Finite Group Databasebeta

← C31×#24440 #21481199

Subgroups — C31×#24440 #21481199

Order 7936.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C31C211yesmaximal, characteristic, complemented
2C2×C31×#469C211yesmaximal, characteristic, complemented
3C2×C31×#447C211yesmaximal, characteristic, complemented
4C2×C31×#447C211yesmaximal, characteristic, complemented
5C2×C31×#418C211yesmaximal, characteristic, complemented
6C31×#2414C211yesmaximal, characteristic, complemented
7C31×#2041C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic, complemented
9C31×#2011C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1879C211yesmaximal, characteristic, complemented
12C31×#1875C211yesmaximal, characteristic, complemented
13C31×#1870C211yesmaximal, characteristic, complemented
14C31×#1864C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C31—21no—
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C22×D8×C31C2211yescharacteristic, complemented
21C22×D8×C31C2211yescharacteristic, complemented
22C22×M16×C31C2211yescharacteristic, complemented
23D42×C31—24no—
24D42×C31—24no—
25C2×C31×#127C2211yescharacteristic
26C2×C31×#121—21no—
27C2×C31×#121C2211yescharacteristic
28C2×C31×#121C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic, complemented
30C2×C31×#121C2211yescharacteristic, complemented
31C2×C31×#120—21no—
32C2×C31×#120—21no—
33C2×C4×D4×C31C2211yescharacteristic
34C2×C4×D4×C31C2211yescharacteristic
35C2×C31×#117C2211yescharacteristic, complemented
36C31×#469—24no—
37C31×#447—24no—
38C31×#447—24no—
39C2×C31×#106C2211yescharacteristic, complemented
40C31×#418—24no—
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic, complemented
45C2×C31×#102C2211yescharacteristic, complemented
46C2×C31×#102C2211yescharacteristic, complemented
47C2×C31×#102C2211yescharacteristic, complemented
48C2×C31×#102C2211yescharacteristic, complemented
49C2×C31×#102C2211yescharacteristic, complemented
50C2×C31×#102C2211yescharacteristic, complemented
51C2×C31×C22⋊C8C2211yescharacteristic, complemented
52C2×C31×C22⋊C8C2211yescharacteristic, complemented
53C2×C31×C22⋊C8C2211yescharacteristic, complemented
54C31×#394—21no—
55C31×#392—21no—
56C31×#390—21no—
57C31×#390C2211yescharacteristic, complemented
58C31×#389C2211yescharacteristic, complemented
59C31×#388—21no—
60C31×#380C2211yescharacteristic, complemented
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C31×#336C2211yescharacteristic, complemented
64C31×#336C2211yescharacteristic, complemented
65C25×C31—21no—
66C25×C31—21no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—28no—
70C22×D4×C31—21no—
71C22×D4×C31—21no—
72C22×D4×C31—22no—
73C22×D4×C31—22no—
74C22×D4×C31—22no—
75C22×D4×C31—22no—
76C22×D4×C31—21no—
77C22×D4×C31—21no—
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31—22no—
82C22×D4×C31—21no—
83C22×D4×C31—41no—
84C22×D4×C31—41no—
85C22×D4×C31—41no—
86C22×D4×C31—41no—
87C22×D4×C31—44no—
88C22×D4×C31—44no—
89C22×D4×C31D411yescharacteristic
90C22×D4×C31D414yescomplemented
91C22×D4×C31C2311yescharacteristic
92C22×D4×C31C2311yescharacteristic
93C22×D4×C31C2311yescharacteristic
94C22×D4×C31C2311yescharacteristic
95C23×C4×C31—21no—
96C23×C4×C31C2311yescharacteristic
97C23×C4×C31C2311yescharacteristic
98C2×D8×C31—22no—
99C2×D8×C31—22no—
100C2×D8×C31—22no—
101C2×D8×C31—22no—
102C2×D8×C31—22no—
103C2×D8×C31—22no—
104C2×D8×C31—41no—
105C2×D8×C31—41no—
106C2×D8×C31—41no—
107C2×M16×C31—22no—
108C2×M16×C31—22no—
109C2×M16×C31—41no—
110C22×C8×C31C2311yescharacteristic
111C22×C8×C31C2311yescharacteristic
112C22×C8×C31C2311yescharacteristic
113C22×C8×C31C2311yescharacteristic
114C31×#127—22no—
115C31×#127—22no—
116C31×#121—28no—
117C31×#121—22no—
118C31×#121—22no—
119C31×#121—22no—
120C31×#121—22no—
121C31×#121—22no—
122C31×#121—22no—
123C31×#121—41no—
124C31×#121D414yescomplemented
125C31×#120—28no—
126C31×#120—28no—
127C4×D4×C31—22no—
128C4×D4×C31—22no—
129C4×D4×C31—22no—
130C4×D4×C31—22no—
131C31×#117—22no—
132C31×#117—41no—
133C2×C4⋊C4×C31—21no—
134C2×C4⋊C4×C31D411yescharacteristic
135C2×C4⋊C4×C31C2311yescharacteristic
136C2×C4⋊C4×C31C2311yescharacteristic
137C2×C4⋊C4×C31C2311yescharacteristic
138C2×C4⋊C4×C31C2311yescharacteristic
139C2×C22⋊C4×C31—21no—
140C2×C22⋊C4×C31—21no—
141C2×C22⋊C4×C31—21no—
142C2×C22⋊C4×C31—21no—
143C2×C22⋊C4×C31—21no—
144C2×C22⋊C4×C31—21no—
145C2×C22⋊C4×C31—21no—
146C2×C22⋊C4×C31—21no—
147C2×C22⋊C4×C31—21no—
148C2×C22⋊C4×C31D411yescharacteristic
149C2×C22⋊C4×C31D411yescharacteristic
150C2×C42×C31—21no—
151C2×C42×C31C2311yescharacteristic
152C31×#106—22no—
153C31×#102—22no—
154C31×#102—22no—
155C31×#102—22no—
156C31×#102—22no—
157C31×#102—22no—
158C31×#102—22no—
159C31×#102—22no—
160C31×#102—22no—
161C31×#102—41no—
162C31×#102D414yescomplemented
163C31×C22⋊C8—22no—
164C31×C22⋊C8—22no—
165C31×C22⋊C8—41no—
166C31×#95—21no—
167C31×#95—21no—
168C24×C31—21no—
169C24×C31—24no—
170C24×C31—21no—
171C24×C31—21no—
172C24×C31—24no—
173C24×C31—21no—
174C24×C31—42no—
175C24×C31—42no—
176C24×C31—42no—
177C24×C31—42no—
178C24×C31—42no—
179C24×C31—42no—
180C24×C31—42no—
181C24×C31—42no—
182C24×C31—81no—
183C24×C31—81no—
184C24×C31—81no—
185C24×C31—81no—
186C24×C31C2×D411yescharacteristic
187C24×C31C2×D411yescharacteristic
188C2×D4×C31—22no—
189C2×D4×C31—22no—
190C2×D4×C31—28no—
191C2×D4×C31—24no—
192C2×D4×C31—24no—
193C2×D4×C31—24no—
194C2×D4×C31—24no—
195C2×D4×C31—24no—
196C2×D4×C31—24no—
197C2×D4×C31—22no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—21no—
207C2×D4×C31—21no—
208C2×D4×C31—21no—
209C2×D4×C31—21no—
210C2×D4×C31—21no—
211C2×D4×C31—21no—
212C2×D4×C31—21no—
213C2×D4×C31—21no—
214C2×D4×C31—21no—
215C2×D4×C31—21no—
216C2×D4×C31—21no—
217C2×D4×C31—44no—
218C2×D4×C31—44no—
219C2×D4×C31—44no—
220C2×D4×C31—42no—
221C2×D4×C31—42no—
222C2×D4×C31—42no—
223C2×D4×C31—42no—
224C2×D4×C31—42no—
225C2×D4×C31—42no—
226C2×D4×C31—44no—
227C2×D4×C31—44no—
228C2×D4×C31—432no—
229C2×D4×C31—44no—
230C2×D4×C31—42no—
231C2×D4×C31—42no—
232C2×D4×C31—42no—
233C2×D4×C31—42no—
234C2×D4×C31—44no—
235C2×D4×C31—42no—
236C2×D4×C31—42no—
237C2×D4×C31—42no—
238C2×D4×C31—81no—
239C2×D4×C31—81no—
240C2×D4×C31—81no—
241C2×D4×C31—81no—
242C2×D4×C31—81no—
243C2×D4×C31C2×D412yes—
244C2×D4×C31C2×D412yes—
245C2×D4×C31C2×D412yes—
246C2×D4×C31C2×D412yes—
247C2×D4×C31#4112yes—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—24no—
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—42no—
264C22×C4×C31—42no—
265C22×C4×C31C2×D411yescharacteristic
266C22×C4×C31C2×D411yescharacteristic
267C22×C4×C31C2×D411yescharacteristic
268C22×C4×C31C2×D412yes—
269C22×C4×C31C2×D412yes—
270C22×C4×C31C2×D411yescharacteristic
271C22×C4×C31C2411yescharacteristic
272D8×C31—44no—
273D8×C31—44no—
274D8×C31—44no—
275M16×C31—44no—
276C2×C8×C31—21no—
277C2×C8×C31—21no—
278C2×C8×C31—21no—
279C2×C8×C31—21no—
280C2×C8×C31—21no—
281C2×C8×C31—21no—
282C2×C8×C31—21no—
283C2×C8×C31—21no—
284C2×C8×C31—21no—
285C2×C8×C31—21no—
286C2×C8×C31—21no—
287C2×C8×C31C2×D412yescomplemented
288C4⋊C4×C31—22no—
289C4⋊C4×C31—21no—
290C4⋊C4×C31—21no—
291C4⋊C4×C31—21no—
292C4⋊C4×C31—21no—
293C4⋊C4×C31—21no—
294C4⋊C4×C31—21no—
295C4⋊C4×C31—81no—
296C4⋊C4×C31C2×D412yes—
297C4⋊C4×C31C2×D412yescomplemented
298C22⋊C4×C31—24no—
299C22⋊C4×C31—24no—
300C22⋊C4×C31—22no—
301C22⋊C4×C31—24no—
302C22⋊C4×C31—22no—
303C22⋊C4×C31—42no—
304C22⋊C4×C31—42no—
305C22⋊C4×C31—42no—
306C22⋊C4×C31—42no—
307C22⋊C4×C31—81no—
308C22⋊C4×C31—81no—
309C42×C31—21no—
310C42×C31—21no—
311C42×C31—42no—
312#24440C3111yesmaximal, characteristic, direct product factor, Sylow
313C23×C31—21no—
314C23×C31—22no—
315C23×C31—21no—
316C23×C31—21no—
317C23×C31—22no—
318C23×C31—21no—
319C23×C31—21no—
320C23×C31—22no—
321C23×C31—21no—
322C23×C31—21no—
323C23×C31—21no—
324C23×C31—21no—
325C23×C31—21no—
326C23×C31—21no—
327C23×C31—21no—
328C23×C31—22no—
329C23×C31—22no—
330C23×C31—48no—
331C23×C31—48no—
332C23×C31—48no—
333C23×C31—48no—
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—84no—
358C23×C31—84no—
359C23×C31—84no—
360C23×C31—84no—
361C23×C31—84no—
362C23×C31—84no—
363C23×C31—84no—
364C23×C31—84no—
365C23×C31—84no—
366C23×C31—84no—
367C23×C31#12012yes—
368C23×C31AGL(1,ℤ/8)12yes—
369C23×C31C22×D411yescharacteristic
370D4×C31—28no—
371D4×C31—22no—
372D4×C31—22no—
373D4×C31—22no—
374D4×C31—22no—
375D4×C31—22no—
376D4×C31—22no—
377D4×C31—22no—
378D4×C31—48no—
379D4×C31—48no—
380D4×C31—48no—
381D4×C31—48no—
382D4×C31—48no—
383D4×C31—41no—
384D4×C31—41no—
385D4×C31—41no—
386D4×C31—41no—
387D4×C31—41no—
388D4×C31—41no—
389D4×C31—41no—
390D4×C31—41no—
391D4×C31—84no—
392D4×C31—84no—
393D4×C31—84no—
394D4×C31#12114yes—
395C2×C4×C31—21no—
396C2×C4×C31—21no—
397C2×C4×C31—21no—
398C2×C4×C31—21no—
399C2×C4×C31—22no—
400C2×C4×C31—22no—
401C2×C4×C31—22no—
402C2×C4×C31—22no—
403C2×C4×C31—21no—
404C2×C4×C31—21no—
405C2×C4×C31—22no—
406C2×C4×C31—22no—
407C2×C4×C31—21no—
408C2×C4×C31—21no—
409C2×C4×C31—21no—
410C2×C4×C31—21no—
411C2×C4×C31—48no—
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#12012yes—
427C2×C4×C31AGL(1,ℤ/8)12yes—
428C2×C4×C31C22×D411yescharacteristic
429C2×C4×C31C22×D411yescharacteristic
430C2×C4×C31C22×D411yescharacteristic
431C2×C4×C31C2×#4111yescharacteristic
432C2×C4×C31H(5,𝔽2)11yescharacteristic
433C2×C4×C31H(5,𝔽2)11yescharacteristic
434C8×C31—22no—
435C8×C31—41no—
436C8×C31—41no—
437C8×C31—41no—
438C2×D42C2×C3111yescharacteristic, complemented
439C2×#469C2×C3111yescharacteristic, complemented
440C2×#447C2×C3111yescharacteristic, complemented
441C2×#447C2×C3111yescharacteristic, complemented
442C2×#418C2×C3111yescharacteristic, complemented
443#2414C2×C3111yescharacteristic, complemented
444#2041C2×C3111yescharacteristic, complemented
445#2034C2×C3111yescharacteristic, complemented
446#2011C2×C3111yescharacteristic, complemented
447#1999C2×C3111yescharacteristic, complemented
448#1879C2×C3111yescharacteristic, complemented
449#1875C2×C3111yescharacteristic, complemented
450#1870C2×C3111yescharacteristic, complemented
451#1864C2×C3111yescharacteristic, complemented
452#1786C2×C3111yescharacteristic, complemented
453C22×C31—22no—
454C22×C31—24no—
455C22×C31—22no—
456C22×C31—22no—
457C22×C31—22no—
458C22×C31—22no—
459C22×C31—22no—
460C22×C31—41no—
461C22×C31—42no—
462C22×C31—41no—
463C22×C31—42no—
464C22×C31—41no—
465C22×C31—42no—
466C22×C31—41no—
467C22×C31—41no—
468C22×C31—42no—
469C22×C31—41no—
470C22×C31—42no—
471C22×C31—41no—
472C22×C31—41no—
473C22×C31—42no—
474C22×C31—42no—
475C22×C31—42no—
476C22×C31—42no—
477C22×C31—42no—
478C22×C31—42no—
479C22×C31—42no—
480C22×C31—816no—
481C22×C31—816no—
482C22×C31—81no—
483C22×C31—81no—
484C22×C31—81no—
485C22×C31—81no—
486C22×C31—81no—
487C22×C31—81no—
488C22×C31—81no—
489C22×C31—81no—
490C22×C31—81no—
491C22×C31—81no—
492C22×C31—81no—
493C22×C31—81no—
494C22×C31—81no—
495C22×C31—81no—
496C22×C31—81no—
497C22×C31C2×#12011yescharacteristic
498C22×C31D4211yescharacteristic
499C22×C31#54611yescharacteristic
500C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
501C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
502C22×C31#57611yescharacteristic
503C22×C31#57611yescharacteristic
504C4×C31—22no—
505C4×C31—22no—
506C4×C31—41no—
507C4×C31—42no—
508C4×C31—41no—
509C4×C31—42no—
510C4×C31—81no—
511C4×C31—81no—
512C4×C31C2×#12111yescharacteristic
513C4×C31#53411yescharacteristic
514C4×C31D4211yescharacteristic
515C4×C31#54611yescharacteristic
516C23×D4—21no—
517C23×D4C22×C3111yescharacteristic
518C23×D4C22×C3111yescharacteristic
519C22×D8C22×C3111yescharacteristic
520C22×D8C22×C3111yescharacteristic, complemented
521C22×D8C22×C3111yescharacteristic, complemented
522C22×M16C22×C3111yescharacteristic, complemented
523D42—24no—
524D42—24no—
525C2×#127C22×C3111yescharacteristic
526C2×#121—21no—
527C2×#121C22×C3111yescharacteristic
528C2×#121C22×C3111yescharacteristic
529C2×#121C22×C3111yescharacteristic, complemented
530C2×#121C22×C3111yescharacteristic, complemented
531C2×#120—21no—
532C2×#120—21no—
533C2×C4×D4C22×C3111yescharacteristic
534C2×C4×D4C22×C3111yescharacteristic
535C2×#117C22×C3111yescharacteristic, complemented
536#469—24no—
537#447—24no—
538#447—24no—
539C2×#106C22×C3111yescharacteristic, complemented
540#418—24no—
541C2×#102C22×C3111yescharacteristic
542C2×#102C22×C3111yescharacteristic
543C2×#102C22×C3111yescharacteristic
544C2×#102C22×C3111yescharacteristic, complemented
545C2×#102C22×C3111yescharacteristic, complemented
546C2×#102C22×C3111yescharacteristic, complemented
547C2×#102C22×C3111yescharacteristic, complemented
548C2×#102C22×C3111yescharacteristic, complemented
549C2×#102C22×C3111yescharacteristic, complemented
550C2×#102C22×C3111yescharacteristic, complemented
551C2×C22⋊C8C22×C3111yescharacteristic, complemented
552C2×C22⋊C8C22×C3111yescharacteristic, complemented
553C2×C22⋊C8C22×C3111yescharacteristic, complemented
554#394—21no—
555#392—21no—
556#390—21no—
557#390C22×C3111yescharacteristic, complemented
558#389C22×C3111yescharacteristic, complemented
559#388—21no—
560#380C22×C3111yescharacteristic, complemented
561#340C22×C3111yescharacteristic, complemented
562#340C22×C3111yescharacteristic, complemented
563#336C22×C3111yescharacteristic, complemented
564#336C22×C3111yescharacteristic, complemented
565C2×C31—42no—
566C2×C31—42no—
567C2×C31—44no—
568C2×C31—82no—
569C2×C31—82no—
570C2×C31—161no—
571C2×C31#241011yescharacteristic
572C2×C31#300311yescharacteristic
573C2×C31#300811yescharacteristic
574C2×C31#326411yescharacteristic
575C2×C31#327411yescharacteristic
576C2×C31#331811yescharacteristic
577C2×C31#332511yescharacteristic
578C25—21no—
579C25—21no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—28no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—21no—
596C22×D4—41no—
597C22×D4—41no—
598C22×D4—41no—
599C22×D4—41no—
600C22×D4—44no—
601C22×D4—44no—
602C22×D4D4×C3111yescharacteristic
603C22×D4D4×C3114yescomplemented
604C22×D4C23×C3111yescharacteristic
605C22×D4C23×C3111yescharacteristic
606C22×D4C23×C3111yescharacteristic
607C22×D4C23×C3111yescharacteristic
608C23×C4—21no—
609C23×C4C23×C3111yescharacteristic
610C23×C4C23×C3111yescharacteristic
611C2×D8—22no—
612C2×D8—22no—
613C2×D8—22no—
614C2×D8—22no—
615C2×D8—22no—
616C2×D8—22no—
617C2×D8—41no—
618C2×D8—41no—
619C2×D8—41no—
620C2×M16—22no—
621C2×M16—22no—
622C2×M16—41no—
623C22×C8C23×C3111yescharacteristic
624C22×C8C23×C3111yescharacteristic
625C22×C8C23×C3111yescharacteristic
626C22×C8C23×C3111yescharacteristic
627#127—22no—
628#127—22no—
629#121—28no—
630#121—22no—
631#121—22no—
632#121—22no—
633#121—22no—
634#121—22no—
635#121—22no—
636#121—41no—
637#121D4×C3114yescomplemented
638#120—28no—
639#120—28no—
640C4×D4—22no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644#117—22no—
645#117—41no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4D4×C3111yescharacteristic
648C2×C4⋊C4C23×C3111yescharacteristic
649C2×C4⋊C4C23×C3111yescharacteristic
650C2×C4⋊C4C23×C3111yescharacteristic
651C2×C4⋊C4C23×C3111yescharacteristic
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4D4×C3111yescharacteristic
662C2×C22⋊C4D4×C3111yescharacteristic
663C2×C42—21no—
664C2×C42C23×C3111yescharacteristic
665#106—22no—
666#102—22no—
667#102—22no—
668#102—22no—
669#102—22no—
670#102—22no—
671#102—22no—
672#102—22no—
673#102—22no—
674#102—41no—
675#102D4×C3114yescomplemented
676C22⋊C8—22no—
677C22⋊C8—22no—
678C22⋊C8—41no—
679#95—21no—
680#95—21no—
681C31#2444011yescharacteristic, direct product factor, Sylow
682C24—21no—
683C24—24no—
684C24—21no—
685C24—21no—
686C24—24no—
687C24—21no—
688C24—42no—
689C24—42no—
690C24—42no—
691C24—42no—
692C24—42no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24—81no—
700C24C2×D4×C3111yescharacteristic
701C24C2×D4×C3111yescharacteristic
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—22no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—432no—
743C2×D4—44no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—44no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4—81no—
757C2×D4C2×D4×C3112yes—
758C2×D4C2×D4×C3112yes—
759C2×D4C2×D4×C3112yes—
760C2×D4C2×D4×C3112yes—
761C2×D4#41×C3112yes—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
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—42no—
778C22×C4—42no—
779C22×C4C2×D4×C3111yescharacteristic
780C22×C4C2×D4×C3111yescharacteristic
781C22×C4C2×D4×C3111yescharacteristic
782C22×C4C2×D4×C3112yes—
783C22×C4C2×D4×C3112yes—
784C22×C4C2×D4×C3111yescharacteristic
785C22×C4C24×C3111yescharacteristic
786D8—44no—
787D8—44no—
788D8—44no—
789M16—44no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8C2×D4×C3112yescomplemented
802C4⋊C4—22no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—81no—
810C4⋊C4C2×D4×C3112yes—
811C4⋊C4C2×D4×C3112yescomplemented
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4—22no—
815C22⋊C4—24no—
816C22⋊C4—22no—
817C22⋊C4—42no—
818C22⋊C4—42no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—81no—
822C22⋊C4—81no—
823C42—21no—
824C42—21no—
825C42—42no—
826C23—21no—
827C23—22no—
828C23—21no—
829C23—21no—
830C23—22no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—22no—
842C23—22no—
843C23—48no—
844C23—48no—
845C23—48no—
846C23—48no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23C31×#12012yes—
881C23C31×AGL(1,ℤ/8)12yes—
882C23C22×D4×C3111yescharacteristic
883D4—28no—
884D4—22no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—48no—
892D4—48no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—41no—
901D4—41no—
902D4—41no—
903D4—41no—
904D4—84no—
905D4—84no—
906D4—84no—
907D4C31×#12114yes—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—48no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4C31×#12012yes—
940C2×C4C31×AGL(1,ℤ/8)12yes—
941C2×C4C22×D4×C3111yescharacteristic
942C2×C4C22×D4×C3111yescharacteristic
943C2×C4C22×D4×C3111yescharacteristic
944C2×C4C2×#41×C3111yescharacteristic
945C2×C4C31×H(5,𝔽2)11yescharacteristic
946C2×C4C31×H(5,𝔽2)11yescharacteristic
947C8—22no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—24no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—41no—
959C22—42no—
960C22—41no—
961C22—42no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—816no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22C2×C31×#12011yescharacteristic
996C22D42×C3111yescharacteristic
997C22C31×#54611yescharacteristic
998C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
999C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
1000C22C31×#57611yescharacteristic
1001C22C31×#57611yescharacteristic
1002C4—22no—
1003C4—22no—
1004C4—41no—
1005C4—42no—
1006C4—41no—
1007C4—42no—
1008C4—81no—
1009C4—81no—
1010C4C2×C31×#12111yescharacteristic
1011C4C31×#53411yescharacteristic
1012C4D42×C3111yescharacteristic
1013C4C31×#54611yescharacteristic
1014C2—42no—
1015C2—42no—
1016C2—44no—
1017C2—82no—
1018C2—82no—
1019C2—161no—
1020C2C31×#241011yescharacteristic
1021C2C31×#300311yescharacteristic
1022C2C31×#300811yescharacteristic
1023C2C31×#326411yescharacteristic
1024C2C31×#327411yescharacteristic
1025C2C31×#331811yescharacteristic
1026C2C31×#332511yescharacteristic
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×D42×C31C2semidirect
2. C2×C31×#469C2semidirect
3. C2×C31×#447C2semidirect
4. C2×C31×#447C2semidirect
5. C2×C31×#418C2semidirect
6. C31×#2414C2semidirect
7. C31×#2041C2semidirect
8. C31×#2034C2semidirect
9. C31×#2011C2semidirect
10. C31×#1999C2semidirect
11. C31×#1879C2semidirect
12. C31×#1875C2semidirect
13. C31×#1870C2semidirect
14. C31×#1864C2semidirect
15. C31×#1786C2semidirect
20. C22×D8×C31C22semidirect
21. C22×D8×C31C22semidirect
22. C22×M16×C31C22semidirect
29. C2×C31×#121C22semidirect
30. C2×C31×#121C22semidirect
35. C2×C31×#117C22semidirect
39. C2×C31×#106C22semidirect
44. C2×C31×#102C22semidirect
45. C2×C31×#102C22semidirect
46. C2×C31×#102C22semidirect
47. C2×C31×#102C22semidirect
48. C2×C31×#102C22semidirect
49. C2×C31×#102C22semidirect
50. C2×C31×#102C22semidirect
51. C2×C31×C22⋊C8C22semidirect
52. C2×C31×C22⋊C8C22semidirect
53. C2×C31×C22⋊C8C22semidirect
57. C31×#390C22semidirect
58. C31×#389C22semidirect
60. C31×#380C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#336C22semidirect
64. C31×#336C22semidirect
90. C22×D4×C31D4semidirect
124. C31×#121D4semidirect
162. C31×#102D4semidirect
287. C2×C8×C31C2×D4semidirect
297. C4⋊C4×C31C2×D4semidirect
312. #24440C31direct (N × H)
438. C2×D42C2×C31semidirect
439. C2×#469C2×C31semidirect
440. C2×#447C2×C31semidirect
441. C2×#447C2×C31semidirect
442. C2×#418C2×C31semidirect
443. #2414C2×C31semidirect
444. #2041C2×C31semidirect
445. #2034C2×C31semidirect
446. #2011C2×C31semidirect
447. #1999C2×C31semidirect
448. #1879C2×C31semidirect
449. #1875C2×C31semidirect
450. #1870C2×C31semidirect
451. #1864C2×C31semidirect
452. #1786C2×C31semidirect
520. C22×D8C22×C31semidirect
521. C22×D8C22×C31semidirect
522. C22×M16C22×C31semidirect
529. C2×#121C22×C31semidirect
530. C2×#121C22×C31semidirect
535. C2×#117C22×C31semidirect
539. C2×#106C22×C31semidirect
544. C2×#102C22×C31semidirect
545. C2×#102C22×C31semidirect
546. C2×#102C22×C31semidirect
547. C2×#102C22×C31semidirect
548. C2×#102C22×C31semidirect
549. C2×#102C22×C31semidirect
550. C2×#102C22×C31semidirect
551. C2×C22⋊C8C22×C31semidirect
552. C2×C22⋊C8C22×C31semidirect
553. C2×C22⋊C8C22×C31semidirect
557. #390C22×C31semidirect
558. #389C22×C31semidirect
560. #380C22×C31semidirect
561. #340C22×C31semidirect
562. #340C22×C31semidirect
563. #336C22×C31semidirect
564. #336C22×C31semidirect
603. C22×D4D4×C31semidirect
637. #121D4×C31semidirect
675. #102D4×C31semidirect
681. C31#24440direct (N × H)
801. C2×C8C2×D4×C31semidirect
811. C4⋊C4C2×D4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C312
C2×C31×#4692
C2×C31×#4472
C2×C31×#4182
C31×#24142
C31×#20412
C31×#20342
C31×#20112
C31×#19992
C31×#18792
C31×#18752
C31×#18702
C31×#18642
C31×#17862
#2444031