Finite Group Databasebeta

← C31×#16527 #21473286

Subgroups — C31×#16527 #21473286

Order 7936.

1590 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#397C211yesmaximal, characteristic, complemented
2C2×C31×#397C211yesmaximal, characteristic, complemented
3C2×C31×#394C211yesmaximal, characteristic
4C2×C31×#390C211yesmaximal, characteristic
5C31×#1444C211yesmaximal, 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×#1438C211yesmaximal, characteristic
14C31×#1436C211yesmaximal, characteristic, complemented
15C31×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊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
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C42×C31C2211yescharacteristic
35C31×#397—24no—
36C31×#397—24no—
37C31×#394—24no—
38C31×#390—24no—
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
53C2×C31×#95C2211yescharacteristic
54C2×C31×#95C2211yescharacteristic
55C25×C31C2311yescharacteristic
56C25×C31C2311yescharacteristic
57C22×D4×C31—22no—
58C22×D4×C31—22no—
59C22×D4×C31—41no—
60C22×D4×C31—41no—
61C22×D4×C31—41no—
62C22×D4×C31—41no—
63C22×D4×C31D414yes—
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
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31—41no—
85C2×C4⋊C4×C31—41no—
86C2×C4⋊C4×C31—41no—
87C2×C4⋊C4×C31—41no—
88C2×C4⋊C4×C31—41no—
89C2×C4⋊C4×C31—41no—
90C2×C4⋊C4×C31—41no—
91C2×C4⋊C4×C31—41no—
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—22no—
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—22no—
106C2×C22⋊C4×C31—22no—
107C2×C22⋊C4×C31—22no—
108C2×C22⋊C4×C31—22no—
109C2×C22⋊C4×C31—22no—
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—22no—
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×C31—41no—
123C2×C22⋊C4×C31—41no—
124C2×C22⋊C4×C31—41no—
125C2×C22⋊C4×C31—41no—
126C2×C22⋊C4×C31—41no—
127C2×C22⋊C4×C31—41no—
128C2×C42×C31—22no—
129C2×C42×C31—41no—
130C2×C42×C31—41no—
131C31×#95—22no—
132C31×#95—22no—
133C31×#95—22no—
134C31×#95—22no—
135C31×#95—22no—
136C31×#95—22no—
137C31×#95—22no—
138C31×#95—22no—
139C31×#95—22no—
140C31×#95—41no—
141C31×#95—41no—
142C31×#95—41no—
143C31×#95—41no—
144C31×#95—41no—
145C31×#95—41no—
146C31×#95D414yescomplemented
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×C31—21no—
170C24×C31—21no—
171C24×C31—21no—
172C24×C31—21no—
173C24×C31—21no—
174C24×C31—21no—
175C24×C31C2×D412yes—
176C24×C31C2×D412yes—
177C24×C31C2411yescharacteristic
178C2×D4×C31—28no—
179C2×D4×C31—44no—
180C2×D4×C31—44no—
181C2×D4×C31—44no—
182C2×D4×C31—44no—
183C2×D4×C31—44no—
184C2×D4×C31—44no—
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×C31—21no—
266C22×C4×C31—21no—
267C22×C4×C31C2×D412yes—
268C22×C4×C31C2×D412yes—
269C22×C4×C31C2×D412yes—
270C22×C4×C31C2×D412yes—
271C22×C4×C31#4112yes—
272C22×C4×C31#4112yes—
273C22×C4×C31#4112yes—
274C22×C4×C31#4112yes—
275C22×C4×C31#4112yes—
276C4⋊C4×C31—44no—
277C4⋊C4×C31—44no—
278C4⋊C4×C31—44no—
279C4⋊C4×C31—44no—
280C4⋊C4×C31—44no—
281C22⋊C4×C31—44no—
282C22⋊C4×C31—44no—
283C22⋊C4×C31—44no—
284C22⋊C4×C31—44no—
285C22⋊C4×C31—44no—
286C22⋊C4×C31—44no—
287C22⋊C4×C31—44no—
288C22⋊C4×C31—44no—
289C22⋊C4×C31—44no—
290C22⋊C4×C31—44no—
291C22⋊C4×C31—44no—
292C22⋊C4×C31—44no—
293C42×C31—44no—
294#16527C3111yesmaximal, characteristic, direct product factor, Sylow
295C23×C31—22no—
296C23×C31—22no—
297C23×C31—22no—
298C23×C31—22no—
299C23×C31—22no—
300C23×C31—22no—
301C23×C31—22no—
302C23×C31—22no—
303C23×C31—22no—
304C23×C31—22no—
305C23×C31—22no—
306C23×C31—22no—
307C23×C31—22no—
308C23×C31—22no—
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×C31—41no—
358C23×C31—41no—
359C23×C31—41no—
360C23×C31—41no—
361C23×C31—41no—
362C23×C31—41no—
363C23×C31—41no—
364C23×C31—41no—
365C23×C31C22×D411yescharacteristic
366C23×C31C22×D411yescharacteristic
367C23×C31C2×#4111yescharacteristic
368C23×C31C2×#4111yescharacteristic
369C23×C31C2×#4111yescharacteristic
370C23×C31C2×#4111yescharacteristic
371C23×C31C2×#4111yescharacteristic
372C23×C31H(5,𝔽2)11yescharacteristic
373C23×C31H(5,𝔽2)11yescharacteristic
374C23×C31H(5,𝔽2)11yescharacteristic
375C23×C31H(5,𝔽2)11yescharacteristic
376C23×C31H(5,𝔽2)11yescharacteristic
377C23×C31H(5,𝔽2)11yescharacteristic
378C23×C312−1+411yescharacteristic
379C23×C312−1+411yescharacteristic
380D4×C31—416no—
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—22no—
389C2×C4×C31—22no—
390C2×C4×C31—22no—
391C2×C4×C31—22no—
392C2×C4×C31—22no—
393C2×C4×C31—22no—
394C2×C4×C31—22no—
395C2×C4×C31—22no—
396C2×C4×C31—22no—
397C2×C4×C31—22no—
398C2×C4×C31—22no—
399C2×C4×C31—22no—
400C2×C4×C31—22no—
401C2×C4×C31—22no—
402C2×C4×C31—22no—
403C2×C4×C31—22no—
404C2×C4×C31—22no—
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×C4×C31—41no—
465C2×C4×C31—41no—
466C2×C4×C31—41no—
467C2×C4×C31—41no—
468C2×C4×C31—41no—
469C2×C4×C31—41no—
470C2×C4×C31—41no—
471C2×C4×C31#12314yes—
472C2×#397C2×C3111yescharacteristic, complemented
473C2×#397C2×C3111yescharacteristic, complemented
474C2×#394C2×C3111yescharacteristic
475C2×#390C2×C3111yescharacteristic
476#1444C2×C3111yescharacteristic, complemented
477#1441C2×C3111yescharacteristic, complemented
478#1440C2×C3111yescharacteristic, complemented
479#1440C2×C3111yescharacteristic, complemented
480#1439C2×C3111yescharacteristic, complemented
481#1439C2×C3111yescharacteristic, complemented
482#1439C2×C3111yescharacteristic, complemented
483#1439C2×C3111yescharacteristic, complemented
484#1438C2×C3111yescharacteristic
485#1436C2×C3111yescharacteristic, complemented
486#1436C2×C3111yescharacteristic, complemented
487C22×C31—42no—
488C22×C31—42no—
489C22×C31—42no—
490C22×C31—42no—
491C22×C31—42no—
492C22×C31—42no—
493C22×C31—42no—
494C22×C31—42no—
495C22×C31—42no—
496C22×C31—42no—
497C22×C31—42no—
498C22×C31—42no—
499C22×C31—42no—
500C22×C31—42no—
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—81no—
510C22×C31—81no—
511C22×C31—81no—
512C22×C31—81no—
513C22×C31—81no—
514C22×C31—81no—
515C22×C31—81no—
516C22×C31—81no—
517C22×C31C2×#12311yescharacteristic
518C22×C31#52911yescharacteristic
519C22×C31#53211yescharacteristic
520C22×C31#53411yescharacteristic
521C22×C31#53411yescharacteristic
522C22×C31#53511yescharacteristic
523C22×C31#53711yescharacteristic
524C22×C31#53811yescharacteristic
525C22×C31#53811yescharacteristic
526C22×C31#53811yescharacteristic
527C22×C31#53811yescharacteristic
528C22×C31#53811yescharacteristic
529C22×C31#53911yescharacteristic
530C22×C31#54011yescharacteristic
531C22×C31#54011yescharacteristic
532C22×C31#54211yescharacteristic
533C22×C31#54211yescharacteristic
534C22×C31#54211yescharacteristic
535C22×C31#54211yescharacteristic
536C22×C31D4211yescharacteristic
537C22×C31#54611yescharacteristic
538C22×C31#54611yescharacteristic
539C22×C31#54711yescharacteristic
540C22×C31#54711yescharacteristic
541C22×C31#54711yescharacteristic
542C22×C31#55011yescharacteristic
543C22×C31#55111yescharacteristic
544C22×C31#55311yescharacteristic
545C22×C31#55311yescharacteristic
546C22×C31#55611yescharacteristic
547C22×C31#55911yescharacteristic
548C22×C31#56011yescharacteristic
549C22×C31#56211yescharacteristic
550C22×C31#56211yescharacteristic
551C22×C31#56311yescharacteristic
552C4×C31—24no—
553C4×C31—42no—
554C4×C31—42no—
555C4×C31—42no—
556C4×C31—42no—
557C4×C31—42no—
558C4×C31—42no—
559C4×C31—81no—
560C4×C31—81no—
561C4×C31—81no—
562C4×C31—81no—
563C4×C31—81no—
564C4×C31—81no—
565C23×D4C22×C3111yescharacteristic
566C22×C4⋊C4C22×C3111yescharacteristic
567C22×C4⋊C4C22×C3111yescharacteristic
568C22×C4⋊C4C22×C3111yescharacteristic
569C22×C4⋊C4C22×C3111yescharacteristic
570C22×C4⋊C4C22×C3111yescharacteristic
571C22×C22⋊C4C22×C3111yescharacteristic
572C22×C22⋊C4C22×C3111yescharacteristic
573C22×C22⋊C4C22×C3111yescharacteristic
574C22×C22⋊C4C22×C3111yescharacteristic
575C22×C22⋊C4C22×C3111yescharacteristic
576C22×C22⋊C4C22×C3111yescharacteristic
577C22×C22⋊C4C22×C3111yescharacteristic
578C22×C22⋊C4C22×C3111yescharacteristic
579C22×C22⋊C4C22×C3111yescharacteristic
580C22×C22⋊C4C22×C3111yescharacteristic
581C22×C22⋊C4C22×C3111yescharacteristic
582C22×C22⋊C4C22×C3111yescharacteristic
583C22×C42C22×C3111yescharacteristic
584#397—24no—
585#397—24no—
586#394—24no—
587#390—24no—
588C2×#95C22×C3111yescharacteristic
589C2×#95C22×C3111yescharacteristic
590C2×#95C22×C3111yescharacteristic
591C2×#95C22×C3111yescharacteristic
592C2×#95C22×C3111yescharacteristic
593C2×#95C22×C3111yescharacteristic
594C2×#95C22×C3111yescharacteristic
595C2×#95C22×C3111yescharacteristic
596C2×#95C22×C3111yescharacteristic
597C2×#95C22×C3111yescharacteristic
598C2×#95C22×C3111yescharacteristic
599C2×#95C22×C3111yescharacteristic
600C2×#95C22×C3111yescharacteristic
601C2×#95C22×C3111yescharacteristic
602C2×#95C22×C3111yescharacteristic
603C2×#95C22×C3111yescharacteristic
604C2×C31—82no—
605C2×C31—82no—
606C2×C31#242211yescharacteristic
607C2×C31#244711yescharacteristic
608C2×C31#255411yescharacteristic
609C2×C31#262211yescharacteristic
610C2×C31#265111yescharacteristic
611C2×C31#266211yescharacteristic
612C2×C31#267111yescharacteristic
613C2×C31#267311yescharacteristic
614C2×C31#270811yescharacteristic
615C2×C31#271011yescharacteristic
616C2×C31#271711yescharacteristic
617C2×C31#272711yescharacteristic
618C2×C31#279711yescharacteristic
619C2×C31#280011yescharacteristic
620C2×C31#283011yescharacteristic
621C25C23×C3111yescharacteristic
622C25C23×C3111yescharacteristic
623C22×D4—22no—
624C22×D4—22no—
625C22×D4—41no—
626C22×D4—41no—
627C22×D4—41no—
628C22×D4—41no—
629C22×D4D4×C3114yes—
630C23×C4C23×C3111yescharacteristic
631C23×C4C23×C3111yescharacteristic
632C23×C4C23×C3111yescharacteristic
633C23×C4C23×C3111yescharacteristic
634C23×C4C23×C3111yescharacteristic
635C23×C4C23×C3111yescharacteristic
636C23×C4C23×C3111yescharacteristic
637C23×C4C23×C3111yescharacteristic
638C23×C4C23×C3111yescharacteristic
639C23×C4C23×C3111yescharacteristic
640C23×C4C23×C3111yescharacteristic
641C23×C4C23×C3111yescharacteristic
642C23×C4C23×C3111yescharacteristic
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C42—22no—
695C2×C42—41no—
696C2×C42—41no—
697#95—22no—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—22no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95D4×C3114yescomplemented
713C31#1652711yescharacteristic, direct product factor, Sylow
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—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24C2×D4×C3112yes—
743C24C2×D4×C3112yes—
744C24C24×C3111yescharacteristic
745C2×D4—28no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
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×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4C2×D4×C3112yes—
835C22×C4C2×D4×C3112yes—
836C22×C4C2×D4×C3112yes—
837C22×C4C2×D4×C3112yes—
838C22×C4#41×C3112yes—
839C22×C4#41×C3112yes—
840C22×C4#41×C3112yes—
841C22×C4#41×C3112yes—
842C22×C4#41×C3112yes—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C42—44no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
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—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23C22×D4×C3111yescharacteristic
932C23C22×D4×C3111yescharacteristic
933C23C2×#41×C3111yescharacteristic
934C23C2×#41×C3111yescharacteristic
935C23C2×#41×C3111yescharacteristic
936C23C2×#41×C3111yescharacteristic
937C23C2×#41×C3111yescharacteristic
938C23C31×H(5,𝔽2)11yescharacteristic
939C23C31×H(5,𝔽2)11yescharacteristic
940C23C31×H(5,𝔽2)11yescharacteristic
941C23C31×H(5,𝔽2)11yescharacteristic
942C23C31×H(5,𝔽2)11yescharacteristic
943C23C31×H(5,𝔽2)11yescharacteristic
944C23C31×2−1+411yescharacteristic
945C23C31×2−1+411yescharacteristic
946D4—416no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
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—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4C31×#12314yes—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—81no—
1068C22C2×C31×#12311yescharacteristic
1069C22C31×#52911yescharacteristic
1070C22C31×#53211yescharacteristic
1071C22C31×#53411yescharacteristic
1072C22C31×#53411yescharacteristic
1073C22C31×#53511yescharacteristic
1074C22C31×#53711yescharacteristic
1075C22C31×#53811yescharacteristic
1076C22C31×#53811yescharacteristic
1077C22C31×#53811yescharacteristic
1078C22C31×#53811yescharacteristic
1079C22C31×#53811yescharacteristic
1080C22C31×#53911yescharacteristic
1081C22C31×#54011yescharacteristic
1082C22C31×#54011yescharacteristic
1083C22C31×#54211yescharacteristic
1084C22C31×#54211yescharacteristic
1085C22C31×#54211yescharacteristic
1086C22C31×#54211yescharacteristic
1087C22D42×C3111yescharacteristic
1088C22C31×#54611yescharacteristic
1089C22C31×#54611yescharacteristic
1090C22C31×#54711yescharacteristic
1091C22C31×#54711yescharacteristic
1092C22C31×#54711yescharacteristic
1093C22C31×#55011yescharacteristic
1094C22C31×#55111yescharacteristic
1095C22C31×#55311yescharacteristic
1096C22C31×#55311yescharacteristic
1097C22C31×#55611yescharacteristic
1098C22C31×#55911yescharacteristic
1099C22C31×#56011yescharacteristic
1100C22C31×#56211yescharacteristic
1101C22C31×#56211yescharacteristic
1102C22C31×#56311yescharacteristic
1103C4—24no—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—81no—
1111C4—81no—
1112C4—81no—
1113C4—81no—
1114C4—81no—
1115C4—81no—
1116C2—82no—
1117C2—82no—
1118C2C31×#242211yescharacteristic
1119C2C31×#244711yescharacteristic
1120C2C31×#255411yescharacteristic
1121C2C31×#262211yescharacteristic
1122C2C31×#265111yescharacteristic
1123C2C31×#266211yescharacteristic
1124C2C31×#267111yescharacteristic
1125C2C31×#267311yescharacteristic
1126C2C31×#270811yescharacteristic
1127C2C31×#271011yescharacteristic
1128C2C31×#271711yescharacteristic
1129C2C31×#272711yescharacteristic
1130C2C31×#279711yescharacteristic
1131C2C31×#280011yescharacteristic
1132C2C31×#283011yescharacteristic
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
2. C2×C31×#397C2semidirect
5. C31×#1444C2semidirect
6. C31×#1441C2semidirect
7. C31×#1440C2semidirect
8. C31×#1440C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
11. C31×#1439C2semidirect
12. C31×#1439C2semidirect
14. C31×#1436C2semidirect
15. C31×#1436C2semidirect
146. C31×#95D4semidirect
294. #16527C31direct (N × H)
472. C2×#397C2×C31semidirect
473. C2×#397C2×C31semidirect
476. #1444C2×C31semidirect
477. #1441C2×C31semidirect
478. #1440C2×C31semidirect
479. #1440C2×C31semidirect
480. #1439C2×C31semidirect
481. #1439C2×C31semidirect
482. #1439C2×C31semidirect
483. #1439C2×C31semidirect
485. #1436C2×C31semidirect
486. #1436C2×C31semidirect
712. #95D4×C31semidirect
713. C31#16527direct (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
C2×C31×#3902
C31×#14442
C31×#14412
C31×#14402
C31×#14392
C31×#14382
C31×#14362
#1652731