Finite Group Databasebeta

← C31×#25958 #21482717

Subgroups — C31×#25958 #21482717

Order 7936.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#476C211yesmaximal, characteristic, complemented
2C22×C31×#102C211yesmaximal, characteristic
3C31×#2440C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C31C211yesmaximal, characteristic
5C31×#2094C211yesmaximal, characteristic, complemented
6C31×#2065C211yesmaximal, characteristic, complemented
7C31×#2065C211yesmaximal, characteristic, complemented
8C31×#2023C211yesmaximal, characteristic, complemented
9C31×#1864C211yesmaximal, characteristic, complemented
10C31×#1864C211yesmaximal, characteristic, complemented
11C31×#1853C211yesmaximal, characteristic, complemented
12C31×#1850C211yesmaximal, characteristic, complemented
13C31×#1807C211yesmaximal, characteristic, complemented
14C31×#1802C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic
16C23×D4×C31C2211yescharacteristic
17C23×C8×C31C2211yescharacteristic
18C2×C31×C4⋊Q8C2211yescharacteristic, complemented
19C2×C31×C22⋊Q8—21no—
20C2×C4×D4×C31C2211yescharacteristic
21C2×C4×D4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31—21no—
24C31×#476—24no—
25C2×C31×#106C2211yescharacteristic, complemented
26C2×C31×#106C2211yescharacteristic, complemented
27C2×C31×#106C2211yescharacteristic, complemented
28C2×C31×#106C2211yescharacteristic, complemented
29C2×C31×C4⋊C8C2211yescharacteristic, complemented
30C2×C31×C4⋊C8C2211yescharacteristic, complemented
31C2×C31×#102—24no—
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×C22⋊C8C2211yescharacteristic
41C31×#398—21no—
42C31×#395—21no—
43C31×#390C2211yescharacteristic
44C31×#390C2211yescharacteristic
45C31×#389C2211yescharacteristic, complemented
46C31×#389C2211yescharacteristic, complemented
47C31×#386—21no—
48C31×#386—21no—
49C31×#385—21no—
50C31×#384C2211yescharacteristic, complemented
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C31×#379—21no—
54C4×C22⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic, complemented
56C31×#340C2211yescharacteristic, complemented
57C31×#340C2211yescharacteristic, complemented
58C31×#340C2211yescharacteristic, complemented
59C31×#336C2211yescharacteristic, complemented
60C31×#336C2211yescharacteristic, complemented
61C25×C31—21no—
62C22×Q8×C31—21no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—21no—
66C22×D4×C31—22no—
67C22×D4×C31—41no—
68C22×D4×C31—41no—
69C22×D4×C31Q814yescomplemented
70C22×D4×C31C2311yescharacteristic
71C22×D4×C31C2311yescharacteristic
72C23×C4×C31—21no—
73C23×C4×C31—21no—
74C23×C4×C31—21no—
75C23×C4×C31C2311yescharacteristic
76C22×C8×C31—22no—
77C22×C8×C31—22no—
78C22×C8×C31—41no—
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C31×C4⋊Q8—22no—
84C31×C4⋊Q8—41no—
85C31×C22⋊Q8—44no—
86C4×D4×C31—22no—
87C4×D4×C31—22no—
88C4×D4×C31—41no—
89C4×D4×C31—41no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—41no—
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
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—44no—
113C2×C22⋊C4×C31D411yescharacteristic
114C2×C22⋊C4×C31D411yescharacteristic
115C2×C42×C31C2311yescharacteristic
116C2×C42×C31C2311yescharacteristic
117C31×#106—22no—
118C31×#106—22no—
119C31×#106—41no—
120C31×#106—41no—
121C31×C4⋊C8—22no—
122C31×C4⋊C8—41no—
123C31×#102—22no—
124C31×#102—22no—
125C31×#102—22no—
126C31×#102—22no—
127C31×#102—22no—
128C31×#102—41no—
129C31×#102—41no—
130C31×#102D414yes—
131C31×C22⋊C8—22no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95D411yescharacteristic
137C31×#95D411yescharacteristic
138C24×C31—21no—
139C24×C31—21no—
140C24×C31—24no—
141C24×C31—42no—
142C24×C31—42no—
143C24×C31—42no—
144C24×C31—42no—
145C24×C31—81no—
146C24×C31—81no—
147C24×C31C2×D411yescharacteristic
148C2×Q8×C31—42no—
149C2×Q8×C31—42no—
150C2×Q8×C31—81no—
151C2×D4×C31—28no—
152C2×D4×C31—24no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—44no—
162C2×D4×C31—44no—
163C2×D4×C31—44no—
164C2×D4×C31—42no—
165C2×D4×C31—42no—
166C2×D4×C31C2×D412yes—
167C2×D4×C31C2×Q812yes—
168C2×D4×C31C2×Q812yes—
169C2×D4×C31#4112yes—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—42no—
181C22×C4×C31—42no—
182C22×C4×C31—42no—
183C22×C4×C31—42no—
184C22×C4×C31—42no—
185C22×C4×C31—42no—
186C22×C4×C31—81no—
187C22×C4×C31—81no—
188C22×C4×C31—81no—
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31C2×D411yescharacteristic
191C22×C4×C31C2×D411yescharacteristic
192C22×C4×C31C2×D411yescharacteristic
193C22×C4×C31C2×D411yescharacteristic
194C22×C4×C31C2×Q812yes—
195C22×C4×C31#4112yes—
196C22×C4×C31C2411yescharacteristic
197C2×C8×C31—21no—
198C2×C8×C31—21no—
199C2×C8×C31—21no—
200C2×C8×C31—21no—
201C2×C8×C31—21no—
202C2×C8×C31—21no—
203C2×C8×C31—21no—
204C2×C8×C31—21no—
205C2×C8×C31—21no—
206C2×C8×C31—21no—
207C2×C8×C31—21no—
208C2×C8×C31—44no—
209C2×C8×C31C2×D412yes—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—42no—
222C4⋊C4×C31—42no—
223C4⋊C4×C31—42no—
224C4⋊C4×C31—42no—
225C4⋊C4×C31—42no—
226C4⋊C4×C31—81no—
227C4⋊C4×C31C2×D412yes—
228C22⋊C4×C31—22no—
229C22⋊C4×C31—42no—
230C22⋊C4×C31—42no—
231C22⋊C4×C31—42no—
232C22⋊C4×C31—42no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—81no—
236C22⋊C4×C31—81no—
237C22⋊C4×C31SD1614yes—
238C42×C31—21no—
239C42×C31—21no—
240C42×C31—21no—
241C42×C31—21no—
242#25958C3111yesmaximal, characteristic, direct product factor, Sylow
243C23×C31—21no—
244C23×C31—21no—
245C23×C31—21no—
246C23×C31—21no—
247C23×C31—22no—
248C23×C31—22no—
249C23×C31—22no—
250C23×C31—22no—
251C23×C31—48no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31—41no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—41no—
262C23×C31—48no—
263C23×C31—84no—
264C23×C31—84no—
265C23×C31—84no—
266C23×C31—84no—
267C23×C31—84no—
268C23×C31C22⋊Q812yes—
269C23×C31C2×SD1612yes—
270C23×C31AGL(1,ℤ/8)12yes—
271C23×C31C22×D411yescharacteristic
272Q8×C31—84no—
273D4×C31—22no—
274D4×C31—22no—
275D4×C31—22no—
276D4×C31—22no—
277D4×C31—22no—
278D4×C31—48no—
279D4×C31—41no—
280D4×C31—41no—
281D4×C31C22⋊Q814yescomplemented
282C2×C4×C31—21no—
283C2×C4×C31—21no—
284C2×C4×C31—21no—
285C2×C4×C31—21no—
286C2×C4×C31—21no—
287C2×C4×C31—21no—
288C2×C4×C31—22no—
289C2×C4×C31—22no—
290C2×C4×C31—22no—
291C2×C4×C31—22no—
292C2×C4×C31—21no—
293C2×C4×C31—22no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—41no—
300C2×C4×C31—41no—
301C2×C4×C31—41no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
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—84no—
317C2×C4×C31—84no—
318C2×C4×C31—84no—
319C2×C4×C31C22⋊Q812yes—
320C2×C4×C31C2×SD1612yes—
321C2×C4×C31C2×SD1612yes—
322C2×C4×C31C22×D411yescharacteristic
323C2×C4×C31C22×Q811yescharacteristic
324C2×C4×C31C2×#4111yescharacteristic
325C2×C4×C31C2×#4111yescharacteristic
326C2×C4×C31H(5,𝔽2)11yescharacteristic
327C2×C4×C31H(5,𝔽2)11yescharacteristic
328C8×C31—22no—
329C8×C31—41no—
330C8×C31—41no—
331C8×C31—41no—
332C2×#476C2×C3111yescharacteristic, complemented
333C22×#102C2×C3111yescharacteristic
334#2440C2×C3111yescharacteristic, complemented
335D4×C22⋊C4C2×C3111yescharacteristic
336#2094C2×C3111yescharacteristic, complemented
337#2065C2×C3111yescharacteristic, complemented
338#2065C2×C3111yescharacteristic, complemented
339#2023C2×C3111yescharacteristic, complemented
340#1864C2×C3111yescharacteristic, complemented
341#1864C2×C3111yescharacteristic, complemented
342#1853C2×C3111yescharacteristic, complemented
343#1850C2×C3111yescharacteristic, complemented
344#1807C2×C3111yescharacteristic, complemented
345#1802C2×C3111yescharacteristic, complemented
346#1786C2×C3111yescharacteristic
347C22×C31—22no—
348C22×C31—22no—
349C22×C31—22no—
350C22×C31—22no—
351C22×C31—22no—
352C22×C31—22no—
353C22×C31—24no—
354C22×C31—42no—
355C22×C31—42no—
356C22×C31—42no—
357C22×C31—42no—
358C22×C31—42no—
359C22×C31—42no—
360C22×C31—42no—
361C22×C31—42no—
362C22×C31—42no—
363C22×C31—816no—
364C22×C31—81no—
365C22×C31—81no—
366C22×C31—81no—
367C22×C31—81no—
368C22×C31#47614yescomplemented
369C22×C31C2×C22⋊Q811yescharacteristic
370C22×C31D4211yescharacteristic
371C22×C31#54611yescharacteristic
372C22×C31C22×SD1611yescharacteristic
373C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
374C22×C31#57611yescharacteristic
375C22×C31#57711yescharacteristic
376C4×C31—22no—
377C4×C31—22no—
378C4×C31—22no—
379C4×C31—41no—
380C4×C31—42no—
381C4×C31—41no—
382C4×C31—81no—
383C4×C31—81no—
384C4×C31—81no—
385C4×C31—81no—
386C4×C31—81no—
387C4×C31C2×C22⋊Q811yescharacteristic
388C4×C31#54311yescharacteristic
389C4×C31#54611yescharacteristic
390C4×C31#55111yescharacteristic
391C23×D4C22×C3111yescharacteristic
392C23×C8C22×C3111yescharacteristic
393C2×C4⋊Q8C22×C3111yescharacteristic, complemented
394C2×C22⋊Q8—21no—
395C2×C4×D4C22×C3111yescharacteristic
396C2×C4×D4C22×C3111yescharacteristic
397C22×C4⋊C4C22×C3111yescharacteristic
398C22×C22⋊C4—21no—
399#476—24no—
400C2×#106C22×C3111yescharacteristic, complemented
401C2×#106C22×C3111yescharacteristic, complemented
402C2×#106C22×C3111yescharacteristic, complemented
403C2×#106C22×C3111yescharacteristic, complemented
404C2×C4⋊C8C22×C3111yescharacteristic, complemented
405C2×C4⋊C8C22×C3111yescharacteristic, complemented
406C2×#102—24no—
407C2×#102C22×C3111yescharacteristic
408C2×#102C22×C3111yescharacteristic
409C2×#102C22×C3111yescharacteristic
410C2×#102C22×C3111yescharacteristic
411C2×#102C22×C3111yescharacteristic
412C2×#102C22×C3111yescharacteristic
413C2×#102C22×C3111yescharacteristic
414C2×#102C22×C3111yescharacteristic
415C2×C22⋊C8C22×C3111yescharacteristic
416#398—21no—
417#395—21no—
418#390C22×C3111yescharacteristic
419#390C22×C3111yescharacteristic
420#389C22×C3111yescharacteristic, complemented
421#389C22×C3111yescharacteristic, complemented
422#386—21no—
423#386—21no—
424#385—21no—
425#384C22×C3111yescharacteristic, complemented
426#380C22×C3111yescharacteristic
427#380C22×C3111yescharacteristic
428#379—21no—
429C4×C22⋊C4C22×C3111yescharacteristic
430#340C22×C3111yescharacteristic, complemented
431#340C22×C3111yescharacteristic, complemented
432#340C22×C3111yescharacteristic, complemented
433#340C22×C3111yescharacteristic, complemented
434#336C22×C3111yescharacteristic, complemented
435#336C22×C3111yescharacteristic, complemented
436C2×C31—24no—
437C2×C31—44no—
438C2×C31—82no—
439C2×C31#243711yescharacteristic
440C2×C31C2×#47611yescharacteristic
441C2×C31#308111yescharacteristic
442C2×C31#326411yescharacteristic
443C2×C31D4×SD1611yescharacteristic
444C2×C31#329511yescharacteristic
445C2×C31#330611yescharacteristic
446C25—21no—
447C22×Q8—21no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4—21no—
451C22×D4—22no—
452C22×D4—41no—
453C22×D4—41no—
454C22×D4Q8×C3114yescomplemented
455C22×D4C23×C3111yescharacteristic
456C22×D4C23×C3111yescharacteristic
457C23×C4—21no—
458C23×C4—21no—
459C23×C4—21no—
460C23×C4C23×C3111yescharacteristic
461C22×C8—22no—
462C22×C8—22no—
463C22×C8—41no—
464C22×C8C23×C3111yescharacteristic
465C22×C8C23×C3111yescharacteristic
466C22×C8C23×C3111yescharacteristic
467C22×C8C23×C3111yescharacteristic
468C4⋊Q8—22no—
469C4⋊Q8—41no—
470C22⋊Q8—44no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—41no—
474C4×D4—41no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4C23×C3111yescharacteristic
484C2×C4⋊C4C23×C3111yescharacteristic
485C2×C4⋊C4C23×C3111yescharacteristic
486C2×C4⋊C4C23×C3111yescharacteristic
487C2×C4⋊C4C23×C3111yescharacteristic
488C2×C4⋊C4C23×C3111yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—44no—
498C2×C22⋊C4D4×C3111yescharacteristic
499C2×C22⋊C4D4×C3111yescharacteristic
500C2×C42C23×C3111yescharacteristic
501C2×C42C23×C3111yescharacteristic
502#106—22no—
503#106—22no—
504#106—41no—
505#106—41no—
506C4⋊C8—22no—
507C4⋊C8—41no—
508#102—22no—
509#102—22no—
510#102—22no—
511#102—22no—
512#102—22no—
513#102—41no—
514#102—41no—
515#102D4×C3114yes—
516C22⋊C8—22no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95D4×C3111yescharacteristic
522#95D4×C3111yescharacteristic
523C31#2595811yescharacteristic, direct product factor, Sylow
524C24—21no—
525C24—21no—
526C24—24no—
527C24—42no—
528C24—42no—
529C24—42no—
530C24—42no—
531C24—81no—
532C24—81no—
533C24C2×D4×C3111yescharacteristic
534C2×Q8—42no—
535C2×Q8—42no—
536C2×Q8—81no—
537C2×D4—28no—
538C2×D4—24no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4C2×D4×C3112yes—
553C2×D4C2×Q8×C3112yes—
554C2×D4C2×Q8×C3112yes—
555C2×D4#41×C3112yes—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—81no—
573C22×C4—81no—
574C22×C4—81no—
575C22×C4C2×D4×C3111yescharacteristic
576C22×C4C2×D4×C3111yescharacteristic
577C22×C4C2×D4×C3111yescharacteristic
578C22×C4C2×D4×C3111yescharacteristic
579C22×C4C2×D4×C3111yescharacteristic
580C22×C4C2×Q8×C3112yes—
581C22×C4#41×C3112yes—
582C22×C4C24×C3111yescharacteristic
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—44no—
595C2×C8C2×D4×C3112yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—81no—
613C4⋊C4C2×D4×C3112yes—
614C22⋊C4—22no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—81no—
622C22⋊C4—81no—
623C22⋊C4SD16×C3114yes—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—48no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—48no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23C31×C22⋊Q812yes—
654C23C2×SD16×C3112yes—
655C23C31×AGL(1,ℤ/8)12yes—
656C23C22×D4×C3111yescharacteristic
657Q8—84no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—41no—
665D4—41no—
666D4C31×C22⋊Q814yescomplemented
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—84no—
702C2×C4—84no—
703C2×C4—84no—
704C2×C4C31×C22⋊Q812yes—
705C2×C4C2×SD16×C3112yes—
706C2×C4C2×SD16×C3112yes—
707C2×C4C22×D4×C3111yescharacteristic
708C2×C4C22×Q8×C3111yescharacteristic
709C2×C4C2×#41×C3111yescharacteristic
710C2×C4C2×#41×C3111yescharacteristic
711C2×C4C31×H(5,𝔽2)11yescharacteristic
712C2×C4C31×H(5,𝔽2)11yescharacteristic
713C8—22no—
714C8—41no—
715C8—41no—
716C8—41no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—816no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22C31×#47614yescomplemented
739C22C2×C31×C22⋊Q811yescharacteristic
740C22D42×C3111yescharacteristic
741C22C31×#54611yescharacteristic
742C22C22×SD16×C3111yescharacteristic
743C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
744C22C31×#57611yescharacteristic
745C22C31×#57711yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4—81no—
756C4—81no—
757C4C2×C31×C22⋊Q811yescharacteristic
758C4C31×#54311yescharacteristic
759C4C31×#54611yescharacteristic
760C4C31×#55111yescharacteristic
761C2—24no—
762C2—44no—
763C2—82no—
764C2C31×#243711yescharacteristic
765C2C2×C31×#47611yescharacteristic
766C2C31×#308111yescharacteristic
767C2C31×#326411yescharacteristic
768C2D4×SD16×C3111yescharacteristic
769C2C31×#329511yescharacteristic
770C2C31×#330611yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C22×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
1. C2×C31×#476C2semidirect
3. C31×#2440C2semidirect
5. C31×#2094C2semidirect
6. C31×#2065C2semidirect
7. C31×#2065C2semidirect
8. C31×#2023C2semidirect
9. C31×#1864C2semidirect
10. C31×#1864C2semidirect
11. C31×#1853C2semidirect
12. C31×#1850C2semidirect
13. C31×#1807C2semidirect
14. C31×#1802C2semidirect
18. C2×C31×C4⋊Q8C22semidirect
25. C2×C31×#106C22semidirect
26. C2×C31×#106C22semidirect
27. C2×C31×#106C22semidirect
28. C2×C31×#106C22semidirect
29. C2×C31×C4⋊C8C22semidirect
30. C2×C31×C4⋊C8C22semidirect
45. C31×#389C22semidirect
46. C31×#389C22semidirect
50. C31×#384C22semidirect
55. C31×#340C22semidirect
56. C31×#340C22semidirect
57. C31×#340C22semidirect
58. C31×#340C22semidirect
59. C31×#336C22semidirect
60. C31×#336C22semidirect
69. C22×D4×C31Q8semidirect
242. #25958C31direct (N × H)
281. D4×C31C22⋊Q8semidirect
332. C2×#476C2×C31semidirect
334. #2440C2×C31semidirect
336. #2094C2×C31semidirect
337. #2065C2×C31semidirect
338. #2065C2×C31semidirect
339. #2023C2×C31semidirect
340. #1864C2×C31semidirect
341. #1864C2×C31semidirect
342. #1853C2×C31semidirect
343. #1850C2×C31semidirect
344. #1807C2×C31semidirect
345. #1802C2×C31semidirect
368. C22×C31#476semidirect
393. C2×C4⋊Q8C22×C31semidirect
400. C2×#106C22×C31semidirect
401. C2×#106C22×C31semidirect
402. C2×#106C22×C31semidirect
403. C2×#106C22×C31semidirect
404. C2×C4⋊C8C22×C31semidirect
405. C2×C4⋊C8C22×C31semidirect
420. #389C22×C31semidirect
421. #389C22×C31semidirect
425. #384C22×C31semidirect
430. #340C22×C31semidirect
431. #340C22×C31semidirect
432. #340C22×C31semidirect
433. #340C22×C31semidirect
434. #336C22×C31semidirect
435. #336C22×C31semidirect
454. C22×D4Q8×C31semidirect
523. C31#25958direct (N × H)
666. D4C31×C22⋊Q8semidirect
738. C22C31×#476semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4762
C22×C31×#1022
C31×#24402
D4×C22⋊C4×C312
C31×#20942
C31×#20652
C31×#20232
C31×#18642
C31×#18532
C31×#18502
C31×#18072
C31×#18022
C31×#17862
#2595831