Finite Group Databasebeta

← C31×#17145 #21473904

Subgroups — C31×#17145 #21473904

Order 7936.

1466 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#397C211yesmaximal, characteristic, complemented
2C2×C31×#394C211yesmaximal, characteristic
3C31×#1445C211yesmaximal, characteristic, complemented
4C31×#1443C211yesmaximal, characteristic, complemented
5C31×#1441C211yesmaximal, characteristic, complemented
6C31×#1441C211yesmaximal, characteristic, complemented
7C31×#1440C211yesmaximal, characteristic, complemented
8C31×#1440C211yesmaximal, characteristic, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1439C211yesmaximal, characteristic, complemented
13C31×#1439C211yesmaximal, characteristic, complemented
14C31×#1438C211yesmaximal, characteristic
15C31×#1438C211yesmaximal, characteristic
16C23×D4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊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×C22⋊C4×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2211yescharacteristic
33C31×#397—24no—
34C31×#394—24no—
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
51C2×C31×#95C2211yescharacteristic
52C2×C31×#95C2211yescharacteristic
53C25×C31C2311yescharacteristic
54C25×C31C2311yescharacteristic
55C22×D4×C31—22no—
56C22×D4×C31—22no—
57C22×D4×C31—22no—
58C22×D4×C31—41no—
59C22×D4×C31—41no—
60C22×D4×C31—41no—
61C22×D4×C31—41no—
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
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31—41no—
81C2×C4⋊C4×C31—41no—
82C2×C4⋊C4×C31—41no—
83C2×C4⋊C4×C31—41no—
84C2×C4⋊C4×C31—41no—
85C2×C4⋊C4×C31—41no—
86C2×C4⋊C4×C31—41no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—22no—
94C2×C22⋊C4×C31—22no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—22no—
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×C22⋊C4×C31—41no—
113C2×C22⋊C4×C31—41no—
114C2×C22⋊C4×C31—41no—
115C2×C22⋊C4×C31—41no—
116C2×C22⋊C4×C31—41no—
117C2×C22⋊C4×C31—41no—
118C2×C22⋊C4×C31—41no—
119C2×C22⋊C4×C31—41no—
120C2×C22⋊C4×C31—41no—
121C2×C22⋊C4×C31—41no—
122C2×C22⋊C4×C31D414yes—
123C31×#95—22no—
124C31×#95—22no—
125C31×#95—22no—
126C31×#95—22no—
127C31×#95—22no—
128C31×#95—41no—
129C31×#95—41no—
130C31×#95—41no—
131C31×#95—41no—
132C31×#95—41no—
133C31×#95—41no—
134C31×#95—41no—
135C31×#95—41no—
136C31×#95—41no—
137C31×#95—41no—
138C31×#95—41no—
139C31×#95—41no—
140C31×#95—41no—
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—21no—
164C24×C31—21no—
165C24×C31—21no—
166C24×C31—21no—
167C24×C31—21no—
168C24×C31—21no—
169C24×C31C2×D412yes—
170C24×C31#4112yes—
171C24×C31C2411yescharacteristic
172C2×D4×C31—44no—
173C2×D4×C31—44no—
174C2×D4×C31—44no—
175C2×D4×C31—44no—
176C2×D4×C31—44no—
177C2×D4×C31—44no—
178C2×D4×C31—44no—
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—21no—
260C22×C4×C31—21no—
261C22×C4×C31—21no—
262C22×C4×C31—21no—
263C22×C4×C31—21no—
264C22×C4×C31—21no—
265C22×C4×C31C2×D412yes—
266C22×C4×C31C2×D412yes—
267C22×C4×C31#4112yes—
268C22×C4×C31#4112yes—
269C22×C4×C31#4112yes—
270C4⋊C4×C31—44no—
271C4⋊C4×C31—44no—
272C4⋊C4×C31—44no—
273C4⋊C4×C31—44no—
274C22⋊C4×C31—44no—
275C22⋊C4×C31—44no—
276C22⋊C4×C31—44no—
277C22⋊C4×C31—44no—
278C22⋊C4×C31—44no—
279C22⋊C4×C31—44no—
280C22⋊C4×C31—44no—
281C22⋊C4×C31—44no—
282C22⋊C4×C31—44no—
283C22⋊C4×C31—44no—
284C22⋊C4×C31—44no—
285C22⋊C4×C31—44no—
286#17145C3111yesmaximal, characteristic, direct product factor, Sylow
287C23×C31—22no—
288C23×C31—22no—
289C23×C31—22no—
290C23×C31—22no—
291C23×C31—22no—
292C23×C31—22no—
293C23×C31—22no—
294C23×C31—22no—
295C23×C31—22no—
296C23×C31—22no—
297C23×C31—22no—
298C23×C31—22no—
299C23×C31—22no—
300C23×C31—22no—
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×C31—41no—
350C23×C31—41no—
351C23×C31—41no—
352C23×C31—41no—
353C23×C31—41no—
354C23×C31—41no—
355C23×C31—41no—
356C23×C31—41no—
357C23×C31C22×D411yescharacteristic
358C23×C31C2×#4111yescharacteristic
359C23×C31C2×#4111yescharacteristic
360C23×C31C2×#4111yescharacteristic
361C23×C31C2×#4111yescharacteristic
362C23×C31H(5,𝔽2)11yescharacteristic
363C23×C31H(5,𝔽2)11yescharacteristic
364C23×C31H(5,𝔽2)11yescharacteristic
365C23×C31H(5,𝔽2)11yescharacteristic
366C23×C31H(5,𝔽2)11yescharacteristic
367C23×C31H(5,𝔽2)11yescharacteristic
368C23×C31H(5,𝔽2)11yescharacteristic
369C23×C31H(5,𝔽2)11yescharacteristic
370C23×C312−1+411yescharacteristic
371C23×C312−1+411yescharacteristic
372D4×C31—416no—
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—22no—
381C2×C4×C31—22no—
382C2×C4×C31—22no—
383C2×C4×C31—22no—
384C2×C4×C31—22no—
385C2×C4×C31—22no—
386C2×C4×C31—22no—
387C2×C4×C31—22no—
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—
456C2×C4×C31—41no—
457C2×C4×C31—41no—
458C2×C4×C31—41no—
459C2×C4×C31—41no—
460C2×C4×C31—41no—
461C2×C4×C31—41no—
462C2×C4×C31—41no—
463C2×C4×C31—41no—
464C2×#397C2×C3111yescharacteristic, complemented
465C2×#394C2×C3111yescharacteristic
466#1445C2×C3111yescharacteristic, complemented
467#1443C2×C3111yescharacteristic, complemented
468#1441C2×C3111yescharacteristic, complemented
469#1441C2×C3111yescharacteristic, complemented
470#1440C2×C3111yescharacteristic, complemented
471#1440C2×C3111yescharacteristic, complemented
472#1439C2×C3111yescharacteristic, complemented
473#1439C2×C3111yescharacteristic, complemented
474#1439C2×C3111yescharacteristic, complemented
475#1439C2×C3111yescharacteristic, complemented
476#1439C2×C3111yescharacteristic, complemented
477#1438C2×C3111yescharacteristic
478#1438C2×C3111yescharacteristic
479C22×C31—42no—
480C22×C31—42no—
481C22×C31—42no—
482C22×C31—42no—
483C22×C31—42no—
484C22×C31—42no—
485C22×C31—42no—
486C22×C31—42no—
487C22×C31—42no—
488C22×C31—42no—
489C22×C31—42no—
490C22×C31—42no—
491C22×C31—42no—
492C22×C31—42no—
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—81no—
502C22×C31—81no—
503C22×C31—81no—
504C22×C31—81no—
505C22×C31—81no—
506C22×C31—81no—
507C22×C31—81no—
508C22×C31—81no—
509C22×C31#53411yescharacteristic
510C22×C31#53511yescharacteristic
511C22×C31#53711yescharacteristic
512C22×C31#53811yescharacteristic
513C22×C31#53811yescharacteristic
514C22×C31#53811yescharacteristic
515C22×C31#53811yescharacteristic
516C22×C31#53811yescharacteristic
517C22×C31#53911yescharacteristic
518C22×C31#53911yescharacteristic
519C22×C31#53911yescharacteristic
520C22×C31#54011yescharacteristic
521C22×C31#54011yescharacteristic
522C22×C31#54211yescharacteristic
523C22×C31#54211yescharacteristic
524C22×C31#54611yescharacteristic
525C22×C31#54611yescharacteristic
526C22×C31#54611yescharacteristic
527C22×C31#54711yescharacteristic
528C22×C31#55111yescharacteristic
529C22×C31#55111yescharacteristic
530C22×C31#55311yescharacteristic
531C22×C31#55511yescharacteristic
532C22×C31#55611yescharacteristic
533C22×C31#55911yescharacteristic
534C22×C31#56011yescharacteristic
535C22×C31#56011yescharacteristic
536C22×C31#56011yescharacteristic
537C22×C31#56011yescharacteristic
538C22×C31#56011yescharacteristic
539C22×C31#56211yescharacteristic
540C22×C31#56211yescharacteristic
541C22×C31#56211yescharacteristic
542C22×C31#56211yescharacteristic
543C22×C31#56311yescharacteristic
544C4×C31—42no—
545C4×C31—42no—
546C4×C31—42no—
547C4×C31—42no—
548C4×C31—42no—
549C4×C31—81no—
550C4×C31—81no—
551C4×C31—81no—
552C4×C31—81no—
553C4×C31—81no—
554C4×C31—81no—
555C4×C31—81no—
556C4×C31—81no—
557C23×D4C22×C3111yescharacteristic
558C22×C4⋊C4C22×C3111yescharacteristic
559C22×C4⋊C4C22×C3111yescharacteristic
560C22×C4⋊C4C22×C3111yescharacteristic
561C22×C4⋊C4C22×C3111yescharacteristic
562C22×C22⋊C4C22×C3111yescharacteristic
563C22×C22⋊C4C22×C3111yescharacteristic
564C22×C22⋊C4C22×C3111yescharacteristic
565C22×C22⋊C4C22×C3111yescharacteristic
566C22×C22⋊C4C22×C3111yescharacteristic
567C22×C22⋊C4C22×C3111yescharacteristic
568C22×C22⋊C4C22×C3111yescharacteristic
569C22×C22⋊C4C22×C3111yescharacteristic
570C22×C22⋊C4C22×C3111yescharacteristic
571C22×C22⋊C4C22×C3111yescharacteristic
572C22×C22⋊C4C22×C3111yescharacteristic
573C22×C22⋊C4C22×C3111yescharacteristic
574#397—24no—
575#394—24no—
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×#95C22×C3111yescharacteristic
585C2×#95C22×C3111yescharacteristic
586C2×#95C22×C3111yescharacteristic
587C2×#95C22×C3111yescharacteristic
588C2×#95C22×C3111yescharacteristic
589C2×#95C22×C3111yescharacteristic
590C2×#95C22×C3111yescharacteristic
591C2×#95C22×C3111yescharacteristic
592C2×#95C22×C3111yescharacteristic
593C2×#95C22×C3111yescharacteristic
594C2×C31—82no—
595C2×C31—82no—
596C2×C31#268511yescharacteristic
597C2×C31#269311yescharacteristic
598C2×C31#269911yescharacteristic
599C2×C31#270811yescharacteristic
600C2×C31#271011yescharacteristic
601C2×C31#271511yescharacteristic
602C2×C31#273711yescharacteristic
603C2×C31#278611yescharacteristic
604C2×C31#279711yescharacteristic
605C2×C31#280811yescharacteristic
606C2×C31#281311yescharacteristic
607C2×C31#282511yescharacteristic
608C2×C31#282711yescharacteristic
609C2×C31#282911yescharacteristic
610C2×C31#283711yescharacteristic
611C25C23×C3111yescharacteristic
612C25C23×C3111yescharacteristic
613C22×D4—22no—
614C22×D4—22no—
615C22×D4—22no—
616C22×D4—41no—
617C22×D4—41no—
618C22×D4—41no—
619C22×D4—41no—
620C23×C4C23×C3111yescharacteristic
621C23×C4C23×C3111yescharacteristic
622C23×C4C23×C3111yescharacteristic
623C23×C4C23×C3111yescharacteristic
624C23×C4C23×C3111yescharacteristic
625C23×C4C23×C3111yescharacteristic
626C23×C4C23×C3111yescharacteristic
627C23×C4C23×C3111yescharacteristic
628C23×C4C23×C3111yescharacteristic
629C23×C4C23×C3111yescharacteristic
630C23×C4C23×C3111yescharacteristic
631C23×C4C23×C3111yescharacteristic
632C23×C4C23×C3111yescharacteristic
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
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×C22⋊C4—41no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—41no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—41no—
669C2×C22⋊C4—41no—
670C2×C22⋊C4—41no—
671C2×C22⋊C4—41no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4D4×C3114yes—
681#95—22no—
682#95—22no—
683#95—22no—
684#95—22no—
685#95—22no—
686#95—41no—
687#95—41no—
688#95—41no—
689#95—41no—
690#95—41no—
691#95—41no—
692#95—41no—
693#95—41no—
694#95—41no—
695#95—41no—
696#95—41no—
697#95—41no—
698#95—41no—
699C31#1714511yescharacteristic, direct product factor, Sylow
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—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24C2×D4×C3112yes—
729C24#41×C3112yes—
730C24C24×C3111yescharacteristic
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
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—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4C2×D4×C3112yes—
825C22×C4C2×D4×C3112yes—
826C22×C4#41×C3112yes—
827C22×C4#41×C3112yes—
828C22×C4#41×C3112yes—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
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—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23C22×D4×C3111yescharacteristic
916C23C2×#41×C3111yescharacteristic
917C23C2×#41×C3111yescharacteristic
918C23C2×#41×C3111yescharacteristic
919C23C2×#41×C3111yescharacteristic
920C23C31×H(5,𝔽2)11yescharacteristic
921C23C31×H(5,𝔽2)11yescharacteristic
922C23C31×H(5,𝔽2)11yescharacteristic
923C23C31×H(5,𝔽2)11yescharacteristic
924C23C31×H(5,𝔽2)11yescharacteristic
925C23C31×H(5,𝔽2)11yescharacteristic
926C23C31×H(5,𝔽2)11yescharacteristic
927C23C31×H(5,𝔽2)11yescharacteristic
928C23C31×2−1+411yescharacteristic
929C23C31×2−1+411yescharacteristic
930D4—416no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
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—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—81no—
1037C22—81no—
1038C22—81no—
1039C22—81no—
1040C22—81no—
1041C22—81no—
1042C22—81no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22C31×#53411yescharacteristic
1053C22C31×#53511yescharacteristic
1054C22C31×#53711yescharacteristic
1055C22C31×#53811yescharacteristic
1056C22C31×#53811yescharacteristic
1057C22C31×#53811yescharacteristic
1058C22C31×#53811yescharacteristic
1059C22C31×#53811yescharacteristic
1060C22C31×#53911yescharacteristic
1061C22C31×#53911yescharacteristic
1062C22C31×#53911yescharacteristic
1063C22C31×#54011yescharacteristic
1064C22C31×#54011yescharacteristic
1065C22C31×#54211yescharacteristic
1066C22C31×#54211yescharacteristic
1067C22C31×#54611yescharacteristic
1068C22C31×#54611yescharacteristic
1069C22C31×#54611yescharacteristic
1070C22C31×#54711yescharacteristic
1071C22C31×#55111yescharacteristic
1072C22C31×#55111yescharacteristic
1073C22C31×#55311yescharacteristic
1074C22C31×#55511yescharacteristic
1075C22C31×#55611yescharacteristic
1076C22C31×#55911yescharacteristic
1077C22C31×#56011yescharacteristic
1078C22C31×#56011yescharacteristic
1079C22C31×#56011yescharacteristic
1080C22C31×#56011yescharacteristic
1081C22C31×#56011yescharacteristic
1082C22C31×#56211yescharacteristic
1083C22C31×#56211yescharacteristic
1084C22C31×#56211yescharacteristic
1085C22C31×#56211yescharacteristic
1086C22C31×#56311yescharacteristic
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4—42no—
1092C4—81no—
1093C4—81no—
1094C4—81no—
1095C4—81no—
1096C4—81no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C2—82no—
1101C2—82no—
1102C2C31×#268511yescharacteristic
1103C2C31×#269311yescharacteristic
1104C2C31×#269911yescharacteristic
1105C2C31×#270811yescharacteristic
1106C2C31×#271011yescharacteristic
1107C2C31×#271511yescharacteristic
1108C2C31×#273711yescharacteristic
1109C2C31×#278611yescharacteristic
1110C2C31×#279711yescharacteristic
1111C2C31×#280811yescharacteristic
1112C2C31×#281311yescharacteristic
1113C2C31×#282511yescharacteristic
1114C2C31×#282711yescharacteristic
1115C2C31×#282911yescharacteristic
1116C2C31×#283711yescharacteristic
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. C2×C31×#397C2semidirect
3. C31×#1445C2semidirect
4. C31×#1443C2semidirect
5. C31×#1441C2semidirect
6. C31×#1441C2semidirect
7. C31×#1440C2semidirect
8. C31×#1440C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
11. C31×#1439C2semidirect
12. C31×#1439C2semidirect
13. C31×#1439C2semidirect
286. #17145C31direct (N × H)
464. C2×#397C2×C31semidirect
466. #1445C2×C31semidirect
467. #1443C2×C31semidirect
468. #1441C2×C31semidirect
469. #1441C2×C31semidirect
470. #1440C2×C31semidirect
471. #1440C2×C31semidirect
472. #1439C2×C31semidirect
473. #1439C2×C31semidirect
474. #1439C2×C31semidirect
475. #1439C2×C31semidirect
476. #1439C2×C31semidirect
699. C31#17145direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3972
C2×C31×#3942
C31×#14452
C31×#14432
C31×#14412
C31×#14402
C31×#14392
C31×#14382
#1714531