Finite Group Databasebeta

← C31×#22884 #21479643

Subgroups — C31×#22884 #21479643

Order 7936.

1274 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#450C211yesmaximal, characteristic
2C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
3C2×C31×#418C211yesmaximal, characteristic
4C31×#2362C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C31C211yesmaximal, characteristic
6C31×#1973C211yesmaximal, characteristic, complemented
7C31×#1934C211yesmaximal, characteristic, complemented
8C31×#1926C211yesmaximal, characteristic, complemented
9C31×#1894C211yesmaximal, characteristic, complemented
10C31×#1880C211yesmaximal, characteristic, complemented
11C31×#1877C211yesmaximal, characteristic, complemented
12C31×#1862C211yesmaximal, characteristic, complemented
13C31×#1854C211yesmaximal, characteristic, complemented
14C31×#1762C211yesmaximal, characteristic, complemented
15C31×#1753C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic
20C2×C31×C22⋊Q8C2211yescharacteristic
21C2×C4×Q8×C31C2211yescharacteristic, complemented
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C2×C31×#117C2211yescharacteristic
25C22×C22⋊C4×C31—21no—
26C31×#450C418yescomplemented
27C4×SD16×C31—24no—
28C2×C31×#107C2211yescharacteristic, complemented
29C2×C31×#106C2211yescharacteristic, complemented
30C31×#418—24no—
31C2×C31×#103C2211yescharacteristic, complemented
32C2×C31×#103C2211yescharacteristic, complemented
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C2×C31×#97C2211yescharacteristic, complemented
41C2×C4×C8×C31C2211yescharacteristic, complemented
42C31×#391C2211yescharacteristic, complemented
43C31×#390C2211yescharacteristic
44C31×#390C2211yescharacteristic
45C31×#389C2211yescharacteristic, complemented
46C31×#388—21no—
47C31×#388—21no—
48C31×#387—21no—
49C31×#386—21no—
50C31×#386—21no—
51C31×#380C2211yescharacteristic
52C31×#379—21no—
53C4×C4⋊C4×C31—21no—
54C4×C4⋊C4×C31C2211yescharacteristic, complemented
55C4×C22⋊C4×C31C2211yescharacteristic
56C31×#340C2211yescharacteristic, complemented
57C31×#340C2211yescharacteristic, complemented
58C31×#340C2211yescharacteristic, complemented
59C31×#340C2211yescharacteristic, complemented
60C31×#336C2211yescharacteristic, complemented
61C31×#336C2211yescharacteristic, complemented
62C25×C31—21no—
63C22×Q8×C31C2311yescharacteristic
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—21no—
67C22×D4×C31—22no—
68C22×D4×C31—41no—
69C22×D4×C31—41no—
70C22×D4×C31C2×C414yes—
71C22×D4×C31C2311yescharacteristic
72C22×D4×C31C2311yescharacteristic
73C23×C4×C31—21no—
74C23×C4×C31—21no—
75C23×C4×C31C2311yescharacteristic
76C2×SD16×C31—22no—
77C2×SD16×C31—22no—
78C2×SD16×C31—41no—
79C2×SD16×C31—41no—
80C2×SD16×C31C2×C414yes—
81C2×SD16×C31C2×C414yescomplemented
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×C22⋊Q8—22no—
90C31×C22⋊Q8C2×C414yescomplemented
91C4×Q8×C31—22no—
92C4×Q8×C31—41no—
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C4×D4×C31—41no—
96C4×D4×C31—41no—
97C31×#117—22no—
98C31×#117—41no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—44no—
117C2×C22⋊C4×C31D411yescharacteristic
118C2×C22⋊C4×C31D411yescharacteristic
119C2×C42×C31—21no—
120C2×C42×C31—21no—
121C2×C42×C31—21no—
122C2×C42×C31C2311yescharacteristic
123C2×C42×C31C2311yescharacteristic
124C31×#107—41no—
125C31×#106—22no—
126C31×#103—22no—
127C31×#103—41no—
128C31×#102—22no—
129C31×#102—22no—
130C31×#102—22no—
131C31×#102C2×C414yes—
132C31×#102C2×C414yescomplemented
133C31×#102D414yes—
134C31×C22⋊C8C2×C414yescomplemented
135C31×#97—41no—
136C4×C8×C31—22no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95D411yescharacteristic
143C31×#95D411yescharacteristic
144C24×C31—21no—
145C24×C31—21no—
146C24×C31—24no—
147C24×C31—42no—
148C24×C31—42no—
149C24×C31—42no—
150C24×C31—42no—
151C24×C31—81no—
152C24×C31—81no—
153C24×C31C2×D411yescharacteristic
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31—21no—
157C2×Q8×C31—21no—
158C2×Q8×C31—21no—
159C2×Q8×C31C22×C412yes—
160C2×D4×C31—28no—
161C2×D4×C31—24no—
162C2×D4×C31—21no—
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—44no—
171C2×D4×C31—44no—
172C2×D4×C31—44no—
173C2×D4×C31—42no—
174C2×D4×C31—42no—
175C2×D4×C31C22×C412yes—
176C2×D4×C31C22×C412yes—
177C2×D4×C31C2×D412yes—
178C2×D4×C31#4112yes—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
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—42no—
190C22×C4×C31—42no—
191C22×C4×C31—42no—
192C22×C4×C31—42no—
193C22×C4×C31—81no—
194C22×C4×C31—81no—
195C22×C4×C31C22×C412yes—
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31#4112yes—
202C22×C4×C31C2411yescharacteristic
203SD16×C31—28no—
204SD16×C31—44no—
205M16×C31—44no—
206C2×C8×C31—21no—
207C2×C8×C31—21no—
208C2×C8×C31—21no—
209C2×C8×C31—21no—
210C2×C8×C31—21no—
211C2×C8×C31—21no—
212C2×C8×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31—21no—
215C2×C8×C31C22×C412yes—
216C2×C8×C31C22×C412yes—
217C2×C8×C31C2×D412yes—
218C4⋊C4×C31—24no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—42no—
228C4⋊C4×C31—42no—
229C4⋊C4×C31C22×C412yes—
230C4⋊C4×C31C2×D412yes—
231C22⋊C4×C31—24no—
232C22⋊C4×C31—22no—
233C22⋊C4×C31—41no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—42no—
236C22⋊C4×C31—42no—
237C22⋊C4×C31—42no—
238C22⋊C4×C31—42no—
239C22⋊C4×C31—42no—
240C22⋊C4×C31—81no—
241C22⋊C4×C31—81no—
242C42×C31—21no—
243C42×C31—21no—
244C42×C31—21no—
245C42×C31—21no—
246C42×C31—42no—
247C42×C31—42no—
248C42×C31—42no—
249#22884C3111yesmaximal, characteristic, direct product factor, Sylow
250C23×C31—22no—
251C23×C31—21no—
252C23×C31—22no—
253C23×C31—22no—
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—21no—
259C23×C31—22no—
260C23×C31—48no—
261C23×C31—48no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—84no—
273C23×C31—84no—
274C23×C31—84no—
275C23×C31—84no—
276C23×C31—84no—
277C23×C31C4×D412yes—
278C23×C31C22×D411yescharacteristic
279Q8×C31—22no—
280Q8×C31—22no—
281Q8×C31—41no—
282Q8×C31—41no—
283D4×C31—22no—
284D4×C31—22no—
285D4×C31—22no—
286D4×C31—22no—
287D4×C31—22no—
288D4×C31—48no—
289D4×C31—41no—
290D4×C31—41no—
291D4×C31C4×D414yes—
292C2×C4×C31—21no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—22no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
299C2×C4×C31—22no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—21no—
303C2×C4×C31—22no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
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—84no—
328C2×C4×C31—84no—
329C2×C4×C31C4×D412yes—
330C2×C4×C31AGL(1,ℤ/8)12yes—
331C2×C4×C31C23×C411yescharacteristic
332C2×C4×C31C22×D411yescharacteristic
333C2×C4×C31C2×#4111yescharacteristic
334C2×C4×C31C2×#4111yescharacteristic
335C2×C4×C31H(5,𝔽2)11yescharacteristic
336C2×C4×C31H(5,𝔽2)11yescharacteristic
337C8×C31—22no—
338C8×C31—22no—
339C8×C31—22no—
340C8×C31—41no—
341C2×#450C2×C3111yescharacteristic
342C2×C4×SD16C2×C3111yescharacteristic, complemented
343C2×#418C2×C3111yescharacteristic
344#2362C2×C3111yescharacteristic, complemented
345D4×C22⋊C4C2×C3111yescharacteristic
346#1973C2×C3111yescharacteristic, complemented
347#1934C2×C3111yescharacteristic, complemented
348#1926C2×C3111yescharacteristic, complemented
349#1894C2×C3111yescharacteristic, complemented
350#1880C2×C3111yescharacteristic, complemented
351#1877C2×C3111yescharacteristic, complemented
352#1862C2×C3111yescharacteristic, complemented
353#1854C2×C3111yescharacteristic, complemented
354#1762C2×C3111yescharacteristic, complemented
355#1753C2×C3111yescharacteristic, complemented
356C22×C31—22no—
357C22×C31—24no—
358C22×C31—22no—
359C22×C31—22no—
360C22×C31—42no—
361C22×C31—42no—
362C22×C31—42no—
363C22×C31—41no—
364C22×C31—41no—
365C22×C31—42no—
366C22×C31—41no—
367C22×C31—42no—
368C22×C31—42no—
369C22×C31—41no—
370C22×C31—42no—
371C22×C31—42no—
372C22×C31—42no—
373C22×C31—816no—
374C22×C31—81no—
375C22×C31—81no—
376C22×C31—81no—
377C22×C31—81no—
378C22×C31C2×C4×D411yescharacteristic
379C22×C31D4211yescharacteristic
380C22×C31#54611yescharacteristic
381C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
382C22×C31#57511yescharacteristic
383C22×C31#57711yescharacteristic
384C22×C31#57711yescharacteristic
385C4×C31—22no—
386C4×C31—22no—
387C4×C31—42no—
388C4×C31—42no—
389C4×C31—41no—
390C4×C31—42no—
391C4×C31—41no—
392C4×C31—41no—
393C4×C31—81no—
394C4×C31—81no—
395C4×C31—81no—
396C4×C31C2×C4×D411yescharacteristic
397C4×C31#51811yescharacteristic
398C4×C31#54611yescharacteristic
399C4×C31#55111yescharacteristic
400C23×D4C22×C3111yescharacteristic
401C22×SD16C22×C3111yescharacteristic
402C22×SD16C22×C3111yescharacteristic
403C22×M16C22×C3111yescharacteristic
404C2×C22⋊Q8C22×C3111yescharacteristic
405C2×C4×Q8C22×C3111yescharacteristic, complemented
406C2×C4×D4C22×C3111yescharacteristic
407C2×C4×D4C22×C3111yescharacteristic
408C2×#117C22×C3111yescharacteristic
409C22×C22⋊C4—21no—
410#450C4×C3118yescomplemented
411C4×SD16—24no—
412C2×#107C22×C3111yescharacteristic, complemented
413C2×#106C22×C3111yescharacteristic, complemented
414#418—24no—
415C2×#103C22×C3111yescharacteristic, complemented
416C2×#103C22×C3111yescharacteristic, complemented
417C2×#102C22×C3111yescharacteristic
418C2×#102C22×C3111yescharacteristic
419C2×#102C22×C3111yescharacteristic
420C2×#102C22×C3111yescharacteristic
421C2×#102C22×C3111yescharacteristic
422C2×#102C22×C3111yescharacteristic
423C2×C22⋊C8C22×C3111yescharacteristic
424C2×#97C22×C3111yescharacteristic, complemented
425C2×C4×C8C22×C3111yescharacteristic, complemented
426#391C22×C3111yescharacteristic, complemented
427#390C22×C3111yescharacteristic
428#390C22×C3111yescharacteristic
429#389C22×C3111yescharacteristic, complemented
430#388—21no—
431#388—21no—
432#387—21no—
433#386—21no—
434#386—21no—
435#380C22×C3111yescharacteristic
436#379—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4C22×C3111yescharacteristic, complemented
439C4×C22⋊C4C22×C3111yescharacteristic
440#340C22×C3111yescharacteristic, complemented
441#340C22×C3111yescharacteristic, complemented
442#340C22×C3111yescharacteristic, complemented
443#340C22×C3111yescharacteristic, complemented
444#336C22×C3111yescharacteristic, complemented
445#336C22×C3111yescharacteristic, complemented
446C2×C31—42no—
447C2×C31—44no—
448C2×C31—82no—
449C2×C31#235811yescharacteristic
450C2×C31C4×AGL(1,ℤ/8)11yescharacteristic
451C2×C31#294911yescharacteristic
452C2×C31#326511yescharacteristic
453C2×C31#326711yescharacteristic
454C2×C31#332311yescharacteristic
455C2×C31#332411yescharacteristic
456C25—21no—
457C22×Q8C23×C3111yescharacteristic
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—21no—
461C22×D4—22no—
462C22×D4—41no—
463C22×D4—41no—
464C22×D4C2×C4×C3114yes—
465C22×D4C23×C3111yescharacteristic
466C22×D4C23×C3111yescharacteristic
467C23×C4—21no—
468C23×C4—21no—
469C23×C4C23×C3111yescharacteristic
470C2×SD16—22no—
471C2×SD16—22no—
472C2×SD16—41no—
473C2×SD16—41no—
474C2×SD16C2×C4×C3114yes—
475C2×SD16C2×C4×C3114yescomplemented
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—41no—
479C22×C8C23×C3111yescharacteristic
480C22×C8C23×C3111yescharacteristic
481C22×C8C23×C3111yescharacteristic
482C22×C8C23×C3111yescharacteristic
483C22⋊Q8—22no—
484C22⋊Q8C2×C4×C3114yescomplemented
485C4×Q8—22no—
486C4×Q8—41no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—41no—
490C4×D4—41no—
491#117—22no—
492#117—41no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4C23×C3111yescharacteristic
497C2×C4⋊C4C23×C3111yescharacteristic
498C2×C4⋊C4C23×C3111yescharacteristic
499C2×C4⋊C4C23×C3111yescharacteristic
500C2×C4⋊C4C23×C3111yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—44no—
511C2×C22⋊C4D4×C3111yescharacteristic
512C2×C22⋊C4D4×C3111yescharacteristic
513C2×C42—21no—
514C2×C42—21no—
515C2×C42—21no—
516C2×C42C23×C3111yescharacteristic
517C2×C42C23×C3111yescharacteristic
518#107—41no—
519#106—22no—
520#103—22no—
521#103—41no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102C2×C4×C3114yes—
526#102C2×C4×C3114yescomplemented
527#102D4×C3114yes—
528C22⋊C8C2×C4×C3114yescomplemented
529#97—41no—
530C4×C8—22no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95D4×C3111yescharacteristic
537#95D4×C3111yescharacteristic
538C31#2288411yescharacteristic, direct product factor, Sylow
539C24—21no—
540C24—21no—
541C24—24no—
542C24—42no—
543C24—42no—
544C24—42no—
545C24—42no—
546C24—81no—
547C24—81no—
548C24C2×D4×C3111yescharacteristic
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8C22×C4×C3112yes—
555C2×D4—28no—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4C22×C4×C3112yes—
571C2×D4C22×C4×C3112yes—
572C2×D4C2×D4×C3112yes—
573C2×D4#41×C3112yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4C22×C4×C3112yes—
591C22×C4C2×D4×C3111yescharacteristic
592C22×C4C2×D4×C3111yescharacteristic
593C22×C4C2×D4×C3111yescharacteristic
594C22×C4C2×D4×C3111yescharacteristic
595C22×C4C2×D4×C3111yescharacteristic
596C22×C4#41×C3112yes—
597C22×C4C24×C3111yescharacteristic
598SD16—28no—
599SD16—44no—
600M16—44no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C22×C4×C3112yes—
611C2×C8C22×C4×C3112yes—
612C2×C8C2×D4×C3112yes—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4C22×C4×C3112yes—
625C4⋊C4C2×D4×C3112yes—
626C22⋊C4—24no—
627C22⋊C4—22no—
628C22⋊C4—41no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C42—42no—
644C23—22no—
645C23—21no—
646C23—22no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—48no—
655C23—48no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—84no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23C4×D4×C3112yes—
672C23C22×D4×C3111yescharacteristic
673Q8—22no—
674Q8—22no—
675Q8—41no—
676Q8—41no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—41no—
684D4—41no—
685D4C4×D4×C3114yes—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4C4×D4×C3112yes—
724C2×C4C31×AGL(1,ℤ/8)12yes—
725C2×C4C23×C4×C3111yescharacteristic
726C2×C4C22×D4×C3111yescharacteristic
727C2×C4C2×#41×C3111yescharacteristic
728C2×C4C2×#41×C3111yescharacteristic
729C2×C4C31×H(5,𝔽2)11yescharacteristic
730C2×C4C31×H(5,𝔽2)11yescharacteristic
731C8—22no—
732C8—22no—
733C8—22no—
734C8—41no—
735C22—22no—
736C22—24no—
737C22—22no—
738C22—22no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—41no—
743C22—41no—
744C22—42no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—816no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22C2×C4×D4×C3111yescharacteristic
758C22D42×C3111yescharacteristic
759C22C31×#54611yescharacteristic
760C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
761C22C31×#57511yescharacteristic
762C22C31×#57711yescharacteristic
763C22C31×#57711yescharacteristic
764C4—22no—
765C4—22no—
766C4—42no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—81no—
773C4—81no—
774C4—81no—
775C4C2×C4×D4×C3111yescharacteristic
776C4C31×#51811yescharacteristic
777C4C31×#54611yescharacteristic
778C4C31×#55111yescharacteristic
779C2—42no—
780C2—44no—
781C2—82no—
782C2C31×#235811yescharacteristic
783C2C4×C31×AGL(1,ℤ/8)11yescharacteristic
784C2C31×#294911yescharacteristic
785C2C31×#326511yescharacteristic
786C2C31×#326711yescharacteristic
787C2C31×#332311yescharacteristic
788C2C31×#332411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C31C2semidirect
4. C31×#2362C2semidirect
6. C31×#1973C2semidirect
7. C31×#1934C2semidirect
8. C31×#1926C2semidirect
9. C31×#1894C2semidirect
10. C31×#1880C2semidirect
11. C31×#1877C2semidirect
12. C31×#1862C2semidirect
13. C31×#1854C2semidirect
14. C31×#1762C2semidirect
15. C31×#1753C2semidirect
21. C2×C4×Q8×C31C22semidirect
26. C31×#450C4semidirect
28. C2×C31×#107C22semidirect
29. C2×C31×#106C22semidirect
31. C2×C31×#103C22semidirect
32. C2×C31×#103C22semidirect
40. C2×C31×#97C22semidirect
41. C2×C4×C8×C31C22semidirect
42. C31×#391C22semidirect
45. C31×#389C22semidirect
54. C4×C4⋊C4×C31C22semidirect
56. C31×#340C22semidirect
57. C31×#340C22semidirect
58. C31×#340C22semidirect
59. C31×#340C22semidirect
60. C31×#336C22semidirect
61. C31×#336C22semidirect
81. C2×SD16×C31C2×C4semidirect
90. C31×C22⋊Q8C2×C4semidirect
132. C31×#102C2×C4semidirect
134. C31×C22⋊C8C2×C4semidirect
249. #22884C31direct (N × H)
342. C2×C4×SD16C2×C31semidirect
344. #2362C2×C31semidirect
346. #1973C2×C31semidirect
347. #1934C2×C31semidirect
348. #1926C2×C31semidirect
349. #1894C2×C31semidirect
350. #1880C2×C31semidirect
351. #1877C2×C31semidirect
352. #1862C2×C31semidirect
353. #1854C2×C31semidirect
354. #1762C2×C31semidirect
355. #1753C2×C31semidirect
405. C2×C4×Q8C22×C31semidirect
410. #450C4×C31semidirect
412. C2×#107C22×C31semidirect
413. C2×#106C22×C31semidirect
415. C2×#103C22×C31semidirect
416. C2×#103C22×C31semidirect
424. C2×#97C22×C31semidirect
425. C2×C4×C8C22×C31semidirect
426. #391C22×C31semidirect
429. #389C22×C31semidirect
438. C4×C4⋊C4C22×C31semidirect
440. #340C22×C31semidirect
441. #340C22×C31semidirect
442. #340C22×C31semidirect
443. #340C22×C31semidirect
444. #336C22×C31semidirect
445. #336C22×C31semidirect
475. C2×SD16C2×C4×C31semidirect
484. C22⋊Q8C2×C4×C31semidirect
526. #102C2×C4×C31semidirect
528. C22⋊C8C2×C4×C31semidirect
538. C31#22884direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4502
C2×C4×SD16×C312
C2×C31×#4182
C31×#23622
D4×C22⋊C4×C312
C31×#19732
C31×#19342
C31×#19262
C31×#18942
C31×#18802
C31×#18772
C31×#18622
C31×#18542
C31×#17622
C31×#17532
#2288431