Finite Group Databasebeta

← C31×#25024 #21481783

Subgroups — C31×#25024 #21481783

Order 7936.

884 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#484C211yesmaximal, characteristic, complemented
2C2×C31×#483C211yesmaximal, characteristic, complemented
3C31×#2536C211yesmaximal, characteristic
4D4×C4⋊C4×C31C211yesmaximal, characteristic
5C31×#2077C211yesmaximal, characteristic, complemented
6C31×#2075C211yesmaximal, characteristic, complemented
7C31×#2036C211yesmaximal, characteristic, complemented
8C31×#2035C211yesmaximal, characteristic, complemented
9C31×#1955C211yesmaximal, characteristic
10C31×#1949C211yesmaximal, characteristic, complemented
11C31×#1853C211yesmaximal, characteristic, complemented
12C31×#1852C211yesmaximal, characteristic, complemented
13C31×#1847C211yesmaximal, characteristic, complemented
14C31×#1803C211yesmaximal, characteristic, complemented
15C31×#1763C211yesmaximal, characteristic, complemented
16C2×C31×C22⋊Q8C2211yescharacteristic
17C2×C31×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C31C2211yescharacteristic
19C2×C4×D4×C31—21no—
20C2×C4×D4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C31×#484—24no—
24C31×#483—24no—
25C2×C31×#107C2211yescharacteristic
26C2×C31×#107C2211yescharacteristic
27C2×C31×#107C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C2×C31×#106C2211yescharacteristic
30C2×C31×#106C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×C22⋊C8C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C2×C31×#97C2211yescharacteristic
41C31×#398—21no—
42C31×#394—21no—
43C31×#389—21no—
44C31×#388—21no—
45C31×#388—21no—
46C31×#385—21no—
47C31×#385—21no—
48C31×#384C2211yescharacteristic
49C31×#382C2211yescharacteristic
50C31×#380C2211yescharacteristic
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C31×#380C2211yescharacteristic
54C4×C4⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C22×Q8×C31C2311yescharacteristic
62C22×D4×C31D411yescharacteristic
63C23×C4×C31—21no—
64C23×C4×C31—21no—
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C22×C8×C31C2311yescharacteristic
68C22×C8×C31C2311yescharacteristic
69C22×C8×C31C2311yescharacteristic
70C22×C8×C31C2311yescharacteristic
71C31×C22⋊Q8—22no—
72C31×C22⋊Q8—22no—
73C31×C22⋊Q8—41no—
74C31×C22⋊Q8—41no—
75C4×Q8×C31—22no—
76C4×Q8×C31—22no—
77C4×D4×C31—22no—
78C4×D4×C31—22no—
79C4×D4×C31—44no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—21no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—41no—
90C2×C4⋊C4×C31—41no—
91C2×C4⋊C4×C31D411yescharacteristic
92C2×C4⋊C4×C31C2311yescharacteristic
93C2×C4⋊C4×C31C2311yescharacteristic
94C2×C4⋊C4×C31C2311yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—21no—
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31D411yescharacteristic
106C2×C22⋊C4×C31D411yescharacteristic
107C2×C42×C31—21no—
108C2×C42×C31—21no—
109C2×C42×C31C2311yescharacteristic
110C31×#107—22no—
111C31×#107—22no—
112C31×#107—41no—
113C31×#106—22no—
114C31×#106—22no—
115C31×#106—41no—
116C31×C4⋊C8—22no—
117C31×#103—22no—
118C31×#103—22no—
119C31×#103—22no—
120C31×#103D414yescomplemented
121C31×C22⋊C8—22no—
122C31×C22⋊C8—22no—
123C31×C22⋊C8—22no—
124C31×C22⋊C8—22no—
125C31×#97—22no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C24×C31C2×D411yescharacteristic
134C24×C31C2×D411yescharacteristic
135C2×Q8×C31—21no—
136C2×Q8×C31—21no—
137C2×Q8×C31—21no—
138C2×Q8×C31—21no—
139C2×Q8×C31—21no—
140C2×Q8×C31C2×D412yes—
141C2×D4×C31—22no—
142C2×D4×C31—22no—
143C2×D4×C31—22no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—42no—
165C22×C4×C31—42no—
166C22×C4×C31—42no—
167C22×C4×C31—42no—
168C22×C4×C31—81no—
169C22×C4×C31—81no—
170C22×C4×C31C2×D411yescharacteristic
171C22×C4×C31C2×D411yescharacteristic
172C22×C4×C31C2×D411yescharacteristic
173C22×C4×C31C2×D411yescharacteristic
174C22×C4×C31C2411yescharacteristic
175C2×C8×C31—21no—
176C2×C8×C31—21no—
177C2×C8×C31—21no—
178C2×C8×C31—21no—
179C2×C8×C31—21no—
180C2×C8×C31—21no—
181C2×C8×C31—21no—
182C2×C8×C31—21no—
183C2×C8×C31—21no—
184C2×C8×C31—21no—
185C2×C8×C31C2×D412yes—
186C2×C8×C31#4112yes—
187C4⋊C4×C31—22no—
188C4⋊C4×C31—21no—
189C4⋊C4×C31—21no—
190C4⋊C4×C31—21no—
191C4⋊C4×C31—21no—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—42no—
202C4⋊C4×C31—42no—
203C4⋊C4×C31—42no—
204C4⋊C4×C31—42no—
205C4⋊C4×C31—42no—
206C4⋊C4×C31—42no—
207C4⋊C4×C31—81no—
208C4⋊C4×C31C2×D412yes—
209C22⋊C4×C31—22no—
210C22⋊C4×C31—22no—
211C22⋊C4×C31—42no—
212C22⋊C4×C31—42no—
213C22⋊C4×C31—42no—
214C22⋊C4×C31—42no—
215C22⋊C4×C31—42no—
216C22⋊C4×C31—42no—
217C42×C31—42no—
218C42×C31—42no—
219C42×C31#4112yes—
220C42×C31#4112yes—
221#25024C3111yesmaximal, characteristic, direct product factor, Sylow
222C23×C31—21no—
223C23×C31—21no—
224C23×C31—21no—
225C23×C31—21no—
226C23×C31—21no—
227C23×C31—21no—
228C23×C31—21no—
229C23×C31—21no—
230C23×C31—21no—
231C23×C31—21no—
232C23×C31—21no—
233C23×C31—21no—
234C23×C31AGL(1,ℤ/8)12yes—
235C23×C31#13712yes—
236C23×C31C22×D411yescharacteristic
237Q8×C31—22no—
238Q8×C31—22no—
239Q8×C31—41no—
240Q8×C31—41no—
241D4×C31—28no—
242C2×C4×C31—21no—
243C2×C4×C31—21no—
244C2×C4×C31—21no—
245C2×C4×C31—21no—
246C2×C4×C31—21no—
247C2×C4×C31—21no—
248C2×C4×C31—22no—
249C2×C4×C31—22no—
250C2×C4×C31—21no—
251C2×C4×C31—21no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—41no—
255C2×C4×C31—41no—
256C2×C4×C31—41no—
257C2×C4×C31—41no—
258C2×C4×C31—41no—
259C2×C4×C31—41no—
260C2×C4×C31—41no—
261C2×C4×C31—41no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—41no—
265C2×C4×C31—41no—
266C2×C4×C31—41no—
267C2×C4×C31—41no—
268C2×C4×C31—41no—
269C2×C4×C31—41no—
270C2×C4×C31—41no—
271C2×C4×C31—41no—
272C2×C4×C31—41no—
273C2×C4×C31—41no—
274C2×C4×C31—41no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31—84no—
285C2×C4×C31—84no—
286C2×C4×C31#12312yes—
287C2×C4×C31#12312yes—
288C2×C4×C31C22×D411yescharacteristic
289C2×C4×C31C2×#4111yescharacteristic
290C2×C4×C31C2×#4111yescharacteristic
291C2×C4×C31C2×#4111yescharacteristic
292C2×C4×C31H(5,𝔽2)11yescharacteristic
293C2×C4×C312−1+411yescharacteristic
294C8×C31—22no—
295C8×C31—22no—
296C8×C31—41no—
297C8×C31—41no—
298C2×#484C2×C3111yescharacteristic, complemented
299C2×#483C2×C3111yescharacteristic, complemented
300#2536C2×C3111yescharacteristic
301D4×C4⋊C4C2×C3111yescharacteristic
302#2077C2×C3111yescharacteristic, complemented
303#2075C2×C3111yescharacteristic, complemented
304#2036C2×C3111yescharacteristic, complemented
305#2035C2×C3111yescharacteristic, complemented
306#1955C2×C3111yescharacteristic
307#1949C2×C3111yescharacteristic, complemented
308#1853C2×C3111yescharacteristic, complemented
309#1852C2×C3111yescharacteristic, complemented
310#1847C2×C3111yescharacteristic, complemented
311#1803C2×C3111yescharacteristic, complemented
312#1763C2×C3111yescharacteristic, complemented
313C22×C31—22no—
314C22×C31—22no—
315C22×C31—22no—
316C22×C31—22no—
317C22×C31—22no—
318C22×C31—22no—
319C22×C31—41no—
320C22×C31—41no—
321C22×C31—41no—
322C22×C31—41no—
323C22×C31—41no—
324C22×C31—41no—
325C22×C31—41no—
326C22×C31—41no—
327C22×C31C2×#12311yescharacteristic
328C22×C31D4211yescharacteristic
329C22×C31#54711yescharacteristic
330C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C31C2×#13711yescharacteristic
332C22×C31#57711yescharacteristic
333C22×C31#57811yescharacteristic
334C4×C31—22no—
335C4×C31—22no—
336C4×C31—41no—
337C4×C31—41no—
338C4×C31—42no—
339C4×C31—42no—
340C4×C31—81no—
341C4×C31—81no—
342C4×C31—81no—
343C4×C31—81no—
344C4×C31—81no—
345C4×C31—81no—
346C4×C31#53211yescharacteristic
347C4×C31#54211yescharacteristic
348C4×C31#54711yescharacteristic
349C4×C31#55311yescharacteristic
350C2×C22⋊Q8C22×C3111yescharacteristic
351C2×C22⋊Q8C22×C3111yescharacteristic
352C2×C4×Q8C22×C3111yescharacteristic
353C2×C4×D4—21no—
354C2×C4×D4C22×C3111yescharacteristic
355C22×C4⋊C4C22×C3111yescharacteristic
356C22×C4⋊C4C22×C3111yescharacteristic
357#484—24no—
358#483—24no—
359C2×#107C22×C3111yescharacteristic
360C2×#107C22×C3111yescharacteristic
361C2×#107C22×C3111yescharacteristic
362C2×#106C22×C3111yescharacteristic
363C2×#106C22×C3111yescharacteristic
364C2×#106C22×C3111yescharacteristic
365C2×C4⋊C8C22×C3111yescharacteristic
366C2×#103C22×C3111yescharacteristic
367C2×#103C22×C3111yescharacteristic
368C2×#103C22×C3111yescharacteristic
369C2×#103C22×C3111yescharacteristic
370C2×C22⋊C8C22×C3111yescharacteristic
371C2×C22⋊C8C22×C3111yescharacteristic
372C2×C22⋊C8C22×C3111yescharacteristic
373C2×C22⋊C8C22×C3111yescharacteristic
374C2×#97C22×C3111yescharacteristic
375#398—21no—
376#394—21no—
377#389—21no—
378#388—21no—
379#388—21no—
380#385—21no—
381#385—21no—
382#384C22×C3111yescharacteristic
383#382C22×C3111yescharacteristic
384#380C22×C3111yescharacteristic
385#380C22×C3111yescharacteristic
386#380C22×C3111yescharacteristic
387#380C22×C3111yescharacteristic
388C4×C4⋊C4C22×C3111yescharacteristic
389#340C22×C3111yescharacteristic
390#340C22×C3111yescharacteristic
391#340C22×C3111yescharacteristic
392#340C22×C3111yescharacteristic
393#340C22×C3111yescharacteristic
394#340C22×C3111yescharacteristic
395C2×C31—42no—
396C2×C31—42no—
397C2×C31#242211yescharacteristic
398C2×C31#309211yescharacteristic
399C2×C31#309711yescharacteristic
400C2×C31#326511yescharacteristic
401C2×C31#327011yescharacteristic
402C2×C31#334311yescharacteristic
403C2×C31#334411yescharacteristic
404C22×Q8C23×C3111yescharacteristic
405C22×D4D4×C3111yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4C23×C3111yescharacteristic
409C23×C4C23×C3111yescharacteristic
410C22×C8C23×C3111yescharacteristic
411C22×C8C23×C3111yescharacteristic
412C22×C8C23×C3111yescharacteristic
413C22×C8C23×C3111yescharacteristic
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—41no—
417C22⋊Q8—41no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—44no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—41no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4D4×C3111yescharacteristic
435C2×C4⋊C4C23×C3111yescharacteristic
436C2×C4⋊C4C23×C3111yescharacteristic
437C2×C4⋊C4C23×C3111yescharacteristic
438C2×C4⋊C4C23×C3111yescharacteristic
439C2×C4⋊C4C23×C3111yescharacteristic
440C2×C4⋊C4C23×C3111yescharacteristic
441C2×C4⋊C4C23×C3111yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4D4×C3111yescharacteristic
449C2×C22⋊C4D4×C3111yescharacteristic
450C2×C42—21no—
451C2×C42—21no—
452C2×C42C23×C3111yescharacteristic
453#107—22no—
454#107—22no—
455#107—41no—
456#106—22no—
457#106—22no—
458#106—41no—
459C4⋊C8—22no—
460#103—22no—
461#103—22no—
462#103—22no—
463#103D4×C3114yescomplemented
464C22⋊C8—22no—
465C22⋊C8—22no—
466C22⋊C8—22no—
467C22⋊C8—22no—
468#97—22no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476C31#2502411yescharacteristic, direct product factor, Sylow
477C24C2×D4×C3111yescharacteristic
478C24C2×D4×C3111yescharacteristic
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8C2×D4×C3112yes—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—81no—
513C22×C4—81no—
514C22×C4C2×D4×C3111yescharacteristic
515C22×C4C2×D4×C3111yescharacteristic
516C22×C4C2×D4×C3111yescharacteristic
517C22×C4C2×D4×C3111yescharacteristic
518C22×C4C24×C3111yescharacteristic
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8C2×D4×C3112yes—
530C2×C8#41×C3112yes—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—81no—
552C4⋊C4C2×D4×C3112yes—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C42—42no—
562C42—42no—
563C42#41×C3112yes—
564C42#41×C3112yes—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23C31×AGL(1,ℤ/8)12yes—
578C23C31×#13712yes—
579C23C22×D4×C3111yescharacteristic
580Q8—22no—
581Q8—22no—
582Q8—41no—
583Q8—41no—
584D4—28no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—84no—
628C2×C4—84no—
629C2×C4C31×#12312yes—
630C2×C4C31×#12312yes—
631C2×C4C22×D4×C3111yescharacteristic
632C2×C4C2×#41×C3111yescharacteristic
633C2×C4C2×#41×C3111yescharacteristic
634C2×C4C2×#41×C3111yescharacteristic
635C2×C4C31×H(5,𝔽2)11yescharacteristic
636C2×C4C31×2−1+411yescharacteristic
637C8—22no—
638C8—22no—
639C8—41no—
640C8—41no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22C2×C31×#12311yescharacteristic
656C22D42×C3111yescharacteristic
657C22C31×#54711yescharacteristic
658C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
659C22C2×C31×#13711yescharacteristic
660C22C31×#57711yescharacteristic
661C22C31×#57811yescharacteristic
662C4—22no—
663C4—22no—
664C4—41no—
665C4—41no—
666C4—42no—
667C4—42no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4—81no—
674C4C31×#53211yescharacteristic
675C4C31×#54211yescharacteristic
676C4C31×#54711yescharacteristic
677C4C31×#55311yescharacteristic
678C2—42no—
679C2—42no—
680C2C31×#242211yescharacteristic
681C2C31×#309211yescharacteristic
682C2C31×#309711yescharacteristic
683C2C31×#326511yescharacteristic
684C2C31×#327011yescharacteristic
685C2C31×#334311yescharacteristic
686C2C31×#334411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#484C2semidirect
2. C2×C31×#483C2semidirect
5. C31×#2077C2semidirect
6. C31×#2075C2semidirect
7. C31×#2036C2semidirect
8. C31×#2035C2semidirect
10. C31×#1949C2semidirect
11. C31×#1853C2semidirect
12. C31×#1852C2semidirect
13. C31×#1847C2semidirect
14. C31×#1803C2semidirect
15. C31×#1763C2semidirect
120. C31×#103D4semidirect
221. #25024C31direct (N × H)
298. C2×#484C2×C31semidirect
299. C2×#483C2×C31semidirect
302. #2077C2×C31semidirect
303. #2075C2×C31semidirect
304. #2036C2×C31semidirect
305. #2035C2×C31semidirect
307. #1949C2×C31semidirect
308. #1853C2×C31semidirect
309. #1852C2×C31semidirect
310. #1847C2×C31semidirect
311. #1803C2×C31semidirect
312. #1763C2×C31semidirect
463. #103D4×C31semidirect
476. C31#25024direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4842
C2×C31×#4832
C31×#25362
D4×C4⋊C4×C312
C31×#20772
C31×#20752
C31×#20362
C31×#20352
C31×#19552
C31×#19492
C31×#18532
C31×#18522
C31×#18472
C31×#18032
C31×#17632
#2502431