Finite Group Databasebeta

← C31×#25575 #21482334

Subgroups — C31×#25575 #21482334

Order 7936.

1238 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#553C211yesmaximal, characteristic, complemented
2C2×C31×#488C211yesmaximal, characteristic, complemented
3C2×C31×#463C211yesmaximal, characteristic, complemented
4C31×#2540C211yesmaximal, characteristic, complemented
5C31×#2000C211yesmaximal, characteristic, complemented
6C31×#2000C211yesmaximal, characteristic, complemented
7C31×#1999C211yesmaximal, characteristic, complemented
8C31×#1999C211yesmaximal, characteristic, complemented
9C31×#1989C211yesmaximal, characteristic, complemented
10C31×#1954C211yesmaximal, characteristic, complemented
11C31×#1875C211yesmaximal, characteristic, complemented
12C31×#1874C211yesmaximal, characteristic, complemented
13C31×#1873C211yesmaximal, characteristic, complemented
14C31×#1872C211yesmaximal, characteristic, complemented
15C4×C31×#102C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C31×#553—24no—
19C31×#553—24no—
20C2×C31×#126—21no—
21C2×C31×#125C2211yescharacteristic
22C2×C31×#124C2211yescharacteristic
23C2×C31×#123—21no—
24C2×C31×C22⋊Q8C2211yescharacteristic
25C2×C31×C22⋊Q8C2211yescharacteristic
26C2×C31×#121—21no—
27C2×C31×#121C2211yescharacteristic
28C2×C31×#121C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C4×D4×C31—21no—
32C2×C4×D4×C31C2211yescharacteristic
33C2×C4×D4×C31C2211yescharacteristic
34C2×C31×#117C2211yescharacteristic
35C22×C4⋊C4×C31C2211yescharacteristic
36C31×#488—24no—
37C31×#463—24no—
38C2×C31×C4⋊C8C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×C22⋊C8C2211yescharacteristic
49C2×C31×C22⋊C8C2211yescharacteristic
50C2×C31×C22⋊C8C2211yescharacteristic
51C2×C4×C8×C31C2211yescharacteristic
52C31×#399—21no—
53C31×#392—21no—
54C31×#390—21no—
55C31×#390—21no—
56C4×C4⋊C4×C31C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31D411yescharacteristic
69C22×D4×C31C2311yescharacteristic
70C22×D4×C31C2311yescharacteristic
71C23×C4×C31—21no—
72C23×C4×C31—21no—
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C2×SD16×C31—22no—
76C2×SD16×C31—41no—
77C2×SD16×C31—41no—
78C2×D8×C31—22no—
79C2×D8×C31—41no—
80C2×D8×C31—41no—
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C31×#126—28no—
86C31×#125—22no—
87C31×#125D414yescomplemented
88C31×#124—22no—
89C31×#124—22no—
90C31×#123—28no—
91C31×C22⋊Q8—22no—
92C31×C22⋊Q8—22no—
93C31×C22⋊Q8—41no—
94C31×C22⋊Q8—41no—
95C31×#121—28no—
96C31×#121—22no—
97C31×#121—22no—
98C31×#121—22no—
99C31×#121—22no—
100C31×#121—22no—
101C31×#121—22no—
102C31×#121—41no—
103C31×#121—41no—
104C4×D4×C31—28no—
105C4×D4×C31—22no—
106C4×D4×C31—22no—
107C4×D4×C31—22no—
108C4×D4×C31D414yescomplemented
109C31×#117—22no—
110C31×#117—22no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31—22no—
115C2×C4⋊C4×C31—22no—
116C2×C4⋊C4×C31—21no—
117C2×C4⋊C4×C31—21no—
118C2×C4⋊C4×C31D411yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C4⋊C4×C31C2311yescharacteristic
121C2×C4⋊C4×C31C2311yescharacteristic
122C2×C4⋊C4×C31C2311yescharacteristic
123C2×C4⋊C4×C31C2311yescharacteristic
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×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31D411yescharacteristic
135C2×C22⋊C4×C31D411yescharacteristic
136C2×C42×C31—21no—
137C2×C42×C31—21no—
138C2×C42×C31C2311yescharacteristic
139C31×C4⋊C8—22no—
140C31×#103—22no—
141C31×#103—22no—
142C31×#103—22no—
143C31×#102—22no—
144C31×#102—22no—
145C31×#102—22no—
146C31×#102—22no—
147C31×#102—22no—
148C31×C22⋊C8—41no—
149C31×C22⋊C8—41no—
150C31×C22⋊C8—41no—
151C31×C22⋊C8—41no—
152C4×C8×C31—22no—
153C31×#95—21no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31C2×D411yescharacteristic
157C24×C31C2×D411yescharacteristic
158C2×Q8×C31—21no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31—21no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×D4×C31—24no—
165C2×D4×C31—22no—
166C2×D4×C31—24no—
167C2×D4×C31—22no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—41no—
180C2×D4×C31—42no—
181C2×D4×C31—42no—
182C2×D4×C31—42no—
183C2×D4×C31—42no—
184C2×D4×C31—42no—
185C2×D4×C31—42no—
186C2×D4×C31—81no—
187C2×D4×C31—81no—
188C2×D4×C31—81no—
189C2×D4×C31—81no—
190C2×D4×C31C2×D412yes—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—24no—
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—24no—
210C22×C4×C31—21no—
211C22×C4×C31—81no—
212C22×C4×C31—81no—
213C22×C4×C31—81no—
214C22×C4×C31—81no—
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219C22×C4×C31C2411yescharacteristic
220SD16×C31—44no—
221D8×C31—44no—
222C2×C8×C31—21no—
223C2×C8×C31—21no—
224C2×C8×C31—21no—
225C2×C8×C31—21no—
226C2×C8×C31—21no—
227C2×C8×C31—21no—
228C2×C8×C31—21no—
229C2×C8×C31—21no—
230C2×C8×C31—21no—
231C2×C8×C31—21no—
232C2×C8×C31—21no—
233C2×C8×C31—21no—
234C4⋊C4×C31—24no—
235C4⋊C4×C31—24no—
236C4⋊C4×C31—24no—
237C4⋊C4×C31—22no—
238C4⋊C4×C31—21no—
239C4⋊C4×C31—21no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—21no—
243C4⋊C4×C31—42no—
244C4⋊C4×C31—42no—
245C4⋊C4×C31C2×D412yes—
246C4⋊C4×C31C2×D412yes—
247C4⋊C4×C31C2×D412yes—
248C4⋊C4×C31#4112yes—
249C4⋊C4×C31#4112yes—
250C22⋊C4×C31—24no—
251C22⋊C4×C31—24no—
252C22⋊C4×C31—24no—
253C22⋊C4×C31—24no—
254C22⋊C4×C31—22no—
255C22⋊C4×C31—22no—
256C22⋊C4×C31—42no—
257C22⋊C4×C31—42no—
258C22⋊C4×C31—42no—
259C22⋊C4×C31—42no—
260C22⋊C4×C31—42no—
261C22⋊C4×C31—42no—
262C42×C31—24no—
263C42×C31—81no—
264C42×C31C2×D412yes—
265C42×C31C2×D412yes—
266#25575C3111yesmaximal, characteristic, direct product factor, Sylow
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—22no—
275C23×C31—21no—
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31—41no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31#13512yes—
295C23×C31C22×D411yescharacteristic
296Q8×C31—41no—
297Q8×C31—41no—
298Q8×C31—41no—
299Q8×C31—41no—
300D4×C31—22no—
301D4×C31—22no—
302D4×C31—44no—
303D4×C31—48no—
304D4×C31—41no—
305D4×C31—41no—
306D4×C31—41no—
307D4×C31—41no—
308D4×C31—41no—
309D4×C31—41no—
310D4×C31—84no—
311D4×C31—84no—
312D4×C31—84no—
313C2×C4×C31—21no—
314C2×C4×C31—21no—
315C2×C4×C31—21no—
316C2×C4×C31—21no—
317C2×C4×C31—21no—
318C2×C4×C31—22no—
319C2×C4×C31—22no—
320C2×C4×C31—21no—
321C2×C4×C31—22no—
322C2×C4×C31—22no—
323C2×C4×C31—22no—
324C2×C4×C31—21no—
325C2×C4×C31—21no—
326C2×C4×C31—21no—
327C2×C4×C31—21no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—84no—
350C2×C4×C31—84no—
351C2×C4×C31#12012yes—
352C2×C4×C31#12012yes—
353C2×C4×C31C22×D411yescharacteristic
354C2×C4×C31C22×D411yescharacteristic
355C2×C4×C31C2×#4111yescharacteristic
356C2×C4×C31C2×#4111yescharacteristic
357C2×C4×C31H(5,𝔽2)11yescharacteristic
358C2×C4×C31H(5,𝔽2)11yescharacteristic
359C8×C31—41no—
360C8×C31—41no—
361C8×C31—41no—
362C8×C31—41no—
363C2×#553C2×C3111yescharacteristic, complemented
364C2×#488C2×C3111yescharacteristic, complemented
365C2×#463C2×C3111yescharacteristic, complemented
366#2540C2×C3111yescharacteristic, complemented
367#2000C2×C3111yescharacteristic, complemented
368#2000C2×C3111yescharacteristic, complemented
369#1999C2×C3111yescharacteristic, complemented
370#1999C2×C3111yescharacteristic, complemented
371#1989C2×C3111yescharacteristic, complemented
372#1954C2×C3111yescharacteristic, complemented
373#1875C2×C3111yescharacteristic, complemented
374#1874C2×C3111yescharacteristic, complemented
375#1873C2×C3111yescharacteristic, complemented
376#1872C2×C3111yescharacteristic, complemented
377C4×#102C2×C3111yescharacteristic, complemented
378C22×C31—22no—
379C22×C31—22no—
380C22×C31—22no—
381C22×C31—41no—
382C22×C31—41no—
383C22×C31—41no—
384C22×C31—41no—
385C22×C31—41no—
386C22×C31—42no—
387C22×C31—41no—
388C22×C31—42no—
389C22×C31—42no—
390C22×C31—41no—
391C22×C31—41no—
392C22×C31—41no—
393C22×C31—41no—
394C22×C31—41no—
395C22×C31—81no—
396C22×C31—81no—
397C22×C31—81no—
398C22×C31—81no—
399C22×C31—81no—
400C22×C31—81no—
401C22×C31—81no—
402C22×C31—81no—
403C22×C31—81no—
404C22×C31—81no—
405C22×C31—81no—
406C22×C31C2×#12011yescharacteristic
407C22×C31#54611yescharacteristic
408C22×C31#54611yescharacteristic
409C22×C31C2×#13511yescharacteristic
410C22×C31#57511yescharacteristic
411C22×C31#57611yescharacteristic
412C22×C31#57711yescharacteristic
413C4×C31—22no—
414C4×C31—22no—
415C4×C31—41no—
416C4×C31—41no—
417C4×C31—42no—
418C4×C31—42no—
419C4×C31—42no—
420C4×C31—42no—
421C4×C31—42no—
422C4×C31—81no—
423C4×C31#53211yescharacteristic
424C4×C31#53511yescharacteristic
425C4×C31#55011yescharacteristic
426C4×C31#55011yescharacteristic
427C22×SD16C22×C3111yescharacteristic
428C22×D8C22×C3111yescharacteristic
429#553—24no—
430#553—24no—
431C2×#126—21no—
432C2×#125C22×C3111yescharacteristic
433C2×#124C22×C3111yescharacteristic
434C2×#123—21no—
435C2×C22⋊Q8C22×C3111yescharacteristic
436C2×C22⋊Q8C22×C3111yescharacteristic
437C2×#121—21no—
438C2×#121C22×C3111yescharacteristic
439C2×#121C22×C3111yescharacteristic
440C2×#121C22×C3111yescharacteristic
441C2×#121C22×C3111yescharacteristic
442C2×C4×D4—21no—
443C2×C4×D4C22×C3111yescharacteristic
444C2×C4×D4C22×C3111yescharacteristic
445C2×#117C22×C3111yescharacteristic
446C22×C4⋊C4C22×C3111yescharacteristic
447#488—24no—
448#463—24no—
449C2×C4⋊C8C22×C3111yescharacteristic
450C2×#103C22×C3111yescharacteristic
451C2×#103C22×C3111yescharacteristic
452C2×#103C22×C3111yescharacteristic
453C2×#102C22×C3111yescharacteristic
454C2×#102C22×C3111yescharacteristic
455C2×#102C22×C3111yescharacteristic
456C2×#102C22×C3111yescharacteristic
457C2×#102C22×C3111yescharacteristic
458C2×C22⋊C8C22×C3111yescharacteristic
459C2×C22⋊C8C22×C3111yescharacteristic
460C2×C22⋊C8C22×C3111yescharacteristic
461C2×C22⋊C8C22×C3111yescharacteristic
462C2×C4×C8C22×C3111yescharacteristic
463#399—21no—
464#392—21no—
465#390—21no—
466#390—21no—
467C4×C4⋊C4C22×C3111yescharacteristic
468#340C22×C3111yescharacteristic
469#340C22×C3111yescharacteristic
470#340C22×C3111yescharacteristic
471#340C22×C3111yescharacteristic
472#340C22×C3111yescharacteristic
473#340C22×C3111yescharacteristic
474C2×C31—42no—
475C2×C31—81no—
476C2×C31—82no—
477C2×C31—161no—
478C2×C31#243111yescharacteristic
479C2×C31#300211yescharacteristic
480C2×C31#301211yescharacteristic
481C2×C31#329711yescharacteristic
482C2×C31#330111yescharacteristic
483C2×C31#332211yescharacteristic
484C2×C31#332611yescharacteristic
485C22×Q8C23×C3111yescharacteristic
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4D4×C3111yescharacteristic
491C22×D4C23×C3111yescharacteristic
492C22×D4C23×C3111yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4C23×C3111yescharacteristic
496C23×C4C23×C3111yescharacteristic
497C2×SD16—22no—
498C2×SD16—41no—
499C2×SD16—41no—
500C2×D8—22no—
501C2×D8—41no—
502C2×D8—41no—
503C22×C8C23×C3111yescharacteristic
504C22×C8C23×C3111yescharacteristic
505C22×C8C23×C3111yescharacteristic
506C22×C8C23×C3111yescharacteristic
507#126—28no—
508#125—22no—
509#125D4×C3114yescomplemented
510#124—22no—
511#124—22no—
512#123—28no—
513C22⋊Q8—22no—
514C22⋊Q8—22no—
515C22⋊Q8—41no—
516C22⋊Q8—41no—
517#121—28no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—41no—
525#121—41no—
526C4×D4—28no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4D4×C3114yescomplemented
531#117—22no—
532#117—22no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4D4×C3111yescharacteristic
541C2×C4⋊C4C23×C3111yescharacteristic
542C2×C4⋊C4C23×C3111yescharacteristic
543C2×C4⋊C4C23×C3111yescharacteristic
544C2×C4⋊C4C23×C3111yescharacteristic
545C2×C4⋊C4C23×C3111yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4D4×C3111yescharacteristic
557C2×C22⋊C4D4×C3111yescharacteristic
558C2×C42—21no—
559C2×C42—21no—
560C2×C42C23×C3111yescharacteristic
561C4⋊C8—22no—
562#103—22no—
563#103—22no—
564#103—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570C22⋊C8—41no—
571C22⋊C8—41no—
572C22⋊C8—41no—
573C22⋊C8—41no—
574C4×C8—22no—
575#95—21no—
576C31#2557511yescharacteristic, direct product factor, Sylow
577C24—21no—
578C24—21no—
579C24C2×D4×C3111yescharacteristic
580C24C2×D4×C3111yescharacteristic
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×D4—24no—
588C2×D4—22no—
589C2×D4—24no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—41no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4C2×D4×C3112yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—81no—
635C22×C4—81no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4C2×D4×C3111yescharacteristic
639C22×C4C2×D4×C3111yescharacteristic
640C22×C4C2×D4×C3111yescharacteristic
641C22×C4C2×D4×C3111yescharacteristic
642C22×C4C24×C3111yescharacteristic
643SD16—44no—
644D8—44no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4C2×D4×C3112yes—
669C4⋊C4C2×D4×C3112yes—
670C4⋊C4C2×D4×C3112yes—
671C4⋊C4#41×C3112yes—
672C4⋊C4#41×C3112yes—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C42—24no—
686C42—81no—
687C42C2×D4×C3112yes—
688C42C2×D4×C3112yes—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23C31×#13512yes—
717C23C22×D4×C3111yescharacteristic
718Q8—41no—
719Q8—41no—
720Q8—41no—
721Q8—41no—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—84no—
733D4—84no—
734D4—84no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4C31×#12012yes—
774C2×C4C31×#12012yes—
775C2×C4C22×D4×C3111yescharacteristic
776C2×C4C22×D4×C3111yescharacteristic
777C2×C4C2×#41×C3111yescharacteristic
778C2×C4C2×#41×C3111yescharacteristic
779C2×C4C31×H(5,𝔽2)11yescharacteristic
780C2×C4C31×H(5,𝔽2)11yescharacteristic
781C8—41no—
782C8—41no—
783C8—41no—
784C8—41no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—42no—
794C22—41no—
795C22—42no—
796C22—42no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22C2×C31×#12011yescharacteristic
814C22C31×#54611yescharacteristic
815C22C31×#54611yescharacteristic
816C22C2×C31×#13511yescharacteristic
817C22C31×#57511yescharacteristic
818C22C31×#57611yescharacteristic
819C22C31×#57711yescharacteristic
820C4—22no—
821C4—22no—
822C4—41no—
823C4—41no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—81no—
830C4C31×#53211yescharacteristic
831C4C31×#53511yescharacteristic
832C4C31×#55011yescharacteristic
833C4C31×#55011yescharacteristic
834C2—42no—
835C2—81no—
836C2—82no—
837C2—161no—
838C2C31×#243111yescharacteristic
839C2C31×#300211yescharacteristic
840C2C31×#301211yescharacteristic
841C2C31×#329711yescharacteristic
842C2C31×#330111yescharacteristic
843C2C31×#332211yescharacteristic
844C2C31×#332611yescharacteristic
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×#488C2semidirect
3. C2×C31×#463C2semidirect
4. C31×#2540C2semidirect
5. C31×#2000C2semidirect
6. C31×#2000C2semidirect
7. C31×#1999C2semidirect
8. C31×#1999C2semidirect
9. C31×#1989C2semidirect
10. C31×#1954C2semidirect
11. C31×#1875C2semidirect
12. C31×#1874C2semidirect
13. C31×#1873C2semidirect
14. C31×#1872C2semidirect
15. C4×C31×#102C2semidirect
87. C31×#125D4semidirect
108. C4×D4×C31D4semidirect
266. #25575C31direct (N × H)
363. C2×#553C2×C31semidirect
364. C2×#488C2×C31semidirect
365. C2×#463C2×C31semidirect
366. #2540C2×C31semidirect
367. #2000C2×C31semidirect
368. #2000C2×C31semidirect
369. #1999C2×C31semidirect
370. #1999C2×C31semidirect
371. #1989C2×C31semidirect
372. #1954C2×C31semidirect
373. #1875C2×C31semidirect
374. #1874C2×C31semidirect
375. #1873C2×C31semidirect
376. #1872C2×C31semidirect
377. C4×#102C2×C31semidirect
509. #125D4×C31semidirect
530. C4×D4D4×C31semidirect
576. C31#25575direct (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×#4882
C2×C31×#4632
C31×#25402
C31×#20002
C31×#19992
C31×#19892
C31×#19542
C31×#18752
C31×#18742
C31×#18732
C31×#18722
C4×C31×#1022
#2557531