Finite Group Databasebeta

← C31×#24789 #21481548

Subgroups — C31×#24789 #21481548

Order 7936.

1032 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#468C211yesmaximal, characteristic, complemented
2C2×C31×#465C211yesmaximal, characteristic, complemented
3C2×C31×#435C211yesmaximal, characteristic, complemented
4C2×C31×#428C211yesmaximal, characteristic, complemented
5C31×#2416C211yesmaximal, characteristic
6C31×#2415C211yesmaximal, characteristic, complemented
7C31×#2068C211yesmaximal, characteristic, complemented
8C31×#2065C211yesmaximal, characteristic, complemented
9C31×#2035C211yesmaximal, characteristic, complemented
10C31×#2033C211yesmaximal, characteristic, complemented
11C31×#1973C211yesmaximal, characteristic, complemented
12C31×#1944C211yesmaximal, characteristic, complemented
13C31×#1875C211yesmaximal, characteristic, complemented
14C31×#1872C211yesmaximal, characteristic, complemented
15C31×#1808C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×M16×C31C2211yescharacteristic
18C23×C8×C31C2211yescharacteristic
19C2×C31×C22⋊Q8C2211yescharacteristic
20C2×C31×C22⋊Q8C2211yescharacteristic
21C2×C31×#121—21no—
22C2×C31×#121C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C4×D4×C31C2211yescharacteristic
25C2×C31×#117C2211yescharacteristic
26C22×C4⋊C4×C31C2211yescharacteristic
27C31×#468—24no—
28C31×#465—24no—
29C31×#435—24no—
30C31×#428—24no—
31C2×C31×#107C2211yescharacteristic
32C2×C31×#107C2211yescharacteristic
33C2×C31×#107C2211yescharacteristic
34C2×C31×#106C2211yescharacteristic
35C2×C31×#106C2211yescharacteristic
36C2×C31×C4⋊C8C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic
45C2×C31×#97C2211yescharacteristic
46C31×#397—21no—
47C31×#396—21no—
48C31×#394—21no—
49C31×#394—21no—
50C31×#391C2211yescharacteristic
51C31×#390C2211yescharacteristic
52C31×#389—21no—
53C31×#389C2211yescharacteristic
54C31×#389C2211yescharacteristic
55C31×#388—21no—
56C31×#386—21no—
57C31×#380C2211yescharacteristic
58C31×#380C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31D411yescharacteristic
67C22×D4×C31C2311yescharacteristic
68C23×C4×C31—21no—
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C2×SD16×C31—22no—
72C2×SD16×C31—22no—
73C2×SD16×C31—22no—
74C2×M16×C31—22no—
75C2×M16×C31—22no—
76C2×M16×C31D414yescomplemented
77C22×C8×C31—22no—
78C22×C8×C31—22no—
79C22×C8×C31—22no—
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C31×C22⋊Q8—22no—
85C31×C22⋊Q8—22no—
86C31×C22⋊Q8—22no—
87C31×C22⋊Q8—41no—
88C31×#121—22no—
89C31×#121—22no—
90C31×#121—22no—
91C31×#121—41no—
92C31×#121—44no—
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C31×#117—22no—
96C31×#117—41no—
97C2×C4⋊C4×C31—22no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—41no—
104C2×C4⋊C4×C31D411yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
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—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31D411yescharacteristic
121C2×C22⋊C4×C31D411yescharacteristic
122C2×C42×C31—21no—
123C2×C42×C31C2311yescharacteristic
124C31×#107—22no—
125C31×#107—22no—
126C31×#107—22no—
127C31×#106—22no—
128C31×#106D414yescomplemented
129C31×C4⋊C8—22no—
130C31×#103—22no—
131C31×#103—22no—
132C31×#103—41no—
133C31×#102—22no—
134C31×#102—22no—
135C31×#102—41no—
136C31×C22⋊C8—22no—
137C31×C22⋊C8—22no—
138C31×#97—22no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95—21no—
143C31×#95—21no—
144C31×#95—21no—
145C24×C31—21no—
146C24×C31C2×D411yescharacteristic
147C24×C31C2×D411yescharacteristic
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×D4×C31—22no—
155C2×D4×C31—22no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—41no—
163C2×D4×C31—42no—
164C2×D4×C31—42no—
165C2×D4×C31—42no—
166C2×D4×C31—42no—
167C2×D4×C31—42no—
168C2×D4×C31—81no—
169C22×C4×C31—21no—
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—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—42no—
187C22×C4×C31—42no—
188C22×C4×C31—81no—
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31C2×D411yescharacteristic
191C22×C4×C31C2×D411yescharacteristic
192C22×C4×C31C2×D411yescharacteristic
193C22×C4×C31C2×D412yes—
194C22×C4×C31#4112yes—
195C22×C4×C31C2411yescharacteristic
196SD16×C31—44no—
197M16×C31—28no—
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—44no—
207C2×C8×C31C2×D412yes—
208C2×C8×C31C2×D412yes—
209C2×C8×C31C2×D412yes—
210C2×C8×C31#4112yes—
211C4⋊C4×C31—22no—
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—21no—
222C4⋊C4×C31—42no—
223C4⋊C4×C31—42no—
224C4⋊C4×C31—42no—
225C4⋊C4×C31—42no—
226C4⋊C4×C31—42no—
227C4⋊C4×C31C2×D412yes—
228C4⋊C4×C31C2×D412yes—
229C22⋊C4×C31—22no—
230C22⋊C4×C31—22no—
231C22⋊C4×C31—42no—
232C22⋊C4×C31—42no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—42no—
236C22⋊C4×C31—42no—
237C22⋊C4×C31—42no—
238C22⋊C4×C31—42no—
239C22⋊C4×C31—81no—
240C42×C31—21no—
241C42×C31—21no—
242C42×C31—42no—
243#24789C3111yesmaximal, characteristic, direct product factor, Sylow
244C23×C31—21no—
245C23×C31—21no—
246C23×C31—21no—
247C23×C31—21no—
248C23×C31—21no—
249C23×C31—21no—
250C23×C31—21no—
251C23×C31—21no—
252C23×C31—21no—
253C23×C31—21no—
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—41no—
257C23×C31—41no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31#12112yes—
264C23×C31AGL(1,ℤ/8)12yes—
265C23×C31C22×D411yescharacteristic
266Q8×C31—41no—
267Q8×C31—41no—
268Q8×C31—41no—
269Q8×C31—41no—
270D4×C31—44no—
271D4×C31—41no—
272D4×C31—41no—
273D4×C31—41no—
274D4×C31—41no—
275D4×C31—84no—
276D4×C31—84no—
277C2×C4×C31—21no—
278C2×C4×C31—21no—
279C2×C4×C31—22no—
280C2×C4×C31—22no—
281C2×C4×C31—22no—
282C2×C4×C31—22no—
283C2×C4×C31—21no—
284C2×C4×C31—21no—
285C2×C4×C31—21no—
286C2×C4×C31—22no—
287C2×C4×C31—21no—
288C2×C4×C31—22no—
289C2×C4×C31—21no—
290C2×C4×C31—21no—
291C2×C4×C31—21no—
292C2×C4×C31—21no—
293C2×C4×C31—21no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—41no—
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—41no—
317C2×C4×C31—84no—
318C2×C4×C31#12112yes—
319C2×C4×C31C22×D411yescharacteristic
320C2×C4×C31C22×D411yescharacteristic
321C2×C4×C31C2×#4111yescharacteristic
322C2×C4×C31C2×#4111yescharacteristic
323C2×C4×C31H(5,𝔽2)11yescharacteristic
324C2×C4×C312−1+411yescharacteristic
325C8×C31—22no—
326C8×C31—41no—
327C8×C31—41no—
328C8×C31#12114yescomplemented
329C2×#468C2×C3111yescharacteristic, complemented
330C2×#465C2×C3111yescharacteristic, complemented
331C2×#435C2×C3111yescharacteristic, complemented
332C2×#428C2×C3111yescharacteristic, complemented
333#2416C2×C3111yescharacteristic
334#2415C2×C3111yescharacteristic, complemented
335#2068C2×C3111yescharacteristic, complemented
336#2065C2×C3111yescharacteristic, complemented
337#2035C2×C3111yescharacteristic, complemented
338#2033C2×C3111yescharacteristic, complemented
339#1973C2×C3111yescharacteristic, complemented
340#1944C2×C3111yescharacteristic, complemented
341#1875C2×C3111yescharacteristic, complemented
342#1872C2×C3111yescharacteristic, complemented
343#1808C2×C3111yescharacteristic, complemented
344C22×C31—22no—
345C22×C31—22no—
346C22×C31—22no—
347C22×C31—22no—
348C22×C31—22no—
349C22×C31—22no—
350C22×C31—41no—
351C22×C31—41no—
352C22×C31—41no—
353C22×C31—41no—
354C22×C31—41no—
355C22×C31—41no—
356C22×C31—41no—
357C22×C31—41no—
358C22×C31—81no—
359C22×C31—81no—
360C22×C31—81no—
361C22×C31—81no—
362C22×C31—81no—
363C22×C31—81no—
364C22×C31—81no—
365C22×C31C2×#12111yescharacteristic
366C22×C31D4211yescharacteristic
367C22×C31#54711yescharacteristic
368C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C31#57511yescharacteristic
370C22×C31#57711yescharacteristic
371C22×C31#57811yescharacteristic
372C4×C31—22no—
373C4×C31—41no—
374C4×C31—42no—
375C4×C31—42no—
376C4×C31—41no—
377C4×C31—41no—
378C4×C31—81no—
379C4×C31—81no—
380C4×C31—81no—
381C4×C31—81no—
382C4×C31—81no—
383C4×C31C2×#12111yescharacteristic
384C4×C31#53711yescharacteristic
385C4×C31#54811yescharacteristic
386C4×C31#55311yescharacteristic
387C22×SD16C22×C3111yescharacteristic
388C22×M16C22×C3111yescharacteristic
389C23×C8C22×C3111yescharacteristic
390C2×C22⋊Q8C22×C3111yescharacteristic
391C2×C22⋊Q8C22×C3111yescharacteristic
392C2×#121—21no—
393C2×#121C22×C3111yescharacteristic
394C2×#121C22×C3111yescharacteristic
395C2×C4×D4C22×C3111yescharacteristic
396C2×#117C22×C3111yescharacteristic
397C22×C4⋊C4C22×C3111yescharacteristic
398#468—24no—
399#465—24no—
400#435—24no—
401#428—24no—
402C2×#107C22×C3111yescharacteristic
403C2×#107C22×C3111yescharacteristic
404C2×#107C22×C3111yescharacteristic
405C2×#106C22×C3111yescharacteristic
406C2×#106C22×C3111yescharacteristic
407C2×C4⋊C8C22×C3111yescharacteristic
408C2×#103C22×C3111yescharacteristic
409C2×#103C22×C3111yescharacteristic
410C2×#103C22×C3111yescharacteristic
411C2×#102C22×C3111yescharacteristic
412C2×#102C22×C3111yescharacteristic
413C2×#102C22×C3111yescharacteristic
414C2×C22⋊C8C22×C3111yescharacteristic
415C2×C22⋊C8C22×C3111yescharacteristic
416C2×#97C22×C3111yescharacteristic
417#397—21no—
418#396—21no—
419#394—21no—
420#394—21no—
421#391C22×C3111yescharacteristic
422#390C22×C3111yescharacteristic
423#389—21no—
424#389C22×C3111yescharacteristic
425#389C22×C3111yescharacteristic
426#388—21no—
427#386—21no—
428#380C22×C3111yescharacteristic
429#380C22×C3111yescharacteristic
430#340C22×C3111yescharacteristic
431#340C22×C3111yescharacteristic
432#340C22×C3111yescharacteristic
433#340C22×C3111yescharacteristic
434C2×C31—42no—
435C2×C31—42no—
436C2×C31—161no—
437C2×C31#241611yescharacteristic
438C2×C31#305511yescharacteristic
439C2×C31#306311yescharacteristic
440C2×C31#326511yescharacteristic
441C2×C31#326911yescharacteristic
442C2×C31#334311yescharacteristic
443C2×C31#335011yescharacteristic
444C22×Q8C23×C3111yescharacteristic
445C22×D4—21no—
446C22×D4—21no—
447C22×D4D4×C3111yescharacteristic
448C22×D4C23×C3111yescharacteristic
449C23×C4—21no—
450C23×C4C23×C3111yescharacteristic
451C23×C4C23×C3111yescharacteristic
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—22no—
455C2×M16—22no—
456C2×M16—22no—
457C2×M16D4×C3114yescomplemented
458C22×C8—22no—
459C22×C8—22no—
460C22×C8—22no—
461C22×C8C23×C3111yescharacteristic
462C22×C8C23×C3111yescharacteristic
463C22×C8C23×C3111yescharacteristic
464C22×C8C23×C3111yescharacteristic
465C22⋊Q8—22no—
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8—41no—
469#121—22no—
470#121—22no—
471#121—22no—
472#121—41no—
473#121—44no—
474C4×D4—22no—
475C4×D4—22no—
476#117—22no—
477#117—41no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—41no—
485C2×C4⋊C4D4×C3111yescharacteristic
486C2×C4⋊C4C23×C3111yescharacteristic
487C2×C4⋊C4C23×C3111yescharacteristic
488C2×C4⋊C4C23×C3111yescharacteristic
489C2×C4⋊C4C23×C3111yescharacteristic
490C2×C4⋊C4C23×C3111yescharacteristic
491C2×C4⋊C4C23×C3111yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4D4×C3111yescharacteristic
502C2×C22⋊C4D4×C3111yescharacteristic
503C2×C42—21no—
504C2×C42C23×C3111yescharacteristic
505#107—22no—
506#107—22no—
507#107—22no—
508#106—22no—
509#106D4×C3114yescomplemented
510C4⋊C8—22no—
511#103—22no—
512#103—22no—
513#103—41no—
514#102—22no—
515#102—22no—
516#102—41no—
517C22⋊C8—22no—
518C22⋊C8—22no—
519#97—22no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526C31#2478911yescharacteristic, direct product factor, Sylow
527C24—21no—
528C24C2×D4×C3111yescharacteristic
529C24C2×D4×C3111yescharacteristic
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—41no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—81no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
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—21no—
567C22×C4—21no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—81no—
571C22×C4C2×D4×C3111yescharacteristic
572C22×C4C2×D4×C3111yescharacteristic
573C22×C4C2×D4×C3111yescharacteristic
574C22×C4C2×D4×C3111yescharacteristic
575C22×C4C2×D4×C3112yes—
576C22×C4#41×C3112yes—
577C22×C4C24×C3111yescharacteristic
578SD16—44no—
579M16—28no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—44no—
589C2×C8C2×D4×C3112yes—
590C2×C8C2×D4×C3112yes—
591C2×C8C2×D4×C3112yes—
592C2×C8#41×C3112yes—
593C4⋊C4—22no—
594C4⋊C4—21no—
595C4⋊C4—21no—
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—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4C2×D4×C3112yes—
610C4⋊C4C2×D4×C3112yes—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—81no—
622C42—21no—
623C42—21no—
624C42—42no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23C31×#12112yes—
645C23C31×AGL(1,ℤ/8)12yes—
646C23C22×D4×C3111yescharacteristic
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651D4—44no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—84no—
657D4—84no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
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—84no—
699C2×C4C31×#12112yes—
700C2×C4C22×D4×C3111yescharacteristic
701C2×C4C22×D4×C3111yescharacteristic
702C2×C4C2×#41×C3111yescharacteristic
703C2×C4C2×#41×C3111yescharacteristic
704C2×C4C31×H(5,𝔽2)11yescharacteristic
705C2×C4C31×2−1+411yescharacteristic
706C8—22no—
707C8—41no—
708C8—41no—
709C8C31×#12114yescomplemented
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C2×C31×#12111yescharacteristic
732C22D42×C3111yescharacteristic
733C22C31×#54711yescharacteristic
734C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
735C22C31×#57511yescharacteristic
736C22C31×#57711yescharacteristic
737C22C31×#57811yescharacteristic
738C4—22no—
739C4—41no—
740C4—42no—
741C4—42no—
742C4—41no—
743C4—41no—
744C4—81no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4C2×C31×#12111yescharacteristic
750C4C31×#53711yescharacteristic
751C4C31×#54811yescharacteristic
752C4C31×#55311yescharacteristic
753C2—42no—
754C2—42no—
755C2—161no—
756C2C31×#241611yescharacteristic
757C2C31×#305511yescharacteristic
758C2C31×#306311yescharacteristic
759C2C31×#326511yescharacteristic
760C2C31×#326911yescharacteristic
761C2C31×#334311yescharacteristic
762C2C31×#335011yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2416C2
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×#468C2semidirect
2. C2×C31×#465C2semidirect
3. C2×C31×#435C2semidirect
4. C2×C31×#428C2semidirect
6. C31×#2415C2semidirect
7. C31×#2068C2semidirect
8. C31×#2065C2semidirect
9. C31×#2035C2semidirect
10. C31×#2033C2semidirect
11. C31×#1973C2semidirect
12. C31×#1944C2semidirect
13. C31×#1875C2semidirect
14. C31×#1872C2semidirect
15. C31×#1808C2semidirect
76. C2×M16×C31D4semidirect
128. C31×#106D4semidirect
243. #24789C31direct (N × H)
328. C8×C31#121semidirect
329. C2×#468C2×C31semidirect
330. C2×#465C2×C31semidirect
331. C2×#435C2×C31semidirect
332. C2×#428C2×C31semidirect
334. #2415C2×C31semidirect
335. #2068C2×C31semidirect
336. #2065C2×C31semidirect
337. #2035C2×C31semidirect
338. #2033C2×C31semidirect
339. #1973C2×C31semidirect
340. #1944C2×C31semidirect
341. #1875C2×C31semidirect
342. #1872C2×C31semidirect
343. #1808C2×C31semidirect
457. C2×M16D4×C31semidirect
509. #106D4×C31semidirect
526. C31#24789direct (N × H)
709. C8C31×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4682
C2×C31×#4652
C2×C31×#4352
C2×C31×#4282
C31×#24162
C31×#24152
C31×#20682
C31×#20652
C31×#20352
C31×#20332
C31×#19732
C31×#19442
C31×#18752
C31×#18722
C31×#18082
#2478931