Finite Group Databasebeta

← C31×#24738 #21481497

Subgroups — C31×#24738 #21481497

Order 7936.

1094 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#463C211yesmaximal, characteristic, complemented
2C2×C31×#463C211yesmaximal, characteristic, complemented
3C2×C31×#459C211yesmaximal, characteristic
4C2×C31×#442C211yesmaximal, characteristic, complemented
5C31×#2544C211yesmaximal, characteristic, complemented
6D4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#2066C211yesmaximal, characteristic, complemented
8C31×#2065C211yesmaximal, characteristic, complemented
9C31×#2042C211yesmaximal, characteristic, complemented
10C31×#2041C211yesmaximal, characteristic, complemented
11C31×#1959C211yesmaximal, characteristic, complemented
12C31×#1940C211yesmaximal, characteristic, complemented
13C31×#1879C211yesmaximal, characteristic, complemented
14C31×#1877C211yesmaximal, characteristic, complemented
15C31×#1802C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C2×C31×#127C2211yescharacteristic
20C2×C31×#124C2211yescharacteristic
21C2×C31×#124C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C2×C4×D4×C31C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C22×C4⋊C4×C31—21no—
27C31×#463—24no—
28C31×#463—24no—
29C31×#459—24no—
30C31×#442—24no—
31C2×C31×#106C2211yescharacteristic
32C2×C31×C4⋊C8C2211yescharacteristic
33C2×C31×C4⋊C8C2211yescharacteristic
34C2×C31×C4⋊C8C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#97C2211yescharacteristic
46C31×#394—21no—
47C31×#394—21no—
48C31×#391C2211yescharacteristic
49C31×#390C2211yescharacteristic
50C31×#389C2211yescharacteristic
51C31×#389C2211yescharacteristic
52C31×#386—21no—
53C31×#386—21no—
54C31×#385—21no—
55C31×#385—21no—
56C31×#384C2211yescharacteristic
57C31×#380—21no—
58C4×C4⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31C2311yescharacteristic
67C22×D4×C31C2311yescharacteristic
68C22×D4×C31C2311yescharacteristic
69C23×C4×C31—21no—
70C23×C4×C31—21no—
71C23×C4×C31—21no—
72C23×C4×C31—21no—
73C2×SD16×C31—22no—
74C2×SD16×C31—22no—
75C2×SD16×C31—22no—
76C2×D8×C31—22no—
77C2×D8×C31—22no—
78C2×D8×C31—22no—
79C2×D8×C31—22no—
80C2×D8×C31—22no—
81C2×D8×C31D414yes—
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C22×C8×C31C2311yescharacteristic
86C31×#127—22no—
87C31×#127—41no—
88C31×#124—22no—
89C31×#124—22no—
90C31×#124—22no—
91C31×#124—41no—
92C4×D4×C31—22no—
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C4×D4×C31—22no—
96C4×D4×C31—22no—
97C4×D4×C31—41no—
98C4×D4×C31—41no—
99C4×D4×C31D414yescomplemented
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31—44no—
105C2×C4⋊C4×C31D411yescharacteristic
106C2×C4⋊C4×C31D411yescharacteristic
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×C31—21no—
121C2×C42×C31C2311yescharacteristic
122C2×C42×C31C2311yescharacteristic
123C2×C42×C31C2311yescharacteristic
124C31×#106—22no—
125C31×C4⋊C8—22no—
126C31×C4⋊C8—22no—
127C31×C4⋊C8—22no—
128C31×#103—22no—
129C31×#103—22no—
130C31×#103—41no—
131C31×#102—22no—
132C31×#102—22no—
133C31×#102—22no—
134C31×#102—22no—
135C31×#102—22no—
136C31×#102—22no—
137C31×#102—41no—
138C31×#97—22no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95—21no—
143C31×#95D411yescharacteristic
144C31×#95D411yescharacteristic
145C24×C31—21no—
146C24×C31—21no—
147C24×C31—21no—
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—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—21no—
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—42no—
169C2×D4×C31—42no—
170C2×D4×C31—42no—
171C2×D4×C31—42no—
172C2×D4×C31—81no—
173C2×D4×C31—81no—
174C2×D4×C31C2×D412yes—
175C2×D4×C31C2×D412yes—
176C2×D4×C31C2×D412yes—
177C2×D4×C31#4112yes—
178C22×C4×C31—21no—
179C22×C4×C31—24no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—42no—
185C22×C4×C31—42no—
186C22×C4×C31—42no—
187C22×C4×C31—42no—
188C22×C4×C31—42no—
189C22×C4×C31—42no—
190C22×C4×C31—42no—
191C22×C4×C31—81no—
192C22×C4×C31—81no—
193C22×C4×C31—81no—
194C22×C4×C31—81no—
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2411yescharacteristic
202SD16×C31—44no—
203D8×C31—28no—
204D8×C31—44no—
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—21no—
212C2×C8×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31—21no—
215C2×C8×C31—21no—
216C2×C8×C31C2×D412yes—
217C4⋊C4×C31—22no—
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—21no—
225C4⋊C4×C31—41no—
226C4⋊C4×C31—42no—
227C4⋊C4×C31—42no—
228C4⋊C4×C31—42no—
229C4⋊C4×C31—81no—
230C4⋊C4×C31C2×D412yes—
231C22⋊C4×C31—24no—
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—
240C22⋊C4×C31—81no—
241C42×C31—21no—
242C42×C31—21no—
243C42×C31—21no—
244C42×C31—21no—
245C42×C31C2×D412yes—
246C42×C31#4112yes—
247#24738C3111yesmaximal, characteristic, direct product factor, Sylow
248C23×C31—22no—
249C23×C31—22no—
250C23×C31—22no—
251C23×C31—22no—
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—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31C22×D411yescharacteristic
270Q8×C31—41no—
271Q8×C31—41no—
272Q8×C31—41no—
273Q8×C31—41no—
274D4×C31—22no—
275D4×C31—22no—
276D4×C31—22no—
277D4×C31—22no—
278D4×C31—22no—
279D4×C31—41no—
280D4×C31—41no—
281D4×C31—41no—
282D4×C31—41no—
283D4×C31—41no—
284D4×C31—41no—
285D4×C31—84no—
286D4×C31—84no—
287D4×C31#12114yes—
288C2×C4×C31—21no—
289C2×C4×C31—21no—
290C2×C4×C31—21no—
291C2×C4×C31—21no—
292C2×C4×C31—21no—
293C2×C4×C31—21no—
294C2×C4×C31—22no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—48no—
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—41no—
318C2×C4×C31—41no—
319C2×C4×C31—84no—
320C2×C4×C31—84no—
321C2×C4×C31—84no—
322C2×C4×C31#12112yes—
323C2×C4×C31#12112yes—
324C2×C4×C31AGL(1,ℤ/8)12yes—
325C2×C4×C31C22×D411yescharacteristic
326C2×C4×C31C22×D411yescharacteristic
327C2×C4×C31C2×#4111yescharacteristic
328C2×C4×C31C2×#4111yescharacteristic
329C2×C4×C31H(5,𝔽2)11yescharacteristic
330C2×C4×C312−1+411yescharacteristic
331C8×C31—22no—
332C8×C31—41no—
333C8×C31—41no—
334C8×C31—41no—
335C2×#463C2×C3111yescharacteristic, complemented
336C2×#463C2×C3111yescharacteristic, complemented
337C2×#459C2×C3111yescharacteristic
338C2×#442C2×C3111yescharacteristic, complemented
339#2544C2×C3111yescharacteristic, complemented
340D4×C4⋊C4C2×C3111yescharacteristic, complemented
341#2066C2×C3111yescharacteristic, complemented
342#2065C2×C3111yescharacteristic, complemented
343#2042C2×C3111yescharacteristic, complemented
344#2041C2×C3111yescharacteristic, complemented
345#1959C2×C3111yescharacteristic, complemented
346#1940C2×C3111yescharacteristic, complemented
347#1879C2×C3111yescharacteristic, complemented
348#1877C2×C3111yescharacteristic, complemented
349#1802C2×C3111yescharacteristic, complemented
350C22×C31—24no—
351C22×C31—42no—
352C22×C31—42no—
353C22×C31—42no—
354C22×C31—42no—
355C22×C31—42no—
356C22×C31—42no—
357C22×C31—42no—
358C22×C31—42no—
359C22×C31—42no—
360C22×C31—81no—
361C22×C31—81no—
362C22×C31—81no—
363C22×C31—81no—
364C22×C31—81no—
365C22×C31—81no—
366C22×C31—81no—
367C22×C31—81no—
368C22×C31—81no—
369C22×C31—81no—
370C22×C31—81no—
371C22×C31C2×#12111yescharacteristic
372C22×C31D4211yescharacteristic
373C22×C31#54811yescharacteristic
374C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C31#57511yescharacteristic
376C22×C31#57611yescharacteristic
377C22×C31#57711yescharacteristic
378C4×C31—22no—
379C4×C31—22no—
380C4×C31—22no—
381C4×C31—41no—
382C4×C31—41no—
383C4×C31—41no—
384C4×C31—42no—
385C4×C31—81no—
386C4×C31—81no—
387C4×C31—81no—
388C4×C31—81no—
389C4×C31C2×#12111yescharacteristic
390C4×C31#53711yescharacteristic
391C4×C31#54711yescharacteristic
392C4×C31#55311yescharacteristic
393C22×SD16C22×C3111yescharacteristic
394C22×D8C22×C3111yescharacteristic
395C22×D8C22×C3111yescharacteristic
396C2×#127C22×C3111yescharacteristic
397C2×#124C22×C3111yescharacteristic
398C2×#124C22×C3111yescharacteristic
399C2×C4×D4C22×C3111yescharacteristic
400C2×C4×D4C22×C3111yescharacteristic
401C2×C4×D4C22×C3111yescharacteristic
402C2×C4×D4C22×C3111yescharacteristic
403C22×C4⋊C4—21no—
404#463—24no—
405#463—24no—
406#459—24no—
407#442—24no—
408C2×#106C22×C3111yescharacteristic
409C2×C4⋊C8C22×C3111yescharacteristic
410C2×C4⋊C8C22×C3111yescharacteristic
411C2×C4⋊C8C22×C3111yescharacteristic
412C2×#103C22×C3111yescharacteristic
413C2×#103C22×C3111yescharacteristic
414C2×#103C22×C3111yescharacteristic
415C2×#102C22×C3111yescharacteristic
416C2×#102C22×C3111yescharacteristic
417C2×#102C22×C3111yescharacteristic
418C2×#102C22×C3111yescharacteristic
419C2×#102C22×C3111yescharacteristic
420C2×#102C22×C3111yescharacteristic
421C2×#102C22×C3111yescharacteristic
422C2×#97C22×C3111yescharacteristic
423#394—21no—
424#394—21no—
425#391C22×C3111yescharacteristic
426#390C22×C3111yescharacteristic
427#389C22×C3111yescharacteristic
428#389C22×C3111yescharacteristic
429#386—21no—
430#386—21no—
431#385—21no—
432#385—21no—
433#384C22×C3111yescharacteristic
434#380—21no—
435C4×C4⋊C4C22×C3111yescharacteristic
436#340C22×C3111yescharacteristic
437#340C22×C3111yescharacteristic
438#336C22×C3111yescharacteristic
439#336C22×C3111yescharacteristic
440C2×C31—44no—
441C2×C31—82no—
442C2×C31—161no—
443C2×C31#241611yescharacteristic
444C2×C31#303611yescharacteristic
445C2×C31#304511yescharacteristic
446C2×C31#326411yescharacteristic
447C2×C31#326711yescharacteristic
448C2×C31#337011yescharacteristic
449C2×C31#337311yescharacteristic
450C22×Q8C23×C3111yescharacteristic
451C22×D4—21no—
452C22×D4—21no—
453C22×D4C23×C3111yescharacteristic
454C22×D4C23×C3111yescharacteristic
455C22×D4C23×C3111yescharacteristic
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—21no—
459C23×C4—21no—
460C2×SD16—22no—
461C2×SD16—22no—
462C2×SD16—22no—
463C2×D8—22no—
464C2×D8—22no—
465C2×D8—22no—
466C2×D8—22no—
467C2×D8—22no—
468C2×D8D4×C3114yes—
469C22×C8C23×C3111yescharacteristic
470C22×C8C23×C3111yescharacteristic
471C22×C8C23×C3111yescharacteristic
472C22×C8C23×C3111yescharacteristic
473#127—22no—
474#127—41no—
475#124—22no—
476#124—22no—
477#124—22no—
478#124—41no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—41no—
485C4×D4—41no—
486C4×D4D4×C3114yescomplemented
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—44no—
492C2×C4⋊C4D4×C3111yescharacteristic
493C2×C4⋊C4D4×C3111yescharacteristic
494C2×C4⋊C4C23×C3111yescharacteristic
495C2×C4⋊C4C23×C3111yescharacteristic
496C2×C4⋊C4C23×C3111yescharacteristic
497C2×C4⋊C4C23×C3111yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
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×C42C23×C3111yescharacteristic
509C2×C42C23×C3111yescharacteristic
510C2×C42C23×C3111yescharacteristic
511#106—22no—
512C4⋊C8—22no—
513C4⋊C8—22no—
514C4⋊C8—22no—
515#103—22no—
516#103—22no—
517#103—41no—
518#102—22no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—41no—
525#97—22no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95D4×C3111yescharacteristic
531#95D4×C3111yescharacteristic
532C31#2473811yescharacteristic, direct product factor, Sylow
533C24—21no—
534C24—21no—
535C24—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—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—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—81no—
561C2×D4—81no—
562C2×D4C2×D4×C3112yes—
563C2×D4C2×D4×C3112yes—
564C2×D4C2×D4×C3112yes—
565C2×D4#41×C3112yes—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4C2×D4×C3111yescharacteristic
584C22×C4C2×D4×C3111yescharacteristic
585C22×C4C2×D4×C3111yescharacteristic
586C22×C4C2×D4×C3111yescharacteristic
587C22×C4C2×D4×C3111yescharacteristic
588C22×C4C2×D4×C3111yescharacteristic
589C22×C4C24×C3111yescharacteristic
590SD16—44no—
591D8—28no—
592D8—44no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8C2×D4×C3112yes—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—41no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—81no—
618C4⋊C4C2×D4×C3112yes—
619C22⋊C4—24no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42C2×D4×C3112yes—
634C42#41×C3112yes—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23C22×D4×C3111yescharacteristic
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—22no—
665D4—22no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—84no—
673D4—84no—
674D4C31×#12114yes—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—48no—
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—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—84no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4C31×#12112yes—
710C2×C4C31×#12112yes—
711C2×C4C31×AGL(1,ℤ/8)12yes—
712C2×C4C22×D4×C3111yescharacteristic
713C2×C4C22×D4×C3111yescharacteristic
714C2×C4C2×#41×C3111yescharacteristic
715C2×C4C2×#41×C3111yescharacteristic
716C2×C4C31×H(5,𝔽2)11yescharacteristic
717C2×C4C31×2−1+411yescharacteristic
718C8—22no—
719C8—41no—
720C8—41no—
721C8—41no—
722C22—24no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22C2×C31×#12111yescharacteristic
744C22D42×C3111yescharacteristic
745C22C31×#54811yescharacteristic
746C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
747C22C31×#57511yescharacteristic
748C22C31×#57611yescharacteristic
749C22C31×#57711yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—42no—
757C4—81no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4C2×C31×#12111yescharacteristic
762C4C31×#53711yescharacteristic
763C4C31×#54711yescharacteristic
764C4C31×#55311yescharacteristic
765C2—44no—
766C2—82no—
767C2—161no—
768C2C31×#241611yescharacteristic
769C2C31×#303611yescharacteristic
770C2C31×#304511yescharacteristic
771C2C31×#326411yescharacteristic
772C2C31×#326711yescharacteristic
773C2C31×#337011yescharacteristic
774C2C31×#337311yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#459C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#463C2semidirect
2. C2×C31×#463C2semidirect
4. C2×C31×#442C2semidirect
5. C31×#2544C2semidirect
6. D4×C4⋊C4×C31C2semidirect
7. C31×#2066C2semidirect
8. C31×#2065C2semidirect
9. C31×#2042C2semidirect
10. C31×#2041C2semidirect
11. C31×#1959C2semidirect
12. C31×#1940C2semidirect
13. C31×#1879C2semidirect
14. C31×#1877C2semidirect
15. C31×#1802C2semidirect
99. C4×D4×C31D4semidirect
247. #24738C31direct (N × H)
335. C2×#463C2×C31semidirect
336. C2×#463C2×C31semidirect
338. C2×#442C2×C31semidirect
339. #2544C2×C31semidirect
340. D4×C4⋊C4C2×C31semidirect
341. #2066C2×C31semidirect
342. #2065C2×C31semidirect
343. #2042C2×C31semidirect
344. #2041C2×C31semidirect
345. #1959C2×C31semidirect
346. #1940C2×C31semidirect
347. #1879C2×C31semidirect
348. #1877C2×C31semidirect
349. #1802C2×C31semidirect
486. C4×D4D4×C31semidirect
532. C31#24738direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4632
C2×C31×#4592
C2×C31×#4422
C31×#25442
D4×C4⋊C4×C312
C31×#20662
C31×#20652
C31×#20422
C31×#20412
C31×#19592
C31×#19402
C31×#18792
C31×#18772
C31×#18022
#2473831