Finite Group Databasebeta

← C31×#14072 #21470831

Subgroups — C31×#14072 #21470831

Order 7936.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#117C211yesmaximal, characteristic
2C2×C31×#389C211yesmaximal, characteristic, complemented
3C2×C31×#388C211yesmaximal, characteristic
4C2×C31×#387C211yesmaximal, characteristic, complemented
5C2×C31×#385C211yesmaximal, characteristic
6C31×#1442C211yesmaximal, characteristic, complemented
7C31×#1441C211yesmaximal, characteristic, complemented
8C31×#1440C211yesmaximal, characteristic
9C31×#1439C211yesmaximal, characteristic
10C31×#1437C211yesmaximal, characteristic
11C31×#1436C211yesmaximal, characteristic, complemented
12C31×#1436C211yesmaximal, characteristic, complemented
13C31×#1436C211yesmaximal, characteristic, complemented
14C31×C22⋊#95C211yesmaximal, characteristic
15C4×C31×#95C211yesmaximal, characteristic, complemented
16C24×C4×C31C2211yescharacteristic
17C2×C31×#117—24no—
18C2×C31×#117—24no—
19C2×C31×#117—24no—
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C4⋊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×C42×C31C2211yescharacteristic
33C22×C42×C31C2211yescharacteristic
34C22×C42×C31C2211yescharacteristic
35C22×C42×C31C2211yescharacteristic
36C31×#389—24no—
37C31×#388—24no—
38C31×#387—24no—
39C31×#385C418yescomplemented
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
55C2×C31×#95C2211yescharacteristic
56C2×C31×#95C2211yescharacteristic
57C2×C31×#95C2211yescharacteristic
58C25×C31C2311yescharacteristic
59C23×C4×C31—22no—
60C23×C4×C31—22no—
61C23×C4×C31—22no—
62C23×C4×C31—22no—
63C23×C4×C31—22no—
64C23×C4×C31—22no—
65C23×C4×C31C2×C414yes—
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
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C31×#117—232no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31—22no—
85C2×C4⋊C4×C31—22no—
86C2×C4⋊C4×C31—22no—
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—22no—
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31—22no—
93C2×C4⋊C4×C31—22no—
94C2×C4⋊C4×C31—22no—
95C2×C4⋊C4×C31—41no—
96C2×C4⋊C4×C31C2×C414yes—
97C2×C4⋊C4×C31C2×C414yes—
98C2×C4⋊C4×C31D414yes—
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×C31C2×C414yes—
115C2×C22⋊C4×C31C2×C414yes—
116C2×C22⋊C4×C31D414yes—
117C2×C42×C31—22no—
118C2×C42×C31—22no—
119C2×C42×C31—22no—
120C2×C42×C31—22no—
121C2×C42×C31—22no—
122C2×C42×C31—22no—
123C2×C42×C31—22no—
124C2×C42×C31—22no—
125C2×C42×C31—22no—
126C2×C42×C31—41no—
127C2×C42×C31—41no—
128C2×C42×C31D414yes—
129C31×#95—22no—
130C31×#95—22no—
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—22no—
141C31×#95—22no—
142C31×#95—22no—
143C31×#95—22no—
144C31×#95—41no—
145C31×#95C2×C414yes—
146C31×#95C2×C414yes—
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×C31C22×C412yes—
160C24×C31C2×D412yes—
161C24×C31#4112yes—
162C24×C31C2411yescharacteristic
163C22×C4×C31—28no—
164C22×C4×C31—28no—
165C22×C4×C31—28no—
166C22×C4×C31—28no—
167C22×C4×C31—28no—
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—28no—
185C22×C4×C31—28no—
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×C31C22×C412yes—
249C22×C4×C31C22×C412yes—
250C22×C4×C31C22×C412yes—
251C22×C4×C31C22×C412yes—
252C22×C4×C31C22×C412yes—
253C22×C4×C31C22×C412yes—
254C22×C4×C31C2×D412yes—
255C22×C4×C31C2×D412yes—
256C22×C4×C31C2×D412yes—
257C22×C4×C31C2×D412yes—
258C22×C4×C31C2×D412yes—
259C22×C4×C31C2×D412yes—
260C22×C4×C31C2×D412yes—
261C22×C4×C31C2×D412yes—
262C22×C4×C31#4112yes—
263C22×C4×C31#4112yes—
264C22×C4×C31#4112yes—
265C22×C4×C31#4112yes—
266C22×C4×C31#4112yes—
267C22×C4×C31#4112yes—
268C4⋊C4×C31—28no—
269C4⋊C4×C31—28no—
270C4⋊C4×C31—28no—
271C4⋊C4×C31—28no—
272C4⋊C4×C31—44no—
273C4⋊C4×C31—44no—
274C22⋊C4×C31—28no—
275C22⋊C4×C31—28no—
276C22⋊C4×C31—28no—
277C22⋊C4×C31—28no—
278C22⋊C4×C31—44no—
279C22⋊C4×C31—44no—
280C42×C31—28no—
281C42×C31—28no—
282C42×C31—44no—
283C42×C31—44no—
284#14072C3111yesmaximal, characteristic, direct product factor, Sylow
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—22no—
294C23×C31—22no—
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—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×C31C4×D414yes—
320C23×C31C23×C411yescharacteristic
321C23×C31C22×D411yescharacteristic
322C23×C31C22×D411yescharacteristic
323C23×C31C22×D411yescharacteristic
324C23×C31C2×#4111yescharacteristic
325C23×C31C2×#4111yescharacteristic
326C23×C31C2×#4111yescharacteristic
327C23×C31C2×#4111yescharacteristic
328C23×C31C2×#4111yescharacteristic
329C23×C31C2×#4111yescharacteristic
330C23×C31C2×#4111yescharacteristic
331C23×C31H(5,𝔽2)11yescharacteristic
332C23×C312−1+411yescharacteristic
333C23×C312−1+411yescharacteristic
334C23×C312−1+411yescharacteristic
335C2×C4×C31—232no—
336C2×C4×C31—22no—
337C2×C4×C31—22no—
338C2×C4×C31—22no—
339C2×C4×C31—22no—
340C2×C4×C31—22no—
341C2×C4×C31—22no—
342C2×C4×C31—22no—
343C2×C4×C31—22no—
344C2×C4×C31—22no—
345C2×C4×C31—22no—
346C2×C4×C31—22no—
347C2×C4×C31—22no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—22no—
357C2×C4×C31—22no—
358C2×C4×C31—22no—
359C2×C4×C31—22no—
360C2×C4×C31—22no—
361C2×C4×C31—22no—
362C2×C4×C31—22no—
363C2×C4×C31—22no—
364C2×C4×C31—22no—
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—22no—
381C2×C4×C31—22no—
382C2×C4×C31—22no—
383C2×C4×C31—22no—
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#11714yescomplemented
431C2×C4×C31C4×D414yes—
432C2×C4×C31C4×D414yes—
433C2×C4×C31#12014yes—
434C22×#117C2×C3111yescharacteristic
435C2×#389C2×C3111yescharacteristic, complemented
436C2×#388C2×C3111yescharacteristic
437C2×#387C2×C3111yescharacteristic, complemented
438C2×#385C2×C3111yescharacteristic
439#1442C2×C3111yescharacteristic, complemented
440#1441C2×C3111yescharacteristic, complemented
441#1440C2×C3111yescharacteristic
442#1439C2×C3111yescharacteristic
443#1437C2×C3111yescharacteristic
444#1436C2×C3111yescharacteristic, complemented
445#1436C2×C3111yescharacteristic, complemented
446#1436C2×C3111yescharacteristic, complemented
447C22⋊#95C2×C3111yescharacteristic
448C4×#95C2×C3111yescharacteristic, complemented
449C22×C31—24no—
450C22×C31—24no—
451C22×C31—24no—
452C22×C31—42no—
453C22×C31—42no—
454C22×C31—42no—
455C22×C31—42no—
456C22×C31—42no—
457C22×C31—42no—
458C22×C31—42no—
459C22×C31—42no—
460C22×C31—42no—
461C22×C31—42no—
462C22×C31—42no—
463C22×C31—42no—
464C22×C31C2×#11711yescharacteristic
465C22×C31C2×C4×D411yescharacteristic
466C22×C31C2×C4×D411yescharacteristic
467C22×C31C2×C4×D411yescharacteristic
468C22×C31C4×#4111yescharacteristic
469C22×C31#51911yescharacteristic
470C22×C31#52011yescharacteristic
471C22×C31C2×#12011yescharacteristic
472C22×C31#52511yescharacteristic
473C22×C31#52511yescharacteristic
474C22×C31#52511yescharacteristic
475C22×C31#52911yescharacteristic
476C22×C31#52911yescharacteristic
477C22×C31#53211yescharacteristic
478C22×C31#53211yescharacteristic
479C22×C31#53611yescharacteristic
480C22×C31#53711yescharacteristic
481C22×C31#54111yescharacteristic
482C22×C31#54211yescharacteristic
483C22×C31#54611yescharacteristic
484C22×C31#54611yescharacteristic
485C22×C31#54711yescharacteristic
486C22×C31#54711yescharacteristic
487C22×C31#54711yescharacteristic
488C22×C31#54711yescharacteristic
489C22×C31#54811yescharacteristic
490C22×C31#54811yescharacteristic
491C22×C31#55111yescharacteristic
492C22×C31#55211yescharacteristic
493C22×C31#55211yescharacteristic
494C22×C31#55211yescharacteristic
495C22×C31#55211yescharacteristic
496C22×C31#55211yescharacteristic
497C22×C31#55311yescharacteristic
498C22×C31#55611yescharacteristic
499C4×C31—24no—
500C4×C31—24no—
501C4×C31—24no—
502C4×C31—24no—
503C4×C31—42no—
504C4×C31—42no—
505C4×C31—42no—
506C4×C31—42no—
507C4×C31—42no—
508C4×C31—42no—
509C4×C31—42no—
510C4×C31—42no—
511C4×C31—81no—
512C4×C31—81no—
513C24×C4C22×C3111yescharacteristic
514C2×#117—24no—
515C2×#117—24no—
516C2×#117—24no—
517C22×C4⋊C4C22×C3111yescharacteristic
518C22×C4⋊C4C22×C3111yescharacteristic
519C22×C4⋊C4C22×C3111yescharacteristic
520C22×C4⋊C4C22×C3111yescharacteristic
521C22×C4⋊C4C22×C3111yescharacteristic
522C22×C4⋊C4C22×C3111yescharacteristic
523C22×C22⋊C4C22×C3111yescharacteristic
524C22×C22⋊C4C22×C3111yescharacteristic
525C22×C22⋊C4C22×C3111yescharacteristic
526C22×C22⋊C4C22×C3111yescharacteristic
527C22×C22⋊C4C22×C3111yescharacteristic
528C22×C22⋊C4C22×C3111yescharacteristic
529C22×C42C22×C3111yescharacteristic
530C22×C42C22×C3111yescharacteristic
531C22×C42C22×C3111yescharacteristic
532C22×C42C22×C3111yescharacteristic
533#389—24no—
534#388—24no—
535#387—24no—
536#385C4×C3118yescomplemented
537C2×#95C22×C3111yescharacteristic
538C2×#95C22×C3111yescharacteristic
539C2×#95C22×C3111yescharacteristic
540C2×#95C22×C3111yescharacteristic
541C2×#95C22×C3111yescharacteristic
542C2×#95C22×C3111yescharacteristic
543C2×#95C22×C3111yescharacteristic
544C2×#95C22×C3111yescharacteristic
545C2×#95C22×C3111yescharacteristic
546C2×#95C22×C3111yescharacteristic
547C2×#95C22×C3111yescharacteristic
548C2×#95C22×C3111yescharacteristic
549C2×#95C22×C3111yescharacteristic
550C2×#95C22×C3111yescharacteristic
551C2×#95C22×C3111yescharacteristic
552C2×#95C22×C3111yescharacteristic
553C2×#95C22×C3111yescharacteristic
554C2×#95C22×C3111yescharacteristic
555C2×C31—44no—
556C2×C31#229311yescharacteristic
557C2×C31C4×#12011yescharacteristic
558C2×C31#232311yescharacteristic
559C2×C31#234411yescharacteristic
560C2×C31#235211yescharacteristic
561C2×C31#235911yescharacteristic
562C2×C31#236211yescharacteristic
563C2×C31#243011yescharacteristic
564C2×C31#243211yescharacteristic
565C2×C31#247011yescharacteristic
566C2×C31#247511yescharacteristic
567C2×C31#247711yescharacteristic
568C2×C31#247811yescharacteristic
569C2×C31#260111yescharacteristic
570C2×C31#261111yescharacteristic
571C25C23×C3111yescharacteristic
572C23×C4—22no—
573C23×C4—22no—
574C23×C4—22no—
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4C2×C4×C3114yes—
579C23×C4C23×C3111yescharacteristic
580C23×C4C23×C3111yescharacteristic
581C23×C4C23×C3111yescharacteristic
582C23×C4C23×C3111yescharacteristic
583C23×C4C23×C3111yescharacteristic
584C23×C4C23×C3111yescharacteristic
585C23×C4C23×C3111yescharacteristic
586C23×C4C23×C3111yescharacteristic
587C23×C4C23×C3111yescharacteristic
588C23×C4C23×C3111yescharacteristic
589C23×C4C23×C3111yescharacteristic
590C23×C4C23×C3111yescharacteristic
591C23×C4C23×C3111yescharacteristic
592C23×C4C23×C3111yescharacteristic
593#117—232no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4C2×C4×C3114yes—
610C2×C4⋊C4C2×C4×C3114yes—
611C2×C4⋊C4D4×C3114yes—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—22no—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4—41no—
627C2×C22⋊C4C2×C4×C3114yes—
628C2×C22⋊C4C2×C4×C3114yes—
629C2×C22⋊C4D4×C3114yes—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—22no—
635C2×C42—22no—
636C2×C42—22no—
637C2×C42—22no—
638C2×C42—22no—
639C2×C42—41no—
640C2×C42—41no—
641C2×C42D4×C3114yes—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—22no—
652#95—22no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—41no—
658#95C2×C4×C3114yes—
659#95C2×C4×C3114yes—
660C31#1407211yescharacteristic, direct product factor, Sylow
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24C22×C4×C3112yes—
674C24C2×D4×C3112yes—
675C24#41×C3112yes—
676C24C24×C3111yescharacteristic
677C22×C4—28no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—28no—
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—28no—
699C22×C4—28no—
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—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
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×C4C22×C4×C3112yes—
763C22×C4C22×C4×C3112yes—
764C22×C4C22×C4×C3112yes—
765C22×C4C22×C4×C3112yes—
766C22×C4C22×C4×C3112yes—
767C22×C4C22×C4×C3112yes—
768C22×C4C2×D4×C3112yes—
769C22×C4C2×D4×C3112yes—
770C22×C4C2×D4×C3112yes—
771C22×C4C2×D4×C3112yes—
772C22×C4C2×D4×C3112yes—
773C22×C4C2×D4×C3112yes—
774C22×C4C2×D4×C3112yes—
775C22×C4C2×D4×C3112yes—
776C22×C4#41×C3112yes—
777C22×C4#41×C3112yes—
778C22×C4#41×C3112yes—
779C22×C4#41×C3112yes—
780C22×C4#41×C3112yes—
781C22×C4#41×C3112yes—
782C4⋊C4—28no—
783C4⋊C4—28no—
784C4⋊C4—28no—
785C4⋊C4—28no—
786C4⋊C4—44no—
787C4⋊C4—44no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—28no—
792C22⋊C4—44no—
793C22⋊C4—44no—
794C42—28no—
795C42—28no—
796C42—44no—
797C42—44no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23C4×D4×C3114yes—
833C23C23×C4×C3111yescharacteristic
834C23C22×D4×C3111yescharacteristic
835C23C22×D4×C3111yescharacteristic
836C23C22×D4×C3111yescharacteristic
837C23C2×#41×C3111yescharacteristic
838C23C2×#41×C3111yescharacteristic
839C23C2×#41×C3111yescharacteristic
840C23C2×#41×C3111yescharacteristic
841C23C2×#41×C3111yescharacteristic
842C23C2×#41×C3111yescharacteristic
843C23C2×#41×C3111yescharacteristic
844C23C31×H(5,𝔽2)11yescharacteristic
845C23C31×2−1+411yescharacteristic
846C23C31×2−1+411yescharacteristic
847C23C31×2−1+411yescharacteristic
848C2×C4—232no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
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×C4C31×#11714yescomplemented
944C2×C4C4×D4×C3114yes—
945C2×C4C4×D4×C3114yes—
946C2×C4C31×#12014yes—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22C2×C31×#11711yescharacteristic
963C22C2×C4×D4×C3111yescharacteristic
964C22C2×C4×D4×C3111yescharacteristic
965C22C2×C4×D4×C3111yescharacteristic
966C22C4×#41×C3111yescharacteristic
967C22C31×#51911yescharacteristic
968C22C31×#52011yescharacteristic
969C22C2×C31×#12011yescharacteristic
970C22C31×#52511yescharacteristic
971C22C31×#52511yescharacteristic
972C22C31×#52511yescharacteristic
973C22C31×#52911yescharacteristic
974C22C31×#52911yescharacteristic
975C22C31×#53211yescharacteristic
976C22C31×#53211yescharacteristic
977C22C31×#53611yescharacteristic
978C22C31×#53711yescharacteristic
979C22C31×#54111yescharacteristic
980C22C31×#54211yescharacteristic
981C22C31×#54611yescharacteristic
982C22C31×#54611yescharacteristic
983C22C31×#54711yescharacteristic
984C22C31×#54711yescharacteristic
985C22C31×#54711yescharacteristic
986C22C31×#54711yescharacteristic
987C22C31×#54811yescharacteristic
988C22C31×#54811yescharacteristic
989C22C31×#55111yescharacteristic
990C22C31×#55211yescharacteristic
991C22C31×#55211yescharacteristic
992C22C31×#55211yescharacteristic
993C22C31×#55211yescharacteristic
994C22C31×#55211yescharacteristic
995C22C31×#55311yescharacteristic
996C22C31×#55611yescharacteristic
997C4—24no—
998C4—24no—
999C4—24no—
1000C4—24no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—42no—
1009C4—81no—
1010C4—81no—
1011C2—44no—
1012C2C31×#229311yescharacteristic
1013C2C4×C31×#12011yescharacteristic
1014C2C31×#232311yescharacteristic
1015C2C31×#234411yescharacteristic
1016C2C31×#235211yescharacteristic
1017C2C31×#235911yescharacteristic
1018C2C31×#236211yescharacteristic
1019C2C31×#243011yescharacteristic
1020C2C31×#243211yescharacteristic
1021C2C31×#247011yescharacteristic
1022C2C31×#247511yescharacteristic
1023C2C31×#247711yescharacteristic
1024C2C31×#247811yescharacteristic
1025C2C31×#260111yescharacteristic
1026C2C31×#261111yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#389C2semidirect
4. C2×C31×#387C2semidirect
6. C31×#1442C2semidirect
7. C31×#1441C2semidirect
11. C31×#1436C2semidirect
12. C31×#1436C2semidirect
13. C31×#1436C2semidirect
15. C4×C31×#95C2semidirect
39. C31×#385C4semidirect
284. #14072C31direct (N × H)
430. C2×C4×C31#117semidirect
435. C2×#389C2×C31semidirect
437. C2×#387C2×C31semidirect
439. #1442C2×C31semidirect
440. #1441C2×C31semidirect
444. #1436C2×C31semidirect
445. #1436C2×C31semidirect
446. #1436C2×C31semidirect
448. C4×#95C2×C31semidirect
536. #385C4×C31semidirect
660. C31#14072direct (N × H)
943. C2×C4C31×#117semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1172
C2×C31×#3892
C2×C31×#3882
C2×C31×#3872
C2×C31×#3852
C31×#14422
C31×#14412
C31×#14402
C31×#14392
C31×#14372
C31×#14362
C31×C22⋊#952
C4×C31×#952
#1407231