Finite Group Databasebeta

← C31×#25938 #21482697

Subgroups — C31×#25938 #21482697

Order 7936.

1104 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#554C211yesmaximal, characteristic, complemented
2C2×C31×#488C211yesmaximal, characteristic, complemented
3C2×C31×#463C211yesmaximal, characteristic
4C31×#2592C211yesmaximal, characteristic, complemented
5C31×#2026C211yesmaximal, characteristic, complemented
6C31×#2025C211yesmaximal, characteristic, complemented
7C31×#2024C211yesmaximal, characteristic, complemented
8C31×#2023C211yesmaximal, characteristic, complemented
9C31×#1989C211yesmaximal, characteristic, complemented
10C31×#1984C211yesmaximal, characteristic, complemented
11C31×#1879C211yesmaximal, characteristic
12C31×#1879C211yesmaximal, characteristic
13C31×#1877C211yesmaximal, characteristic, complemented
14C31×#1877C211yesmaximal, characteristic, complemented
15C4×C31×#102C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C31×#554—24no—
19C31×#554—24no—
20C2×C31×C4⋊Q8C2211yescharacteristic
21C2×C31×#125C2211yescharacteristic
22C2×C31×#125C2211yescharacteristic
23C2×C31×#124C2211yescharacteristic
24C2×C31×C22⋊Q8—21no—
25C2×C31×C22⋊Q8—21no—
26C2×C31×C22⋊Q8—21no—
27C2×C4×Q8×C31C2211yescharacteristic
28C2×C4×D4×C31C2211yescharacteristic
29C2×C4×D4×C31C2211yescharacteristic
30C2×C4×D4×C31C2211yescharacteristic
31C22×C4⋊C4×C31—21no—
32C31×#488—24no—
33C31×#463—24no—
34C2×C31×C4⋊C8C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C4×C8×C31C2211yescharacteristic
44C31×#397—21no—
45C31×#393—21no—
46C31×#391C2211yescharacteristic
47C31×#391C2211yescharacteristic
48C31×#390C2211yescharacteristic
49C31×#390C2211yescharacteristic
50C31×#388—21no—
51C31×#388—21no—
52C4×C4⋊C4×C31C2211yescharacteristic
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×Q8×C31C2311yescharacteristic
66C22×D4×C31C2311yescharacteristic
67C22×D4×C31C2311yescharacteristic
68C23×C4×C31—21no—
69C23×C4×C31—21no—
70C23×C4×C31—21no—
71C2×SD16×C31—22no—
72C2×SD16×C31—22no—
73C2×SD16×C31—22no—
74C2×D8×C31—22no—
75C2×D8×C31—22no—
76C2×D8×C31—22no—
77C22×C8×C31C2311yescharacteristic
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C31×C4⋊Q8—22no—
82C31×C4⋊Q8—22no—
83C31×#125—22no—
84C31×#125—22no—
85C31×#125—22no—
86C31×#125D414yes—
87C31×#124—22no—
88C31×#124—22no—
89C31×C22⋊Q8—28no—
90C31×C22⋊Q8—28no—
91C31×C22⋊Q8—28no—
92C4×Q8×C31—22no—
93C4×Q8×C31—22no—
94C4×D4×C31—22no—
95C4×D4×C31—22no—
96C4×D4×C31—22no—
97C4×D4×C31—22no—
98C4×D4×C31—22no—
99C4×D4×C31D414yes—
100C2×C4⋊C4×C31—28no—
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×C31D411yescharacteristic
107C2×C4⋊C4×C31D411yescharacteristic
108C2×C4⋊C4×C31D411yescharacteristic
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×C42×C31—21no—
124C2×C42×C31C2311yescharacteristic
125C2×C42×C31C2311yescharacteristic
126C2×C42×C31C2311yescharacteristic
127C31×C4⋊C8—22no—
128C31×#103—22no—
129C31×#103—22no—
130C31×#103—22no—
131C31×#102—22no—
132C31×#102—22no—
133C31×#102—22no—
134C31×#102—22no—
135C31×#102—22no—
136C4×C8×C31—22no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C24×C31—21no—
143C24×C31—21no—
144C2×Q8×C31—24no—
145C2×Q8×C31—22no—
146C2×Q8×C31—22no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
153C2×Q8×C31—41no—
154C2×Q8×C31—81no—
155C2×Q8×C31—81no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31C2×D412yes—
166C2×D4×C31#4112yes—
167C2×D4×C31#4112yes—
168C22×C4×C31—24no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—24no—
173C22×C4×C31—24no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—42no—
178C22×C4×C31—42no—
179C22×C4×C31—81no—
180C22×C4×C31—81no—
181C22×C4×C31—81no—
182C22×C4×C31—81no—
183C22×C4×C31C2×D411yescharacteristic
184C22×C4×C31C2×D411yescharacteristic
185C22×C4×C31C2×D411yescharacteristic
186C22×C4×C31C2×D411yescharacteristic
187C22×C4×C31C2×D411yescharacteristic
188C22×C4×C31C2×D411yescharacteristic
189C22×C4×C31C2411yescharacteristic
190SD16×C31—44no—
191D8×C31—44no—
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×C31—21no—
199C2×C8×C31—21no—
200C2×C8×C31—21no—
201C2×C8×C31—21no—
202C2×C8×C31—21no—
203C2×C8×C31—21no—
204C4⋊C4×C31—24no—
205C4⋊C4×C31—24no—
206C4⋊C4×C31—24no—
207C4⋊C4×C31—22no—
208C4⋊C4×C31—24no—
209C4⋊C4×C31—24no—
210C4⋊C4×C31—22no—
211C4⋊C4×C31—22no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31C2×D412yes—
220C4⋊C4×C31C2×D412yes—
221C4⋊C4×C31C2×D412yes—
222C22⋊C4×C31—24no—
223C22⋊C4×C31—24no—
224C22⋊C4×C31—24no—
225C22⋊C4×C31—42no—
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×C31—81no—
236C42×C31C2×D412yes—
237C42×C31C2×D412yes—
238#25938C3111yesmaximal, characteristic, direct product factor, Sylow
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×C31—41no—
253C23×C31C22×D411yescharacteristic
254Q8×C31—44no—
255Q8×C31—41no—
256Q8×C31—41no—
257Q8×C31—41no—
258Q8×C31—41no—
259Q8×C31—84no—
260D4×C31—22no—
261D4×C31—22no—
262D4×C31—22no—
263D4×C31—41no—
264D4×C31—41no—
265D4×C31—41no—
266D4×C31—41no—
267D4×C31#12414yes—
268C2×C4×C31—21no—
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—21no—
276C2×C4×C31—21no—
277C2×C4×C31—22no—
278C2×C4×C31—22no—
279C2×C4×C31—22no—
280C2×C4×C31—21no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
283C2×C4×C31—21no—
284C2×C4×C31—21no—
285C2×C4×C31—21no—
286C2×C4×C31—48no—
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—41no—
298C2×C4×C31—41no—
299C2×C4×C31—41no—
300C2×C4×C31—41no—
301C2×C4×C31—41no—
302C2×C4×C31—84no—
303C2×C4×C31—84no—
304C2×C4×C31#12012yes—
305C2×C4×C31#12012yes—
306C2×C4×C31#13512yes—
307C2×C4×C31C22×D411yescharacteristic
308C2×C4×C31C22×D411yescharacteristic
309C2×C4×C31C2×#4111yescharacteristic
310C2×C4×C31C2×#4111yescharacteristic
311C2×C4×C312−1+411yescharacteristic
312C2×C4×C312−1+411yescharacteristic
313C8×C31—41no—
314C8×C31—41no—
315C8×C31—41no—
316C8×C31—41no—
317C2×#554C2×C3111yescharacteristic, complemented
318C2×#488C2×C3111yescharacteristic, complemented
319C2×#463C2×C3111yescharacteristic
320#2592C2×C3111yescharacteristic, complemented
321#2026C2×C3111yescharacteristic, complemented
322#2025C2×C3111yescharacteristic, complemented
323#2024C2×C3111yescharacteristic, complemented
324#2023C2×C3111yescharacteristic, complemented
325#1989C2×C3111yescharacteristic, complemented
326#1984C2×C3111yescharacteristic, complemented
327#1879C2×C3111yescharacteristic
328#1879C2×C3111yescharacteristic
329#1877C2×C3111yescharacteristic, complemented
330#1877C2×C3111yescharacteristic, complemented
331C4×#102C2×C3111yescharacteristic, complemented
332C22×C31—24no—
333C22×C31—42no—
334C22×C31—42no—
335C22×C31—42no—
336C22×C31—42no—
337C22×C31—42no—
338C22×C31—42no—
339C22×C31—81no—
340C22×C31—81no—
341C22×C31—81no—
342C22×C31—81no—
343C22×C31—81no—
344C22×C31—81no—
345C22×C31—81no—
346C22×C31C2×#12011yescharacteristic
347C22×C31#54811yescharacteristic
348C22×C31#54811yescharacteristic
349C22×C31C2×#13511yescharacteristic
350C22×C31#57511yescharacteristic
351C22×C31#57611yescharacteristic
352C22×C31#57711yescharacteristic
353C4×C31—22no—
354C4×C31—22no—
355C4×C31—22no—
356C4×C31—41no—
357C4×C31—42no—
358C4×C31—41no—
359C4×C31—41no—
360C4×C31—42no—
361C4×C31—42no—
362C4×C31—81no—
363C4×C31—81no—
364C4×C31—81no—
365C4×C31C2×#12411yescharacteristic
366C4×C31#53611yescharacteristic
367C4×C31#54811yescharacteristic
368C4×C31#54811yescharacteristic
369C22×SD16C22×C3111yescharacteristic
370C22×D8C22×C3111yescharacteristic
371#554—24no—
372#554—24no—
373C2×C4⋊Q8C22×C3111yescharacteristic
374C2×#125C22×C3111yescharacteristic
375C2×#125C22×C3111yescharacteristic
376C2×#124C22×C3111yescharacteristic
377C2×C22⋊Q8—21no—
378C2×C22⋊Q8—21no—
379C2×C22⋊Q8—21no—
380C2×C4×Q8C22×C3111yescharacteristic
381C2×C4×D4C22×C3111yescharacteristic
382C2×C4×D4C22×C3111yescharacteristic
383C2×C4×D4C22×C3111yescharacteristic
384C22×C4⋊C4—21no—
385#488—24no—
386#463—24no—
387C2×C4⋊C8C22×C3111yescharacteristic
388C2×#103C22×C3111yescharacteristic
389C2×#103C22×C3111yescharacteristic
390C2×#103C22×C3111yescharacteristic
391C2×#102C22×C3111yescharacteristic
392C2×#102C22×C3111yescharacteristic
393C2×#102C22×C3111yescharacteristic
394C2×#102C22×C3111yescharacteristic
395C2×#102C22×C3111yescharacteristic
396C2×C4×C8C22×C3111yescharacteristic
397#397—21no—
398#393—21no—
399#391C22×C3111yescharacteristic
400#391C22×C3111yescharacteristic
401#390C22×C3111yescharacteristic
402#390C22×C3111yescharacteristic
403#388—21no—
404#388—21no—
405C4×C4⋊C4C22×C3111yescharacteristic
406#340C22×C3111yescharacteristic
407#340C22×C3111yescharacteristic
408#340C22×C3111yescharacteristic
409#340C22×C3111yescharacteristic
410#340C22×C3111yescharacteristic
411#340C22×C3111yescharacteristic
412#336C22×C3111yescharacteristic
413#336C22×C3111yescharacteristic
414#336C22×C3111yescharacteristic
415#336C22×C3111yescharacteristic
416C2×C31—44no—
417C2×C31—161no—
418C2×C31#243611yescharacteristic
419C2×C31#300211yescharacteristic
420C2×C31#301211yescharacteristic
421C2×C31#336011yescharacteristic
422C2×C31#336111yescharacteristic
423C2×C31#337011yescharacteristic
424C2×C31#337611yescharacteristic
425C22×Q8—21no—
426C22×Q8D4×C3111yescharacteristic
427C22×Q8C23×C3111yescharacteristic
428C22×D4C23×C3111yescharacteristic
429C22×D4C23×C3111yescharacteristic
430C23×C4—21no—
431C23×C4—21no—
432C23×C4—21no—
433C2×SD16—22no—
434C2×SD16—22no—
435C2×SD16—22no—
436C2×D8—22no—
437C2×D8—22no—
438C2×D8—22no—
439C22×C8C23×C3111yescharacteristic
440C22×C8C23×C3111yescharacteristic
441C22×C8C23×C3111yescharacteristic
442C22×C8C23×C3111yescharacteristic
443C4⋊Q8—22no—
444C4⋊Q8—22no—
445#125—22no—
446#125—22no—
447#125—22no—
448#125D4×C3114yes—
449#124—22no—
450#124—22no—
451C22⋊Q8—28no—
452C22⋊Q8—28no—
453C22⋊Q8—28no—
454C4×Q8—22no—
455C4×Q8—22no—
456C4×D4—22no—
457C4×D4—22no—
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4D4×C3114yes—
462C2×C4⋊C4—28no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4D4×C3111yescharacteristic
469C2×C4⋊C4D4×C3111yescharacteristic
470C2×C4⋊C4D4×C3111yescharacteristic
471C2×C4⋊C4C23×C3111yescharacteristic
472C2×C4⋊C4C23×C3111yescharacteristic
473C2×C4⋊C4C23×C3111yescharacteristic
474C2×C4⋊C4C23×C3111yescharacteristic
475C2×C4⋊C4C23×C3111yescharacteristic
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×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C42—21no—
486C2×C42C23×C3111yescharacteristic
487C2×C42C23×C3111yescharacteristic
488C2×C42C23×C3111yescharacteristic
489C4⋊C8—22no—
490#103—22no—
491#103—22no—
492#103—22no—
493#102—22no—
494#102—22no—
495#102—22no—
496#102—22no—
497#102—22no—
498C4×C8—22no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504C31#2593811yescharacteristic, direct product factor, Sylow
505C24—21no—
506C24—21no—
507C2×Q8—24no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—41no—
517C2×Q8—81no—
518C2×Q8—81no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4C2×D4×C3112yes—
529C2×D4#41×C3112yes—
530C2×D4#41×C3112yes—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—81no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4C2×D4×C3111yescharacteristic
547C22×C4C2×D4×C3111yescharacteristic
548C22×C4C2×D4×C3111yescharacteristic
549C22×C4C2×D4×C3111yescharacteristic
550C22×C4C2×D4×C3111yescharacteristic
551C22×C4C2×D4×C3111yescharacteristic
552C22×C4C24×C3111yescharacteristic
553SD16—44no—
554D8—44no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4C2×D4×C3112yes—
583C4⋊C4C2×D4×C3112yes—
584C4⋊C4C2×D4×C3112yes—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—81no—
593C22⋊C4—81no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—81no—
599C42C2×D4×C3112yes—
600C42C2×D4×C3112yes—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23C22×D4×C3111yescharacteristic
616Q8—44no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620Q8—41no—
621Q8—84no—
622D4—22no—
623D4—22no—
624D4—22no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4—41no—
629D4C31×#12414yes—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—48no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—84no—
665C2×C4—84no—
666C2×C4C31×#12012yes—
667C2×C4C31×#12012yes—
668C2×C4C31×#13512yes—
669C2×C4C22×D4×C3111yescharacteristic
670C2×C4C22×D4×C3111yescharacteristic
671C2×C4C2×#41×C3111yescharacteristic
672C2×C4C2×#41×C3111yescharacteristic
673C2×C4C31×2−1+411yescharacteristic
674C2×C4C31×2−1+411yescharacteristic
675C8—41no—
676C8—41no—
677C8—41no—
678C8—41no—
679C22—24no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22C2×C31×#12011yescharacteristic
694C22C31×#54811yescharacteristic
695C22C31×#54811yescharacteristic
696C22C2×C31×#13511yescharacteristic
697C22C31×#57511yescharacteristic
698C22C31×#57611yescharacteristic
699C22C31×#57711yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—41no—
704C4—42no—
705C4—41no—
706C4—41no—
707C4—42no—
708C4—42no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4C2×C31×#12411yescharacteristic
713C4C31×#53611yescharacteristic
714C4C31×#54811yescharacteristic
715C4C31×#54811yescharacteristic
716C2—44no—
717C2—161no—
718C2C31×#243611yescharacteristic
719C2C31×#300211yescharacteristic
720C2C31×#301211yescharacteristic
721C2C31×#336011yescharacteristic
722C2C31×#336111yescharacteristic
723C2C31×#337011yescharacteristic
724C2C31×#337611yescharacteristic
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×#488C2semidirect
4. C31×#2592C2semidirect
5. C31×#2026C2semidirect
6. C31×#2025C2semidirect
7. C31×#2024C2semidirect
8. C31×#2023C2semidirect
9. C31×#1989C2semidirect
10. C31×#1984C2semidirect
13. C31×#1877C2semidirect
14. C31×#1877C2semidirect
15. C4×C31×#102C2semidirect
238. #25938C31direct (N × H)
317. C2×#554C2×C31semidirect
318. C2×#488C2×C31semidirect
320. #2592C2×C31semidirect
321. #2026C2×C31semidirect
322. #2025C2×C31semidirect
323. #2024C2×C31semidirect
324. #2023C2×C31semidirect
325. #1989C2×C31semidirect
326. #1984C2×C31semidirect
329. #1877C2×C31semidirect
330. #1877C2×C31semidirect
331. C4×#102C2×C31semidirect
504. C31#25938direct (N × H)

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×#4882
C2×C31×#4632
C31×#25922
C31×#20262
C31×#20252
C31×#20242
C31×#20232
C31×#19892
C31×#19842
C31×#18792
C31×#18772
C4×C31×#1022
#2593831