Finite Group Databasebeta

← C31×#25217 #21481976

Subgroups — C31×#25217 #21481976

Order 7936.

906 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#484C211yesmaximal, characteristic, complemented
2C2×C31×#468C211yesmaximal, characteristic
3C31×#2501C211yesmaximal, characteristic
4C31×#2362C211yesmaximal, characteristic, complemented
5C31×#2083C211yesmaximal, characteristic, complemented
6C31×#2072C211yesmaximal, characteristic, complemented
7C31×#2067C211yesmaximal, characteristic, complemented
8C31×#2055C211yesmaximal, characteristic, complemented
9C31×#1947C211yesmaximal, characteristic, complemented
10C31×#1925C211yesmaximal, characteristic, complemented
11C31×#1880C211yesmaximal, characteristic, complemented
12C31×#1875C211yesmaximal, characteristic
13C31×#1851C211yesmaximal, characteristic, complemented
14C31×#1803C211yesmaximal, characteristic, complemented
15C31×#1736C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×M16×C31C2211yescharacteristic
18C2×C31×#123—21no—
19C2×C31×#123—21no—
20C2×C31×C22⋊Q8C2211yescharacteristic
21C2×C31×#121C2211yescharacteristic
22C2×C4×Q8×C31C2211yescharacteristic
23C2×C31×#117C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C31×#484—24no—
26C31×#468—24no—
27C2×C31×#107C2211yescharacteristic
28C2×C31×#107C2211yescharacteristic
29C2×C31×#107C2211yescharacteristic
30C2×C31×C4⋊C8C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C31×#399—21no—
40C31×#399—21no—
41C31×#391C2211yescharacteristic
42C31×#390C2211yescharacteristic
43C31×#390C2211yescharacteristic
44C31×#389C2211yescharacteristic
45C31×#388—21no—
46C31×#388—21no—
47C31×#387—21no—
48C31×#384C2211yescharacteristic
49C31×#384C2211yescharacteristic
50C4×C4⋊C4×C31—21no—
51C4×C4⋊C4×C31C2211yescharacteristic
52C4×C22⋊C4×C31C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×Q8×C31C2311yescharacteristic
62C22×D4×C31—21no—
63C22×D4×C31C2311yescharacteristic
64C23×C4×C31—21no—
65C23×C4×C31C2311yescharacteristic
66C2×SD16×C31—22no—
67C2×SD16×C31—22no—
68C2×SD16×C31—41no—
69C2×M16×C31—22no—
70C2×M16×C31—22no—
71C2×M16×C31—41no—
72C22×C8×C31C2311yescharacteristic
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C31×#123—44no—
77C31×#123—44no—
78C31×C22⋊Q8—22no—
79C31×C22⋊Q8D414yes—
80C31×#121—22no—
81C31×#121—22no—
82C4×Q8×C31—22no—
83C4×Q8×C31—41no—
84C31×#117—22no—
85C31×#117—41no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—22no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31D411yescharacteristic
110C2×C22⋊C4×C31D411yescharacteristic
111C2×C42×C31—21no—
112C2×C42×C31—21no—
113C2×C42×C31—21no—
114C2×C42×C31C2311yescharacteristic
115C2×C42×C31C2311yescharacteristic
116C31×#107—22no—
117C31×#107—22no—
118C31×#107—22no—
119C31×C4⋊C8—22no—
120C31×C4⋊C8—41no—
121C31×#103—22no—
122C31×#103—22no—
123C31×#103—22no—
124C31×#102—22no—
125C31×#102—22no—
126C31×#102—41no—
127C31×C22⋊C8—22no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95D411yescharacteristic
133C31×#95D411yescharacteristic
134C24×C31—21no—
135C24×C31C2×D411yescharacteristic
136C2×Q8×C31—21no—
137C2×Q8×C31—21no—
138C2×Q8×C31—21no—
139C2×Q8×C31—21no—
140C2×Q8×C31—21no—
141C2×Q8×C31C2×D412yes—
142C2×D4×C31—21no—
143C2×D4×C31—21no—
144C2×D4×C31—21no—
145C2×D4×C31—21no—
146C2×D4×C31—21no—
147C2×D4×C31—21no—
148C2×D4×C31—42no—
149C2×D4×C31—42no—
150C2×D4×C31—42no—
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—42no—
163C22×C4×C31—42no—
164C22×C4×C31—42no—
165C22×C4×C31C2×D411yescharacteristic
166C22×C4×C31C2×D411yescharacteristic
167C22×C4×C31C2×D411yescharacteristic
168C22×C4×C31C2×D412yes—
169C22×C4×C31C2×D411yescharacteristic
170C22×C4×C31C2×D411yescharacteristic
171C22×C4×C31#4112yes—
172C22×C4×C31C2411yescharacteristic
173SD16×C31—44no—
174M16×C31—44no—
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×C31—21no—
186C2×C8×C31#4112yes—
187C4⋊C4×C31—24no—
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—42no—
199C4⋊C4×C31—42no—
200C4⋊C4×C31—42no—
201C4⋊C4×C31—42no—
202C4⋊C4×C31—42no—
203C4⋊C4×C31—42no—
204C4⋊C4×C31—42no—
205C4⋊C4×C31C2×D412yes—
206C4⋊C4×C31#4112yes—
207C22⋊C4×C31—24no—
208C22⋊C4×C31—22no—
209C22⋊C4×C31—22no—
210C22⋊C4×C31—42no—
211C22⋊C4×C31—42no—
212C22⋊C4×C31—42no—
213C22⋊C4×C31—42no—
214C22⋊C4×C31—42no—
215C22⋊C4×C31—42no—
216C42×C31—21no—
217C42×C31—21no—
218C42×C31—21no—
219C42×C31—21no—
220C42×C31—42no—
221C42×C31—42no—
222C42×C31—42no—
223#25217C3111yesmaximal, characteristic, direct product factor, Sylow
224C23×C31—21no—
225C23×C31—21no—
226C23×C31—21no—
227C23×C31—21no—
228C23×C31—21no—
229C23×C31—21no—
230C23×C31—41no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31#12112yes—
238C23×C31C22×D411yescharacteristic
239Q8×C31—22no—
240Q8×C31—22no—
241Q8×C31—41no—
242Q8×C31—41no—
243D4×C31—41no—
244D4×C31—41no—
245D4×C31—41no—
246D4×C31—41no—
247D4×C31—84no—
248C2×C4×C31—21no—
249C2×C4×C31—21no—
250C2×C4×C31—21no—
251C2×C4×C31—21no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—22no—
255C2×C4×C31—22no—
256C2×C4×C31—22no—
257C2×C4×C31—22no—
258C2×C4×C31—22no—
259C2×C4×C31—22no—
260C2×C4×C31—21no—
261C2×C4×C31—22no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
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—41no—
285C2×C4×C31—84no—
286C2×C4×C31#12112yes—
287C2×C4×C31AGL(1,ℤ/8)12yes—
288C2×C4×C31AGL(1,ℤ/8)12yes—
289C2×C4×C31C22×D411yescharacteristic
290C2×C4×C31C2×#4111yescharacteristic
291C2×C4×C31C2×#4111yescharacteristic
292C2×C4×C31C2×#4111yescharacteristic
293C2×C4×C31H(5,𝔽2)11yescharacteristic
294C2×C4×C312−1+411yescharacteristic
295C8×C31—22no—
296C8×C31—41no—
297C8×C31—41no—
298C8×C31—41no—
299C2×#484C2×C3111yescharacteristic, complemented
300C2×#468C2×C3111yescharacteristic
301#2501C2×C3111yescharacteristic
302#2362C2×C3111yescharacteristic, complemented
303#2083C2×C3111yescharacteristic, complemented
304#2072C2×C3111yescharacteristic, complemented
305#2067C2×C3111yescharacteristic, complemented
306#2055C2×C3111yescharacteristic, complemented
307#1947C2×C3111yescharacteristic, complemented
308#1925C2×C3111yescharacteristic, complemented
309#1880C2×C3111yescharacteristic, complemented
310#1875C2×C3111yescharacteristic
311#1851C2×C3111yescharacteristic, complemented
312#1803C2×C3111yescharacteristic, complemented
313#1736C2×C3111yescharacteristic, complemented
314C22×C31—22no—
315C22×C31—22no—
316C22×C31—22no—
317C22×C31—41no—
318C22×C31—41no—
319C22×C31—41no—
320C22×C31—41no—
321C22×C31—81no—
322C22×C31—81no—
323C22×C31—81no—
324C22×C31—81no—
325C22×C31—81no—
326C22×C31—81no—
327C22×C31—81no—
328C22×C31C2×#12111yescharacteristic
329C22×C31#54611yescharacteristic
330C22×C31#54711yescharacteristic
331C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C31#57811yescharacteristic
334C22×C31#57811yescharacteristic
335C4×C31—22no—
336C4×C31—22no—
337C4×C31—22no—
338C4×C31—41no—
339C4×C31—42no—
340C4×C31—41no—
341C4×C31—42no—
342C4×C31—42no—
343C4×C31—81no—
344C4×C31—81no—
345C4×C31—81no—
346C4×C31—81no—
347C4×C31#52911yescharacteristic
348C4×C31#53911yescharacteristic
349C4×C31#54611yescharacteristic
350C4×C31#54711yescharacteristic
351C22×SD16C22×C3111yescharacteristic
352C22×M16C22×C3111yescharacteristic
353C2×#123—21no—
354C2×#123—21no—
355C2×C22⋊Q8C22×C3111yescharacteristic
356C2×#121C22×C3111yescharacteristic
357C2×C4×Q8C22×C3111yescharacteristic
358C2×#117C22×C3111yescharacteristic
359C22×C4⋊C4C22×C3111yescharacteristic
360#484—24no—
361#468—24no—
362C2×#107C22×C3111yescharacteristic
363C2×#107C22×C3111yescharacteristic
364C2×#107C22×C3111yescharacteristic
365C2×C4⋊C8C22×C3111yescharacteristic
366C2×C4⋊C8C22×C3111yescharacteristic
367C2×#103C22×C3111yescharacteristic
368C2×#103C22×C3111yescharacteristic
369C2×#103C22×C3111yescharacteristic
370C2×#102C22×C3111yescharacteristic
371C2×#102C22×C3111yescharacteristic
372C2×#102C22×C3111yescharacteristic
373C2×C22⋊C8C22×C3111yescharacteristic
374#399—21no—
375#399—21no—
376#391C22×C3111yescharacteristic
377#390C22×C3111yescharacteristic
378#390C22×C3111yescharacteristic
379#389C22×C3111yescharacteristic
380#388—21no—
381#388—21no—
382#387—21no—
383#384C22×C3111yescharacteristic
384#384C22×C3111yescharacteristic
385C4×C4⋊C4—21no—
386C4×C4⋊C4C22×C3111yescharacteristic
387C4×C22⋊C4C22×C3111yescharacteristic
388#340C22×C3111yescharacteristic
389#340C22×C3111yescharacteristic
390#340C22×C3111yescharacteristic
391#340C22×C3111yescharacteristic
392#340C22×C3111yescharacteristic
393#340C22×C3111yescharacteristic
394#336C22×C3111yescharacteristic
395#336C22×C3111yescharacteristic
396C2×C31—42no—
397C2×C31—161no—
398C2×C31#242511yescharacteristic
399C2×C31#303811yescharacteristic
400C2×C31#304411yescharacteristic
401C2×C31#330811yescharacteristic
402C2×C31#333011yescharacteristic
403C2×C31#334311yescharacteristic
404C2×C31#335311yescharacteristic
405C22×Q8C23×C3111yescharacteristic
406C22×D4—21no—
407C22×D4C23×C3111yescharacteristic
408C23×C4—21no—
409C23×C4C23×C3111yescharacteristic
410C2×SD16—22no—
411C2×SD16—22no—
412C2×SD16—41no—
413C2×M16—22no—
414C2×M16—22no—
415C2×M16—41no—
416C22×C8C23×C3111yescharacteristic
417C22×C8C23×C3111yescharacteristic
418C22×C8C23×C3111yescharacteristic
419C22×C8C23×C3111yescharacteristic
420#123—44no—
421#123—44no—
422C22⋊Q8—22no—
423C22⋊Q8D4×C3114yes—
424#121—22no—
425#121—22no—
426C4×Q8—22no—
427C4×Q8—41no—
428#117—22no—
429#117—41no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4C23×C3111yescharacteristic
441C2×C4⋊C4C23×C3111yescharacteristic
442C2×C4⋊C4C23×C3111yescharacteristic
443C2×C4⋊C4C23×C3111yescharacteristic
444C2×C4⋊C4C23×C3111yescharacteristic
445C2×C4⋊C4C23×C3111yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4D4×C3111yescharacteristic
454C2×C22⋊C4D4×C3111yescharacteristic
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42C23×C3111yescharacteristic
459C2×C42C23×C3111yescharacteristic
460#107—22no—
461#107—22no—
462#107—22no—
463C4⋊C8—22no—
464C4⋊C8—41no—
465#103—22no—
466#103—22no—
467#103—22no—
468#102—22no—
469#102—22no—
470#102—41no—
471C22⋊C8—22no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95D4×C3111yescharacteristic
477#95D4×C3111yescharacteristic
478C31#2521711yescharacteristic, direct product factor, Sylow
479C24—21no—
480C24C2×D4×C3111yescharacteristic
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8C2×D4×C3112yes—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
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—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4C2×D4×C3111yescharacteristic
511C22×C4C2×D4×C3111yescharacteristic
512C22×C4C2×D4×C3111yescharacteristic
513C22×C4C2×D4×C3112yes—
514C22×C4C2×D4×C3111yescharacteristic
515C22×C4C2×D4×C3111yescharacteristic
516C22×C4#41×C3112yes—
517C22×C4C24×C3111yescharacteristic
518SD16—44no—
519M16—44no—
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×C8—21no—
530C2×C8—21no—
531C2×C8#41×C3112yes—
532C4⋊C4—24no—
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—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4C2×D4×C3112yes—
551C4⋊C4#41×C3112yes—
552C22⋊C4—24no—
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—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—42no—
566C42—42no—
567C42—42no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23C31×#12112yes—
582C23C22×D4×C3111yescharacteristic
583Q8—22no—
584Q8—22no—
585Q8—41no—
586Q8—41no—
587D4—41no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—84no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
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—41no—
628C2×C4—41no—
629C2×C4—84no—
630C2×C4C31×#12112yes—
631C2×C4C31×AGL(1,ℤ/8)12yes—
632C2×C4C31×AGL(1,ℤ/8)12yes—
633C2×C4C22×D4×C3111yescharacteristic
634C2×C4C2×#41×C3111yescharacteristic
635C2×C4C2×#41×C3111yescharacteristic
636C2×C4C2×#41×C3111yescharacteristic
637C2×C4C31×H(5,𝔽2)11yescharacteristic
638C2×C4C31×2−1+411yescharacteristic
639C8—22no—
640C8—41no—
641C8—41no—
642C8—41no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22C2×C31×#12111yescharacteristic
658C22C31×#54611yescharacteristic
659C22C31×#54711yescharacteristic
660C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
661C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
662C22C31×#57811yescharacteristic
663C22C31×#57811yescharacteristic
664C4—22no—
665C4—22no—
666C4—22no—
667C4—41no—
668C4—42no—
669C4—42no—
670C4—41no—
671C4—42no—
672C4—81no—
673C4—81no—
674C4—81no—
675C4—81no—
676C4C31×#52911yescharacteristic
677C4C31×#53911yescharacteristic
678C4C31×#54611yescharacteristic
679C4C31×#54711yescharacteristic
680C2—42no—
681C2—161no—
682C2C31×#242511yescharacteristic
683C2C31×#303811yescharacteristic
684C2C31×#304411yescharacteristic
685C2C31×#330811yescharacteristic
686C2C31×#333011yescharacteristic
687C2C31×#334311yescharacteristic
688C2C31×#335311yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#484C2semidirect
4. C31×#2362C2semidirect
5. C31×#2083C2semidirect
6. C31×#2072C2semidirect
7. C31×#2067C2semidirect
8. C31×#2055C2semidirect
9. C31×#1947C2semidirect
10. C31×#1925C2semidirect
11. C31×#1880C2semidirect
13. C31×#1851C2semidirect
14. C31×#1803C2semidirect
15. C31×#1736C2semidirect
223. #25217C31direct (N × H)
299. C2×#484C2×C31semidirect
302. #2362C2×C31semidirect
303. #2083C2×C31semidirect
304. #2072C2×C31semidirect
305. #2067C2×C31semidirect
306. #2055C2×C31semidirect
307. #1947C2×C31semidirect
308. #1925C2×C31semidirect
309. #1880C2×C31semidirect
311. #1851C2×C31semidirect
312. #1803C2×C31semidirect
313. #1736C2×C31semidirect
478. C31#25217direct (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×#4682
C31×#25012
C31×#23622
C31×#20832
C31×#20722
C31×#20672
C31×#20552
C31×#19472
C31×#19252
C31×#18802
C31×#18752
C31×#18512
C31×#18032
C31×#17362
#2521731