Finite Group Databasebeta

← C31×#24754 #21481513

Subgroups — C31×#24754 #21481513

Order 7936.

1102 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#466C211yesmaximal, characteristic
2C2×C31×#465C211yesmaximal, characteristic, complemented
3C2×C31×#463C211yesmaximal, characteristic, complemented
4C22×C31×C4⋊C8C211yesmaximal, characteristic, complemented
5C31×#2850C211yesmaximal, characteristic, complemented
6C4×C31×#121C211yesmaximal, characteristic, complemented
7C31×#2068C211yesmaximal, characteristic, complemented
8C31×#2065C211yesmaximal, characteristic, complemented
9C31×#2055C211yesmaximal, characteristic, complemented
10C31×#2054C211yesmaximal, characteristic, complemented
11C31×#1983C211yesmaximal, characteristic, complemented
12C31×#1949C211yesmaximal, characteristic, complemented
13C31×#1893C211yesmaximal, characteristic, complemented
14C31×#1892C211yesmaximal, characteristic, complemented
15C31×#1804C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C23×C8×C31C2211yescharacteristic
19C23×C8×C31C2211yescharacteristic
20C2×C31×#124C2211yescharacteristic
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C31×#121C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C4×D4×C31—21no—
25C2×C4×D4×C31C2211yescharacteristic
26C22×C42×C31C2211yescharacteristic
27C31×#466—24no—
28C31×#465—24no—
29C31×#463—24no—
30C2×C31×#107C2211yescharacteristic
31C2×C31×#106C2211yescharacteristic
32C2×C31×C4⋊C8—24no—
33C2×C31×C4⋊C8C2211yescharacteristic
34C2×C31×C4⋊C8C2211yescharacteristic
35C2×C31×C4⋊C8C2211yescharacteristic
36C2×C31×C4⋊C8C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C31×#391C2211yescharacteristic
46C31×#390C2211yescharacteristic
47C31×#390C2211yescharacteristic
48C31×#389C2211yescharacteristic
49C31×#388—21no—
50C31×#388—21no—
51C31×#388—21no—
52C31×#386—21no—
53C31×#386—21no—
54C31×#386—21no—
55C31×#382C2211yescharacteristic
56C31×#380C2211yescharacteristic
57C4×C4⋊C4×C31C2211yescharacteristic
58C4×C22⋊C4×C31—21no—
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31C2311yescharacteristic
67C22×D4×C31C2311yescharacteristic
68C23×C4×C31—21no—
69C23×C4×C31D411yescharacteristic
70C23×C4×C31D411yescharacteristic
71C23×C4×C31C2311yescharacteristic
72C2×SD16×C31—22no—
73C2×SD16×C31—22no—
74C2×SD16×C31—41no—
75C2×D8×C31—22no—
76C2×D8×C31—22no—
77C2×D8×C31—41no—
78C22×C8×C31—22no—
79C22×C8×C31—22no—
80C22×C8×C31—22no—
81C22×C8×C31—22no—
82C22×C8×C31—41no—
83C22×C8×C31—41no—
84C22×C8×C31C2311yescharacteristic
85C22×C8×C31C2311yescharacteristic
86C22×C8×C31C2311yescharacteristic
87C22×C8×C31C2311yescharacteristic
88C31×#124—22no—
89C31×#124—22no—
90C31×C22⋊Q8—22no—
91C31×C22⋊Q8—22no—
92C31×#121—22no—
93C31×#121—22no—
94C31×#121—22no—
95C31×#121D414yes—
96C4×D4×C31—22no—
97C4×D4×C31—22no—
98C4×D4×C31—44no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
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—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C42×C31—22no—
118C2×C42×C31—22no—
119C2×C42×C31—21no—
120C2×C42×C31D411yescharacteristic
121C2×C42×C31D411yescharacteristic
122C2×C42×C31C2311yescharacteristic
123C2×C42×C31C2311yescharacteristic
124C31×#107—22no—
125C31×#106—22no—
126C31×C4⋊C8—22no—
127C31×C4⋊C8—22no—
128C31×C4⋊C8—22no—
129C31×C4⋊C8D414yescomplemented
130C31×#103—22no—
131C31×#103—22no—
132C31×#103—41no—
133C31×#102—22no—
134C31×#102—22no—
135C31×#102—22no—
136C31×#102—22no—
137C31×#102—41no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95—21no—
143C31×#95—21no—
144C31×#95—21no—
145C24×C31—21no—
146C24×C31—21no—
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—24no—
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—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—42no—
167C2×D4×C31—42no—
168C2×D4×C31—42no—
169C2×D4×C31—42no—
170C2×D4×C31—42no—
171C2×D4×C31C2×D412yes—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—22no—
180C22×C4×C31—21no—
181C22×C4×C31—22no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—41no—
188C22×C4×C31—42no—
189C22×C4×C31—42no—
190C22×C4×C31—42no—
191C22×C4×C31C2×D411yescharacteristic
192C22×C4×C31C2×D411yescharacteristic
193C22×C4×C31C2×D411yescharacteristic
194C22×C4×C31C2×D411yescharacteristic
195C22×C4×C31C2×D412yes—
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31#4112yes—
198C22×C4×C31C2411yescharacteristic
199SD16×C31—44no—
200D8×C31—44no—
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—21no—
209C2×C8×C31—21no—
210C2×C8×C31—21no—
211C2×C8×C31—44no—
212C2×C8×C31—44no—
213C2×C8×C31C2×D412yes—
214C2×C8×C31C2×D412yes—
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—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—42no—
225C4⋊C4×C31—42no—
226C4⋊C4×C31C2×D412yes—
227C22⋊C4×C31—24no—
228C22⋊C4×C31—42no—
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—42no—
236C22⋊C4×C31—42no—
237C22⋊C4×C31—42no—
238C42×C31—22no—
239C42×C31—22no—
240C42×C31—21no—
241C42×C31—21no—
242C42×C31—42no—
243C42×C31C2×D412yes—
244C42×C31#4112yes—
245#24754C3111yesmaximal, characteristic, direct product factor, Sylow
246C23×C31—21no—
247C23×C31—21no—
248C23×C31—21no—
249C23×C31—21no—
250C23×C31—22no—
251C23×C31—41no—
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—41no—
263C23×C31—41no—
264C23×C31#12112yes—
265C23×C31#13512yes—
266C23×C31AGL(1,ℤ/8)12yes—
267C23×C31C22×D411yescharacteristic
268Q8×C31—41no—
269Q8×C31—41no—
270Q8×C31—41no—
271Q8×C31—41no—
272D4×C31—22no—
273D4×C31—22no—
274D4×C31—48no—
275D4×C31—41no—
276D4×C31—41no—
277D4×C31—41no—
278D4×C31—41no—
279D4×C31—41no—
280D4×C31—41no—
281D4×C31—84no—
282C2×C4×C31—28no—
283C2×C4×C31—21no—
284C2×C4×C31—21no—
285C2×C4×C31—21no—
286C2×C4×C31—21no—
287C2×C4×C31—21no—
288C2×C4×C31—21no—
289C2×C4×C31—21no—
290C2×C4×C31—21no—
291C2×C4×C31—22no—
292C2×C4×C31—22no—
293C2×C4×C31—22no—
294C2×C4×C31—22no—
295C2×C4×C31—21no—
296C2×C4×C31—22no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—44no—
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×C31#12112yes—
320C2×C4×C31#12112yes—
321C2×C4×C31#13512yes—
322C2×C4×C31C22×D411yescharacteristic
323C2×C4×C31C22×D411yescharacteristic
324C2×C4×C31C2×#4111yescharacteristic
325C2×C4×C31C2×#4111yescharacteristic
326C2×C4×C31H(5,𝔽2)11yescharacteristic
327C2×C4×C312−1+411yescharacteristic
328C8×C31—22no—
329C8×C31—22no—
330C8×C31—41no—
331C8×C31—41no—
332C2×#466C2×C3111yescharacteristic
333C2×#465C2×C3111yescharacteristic, complemented
334C2×#463C2×C3111yescharacteristic, complemented
335C22×C4⋊C8C2×C3111yescharacteristic, complemented
336#2850C2×C3111yescharacteristic, complemented
337C4×#121C2×C3111yescharacteristic, complemented
338#2068C2×C3111yescharacteristic, complemented
339#2065C2×C3111yescharacteristic, complemented
340#2055C2×C3111yescharacteristic, complemented
341#2054C2×C3111yescharacteristic, complemented
342#1983C2×C3111yescharacteristic, complemented
343#1949C2×C3111yescharacteristic, complemented
344#1893C2×C3111yescharacteristic, complemented
345#1892C2×C3111yescharacteristic, complemented
346#1804C2×C3111yescharacteristic, complemented
347C22×C31—22no—
348C22×C31—22no—
349C22×C31—22no—
350C22×C31—22no—
351C22×C31—22no—
352C22×C31—22no—
353C22×C31—42no—
354C22×C31—42no—
355C22×C31—42no—
356C22×C31—81no—
357C22×C31—81no—
358C22×C31—81no—
359C22×C31—81no—
360C22×C31—81no—
361C22×C31—81no—
362C22×C31—81no—
363C22×C31—81no—
364C22×C31—81no—
365C22×C31—81no—
366C22×C31—81no—
367C22×C31#46314yescomplemented
368C22×C31C2×#12111yescharacteristic
369C22×C31C2×#12111yescharacteristic
370C22×C31#53711yescharacteristic
371C22×C31C2×#13511yescharacteristic
372C22×C31C2×#13511yescharacteristic
373C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
374C22×C31#57511yescharacteristic
375C4×C31—22no—
376C4×C31—22no—
377C4×C31—22no—
378C4×C31—22no—
379C4×C31—42no—
380C4×C31—41no—
381C4×C31—81no—
382C4×C31—81no—
383C4×C31—81no—
384C4×C31—81no—
385C4×C31—81no—
386C4×C31D4211yescharacteristic
387C4×C31#54711yescharacteristic
388C4×C31#54811yescharacteristic
389C4×C31#55311yescharacteristic
390C22×SD16C22×C3111yescharacteristic
391C22×D8C22×C3111yescharacteristic
392C23×C8C22×C3111yescharacteristic
393C23×C8C22×C3111yescharacteristic
394C2×#124C22×C3111yescharacteristic
395C2×C22⋊Q8C22×C3111yescharacteristic
396C2×#121C22×C3111yescharacteristic
397C2×#121C22×C3111yescharacteristic
398C2×C4×D4—21no—
399C2×C4×D4C22×C3111yescharacteristic
400C22×C42C22×C3111yescharacteristic
401#466—24no—
402#465—24no—
403#463—24no—
404C2×#107C22×C3111yescharacteristic
405C2×#106C22×C3111yescharacteristic
406C2×C4⋊C8—24no—
407C2×C4⋊C8C22×C3111yescharacteristic
408C2×C4⋊C8C22×C3111yescharacteristic
409C2×C4⋊C8C22×C3111yescharacteristic
410C2×C4⋊C8C22×C3111yescharacteristic
411C2×#103C22×C3111yescharacteristic
412C2×#103C22×C3111yescharacteristic
413C2×#103C22×C3111yescharacteristic
414C2×#102C22×C3111yescharacteristic
415C2×#102C22×C3111yescharacteristic
416C2×#102C22×C3111yescharacteristic
417C2×#102C22×C3111yescharacteristic
418C2×#102C22×C3111yescharacteristic
419#391C22×C3111yescharacteristic
420#390C22×C3111yescharacteristic
421#390C22×C3111yescharacteristic
422#389C22×C3111yescharacteristic
423#388—21no—
424#388—21no—
425#388—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#382C22×C3111yescharacteristic
430#380C22×C3111yescharacteristic
431C4×C4⋊C4C22×C3111yescharacteristic
432C4×C22⋊C4—21no—
433#340C22×C3111yescharacteristic
434#340C22×C3111yescharacteristic
435#340C22×C3111yescharacteristic
436#340C22×C3111yescharacteristic
437C2×C31—24no—
438C2×C31—82no—
439C2×C31—161no—
440C2×C31#241611yescharacteristic
441C2×C31C2×#46311yescharacteristic
442C2×C31#303511yescharacteristic
443C2×C31#305011yescharacteristic
444C2×C31#305511yescharacteristic
445C2×C31#324711yescharacteristic
446C2×C31#325011yescharacteristic
447C22×Q8C23×C3111yescharacteristic
448C22×D4—21no—
449C22×D4—21no—
450C22×D4C23×C3111yescharacteristic
451C22×D4C23×C3111yescharacteristic
452C23×C4—21no—
453C23×C4D4×C3111yescharacteristic
454C23×C4D4×C3111yescharacteristic
455C23×C4C23×C3111yescharacteristic
456C2×SD16—22no—
457C2×SD16—22no—
458C2×SD16—41no—
459C2×D8—22no—
460C2×D8—22no—
461C2×D8—41no—
462C22×C8—22no—
463C22×C8—22no—
464C22×C8—22no—
465C22×C8—22no—
466C22×C8—41no—
467C22×C8—41no—
468C22×C8C23×C3111yescharacteristic
469C22×C8C23×C3111yescharacteristic
470C22×C8C23×C3111yescharacteristic
471C22×C8C23×C3111yescharacteristic
472#124—22no—
473#124—22no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121D4×C3114yes—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—44no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4C23×C3111yescharacteristic
486C2×C4⋊C4C23×C3111yescharacteristic
487C2×C4⋊C4C23×C3111yescharacteristic
488C2×C4⋊C4C23×C3111yescharacteristic
489C2×C4⋊C4C23×C3111yescharacteristic
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—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—21no—
504C2×C42D4×C3111yescharacteristic
505C2×C42D4×C3111yescharacteristic
506C2×C42C23×C3111yescharacteristic
507C2×C42C23×C3111yescharacteristic
508#107—22no—
509#106—22no—
510C4⋊C8—22no—
511C4⋊C8—22no—
512C4⋊C8—22no—
513C4⋊C8D4×C3114yescomplemented
514#103—22no—
515#103—22no—
516#103—41no—
517#102—22no—
518#102—22no—
519#102—22no—
520#102—22no—
521#102—41no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529C31#2475411yescharacteristic, direct product factor, Sylow
530C24—21no—
531C24—21no—
532C24C2×D4×C3111yescharacteristic
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4C2×D4×C3112yes—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—41no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4C2×D4×C3111yescharacteristic
577C22×C4C2×D4×C3111yescharacteristic
578C22×C4C2×D4×C3111yescharacteristic
579C22×C4C2×D4×C3111yescharacteristic
580C22×C4C2×D4×C3112yes—
581C22×C4C2×D4×C3111yescharacteristic
582C22×C4#41×C3112yes—
583C22×C4C24×C3111yescharacteristic
584SD16—44no—
585D8—44no—
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—21no—
595C2×C8—21no—
596C2×C8—44no—
597C2×C8—44no—
598C2×C8C2×D4×C3112yes—
599C2×C8C2×D4×C3112yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4C2×D4×C3112yes—
612C22⋊C4—24no—
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—42no—
622C22⋊C4—42no—
623C42—22no—
624C42—22no—
625C42—21no—
626C42—21no—
627C42—42no—
628C42C2×D4×C3112yes—
629C42#41×C3112yes—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—22no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23C31×#12112yes—
649C23C31×#13512yes—
650C23C31×AGL(1,ℤ/8)12yes—
651C23C22×D4×C3111yescharacteristic
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656D4—22no—
657D4—22no—
658D4—48no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—84no—
666C2×C4—28no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—44no—
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×C4C31×#12112yes—
703C2×C4C31×#12112yes—
704C2×C4C31×#12112yes—
705C2×C4C31×#13512yes—
706C2×C4C22×D4×C3111yescharacteristic
707C2×C4C22×D4×C3111yescharacteristic
708C2×C4C2×#41×C3111yescharacteristic
709C2×C4C2×#41×C3111yescharacteristic
710C2×C4C31×H(5,𝔽2)11yescharacteristic
711C2×C4C31×2−1+411yescharacteristic
712C8—22no—
713C8—22no—
714C8—41no—
715C8—41no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22C31×#46314yescomplemented
737C22C2×C31×#12111yescharacteristic
738C22C2×C31×#12111yescharacteristic
739C22C31×#53711yescharacteristic
740C22C2×C31×#13511yescharacteristic
741C22C2×C31×#13511yescharacteristic
742C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
743C22C31×#57511yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—42no—
749C4—41no—
750C4—81no—
751C4—81no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4D42×C3111yescharacteristic
756C4C31×#54711yescharacteristic
757C4C31×#54811yescharacteristic
758C4C31×#55311yescharacteristic
759C2—24no—
760C2—82no—
761C2—161no—
762C2C31×#241611yescharacteristic
763C2C2×C31×#46311yescharacteristic
764C2C31×#303511yescharacteristic
765C2C31×#305011yescharacteristic
766C2C31×#305511yescharacteristic
767C2C31×#324711yescharacteristic
768C2C31×#325011yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#466C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#465C2semidirect
3. C2×C31×#463C2semidirect
4. C22×C31×C4⋊C8C2semidirect
5. C31×#2850C2semidirect
6. C4×C31×#121C2semidirect
7. C31×#2068C2semidirect
8. C31×#2065C2semidirect
9. C31×#2055C2semidirect
10. C31×#2054C2semidirect
11. C31×#1983C2semidirect
12. C31×#1949C2semidirect
13. C31×#1893C2semidirect
14. C31×#1892C2semidirect
15. C31×#1804C2semidirect
129. C31×C4⋊C8D4semidirect
245. #24754C31direct (N × H)
333. C2×#465C2×C31semidirect
334. C2×#463C2×C31semidirect
335. C22×C4⋊C8C2×C31semidirect
336. #2850C2×C31semidirect
337. C4×#121C2×C31semidirect
338. #2068C2×C31semidirect
339. #2065C2×C31semidirect
340. #2055C2×C31semidirect
341. #2054C2×C31semidirect
342. #1983C2×C31semidirect
343. #1949C2×C31semidirect
344. #1893C2×C31semidirect
345. #1892C2×C31semidirect
346. #1804C2×C31semidirect
367. C22×C31#463semidirect
513. C4⋊C8D4×C31semidirect
529. C31#24754direct (N × H)
736. C22C31×#463semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4662
C2×C31×#4652
C2×C31×#4632
C22×C31×C4⋊C82
C31×#28502
C4×C31×#1212
C31×#20682
C31×#20652
C31×#20552
C31×#20542
C31×#19832
C31×#19492
C31×#18932
C31×#18922
C31×#18042
#2475431