Finite Group Databasebeta

← C31×#16158 #21472917

Subgroups — C31×#16158 #21472917

Order 7936.

1294 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#1443C211yesmaximal, characteristic, complemented
2C31×#1443C211yesmaximal, characteristic, complemented
3C31×#1443C211yesmaximal, characteristic, complemented
4C31×#1443C211yesmaximal, characteristic, complemented
5C31×#1443C211yesmaximal, characteristic, complemented
6C31×#1442C211yesmaximal, characteristic, complemented
7C31×#1440C211yesmaximal, characteristic
8C31×#1440C211yesmaximal, characteristic
9C31×#1439C211yesmaximal, characteristic
10C31×#1437C211yesmaximal, characteristic
11C31×#1436C211yesmaximal, characteristic, complemented
12C31×#1434C211yesmaximal, characteristic, complemented
13C31×C22⋊#95C211yesmaximal, characteristic
14C31×C22⋊#95C211yesmaximal, characteristic
15C31×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C42×C31C2211yescharacteristic
25C2×C31×#95C2211yescharacteristic
26C2×C31×#95C2211yescharacteristic
27C2×C31×#95C2211yescharacteristic
28C2×C31×#95C2211yescharacteristic
29C2×C31×#95C2211yescharacteristic
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2211yescharacteristic
39C2×C31×#95C2211yescharacteristic
40C2×C31×#95C2211yescharacteristic
41C2×C31×#95C2211yescharacteristic
42C2×C31×#95C2211yescharacteristic
43C2×C31×#95C2211yescharacteristic
44C2×C31×#95C2211yescharacteristic
45C2×C31×#95C2211yescharacteristic
46C2×C31×#95C2211yescharacteristic
47C2×C31×#95C2211yescharacteristic
48C2×C31×#95C2211yescharacteristic
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C25×C31C2311yescharacteristic
52C23×C4×C31—22no—
53C23×C4×C31—22no—
54C23×C4×C31—22no—
55C23×C4×C31—41no—
56C23×C4×C31—41no—
57C23×C4×C31—41no—
58C23×C4×C31—41no—
59C23×C4×C31C2311yescharacteristic
60C23×C4×C31C2311yescharacteristic
61C23×C4×C31C2311yescharacteristic
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2311yescharacteristic
73C2×C4⋊C4×C31—22no—
74C2×C4⋊C4×C31—41no—
75C2×C4⋊C4×C31—41no—
76C2×C22⋊C4×C31—22no—
77C2×C22⋊C4×C31—22no—
78C2×C22⋊C4×C31—22no—
79C2×C22⋊C4×C31—22no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—22no—
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—41no—
89C2×C22⋊C4×C31—41no—
90C2×C22⋊C4×C31—41no—
91C2×C22⋊C4×C31—41no—
92C2×C22⋊C4×C31—41no—
93C2×C22⋊C4×C31—41no—
94C2×C42×C31—22no—
95C2×C42×C31—41no—
96C2×C42×C31—41no—
97C31×#95—22no—
98C31×#95—22no—
99C31×#95—22no—
100C31×#95—22no—
101C31×#95—22no—
102C31×#95—22no—
103C31×#95—22no—
104C31×#95—22no—
105C31×#95—22no—
106C31×#95—22no—
107C31×#95—41no—
108C31×#95—41no—
109C31×#95—41no—
110C31×#95—41no—
111C31×#95—41no—
112C31×#95—41no—
113C31×#95—41no—
114C31×#95—41no—
115C31×#95—41no—
116C31×#95—41no—
117C31×#95—41no—
118C31×#95—41no—
119C31×#95—41no—
120C31×#95—41no—
121C31×#95—41no—
122C31×#95—41no—
123C24×C31—21no—
124C24×C31—21no—
125C24×C31—21no—
126C24×C31—21no—
127C24×C31—21no—
128C24×C31—21no—
129C24×C31—21no—
130C24×C31—21no—
131C24×C31—21no—
132C24×C31—21no—
133C24×C31—21no—
134C24×C31—21no—
135C24×C31#4112yes—
136C24×C31#4112yes—
137C24×C31#4112yes—
138C24×C31C2411yescharacteristic
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
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—21no—
165C22×C4×C31—21no—
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—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—44no—
232C22×C4×C31—44no—
233C22×C4×C31—44no—
234C22×C4×C31—44no—
235C22×C4×C31—44no—
236C22×C4×C31—44no—
237C22×C4×C31—44no—
238C22×C4×C31#4112yes—
239C22×C4×C31#4112yes—
240C22×C4×C31#4112yes—
241C22×C4×C31#4112yes—
242C22×C4×C31#4112yes—
243C22×C4×C31#4112yes—
244C4⋊C4×C31—44no—
245C22⋊C4×C31—44no—
246C22⋊C4×C31—44no—
247C22⋊C4×C31—44no—
248C22⋊C4×C31—44no—
249C22⋊C4×C31—44no—
250C22⋊C4×C31—44no—
251C42×C31—44no—
252#16158C3111yesmaximal, characteristic, direct product factor, Sylow
253C23×C31—22no—
254C23×C31—22no—
255C23×C31—22no—
256C23×C31—22no—
257C23×C31—22no—
258C23×C31—22no—
259C23×C31—22no—
260C23×C31—22no—
261C23×C31—22no—
262C23×C31—22no—
263C23×C31—22no—
264C23×C31—22no—
265C23×C31—22no—
266C23×C31—22no—
267C23×C31—22no—
268C23×C31—22no—
269C23×C31—22no—
270C23×C31—22no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31—41no—
287C23×C31#12614yes—
288C23×C31C2×#4111yescharacteristic
289C23×C31C2×#4111yescharacteristic
290C23×C31C2×#4111yescharacteristic
291C23×C31C2×#4111yescharacteristic
292C23×C31C2×#4111yescharacteristic
293C23×C31C2×#4111yescharacteristic
294C23×C31C2×#4111yescharacteristic
295C23×C31C2×#4111yescharacteristic
296C23×C31C2×#4111yescharacteristic
297C23×C31H(5,𝔽2)11yescharacteristic
298C23×C31H(5,𝔽2)11yescharacteristic
299C23×C31H(5,𝔽2)11yescharacteristic
300C23×C31H(5,𝔽2)11yescharacteristic
301C23×C31H(5,𝔽2)11yescharacteristic
302C23×C312−1+411yescharacteristic
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—22no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—22no—
311C2×C4×C31—22no—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—22no—
316C2×C4×C31—22no—
317C2×C4×C31—22no—
318C2×C4×C31—22no—
319C2×C4×C31—22no—
320C2×C4×C31—22no—
321C2×C4×C31—416no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—41no—
357C2×C4×C31—41no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—41no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—41no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—41no—
374C2×C4×C31—41no—
375C2×C4×C31—41no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—41no—
379C2×C4×C31—41no—
380C2×C4×C31—41no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—41no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—41no—
392C2×C4×C31—41no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31—41no—
397C2×C4×C31—41no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402#1443C2×C3111yescharacteristic, complemented
403#1443C2×C3111yescharacteristic, complemented
404#1443C2×C3111yescharacteristic, complemented
405#1443C2×C3111yescharacteristic, complemented
406#1443C2×C3111yescharacteristic, complemented
407#1442C2×C3111yescharacteristic, complemented
408#1440C2×C3111yescharacteristic
409#1440C2×C3111yescharacteristic
410#1439C2×C3111yescharacteristic
411#1437C2×C3111yescharacteristic
412#1436C2×C3111yescharacteristic, complemented
413#1434C2×C3111yescharacteristic, complemented
414C22⋊#95C2×C3111yescharacteristic
415C22⋊#95C2×C3111yescharacteristic
416C22⋊#95C2×C3111yescharacteristic
417C22×C31—24no—
418C22×C31—24no—
419C22×C31—24no—
420C22×C31—42no—
421C22×C31—42no—
422C22×C31—42no—
423C22×C31—42no—
424C22×C31—42no—
425C22×C31—42no—
426C22×C31—42no—
427C22×C31—42no—
428C22×C31—42no—
429C22×C31—42no—
430C22×C31—42no—
431C22×C31—42no—
432C22×C31C2×#12611yescharacteristic
433C22×C31#52911yescharacteristic
434C22×C31#52911yescharacteristic
435C22×C31#52911yescharacteristic
436C22×C31#52911yescharacteristic
437C22×C31#52911yescharacteristic
438C22×C31#53811yescharacteristic
439C22×C31#53811yescharacteristic
440C22×C31#53811yescharacteristic
441C22×C31#53811yescharacteristic
442C22×C31#53811yescharacteristic
443C22×C31#53811yescharacteristic
444C22×C31#53911yescharacteristic
445C22×C31#54211yescharacteristic
446C22×C31#54211yescharacteristic
447C22×C31#55111yescharacteristic
448C22×C31#55111yescharacteristic
449C22×C31#55111yescharacteristic
450C22×C31#55111yescharacteristic
451C22×C31#55111yescharacteristic
452C22×C31#55111yescharacteristic
453C22×C31#55111yescharacteristic
454C22×C31#55211yescharacteristic
455C22×C31#55211yescharacteristic
456C22×C31#55211yescharacteristic
457C22×C31#55311yescharacteristic
458C22×C31#55311yescharacteristic
459C22×C31#55311yescharacteristic
460C22×C31#55311yescharacteristic
461C22×C31#55311yescharacteristic
462C22×C31#55311yescharacteristic
463C22×C31#55311yescharacteristic
464C22×C31#55911yescharacteristic
465C22×C31#56011yescharacteristic
466C22×C31#56211yescharacteristic
467C4×C31—42no—
468C4×C31—42no—
469C4×C31—42no—
470C4×C31—42no—
471C4×C31—42no—
472C4×C31—42no—
473C4×C31—81no—
474C4×C31—81no—
475C4×C31—81no—
476C4×C31—81no—
477C4×C31—81no—
478C4×C31—81no—
479C4×C31—81no—
480C4×C31—81no—
481C24×C4C22×C3111yescharacteristic
482C22×C4⋊C4C22×C3111yescharacteristic
483C22×C22⋊C4C22×C3111yescharacteristic
484C22×C22⋊C4C22×C3111yescharacteristic
485C22×C22⋊C4C22×C3111yescharacteristic
486C22×C22⋊C4C22×C3111yescharacteristic
487C22×C22⋊C4C22×C3111yescharacteristic
488C22×C22⋊C4C22×C3111yescharacteristic
489C22×C42C22×C3111yescharacteristic
490C2×#95C22×C3111yescharacteristic
491C2×#95C22×C3111yescharacteristic
492C2×#95C22×C3111yescharacteristic
493C2×#95C22×C3111yescharacteristic
494C2×#95C22×C3111yescharacteristic
495C2×#95C22×C3111yescharacteristic
496C2×#95C22×C3111yescharacteristic
497C2×#95C22×C3111yescharacteristic
498C2×#95C22×C3111yescharacteristic
499C2×#95C22×C3111yescharacteristic
500C2×#95C22×C3111yescharacteristic
501C2×#95C22×C3111yescharacteristic
502C2×#95C22×C3111yescharacteristic
503C2×#95C22×C3111yescharacteristic
504C2×#95C22×C3111yescharacteristic
505C2×#95C22×C3111yescharacteristic
506C2×#95C22×C3111yescharacteristic
507C2×#95C22×C3111yescharacteristic
508C2×#95C22×C3111yescharacteristic
509C2×#95C22×C3111yescharacteristic
510C2×#95C22×C3111yescharacteristic
511C2×#95C22×C3111yescharacteristic
512C2×#95C22×C3111yescharacteristic
513C2×#95C22×C3111yescharacteristic
514C2×#95C22×C3111yescharacteristic
515C2×#95C22×C3111yescharacteristic
516C2×C31—44no—
517C2×C31#249311yescharacteristic
518C2×C31#251011yescharacteristic
519C2×C31#251011yescharacteristic
520C2×C31#251511yescharacteristic
521C2×C31#253011yescharacteristic
522C2×C31#257611yescharacteristic
523C2×C31#257811yescharacteristic
524C2×C31#259511yescharacteristic
525C2×C31#259711yescharacteristic
526C2×C31#273511yescharacteristic
527C2×C31#275011yescharacteristic
528C2×C31#275111yescharacteristic
529C2×C31#275711yescharacteristic
530C2×C31#277811yescharacteristic
531C2×C31#277911yescharacteristic
532C25C23×C3111yescharacteristic
533C23×C4—22no—
534C23×C4—22no—
535C23×C4—22no—
536C23×C4—41no—
537C23×C4—41no—
538C23×C4—41no—
539C23×C4—41no—
540C23×C4C23×C3111yescharacteristic
541C23×C4C23×C3111yescharacteristic
542C23×C4C23×C3111yescharacteristic
543C23×C4C23×C3111yescharacteristic
544C23×C4C23×C3111yescharacteristic
545C23×C4C23×C3111yescharacteristic
546C23×C4C23×C3111yescharacteristic
547C23×C4C23×C3111yescharacteristic
548C23×C4C23×C3111yescharacteristic
549C23×C4C23×C3111yescharacteristic
550C23×C4C23×C3111yescharacteristic
551C23×C4C23×C3111yescharacteristic
552C23×C4C23×C3111yescharacteristic
553C23×C4C23×C3111yescharacteristic
554C2×C4⋊C4—22no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4—41no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—41no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—41no—
575C2×C42—22no—
576C2×C42—41no—
577C2×C42—41no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—22no—
584#95—22no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—41no—
589#95—41no—
590#95—41no—
591#95—41no—
592#95—41no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—41no—
598#95—41no—
599#95—41no—
600#95—41no—
601#95—41no—
602#95—41no—
603#95—41no—
604C31#1615811yescharacteristic, direct product factor, Sylow
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24#41×C3112yes—
618C24#41×C3112yes—
619C24#41×C3112yes—
620C24C24×C3111yescharacteristic
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4#41×C3112yes—
721C22×C4#41×C3112yes—
722C22×C4#41×C3112yes—
723C22×C4#41×C3112yes—
724C22×C4#41×C3112yes—
725C22×C4#41×C3112yes—
726C4⋊C4—44no—
727C22⋊C4—44no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—44no—
732C22⋊C4—44no—
733C42—44no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23C31×#12614yes—
769C23C2×#41×C3111yescharacteristic
770C23C2×#41×C3111yescharacteristic
771C23C2×#41×C3111yescharacteristic
772C23C2×#41×C3111yescharacteristic
773C23C2×#41×C3111yescharacteristic
774C23C2×#41×C3111yescharacteristic
775C23C2×#41×C3111yescharacteristic
776C23C2×#41×C3111yescharacteristic
777C23C2×#41×C3111yescharacteristic
778C23C31×H(5,𝔽2)11yescharacteristic
779C23C31×H(5,𝔽2)11yescharacteristic
780C23C31×H(5,𝔽2)11yescharacteristic
781C23C31×H(5,𝔽2)11yescharacteristic
782C23C31×H(5,𝔽2)11yescharacteristic
783C23C31×2−1+411yescharacteristic
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—416no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C22—24no—
884C22—24no—
885C22—24no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22C2×C31×#12611yescharacteristic
899C22C31×#52911yescharacteristic
900C22C31×#52911yescharacteristic
901C22C31×#52911yescharacteristic
902C22C31×#52911yescharacteristic
903C22C31×#52911yescharacteristic
904C22C31×#53811yescharacteristic
905C22C31×#53811yescharacteristic
906C22C31×#53811yescharacteristic
907C22C31×#53811yescharacteristic
908C22C31×#53811yescharacteristic
909C22C31×#53811yescharacteristic
910C22C31×#53911yescharacteristic
911C22C31×#54211yescharacteristic
912C22C31×#54211yescharacteristic
913C22C31×#55111yescharacteristic
914C22C31×#55111yescharacteristic
915C22C31×#55111yescharacteristic
916C22C31×#55111yescharacteristic
917C22C31×#55111yescharacteristic
918C22C31×#55111yescharacteristic
919C22C31×#55111yescharacteristic
920C22C31×#55211yescharacteristic
921C22C31×#55211yescharacteristic
922C22C31×#55211yescharacteristic
923C22C31×#55311yescharacteristic
924C22C31×#55311yescharacteristic
925C22C31×#55311yescharacteristic
926C22C31×#55311yescharacteristic
927C22C31×#55311yescharacteristic
928C22C31×#55311yescharacteristic
929C22C31×#55311yescharacteristic
930C22C31×#55911yescharacteristic
931C22C31×#56011yescharacteristic
932C22C31×#56211yescharacteristic
933C4—42no—
934C4—42no—
935C4—42no—
936C4—42no—
937C4—42no—
938C4—42no—
939C4—81no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4—81no—
947C2—44no—
948C2C31×#249311yescharacteristic
949C2C31×#251011yescharacteristic
950C2C31×#251011yescharacteristic
951C2C31×#251511yescharacteristic
952C2C31×#253011yescharacteristic
953C2C31×#257611yescharacteristic
954C2C31×#257811yescharacteristic
955C2C31×#259511yescharacteristic
956C2C31×#259711yescharacteristic
957C2C31×#273511yescharacteristic
958C2C31×#275011yescharacteristic
959C2C31×#275111yescharacteristic
960C2C31×#275711yescharacteristic
961C2C31×#277811yescharacteristic
962C2C31×#277911yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#1443C2semidirect
2. C31×#1443C2semidirect
3. C31×#1443C2semidirect
4. C31×#1443C2semidirect
5. C31×#1443C2semidirect
6. C31×#1442C2semidirect
11. C31×#1436C2semidirect
12. C31×#1434C2semidirect
252. #16158C31direct (N × H)
402. #1443C2×C31semidirect
403. #1443C2×C31semidirect
404. #1443C2×C31semidirect
405. #1443C2×C31semidirect
406. #1443C2×C31semidirect
407. #1442C2×C31semidirect
412. #1436C2×C31semidirect
413. #1434C2×C31semidirect
604. C31#16158direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#14432
C31×#14422
C31×#14402
C31×#14392
C31×#14372
C31×#14362
C31×#14342
C31×C22⋊#952
#1615831