Finite Group Databasebeta

← C31×#16690 #21473449

Subgroups — C31×#16690 #21473449

Order 7936.

1622 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#386C211yesmaximal, characteristic
2C2×C31×#381C211yesmaximal, characteristic, complemented
3C31×#1445C211yesmaximal, characteristic, complemented
4C31×#1443C211yesmaximal, characteristic, complemented
5C31×#1443C211yesmaximal, characteristic, complemented
6C31×#1442C211yesmaximal, 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×#1438C211yesmaximal, characteristic
15C31×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C24×C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2211yescharacteristic
31C31×#386—24no—
32C31×#381—24no—
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2211yescharacteristic
39C2×C31×#95C2211yescharacteristic
40C2×C31×#95C2211yescharacteristic
41C2×C31×#95C2211yescharacteristic
42C2×C31×#95C2211yescharacteristic
43C2×C31×#95C2211yescharacteristic
44C2×C31×#95C2211yescharacteristic
45C2×C31×#95C2211yescharacteristic
46C2×C31×#95C2211yescharacteristic
47C2×C31×#95C2211yescharacteristic
48C2×C31×#95C2211yescharacteristic
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C2×C31×#95C2211yescharacteristic
52C2×C31×#95C2211yescharacteristic
53C25×C31C2311yescharacteristic
54C25×C31C2311yescharacteristic
55C22×D4×C31—22no—
56C22×D4×C31—22no—
57C22×D4×C31—22no—
58C22×D4×C31—22no—
59C22×D4×C31—22no—
60C22×D4×C31—41no—
61C22×D4×C31—41no—
62C23×C4×C31—22no—
63C23×C4×C31—22no—
64C23×C4×C31—41no—
65C23×C4×C31—41no—
66C23×C4×C31—41no—
67C23×C4×C31—41no—
68C23×C4×C31D414yes—
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
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—41no—
84C2×C4⋊C4×C31—41no—
85C2×C4⋊C4×C31—41no—
86C2×C4⋊C4×C31—41no—
87C2×C4⋊C4×C31—41no—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—22no—
94C2×C22⋊C4×C31—22no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—22no—
98C2×C22⋊C4×C31—22no—
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—41no—
102C2×C22⋊C4×C31—41no—
103C2×C22⋊C4×C31—41no—
104C2×C22⋊C4×C31—41no—
105C2×C22⋊C4×C31—41no—
106C2×C22⋊C4×C31—41no—
107C2×C22⋊C4×C31—41no—
108C2×C22⋊C4×C31—41no—
109C2×C22⋊C4×C31—41no—
110C2×C22⋊C4×C31—41no—
111C2×C22⋊C4×C31—41no—
112C2×C22⋊C4×C31—41no—
113C2×C22⋊C4×C31—41no—
114C2×C22⋊C4×C31—41no—
115C2×C22⋊C4×C31—41no—
116C2×C22⋊C4×C31—41no—
117C2×C22⋊C4×C31—41no—
118C2×C22⋊C4×C31—41no—
119C2×C22⋊C4×C31—41no—
120C2×C22⋊C4×C31—41no—
121C31×#95—22no—
122C31×#95—22no—
123C31×#95—22no—
124C31×#95—22no—
125C31×#95—22no—
126C31×#95—22no—
127C31×#95—22no—
128C31×#95—22no—
129C31×#95—22no—
130C31×#95—41no—
131C31×#95—41no—
132C31×#95—41no—
133C31×#95—41no—
134C31×#95—41no—
135C31×#95—41no—
136C31×#95—41no—
137C31×#95—41no—
138C31×#95—41no—
139C31×#95—41no—
140C31×#95—41no—
141C24×C31—21no—
142C24×C31—21no—
143C24×C31—21no—
144C24×C31—21no—
145C24×C31—21no—
146C24×C31—21no—
147C24×C31—21no—
148C24×C31—21no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31—21no—
152C24×C31—21no—
153C24×C31—21no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31—21no—
157C24×C31—21no—
158C24×C31—21no—
159C24×C31—21no—
160C24×C31—21no—
161C24×C31—21no—
162C24×C31—21no—
163C24×C31—21no—
164C24×C31—21no—
165C24×C31—21no—
166C24×C31—21no—
167C24×C31C2×D412yes—
168C24×C31#4112yes—
169C24×C31#4112yes—
170C24×C31#4112yes—
171C24×C31C2411yescharacteristic
172C2×D4×C31—28no—
173C2×D4×C31—44no—
174C2×D4×C31—44no—
175C2×D4×C31—44no—
176C2×D4×C31—44no—
177C2×D4×C31—44no—
178C2×D4×C31—44no—
179C22×C4×C31—28no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—21no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
256C22×C4×C31—21no—
257C22×C4×C31—21no—
258C22×C4×C31—21no—
259C22×C4×C31—21no—
260C22×C4×C31—21no—
261C22×C4×C31—21no—
262C22×C4×C31—21no—
263C22×C4×C31—21no—
264C22×C4×C31—21no—
265C22×C4×C31—21no—
266C22×C4×C31—44no—
267C22×C4×C31—44no—
268C22×C4×C31—44no—
269C22×C4×C31—44no—
270C22×C4×C31—44no—
271C22×C4×C31—44no—
272C22×C4×C31C2×D412yes—
273C22×C4×C31C2×D412yes—
274C22×C4×C31#4112yes—
275C22×C4×C31#4112yes—
276C22×C4×C31#4112yes—
277C4⋊C4×C31—44no—
278C4⋊C4×C31—44no—
279C22⋊C4×C31—44no—
280C22⋊C4×C31—44no—
281C22⋊C4×C31—44no—
282C22⋊C4×C31—44no—
283C22⋊C4×C31—44no—
284C22⋊C4×C31—44no—
285C22⋊C4×C31—44no—
286C22⋊C4×C31—44no—
287C22⋊C4×C31—44no—
288C22⋊C4×C31—44no—
289C22⋊C4×C31—44no—
290#16690C3111yesmaximal, characteristic, direct product factor, Sylow
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—22no—
304C23×C31—22no—
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—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#12314yes—
361C23×C31C22×D411yescharacteristic
362C23×C31C2×#4111yescharacteristic
363C23×C31C2×#4111yescharacteristic
364C23×C31C2×#4111yescharacteristic
365C23×C31C2×#4111yescharacteristic
366C23×C31C2×#4111yescharacteristic
367C23×C31C2×#4111yescharacteristic
368C23×C31H(5,𝔽2)11yescharacteristic
369C23×C31H(5,𝔽2)11yescharacteristic
370C23×C31H(5,𝔽2)11yescharacteristic
371C23×C31H(5,𝔽2)11yescharacteristic
372C23×C31H(5,𝔽2)11yescharacteristic
373C23×C31H(5,𝔽2)11yescharacteristic
374C23×C31H(5,𝔽2)11yescharacteristic
375C23×C312−1+411yescharacteristic
376D4×C31—416no—
377C2×C4×C31—22no—
378C2×C4×C31—22no—
379C2×C4×C31—22no—
380C2×C4×C31—22no—
381C2×C4×C31—22no—
382C2×C4×C31—22no—
383C2×C4×C31—22no—
384C2×C4×C31—22no—
385C2×C4×C31—22no—
386C2×C4×C31—22no—
387C2×C4×C31—22no—
388C2×C4×C31—22no—
389C2×C4×C31—22no—
390C2×C4×C31—22no—
391C2×C4×C31—22no—
392C2×C4×C31—416no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31—41no—
397C2×C4×C31—41no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402C2×C4×C31—41no—
403C2×C4×C31—41no—
404C2×C4×C31—41no—
405C2×C4×C31—41no—
406C2×C4×C31—41no—
407C2×C4×C31—41no—
408C2×C4×C31—41no—
409C2×C4×C31—41no—
410C2×C4×C31—41no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—41no—
414C2×C4×C31—41no—
415C2×C4×C31—41no—
416C2×C4×C31—41no—
417C2×C4×C31—41no—
418C2×C4×C31—41no—
419C2×C4×C31—41no—
420C2×C4×C31—41no—
421C2×C4×C31—41no—
422C2×C4×C31—41no—
423C2×C4×C31—41no—
424C2×C4×C31—41no—
425C2×C4×C31—41no—
426C2×C4×C31—41no—
427C2×C4×C31—41no—
428C2×C4×C31—41no—
429C2×C4×C31—41no—
430C2×C4×C31—41no—
431C2×C4×C31—41no—
432C2×C4×C31—41no—
433C2×C4×C31—41no—
434C2×C4×C31—41no—
435C2×C4×C31—41no—
436C2×C4×C31—41no—
437C2×C4×C31—41no—
438C2×C4×C31—41no—
439C2×C4×C31—41no—
440C2×C4×C31—41no—
441C2×C4×C31—41no—
442C2×C4×C31—41no—
443C2×C4×C31—41no—
444C2×C4×C31—41no—
445C2×C4×C31—41no—
446C2×C4×C31—41no—
447C2×C4×C31—41no—
448C2×C4×C31—41no—
449C2×C4×C31—41no—
450C2×C4×C31—41no—
451C2×C4×C31—41no—
452C2×C4×C31—41no—
453C2×C4×C31—41no—
454C2×C4×C31—41no—
455C2×C4×C31—41no—
456C2×C4×C31—41no—
457C2×C4×C31—41no—
458C2×C4×C31—41no—
459C2×C4×C31—41no—
460C2×C4×C31—41no—
461C2×C4×C31—41no—
462C2×C4×C31—41no—
463C2×C4×C31—41no—
464C2×C4×C31—41no—
465C2×C4×C31—41no—
466C2×C4×C31—41no—
467C2×C4×C31—41no—
468C2×C4×C31—41no—
469C2×#386C2×C3111yescharacteristic
470C2×#381C2×C3111yescharacteristic, complemented
471#1445C2×C3111yescharacteristic, complemented
472#1443C2×C3111yescharacteristic, complemented
473#1443C2×C3111yescharacteristic, complemented
474#1442C2×C3111yescharacteristic, complemented
475#1440C2×C3111yescharacteristic, complemented
476#1440C2×C3111yescharacteristic, complemented
477#1439C2×C3111yescharacteristic, complemented
478#1439C2×C3111yescharacteristic, complemented
479#1439C2×C3111yescharacteristic, complemented
480#1439C2×C3111yescharacteristic, complemented
481#1438C2×C3111yescharacteristic
482#1438C2×C3111yescharacteristic
483C22⋊#95C2×C3111yescharacteristic, complemented
484C22×C31—24no—
485C22×C31—24no—
486C22×C31—24no—
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—42no—
502C22×C31—42no—
503C22×C31—42no—
504C22×C31—42no—
505C22×C31—42no—
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×C31C2×#12311yescharacteristic
515C22×C31#52511yescharacteristic
516C22×C31#53211yescharacteristic
517C22×C31#53411yescharacteristic
518C22×C31#53411yescharacteristic
519C22×C31#53511yescharacteristic
520C22×C31#53711yescharacteristic
521C22×C31#53811yescharacteristic
522C22×C31#53811yescharacteristic
523C22×C31#53811yescharacteristic
524C22×C31#53811yescharacteristic
525C22×C31#53811yescharacteristic
526C22×C31#53811yescharacteristic
527C22×C31#53811yescharacteristic
528C22×C31#53911yescharacteristic
529C22×C31#54011yescharacteristic
530C22×C31#54011yescharacteristic
531C22×C31#54011yescharacteristic
532C22×C31#54211yescharacteristic
533C22×C31#55111yescharacteristic
534C22×C31#55111yescharacteristic
535C22×C31#55111yescharacteristic
536C22×C31#55111yescharacteristic
537C22×C31#55111yescharacteristic
538C22×C31#55111yescharacteristic
539C22×C31#55111yescharacteristic
540C22×C31#55211yescharacteristic
541C22×C31#55211yescharacteristic
542C22×C31#55311yescharacteristic
543C22×C31#55311yescharacteristic
544C22×C31#55911yescharacteristic
545C22×C31#56011yescharacteristic
546C22×C31#56011yescharacteristic
547C22×C31#56211yescharacteristic
548C22×C31#56211yescharacteristic
549C4×C31—42no—
550C4×C31—42no—
551C4×C31—42no—
552C4×C31—42no—
553C4×C31—42no—
554C4×C31—81no—
555C4×C31—81no—
556C4×C31—81no—
557C4×C31—81no—
558C4×C31—81no—
559C4×C31—81no—
560C4×C31—81no—
561C4×C31—81no—
562C23×D4C22×C3111yescharacteristic
563C24×C4C22×C3111yescharacteristic
564C22×C4⋊C4C22×C3111yescharacteristic
565C22×C4⋊C4C22×C3111yescharacteristic
566C22×C22⋊C4C22×C3111yescharacteristic
567C22×C22⋊C4C22×C3111yescharacteristic
568C22×C22⋊C4C22×C3111yescharacteristic
569C22×C22⋊C4C22×C3111yescharacteristic
570C22×C22⋊C4C22×C3111yescharacteristic
571C22×C22⋊C4C22×C3111yescharacteristic
572C22×C22⋊C4C22×C3111yescharacteristic
573C22×C22⋊C4C22×C3111yescharacteristic
574C22×C22⋊C4C22×C3111yescharacteristic
575C22×C22⋊C4C22×C3111yescharacteristic
576C22×C22⋊C4C22×C3111yescharacteristic
577#386—24no—
578#381—24no—
579C2×#95C22×C3111yescharacteristic
580C2×#95C22×C3111yescharacteristic
581C2×#95C22×C3111yescharacteristic
582C2×#95C22×C3111yescharacteristic
583C2×#95C22×C3111yescharacteristic
584C2×#95C22×C3111yescharacteristic
585C2×#95C22×C3111yescharacteristic
586C2×#95C22×C3111yescharacteristic
587C2×#95C22×C3111yescharacteristic
588C2×#95C22×C3111yescharacteristic
589C2×#95C22×C3111yescharacteristic
590C2×#95C22×C3111yescharacteristic
591C2×#95C22×C3111yescharacteristic
592C2×#95C22×C3111yescharacteristic
593C2×#95C22×C3111yescharacteristic
594C2×#95C22×C3111yescharacteristic
595C2×#95C22×C3111yescharacteristic
596C2×#95C22×C3111yescharacteristic
597C2×#95C22×C3111yescharacteristic
598C2×#95C22×C3111yescharacteristic
599C2×C31—44no—
600C2×C31—82no—
601C2×C31#248211yescharacteristic
602C2×C31#249811yescharacteristic
603C2×C31#260211yescharacteristic
604C2×C31#262211yescharacteristic
605C2×C31#263011yescharacteristic
606C2×C31#266111yescharacteristic
607C2×C31#274311yescharacteristic
608C2×C31#274911yescharacteristic
609C2×C31#274911yescharacteristic
610C2×C31#275011yescharacteristic
611C2×C31#275111yescharacteristic
612C2×C31#275211yescharacteristic
613C2×C31#276011yescharacteristic
614C2×C31#276111yescharacteristic
615C2×C31#281311yescharacteristic
616C25C23×C3111yescharacteristic
617C25C23×C3111yescharacteristic
618C22×D4—22no—
619C22×D4—22no—
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—22no—
623C22×D4—41no—
624C22×D4—41no—
625C23×C4—22no—
626C23×C4—22no—
627C23×C4—41no—
628C23×C4—41no—
629C23×C4—41no—
630C23×C4—41no—
631C23×C4D4×C3114yes—
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
643C23×C4C23×C3111yescharacteristic
644C23×C4C23×C3111yescharacteristic
645C2×C4⋊C4—22no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—41no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
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—41no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—41no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—41no—
669C2×C22⋊C4—41no—
670C2×C22⋊C4—41no—
671C2×C22⋊C4—41no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684#95—22no—
685#95—22no—
686#95—22no—
687#95—22no—
688#95—22no—
689#95—22no—
690#95—22no—
691#95—22no—
692#95—22no—
693#95—41no—
694#95—41no—
695#95—41no—
696#95—41no—
697#95—41no—
698#95—41no—
699#95—41no—
700#95—41no—
701#95—41no—
702#95—41no—
703#95—41no—
704C31#1669011yescharacteristic, direct product factor, Sylow
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24C2×D4×C3112yes—
732C24#41×C3112yes—
733C24#41×C3112yes—
734C24#41×C3112yes—
735C24C24×C3111yescharacteristic
736C2×D4—28no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
743C22×C4—28no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4C2×D4×C3112yes—
837C22×C4C2×D4×C3112yes—
838C22×C4#41×C3112yes—
839C22×C4#41×C3112yes—
840C22×C4#41×C3112yes—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
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—22no—
876C23—22no—
877C23—22no—
878C23—22no—
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—
923C23C31×#12314yes—
924C23C22×D4×C3111yescharacteristic
925C23C2×#41×C3111yescharacteristic
926C23C2×#41×C3111yescharacteristic
927C23C2×#41×C3111yescharacteristic
928C23C2×#41×C3111yescharacteristic
929C23C2×#41×C3111yescharacteristic
930C23C2×#41×C3111yescharacteristic
931C23C31×H(5,𝔽2)11yescharacteristic
932C23C31×H(5,𝔽2)11yescharacteristic
933C23C31×H(5,𝔽2)11yescharacteristic
934C23C31×H(5,𝔽2)11yescharacteristic
935C23C31×H(5,𝔽2)11yescharacteristic
936C23C31×H(5,𝔽2)11yescharacteristic
937C23C31×H(5,𝔽2)11yescharacteristic
938C23C31×2−1+411yescharacteristic
939D4—416no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
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—416no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
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—
1032C22—24no—
1033C22—24no—
1034C22—24no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
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—42no—
1053C22—42no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22C2×C31×#12311yescharacteristic
1063C22C31×#52511yescharacteristic
1064C22C31×#53211yescharacteristic
1065C22C31×#53411yescharacteristic
1066C22C31×#53411yescharacteristic
1067C22C31×#53511yescharacteristic
1068C22C31×#53711yescharacteristic
1069C22C31×#53811yescharacteristic
1070C22C31×#53811yescharacteristic
1071C22C31×#53811yescharacteristic
1072C22C31×#53811yescharacteristic
1073C22C31×#53811yescharacteristic
1074C22C31×#53811yescharacteristic
1075C22C31×#53811yescharacteristic
1076C22C31×#53911yescharacteristic
1077C22C31×#54011yescharacteristic
1078C22C31×#54011yescharacteristic
1079C22C31×#54011yescharacteristic
1080C22C31×#54211yescharacteristic
1081C22C31×#55111yescharacteristic
1082C22C31×#55111yescharacteristic
1083C22C31×#55111yescharacteristic
1084C22C31×#55111yescharacteristic
1085C22C31×#55111yescharacteristic
1086C22C31×#55111yescharacteristic
1087C22C31×#55111yescharacteristic
1088C22C31×#55211yescharacteristic
1089C22C31×#55211yescharacteristic
1090C22C31×#55311yescharacteristic
1091C22C31×#55311yescharacteristic
1092C22C31×#55911yescharacteristic
1093C22C31×#56011yescharacteristic
1094C22C31×#56011yescharacteristic
1095C22C31×#56211yescharacteristic
1096C22C31×#56211yescharacteristic
1097C4—42no—
1098C4—42no—
1099C4—42no—
1100C4—42no—
1101C4—42no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C2—44no—
1111C2—82no—
1112C2C31×#248211yescharacteristic
1113C2C31×#249811yescharacteristic
1114C2C31×#260211yescharacteristic
1115C2C31×#262211yescharacteristic
1116C2C31×#263011yescharacteristic
1117C2C31×#266111yescharacteristic
1118C2C31×#274311yescharacteristic
1119C2C31×#274911yescharacteristic
1120C2C31×#274911yescharacteristic
1121C2C31×#275011yescharacteristic
1122C2C31×#275111yescharacteristic
1123C2C31×#275211yescharacteristic
1124C2C31×#276011yescharacteristic
1125C2C31×#276111yescharacteristic
1126C2C31×#281311yescharacteristic
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×#381C2semidirect
3. C31×#1445C2semidirect
4. C31×#1443C2semidirect
5. C31×#1443C2semidirect
6. C31×#1442C2semidirect
7. C31×#1440C2semidirect
8. C31×#1440C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
11. C31×#1439C2semidirect
12. C31×#1439C2semidirect
15. C31×C22⋊#95C2semidirect
290. #16690C31direct (N × H)
470. C2×#381C2×C31semidirect
471. #1445C2×C31semidirect
472. #1443C2×C31semidirect
473. #1443C2×C31semidirect
474. #1442C2×C31semidirect
475. #1440C2×C31semidirect
476. #1440C2×C31semidirect
477. #1439C2×C31semidirect
478. #1439C2×C31semidirect
479. #1439C2×C31semidirect
480. #1439C2×C31semidirect
483. C22⋊#95C2×C31semidirect
704. C31#16690direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3862
C2×C31×#3812
C31×#14452
C31×#14432
C31×#14422
C31×#14402
C31×#14392
C31×#14382
C31×C22⋊#952
#1669031