8—22no—
668C8—41no—
669C8—41no—
670C8—41no—
671C22—24no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22C2×C31×#12011yescharacteristic
686C22C31×#54811yescharacteristic
687C22D4×Q8×C3111yescharacteristic
688C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
689C22C31×#57511yescharacteristic
690C22C31×#57611yescharacteristic
691C22C31×#57711yescharacteristic
692C4—22no—
693C4—22no—
694C4—22no—
695C4—41no—
696C4—42no—
697C4—41no—
698C4—41no—
699C4—42no—
700C4—42no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4C2×C31×C22⋊Q811yescharacteristic
705C4C31×#53611yescharacteristic
706C4C31×#54811yescharacteristic
707C4D4×Q8×C3111yescharacteristic
708C2—44no—
709C2—82no—
710C2C31×#240911yescharacteristic
711C2C31×#300611yescharacteristic
712C2C31×#301211yescharacteristic
713C2C31×#336611yescharacteristic
714C2C31×#337611yescharacteristic
715C2C31×#338411yescharacteristic
716C2C31×#338911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D8×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#554C2semidirect
2. C2×C31×#478C2semidirect
4. C31×#2538C2semidirect
5. C31×#2059C2semidirect
6. C31×#2058C2semidirect
7. C31×#2025C2semidirect
8. C31×#2023C2semidirect
9. C31×#1992C2semidirect
10. C31×#1985C2semidirect
13. C31×#1864C2semidirect
14. C31×#1862C2semidirect
15. C31×#1802C2semidirect
73. C2×D8×C31Q8semidirect
237. #24347C31direct (N × H)
262. D4×C31C22⋊Q8semidirect
313. C2×#554C2×C31semidirect
314. C2×#478C2×C31semidirect
316. #2538C2×C31semidirect
317. #2059C2×C31semidirect
318. #2058C2×C31semidirect
319. #2025C2×C31semidirect
320. #2023C2×C31semidirect
321. #1992C2×C31semidirect
322. #1985C2×C31semidirect
325. #1864C2×C31semidirect
326. #1862C2×C31semidirect
327. #1802C2×C31semidirect
431. C2×D8Q8×C31semidirect
499. C31#24347direct (N × H)
620. D4C31×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5542
C2×C31×#4782
C2×C31×#4422
C31×#25382
C31×#20592
C31×#20582
C31×#20252
C31×#20232
C31×#19922
C31×#19852
C31×#18792
C31×#18642
C31×#18622
C31×#18022
#2434731