Finite Group Databasebeta

← C31×#20746 #21477505

Subgroups — C31×#20746 #21477505

Order 7936.

1298 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×#520C211yesmaximal, characteristic
2C2×C31×#433C211yesmaximal, characteristic, complemented
3C31×#2314C211yesmaximal, characteristic, complemented
4C31×#1824C211yesmaximal, characteristic, complemented
5C31×#1823C211yesmaximal, characteristic, complemented
6C31×#1805C211yesmaximal, characteristic, complemented
7C31×#1804C211yesmaximal, characteristic, complemented
8C31×#1803C211yesmaximal, characteristic, complemented
9C31×#1802C211yesmaximal, characteristic, complemented
10C31×#1788C211yesmaximal, characteristic
11C31×#1788C211yesmaximal, characteristic
12C31×#1763C211yesmaximal, characteristic, complemented
13C31×#1762C211yesmaximal, characteristic, complemented
14C4×C31×#103C211yesmaximal, characteristic, complemented
15C4×C31×#102C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C31×#520—24no—
18C31×#520C418yescomplemented
19C2×C4×Q8×C31C2211yescharacteristic
20C2×C4×Q8×C31C2211yescharacteristic
21C2×C4×D4×C31—21no—
22C2×C4×D4×C31—21no—
23C2×C4×D4×C31C2211yescharacteristic
24C2×C4×D4×C31C2211yescharacteristic
25C2×C31×#117—21no—
26C2×C31×#117C2211yescharacteristic
27C22×C4⋊C4×C31—21no—
28C22×C4⋊C4×C31C2211yescharacteristic
29C31×#433—24no—
30C2×C31×C4⋊C8C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×C22⋊C8C2211yescharacteristic
41C2×C31×C22⋊C8C2211yescharacteristic
42C2×C31×#97C2211yescharacteristic
43C2×C4×C8×C31C2211yescharacteristic
44C31×#388—21no—
45C31×#388—21no—
46C31×#387—21no—
47C31×#387—21no—
48C31×#384C2211yescharacteristic
49C31×#382C2211yescharacteristic
50C31×#380C2211yescharacteristic
51C31×#380C2211yescharacteristic
52C4×C4⋊C4×C31C2211yescharacteristic
53C4×C4⋊C4×C31C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C2×#41×C31—22no—
63C2×#41×C31—22no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31C2×C414yes—
68C22×Q8×C31C2311yescharacteristic
69C22×D4×C31—21no—
70C22×D4×C31C2311yescharacteristic
71C23×C4×C31—21no—
72C23×C4×C31—21no—
73C23×C4×C31—21no—
74C23×C4×C31—21no—
75C23×C4×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C4×Q8×C31—22no—
81C4×Q8×C31—22no—
82C4×Q8×C31C2×C414yes—
83C4×Q8×C31C2×C414yes—
84C4×D4×C31—28no—
85C4×D4×C31—28no—
86C4×D4×C31—22no—
87C4×D4×C31—22no—
88C4×D4×C31C2×C414yes—
89C4×D4×C31C2×C414yes—
90C31×#117—28no—
91C31×#117C2×C414yes—
92C31×#117D414yes—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—22no—
97C2×C4⋊C4×C31—28no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31C2×C414yes—
101C2×C4⋊C4×C31D411yescharacteristic
102C2×C4⋊C4×C31D411yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31D411yescharacteristic
114C2×C22⋊C4×C31D411yescharacteristic
115C2×C42×C31—21no—
116C2×C42×C31—21no—
117C2×C42×C31—21no—
118C2×C42×C31—21no—
119C2×C42×C31C2311yescharacteristic
120C2×C42×C31C2311yescharacteristic
121C31×C4⋊C8—22no—
122C31×C4⋊C8—22no—
123C31×#103—22no—
124C31×#103—22no—
125C31×#103—22no—
126C31×#103—22no—
127C31×#102—22no—
128C31×#102—22no—
129C31×#102—22no—
130C31×#102—22no—
131C31×C22⋊C8—22no—
132C31×C22⋊C8—22no—
133C31×#97—22no—
134C4×C8×C31—22no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C24×C31—21no—
142C24×C31C2×D411yescharacteristic
143#41×C31—28no—
144#41×C31—28no—
145#41×C31—28no—
146#41×C31—28no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31C22×C412yes—
151C2×Q8×C31#4112yes—
152C2×Q8×C31#4112yes—
153C2×D4×C31—24no—
154C2×D4×C31—24no—
155C2×D4×C31—24no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31C22×C412yes—
160C2×D4×C31#4112yes—
161C2×D4×C31#4112yes—
162C22×C4×C31—24no—
163C22×C4×C31—24no—
164C22×C4×C31—21no—
165C22×C4×C31—24no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—24no—
173C22×C4×C31—24no—
174C22×C4×C31—24no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—81no—
180C22×C4×C31—81no—
181C22×C4×C31—81no—
182C22×C4×C31—81no—
183C22×C4×C31—81no—
184C22×C4×C31—81no—
185C22×C4×C31C22×C412yes—
186C22×C4×C31C2×D411yescharacteristic
187C22×C4×C31C2×D411yescharacteristic
188C22×C4×C31C2×D411yescharacteristic
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31C2×D411yescharacteristic
191C22×C4×C31C2×D412yes—
192C22×C4×C31C2411yescharacteristic
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—
204C2×C8×C31—21no—
205C4⋊C4×C31—24no—
206C4⋊C4×C31—24no—
207C4⋊C4×C31—24no—
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—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—81no—
219C4⋊C4×C31—81no—
220C4⋊C4×C31C22⋊C414yes—
221C4⋊C4×C31C22⋊C414yes—
222C4⋊C4×C31C22×C412yes—
223C4⋊C4×C31C22×C412yes—
224C22⋊C4×C31—24no—
225C22⋊C4×C31—24no—
226C22⋊C4×C31—81no—
227C22⋊C4×C31—81no—
228C22⋊C4×C31C22⋊C414yes—
229C22⋊C4×C31C22⋊C414yes—
230C42×C31—24no—
231C42×C31—24no—
232C42×C31—81no—
233C42×C31—81no—
234C42×C31C22×C412yes—
235C42×C31C22×C412yes—
236C42×C31C2×D412yes—
237C42×C31C2×D412yes—
238#20746C3111yesmaximal, characteristic, direct product factor, Sylow
239C23×C31—22no—
240C23×C31—21no—
241C23×C31—21no—
242C23×C31—22no—
243C23×C31—22no—
244C23×C31—21no—
245C23×C31—21no—
246C23×C31—21no—
247C23×C31—21no—
248C23×C31—41no—
249C23×C31—41no—
250C23×C31—41no—
251C23×C31—41no—
252C23×C31C2×C22⋊C412yes—
253C23×C31C22×D411yescharacteristic
254Q8×C31—22no—
255Q8×C31—22no—
256Q8×C31—22no—
257Q8×C31#11714yes—
258D4×C31—216no—
259D4×C31—22no—
260D4×C31—22no—
261D4×C31—22no—
262D4×C31#11714yes—
263C2×C4×C31—216no—
264C2×C4×C31—22no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—22no—
268C2×C4×C31—22no—
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—22no—
281C2×C4×C31—22no—
282C2×C4×C31—22no—
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—41no—
298C2×C4×C31—41no—
299C2×C4×C31—84no—
300C2×C4×C31—84no—
301C2×C4×C31—84no—
302C2×C4×C31C2×C22⋊C412yes—
303C2×C4×C31C2×C22⋊C412yes—
304C2×C4×C31C2×C22⋊C412yes—
305C2×C4×C31C2×C22⋊C412yes—
306C2×C4×C31C2×C22⋊C412yes—
307C2×C4×C31C23×C411yescharacteristic
308C2×C4×C31C22×D411yescharacteristic
309C2×C4×C31C2×#4111yescharacteristic
310C2×C4×C31C2×#4111yescharacteristic
311C2×C4×C31C2×#4111yescharacteristic
312C2×C4×C31C2×#4111yescharacteristic
313C8×C31—41no—
314C8×C31—41no—
315C8×C31—41no—
316C8×C31—41no—
317C2×#520C2×C3111yescharacteristic
318C2×#433C2×C3111yescharacteristic, complemented
319#2314C2×C3111yescharacteristic, complemented
320#1824C2×C3111yescharacteristic, complemented
321#1823C2×C3111yescharacteristic, complemented
322#1805C2×C3111yescharacteristic, complemented
323#1804C2×C3111yescharacteristic, complemented
324#1803C2×C3111yescharacteristic, complemented
325#1802C2×C3111yescharacteristic, complemented
326#1788C2×C3111yescharacteristic
327#1788C2×C3111yescharacteristic
328#1763C2×C3111yescharacteristic, complemented
329#1762C2×C3111yescharacteristic, complemented
330C4×#103C2×C3111yescharacteristic, complemented
331C4×#102C2×C3111yescharacteristic, complemented
332C22×C31—22no—
333C22×C31—22no—
334C22×C31—22no—
335C22×C31—24no—
336C22×C31—41no—
337C22×C31—42no—
338C22×C31—41no—
339C22×C31—42no—
340C22×C31—41no—
341C22×C31—42no—
342C22×C31—41no—
343C22×C31—42no—
344C22×C31—42no—
345C22×C31—42no—
346C22×C31C22×C22⋊C411yescharacteristic
347C22×C31#52511yescharacteristic
348C22×C31#52511yescharacteristic
349C22×C31#57611yescharacteristic
350C22×C31#57711yescharacteristic
351C22×C31#57711yescharacteristic
352C22×C31#57811yescharacteristic
353C4×C31—22no—
354C4×C31—22no—
355C4×C31—22no—
356C4×C31—22no—
357C4×C31—22no—
358C4×C31—24no—
359C4×C31—42no—
360C4×C31—42no—
361C4×C31—81no—
362C4×C31—81no—
363C4×C31—81no—
364C4×C31—81no—
365C4×C31C2×#11711yescharacteristic
366C4×C31C2×#11711yescharacteristic
367C4×C31#52511yescharacteristic
368C4×C31#52511yescharacteristic
369C22×#41C22×C3111yescharacteristic
370#520—24no—
371#520C4×C3118yescomplemented
372C2×C4×Q8C22×C3111yescharacteristic
373C2×C4×Q8C22×C3111yescharacteristic
374C2×C4×D4—21no—
375C2×C4×D4—21no—
376C2×C4×D4C22×C3111yescharacteristic
377C2×C4×D4C22×C3111yescharacteristic
378C2×#117—21no—
379C2×#117C22×C3111yescharacteristic
380C22×C4⋊C4—21no—
381C22×C4⋊C4C22×C3111yescharacteristic
382#433—24no—
383C2×C4⋊C8C22×C3111yescharacteristic
384C2×C4⋊C8C22×C3111yescharacteristic
385C2×#103C22×C3111yescharacteristic
386C2×#103C22×C3111yescharacteristic
387C2×#103C22×C3111yescharacteristic
388C2×#103C22×C3111yescharacteristic
389C2×#102C22×C3111yescharacteristic
390C2×#102C22×C3111yescharacteristic
391C2×#102C22×C3111yescharacteristic
392C2×#102C22×C3111yescharacteristic
393C2×C22⋊C8C22×C3111yescharacteristic
394C2×C22⋊C8C22×C3111yescharacteristic
395C2×#97C22×C3111yescharacteristic
396C2×C4×C8C22×C3111yescharacteristic
397#388—21no—
398#388—21no—
399#387—21no—
400#387—21no—
401#384C22×C3111yescharacteristic
402#382C22×C3111yescharacteristic
403#380C22×C3111yescharacteristic
404#380C22×C3111yescharacteristic
405C4×C4⋊C4C22×C3111yescharacteristic
406C4×C4⋊C4C22×C3111yescharacteristic
407#340C22×C3111yescharacteristic
408#340C22×C3111yescharacteristic
409#340C22×C3111yescharacteristic
410#340C22×C3111yescharacteristic
411#340C22×C3111yescharacteristic
412#340C22×C3111yescharacteristic
413#340C22×C3111yescharacteristic
414#340C22×C3111yescharacteristic
415C2×C31—42no—
416C2×C31—44no—
417C2×C31#228011yescharacteristic
418C2×C31#289711yescharacteristic
419C2×C31#289811yescharacteristic
420C2×C31#311911yescharacteristic
421C2×C31#312011yescharacteristic
422C2×C31#312411yescharacteristic
423C2×C31#312511yescharacteristic
424C2×#41—22no—
425C2×#41—22no—
426C2×#41—22no—
427C2×#41—22no—
428C2×#41—22no—
429C2×#41C2×C4×C3114yes—
430C22×Q8C23×C3111yescharacteristic
431C22×D4—21no—
432C22×D4C23×C3111yescharacteristic
433C23×C4—21no—
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—21no—
437C23×C4C23×C3111yescharacteristic
438C22×C8C23×C3111yescharacteristic
439C22×C8C23×C3111yescharacteristic
440C22×C8C23×C3111yescharacteristic
441C22×C8C23×C3111yescharacteristic
442C4×Q8—22no—
443C4×Q8—22no—
444C4×Q8C2×C4×C3114yes—
445C4×Q8C2×C4×C3114yes—
446C4×D4—28no—
447C4×D4—28no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4C2×C4×C3114yes—
451C4×D4C2×C4×C3114yes—
452#117—28no—
453#117C2×C4×C3114yes—
454#117D4×C3114yes—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—28no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4C2×C4×C3114yes—
463C2×C4⋊C4D4×C3111yescharacteristic
464C2×C4⋊C4D4×C3111yescharacteristic
465C2×C4⋊C4C23×C3111yescharacteristic
466C2×C4⋊C4C23×C3111yescharacteristic
467C2×C4⋊C4C23×C3111yescharacteristic
468C2×C4⋊C4C23×C3111yescharacteristic
469C2×C4⋊C4C23×C3111yescharacteristic
470C2×C4⋊C4C23×C3111yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4D4×C3111yescharacteristic
476C2×C22⋊C4D4×C3111yescharacteristic
477C2×C42—21no—
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42C23×C3111yescharacteristic
482C2×C42C23×C3111yescharacteristic
483C4⋊C8—22no—
484C4⋊C8—22no—
485#103—22no—
486#103—22no—
487#103—22no—
488#103—22no—
489#102—22no—
490#102—22no—
491#102—22no—
492#102—22no—
493C22⋊C8—22no—
494C22⋊C8—22no—
495#97—22no—
496C4×C8—22no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503C31#2074611yescharacteristic, direct product factor, Sylow
504C24—21no—
505C24C2×D4×C3111yescharacteristic
506#41—28no—
507#41—28no—
508#41—28no—
509#41—28no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8C22×C4×C3112yes—
514C2×Q8#41×C3112yes—
515C2×Q8#41×C3112yes—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4C22×C4×C3112yes—
523C2×D4#41×C3112yes—
524C2×D4#41×C3112yes—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—81no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4—81no—
548C22×C4C22×C4×C3112yes—
549C22×C4C2×D4×C3111yescharacteristic
550C22×C4C2×D4×C3111yescharacteristic
551C22×C4C2×D4×C3111yescharacteristic
552C22×C4C2×D4×C3111yescharacteristic
553C22×C4C2×D4×C3111yescharacteristic
554C22×C4C2×D4×C3112yes—
555C22×C4C24×C3111yescharacteristic
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—
567C2×C8—21no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—81no—
582C4⋊C4—81no—
583C4⋊C4C22⋊C4×C3114yes—
584C4⋊C4C22⋊C4×C3114yes—
585C4⋊C4C22×C4×C3112yes—
586C4⋊C4C22×C4×C3112yes—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—81no—
590C22⋊C4—81no—
591C22⋊C4C22⋊C4×C3114yes—
592C22⋊C4C22⋊C4×C3114yes—
593C42—24no—
594C42—24no—
595C42—81no—
596C42—81no—
597C42C22×C4×C3112yes—
598C42C22×C4×C3112yes—
599C42C2×D4×C3112yes—
600C42C2×D4×C3112yes—
601C23—22no—
602C23—21no—
603C23—21no—
604C23—22no—
605C23—22no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23C2×C22⋊C4×C3112yes—
615C23C22×D4×C3111yescharacteristic
616Q8—22no—
617Q8—22no—
618Q8—22no—
619Q8C31×#11714yes—
620D4—216no—
621D4—22no—
622D4—22no—
623D4—22no—
624D4C31×#11714yes—
625C2×C4—216no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
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—22no—
643C2×C4—22no—
644C2×C4—22no—
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—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—84no—
662C2×C4—84no—
663C2×C4—84no—
664C2×C4C2×C22⋊C4×C3112yes—
665C2×C4C2×C22⋊C4×C3112yes—
666C2×C4C2×C22⋊C4×C3112yes—
667C2×C4C2×C22⋊C4×C3112yes—
668C2×C4C2×C22⋊C4×C3112yes—
669C2×C4C23×C4×C3111yescharacteristic
670C2×C4C22×D4×C3111yescharacteristic
671C2×C4C2×#41×C3111yescharacteristic
672C2×C4C2×#41×C3111yescharacteristic
673C2×C4C2×#41×C3111yescharacteristic
674C2×C4C2×#41×C3111yescharacteristic
675C8—41no—
676C8—41no—
677C8—41no—
678C8—41no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—24no—
683C22—41no—
684C22—42no—
685C22—41no—
686C22—42no—
687C22—41no—
688C22—42no—
689C22—41no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22C22×C22⋊C4×C3111yescharacteristic
694C22C31×#52511yescharacteristic
695C22C31×#52511yescharacteristic
696C22C31×#57611yescharacteristic
697C22C31×#57711yescharacteristic
698C22C31×#57711yescharacteristic
699C22C31×#57811yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—22no—
704C4—22no—
705C4—24no—
706C4—42no—
707C4—42no—
708C4—81no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4C2×C31×#11711yescharacteristic
713C4C2×C31×#11711yescharacteristic
714C4C31×#52511yescharacteristic
715C4C31×#52511yescharacteristic
716C2—42no—
717C2—44no—
718C2C31×#228011yescharacteristic
719C2C31×#289711yescharacteristic
720C2C31×#289811yescharacteristic
721C2C31×#311911yescharacteristic
722C2C31×#312011yescharacteristic
723C2C31×#312411yescharacteristic
724C2C31×#312511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#433C2semidirect
3. C31×#2314C2semidirect
4. C31×#1824C2semidirect
5. C31×#1823C2semidirect
6. C31×#1805C2semidirect
7. C31×#1804C2semidirect
8. C31×#1803C2semidirect
9. C31×#1802C2semidirect
12. C31×#1763C2semidirect
13. C31×#1762C2semidirect
14. C4×C31×#103C2semidirect
15. C4×C31×#102C2semidirect
18. C31×#520C4semidirect
238. #20746C31direct (N × H)
318. C2×#433C2×C31semidirect
319. #2314C2×C31semidirect
320. #1824C2×C31semidirect
321. #1823C2×C31semidirect
322. #1805C2×C31semidirect
323. #1804C2×C31semidirect
324. #1803C2×C31semidirect
325. #1802C2×C31semidirect
328. #1763C2×C31semidirect
329. #1762C2×C31semidirect
330. C4×#103C2×C31semidirect
331. C4×#102C2×C31semidirect
371. #520C4×C31semidirect
503. C31#20746direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5202
C2×C31×#4332
C31×#23142
C31×#18242
C31×#18232
C31×#18052
C31×#18042
C31×#18032
C31×#18022
C31×#17882
C31×#17632
C31×#17622
C4×C31×#1032
C4×C31×#1022
#2074631