Finite Group Databasebeta

← C31×#24008 #21480767

Subgroups — C31×#24008 #21480767

Order 7936.

1448 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#525C211yesmaximal, characteristic
2C2×C31×#485C211yesmaximal, characteristic, complemented
3C2×C31×#482C211yesmaximal, characteristic, complemented
4C31×#2280C211yesmaximal, characteristic, complemented
5C31×#2036C211yesmaximal, characteristic, complemented
6C31×#2035C211yesmaximal, characteristic, complemented
7C31×#2034C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#1875C211yesmaximal, characteristic, complemented
10C31×#1873C211yesmaximal, characteristic, complemented
11C31×#1854C211yesmaximal, characteristic, complemented
12C31×#1854C211yesmaximal, characteristic, complemented
13C31×#1788C211yesmaximal, characteristic, complemented
14C31×#1788C211yesmaximal, characteristic, complemented
15C31×#1779C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C24×C4×C31C2211yescharacteristic
18C31×#525—24no—
19C31×#525—24no—
20C2×C31×#123—21no—
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C31×C22⋊Q8C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C31×#120—21no—
26C2×C4×D4×C31—21no—
27C2×C4×D4×C31—21no—
28C2×C31×#117C2211yescharacteristic
29C2×C31×#117C2211yescharacteristic
30C2×C31×#117C2211yescharacteristic
31C31×#485—24no—
32C31×#482—24no—
33C2×C31×#107C2211yescharacteristic, complemented
34C2×C31×#107C2211yescharacteristic, complemented
35C2×C31×#106C2211yescharacteristic, complemented
36C2×C31×#106C2211yescharacteristic, complemented
37C2×C31×#103C2211yescharacteristic, complemented
38C2×C31×#103C2211yescharacteristic, complemented
39C2×C31×#103C2211yescharacteristic, complemented
40C2×C31×#103C2211yescharacteristic, complemented
41C2×C31×#102C2211yescharacteristic, complemented
42C2×C31×#102C2211yescharacteristic, complemented
43C2×C31×#102C2211yescharacteristic, complemented
44C2×C31×#102C2211yescharacteristic, complemented
45C2×C31×C22⋊C8C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×C22⋊C8C2211yescharacteristic
49C2×C31×C22⋊C8C2211yescharacteristic
50C2×C31×C22⋊C8C2211yescharacteristic
51C31×#381—21no—
52C31×#380C2211yescharacteristic
53C31×#380C2211yescharacteristic
54C31×#380C2211yescharacteristic
55C31×#380C2211yescharacteristic
56C31×#379—21no—
57C4×C22⋊C4×C31—21no—
58C4×C22⋊C4×C31—21no—
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C25×C31D411yescharacteristic
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—41no—
69C2×#41×C31—41no—
70C22×Q8×C31C2311yescharacteristic
71C22×D4×C31—21no—
72C22×D4×C31—21no—
73C22×D4×C31—21no—
74C22×D4×C31C2311yescharacteristic
75C23×C4×C31—21no—
76C23×C4×C31—22no—
77C23×C4×C31—22no—
78C23×C4×C31—22no—
79C23×C4×C31—22no—
80C23×C4×C31—41no—
81C23×C4×C31—41no—
82C23×C4×C31D411yescharacteristic
83C23×C4×C31D411yescharacteristic
84C23×C4×C31D411yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C23×C4×C31C2311yescharacteristic
88C22×C8×C31C2311yescharacteristic
89C22×C8×C31C2311yescharacteristic
90C22×C8×C31C2311yescharacteristic
91C22×C8×C31C2311yescharacteristic
92C31×#123—28no—
93C31×C22⋊Q8—22no—
94C31×C22⋊Q8—22no—
95C31×C22⋊Q8—22no—
96C31×C22⋊Q8D414yes—
97C31×#121—22no—
98C31×#121—22no—
99C31×#121—22no—
100C31×#121D414yes—
101C31×#120—28no—
102C4×D4×C31—28no—
103C4×D4×C31—28no—
104C31×#117—22no—
105C31×#117—22no—
106C31×#117—22no—
107C31×#117—22no—
108C31×#117—41no—
109C31×#117—41no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C42×C31—21no—
130C2×C42×C31—21no—
131C2×C42×C31—21no—
132C31×#107—22no—
133C31×#107—22no—
134C31×#106—22no—
135C31×#106—22no—
136C31×#103—22no—
137C31×#103—22no—
138C31×#103—41no—
139C31×#103—41no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—41no—
143C31×#102—41no—
144C31×C22⋊C8—22no—
145C31×C22⋊C8—22no—
146C31×C22⋊C8—22no—
147C31×C22⋊C8—22no—
148C31×C22⋊C8—41no—
149C31×C22⋊C8—41no—
150C31×#95—21no—
151C31×#95—21no—
152C31×#95—21no—
153C31×#95—21no—
154C24×C31—22no—
155C24×C31—22no—
156C24×C31—22no—
157C24×C31—21no—
158C24×C31—41no—
159C24×C31—41no—
160C24×C31—41no—
161C24×C31—41no—
162C24×C31C2×D411yescharacteristic
163C24×C31C2×D411yescharacteristic
164C24×C31C2×D411yescharacteristic
165#41×C31—44no—
166#41×C31—44no—
167#41×C31—44no—
168#41×C31—44no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31—21no—
172C2×Q8×C31—21no—
173C2×Q8×C31—21no—
174C2×Q8×C31C2×D412yes—
175C2×D4×C31—24no—
176C2×D4×C31—24no—
177C2×D4×C31—24no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—21no—
183C2×D4×C31—42no—
184C2×D4×C31—42no—
185C2×D4×C31—42no—
186C2×D4×C31—42no—
187C2×D4×C31—42no—
188C2×D4×C31—42no—
189C2×D4×C31C2×D412yes—
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—24no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—22no—
205C22×C4×C31—22no—
206C22×C4×C31—22no—
207C22×C4×C31—22no—
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—41no—
219C22×C4×C31—41no—
220C22×C4×C31—41no—
221C22×C4×C31—44no—
222C22×C4×C31—44no—
223C22×C4×C31—44no—
224C22×C4×C31—44no—
225C22×C4×C31—42no—
226C22×C4×C31—42no—
227C22×C4×C31C2×D411yescharacteristic
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D412yes—
230C22×C4×C31C2×D412yes—
231C22×C4×C31C2×D411yescharacteristic
232C22×C4×C31#4112yes—
233C22×C4×C31#4112yes—
234C22×C4×C31C2411yescharacteristic
235C2×C8×C31—21no—
236C2×C8×C31—21no—
237C2×C8×C31—21no—
238C2×C8×C31—21no—
239C2×C8×C31—21no—
240C2×C8×C31—21no—
241C2×C8×C31—21no—
242C2×C8×C31—21no—
243C2×C8×C31—21no—
244C2×C8×C31—21no—
245C2×C8×C31—21no—
246C2×C8×C31—21no—
247C4⋊C4×C31—24no—
248C4⋊C4×C31—24no—
249C4⋊C4×C31—21no—
250C4⋊C4×C31—21no—
251C4⋊C4×C31—21no—
252C4⋊C4×C31—21no—
253C4⋊C4×C31—21no—
254C4⋊C4×C31—21no—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—21no—
257C4⋊C4×C31—21no—
258C4⋊C4×C31—21no—
259C4⋊C4×C31C2×D412yes—
260C4⋊C4×C31C2×D412yes—
261C22⋊C4×C31—24no—
262C22⋊C4×C31—24no—
263C22⋊C4×C31—24no—
264C22⋊C4×C31—24no—
265C22⋊C4×C31—24no—
266C22⋊C4×C31—42no—
267C22⋊C4×C31—42no—
268C22⋊C4×C31—42no—
269C22⋊C4×C31—42no—
270C22⋊C4×C31—42no—
271C22⋊C4×C31—42no—
272C42×C31—24no—
273C42×C31—42no—
274C42×C31—42no—
275#24008C3111yesmaximal, characteristic, direct product factor, Sylow
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—21no—
282C23×C31—21no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—21no—
289C23×C31—21no—
290C23×C31—21no—
291C23×C31—21no—
292C23×C31—21no—
293C23×C31—21no—
294C23×C31—22no—
295C23×C31—44no—
296C23×C31—44no—
297C23×C31—44no—
298C23×C31—44no—
299C23×C31—44no—
300C23×C31—44no—
301C23×C31—44no—
302C23×C31—41no—
303C23×C31—41no—
304C23×C31—41no—
305C23×C31—41no—
306C23×C31—41no—
307C23×C31—41no—
308C23×C31#12012yes—
309C23×C31#12312yes—
310C23×C31#13512yes—
311C23×C31C22×D411yescharacteristic
312Q8×C31—22no—
313Q8×C31—22no—
314Q8×C31—41no—
315Q8×C31—41no—
316D4×C31—22no—
317D4×C31—22no—
318D4×C31—48no—
319D4×C31—48no—
320D4×C31—48no—
321D4×C31—41no—
322D4×C31—41no—
323C2×C4×C31—21no—
324C2×C4×C31—21no—
325C2×C4×C31—21no—
326C2×C4×C31—21no—
327C2×C4×C31—22no—
328C2×C4×C31—22no—
329C2×C4×C31—22no—
330C2×C4×C31—22no—
331C2×C4×C31—22no—
332C2×C4×C31—22no—
333C2×C4×C31—22no—
334C2×C4×C31—22no—
335C2×C4×C31—22no—
336C2×C4×C31—22no—
337C2×C4×C31—21no—
338C2×C4×C31—22no—
339C2×C4×C31—21no—
340C2×C4×C31—21no—
341C2×C4×C31—44no—
342C2×C4×C31—44no—
343C2×C4×C31—44no—
344C2×C4×C31—48no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—41no—
357C2×C4×C31—41no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—41no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31#12012yes—
368C2×C4×C31#12312yes—
369C2×C4×C31C22×D411yescharacteristic
370C2×C4×C31C22×D411yescharacteristic
371C2×C4×C31C2×#4111yescharacteristic
372C2×C4×C31C2×#4111yescharacteristic
373C2×C4×C31H(5,𝔽2)11yescharacteristic
374C2×C4×C31H(5,𝔽2)11yescharacteristic
375C8×C31—41no—
376C8×C31—41no—
377C8×C31—41no—
378C8×C31—41no—
379C2×#525C2×C3111yescharacteristic
380C2×#485C2×C3111yescharacteristic, complemented
381C2×#482C2×C3111yescharacteristic, complemented
382#2280C2×C3111yescharacteristic, complemented
383#2036C2×C3111yescharacteristic, complemented
384#2035C2×C3111yescharacteristic, complemented
385#2034C2×C3111yescharacteristic, complemented
386#2033C2×C3111yescharacteristic, complemented
387#1875C2×C3111yescharacteristic, complemented
388#1873C2×C3111yescharacteristic, complemented
389#1854C2×C3111yescharacteristic, complemented
390#1854C2×C3111yescharacteristic, complemented
391#1788C2×C3111yescharacteristic, complemented
392#1788C2×C3111yescharacteristic, complemented
393#1779C2×C3111yescharacteristic, complemented
394C22×C31—22no—
395C22×C31—22no—
396C22×C31—22no—
397C22×C31—22no—
398C22×C31—22no—
399C22×C31—22no—
400C22×C31—22no—
401C22×C31—22no—
402C22×C31—22no—
403C22×C31—416no—
404C22×C31—41no—
405C22×C31—41no—
406C22×C31—41no—
407C22×C31—41no—
408C22×C31—41no—
409C22×C31—41no—
410C22×C31—41no—
411C22×C31—41no—
412C22×C31—41no—
413C22×C31—41no—
414C22×C31—41no—
415C22×C31—41no—
416C22×C31—42no—
417C22×C31—42no—
418C22×C31—42no—
419C22×C31—81no—
420C22×C31—81no—
421C22×C31—81no—
422C22×C31—81no—
423C22×C31C2×#12011yescharacteristic
424C22×C31C2×#12311yescharacteristic
425C22×C31#53411yescharacteristic
426C22×C31C2×#13511yescharacteristic
427C22×C31#57511yescharacteristic
428C22×C31#57511yescharacteristic
429C22×C31#57511yescharacteristic
430C4×C31—22no—
431C4×C31—22no—
432C4×C31—41no—
433C4×C31—42no—
434C4×C31—42no—
435C4×C31—42no—
436C4×C31—81no—
437C4×C31—81no—
438C4×C31—81no—
439C4×C31—81no—
440C4×C31#54611yescharacteristic
441C4×C31#54611yescharacteristic
442C4×C31#54611yescharacteristic
443C4×C31#54611yescharacteristic
444C22×#41C22×C3111yescharacteristic
445C24×C4C22×C3111yescharacteristic
446#525—24no—
447#525—24no—
448C2×#123—21no—
449C2×C22⋊Q8C22×C3111yescharacteristic
450C2×C22⋊Q8C22×C3111yescharacteristic
451C2×#121C22×C3111yescharacteristic
452C2×#121C22×C3111yescharacteristic
453C2×#120—21no—
454C2×C4×D4—21no—
455C2×C4×D4—21no—
456C2×#117C22×C3111yescharacteristic
457C2×#117C22×C3111yescharacteristic
458C2×#117C22×C3111yescharacteristic
459#485—24no—
460#482—24no—
461C2×#107C22×C3111yescharacteristic, complemented
462C2×#107C22×C3111yescharacteristic, complemented
463C2×#106C22×C3111yescharacteristic, complemented
464C2×#106C22×C3111yescharacteristic, complemented
465C2×#103C22×C3111yescharacteristic, complemented
466C2×#103C22×C3111yescharacteristic, complemented
467C2×#103C22×C3111yescharacteristic, complemented
468C2×#103C22×C3111yescharacteristic, complemented
469C2×#102C22×C3111yescharacteristic, complemented
470C2×#102C22×C3111yescharacteristic, complemented
471C2×#102C22×C3111yescharacteristic, complemented
472C2×#102C22×C3111yescharacteristic, complemented
473C2×C22⋊C8C22×C3111yescharacteristic
474C2×C22⋊C8C22×C3111yescharacteristic
475C2×C22⋊C8C22×C3111yescharacteristic
476C2×C22⋊C8C22×C3111yescharacteristic
477C2×C22⋊C8C22×C3111yescharacteristic
478C2×C22⋊C8C22×C3111yescharacteristic
479#381—21no—
480#380C22×C3111yescharacteristic
481#380C22×C3111yescharacteristic
482#380C22×C3111yescharacteristic
483#380C22×C3111yescharacteristic
484#379—21no—
485C4×C22⋊C4—21no—
486C4×C22⋊C4—21no—
487#340C22×C3111yescharacteristic, complemented
488#340C22×C3111yescharacteristic, complemented
489#340C22×C3111yescharacteristic, complemented
490#340C22×C3111yescharacteristic, complemented
491C2×C31—42no—
492C2×C31—42no—
493C2×C31—42no—
494C2×C31—82no—
495C2×C31#240511yescharacteristic
496C2×C31#300211yescharacteristic
497C2×C31#300511yescharacteristic
498C2×C31#309111yescharacteristic
499C2×C31#309311yescharacteristic
500C2×C31#319111yescharacteristic
501C2×C31#319711yescharacteristic
502C25D4×C3111yescharacteristic
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8C23×C3111yescharacteristic
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4C23×C3111yescharacteristic
514C23×C4—21no—
515C23×C4—22no—
516C23×C4—22no—
517C23×C4—22no—
518C23×C4—22no—
519C23×C4—41no—
520C23×C4—41no—
521C23×C4D4×C3111yescharacteristic
522C23×C4D4×C3111yescharacteristic
523C23×C4D4×C3111yescharacteristic
524C23×C4C23×C3111yescharacteristic
525C23×C4C23×C3111yescharacteristic
526C23×C4C23×C3111yescharacteristic
527C22×C8C23×C3111yescharacteristic
528C22×C8C23×C3111yescharacteristic
529C22×C8C23×C3111yescharacteristic
530C22×C8C23×C3111yescharacteristic
531#123—28no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8D4×C3114yes—
536#121—22no—
537#121—22no—
538#121—22no—
539#121D4×C3114yes—
540#120—28no—
541C4×D4—28no—
542C4×D4—28no—
543#117—22no—
544#117—22no—
545#117—22no—
546#117—22no—
547#117—41no—
548#117—41no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4C23×C3111yescharacteristic
552C2×C4⋊C4C23×C3111yescharacteristic
553C2×C4⋊C4C23×C3111yescharacteristic
554C2×C4⋊C4C23×C3111yescharacteristic
555C2×C4⋊C4C23×C3111yescharacteristic
556C2×C4⋊C4C23×C3111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C42—21no—
569C2×C42—21no—
570C2×C42—21no—
571#107—22no—
572#107—22no—
573#106—22no—
574#106—22no—
575#103—22no—
576#103—22no—
577#103—41no—
578#103—41no—
579#102—22no—
580#102—22no—
581#102—41no—
582#102—41no—
583C22⋊C8—22no—
584C22⋊C8—22no—
585C22⋊C8—22no—
586C22⋊C8—22no—
587C22⋊C8—41no—
588C22⋊C8—41no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—21no—
593C31#2400811yescharacteristic, direct product factor, Sylow
594C24—22no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—41no—
599C24—41no—
600C24—41no—
601C24—41no—
602C24C2×D4×C3111yescharacteristic
603C24C2×D4×C3111yescharacteristic
604C24C2×D4×C3111yescharacteristic
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8C2×D4×C3112yes—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4C2×D4×C3112yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C3111yescharacteristic
668C22×C4C2×D4×C3111yescharacteristic
669C22×C4C2×D4×C3112yes—
670C22×C4C2×D4×C3112yes—
671C22×C4C2×D4×C3111yescharacteristic
672C22×C4#41×C3112yes—
673C22×C4#41×C3112yes—
674C22×C4C24×C3111yescharacteristic
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4C2×D4×C3112yes—
700C4⋊C4C2×D4×C3112yes—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C42—24no—
713C42—42no—
714C42—42no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23C31×#12012yes—
748C23C31×#12312yes—
749C23C31×#13512yes—
750C23C22×D4×C3111yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—41no—
754Q8—41no—
755D4—22no—
756D4—22no—
757D4—48no—
758D4—48no—
759D4—48no—
760D4—41no—
761D4—41no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—48no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4C31×#12012yes—
807C2×C4C31×#12312yes—
808C2×C4C22×D4×C3111yescharacteristic
809C2×C4C22×D4×C3111yescharacteristic
810C2×C4C2×#41×C3111yescharacteristic
811C2×C4C2×#41×C3111yescharacteristic
812C2×C4C31×H(5,𝔽2)11yescharacteristic
813C2×C4C31×H(5,𝔽2)11yescharacteristic
814C8—41no—
815C8—41no—
816C8—41no—
817C8—41no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—416no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22C2×C31×#12011yescharacteristic
848C22C2×C31×#12311yescharacteristic
849C22C31×#53411yescharacteristic
850C22C2×C31×#13511yescharacteristic
851C22C31×#57511yescharacteristic
852C22C31×#57511yescharacteristic
853C22C31×#57511yescharacteristic
854C4—22no—
855C4—22no—
856C4—41no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4C31×#54611yescharacteristic
865C4C31×#54611yescharacteristic
866C4C31×#54611yescharacteristic
867C4C31×#54611yescharacteristic
868C2—42no—
869C2—42no—
870C2—42no—
871C2—82no—
872C2C31×#240511yescharacteristic
873C2C31×#300211yescharacteristic
874C2C31×#300511yescharacteristic
875C2C31×#309111yescharacteristic
876C2C31×#309311yescharacteristic
877C2C31×#319111yescharacteristic
878C2C31×#319711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#485C2semidirect
3. C2×C31×#482C2semidirect
4. C31×#2280C2semidirect
5. C31×#2036C2semidirect
6. C31×#2035C2semidirect
7. C31×#2034C2semidirect
8. C31×#2033C2semidirect
9. C31×#1875C2semidirect
10. C31×#1873C2semidirect
11. C31×#1854C2semidirect
12. C31×#1854C2semidirect
13. C31×#1788C2semidirect
14. C31×#1788C2semidirect
15. C31×#1779C2semidirect
33. C2×C31×#107C22semidirect
34. C2×C31×#107C22semidirect
35. C2×C31×#106C22semidirect
36. C2×C31×#106C22semidirect
37. C2×C31×#103C22semidirect
38. C2×C31×#103C22semidirect
39. C2×C31×#103C22semidirect
40. C2×C31×#103C22semidirect
41. C2×C31×#102C22semidirect
42. C2×C31×#102C22semidirect
43. C2×C31×#102C22semidirect
44. C2×C31×#102C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
275. #24008C31direct (N × H)
380. C2×#485C2×C31semidirect
381. C2×#482C2×C31semidirect
382. #2280C2×C31semidirect
383. #2036C2×C31semidirect
384. #2035C2×C31semidirect
385. #2034C2×C31semidirect
386. #2033C2×C31semidirect
387. #1875C2×C31semidirect
388. #1873C2×C31semidirect
389. #1854C2×C31semidirect
390. #1854C2×C31semidirect
391. #1788C2×C31semidirect
392. #1788C2×C31semidirect
393. #1779C2×C31semidirect
461. C2×#107C22×C31semidirect
462. C2×#107C22×C31semidirect
463. C2×#106C22×C31semidirect
464. C2×#106C22×C31semidirect
465. C2×#103C22×C31semidirect
466. C2×#103C22×C31semidirect
467. C2×#103C22×C31semidirect
468. C2×#103C22×C31semidirect
469. C2×#102C22×C31semidirect
470. C2×#102C22×C31semidirect
471. C2×#102C22×C31semidirect
472. C2×#102C22×C31semidirect
487. #340C22×C31semidirect
488. #340C22×C31semidirect
489. #340C22×C31semidirect
490. #340C22×C31semidirect
593. C31#24008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5252
C2×C31×#4852
C2×C31×#4822
C31×#22802
C31×#20362
C31×#20352
C31×#20342
C31×#20332
C31×#18752
C31×#18732
C31×#18542
C31×#17882
C31×#17792
#2400831