Finite Group Databasebeta

← C31×#24124 #21480883

Subgroups — C31×#24124 #21480883

Order 7936.

1216 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#553C211yesmaximal, characteristic, complemented
2C2×C31×#478C211yesmaximal, characteristic, complemented
3C2×C4×D8×C31C211yesmaximal, characteristic, complemented
4C31×#2535C211yesmaximal, characteristic, complemented
5C31×#2034C211yesmaximal, characteristic, complemented
6C31×#2033C211yesmaximal, characteristic, complemented
7C31×#1999C211yesmaximal, characteristic, complemented
8C31×#1999C211yesmaximal, characteristic, complemented
9C31×#1991C211yesmaximal, characteristic, complemented
10C31×#1954C211yesmaximal, characteristic, complemented
11C31×#1875C211yesmaximal, characteristic, complemented
12C31×#1874C211yesmaximal, characteristic, complemented
13C31×#1854C211yesmaximal, characteristic, complemented
14C31×#1852C211yesmaximal, characteristic, complemented
15C31×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C31C2211yescharacteristic
17C31×#553—24no—
18C31×#553—24no—
19C2×C31×#126—21no—
20C2×C31×#125C2211yescharacteristic
21C2×C31×#123—21no—
22C2×C31×#121—21no—
23C2×C31×#121C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C31×#121C2211yescharacteristic
26C2×C31×#121C2211yescharacteristic
27C2×C4×D4×C31—21no—
28C2×C4×D4×C31C2211yescharacteristic
29C2×C4×D4×C31C2211yescharacteristic
30C2×C4×D4×C31C2211yescharacteristic
31C2×C31×#117C2211yescharacteristic
32C22×C4⋊C4×C31C2211yescharacteristic
33C31×#478—24no—
34C4×D8×C31—24no—
35C2×C31×#107C2211yescharacteristic
36C2×C31×#107C2211yescharacteristic
37C2×C31×#106C2211yescharacteristic
38C2×C31×C4⋊C8C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×C22⋊C8C2211yescharacteristic
49C2×C4×C8×C31C2211yescharacteristic
50C31×#397—21no—
51C31×#392—21no—
52C31×#386—21no—
53C31×#386—21no—
54C31×#382C2211yescharacteristic
55C31×#380C2211yescharacteristic
56C31×#380C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31D411yescharacteristic
68C22×D4×C31C2311yescharacteristic
69C22×D4×C31C2311yescharacteristic
70C23×C4×C31—21no—
71C23×C4×C31—21no—
72C23×C4×C31—21no—
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C2×D8×C31—22no—
76C2×D8×C31—22no—
77C2×D8×C31—22no—
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C31×#126—28no—
83C31×#125—22no—
84C31×#125D414yescomplemented
85C31×#123—28no—
86C31×#121—28no—
87C31×#121—22no—
88C31×#121—22no—
89C31×#121—22no—
90C31×#121—22no—
91C31×#121—22no—
92C31×#121—22no—
93C31×#121—41no—
94C31×#121—41no—
95C4×D4×C31—28no—
96C4×D4×C31—22no—
97C4×D4×C31—22no—
98C4×D4×C31—22no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31D414yescomplemented
102C31×#117—22no—
103C31×#117—22no—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—22no—
108C2×C4⋊C4×C31—22no—
109C2×C4⋊C4×C31D411yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
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×C31D411yescharacteristic
126C2×C22⋊C4×C31D411yescharacteristic
127C2×C42×C31—21no—
128C2×C42×C31C2311yescharacteristic
129C31×#107—22no—
130C31×#107—22no—
131C31×#106—22no—
132C31×C4⋊C8—22no—
133C31×#102—22no—
134C31×#102—22no—
135C31×#102—22no—
136C31×#102—22no—
137C31×#102—41no—
138C31×#102—41no—
139C31×C22⋊C8—22no—
140C31×C22⋊C8—22no—
141C31×C22⋊C8—41no—
142C31×C22⋊C8—41no—
143C4×C8×C31—22no—
144C31×#95—21no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C24×C31—21no—
149C24×C31—21no—
150C24×C31C2×D411yescharacteristic
151C24×C31C2×D411yescharacteristic
152C2×D4×C31—24no—
153C2×D4×C31—22no—
154C2×D4×C31—24no—
155C2×D4×C31—22no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—41no—
167C2×D4×C31—42no—
168C2×D4×C31—42no—
169C2×D4×C31—42no—
170C2×D4×C31—42no—
171C2×D4×C31—42no—
172C2×D4×C31—42no—
173C2×D4×C31—81no—
174C2×D4×C31—81no—
175C2×D4×C31—81no—
176C2×D4×C31—81no—
177C2×D4×C31C2×D412yes—
178C2×D4×C31#4112yes—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—24no—
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—24no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—42no—
200C22×C4×C31—81no—
201C22×C4×C31—81no—
202C22×C4×C31—81no—
203C22×C4×C31—81no—
204C22×C4×C31—81no—
205C22×C4×C31—81no—
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2411yescharacteristic
211D8×C31—28no—
212C2×C8×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31—21no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31—21no—
218C2×C8×C31—21no—
219C2×C8×C31—21no—
220C2×C8×C31—21no—
221C2×C8×C31—21no—
222C2×C8×C31—21no—
223C2×C8×C31#4112yes—
224C4⋊C4×C31—24no—
225C4⋊C4×C31—24no—
226C4⋊C4×C31—24no—
227C4⋊C4×C31—22no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31C2×D412yes—
238C4⋊C4×C31C2×D412yes—
239C4⋊C4×C31C2×D412yes—
240C22⋊C4×C31—24no—
241C22⋊C4×C31—24no—
242C22⋊C4×C31—24no—
243C22⋊C4×C31—24no—
244C22⋊C4×C31—22no—
245C22⋊C4×C31—22no—
246C22⋊C4×C31—42no—
247C22⋊C4×C31—42no—
248C22⋊C4×C31—42no—
249C22⋊C4×C31—81no—
250C22⋊C4×C31—81no—
251C42×C31—24no—
252C42×C31C2×D412yes—
253C42×C31C2×D412yes—
254#24124C3111yesmaximal, characteristic, direct product factor, Sylow
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—22no—
263C23×C31—22no—
264C23×C31—21no—
265C23×C31—21no—
266C23×C31—21no—
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31#13512yes—
283C23×C31C22×D411yescharacteristic
284D4×C31—22no—
285D4×C31—22no—
286D4×C31—22no—
287D4×C31—22no—
288D4×C31—44no—
289D4×C31—48no—
290D4×C31—41no—
291D4×C31—41no—
292D4×C31—41no—
293D4×C31—41no—
294D4×C31—84no—
295D4×C31—84no—
296D4×C31—84no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—21no—
305C2×C4×C31—22no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—84no—
334C2×C4×C31—84no—
335C2×C4×C31—84no—
336C2×C4×C31#12012yes—
337C2×C4×C31#12012yes—
338C2×C4×C31C22×D411yescharacteristic
339C2×C4×C31C22×D411yescharacteristic
340C2×C4×C31C2×#4111yescharacteristic
341C2×C4×C31C2×#4111yescharacteristic
342C2×C4×C31H(5,𝔽2)11yescharacteristic
343C2×C4×C312−1+411yescharacteristic
344C8×C31—22no—
345C8×C31—41no—
346C8×C31—41no—
347C8×C31—41no—
348C2×#553C2×C3111yescharacteristic, complemented
349C2×#478C2×C3111yescharacteristic, complemented
350C2×C4×D8C2×C3111yescharacteristic, complemented
351#2535C2×C3111yescharacteristic, complemented
352#2034C2×C3111yescharacteristic, complemented
353#2033C2×C3111yescharacteristic, complemented
354#1999C2×C3111yescharacteristic, complemented
355#1999C2×C3111yescharacteristic, complemented
356#1991C2×C3111yescharacteristic, complemented
357#1954C2×C3111yescharacteristic, complemented
358#1875C2×C3111yescharacteristic, complemented
359#1874C2×C3111yescharacteristic, complemented
360#1854C2×C3111yescharacteristic, complemented
361#1852C2×C3111yescharacteristic, complemented
362#1804C2×C3111yescharacteristic, complemented
363C22×C31—22no—
364C22×C31—22no—
365C22×C31—22no—
366C22×C31—41no—
367C22×C31—41no—
368C22×C31—41no—
369C22×C31—41no—
370C22×C31—41no—
371C22×C31—41no—
372C22×C31—41no—
373C22×C31—42no—
374C22×C31—42no—
375C22×C31—41no—
376C22×C31—42no—
377C22×C31—42no—
378C22×C31—41no—
379C22×C31—42no—
380C22×C31—41no—
381C22×C31—41no—
382C22×C31—42no—
383C22×C31—81no—
384C22×C31—81no—
385C22×C31—81no—
386C22×C31—81no—
387C22×C31—81no—
388C22×C31—81no—
389C22×C31—81no—
390C22×C31—81no—
391C22×C31C2×#12011yescharacteristic
392C22×C31#54611yescharacteristic
393C22×C31#54711yescharacteristic
394C22×C31C2×#13511yescharacteristic
395C22×C31#57511yescharacteristic
396C22×C31#57611yescharacteristic
397C22×C31#57611yescharacteristic
398C4×C31—22no—
399C4×C31—22no—
400C4×C31—41no—
401C4×C31—41no—
402C4×C31—42no—
403C4×C31—42no—
404C4×C31—42no—
405C4×C31—81no—
406C4×C31—81no—
407C4×C31—81no—
408C4×C31#52511yescharacteristic
409C4×C31#53711yescharacteristic
410C4×C31#54811yescharacteristic
411C4×C31#55011yescharacteristic
412C22×D8C22×C3111yescharacteristic
413#553—24no—
414#553—24no—
415C2×#126—21no—
416C2×#125C22×C3111yescharacteristic
417C2×#123—21no—
418C2×#121—21no—
419C2×#121C22×C3111yescharacteristic
420C2×#121C22×C3111yescharacteristic
421C2×#121C22×C3111yescharacteristic
422C2×#121C22×C3111yescharacteristic
423C2×C4×D4—21no—
424C2×C4×D4C22×C3111yescharacteristic
425C2×C4×D4C22×C3111yescharacteristic
426C2×C4×D4C22×C3111yescharacteristic
427C2×#117C22×C3111yescharacteristic
428C22×C4⋊C4C22×C3111yescharacteristic
429#478—24no—
430C4×D8—24no—
431C2×#107C22×C3111yescharacteristic
432C2×#107C22×C3111yescharacteristic
433C2×#106C22×C3111yescharacteristic
434C2×C4⋊C8C22×C3111yescharacteristic
435C2×#102C22×C3111yescharacteristic
436C2×#102C22×C3111yescharacteristic
437C2×#102C22×C3111yescharacteristic
438C2×#102C22×C3111yescharacteristic
439C2×#102C22×C3111yescharacteristic
440C2×#102C22×C3111yescharacteristic
441C2×C22⋊C8C22×C3111yescharacteristic
442C2×C22⋊C8C22×C3111yescharacteristic
443C2×C22⋊C8C22×C3111yescharacteristic
444C2×C22⋊C8C22×C3111yescharacteristic
445C2×C4×C8C22×C3111yescharacteristic
446#397—21no—
447#392—21no—
448#386—21no—
449#386—21no—
450#382C22×C3111yescharacteristic
451#380C22×C3111yescharacteristic
452#380C22×C3111yescharacteristic
453#340C22×C3111yescharacteristic
454#340C22×C3111yescharacteristic
455#340C22×C3111yescharacteristic
456#340C22×C3111yescharacteristic
457#340C22×C3111yescharacteristic
458#340C22×C3111yescharacteristic
459C2×C31—42no—
460C2×C31—81no—
461C2×C31—82no—
462C2×C31—82no—
463C2×C31#240711yescharacteristic
464C2×C31#300211yescharacteristic
465C2×C31#300811yescharacteristic
466C2×C31#329711yescharacteristic
467C2×C31#332211yescharacteristic
468C2×C31#333911yescharacteristic
469C2×C31#335511yescharacteristic
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4D4×C3111yescharacteristic
475C22×D4C23×C3111yescharacteristic
476C22×D4C23×C3111yescharacteristic
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—21no—
480C23×C4C23×C3111yescharacteristic
481C23×C4C23×C3111yescharacteristic
482C2×D8—22no—
483C2×D8—22no—
484C2×D8—22no—
485C22×C8C23×C3111yescharacteristic
486C22×C8C23×C3111yescharacteristic
487C22×C8C23×C3111yescharacteristic
488C22×C8C23×C3111yescharacteristic
489#126—28no—
490#125—22no—
491#125D4×C3114yescomplemented
492#123—28no—
493#121—28no—
494#121—22no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—41no—
501#121—41no—
502C4×D4—28no—
503C4×D4—22no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4D4×C3114yescomplemented
509#117—22no—
510#117—22no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4D4×C3111yescharacteristic
517C2×C4⋊C4C23×C3111yescharacteristic
518C2×C4⋊C4C23×C3111yescharacteristic
519C2×C4⋊C4C23×C3111yescharacteristic
520C2×C4⋊C4C23×C3111yescharacteristic
521C2×C4⋊C4C23×C3111yescharacteristic
522C2×C4⋊C4C23×C3111yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4D4×C3111yescharacteristic
533C2×C22⋊C4D4×C3111yescharacteristic
534C2×C42—21no—
535C2×C42C23×C3111yescharacteristic
536#107—22no—
537#107—22no—
538#106—22no—
539C4⋊C8—22no—
540#102—22no—
541#102—22no—
542#102—22no—
543#102—22no—
544#102—41no—
545#102—41no—
546C22⋊C8—22no—
547C22⋊C8—22no—
548C22⋊C8—41no—
549C22⋊C8—41no—
550C4×C8—22no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555C31#2412411yescharacteristic, direct product factor, Sylow
556C24—21no—
557C24—21no—
558C24C2×D4×C3111yescharacteristic
559C24C2×D4×C3111yescharacteristic
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—24no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4C2×D4×C3112yes—
586C2×D4#41×C3112yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4C2×D4×C3111yescharacteristic
615C22×C4C2×D4×C3111yescharacteristic
616C22×C4C2×D4×C3111yescharacteristic
617C22×C4C2×D4×C3111yescharacteristic
618C22×C4C24×C3111yescharacteristic
619D8—28no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8#41×C3112yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4C2×D4×C3112yes—
646C4⋊C4C2×D4×C3112yes—
647C4⋊C4C2×D4×C3112yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42C2×D4×C3112yes—
661C42C2×D4×C3112yes—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23C31×#13512yes—
690C23C22×D4×C3111yescharacteristic
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—44no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4—84no—
703D4—84no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4C31×#12012yes—
744C2×C4C31×#12012yes—
745C2×C4C22×D4×C3111yescharacteristic
746C2×C4C22×D4×C3111yescharacteristic
747C2×C4C2×#41×C3111yescharacteristic
748C2×C4C2×#41×C3111yescharacteristic
749C2×C4C31×H(5,𝔽2)11yescharacteristic
750C2×C4C31×2−1+411yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—42no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—41no—
773C22—41no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×C31×#12011yescharacteristic
784C22C31×#54611yescharacteristic
785C22C31×#54711yescharacteristic
786C22C2×C31×#13511yescharacteristic
787C22C31×#57511yescharacteristic
788C22C31×#57611yescharacteristic
789C22C31×#57611yescharacteristic
790C4—22no—
791C4—22no—
792C4—41no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4C31×#52511yescharacteristic
801C4C31×#53711yescharacteristic
802C4C31×#54811yescharacteristic
803C4C31×#55011yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—82no—
808C2C31×#240711yescharacteristic
809C2C31×#300211yescharacteristic
810C2C31×#300811yescharacteristic
811C2C31×#329711yescharacteristic
812C2C31×#332211yescharacteristic
813C2C31×#333911yescharacteristic
814C2C31×#335511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#553C2semidirect
2. C2×C31×#478C2semidirect
3. C2×C4×D8×C31C2semidirect
4. C31×#2535C2semidirect
5. C31×#2034C2semidirect
6. C31×#2033C2semidirect
7. C31×#1999C2semidirect
8. C31×#1999C2semidirect
9. C31×#1991C2semidirect
10. C31×#1954C2semidirect
11. C31×#1875C2semidirect
12. C31×#1874C2semidirect
13. C31×#1854C2semidirect
14. C31×#1852C2semidirect
15. C31×#1804C2semidirect
84. C31×#125D4semidirect
101. C4×D4×C31D4semidirect
254. #24124C31direct (N × H)
348. C2×#553C2×C31semidirect
349. C2×#478C2×C31semidirect
350. C2×C4×D8C2×C31semidirect
351. #2535C2×C31semidirect
352. #2034C2×C31semidirect
353. #2033C2×C31semidirect
354. #1999C2×C31semidirect
355. #1999C2×C31semidirect
356. #1991C2×C31semidirect
357. #1954C2×C31semidirect
358. #1875C2×C31semidirect
359. #1874C2×C31semidirect
360. #1854C2×C31semidirect
361. #1852C2×C31semidirect
362. #1804C2×C31semidirect
491. #125D4×C31semidirect
508. C4×D4D4×C31semidirect
555. C31#24124direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5532
C2×C31×#4782
C2×C4×D8×C312
C31×#25352
C31×#20342
C31×#20332
C31×#19992
C31×#19912
C31×#19542
C31×#18752
C31×#18742
C31×#18542
C31×#18522
C31×#18042
#2412431