Finite Group Databasebeta

← C31×#15321 #21472080

Subgroups — C31×#15321 #21472080

Order 7936.

1982 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#124C211yesmaximal, characteristic
2C2×C31×#396C211yesmaximal, characteristic, complemented
3C2×C31×#395C211yesmaximal, characteristic, complemented
4C2×C31×#394C211yesmaximal, characteristic
5C2×C31×#391C211yesmaximal, characteristic, complemented
6C2×C31×#388C211yesmaximal, characteristic, complemented
7C31×#1440C211yesmaximal, characteristic, complemented
8C31×#1439C211yesmaximal, characteristic, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1438C211yesmaximal, characteristic
13C31×#1437C211yesmaximal, characteristic, complemented
14C31×#1436C211yesmaximal, characteristic, complemented
15C31×#1436C211yesmaximal, characteristic, complemented
16C23×Q8×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C2×C31×#124—24no—
19C2×C31×#124—24no—
20C2×C31×#124—24no—
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×C22⋊C4×C31C2211yescharacteristic
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2211yescharacteristic
36C22×C22⋊C4×C31C2211yescharacteristic
37C22×C22⋊C4×C31C2211yescharacteristic
38C22×C42×C31C2211yescharacteristic
39C22×C42×C31C2211yescharacteristic
40C31×#396—24no—
41C31×#395—24no—
42C31×#394—24no—
43C31×#391—24no—
44C31×#388—24no—
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
58C2×C31×#95C2211yescharacteristic
59C25×C31C2311yescharacteristic
60C25×C31C2311yescharacteristic
61C22×Q8×C31—22no—
62C22×Q8×C31—22no—
63C22×Q8×C31—22no—
64C22×Q8×C31—22no—
65C22×Q8×C31—41no—
66C22×Q8×C31—41no—
67C22×Q8×C31D414yes—
68C22×D4×C31—22no—
69C22×D4×C31—22no—
70C22×D4×C31—22no—
71C22×D4×C31—22no—
72C22×D4×C31—22no—
73C22×D4×C31—41no—
74C22×D4×C31—41no—
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C23×C4×C31C2311yescharacteristic
83C23×C4×C31C2311yescharacteristic
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C23×C4×C31C2311yescharacteristic
88C31×#124—232no—
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—22no—
96C2×C4⋊C4×C31—22no—
97C2×C4⋊C4×C31—22no—
98C2×C4⋊C4×C31—22no—
99C2×C4⋊C4×C31—22no—
100C2×C4⋊C4×C31—41no—
101C2×C4⋊C4×C31—41no—
102C2×C4⋊C4×C31—41no—
103C2×C4⋊C4×C31—41no—
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—22no—
113C2×C22⋊C4×C31—22no—
114C2×C22⋊C4×C31—22no—
115C2×C22⋊C4×C31—22no—
116C2×C22⋊C4×C31—22no—
117C2×C22⋊C4×C31—22no—
118C2×C22⋊C4×C31—22no—
119C2×C22⋊C4×C31—22no—
120C2×C22⋊C4×C31—22no—
121C2×C22⋊C4×C31—22no—
122C2×C22⋊C4×C31—22no—
123C2×C22⋊C4×C31—22no—
124C2×C22⋊C4×C31—22no—
125C2×C22⋊C4×C31—22no—
126C2×C22⋊C4×C31—22no—
127C2×C22⋊C4×C31—22no—
128C2×C22⋊C4×C31—22no—
129C2×C22⋊C4×C31—22no—
130C2×C22⋊C4×C31—41no—
131C2×C22⋊C4×C31—41no—
132C2×C22⋊C4×C31—41no—
133C2×C22⋊C4×C31—41no—
134C2×C22⋊C4×C31—41no—
135C2×C22⋊C4×C31—41no—
136C2×C22⋊C4×C31—41no—
137C2×C22⋊C4×C31—41no—
138C2×C22⋊C4×C31D414yes—
139C2×C22⋊C4×C31D414yes—
140C2×C42×C31—22no—
141C2×C42×C31—22no—
142C2×C42×C31—22no—
143C2×C42×C31—22no—
144C2×C42×C31—22no—
145C2×C42×C31—41no—
146C31×#95—22no—
147C31×#95—22no—
148C31×#95—22no—
149C31×#95—22no—
150C31×#95—22no—
151C31×#95—22no—
152C31×#95—22no—
153C31×#95—22no—
154C31×#95—22no—
155C31×#95—22no—
156C31×#95—22no—
157C31×#95—22no—
158C31×#95—41no—
159C31×#95D414yes—
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×C31—21no—
176C24×C31—21no—
177C24×C31—21no—
178C24×C31—21no—
179C24×C31—21no—
180C24×C31—21no—
181C24×C31—21no—
182C24×C31—21no—
183C24×C31—21no—
184C24×C31—21no—
185C24×C31—21no—
186C24×C31—21no—
187C24×C31—21no—
188C24×C31C2×D412yes—
189C24×C31C2×D412yes—
190C24×C31C2411yescharacteristic
191C2×Q8×C31—28no—
192C2×Q8×C31—28no—
193C2×Q8×C31—44no—
194C2×Q8×C31—44no—
195C2×Q8×C31—44no—
196C2×Q8×C31—44no—
197C2×Q8×C31—44no—
198C2×D4×C31—28no—
199C2×D4×C31—44no—
200C2×D4×C31—44no—
201C2×D4×C31—44no—
202C2×D4×C31—44no—
203C2×D4×C31—44no—
204C2×D4×C31—44no—
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×C31—21no—
268C22×C4×C31—21no—
269C22×C4×C31—21no—
270C22×C4×C31—21no—
271C22×C4×C31—21no—
272C22×C4×C31—21no—
273C22×C4×C31—21no—
274C22×C4×C31—21no—
275C22×C4×C31—21no—
276C22×C4×C31—21no—
277C22×C4×C31—21no—
278C22×C4×C31—21no—
279C22×C4×C31—21no—
280C22×C4×C31—21no—
281C22×C4×C31C2×D412yes—
282C22×C4×C31C2×D412yes—
283C22×C4×C31C2×D412yes—
284C22×C4×C31C2×D412yes—
285C22×C4×C31C2×D412yes—
286C22×C4×C31C2×D412yes—
287C22×C4×C31C2×D412yes—
288C22×C4×C31C2×D412yes—
289C22×C4×C31C2×D412yes—
290C22×C4×C31C2×D412yes—
291C22×C4×C31#4112yes—
292C22×C4×C31#4112yes—
293C22×C4×C31#4112yes—
294C22×C4×C31#4112yes—
295C22×C4×C31#4112yes—
296C4⋊C4×C31—44no—
297C4⋊C4×C31—44no—
298C4⋊C4×C31—44no—
299C4⋊C4×C31—44no—
300C4⋊C4×C31—44no—
301C22⋊C4×C31—28no—
302C22⋊C4×C31—28no—
303C22⋊C4×C31—28no—
304C22⋊C4×C31—28no—
305C22⋊C4×C31—28no—
306C22⋊C4×C31—44no—
307C22⋊C4×C31—44no—
308C22⋊C4×C31—44no—
309C22⋊C4×C31—44no—
310C22⋊C4×C31—44no—
311C22⋊C4×C31—44no—
312C22⋊C4×C31—44no—
313C42×C31—28no—
314C42×C31—44no—
315#15321C3111yesmaximal, characteristic, direct product factor, Sylow
316C23×C31—22no—
317C23×C31—22no—
318C23×C31—22no—
319C23×C31—22no—
320C23×C31—22no—
321C23×C31—22no—
322C23×C31—22no—
323C23×C31—22no—
324C23×C31—22no—
325C23×C31—22no—
326C23×C31—22no—
327C23×C31—22no—
328C23×C31—22no—
329C23×C31—22no—
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×C31—41no—
366C23×C31—41no—
367C23×C31—41no—
368C23×C31—41no—
369C23×C31—41no—
370C23×C31—41no—
371C23×C31—41no—
372C23×C31—41no—
373C23×C31—41no—
374C23×C31—41no—
375C23×C31—41no—
376C23×C31—41no—
377C23×C31—41no—
378C23×C31—41no—
379C23×C31—41no—
380C23×C31—41no—
381C23×C31—41no—
382C23×C31—41no—
383C23×C31—41no—
384C23×C31—41no—
385C23×C31—41no—
386C23×C31C22×D411yescharacteristic
387C23×C31C22×D411yescharacteristic
388C23×C31C22×D411yescharacteristic
389C23×C31C22×D411yescharacteristic
390C23×C31C2×#4111yescharacteristic
391C23×C31C2×#4111yescharacteristic
392C23×C31C2×#4111yescharacteristic
393C23×C31C2×#4111yescharacteristic
394C23×C31C2×#4111yescharacteristic
395C23×C31H(5,𝔽2)11yescharacteristic
396C23×C31H(5,𝔽2)11yescharacteristic
397C23×C31H(5,𝔽2)11yescharacteristic
398C23×C312−1+411yescharacteristic
399C23×C312−1+411yescharacteristic
400C23×C312−1+411yescharacteristic
401Q8×C31—416no—
402D4×C31—416no—
403C2×C4×C31—22no—
404C2×C4×C31—22no—
405C2×C4×C31—22no—
406C2×C4×C31—22no—
407C2×C4×C31—22no—
408C2×C4×C31—22no—
409C2×C4×C31—22no—
410C2×C4×C31—22no—
411C2×C4×C31—22no—
412C2×C4×C31—22no—
413C2×C4×C31—22no—
414C2×C4×C31—22no—
415C2×C4×C31—22no—
416C2×C4×C31—22no—
417C2×C4×C31—22no—
418C2×C4×C31—22no—
419C2×C4×C31—22no—
420C2×C4×C31—22no—
421C2×C4×C31—22no—
422C2×C4×C31—22no—
423C2×C4×C31—22no—
424C2×C4×C31—22no—
425C2×C4×C31—22no—
426C2×C4×C31—22no—
427C2×C4×C31—22no—
428C2×C4×C31—22no—
429C2×C4×C31—22no—
430C2×C4×C31—22no—
431C2×C4×C31—22no—
432C2×C4×C31—22no—
433C2×C4×C31—22no—
434C2×C4×C31—22no—
435C2×C4×C31—22no—
436C2×C4×C31—22no—
437C2×C4×C31—22no—
438C2×C4×C31—22no—
439C2×C4×C31—22no—
440C2×C4×C31—22no—
441C2×C4×C31—22no—
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—41no—
472C2×C4×C31—41no—
473C2×C4×C31—41no—
474C2×C4×C31—41no—
475C2×C4×C31—41no—
476C2×C4×C31—41no—
477C2×C4×C31—41no—
478C2×C4×C31—41no—
479C2×C4×C31—41no—
480C2×C4×C31—41no—
481C2×C4×C31—41no—
482C2×C4×C31—41no—
483C2×C4×C31—41no—
484C2×C4×C31—41no—
485C2×C4×C31—41no—
486C2×C4×C31—41no—
487C2×C4×C31—41no—
488C2×C4×C31—41no—
489C2×C4×C31—41no—
490C2×C4×C31—41no—
491C2×C4×C31—41no—
492C2×C4×C31#12014yes—
493C2×C4×C31#12114yes—
494C22×#124C2×C3111yescharacteristic
495C2×#396C2×C3111yescharacteristic, complemented
496C2×#395C2×C3111yescharacteristic, complemented
497C2×#394C2×C3111yescharacteristic
498C2×#391C2×C3111yescharacteristic, complemented
499C2×#388C2×C3111yescharacteristic, complemented
500#1440C2×C3111yescharacteristic, complemented
501#1439C2×C3111yescharacteristic, complemented
502#1439C2×C3111yescharacteristic, complemented
503#1439C2×C3111yescharacteristic, complemented
504#1439C2×C3111yescharacteristic, complemented
505#1438C2×C3111yescharacteristic
506#1437C2×C3111yescharacteristic, complemented
507#1436C2×C3111yescharacteristic, complemented
508#1436C2×C3111yescharacteristic, complemented
509C22×C31—42no—
510C22×C31—42no—
511C22×C31—42no—
512C22×C31—42no—
513C22×C31—42no—
514C22×C31—42no—
515C22×C31—42no—
516C22×C31—42no—
517C22×C31—42no—
518C22×C31—42no—
519C22×C31—42no—
520C22×C31—42no—
521C22×C31—42no—
522C22×C31—42no—
523C22×C31—81no—
524C22×C31—81no—
525C22×C31—81no—
526C22×C31—81no—
527C22×C31—81no—
528C22×C31—81no—
529C22×C31—81no—
530C22×C31—81no—
531C22×C31—81no—
532C22×C31—81no—
533C22×C31—81no—
534C22×C31—81no—
535C22×C31—81no—
536C22×C31—81no—
537C22×C31—81no—
538C22×C31—81no—
539C22×C31C2×#12011yescharacteristic
540C22×C31C2×#12111yescharacteristic
541C22×C31#52511yescharacteristic
542C22×C31#52911yescharacteristic
543C22×C31#53211yescharacteristic
544C22×C31#53211yescharacteristic
545C22×C31#53411yescharacteristic
546C22×C31#53611yescharacteristic
547C22×C31#53611yescharacteristic
548C22×C31#53711yescharacteristic
549C22×C31#53811yescharacteristic
550C22×C31#54211yescharacteristic
551C22×C31#54211yescharacteristic
552C22×C31#54211yescharacteristic
553C22×C31#54211yescharacteristic
554C22×C31D4211yescharacteristic
555C22×C31D4211yescharacteristic
556C22×C31#54611yescharacteristic
557C22×C31#54611yescharacteristic
558C22×C31#54611yescharacteristic
559C22×C31#54611yescharacteristic
560C22×C31#54711yescharacteristic
561C22×C31#54711yescharacteristic
562C22×C31#54711yescharacteristic
563C22×C31#54811yescharacteristic
564C22×C31#54811yescharacteristic
565C22×C31#54811yescharacteristic
566C22×C31#54811yescharacteristic
567C22×C31#55011yescharacteristic
568C22×C31#55111yescharacteristic
569C22×C31#55511yescharacteristic
570C22×C31#55611yescharacteristic
571C22×C31#55611yescharacteristic
572C22×C31#56211yescharacteristic
573C22×C31#56311yescharacteristic
574C4×C31—24no—
575C4×C31—24no—
576C4×C31—42no—
577C4×C31—42no—
578C4×C31—42no—
579C4×C31—42no—
580C4×C31—42no—
581C4×C31—42no—
582C4×C31—42no—
583C4×C31—42no—
584C4×C31—42no—
585C4×C31—81no—
586C4×C31—81no—
587C23×Q8C22×C3111yescharacteristic
588C23×D4C22×C3111yescharacteristic
589C2×#124—24no—
590C2×#124—24no—
591C2×#124—24no—
592C22×C4⋊C4C22×C3111yescharacteristic
593C22×C4⋊C4C22×C3111yescharacteristic
594C22×C4⋊C4C22×C3111yescharacteristic
595C22×C4⋊C4C22×C3111yescharacteristic
596C22×C4⋊C4C22×C3111yescharacteristic
597C22×C22⋊C4C22×C3111yescharacteristic
598C22×C22⋊C4C22×C3111yescharacteristic
599C22×C22⋊C4C22×C3111yescharacteristic
600C22×C22⋊C4C22×C3111yescharacteristic
601C22×C22⋊C4C22×C3111yescharacteristic
602C22×C22⋊C4C22×C3111yescharacteristic
603C22×C22⋊C4C22×C3111yescharacteristic
604C22×C22⋊C4C22×C3111yescharacteristic
605C22×C22⋊C4C22×C3111yescharacteristic
606C22×C22⋊C4C22×C3111yescharacteristic
607C22×C22⋊C4C22×C3111yescharacteristic
608C22×C22⋊C4C22×C3111yescharacteristic
609C22×C42C22×C3111yescharacteristic
610C22×C42C22×C3111yescharacteristic
611#396—24no—
612#395—24no—
613#394—24no—
614#391—24no—
615#388—24no—
616C2×#95C22×C3111yescharacteristic
617C2×#95C22×C3111yescharacteristic
618C2×#95C22×C3111yescharacteristic
619C2×#95C22×C3111yescharacteristic
620C2×#95C22×C3111yescharacteristic
621C2×#95C22×C3111yescharacteristic
622C2×#95C22×C3111yescharacteristic
623C2×#95C22×C3111yescharacteristic
624C2×#95C22×C3111yescharacteristic
625C2×#95C22×C3111yescharacteristic
626C2×#95C22×C3111yescharacteristic
627C2×#95C22×C3111yescharacteristic
628C2×#95C22×C3111yescharacteristic
629C2×#95C22×C3111yescharacteristic
630C2×C31—82no—
631C2×C31—82no—
632C2×C31#240711yescharacteristic
633C2×C31#241011yescharacteristic
634C2×C31#242611yescharacteristic
635C2×C31#243211yescharacteristic
636C2×C31#246111yescharacteristic
637C2×C31#247411yescharacteristic
638C2×C31#252111yescharacteristic
639C2×C31#254511yescharacteristic
640C2×C31#255511yescharacteristic
641C2×C31#267211yescharacteristic
642C2×C31#267411yescharacteristic
643C2×C31#270011yescharacteristic
644C2×C31#271511yescharacteristic
645C2×C31#273011yescharacteristic
646C2×C31#273111yescharacteristic
647C25C23×C3111yescharacteristic
648C25C23×C3111yescharacteristic
649C22×Q8—22no—
650C22×Q8—22no—
651C22×Q8—22no—
652C22×Q8—22no—
653C22×Q8—41no—
654C22×Q8—41no—
655C22×Q8D4×C3114yes—
656C22×D4—22no—
657C22×D4—22no—
658C22×D4—22no—
659C22×D4—22no—
660C22×D4—22no—
661C22×D4—41no—
662C22×D4—41no—
663C23×C4C23×C3111yescharacteristic
664C23×C4C23×C3111yescharacteristic
665C23×C4C23×C3111yescharacteristic
666C23×C4C23×C3111yescharacteristic
667C23×C4C23×C3111yescharacteristic
668C23×C4C23×C3111yescharacteristic
669C23×C4C23×C3111yescharacteristic
670C23×C4C23×C3111yescharacteristic
671C23×C4C23×C3111yescharacteristic
672C23×C4C23×C3111yescharacteristic
673C23×C4C23×C3111yescharacteristic
674C23×C4C23×C3111yescharacteristic
675C23×C4C23×C3111yescharacteristic
676#124—232no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—22no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—41no—
689C2×C4⋊C4—41no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—41no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—41no—
720C2×C22⋊C4—41no—
721C2×C22⋊C4—41no—
722C2×C22⋊C4—41no—
723C2×C22⋊C4—41no—
724C2×C22⋊C4—41no—
725C2×C22⋊C4—41no—
726C2×C22⋊C4D4×C3114yes—
727C2×C22⋊C4D4×C3114yes—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—41no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—22no—
746#95—41no—
747#95D4×C3114yes—
748C31#1532111yescharacteristic, direct product factor, Sylow
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24C2×D4×C3112yes—
778C24C2×D4×C3112yes—
779C24C24×C3111yescharacteristic
780C2×Q8—28no—
781C2×Q8—28no—
782C2×Q8—44no—
783C2×Q8—44no—
784C2×Q8—44no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×D4—28no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
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×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4C2×D4×C3112yes—
871C22×C4C2×D4×C3112yes—
872C22×C4C2×D4×C3112yes—
873C22×C4C2×D4×C3112yes—
874C22×C4C2×D4×C3112yes—
875C22×C4C2×D4×C3112yes—
876C22×C4C2×D4×C3112yes—
877C22×C4C2×D4×C3112yes—
878C22×C4C2×D4×C3112yes—
879C22×C4C2×D4×C3112yes—
880C22×C4#41×C3112yes—
881C22×C4#41×C3112yes—
882C22×C4#41×C3112yes—
883C22×C4#41×C3112yes—
884C22×C4#41×C3112yes—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C42—28no—
903C42—44no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
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—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23C22×D4×C3111yescharacteristic
975C23C22×D4×C3111yescharacteristic
976C23C22×D4×C3111yescharacteristic
977C23C22×D4×C3111yescharacteristic
978C23C2×#41×C3111yescharacteristic
979C23C2×#41×C3111yescharacteristic
980C23C2×#41×C3111yescharacteristic
981C23C2×#41×C3111yescharacteristic
982C23C2×#41×C3111yescharacteristic
983C23C31×H(5,𝔽2)11yescharacteristic
984C23C31×H(5,𝔽2)11yescharacteristic
985C23C31×H(5,𝔽2)11yescharacteristic
986C23C31×2−1+411yescharacteristic
987C23C31×2−1+411yescharacteristic
988C23C31×2−1+411yescharacteristic
989Q8—416no—
990D4—416no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4C31×#12014yes—
1081C2×C4C31×#12114yes—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—81no—
1097C22—81no—
1098C22—81no—
1099C22—81no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22C2×C31×#12011yescharacteristic
1113C22C2×C31×#12111yescharacteristic
1114C22C31×#52511yescharacteristic
1115C22C31×#52911yescharacteristic
1116C22C31×#53211yescharacteristic
1117C22C31×#53211yescharacteristic
1118C22C31×#53411yescharacteristic
1119C22C31×#53611yescharacteristic
1120C22C31×#53611yescharacteristic
1121C22C31×#53711yescharacteristic
1122C22C31×#53811yescharacteristic
1123C22C31×#54211yescharacteristic
1124C22C31×#54211yescharacteristic
1125C22C31×#54211yescharacteristic
1126C22C31×#54211yescharacteristic
1127C22D42×C3111yescharacteristic
1128C22D42×C3111yescharacteristic
1129C22C31×#54611yescharacteristic
1130C22C31×#54611yescharacteristic
1131C22C31×#54611yescharacteristic
1132C22C31×#54611yescharacteristic
1133C22C31×#54711yescharacteristic
1134C22C31×#54711yescharacteristic
1135C22C31×#54711yescharacteristic
1136C22C31×#54811yescharacteristic
1137C22C31×#54811yescharacteristic
1138C22C31×#54811yescharacteristic
1139C22C31×#54811yescharacteristic
1140C22C31×#55011yescharacteristic
1141C22C31×#55111yescharacteristic
1142C22C31×#55511yescharacteristic
1143C22C31×#55611yescharacteristic
1144C22C31×#55611yescharacteristic
1145C22C31×#56211yescharacteristic
1146C22C31×#56311yescharacteristic
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—81no—
1159C4—81no—
1160C2—82no—
1161C2—82no—
1162C2C31×#240711yescharacteristic
1163C2C31×#241011yescharacteristic
1164C2C31×#242611yescharacteristic
1165C2C31×#243211yescharacteristic
1166C2C31×#246111yescharacteristic
1167C2C31×#247411yescharacteristic
1168C2C31×#252111yescharacteristic
1169C2C31×#254511yescharacteristic
1170C2C31×#255511yescharacteristic
1171C2C31×#267211yescharacteristic
1172C2C31×#267411yescharacteristic
1173C2C31×#270011yescharacteristic
1174C2C31×#271511yescharacteristic
1175C2C31×#273011yescharacteristic
1176C2C31×#273111yescharacteristic
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
2. C2×C31×#396C2semidirect
3. C2×C31×#395C2semidirect
5. C2×C31×#391C2semidirect
6. C2×C31×#388C2semidirect
7. C31×#1440C2semidirect
8. C31×#1439C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
11. C31×#1439C2semidirect
13. C31×#1437C2semidirect
14. C31×#1436C2semidirect
15. C31×#1436C2semidirect
315. #15321C31direct (N × H)
495. C2×#396C2×C31semidirect
496. C2×#395C2×C31semidirect
498. C2×#391C2×C31semidirect
499. C2×#388C2×C31semidirect
500. #1440C2×C31semidirect
501. #1439C2×C31semidirect
502. #1439C2×C31semidirect
503. #1439C2×C31semidirect
504. #1439C2×C31semidirect
506. #1437C2×C31semidirect
507. #1436C2×C31semidirect
508. #1436C2×C31semidirect
748. C31#15321direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1242
C2×C31×#3962
C2×C31×#3952
C2×C31×#3942
C2×C31×#3912
C2×C31×#3882
C31×#14402
C31×#14392
C31×#14382
C31×#14372
C31×#14362
#1532131