Finite Group Databasebeta

← C31×#15508 #21472267

Subgroups — C31×#15508 #21472267

Order 7936.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#400C211yesmaximal, characteristic, complemented
2C2×C31×#396C211yesmaximal, characteristic, complemented
3C2×C31×#390C211yesmaximal, characteristic
4C2×C31×#386C211yesmaximal, characteristic
5C31×#1444C211yesmaximal, characteristic, complemented
6C31×#1439C211yesmaximal, characteristic, complemented
7C31×#1439C211yesmaximal, characteristic, complemented
8C31×#1439C211yesmaximal, characteristic, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1438C211yesmaximal, characteristic
12C31×#1436C211yesmaximal, characteristic, complemented
13C31×#1434C211yesmaximal, characteristic, complemented
14C31×C22⋊#95C211yesmaximal, characteristic, complemented
15C31×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C24×C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C4⋊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×#400—24no—
36C31×#396—24no—
37C31×#390—24no—
38C31×#386—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—22no—
60C22×D4×C31—22no—
61C22×D4×C31—41no—
62C22×D4×C31—41no—
63C22×D4×C31Q814yes—
64C23×C4×C31—22no—
65C23×C4×C31—22no—
66C23×C4×C31—22no—
67C23×C4×C31—41no—
68C23×C4×C31—41no—
69C23×C4×C31—41no—
70C23×C4×C31—41no—
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
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C23×C4×C31C2311yescharacteristic
83C23×C4×C31C2311yescharacteristic
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—41no—
92C2×C4⋊C4×C31—41no—
93C2×C4⋊C4×C31—41no—
94C2×C4⋊C4×C31—41no—
95C2×C4⋊C4×C31—41no—
96C2×C4⋊C4×C31—41no—
97C2×C4⋊C4×C31—41no—
98C2×C4⋊C4×C31—41no—
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—22no—
113C2×C22⋊C4×C31—22no—
114C2×C22⋊C4×C31—22no—
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×C22⋊C4×C31—41no—
129C2×C22⋊C4×C31—41no—
130C2×C22⋊C4×C31—41no—
131C2×C22⋊C4×C31D414yes—
132C2×C42×C31—22no—
133C2×C42×C31—22no—
134C2×C42×C31—41no—
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—22no—
145C31×#95—41no—
146C31×#95—41no—
147C31×#95—41no—
148C31×#95—41no—
149C31×#95—41no—
150C31×#95D414yes—
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×C31—21no—
176C24×C31—21no—
177C24×C31C2×D412yes—
178C24×C31C2×Q812yes—
179C24×C31C2×Q812yes—
180C24×C31#4112yes—
181C24×C31C2411yescharacteristic
182C2×D4×C31—28no—
183C2×D4×C31—28no—
184C2×D4×C31—44no—
185C2×D4×C31—44no—
186C2×D4×C31—44no—
187C2×D4×C31—44no—
188C2×D4×C31—44no—
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×C31—21no—
268C22×C4×C31—21no—
269C22×C4×C31—44no—
270C22×C4×C31—44no—
271C22×C4×C31—44no—
272C22×C4×C31—44no—
273C22×C4×C31—44no—
274C22×C4×C31—44no—
275C22×C4×C31—44no—
276C22×C4×C31C2×D412yes—
277C22×C4×C31C2×D412yes—
278C22×C4×C31C2×D412yes—
279C22×C4×C31C2×D412yes—
280C22×C4×C31C2×D412yes—
281C22×C4×C31C2×Q812yes—
282C22×C4×C31#4112yes—
283C22×C4×C31#4112yes—
284C22×C4×C31#4112yes—
285C22×C4×C31#4112yes—
286C22×C4×C31#4112yes—
287C4⋊C4×C31—44no—
288C4⋊C4×C31—44no—
289C4⋊C4×C31—44no—
290C4⋊C4×C31—44no—
291C4⋊C4×C31—44no—
292C22⋊C4×C31—44no—
293C22⋊C4×C31—44no—
294C22⋊C4×C31—44no—
295C22⋊C4×C31—44no—
296C22⋊C4×C31—44no—
297C22⋊C4×C31—44no—
298C22⋊C4×C31—44no—
299C22⋊C4×C31—44no—
300C22⋊C4×C31—44no—
301C22⋊C4×C31—44no—
302C22⋊C4×C31—44no—
303C42×C31—44no—
304#15508C3111yesmaximal, characteristic, direct product factor, Sylow
305C23×C31—22no—
306C23×C31—22no—
307C23×C31—22no—
308C23×C31—22no—
309C23×C31—22no—
310C23×C31—22no—
311C23×C31—22no—
312C23×C31—22no—
313C23×C31—22no—
314C23×C31—22no—
315C23×C31—22no—
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×C31C22⋊Q814yes—
375C23×C31C22×D411yescharacteristic
376C23×C31C22×D411yescharacteristic
377C23×C31C22×Q811yescharacteristic
378C23×C31C2×#4111yescharacteristic
379C23×C31C2×#4111yescharacteristic
380C23×C31C2×#4111yescharacteristic
381C23×C31C2×#4111yescharacteristic
382C23×C31C2×#4111yescharacteristic
383C23×C31C2×#4111yescharacteristic
384C23×C31H(5,𝔽2)11yescharacteristic
385C23×C31H(5,𝔽2)11yescharacteristic
386C23×C31H(5,𝔽2)11yescharacteristic
387C23×C31H(5,𝔽2)11yescharacteristic
388C23×C31H(5,𝔽2)11yescharacteristic
389C23×C31H(5,𝔽2)11yescharacteristic
390D4×C31—416no—
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—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—416no—
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—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×C31C22⋊Q814yes—
483C2×#400C2×C3111yescharacteristic, complemented
484C2×#396C2×C3111yescharacteristic, complemented
485C2×#390C2×C3111yescharacteristic
486C2×#386C2×C3111yescharacteristic
487#1444C2×C3111yescharacteristic, complemented
488#1439C2×C3111yescharacteristic, complemented
489#1439C2×C3111yescharacteristic, complemented
490#1439C2×C3111yescharacteristic, complemented
491#1439C2×C3111yescharacteristic, complemented
492#1439C2×C3111yescharacteristic, complemented
493#1438C2×C3111yescharacteristic
494#1436C2×C3111yescharacteristic, complemented
495#1434C2×C3111yescharacteristic, complemented
496C22⋊#95C2×C3111yescharacteristic, complemented
497C22⋊#95C2×C3111yescharacteristic, complemented
498C22×C31—24no—
499C22×C31—24no—
500C22×C31—24no—
501C22×C31—42no—
502C22×C31—42no—
503C22×C31—42no—
504C22×C31—42no—
505C22×C31—42no—
506C22×C31—42no—
507C22×C31—42no—
508C22×C31—42no—
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—81no—
521C22×C31—81no—
522C22×C31—81no—
523C22×C31—81no—
524C22×C31—81no—
525C22×C31—81no—
526C22×C31—81no—
527C22×C31—81no—
528C22×C31C2×C22⋊Q811yescharacteristic
529C22×C31C2×C22⋊Q811yescharacteristic
530C22×C31#52911yescharacteristic
531C22×C31#52911yescharacteristic
532C22×C31#53211yescharacteristic
533C22×C31#53211yescharacteristic
534C22×C31#53411yescharacteristic
535C22×C31#53511yescharacteristic
536C22×C31#53811yescharacteristic
537C22×C31#53811yescharacteristic
538C22×C31#53811yescharacteristic
539C22×C31#53811yescharacteristic
540C22×C31#54011yescharacteristic
541C22×C31#54011yescharacteristic
542C22×C31#54311yescharacteristic
543C22×C31D4211yescharacteristic
544C22×C31#54611yescharacteristic
545C22×C31#54611yescharacteristic
546C22×C31#54611yescharacteristic
547C22×C31#54611yescharacteristic
548C22×C31#54611yescharacteristic
549C22×C31#55011yescharacteristic
550C22×C31#55111yescharacteristic
551C22×C31#55111yescharacteristic
552C22×C31#55111yescharacteristic
553C22×C31#55311yescharacteristic
554C22×C31#55311yescharacteristic
555C22×C31#55311yescharacteristic
556C22×C31#55411yescharacteristic
557C22×C31#55411yescharacteristic
558C22×C31#55411yescharacteristic
559C22×C31#55411yescharacteristic
560C22×C31#55511yescharacteristic
561C22×C31#56011yescharacteristic
562C22×C31#56011yescharacteristic
563C4×C31—24no—
564C4×C31—42no—
565C4×C31—42no—
566C4×C31—42no—
567C4×C31—42no—
568C4×C31—42no—
569C4×C31—42no—
570C4×C31—42no—
571C4×C31—42no—
572C4×C31—81no—
573C4×C31—81no—
574C4×C31—81no—
575C4×C31—81no—
576C23×D4C22×C3111yescharacteristic
577C24×C4C22×C3111yescharacteristic
578C22×C4⋊C4C22×C3111yescharacteristic
579C22×C4⋊C4C22×C3111yescharacteristic
580C22×C4⋊C4C22×C3111yescharacteristic
581C22×C4⋊C4C22×C3111yescharacteristic
582C22×C4⋊C4C22×C3111yescharacteristic
583C22×C22⋊C4C22×C3111yescharacteristic
584C22×C22⋊C4C22×C3111yescharacteristic
585C22×C22⋊C4C22×C3111yescharacteristic
586C22×C22⋊C4C22×C3111yescharacteristic
587C22×C22⋊C4C22×C3111yescharacteristic
588C22×C22⋊C4C22×C3111yescharacteristic
589C22×C22⋊C4C22×C3111yescharacteristic
590C22×C22⋊C4C22×C3111yescharacteristic
591C22×C22⋊C4C22×C3111yescharacteristic
592C22×C22⋊C4C22×C3111yescharacteristic
593C22×C22⋊C4C22×C3111yescharacteristic
594C22×C42C22×C3111yescharacteristic
595#400—24no—
596#396—24no—
597#390—24no—
598#386—24no—
599C2×#95C22×C3111yescharacteristic
600C2×#95C22×C3111yescharacteristic
601C2×#95C22×C3111yescharacteristic
602C2×#95C22×C3111yescharacteristic
603C2×#95C22×C3111yescharacteristic
604C2×#95C22×C3111yescharacteristic
605C2×#95C22×C3111yescharacteristic
606C2×#95C22×C3111yescharacteristic
607C2×#95C22×C3111yescharacteristic
608C2×#95C22×C3111yescharacteristic
609C2×#95C22×C3111yescharacteristic
610C2×#95C22×C3111yescharacteristic
611C2×#95C22×C3111yescharacteristic
612C2×#95C22×C3111yescharacteristic
613C2×#95C22×C3111yescharacteristic
614C2×#95C22×C3111yescharacteristic
615C2×C31—44no—
616C2×C31—82no—
617C2×C31#243711yescharacteristic
618C2×C31#245011yescharacteristic
619C2×C31#245411yescharacteristic
620C2×C31#252611yescharacteristic
621C2×C31#255411yescharacteristic
622C2×C31#255511yescharacteristic
623C2×C31#255911yescharacteristic
624C2×C31#256411yescharacteristic
625C2×C31#256611yescharacteristic
626C2×C31#267311yescharacteristic
627C2×C31#268511yescharacteristic
628C2×C31#268811yescharacteristic
629C2×C31#274911yescharacteristic
630C2×C31#278011yescharacteristic
631C2×C31#278411yescharacteristic
632C25C23×C3111yescharacteristic
633C25C23×C3111yescharacteristic
634C22×D4—22no—
635C22×D4—22no—
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—41no—
639C22×D4—41no—
640C22×D4Q8×C3114yes—
641C23×C4—22no—
642C23×C4—22no—
643C23×C4—22no—
644C23×C4—41no—
645C23×C4—41no—
646C23×C4—41no—
647C23×C4—41no—
648C23×C4C23×C3111yescharacteristic
649C23×C4C23×C3111yescharacteristic
650C23×C4C23×C3111yescharacteristic
651C23×C4C23×C3111yescharacteristic
652C23×C4C23×C3111yescharacteristic
653C23×C4C23×C3111yescharacteristic
654C23×C4C23×C3111yescharacteristic
655C23×C4C23×C3111yescharacteristic
656C23×C4C23×C3111yescharacteristic
657C23×C4C23×C3111yescharacteristic
658C23×C4C23×C3111yescharacteristic
659C23×C4C23×C3111yescharacteristic
660C23×C4C23×C3111yescharacteristic
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4—41no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4D4×C3114yes—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—41no—
712#95—22no—
713#95—22no—
714#95—22no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—41no—
723#95—41no—
724#95—41no—
725#95—41no—
726#95—41no—
727#95D4×C3114yes—
728C31#1550811yescharacteristic, direct product factor, Sylow
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—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24C2×D4×C3112yes—
756C24C2×Q8×C3112yes—
757C24C2×Q8×C3112yes—
758C24#41×C3112yes—
759C24C24×C3111yescharacteristic
760C2×D4—28no—
761C2×D4—28no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
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×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—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4C2×D4×C3112yes—
855C22×C4C2×D4×C3112yes—
856C22×C4C2×D4×C3112yes—
857C22×C4C2×D4×C3112yes—
858C22×C4C2×D4×C3112yes—
859C22×C4C2×Q8×C3112yes—
860C22×C4#41×C3112yes—
861C22×C4#41×C3112yes—
862C22×C4#41×C3112yes—
863C22×C4#41×C3112yes—
864C22×C4#41×C3112yes—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C42—44no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
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—
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—
951C23C31×C22⋊Q814yes—
952C23C22×D4×C3111yescharacteristic
953C23C22×D4×C3111yescharacteristic
954C23C22×Q8×C3111yescharacteristic
955C23C2×#41×C3111yescharacteristic
956C23C2×#41×C3111yescharacteristic
957C23C2×#41×C3111yescharacteristic
958C23C2×#41×C3111yescharacteristic
959C23C2×#41×C3111yescharacteristic
960C23C2×#41×C3111yescharacteristic
961C23C31×H(5,𝔽2)11yescharacteristic
962C23C31×H(5,𝔽2)11yescharacteristic
963C23C31×H(5,𝔽2)11yescharacteristic
964C23C31×H(5,𝔽2)11yescharacteristic
965C23C31×H(5,𝔽2)11yescharacteristic
966C23C31×H(5,𝔽2)11yescharacteristic
967D4—416no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—416no—
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×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×C4C31×C22⋊Q814yes—
1060C22—24no—
1061C22—24no—
1062C22—24no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22C2×C31×C22⋊Q811yescharacteristic
1091C22C2×C31×C22⋊Q811yescharacteristic
1092C22C31×#52911yescharacteristic
1093C22C31×#52911yescharacteristic
1094C22C31×#53211yescharacteristic
1095C22C31×#53211yescharacteristic
1096C22C31×#53411yescharacteristic
1097C22C31×#53511yescharacteristic
1098C22C31×#53811yescharacteristic
1099C22C31×#53811yescharacteristic
1100C22C31×#53811yescharacteristic
1101C22C31×#53811yescharacteristic
1102C22C31×#54011yescharacteristic
1103C22C31×#54011yescharacteristic
1104C22C31×#54311yescharacteristic
1105C22D42×C3111yescharacteristic
1106C22C31×#54611yescharacteristic
1107C22C31×#54611yescharacteristic
1108C22C31×#54611yescharacteristic
1109C22C31×#54611yescharacteristic
1110C22C31×#54611yescharacteristic
1111C22C31×#55011yescharacteristic
1112C22C31×#55111yescharacteristic
1113C22C31×#55111yescharacteristic
1114C22C31×#55111yescharacteristic
1115C22C31×#55311yescharacteristic
1116C22C31×#55311yescharacteristic
1117C22C31×#55311yescharacteristic
1118C22C31×#55411yescharacteristic
1119C22C31×#55411yescharacteristic
1120C22C31×#55411yescharacteristic
1121C22C31×#55411yescharacteristic
1122C22C31×#55511yescharacteristic
1123C22C31×#56011yescharacteristic
1124C22C31×#56011yescharacteristic
1125C4—24no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C2—44no—
1139C2—82no—
1140C2C31×#243711yescharacteristic
1141C2C31×#245011yescharacteristic
1142C2C31×#245411yescharacteristic
1143C2C31×#252611yescharacteristic
1144C2C31×#255411yescharacteristic
1145C2C31×#255511yescharacteristic
1146C2C31×#255911yescharacteristic
1147C2C31×#256411yescharacteristic
1148C2C31×#256611yescharacteristic
1149C2C31×#267311yescharacteristic
1150C2C31×#268511yescharacteristic
1151C2C31×#268811yescharacteristic
1152C2C31×#274911yescharacteristic
1153C2C31×#278011yescharacteristic
1154C2C31×#278411yescharacteristic
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×#400C2semidirect
2. C2×C31×#396C2semidirect
5. C31×#1444C2semidirect
6. C31×#1439C2semidirect
7. C31×#1439C2semidirect
8. C31×#1439C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
12. C31×#1436C2semidirect
13. C31×#1434C2semidirect
14. C31×C22⋊#95C2semidirect
15. C31×C22⋊#95C2semidirect
304. #15508C31direct (N × H)
483. C2×#400C2×C31semidirect
484. C2×#396C2×C31semidirect
487. #1444C2×C31semidirect
488. #1439C2×C31semidirect
489. #1439C2×C31semidirect
490. #1439C2×C31semidirect
491. #1439C2×C31semidirect
492. #1439C2×C31semidirect
494. #1436C2×C31semidirect
495. #1434C2×C31semidirect
496. C22⋊#95C2×C31semidirect
497. C22⋊#95C2×C31semidirect
728. C31#15508direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4002
C2×C31×#3962
C2×C31×#3902
C2×C31×#3862
C31×#14442
C31×#14392
C31×#14382
C31×#14362
C31×#14342
C31×C22⋊#952
#1550831