Finite Group Databasebeta

← C31×#26147 #21482906

Subgroups — C31×#26147 #21482906

Order 7936.

938 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#480C211yesmaximal, characteristic, complemented
2C2×C31×#428C211yesmaximal, characteristic, complemented
3C31×#2416C211yesmaximal, characteristic
4C31×#2352C211yesmaximal, characteristic, complemented
5C31×#2092C211yesmaximal, characteristic, complemented
6C31×#2085C211yesmaximal, characteristic, complemented
7C31×#2077C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic, complemented
9C31×#1925C211yesmaximal, characteristic, complemented
10C31×#1921C211yesmaximal, characteristic, complemented
11C31×#1895C211yesmaximal, characteristic, complemented
12C31×#1875C211yesmaximal, characteristic, complemented
13C31×#1870C211yesmaximal, characteristic, complemented
14C31×#1852C211yesmaximal, characteristic, complemented
15C31×#1852C211yesmaximal, characteristic, complemented
16C22×M16×C31C2211yescharacteristic
17C2×C31×#121—21no—
18C2×C31×#121C2211yescharacteristic
19C2×C31×#121C2211yescharacteristic
20C2×C4×D4×C31C2211yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C31×#480—24no—
25C31×#428—24no—
26C2×C31×#107C2211yescharacteristic
27C2×C31×#107C2211yescharacteristic
28C2×C31×#107C2211yescharacteristic
29C2×C31×#107C2211yescharacteristic
30C2×C31×#106C2211yescharacteristic
31C2×C31×#106C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×C22⋊C8C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C31×#396—21no—
40C31×#394—21no—
41C31×#390C2211yescharacteristic
42C31×#389C2211yescharacteristic
43C31×#388—21no—
44C31×#387—21no—
45C31×#386—21no—
46C31×#386—21no—
47C31×#382C2211yescharacteristic
48C31×#380C2211yescharacteristic
49C31×#380C2211yescharacteristic
50C31×#380C2211yescharacteristic
51C4×C4⋊C4×C31C2211yescharacteristic
52C4×C22⋊C4×C31—21no—
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31D411yescharacteristic
64C22×D4×C31C2311yescharacteristic
65C23×C4×C31—21no—
66C23×C4×C31—21no—
67C23×C4×C31C2311yescharacteristic
68C23×C4×C31C2311yescharacteristic
69C2×M16×C31—22no—
70C2×M16×C31—22no—
71C2×M16×C31—22no—
72C22×C8×C31C2311yescharacteristic
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C31×#121—22no—
77C31×#121—22no—
78C31×#121—22no—
79C31×#121—41no—
80C31×#121—44no—
81C4×D4×C31—22no—
82C4×D4×C31—22no—
83C31×#117—22no—
84C31×#117—41no—
85C2×C4⋊C4×C31—22no—
86C2×C4⋊C4×C31—22no—
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—41no—
91C2×C4⋊C4×C31—41no—
92C2×C4⋊C4×C31D411yescharacteristic
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×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31D411yescharacteristic
109C2×C22⋊C4×C31D411yescharacteristic
110C2×C42×C31—21no—
111C2×C42×C31—21no—
112C2×C42×C31C2311yescharacteristic
113C31×#107—22no—
114C31×#107—22no—
115C31×#107—41no—
116C31×#107D414yescomplemented
117C31×#106—22no—
118C31×#106—22no—
119C31×#102—22no—
120C31×#102—22no—
121C31×#102—22no—
122C31×#102—41no—
123C31×C22⋊C8—22no—
124C31×C22⋊C8—22no—
125C31×C22⋊C8—22no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C24×C31—21no—
134C24×C31C2×D411yescharacteristic
135C24×C31C2×D411yescharacteristic
136C2×D4×C31—22no—
137C2×D4×C31—22no—
138C2×D4×C31—21no—
139C2×D4×C31—21no—
140C2×D4×C31—21no—
141C2×D4×C31—21no—
142C2×D4×C31—21no—
143C2×D4×C31—21no—
144C2×D4×C31—41no—
145C2×D4×C31—42no—
146C2×D4×C31—42no—
147C2×D4×C31—42no—
148C2×D4×C31—42no—
149C2×D4×C31—42no—
150C2×D4×C31—81no—
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—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—42no—
169C22×C4×C31—42no—
170C22×C4×C31—42no—
171C22×C4×C31—42no—
172C22×C4×C31—81no—
173C22×C4×C31—81no—
174C22×C4×C31C2×D411yescharacteristic
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31#4112yes—
179C22×C4×C31#4112yes—
180C22×C4×C31C2411yescharacteristic
181M16×C31—28no—
182C2×C8×C31—21no—
183C2×C8×C31—21no—
184C2×C8×C31—21no—
185C2×C8×C31—21no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—21no—
192C2×C8×C31C2×D412yes—
193C2×C8×C31#4112yes—
194C4⋊C4×C31—22no—
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—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—42no—
208C4⋊C4×C31—42no—
209C4⋊C4×C31—42no—
210C4⋊C4×C31C2×D412yes—
211C4⋊C4×C31C2×D412yes—
212C22⋊C4×C31—22no—
213C22⋊C4×C31—22no—
214C22⋊C4×C31—42no—
215C22⋊C4×C31—42no—
216C22⋊C4×C31—42no—
217C22⋊C4×C31—42no—
218C22⋊C4×C31—42no—
219C22⋊C4×C31—42no—
220C22⋊C4×C31—81no—
221C22⋊C4×C31—81no—
222C42×C31—21no—
223C42×C31—21no—
224C42×C31—42no—
225C42×C31—81no—
226#26147C3111yesmaximal, characteristic, direct product factor, Sylow
227C23×C31—21no—
228C23×C31—21no—
229C23×C31—21no—
230C23×C31—21no—
231C23×C31—21no—
232C23×C31—21no—
233C23×C31—21no—
234C23×C31—21no—
235C23×C31—21no—
236C23×C31—21no—
237C23×C31—21no—
238C23×C31—21no—
239C23×C31—41no—
240C23×C31—41no—
241C23×C31—41no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31#12312yes—
247C23×C31AGL(1,ℤ/8)12yes—
248C23×C31C22×D411yescharacteristic
249D4×C31—44no—
250D4×C31—41no—
251D4×C31—41no—
252D4×C31—41no—
253D4×C31—41no—
254D4×C31—84no—
255D4×C31—84no—
256C2×C4×C31—21no—
257C2×C4×C31—21no—
258C2×C4×C31—22no—
259C2×C4×C31—22no—
260C2×C4×C31—22no—
261C2×C4×C31—22no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—22no—
266C2×C4×C31—21no—
267C2×C4×C31—22no—
268C2×C4×C31—21no—
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
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—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—84no—
297C2×C4×C31—84no—
298C2×C4×C31#12312yes—
299C2×C4×C31C22×D411yescharacteristic
300C2×C4×C31C2×#4111yescharacteristic
301C2×C4×C31C2×#4111yescharacteristic
302C2×C4×C31C2×#4111yescharacteristic
303C2×C4×C31H(5,𝔽2)11yescharacteristic
304C2×C4×C312−1+411yescharacteristic
305C8×C31—22no—
306C8×C31—22no—
307C8×C31—41no—
308C8×C31—41no—
309C2×#480C2×C3111yescharacteristic, complemented
310C2×#428C2×C3111yescharacteristic, complemented
311#2416C2×C3111yescharacteristic
312#2352C2×C3111yescharacteristic, complemented
313#2092C2×C3111yescharacteristic, complemented
314#2085C2×C3111yescharacteristic, complemented
315#2077C2×C3111yescharacteristic, complemented
316#2034C2×C3111yescharacteristic, complemented
317#1925C2×C3111yescharacteristic, complemented
318#1921C2×C3111yescharacteristic, complemented
319#1895C2×C3111yescharacteristic, complemented
320#1875C2×C3111yescharacteristic, complemented
321#1870C2×C3111yescharacteristic, complemented
322#1852C2×C3111yescharacteristic, complemented
323#1852C2×C3111yescharacteristic, complemented
324C22×C31—22no—
325C22×C31—22no—
326C22×C31—22no—
327C22×C31—22no—
328C22×C31—22no—
329C22×C31—22no—
330C22×C31—41no—
331C22×C31—41no—
332C22×C31—41no—
333C22×C31—41no—
334C22×C31—41no—
335C22×C31—41no—
336C22×C31—41no—
337C22×C31—41no—
338C22×C31—81no—
339C22×C31—81no—
340C22×C31—81no—
341C22×C31—81no—
342C22×C31—81no—
343C22×C31—81no—
344C22×C31—81no—
345C22×C31C2×#12311yescharacteristic
346C22×C31D4211yescharacteristic
347C22×C31#54711yescharacteristic
348C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C31#57511yescharacteristic
350C22×C31#57611yescharacteristic
351C22×C31#57811yescharacteristic
352C4×C31—22no—
353C4×C31—41no—
354C4×C31—41no—
355C4×C31—41no—
356C4×C31—42no—
357C4×C31—42no—
358C4×C31—81no—
359C4×C31—81no—
360C4×C31—81no—
361C4×C31—81no—
362C4×C31—81no—
363C4×C31#52511yescharacteristic
364C4×C31#53911yescharacteristic
365C4×C31#54811yescharacteristic
366C4×C31#55311yescharacteristic
367C22×M16C22×C3111yescharacteristic
368C2×#121—21no—
369C2×#121C22×C3111yescharacteristic
370C2×#121C22×C3111yescharacteristic
371C2×C4×D4C22×C3111yescharacteristic
372C2×#117C22×C3111yescharacteristic
373C22×C4⋊C4C22×C3111yescharacteristic
374C22×C4⋊C4C22×C3111yescharacteristic
375#480—24no—
376#428—24no—
377C2×#107C22×C3111yescharacteristic
378C2×#107C22×C3111yescharacteristic
379C2×#107C22×C3111yescharacteristic
380C2×#107C22×C3111yescharacteristic
381C2×#106C22×C3111yescharacteristic
382C2×#106C22×C3111yescharacteristic
383C2×#102C22×C3111yescharacteristic
384C2×#102C22×C3111yescharacteristic
385C2×#102C22×C3111yescharacteristic
386C2×#102C22×C3111yescharacteristic
387C2×C22⋊C8C22×C3111yescharacteristic
388C2×C22⋊C8C22×C3111yescharacteristic
389C2×C22⋊C8C22×C3111yescharacteristic
390#396—21no—
391#394—21no—
392#390C22×C3111yescharacteristic
393#389C22×C3111yescharacteristic
394#388—21no—
395#387—21no—
396#386—21no—
397#386—21no—
398#382C22×C3111yescharacteristic
399#380C22×C3111yescharacteristic
400#380C22×C3111yescharacteristic
401#380C22×C3111yescharacteristic
402C4×C4⋊C4C22×C3111yescharacteristic
403C4×C22⋊C4—21no—
404#340C22×C3111yescharacteristic
405#340C22×C3111yescharacteristic
406#340C22×C3111yescharacteristic
407#340C22×C3111yescharacteristic
408#340C22×C3111yescharacteristic
409#340C22×C3111yescharacteristic
410#336C22×C3111yescharacteristic
411#336C22×C3111yescharacteristic
412C2×C31—42no—
413C2×C31—42no—
414C2×C31—161no—
415C2×C31#244311yescharacteristic
416C2×C31#309411yescharacteristic
417C2×C31#309811yescharacteristic
418C2×C31#326411yescharacteristic
419C2×C31#327711yescharacteristic
420C2×C31#334311yescharacteristic
421C2×C31#335511yescharacteristic
422C22×D4—21no—
423C22×D4—21no—
424C22×D4D4×C3111yescharacteristic
425C22×D4C23×C3111yescharacteristic
426C23×C4—21no—
427C23×C4—21no—
428C23×C4C23×C3111yescharacteristic
429C23×C4C23×C3111yescharacteristic
430C2×M16—22no—
431C2×M16—22no—
432C2×M16—22no—
433C22×C8C23×C3111yescharacteristic
434C22×C8C23×C3111yescharacteristic
435C22×C8C23×C3111yescharacteristic
436C22×C8C23×C3111yescharacteristic
437#121—22no—
438#121—22no—
439#121—22no—
440#121—41no—
441#121—44no—
442C4×D4—22no—
443C4×D4—22no—
444#117—22no—
445#117—41no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—41no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4D4×C3111yescharacteristic
454C2×C4⋊C4C23×C3111yescharacteristic
455C2×C4⋊C4C23×C3111yescharacteristic
456C2×C4⋊C4C23×C3111yescharacteristic
457C2×C4⋊C4C23×C3111yescharacteristic
458C2×C4⋊C4C23×C3111yescharacteristic
459C2×C4⋊C4C23×C3111yescharacteristic
460C2×C4⋊C4C23×C3111yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4D4×C3111yescharacteristic
470C2×C22⋊C4D4×C3111yescharacteristic
471C2×C42—21no—
472C2×C42—21no—
473C2×C42C23×C3111yescharacteristic
474#107—22no—
475#107—22no—
476#107—41no—
477#107D4×C3114yescomplemented
478#106—22no—
479#106—22no—
480#102—22no—
481#102—22no—
482#102—22no—
483#102—41no—
484C22⋊C8—22no—
485C22⋊C8—22no—
486C22⋊C8—22no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494C31#2614711yescharacteristic, direct product factor, Sylow
495C24—21no—
496C24C2×D4×C3111yescharacteristic
497C24C2×D4×C3111yescharacteristic
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—41no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4C2×D4×C3111yescharacteristic
537C22×C4C2×D4×C3111yescharacteristic
538C22×C4C2×D4×C3111yescharacteristic
539C22×C4C2×D4×C3111yescharacteristic
540C22×C4#41×C3112yes—
541C22×C4#41×C3112yes—
542C22×C4C24×C3111yescharacteristic
543M16—28no—
544C2×C8—21no—
545C2×C8—21no—
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×C8C2×D4×C3112yes—
555C2×C8#41×C3112yes—
556C4⋊C4—22no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4C2×D4×C3112yes—
573C4⋊C4C2×D4×C3112yes—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C42—21no—
585C42—21no—
586C42—42no—
587C42—81no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23C31×#12312yes—
608C23C31×AGL(1,ℤ/8)12yes—
609C23C22×D4×C3111yescharacteristic
610D4—44no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—84no—
616D4—84no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
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—41no—
656C2×C4—41no—
657C2×C4—84no—
658C2×C4—84no—
659C2×C4C31×#12312yes—
660C2×C4C22×D4×C3111yescharacteristic
661C2×C4C2×#41×C3111yescharacteristic
662C2×C4C2×#41×C3111yescharacteristic
663C2×C4C2×#41×C3111yescharacteristic
664C2×C4C31×H(5,𝔽2)11yescharacteristic
665C2×C4C31×2−1+411yescharacteristic
666C8—22no—
667C8—22no—
668C8—41no—
669C8—41no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22C2×C31×#12311yescharacteristic
692C22D42×C3111yescharacteristic
693C22C31×#54711yescharacteristic
694C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
695C22C31×#57511yescharacteristic
696C22C31×#57611yescharacteristic
697C22C31×#57811yescharacteristic
698C4—22no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—42no—
703C4—42no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4C31×#52511yescharacteristic
710C4C31×#53911yescharacteristic
711C4C31×#54811yescharacteristic
712C4C31×#55311yescharacteristic
713C2—42no—
714C2—42no—
715C2—161no—
716C2C31×#244311yescharacteristic
717C2C31×#309411yescharacteristic
718C2C31×#309811yescharacteristic
719C2C31×#326411yescharacteristic
720C2C31×#327711yescharacteristic
721C2C31×#334311yescharacteristic
722C2C31×#335511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2416C2
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×#480C2semidirect
2. C2×C31×#428C2semidirect
4. C31×#2352C2semidirect
5. C31×#2092C2semidirect
6. C31×#2085C2semidirect
7. C31×#2077C2semidirect
8. C31×#2034C2semidirect
9. C31×#1925C2semidirect
10. C31×#1921C2semidirect
11. C31×#1895C2semidirect
12. C31×#1875C2semidirect
13. C31×#1870C2semidirect
14. C31×#1852C2semidirect
15. C31×#1852C2semidirect
116. C31×#107D4semidirect
226. #26147C31direct (N × H)
309. C2×#480C2×C31semidirect
310. C2×#428C2×C31semidirect
312. #2352C2×C31semidirect
313. #2092C2×C31semidirect
314. #2085C2×C31semidirect
315. #2077C2×C31semidirect
316. #2034C2×C31semidirect
317. #1925C2×C31semidirect
318. #1921C2×C31semidirect
319. #1895C2×C31semidirect
320. #1875C2×C31semidirect
321. #1870C2×C31semidirect
322. #1852C2×C31semidirect
323. #1852C2×C31semidirect
477. #107D4×C31semidirect
494. C31#26147direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4802
C2×C31×#4282
C31×#24162
C31×#23522
C31×#20922
C31×#20852
C31×#20772
C31×#20342
C31×#19252
C31×#19212
C31×#18952
C31×#18752
C31×#18702
C31×#18522
#2614731