Finite Group Databasebeta

← C31×#25549 #21482308

Subgroups — C31×#25549 #21482308

Order 7936.

1390 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#547C211yesmaximal, characteristic, complemented
2C2×C31×#481C211yesmaximal, characteristic, complemented
3C2×C31×#469C211yesmaximal, characteristic, complemented
4C31×#2414C211yesmaximal, characteristic, complemented
5C31×#2058C211yesmaximal, characteristic, complemented
6C31×#2034C211yesmaximal, characteristic, complemented
7C31×#2023C211yesmaximal, characteristic, complemented
8C31×#1999C211yesmaximal, characteristic, complemented
9C31×#1879C211yesmaximal, characteristic, complemented
10C31×#1875C211yesmaximal, characteristic, complemented
11C31×#1874C211yesmaximal, characteristic, complemented
12C31×#1870C211yesmaximal, characteristic, complemented
13C31×#1864C211yesmaximal, characteristic, complemented
14C31×#1853C211yesmaximal, characteristic, complemented
15C31×#1736C211yesmaximal, characteristic, complemented
16C22×#41×C31—21no—
17C22×D8×C31C2211yescharacteristic
18C22×M16×C31C2211yescharacteristic
19C31×#547—24no—
20C31×#547—24no—
21C2×C31×C4⋊Q8C2211yescharacteristic
22C2×C31×#123—21no—
23C2×C31×#123—21no—
24C2×C31×C22⋊Q8—21no—
25C2×C31×#121C2211yescharacteristic
26C2×C31×#121C2211yescharacteristic
27C2×C31×#121C2211yescharacteristic
28C2×C31×#121C2211yescharacteristic
29C2×C4×D4×C31C2211yescharacteristic
30C2×C4×D4×C31C2211yescharacteristic
31C2×C31×#117C2211yescharacteristic
32C22×C4⋊C4×C31C2211yescharacteristic
33C22×C4⋊C4×C31C2211yescharacteristic
34C31×#481—24no—
35C31×#469—24no—
36C2×C31×#106C2211yescharacteristic
37C2×C31×#106C2211yescharacteristic
38C2×C31×#106C2211yescharacteristic
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
48C31×#394—21no—
49C31×#392—21no—
50C31×#390—21no—
51C31×#390C2211yescharacteristic
52C31×#389C2211yescharacteristic
53C31×#388—21no—
54C31×#380C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C2×#41×C31—28no—
64C2×#41×C31—44no—
65C2×#41×C31—44no—
66C22×Q8×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31—21no—
69C22×D4×C31—21no—
70C22×D4×C31—21no—
71C22×D4×C31D411yescharacteristic
72C22×D4×C31C2311yescharacteristic
73C22×D4×C31C2311yescharacteristic
74C23×C4×C31—21no—
75C23×C4×C31—21no—
76C23×C4×C31—21no—
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C2×D8×C31—22no—
80C2×D8×C31—22no—
81C2×D8×C31—41no—
82C2×M16×C31—22no—
83C2×M16×C31—22no—
84C2×M16×C31—41no—
85C22×C8×C31C2311yescharacteristic
86C22×C8×C31C2311yescharacteristic
87C22×C8×C31C2311yescharacteristic
88C22×C8×C31C2311yescharacteristic
89C31×C4⋊Q8—22no—
90C31×C4⋊Q8—22no—
91C31×#123—28no—
92C31×#123—28no—
93C31×C22⋊Q8—28no—
94C31×#121—22no—
95C31×#121—22no—
96C31×#121—22no—
97C31×#121—22no—
98C31×#121—22no—
99C31×#121—22no—
100C31×#121—41no—
101C31×#121D414yescomplemented
102C4×D4×C31—22no—
103C4×D4×C31—22no—
104C4×D4×C31—22no—
105C4×D4×C31—22no—
106C31×#117—22no—
107C31×#117—41no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—22no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—22no—
113C2×C4⋊C4×C31—22no—
114C2×C4⋊C4×C31—21no—
115C2×C4⋊C4×C31D411yescharacteristic
116C2×C4⋊C4×C31D414yescomplemented
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C4⋊C4×C31C2311yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C4⋊C4×C31C2311yescharacteristic
121C2×C4⋊C4×C31C2311yescharacteristic
122C2×C4⋊C4×C31C2311yescharacteristic
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×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31D411yescharacteristic
133C2×C22⋊C4×C31D411yescharacteristic
134C2×C42×C31—21no—
135C2×C42×C31C2311yescharacteristic
136C31×#106—22no—
137C31×#106—22no—
138C31×#106—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—22no—
144C31×#102—41no—
145C31×C22⋊C8—22no—
146C31×C22⋊C8—22no—
147C31×C22⋊C8—41no—
148C31×#95—21no—
149C31×#95—21no—
150C24×C31—21no—
151C24×C31—21no—
152C24×C31C2×D411yescharacteristic
153C24×C31C2×D411yescharacteristic
154#41×C31—432no—
155C2×Q8×C31—24no—
156C2×Q8×C31—42no—
157C2×Q8×C31—42no—
158C2×D4×C31—22no—
159C2×D4×C31—22no—
160C2×D4×C31—24no—
161C2×D4×C31—24no—
162C2×D4×C31—22no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
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—42no—
175C2×D4×C31—42no—
176C2×D4×C31—42no—
177C2×D4×C31—42no—
178C2×D4×C31—42no—
179C2×D4×C31—42no—
180C2×D4×C31—42no—
181C2×D4×C31—81no—
182C2×D4×C31—81no—
183C2×D4×C31—81no—
184C2×D4×C31C2×D412yes—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—24no—
190C22×C4×C31—24no—
191C22×C4×C31—24no—
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—42no—
205C22×C4×C31—42no—
206C22×C4×C31—42no—
207C22×C4×C31—42no—
208C22×C4×C31—42no—
209C22×C4×C31—42no—
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D412yes—
214C22×C4×C31C2×D412yes—
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2411yescharacteristic
217D8×C31—44no—
218M16×C31—44no—
219C2×C8×C31—21no—
220C2×C8×C31—21no—
221C2×C8×C31—21no—
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#4112yescomplemented
231C4⋊C4×C31—24no—
232C4⋊C4×C31—24no—
233C4⋊C4×C31—24no—
234C4⋊C4×C31—22no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—21no—
238C4⋊C4×C31—21no—
239C4⋊C4×C31—21no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—21no—
243C4⋊C4×C31—81no—
244C4⋊C4×C31C2×D412yes—
245C4⋊C4×C31C2×D412yes—
246C4⋊C4×C31C2×D412yes—
247C4⋊C4×C31#4112yescomplemented
248C22⋊C4×C31—24no—
249C22⋊C4×C31—24no—
250C22⋊C4×C31—22no—
251C22⋊C4×C31—24no—
252C22⋊C4×C31—22no—
253C22⋊C4×C31—42no—
254C22⋊C4×C31—42no—
255C22⋊C4×C31—42no—
256C22⋊C4×C31—42no—
257C22⋊C4×C31—81no—
258C22⋊C4×C31—81no—
259C42×C31—21no—
260C42×C31—21no—
261C42×C31—42no—
262#25549C3111yesmaximal, characteristic, direct product factor, Sylow
263C23×C31—21no—
264C23×C31—21no—
265C23×C31—21no—
266C23×C31—21no—
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—21no—
275C23×C31—22no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—41no—
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#12012yes—
290C23×C31AGL(1,ℤ/8)12yes—
291C23×C31C22×D411yescharacteristic
292Q8×C31—48no—
293D4×C31—28no—
294D4×C31—22no—
295D4×C31—22no—
296D4×C31—48no—
297D4×C31—48no—
298D4×C31—41no—
299D4×C31—41no—
300D4×C31—41no—
301D4×C31—41no—
302D4×C31—41no—
303D4×C31—41no—
304D4×C31—84no—
305D4×C31—84no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—22no—
311C2×C4×C31—22no—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—21no—
315C2×C4×C31—21no—
316C2×C4×C31—22no—
317C2×C4×C31—22no—
318C2×C4×C31—22no—
319C2×C4×C31—22no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—21no—
324C2×C4×C31—48no—
325C2×C4×C31—48no—
326C2×C4×C31—48no—
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—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#12012yes—
346C2×C4×C31AGL(1,ℤ/8)12yes—
347C2×C4×C31C22×D411yescharacteristic
348C2×C4×C31C22×D411yescharacteristic
349C2×C4×C31C2×#4111yescharacteristic
350C2×C4×C31C2×#4111yescharacteristic
351C2×C4×C31H(5,𝔽2)11yescharacteristic
352C2×C4×C312−1+411yescharacteristic
353C8×C31—22no—
354C8×C31—41no—
355C8×C31—41no—
356C8×C31—41no—
357C2×#547C2×C3111yescharacteristic, complemented
358C2×#481C2×C3111yescharacteristic, complemented
359C2×#469C2×C3111yescharacteristic, complemented
360#2414C2×C3111yescharacteristic, complemented
361#2058C2×C3111yescharacteristic, complemented
362#2034C2×C3111yescharacteristic, complemented
363#2023C2×C3111yescharacteristic, complemented
364#1999C2×C3111yescharacteristic, complemented
365#1879C2×C3111yescharacteristic, complemented
366#1875C2×C3111yescharacteristic, complemented
367#1874C2×C3111yescharacteristic, complemented
368#1870C2×C3111yescharacteristic, complemented
369#1864C2×C3111yescharacteristic, complemented
370#1853C2×C3111yescharacteristic, complemented
371#1736C2×C3111yescharacteristic, complemented
372C22×C31—22no—
373C22×C31—22no—
374C22×C31—22no—
375C22×C31—22no—
376C22×C31—22no—
377C22×C31—22no—
378C22×C31—41no—
379C22×C31—41no—
380C22×C31—41no—
381C22×C31—41no—
382C22×C31—41no—
383C22×C31—41no—
384C22×C31—41no—
385C22×C31—41no—
386C22×C31—42no—
387C22×C31—42no—
388C22×C31—42no—
389C22×C31—81no—
390C22×C31—81no—
391C22×C31—81no—
392C22×C31—81no—
393C22×C31—81no—
394C22×C31—81no—
395C22×C31—81no—
396C22×C31—81no—
397C22×C31—81no—
398C22×C31—81no—
399C22×C31—81no—
400C22×C31C2×#12011yescharacteristic
401C22×C31#54611yescharacteristic
402C22×C31#54711yescharacteristic
403C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
404C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
405C22×C31#57711yescharacteristic
406C22×C31#57711yescharacteristic
407C4×C31—22no—
408C4×C31—22no—
409C4×C31—41no—
410C4×C31—42no—
411C4×C31—42no—
412C4×C31—42no—
413C4×C31—41no—
414C4×C31—42no—
415C4×C31—81no—
416C4×C31—81no—
417C4×C31#53211yescharacteristic
418C4×C31#53711yescharacteristic
419C4×C31#54611yescharacteristic
420C4×C31#54711yescharacteristic
421C22×#41—21no—
422C22×D8C22×C3111yescharacteristic
423C22×M16C22×C3111yescharacteristic
424#547—24no—
425#547—24no—
426C2×C4⋊Q8C22×C3111yescharacteristic
427C2×#123—21no—
428C2×#123—21no—
429C2×C22⋊Q8—21no—
430C2×#121C22×C3111yescharacteristic
431C2×#121C22×C3111yescharacteristic
432C2×#121C22×C3111yescharacteristic
433C2×#121C22×C3111yescharacteristic
434C2×C4×D4C22×C3111yescharacteristic
435C2×C4×D4C22×C3111yescharacteristic
436C2×#117C22×C3111yescharacteristic
437C22×C4⋊C4C22×C3111yescharacteristic
438C22×C4⋊C4C22×C3111yescharacteristic
439#481—24no—
440#469—24no—
441C2×#106C22×C3111yescharacteristic
442C2×#106C22×C3111yescharacteristic
443C2×#106C22×C3111yescharacteristic
444C2×#102C22×C3111yescharacteristic
445C2×#102C22×C3111yescharacteristic
446C2×#102C22×C3111yescharacteristic
447C2×#102C22×C3111yescharacteristic
448C2×#102C22×C3111yescharacteristic
449C2×#102C22×C3111yescharacteristic
450C2×C22⋊C8C22×C3111yescharacteristic
451C2×C22⋊C8C22×C3111yescharacteristic
452C2×C22⋊C8C22×C3111yescharacteristic
453#394—21no—
454#392—21no—
455#390—21no—
456#390C22×C3111yescharacteristic
457#389C22×C3111yescharacteristic
458#388—21no—
459#380C22×C3111yescharacteristic
460#340C22×C3111yescharacteristic
461#340C22×C3111yescharacteristic
462#340C22×C3111yescharacteristic
463#340C22×C3111yescharacteristic
464#340C22×C3111yescharacteristic
465#340C22×C3111yescharacteristic
466#336C22×C3111yescharacteristic
467#336C22×C3111yescharacteristic
468C2×C31—42no—
469C2×C31—42no—
470C2×C31—82no—
471C2×C31—161no—
472C2×C31#243011yescharacteristic
473C2×C31#300311yescharacteristic
474C2×C31#301011yescharacteristic
475C2×C31#330611yescharacteristic
476C2×C31#333211yescharacteristic
477C2×C31#334511yescharacteristic
478C2×C31#335411yescharacteristic
479C2×#41—28no—
480C2×#41—44no—
481C2×#41—44no—
482C22×Q8—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4D4×C3111yescharacteristic
488C22×D4C23×C3111yescharacteristic
489C22×D4C23×C3111yescharacteristic
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4C23×C3111yescharacteristic
494C23×C4C23×C3111yescharacteristic
495C2×D8—22no—
496C2×D8—22no—
497C2×D8—41no—
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—41no—
501C22×C8C23×C3111yescharacteristic
502C22×C8C23×C3111yescharacteristic
503C22×C8C23×C3111yescharacteristic
504C22×C8C23×C3111yescharacteristic
505C4⋊Q8—22no—
506C4⋊Q8—22no—
507#123—28no—
508#123—28no—
509C22⋊Q8—28no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—41no—
517#121D4×C3114yescomplemented
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522#117—22no—
523#117—41no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4D4×C3111yescharacteristic
532C2×C4⋊C4D4×C3114yescomplemented
533C2×C4⋊C4C23×C3111yescharacteristic
534C2×C4⋊C4C23×C3111yescharacteristic
535C2×C4⋊C4C23×C3111yescharacteristic
536C2×C4⋊C4C23×C3111yescharacteristic
537C2×C4⋊C4C23×C3111yescharacteristic
538C2×C4⋊C4C23×C3111yescharacteristic
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4D4×C3111yescharacteristic
549C2×C22⋊C4D4×C3111yescharacteristic
550C2×C42—21no—
551C2×C42C23×C3111yescharacteristic
552#106—22no—
553#106—22no—
554#106—22no—
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—41no—
561C22⋊C8—22no—
562C22⋊C8—22no—
563C22⋊C8—41no—
564#95—21no—
565#95—21no—
566C31#2554911yescharacteristic, direct product factor, Sylow
567C24—21no—
568C24—21no—
569C24C2×D4×C3111yescharacteristic
570C24C2×D4×C3111yescharacteristic
571#41—432no—
572C2×Q8—24no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4C2×D4×C3112yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4C2×D4×C3111yescharacteristic
628C22×C4C2×D4×C3111yescharacteristic
629C22×C4C2×D4×C3111yescharacteristic
630C22×C4C2×D4×C3112yes—
631C22×C4C2×D4×C3112yes—
632C22×C4C2×D4×C3111yescharacteristic
633C22×C4C24×C3111yescharacteristic
634D8—44no—
635M16—44no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8#41×C3112yescomplemented
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—81no—
661C4⋊C4C2×D4×C3112yes—
662C4⋊C4C2×D4×C3112yes—
663C4⋊C4C2×D4×C3112yes—
664C4⋊C4#41×C3112yescomplemented
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—22no—
668C22⋊C4—24no—
669C22⋊C4—22no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C42—21no—
677C42—21no—
678C42—42no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23C31×#12012yes—
706C23C31×AGL(1,ℤ/8)12yes—
707C23C22×D4×C3111yescharacteristic
708Q8—48no—
709D4—28no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—48no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—48no—
741C2×C4—48no—
742C2×C4—48no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
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×C4C31×#12012yes—
762C2×C4C31×AGL(1,ℤ/8)12yes—
763C2×C4C22×D4×C3111yescharacteristic
764C2×C4C22×D4×C3111yescharacteristic
765C2×C4C2×#41×C3111yescharacteristic
766C2×C4C2×#41×C3111yescharacteristic
767C2×C4C31×H(5,𝔽2)11yescharacteristic
768C2×C4C31×2−1+411yescharacteristic
769C8—22no—
770C8—41no—
771C8—41no—
772C8—41no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C2×C31×#12011yescharacteristic
802C22C31×#54611yescharacteristic
803C22C31×#54711yescharacteristic
804C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
805C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
806C22C31×#57711yescharacteristic
807C22C31×#57711yescharacteristic
808C4—22no—
809C4—22no—
810C4—41no—
811C4—42no—
812C4—42no—
813C4—42no—
814C4—41no—
815C4—42no—
816C4—81no—
817C4—81no—
818C4C31×#53211yescharacteristic
819C4C31×#53711yescharacteristic
820C4C31×#54611yescharacteristic
821C4C31×#54711yescharacteristic
822C2—42no—
823C2—42no—
824C2—82no—
825C2—161no—
826C2C31×#243011yescharacteristic
827C2C31×#300311yescharacteristic
828C2C31×#301011yescharacteristic
829C2C31×#330611yescharacteristic
830C2C31×#333211yescharacteristic
831C2C31×#334511yescharacteristic
832C2C31×#335411yescharacteristic
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×#547C2semidirect
2. C2×C31×#481C2semidirect
3. C2×C31×#469C2semidirect
4. C31×#2414C2semidirect
5. C31×#2058C2semidirect
6. C31×#2034C2semidirect
7. C31×#2023C2semidirect
8. C31×#1999C2semidirect
9. C31×#1879C2semidirect
10. C31×#1875C2semidirect
11. C31×#1874C2semidirect
12. C31×#1870C2semidirect
13. C31×#1864C2semidirect
14. C31×#1853C2semidirect
15. C31×#1736C2semidirect
101. C31×#121D4semidirect
116. C2×C4⋊C4×C31D4semidirect
230. C2×C8×C31#41semidirect
247. C4⋊C4×C31#41semidirect
262. #25549C31direct (N × H)
357. C2×#547C2×C31semidirect
358. C2×#481C2×C31semidirect
359. C2×#469C2×C31semidirect
360. #2414C2×C31semidirect
361. #2058C2×C31semidirect
362. #2034C2×C31semidirect
363. #2023C2×C31semidirect
364. #1999C2×C31semidirect
365. #1879C2×C31semidirect
366. #1875C2×C31semidirect
367. #1874C2×C31semidirect
368. #1870C2×C31semidirect
369. #1864C2×C31semidirect
370. #1853C2×C31semidirect
371. #1736C2×C31semidirect
517. #121D4×C31semidirect
532. C2×C4⋊C4D4×C31semidirect
566. C31#25549direct (N × H)
647. C2×C8#41×C31semidirect
664. C4⋊C4#41×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5472
C2×C31×#4812
C2×C31×#4692
C31×#24142
C31×#20582
C31×#20342
C31×#20232
C31×#19992
C31×#18792
C31×#18752
C31×#18742
C31×#18702
C31×#18642
C31×#18532
C31×#17362
#2554931