Finite Group Databasebeta

← C31×#16764 #21473523

Subgroups — C31×#16764 #21473523

Order 7936.

1414 conjugacy classes of subgroups.

The subgroup lattice has 1102 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×#1442C211yesmaximal, characteristic, complemented
4C31×#1440C211yesmaximal, characteristic, complemented
5C31×#1440C211yesmaximal, characteristic, complemented
6C31×#1440C211yesmaximal, characteristic, complemented
7C31×#1440C211yesmaximal, characteristic, complemented
8C31×#1439C211yesmaximal, characteristic, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1438C211yesmaximal, characteristic
11C31×#1438C211yesmaximal, characteristic
12C31×#1438C211yesmaximal, characteristic
13C31×#1437C211yesmaximal, characteristic, complemented
14C31×#1437C211yesmaximal, characteristic, complemented
15C31×#1434C211yesmaximal, characteristic, complemented
16C23×D4×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×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C42×C31C2211yescharacteristic
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
52C25×C31C2311yescharacteristic
53C22×D4×C31—22no—
54C22×D4×C31—22no—
55C22×D4×C31—22no—
56C22×D4×C31—41no—
57C22×D4×C31—41no—
58C22×D4×C31—41no—
59C22×D4×C31—41no—
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—41no—
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×C22⋊C4×C31—41no—
95C2×C22⋊C4×C31—41no—
96C2×C22⋊C4×C31—41no—
97C2×C22⋊C4×C31—41no—
98C2×C22⋊C4×C31—41no—
99C2×C22⋊C4×C31—41no—
100C2×C22⋊C4×C31—41no—
101C2×C22⋊C4×C31—41no—
102C2×C22⋊C4×C31—41no—
103C2×C22⋊C4×C31—41no—
104C2×C22⋊C4×C31—41no—
105C2×C22⋊C4×C31—41no—
106C2×C22⋊C4×C31—41no—
107C2×C22⋊C4×C31—41no—
108C2×C22⋊C4×C31—41no—
109C2×C22⋊C4×C31—41no—
110C2×C22⋊C4×C31—41no—
111C2×C22⋊C4×C31—41no—
112C2×C42×C31—22no—
113C2×C42×C31—41no—
114C2×C42×C31—41no—
115C31×#95—22no—
116C31×#95—22no—
117C31×#95—22no—
118C31×#95—22no—
119C31×#95—22no—
120C31×#95—41no—
121C31×#95—41no—
122C31×#95—41no—
123C31×#95—41no—
124C31×#95—41no—
125C31×#95—41no—
126C31×#95—41no—
127C31×#95—41no—
128C31×#95—41no—
129C31×#95—41no—
130C31×#95—41no—
131C31×#95—41no—
132C31×#95—41no—
133C31×#95—41no—
134C31×#95—41no—
135C24×C31—21no—
136C24×C31—21no—
137C24×C31—21no—
138C24×C31—21no—
139C24×C31—21no—
140C24×C31—21no—
141C24×C31—21no—
142C24×C31—21no—
143C24×C31—21no—
144C24×C31—21no—
145C24×C31—21no—
146C24×C31—21no—
147C24×C31—21no—
148C24×C31—21no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31—21no—
152C24×C31—21no—
153C24×C31—21no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31—21no—
157C24×C31—21no—
158C24×C31—21no—
159C24×C31—21no—
160C24×C31—21no—
161C24×C31—21no—
162C24×C31—21no—
163C24×C31#4112yes—
164C24×C31#4112yes—
165C24×C31C2411yescharacteristic
166C2×D4×C31—44no—
167C2×D4×C31—44no—
168C2×D4×C31—44no—
169C2×D4×C31—44no—
170C2×D4×C31—44no—
171C2×D4×C31—44no—
172C2×D4×C31—44no—
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—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—21no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
256C22×C4×C31—21no—
257C22×C4×C31—21no—
258C22×C4×C31—21no—
259C22×C4×C31#4112yes—
260C22×C4×C31#4112yes—
261C22×C4×C31#4112yes—
262C22×C4×C31#4112yes—
263C22×C4×C31#4112yes—
264C4⋊C4×C31—44no—
265C22⋊C4×C31—44no—
266C22⋊C4×C31—44no—
267C22⋊C4×C31—44no—
268C22⋊C4×C31—44no—
269C22⋊C4×C31—44no—
270C22⋊C4×C31—44no—
271C22⋊C4×C31—44no—
272C22⋊C4×C31—44no—
273C22⋊C4×C31—44no—
274C22⋊C4×C31—44no—
275C22⋊C4×C31—44no—
276C22⋊C4×C31—44no—
277C42×C31—44no—
278#16764C3111yesmaximal, characteristic, direct product factor, Sylow
279C23×C31—22no—
280C23×C31—22no—
281C23×C31—22no—
282C23×C31—22no—
283C23×C31—22no—
284C23×C31—22no—
285C23×C31—22no—
286C23×C31—22no—
287C23×C31—22no—
288C23×C31—22no—
289C23×C31—22no—
290C23×C31—22no—
291C23×C31—22no—
292C23×C31—22no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31—41no—
300C23×C31—41no—
301C23×C31—41no—
302C23×C31—41no—
303C23×C31—41no—
304C23×C31—41no—
305C23×C31—41no—
306C23×C31—41no—
307C23×C31—41no—
308C23×C31—41no—
309C23×C31—41no—
310C23×C31—41no—
311C23×C31—41no—
312C23×C31—41no—
313C23×C31—41no—
314C23×C31—41no—
315C23×C31—41no—
316C23×C31—41no—
317C23×C31—41no—
318C23×C31—41no—
319C23×C31—41no—
320C23×C31—41no—
321C23×C31—41no—
322C23×C31—41no—
323C23×C31—41no—
324C23×C31—41no—
325C23×C31—41no—
326C23×C31—41no—
327C23×C31—41no—
328C23×C31—41no—
329C23×C31—41no—
330C23×C31—41no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—41no—
334C23×C31—41no—
335C23×C31—41no—
336C23×C31—41no—
337C23×C31—41no—
338C23×C31—41no—
339C23×C31—41no—
340C23×C31—41no—
341C23×C31—41no—
342C23×C31—41no—
343C23×C31—41no—
344C23×C31—41no—
345C23×C31—41no—
346C23×C31—41no—
347C23×C31—41no—
348C23×C31—41no—
349C23×C31C2×#4111yescharacteristic
350C23×C31C2×#4111yescharacteristic
351C23×C31C2×#4111yescharacteristic
352C23×C31C2×#4111yescharacteristic
353C23×C31C2×#4111yescharacteristic
354C23×C31C2×#4111yescharacteristic
355C23×C31C2×#4111yescharacteristic
356C23×C31H(5,𝔽2)11yescharacteristic
357C23×C31H(5,𝔽2)11yescharacteristic
358C23×C31H(5,𝔽2)11yescharacteristic
359C23×C31H(5,𝔽2)11yescharacteristic
360C23×C31H(5,𝔽2)11yescharacteristic
361C23×C31H(5,𝔽2)11yescharacteristic
362C23×C31H(5,𝔽2)11yescharacteristic
363C23×C31H(5,𝔽2)11yescharacteristic
364D4×C31—416no—
365C2×C4×C31—22no—
366C2×C4×C31—22no—
367C2×C4×C31—22no—
368C2×C4×C31—22no—
369C2×C4×C31—22no—
370C2×C4×C31—22no—
371C2×C4×C31—22no—
372C2×C4×C31—22no—
373C2×C4×C31—22no—
374C2×C4×C31—22no—
375C2×C4×C31—22no—
376C2×C4×C31—22no—
377C2×C4×C31—22no—
378C2×C4×C31—22no—
379C2×C4×C31—22no—
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—
402C2×C4×C31—41no—
403C2×C4×C31—41no—
404C2×C4×C31—41no—
405C2×C4×C31—41no—
406C2×C4×C31—41no—
407C2×C4×C31—41no—
408C2×C4×C31—41no—
409C2×C4×C31—41no—
410C2×C4×C31—41no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—41no—
414C2×C4×C31—41no—
415C2×C4×C31—41no—
416C2×C4×C31—41no—
417C2×C4×C31—41no—
418C2×C4×C31—41no—
419C2×C4×C31—41no—
420C2×C4×C31—41no—
421C2×C4×C31—41no—
422C2×C4×C31—41no—
423C2×C4×C31—41no—
424C2×C4×C31—41no—
425C2×C4×C31—41no—
426C2×C4×C31—41no—
427C2×C4×C31—41no—
428C2×C4×C31—41no—
429C2×C4×C31—41no—
430C2×C4×C31—41no—
431C2×C4×C31—41no—
432C2×C4×C31—41no—
433C2×C4×C31—41no—
434C2×C4×C31—41no—
435C2×C4×C31—41no—
436C2×C4×C31—41no—
437C2×C4×C31—41no—
438C2×C4×C31—41no—
439C2×C4×C31—41no—
440C2×C4×C31—41no—
441C2×C4×C31—41no—
442C2×C4×C31—41no—
443C2×C4×C31—41no—
444C2×C4×C31—41no—
445C2×C4×C31—41no—
446C2×C4×C31—41no—
447C2×C4×C31—41no—
448C2×C4×C31—41no—
449C2×C4×C31—41no—
450C2×C4×C31—41no—
451C2×C4×C31—41no—
452C2×C4×C31—41no—
453C2×C4×C31—41no—
454C2×C4×C31—41no—
455C2×C4×C31—41no—
456#1443C2×C3111yescharacteristic, complemented
457#1443C2×C3111yescharacteristic, complemented
458#1442C2×C3111yescharacteristic, complemented
459#1440C2×C3111yescharacteristic, complemented
460#1440C2×C3111yescharacteristic, complemented
461#1440C2×C3111yescharacteristic, complemented
462#1440C2×C3111yescharacteristic, complemented
463#1439C2×C3111yescharacteristic, complemented
464#1439C2×C3111yescharacteristic, complemented
465#1438C2×C3111yescharacteristic
466#1438C2×C3111yescharacteristic
467#1438C2×C3111yescharacteristic
468#1437C2×C3111yescharacteristic, complemented
469#1437C2×C3111yescharacteristic, complemented
470#1434C2×C3111yescharacteristic, complemented
471C22×C31—42no—
472C22×C31—42no—
473C22×C31—42no—
474C22×C31—42no—
475C22×C31—42no—
476C22×C31—42no—
477C22×C31—42no—
478C22×C31—42no—
479C22×C31—42no—
480C22×C31—42no—
481C22×C31—42no—
482C22×C31—42no—
483C22×C31—42no—
484C22×C31—42no—
485C22×C31—81no—
486C22×C31—81no—
487C22×C31—81no—
488C22×C31—81no—
489C22×C31—81no—
490C22×C31—81no—
491C22×C31—81no—
492C22×C31—81no—
493C22×C31—81no—
494C22×C31—81no—
495C22×C31—81no—
496C22×C31—81no—
497C22×C31—81no—
498C22×C31—81no—
499C22×C31—81no—
500C22×C31—81no—
501C22×C31#52911yescharacteristic
502C22×C31#52911yescharacteristic
503C22×C31#52911yescharacteristic
504C22×C31#53811yescharacteristic
505C22×C31#53811yescharacteristic
506C22×C31#53811yescharacteristic
507C22×C31#53811yescharacteristic
508C22×C31#53811yescharacteristic
509C22×C31#53811yescharacteristic
510C22×C31#53811yescharacteristic
511C22×C31#53811yescharacteristic
512C22×C31#53811yescharacteristic
513C22×C31#53811yescharacteristic
514C22×C31#54011yescharacteristic
515C22×C31#54011yescharacteristic
516C22×C31#54011yescharacteristic
517C22×C31#54011yescharacteristic
518C22×C31#54011yescharacteristic
519C22×C31#54011yescharacteristic
520C22×C31#55111yescharacteristic
521C22×C31#55111yescharacteristic
522C22×C31#55111yescharacteristic
523C22×C31#55111yescharacteristic
524C22×C31#55111yescharacteristic
525C22×C31#55111yescharacteristic
526C22×C31#55311yescharacteristic
527C22×C31#55311yescharacteristic
528C22×C31#55311yescharacteristic
529C22×C31#55311yescharacteristic
530C22×C31#55511yescharacteristic
531C22×C31#55911yescharacteristic
532C22×C31#56011yescharacteristic
533C22×C31#56011yescharacteristic
534C22×C31#56011yescharacteristic
535C22×C31H(3,𝔽4)11yescharacteristic
536C4×C31—42no—
537C4×C31—42no—
538C4×C31—42no—
539C4×C31—42no—
540C4×C31—42no—
541C4×C31—81no—
542C4×C31—81no—
543C4×C31—81no—
544C4×C31—81no—
545C4×C31—81no—
546C4×C31—81no—
547C4×C31—81no—
548C4×C31—81no—
549C23×D4C22×C3111yescharacteristic
550C22×C4⋊C4C22×C3111yescharacteristic
551C22×C22⋊C4C22×C3111yescharacteristic
552C22×C22⋊C4C22×C3111yescharacteristic
553C22×C22⋊C4C22×C3111yescharacteristic
554C22×C22⋊C4C22×C3111yescharacteristic
555C22×C22⋊C4C22×C3111yescharacteristic
556C22×C22⋊C4C22×C3111yescharacteristic
557C22×C22⋊C4C22×C3111yescharacteristic
558C22×C22⋊C4C22×C3111yescharacteristic
559C22×C22⋊C4C22×C3111yescharacteristic
560C22×C22⋊C4C22×C3111yescharacteristic
561C22×C22⋊C4C22×C3111yescharacteristic
562C22×C22⋊C4C22×C3111yescharacteristic
563C22×C42C22×C3111yescharacteristic
564C2×#95C22×C3111yescharacteristic
565C2×#95C22×C3111yescharacteristic
566C2×#95C22×C3111yescharacteristic
567C2×#95C22×C3111yescharacteristic
568C2×#95C22×C3111yescharacteristic
569C2×#95C22×C3111yescharacteristic
570C2×#95C22×C3111yescharacteristic
571C2×#95C22×C3111yescharacteristic
572C2×#95C22×C3111yescharacteristic
573C2×#95C22×C3111yescharacteristic
574C2×#95C22×C3111yescharacteristic
575C2×#95C22×C3111yescharacteristic
576C2×#95C22×C3111yescharacteristic
577C2×#95C22×C3111yescharacteristic
578C2×#95C22×C3111yescharacteristic
579C2×#95C22×C3111yescharacteristic
580C2×#95C22×C3111yescharacteristic
581C2×#95C22×C3111yescharacteristic
582C2×#95C22×C3111yescharacteristic
583C2×#95C22×C3111yescharacteristic
584C2×C31—82no—
585C2×C31—82no—
586C2×C31#251611yescharacteristic
587C2×C31#253111yescharacteristic
588C2×C31#257611yescharacteristic
589C2×C31#264811yescharacteristic
590C2×C31#264811yescharacteristic
591C2×C31#264811yescharacteristic
592C2×C31#273611yescharacteristic
593C2×C31#274911yescharacteristic
594C2×C31#274911yescharacteristic
595C2×C31#275211yescharacteristic
596C2×C31#275311yescharacteristic
597C2×C31#275611yescharacteristic
598C2×C31#277811yescharacteristic
599C2×C31#280311yescharacteristic
600C2×C31#282811yescharacteristic
601C25C23×C3111yescharacteristic
602C25C23×C3111yescharacteristic
603C22×D4—22no—
604C22×D4—22no—
605C22×D4—22no—
606C22×D4—41no—
607C22×D4—41no—
608C22×D4—41no—
609C22×D4—41no—
610C23×C4C23×C3111yescharacteristic
611C23×C4C23×C3111yescharacteristic
612C23×C4C23×C3111yescharacteristic
613C23×C4C23×C3111yescharacteristic
614C23×C4C23×C3111yescharacteristic
615C23×C4C23×C3111yescharacteristic
616C23×C4C23×C3111yescharacteristic
617C23×C4C23×C3111yescharacteristic
618C23×C4C23×C3111yescharacteristic
619C23×C4C23×C3111yescharacteristic
620C23×C4C23×C3111yescharacteristic
621C23×C4C23×C3111yescharacteristic
622C23×C4C23×C3111yescharacteristic
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—41no—
639C2×C22⋊C4—41no—
640C2×C22⋊C4—41no—
641C2×C22⋊C4—41no—
642C2×C22⋊C4—41no—
643C2×C22⋊C4—41no—
644C2×C22⋊C4—41no—
645C2×C22⋊C4—41no—
646C2×C22⋊C4—41no—
647C2×C22⋊C4—41no—
648C2×C22⋊C4—41no—
649C2×C22⋊C4—41no—
650C2×C22⋊C4—41no—
651C2×C22⋊C4—41no—
652C2×C22⋊C4—41no—
653C2×C22⋊C4—41no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4—41no—
656C2×C22⋊C4—41no—
657C2×C22⋊C4—41no—
658C2×C22⋊C4—41no—
659C2×C22⋊C4—41no—
660C2×C22⋊C4—41no—
661C2×C22⋊C4—41no—
662C2×C42—22no—
663C2×C42—41no—
664C2×C42—41no—
665#95—22no—
666#95—22no—
667#95—22no—
668#95—22no—
669#95—22no—
670#95—41no—
671#95—41no—
672#95—41no—
673#95—41no—
674#95—41no—
675#95—41no—
676#95—41no—
677#95—41no—
678#95—41no—
679#95—41no—
680#95—41no—
681#95—41no—
682#95—41no—
683#95—41no—
684#95—41no—
685C31#1676411yescharacteristic, direct product factor, Sylow
686C24—21no—
687C24—21no—
688C24—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24#41×C3112yes—
715C24#41×C3112yes—
716C24C24×C3111yescharacteristic
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4#41×C3112yes—
811C22×C4#41×C3112yes—
812C22×C4#41×C3112yes—
813C22×C4#41×C3112yes—
814C22×C4#41×C3112yes—
815C4⋊C4—44no—
816C22⋊C4—44no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—44no—
820C22⋊C4—44no—
821C22⋊C4—44no—
822C22⋊C4—44no—
823C22⋊C4—44no—
824C22⋊C4—44no—
825C22⋊C4—44no—
826C22⋊C4—44no—
827C22⋊C4—44no—
828C42—44no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23C2×#41×C3111yescharacteristic
900C23C2×#41×C3111yescharacteristic
901C23C2×#41×C3111yescharacteristic
902C23C2×#41×C3111yescharacteristic
903C23C2×#41×C3111yescharacteristic
904C23C2×#41×C3111yescharacteristic
905C23C2×#41×C3111yescharacteristic
906C23C31×H(5,𝔽2)11yescharacteristic
907C23C31×H(5,𝔽2)11yescharacteristic
908C23C31×H(5,𝔽2)11yescharacteristic
909C23C31×H(5,𝔽2)11yescharacteristic
910C23C31×H(5,𝔽2)11yescharacteristic
911C23C31×H(5,𝔽2)11yescharacteristic
912C23C31×H(5,𝔽2)11yescharacteristic
913C23C31×H(5,𝔽2)11yescharacteristic
914D4—416no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C22—42no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—42no—
1020C22—81no—
1021C22—81no—
1022C22—81no—
1023C22—81no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—81no—
1031C22—81no—
1032C22—81no—
1033C22—81no—
1034C22—81no—
1035C22—81no—
1036C22C31×#52911yescharacteristic
1037C22C31×#52911yescharacteristic
1038C22C31×#52911yescharacteristic
1039C22C31×#53811yescharacteristic
1040C22C31×#53811yescharacteristic
1041C22C31×#53811yescharacteristic
1042C22C31×#53811yescharacteristic
1043C22C31×#53811yescharacteristic
1044C22C31×#53811yescharacteristic
1045C22C31×#53811yescharacteristic
1046C22C31×#53811yescharacteristic
1047C22C31×#53811yescharacteristic
1048C22C31×#53811yescharacteristic
1049C22C31×#54011yescharacteristic
1050C22C31×#54011yescharacteristic
1051C22C31×#54011yescharacteristic
1052C22C31×#54011yescharacteristic
1053C22C31×#54011yescharacteristic
1054C22C31×#54011yescharacteristic
1055C22C31×#55111yescharacteristic
1056C22C31×#55111yescharacteristic
1057C22C31×#55111yescharacteristic
1058C22C31×#55111yescharacteristic
1059C22C31×#55111yescharacteristic
1060C22C31×#55111yescharacteristic
1061C22C31×#55311yescharacteristic
1062C22C31×#55311yescharacteristic
1063C22C31×#55311yescharacteristic
1064C22C31×#55311yescharacteristic
1065C22C31×#55511yescharacteristic
1066C22C31×#55911yescharacteristic
1067C22C31×#56011yescharacteristic
1068C22C31×#56011yescharacteristic
1069C22C31×#56011yescharacteristic
1070C22C31×H(3,𝔽4)11yescharacteristic
1071C4—42no—
1072C4—42no—
1073C4—42no—
1074C4—42no—
1075C4—42no—
1076C4—81no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C2—82no—
1085C2—82no—
1086C2C31×#251611yescharacteristic
1087C2C31×#253111yescharacteristic
1088C2C31×#257611yescharacteristic
1089C2C31×#264811yescharacteristic
1090C2C31×#264811yescharacteristic
1091C2C31×#264811yescharacteristic
1092C2C31×#273611yescharacteristic
1093C2C31×#274911yescharacteristic
1094C2C31×#274911yescharacteristic
1095C2C31×#275211yescharacteristic
1096C2C31×#275311yescharacteristic
1097C2C31×#275611yescharacteristic
1098C2C31×#277811yescharacteristic
1099C2C31×#280311yescharacteristic
1100C2C31×#282811yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
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×#1442C2semidirect
4. C31×#1440C2semidirect
5. C31×#1440C2semidirect
6. C31×#1440C2semidirect
7. C31×#1440C2semidirect
8. C31×#1439C2semidirect
9. C31×#1439C2semidirect
13. C31×#1437C2semidirect
14. C31×#1437C2semidirect
15. C31×#1434C2semidirect
278. #16764C31direct (N × H)
456. #1443C2×C31semidirect
457. #1443C2×C31semidirect
458. #1442C2×C31semidirect
459. #1440C2×C31semidirect
460. #1440C2×C31semidirect
461. #1440C2×C31semidirect
462. #1440C2×C31semidirect
463. #1439C2×C31semidirect
464. #1439C2×C31semidirect
468. #1437C2×C31semidirect
469. #1437C2×C31semidirect
470. #1434C2×C31semidirect
685. C31#16764direct (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×#14382
C31×#14372
C31×#14342
#1676431