Finite Group Databasebeta

← C31×#24468 #21481227

Subgroups — C31×#24468 #21481227

Order 7936.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3488C211yesmaximal, characteristic, complemented
2C31×#3055C211yesmaximal, characteristic, complemented
3C2×C31×#453C211yesmaximal, characteristic, complemented
4C31×#3006C211yesmaximal, characteristic, complemented
5C2×C31×#421C211yesmaximal, characteristic, complemented
6C31×#2619C211yesmaximal, characteristic, complemented
7C31×#2040C211yesmaximal, characteristic, complemented
8C31×#2037C211yesmaximal, characteristic, complemented
9C31×#2006C211yesmaximal, characteristic, complemented
10C31×#2002C211yesmaximal, characteristic, complemented
11C31×#1900C211yesmaximal, characteristic, complemented
12C31×#1897C211yesmaximal, characteristic, complemented
13C31×#1883C211yesmaximal, characteristic, complemented
14C31×#1860C211yesmaximal, characteristic, complemented
15C31×#1792C211yesmaximal, characteristic, complemented
16C2×C31×H(5,𝔽2)C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C31×AGL(1,ℤ/8)C2211yescharacteristic, complemented
20C2×C31×AGL(1,ℤ/8)C2211yescharacteristic, complemented
21C22×M16×C31C2211yescharacteristic, complemented
22C31×#550—21no—
23C31×#548—21no—
24C31×#546—21no—
25C31×#546—22no—
26D42×C31—22no—
27D42×C31—21no—
28C31×#537—21no—
29C31×#537C2211yescharacteristic
30C31×#535—21no—
31C31×#535C2211yescharacteristic
32C2×C31×#127C2211yescharacteristic, complemented
33C31×#525—21no—
34C31×#525C2211yescharacteristic
35C2×C31×#121—21no—
36C2×C31×#121C2211yescharacteristic
37C2×C31×#121C2211yescharacteristic, complemented
38C31×#520C2211yescharacteristic
39C2×C31×#117C2211yescharacteristic, complemented
40C31×#469—21no—
41C31×#468—21no—
42C31×#466—21no—
43C31×#465—21no—
44C31×#453—24no—
45C31×#449—21no—
46C31×#449—21no—
47C31×#448—21no—
48C31×#447—21no—
49C31×#428C2211yescharacteristic, complemented
50C31×#421—24no—
51C2×C31×#104C2211yescharacteristic
52C2×C31×#104C2211yescharacteristic
53C2×C31×#104C2211yescharacteristic, complemented
54C2×C31×#104C2211yescharacteristic, complemented
55C2×C31×#104C2211yescharacteristic, complemented
56C2×C31×#104C2211yescharacteristic, complemented
57C31×#418C2211yescharacteristic, complemented
58C31×#417C2211yescharacteristic
59C31×#417C2211yescharacteristic, complemented
60C31×#417C2211yescharacteristic, complemented
61C2×C31×#100C2211yescharacteristic, complemented
62C2×C31×#100C2211yescharacteristic, complemented
63C31×#407C2211yescharacteristic, complemented
64C31×#394—22no—
65C31×#392—22no—
66C31×#390C2211yescharacteristic, complemented
67C31×#390C2211yescharacteristic, complemented
68C31×#382C2211yescharacteristic, complemented
69C31×#343C2211yescharacteristic, complemented
70C31×#343C2211yescharacteristic, complemented
71C31×#339C2211yescharacteristic, complemented
72C31×#339C2211yescharacteristic, complemented
73C31×H(5,𝔽2)—22no—
74C31×H(5,𝔽2)—22no—
75C31×H(5,𝔽2)—41no—
76C31×H(5,𝔽2)—41no—
77C2×#41×C31—21no—
78C2×#41×C31—21no—
79C2×#41×C31—21no—
80C2×#41×C31—21no—
81C2×#41×C31—22no—
82C2×#41×C31—22no—
83C2×#41×C31—41no—
84C2×#41×C31—41no—
85C2×#41×C31D411yescharacteristic, complemented
86C2×#41×C31D411yescharacteristic, complemented
87C2×#41×C31C2311yescharacteristic
88C2×#41×C31C2311yescharacteristic
89C2×#41×C31C2311yescharacteristic
90C22×Q8×C31D411yescharacteristic, complemented
91C22×D4×C31—21no—
92C22×D4×C31—22no—
93C22×D4×C31—22no—
94C22×D4×C31—21no—
95C22×D4×C31—21no—
96C22×D4×C31—21no—
97C22×D4×C31—22no—
98C22×D4×C31D412yes—
99C22×D4×C31D411yescharacteristic, complemented
100C22×D4×C31C2311yescharacteristic
101C22×D4×C31C2311yescharacteristic
102C23×C4×C31—21no—
103C23×C4×C31C2311yescharacteristic
104C31×AGL(1,ℤ/8)—22no—
105C31×AGL(1,ℤ/8)—22no—
106C31×AGL(1,ℤ/8)—22no—
107C31×AGL(1,ℤ/8)—41no—
108C31×AGL(1,ℤ/8)—41no—
109C31×AGL(1,ℤ/8)—41no—
110C2×SD16×C31—21no—
111C2×SD16×C31—21no—
112C2×SD16×C31—21no—
113C2×D8×C31—21no—
114C2×D8×C31—21no—
115C2×D8×C31—21no—
116C2×M16×C31—21no—
117C2×M16×C31—22no—
118C2×M16×C31—41no—
119C2×M16×C31C2311yescharacteristic
120C2×M16×C31C2311yescharacteristic
121C2×M16×C31C2311yescharacteristic
122C2×M16×C31C2311yescharacteristic
123C22×C8×C31—21no—
124C31×#127—22no—
125C31×#127—21no—
126C31×#127—22no—
127C31×#127—41no—
128C31×#124—22no—
129C31×#124—21no—
130C31×#123—22no—
131C31×#123—21no—
132C31×C22⋊Q8—22no—
133C31×C22⋊Q8—21no—
134C31×C22⋊Q8—21no—
135C31×C22⋊Q8D411yescharacteristic, complemented
136C31×C22⋊Q8D411yescharacteristic, complemented
137C31×#121—22no—
138C31×#121—22no—
139C31×#121—22no—
140C31×#121—22no—
141C31×#121—22no—
142C31×#121—21no—
143C31×#121—21no—
144C31×#121—21no—
145C31×#121—21no—
146C31×#121—21no—
147C31×#121—21no—
148C31×#121—22no—
149C31×#121—21no—
150C31×#121—21no—
151C31×#121—21no—
152C31×#121—21no—
153C31×#121—21no—
154C31×#121—21no—
155C31×#121D411yescharacteristic, complemented
156C31×#121D411yescharacteristic, complemented
157C31×#120—22no—
158C31×#120—22no—
159C31×#120—22no—
160C31×#120—21no—
161C31×#120—22no—
162C4×Q8×C31—21no—
163C4×D4×C31—22no—
164C4×D4×C31—22no—
165C4×D4×C31—21no—
166C4×D4×C31—22no—
167C4×D4×C31—21no—
168C4×D4×C31—21no—
169C31×#117—21no—
170C31×#117—22no—
171C31×#117—41no—
172C31×#117C2311yescharacteristic
173C2×C4⋊C4×C31—21no—
174C2×C4⋊C4×C31—21no—
175C2×C4⋊C4×C31C2311yescharacteristic
176C2×C4⋊C4×C31C2311yescharacteristic
177C2×C22⋊C4×C31—22no—
178C2×C22⋊C4×C31—21no—
179C2×C22⋊C4×C31—21no—
180C2×C22⋊C4×C31—22no—
181C2×C22⋊C4×C31—22no—
182C2×C22⋊C4×C31D412yes—
183C2×C42×C31C2311yescharacteristic
184C2×C42×C31C2311yescharacteristic
185C31×#107—21no—
186C31×#106—21no—
187C31×#104—22no—
188C31×#104—22no—
189C31×#104—22no—
190C31×#104—22no—
191C31×#104—41no—
192C31×#104D414yescomplemented
193C31×#103—21no—
194C31×#103—21no—
195C31×#103—21no—
196C31×#102—21no—
197C31×#102—21no—
198C31×#102—21no—
199C31×#102—21no—
200C31×#102—21no—
201C31×#100—22no—
202C31×#100—41no—
203C31×C22⋊C8—21no—
204C31×C22⋊C8—21no—
205C31×#95—22no—
206C24×C31—22no—
207C24×C31—21no—
208C24×C31—21no—
209C24×C31C2×D412yes—
210C24×C31C2×D411yescharacteristic
211#41×C31—21no—
212#41×C31—21no—
213#41×C31—22no—
214#41×C31—22no—
215#41×C31—21no—
216#41×C31—21no—
217#41×C31—21no—
218#41×C31—21no—
219#41×C31—21no—
220#41×C31—21no—
221#41×C31—21no—
222#41×C31—21no—
223#41×C31—42no—
224#41×C31—42no—
225#41×C31—41no—
226#41×C31—41no—
227#41×C31—42no—
228#41×C31—42no—
229#41×C31—42no—
230#41×C31—42no—
231#41×C31—42no—
232#41×C31—42no—
233#41×C31C2×D412yes—
234#41×C31#4112yes—
235C2×Q8×C31—21no—
236C2×Q8×C31—22no—
237C2×Q8×C31—41no—
238C2×Q8×C31C2×D411yescharacteristic
239C2×Q8×C31C2×D411yescharacteristic
240C2×Q8×C31C2×D411yescharacteristic
241C2×D4×C31—21no—
242C2×D4×C31—22no—
243C2×D4×C31—22no—
244C2×D4×C31—22no—
245C2×D4×C31—22no—
246C2×D4×C31—21no—
247C2×D4×C31—21no—
248C2×D4×C31—21no—
249C2×D4×C31—21no—
250C2×D4×C31—21no—
251C2×D4×C31—22no—
252C2×D4×C31—22no—
253C2×D4×C31—22no—
254C2×D4×C31—21no—
255C2×D4×C31—22no—
256C2×D4×C31—21no—
257C2×D4×C31—21no—
258C2×D4×C31—21no—
259C2×D4×C31—21no—
260C2×D4×C31—21no—
261C2×D4×C31—21no—
262C2×D4×C31—21no—
263C2×D4×C31—21no—
264C2×D4×C31—21no—
265C2×D4×C31—21no—
266C2×D4×C31—21no—
267C2×D4×C31—21no—
268C2×D4×C31—21no—
269C2×D4×C31—41no—
270C2×D4×C31—42no—
271C2×D4×C31—42no—
272C2×D4×C31—44no—
273C2×D4×C31—42no—
274C2×D4×C31—42no—
275C2×D4×C31—44no—
276C2×D4×C31—44no—
277C2×D4×C31—42no—
278C2×D4×C31—42no—
279C2×D4×C31—41no—
280C2×D4×C31—41no—
281C2×D4×C31—82no—
282C2×D4×C31—82no—
283C2×D4×C31—82no—
284C2×D4×C31—82no—
285C2×D4×C31—84no—
286C2×D4×C31C2×D411yescharacteristic
287C2×D4×C31C2×D411yescharacteristic
288C2×D4×C31C2×D411yescharacteristic
289C22×C4×C31—21no—
290C22×C4×C31—21no—
291C22×C4×C31—21no—
292C22×C4×C31—21no—
293C22×C4×C31—21no—
294C22×C4×C31—22no—
295C22×C4×C31—21no—
296C22×C4×C31—21no—
297C22×C4×C31—22no—
298C22×C4×C31—21no—
299C22×C4×C31—21no—
300C22×C4×C31—21no—
301C22×C4×C31—21no—
302C22×C4×C31—21no—
303C22×C4×C31—21no—
304C22×C4×C31—42no—
305C22×C4×C31—42no—
306C22×C4×C31C2×D411yescharacteristic
307C22×C4×C31C2×D411yescharacteristic
308C22×C4×C31C2×D411yescharacteristic
309C22×C4×C31C2×D411yescharacteristic
310C22×C4×C31C2×D411yescharacteristic
311C22×C4×C31C2×D412yes—
312C22×C4×C31C2411yescharacteristic
313SD16×C31—42no—
314SD16×C31—42no—
315SD16×C31—42no—
316D8×C31—42no—
317D8×C31—42no—
318D8×C31—42no—
319M16×C31—21no—
320M16×C31—21no—
321M16×C31—21no—
322M16×C31—21no—
323M16×C31—21no—
324M16×C31—21no—
325M16×C31—21no—
326M16×C31—42no—
327M16×C31C2×D412yescomplemented
328C2×C8×C31—21no—
329C2×C8×C31—21no—
330C2×C8×C31—21no—
331C2×C8×C31—21no—
332C2×C8×C31—42no—
333C4⋊C4×C31—22no—
334C4⋊C4×C31—22no—
335C4⋊C4×C31—21no—
336C4⋊C4×C31—21no—
337C4⋊C4×C31—21no—
338C4⋊C4×C31—21no—
339C4⋊C4×C31—21no—
340C4⋊C4×C31—21no—
341C4⋊C4×C31—42no—
342C4⋊C4×C31C2×D411yescharacteristic
343C4⋊C4×C31C2×D411yescharacteristic
344C22⋊C4×C31—22no—
345C22⋊C4×C31—22no—
346C22⋊C4×C31—22no—
347C22⋊C4×C31—22no—
348C22⋊C4×C31—22no—
349C22⋊C4×C31—21no—
350C22⋊C4×C31—21no—
351C22⋊C4×C31—21no—
352C22⋊C4×C31—21no—
353C22⋊C4×C31—22no—
354C22⋊C4×C31—22no—
355C22⋊C4×C31—21no—
356C22⋊C4×C31—42no—
357C22⋊C4×C31—41no—
358C22⋊C4×C31—41no—
359C22⋊C4×C31—82no—
360C22⋊C4×C31—82no—
361C42×C31—22no—
362C42×C31—21no—
363C42×C31—21no—
364C42×C31—21no—
365C42×C31—21no—
366C42×C31C2×D412yescomplemented
367#24468C3111yesmaximal, characteristic, direct product factor, Sylow
368C23×C31—21no—
369C23×C31—21no—
370C23×C31—21no—
371C23×C31—22no—
372C23×C31—21no—
373C23×C31—21no—
374C23×C31—22no—
375C23×C31—22no—
376C23×C31—41no—
377C23×C31—41no—
378C23×C31—42no—
379C23×C31—42no—
380C23×C31—44no—
381C23×C31—42no—
382C23×C31—42no—
383C23×C31—42no—
384C23×C31—42no—
385C23×C31—41no—
386C23×C31—41no—
387C23×C31—41no—
388C23×C31—81no—
389C23×C31—82no—
390C23×C31—82no—
391C23×C31#12011yescharacteristic
392C23×C31#12011yescharacteristic
393C23×C31C22×D411yescharacteristic
394Q8×C31—21no—
395Q8×C31—21no—
396Q8×C31—21no—
397Q8×C31—21no—
398Q8×C31—21no—
399Q8×C31—42no—
400Q8×C31#12112yes—
401D4×C31—22no—
402D4×C31—22no—
403D4×C31—21no—
404D4×C31—21no—
405D4×C31—21no—
406D4×C31—21no—
407D4×C31—21no—
408D4×C31—42no—
409D4×C31—42no—
410D4×C31—44no—
411D4×C31—42no—
412D4×C31—44no—
413D4×C31—44no—
414D4×C31—42no—
415D4×C31—41no—
416D4×C31—41no—
417D4×C31—41no—
418D4×C31—41no—
419D4×C31—41no—
420D4×C31—41no—
421D4×C31—41no—
422D4×C31—41no—
423D4×C31—41no—
424D4×C31—41no—
425D4×C31—41no—
426D4×C31—41no—
427D4×C31—81no—
428D4×C31—82no—
429D4×C31—82no—
430D4×C31—82no—
431D4×C31—82no—
432D4×C31—88no—
433D4×C31—82no—
434D4×C31—82no—
435D4×C31#12112yes—
436C2×C4×C31—21no—
437C2×C4×C31—21no—
438C2×C4×C31—21no—
439C2×C4×C31—21no—
440C2×C4×C31—21no—
441C2×C4×C31—21no—
442C2×C4×C31—21no—
443C2×C4×C31—21no—
444C2×C4×C31—21no—
445C2×C4×C31—22no—
446C2×C4×C31—21no—
447C2×C4×C31—21no—
448C2×C4×C31—22no—
449C2×C4×C31—21no—
450C2×C4×C31—22no—
451C2×C4×C31—21no—
452C2×C4×C31—21no—
453C2×C4×C31—21no—
454C2×C4×C31—22no—
455C2×C4×C31—42no—
456C2×C4×C31—42no—
457C2×C4×C31—42no—
458C2×C4×C31—44no—
459C2×C4×C31—41no—
460C2×C4×C31—41no—
461C2×C4×C31—41no—
462C2×C4×C31—41no—
463C2×C4×C31—41no—
464C2×C4×C31—41no—
465C2×C4×C31—42no—
466C2×C4×C31—41no—
467C2×C4×C31—41no—
468C2×C4×C31—42no—
469C2×C4×C31—41no—
470C2×C4×C31—41no—
471C2×C4×C31—82no—
472C2×C4×C31#12011yescharacteristic
473C2×C4×C31#12011yescharacteristic
474C2×C4×C31C22×D411yescharacteristic
475C2×C4×C31C22×D411yescharacteristic
476C2×C4×C31C22×D411yescharacteristic
477C2×C4×C31C2×#4111yescharacteristic
478C2×C4×C31H(5,𝔽2)11yescharacteristic
479C2×C4×C31H(5,𝔽2)11yescharacteristic
480C8×C31—22no—
481C8×C31—41no—
482C8×C31—41no—
483C8×C31—41no—
484#3488C2×C3111yescharacteristic, complemented
485#3055C2×C3111yescharacteristic, complemented
486C2×#453C2×C3111yescharacteristic, complemented
487#3006C2×C3111yescharacteristic, complemented
488C2×#421C2×C3111yescharacteristic, complemented
489#2619C2×C3111yescharacteristic, complemented
490#2040C2×C3111yescharacteristic, complemented
491#2037C2×C3111yescharacteristic, complemented
492#2006C2×C3111yescharacteristic, complemented
493#2002C2×C3111yescharacteristic, complemented
494#1900C2×C3111yescharacteristic, complemented
495#1897C2×C3111yescharacteristic, complemented
496#1883C2×C3111yescharacteristic, complemented
497#1860C2×C3111yescharacteristic, complemented
498#1792C2×C3111yescharacteristic, complemented
499C22×C31—21no—
500C22×C31—21no—
501C22×C31—21no—
502C22×C31—21no—
503C22×C31—22no—
504C22×C31—21no—
505C22×C31—21no—
506C22×C31—21no—
507C22×C31—21no—
508C22×C31—41no—
509C22×C31—41no—
510C22×C31—41no—
511C22×C31—41no—
512C22×C31—42no—
513C22×C31—42no—
514C22×C31—41no—
515C22×C31—41no—
516C22×C31—41no—
517C22×C31—42no—
518C22×C31—41no—
519C22×C31—81no—
520C22×C31—81no—
521C22×C31—82no—
522C22×C31—82no—
523C22×C31—82no—
524C22×C31—82no—
525C22×C31—84no—
526C22×C31—81no—
527C22×C31—81no—
528C22×C31—81no—
529C22×C31—164no—
530C22×C31C2×#12011yescharacteristic
531C22×C31D4211yescharacteristic
532C22×C31#54611yescharacteristic
533C4×C31—21no—
534C4×C31—21no—
535C4×C31—22no—
536C4×C31—42no—
537C4×C31—41no—
538C4×C31—41no—
539C4×C31—42no—
540C4×C31—41no—
541C4×C31—41no—
542C4×C31—81no—
543C4×C31—81no—
544C4×C31C2×#12111yescharacteristic
545C4×C31#53411yescharacteristic
546C4×C31D4211yescharacteristic
547C4×C31#54611yescharacteristic
548C2×H(5,𝔽2)C22×C3111yescharacteristic
549C22×#41C22×C3111yescharacteristic
550C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
551C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
552C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
553C22×M16C22×C3111yescharacteristic, complemented
554#550—21no—
555#548—21no—
556#546—21no—
557#546—22no—
558D42—22no—
559D42—21no—
560#537—21no—
561#537C22×C3111yescharacteristic
562#535—21no—
563#535C22×C3111yescharacteristic
564C2×#127C22×C3111yescharacteristic, complemented
565#525—21no—
566#525C22×C3111yescharacteristic
567C2×#121—21no—
568C2×#121C22×C3111yescharacteristic
569C2×#121C22×C3111yescharacteristic, complemented
570#520C22×C3111yescharacteristic
571C2×#117C22×C3111yescharacteristic, complemented
572#469—21no—
573#468—21no—
574#466—21no—
575#465—21no—
576#453—24no—
577#449—21no—
578#449—21no—
579#448—21no—
580#447—21no—
581#428C22×C3111yescharacteristic, complemented
582#421—24no—
583C2×#104C22×C3111yescharacteristic
584C2×#104C22×C3111yescharacteristic
585C2×#104C22×C3111yescharacteristic, complemented
586C2×#104C22×C3111yescharacteristic, complemented
587C2×#104C22×C3111yescharacteristic, complemented
588C2×#104C22×C3111yescharacteristic, complemented
589#418C22×C3111yescharacteristic, complemented
590#417C22×C3111yescharacteristic
591#417C22×C3111yescharacteristic, complemented
592#417C22×C3111yescharacteristic, complemented
593C2×#100C22×C3111yescharacteristic, complemented
594C2×#100C22×C3111yescharacteristic, complemented
595#407C22×C3111yescharacteristic, complemented
596#394—22no—
597#392—22no—
598#390C22×C3111yescharacteristic, complemented
599#390C22×C3111yescharacteristic, complemented
600#382C22×C3111yescharacteristic, complemented
601#343C22×C3111yescharacteristic, complemented
602#343C22×C3111yescharacteristic, complemented
603#339C22×C3111yescharacteristic, complemented
604#339C22×C3111yescharacteristic, complemented
605C2×C31—21no—
606C2×C31—21no—
607C2×C31—41no—
608C2×C31—41no—
609C2×C31—42no—
610C2×C31—81no—
611C2×C31—82no—
612C2×C31—81no—
613C2×C31—161no—
614C2×C31#241011yescharacteristic
615C2×C31#301911yescharacteristic
616C2×C31#302111yescharacteristic
617H(5,𝔽2)—22no—
618H(5,𝔽2)—22no—
619H(5,𝔽2)—41no—
620H(5,𝔽2)—41no—
621C2×#41—21no—
622C2×#41—21no—
623C2×#41—21no—
624C2×#41—21no—
625C2×#41—22no—
626C2×#41—22no—
627C2×#41—41no—
628C2×#41—41no—
629C2×#41D4×C3111yescharacteristic, complemented
630C2×#41D4×C3111yescharacteristic, complemented
631C2×#41C23×C3111yescharacteristic
632C2×#41C23×C3111yescharacteristic
633C2×#41C23×C3111yescharacteristic
634C22×Q8D4×C3111yescharacteristic, complemented
635C22×D4—21no—
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—21no—
639C22×D4—21no—
640C22×D4—21no—
641C22×D4—22no—
642C22×D4D4×C3112yes—
643C22×D4D4×C3111yescharacteristic, complemented
644C22×D4C23×C3111yescharacteristic
645C22×D4C23×C3111yescharacteristic
646C23×C4—21no—
647C23×C4C23×C3111yescharacteristic
648AGL(1,ℤ/8)—22no—
649AGL(1,ℤ/8)—22no—
650AGL(1,ℤ/8)—22no—
651AGL(1,ℤ/8)—41no—
652AGL(1,ℤ/8)—41no—
653AGL(1,ℤ/8)—41no—
654C2×SD16—21no—
655C2×SD16—21no—
656C2×SD16—21no—
657C2×D8—21no—
658C2×D8—21no—
659C2×D8—21no—
660C2×M16—21no—
661C2×M16—22no—
662C2×M16—41no—
663C2×M16C23×C3111yescharacteristic
664C2×M16C23×C3111yescharacteristic
665C2×M16C23×C3111yescharacteristic
666C2×M16C23×C3111yescharacteristic
667C22×C8—21no—
668#127—22no—
669#127—21no—
670#127—22no—
671#127—41no—
672#124—22no—
673#124—21no—
674#123—22no—
675#123—21no—
676C22⋊Q8—22no—
677C22⋊Q8—21no—
678C22⋊Q8—21no—
679C22⋊Q8D4×C3111yescharacteristic, complemented
680C22⋊Q8D4×C3111yescharacteristic, complemented
681#121—22no—
682#121—22no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—21no—
687#121—21no—
688#121—21no—
689#121—21no—
690#121—21no—
691#121—21no—
692#121—22no—
693#121—21no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121D4×C3111yescharacteristic, complemented
700#121D4×C3111yescharacteristic, complemented
701#120—22no—
702#120—22no—
703#120—22no—
704#120—21no—
705#120—22no—
706C4×Q8—21no—
707C4×D4—22no—
708C4×D4—22no—
709C4×D4—21no—
710C4×D4—22no—
711C4×D4—21no—
712C4×D4—21no—
713#117—21no—
714#117—22no—
715#117—41no—
716#117C23×C3111yescharacteristic
717C2×C4⋊C4—21no—
718C2×C4⋊C4—21no—
719C2×C4⋊C4C23×C3111yescharacteristic
720C2×C4⋊C4C23×C3111yescharacteristic
721C2×C22⋊C4—22no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4D4×C3112yes—
727C2×C42C23×C3111yescharacteristic
728C2×C42C23×C3111yescharacteristic
729#107—21no—
730#106—21no—
731#104—22no—
732#104—22no—
733#104—22no—
734#104—22no—
735#104—41no—
736#104D4×C3114yescomplemented
737#103—21no—
738#103—21no—
739#103—21no—
740#102—21no—
741#102—21no—
742#102—21no—
743#102—21no—
744#102—21no—
745#100—22no—
746#100—41no—
747C22⋊C8—21no—
748C22⋊C8—21no—
749#95—22no—
750C31#2446811yescharacteristic, direct product factor, Sylow
751C24—22no—
752C24—21no—
753C24—21no—
754C24C2×D4×C3112yes—
755C24C2×D4×C3111yescharacteristic
756#41—21no—
757#41—21no—
758#41—22no—
759#41—22no—
760#41—21no—
761#41—21no—
762#41—21no—
763#41—21no—
764#41—21no—
765#41—21no—
766#41—21no—
767#41—21no—
768#41—42no—
769#41—42no—
770#41—41no—
771#41—41no—
772#41—42no—
773#41—42no—
774#41—42no—
775#41—42no—
776#41—42no—
777#41—42no—
778#41C2×D4×C3112yes—
779#41#41×C3112yes—
780C2×Q8—21no—
781C2×Q8—22no—
782C2×Q8—41no—
783C2×Q8C2×D4×C3111yescharacteristic
784C2×Q8C2×D4×C3111yescharacteristic
785C2×Q8C2×D4×C3111yescharacteristic
786C2×D4—21no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—21no—
800C2×D4—22no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—41no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—44no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—41no—
825C2×D4—41no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—82no—
829C2×D4—82no—
830C2×D4—84no—
831C2×D4C2×D4×C3111yescharacteristic
832C2×D4C2×D4×C3111yescharacteristic
833C2×D4C2×D4×C3111yescharacteristic
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4C2×D4×C3111yescharacteristic
852C22×C4C2×D4×C3111yescharacteristic
853C22×C4C2×D4×C3111yescharacteristic
854C22×C4C2×D4×C3111yescharacteristic
855C22×C4C2×D4×C3111yescharacteristic
856C22×C4C2×D4×C3112yes—
857C22×C4C24×C3111yescharacteristic
858SD16—42no—
859SD16—42no—
860SD16—42no—
861D8—42no—
862D8—42no—
863D8—42no—
864M16—21no—
865M16—21no—
866M16—21no—
867M16—21no—
868M16—21no—
869M16—21no—
870M16—21no—
871M16—42no—
872M16C2×D4×C3112yescomplemented
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—42no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—42no—
887C4⋊C4C2×D4×C3111yescharacteristic
888C4⋊C4C2×D4×C3111yescharacteristic
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—21no—
897C22⋊C4—21no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—21no—
901C22⋊C4—42no—
902C22⋊C4—41no—
903C22⋊C4—41no—
904C22⋊C4—82no—
905C22⋊C4—82no—
906C42—22no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42C2×D4×C3112yescomplemented
912C23—21no—
913C23—21no—
914C23—21no—
915C23—22no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—42no—
923C23—42no—
924C23—44no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—81no—
933C23—82no—
934C23—82no—
935C23C31×#12011yescharacteristic
936C23C31×#12011yescharacteristic
937C23C22×D4×C3111yescharacteristic
938Q8—21no—
939Q8—21no—
940Q8—21no—
941Q8—21no—
942Q8—21no—
943Q8—42no—
944Q8C31×#12112yes—
945D4—22no—
946D4—22no—
947D4—21no—
948D4—21no—
949D4—21no—
950D4—21no—
951D4—21no—
952D4—42no—
953D4—42no—
954D4—44no—
955D4—42no—
956D4—44no—
957D4—44no—
958D4—42no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—81no—
972D4—82no—
973D4—82no—
974D4—82no—
975D4—82no—
976D4—88no—
977D4—82no—
978D4—82no—
979D4C31×#12112yes—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—44no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—42no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—42no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—82no—
1016C2×C4C31×#12011yescharacteristic
1017C2×C4C31×#12011yescharacteristic
1018C2×C4C22×D4×C3111yescharacteristic
1019C2×C4C22×D4×C3111yescharacteristic
1020C2×C4C22×D4×C3111yescharacteristic
1021C2×C4C2×#41×C3111yescharacteristic
1022C2×C4C31×H(5,𝔽2)11yescharacteristic
1023C2×C4C31×H(5,𝔽2)11yescharacteristic
1024C8—22no—
1025C8—41no—
1026C8—41no—
1027C8—41no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—22no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—42no—
1042C22—42no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—42no—
1047C22—41no—
1048C22—81no—
1049C22—81no—
1050C22—82no—
1051C22—82no—
1052C22—82no—
1053C22—82no—
1054C22—84no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—164no—
1059C22C2×C31×#12011yescharacteristic
1060C22D42×C3111yescharacteristic
1061C22C31×#54611yescharacteristic
1062C4—21no—
1063C4—21no—
1064C4—22no—
1065C4—42no—
1066C4—41no—
1067C4—41no—
1068C4—42no—
1069C4—41no—
1070C4—41no—
1071C4—81no—
1072C4—81no—
1073C4C2×C31×#12111yescharacteristic
1074C4C31×#53411yescharacteristic
1075C4D42×C3111yescharacteristic
1076C4C31×#54611yescharacteristic
1077C2—21no—
1078C2—21no—
1079C2—41no—
1080C2—41no—
1081C2—42no—
1082C2—81no—
1083C2—82no—
1084C2—81no—
1085C2—161no—
1086C2C31×#241011yescharacteristic
1087C2C31×#301911yescharacteristic
1088C2C31×#302111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3488C2semidirect
2. C31×#3055C2semidirect
3. C2×C31×#453C2semidirect
4. C31×#3006C2semidirect
5. C2×C31×#421C2semidirect
6. C31×#2619C2semidirect
7. C31×#2040C2semidirect
8. C31×#2037C2semidirect
9. C31×#2006C2semidirect
10. C31×#2002C2semidirect
11. C31×#1900C2semidirect
12. C31×#1897C2semidirect
13. C31×#1883C2semidirect
14. C31×#1860C2semidirect
15. C31×#1792C2semidirect
19. C2×C31×AGL(1,ℤ/8)C22semidirect
20. C2×C31×AGL(1,ℤ/8)C22semidirect
21. C22×M16×C31C22semidirect
32. C2×C31×#127C22semidirect
37. C2×C31×#121C22semidirect
39. C2×C31×#117C22semidirect
49. C31×#428C22semidirect
53. C2×C31×#104C22semidirect
54. C2×C31×#104C22semidirect
55. C2×C31×#104C22semidirect
56. C2×C31×#104C22semidirect
57. C31×#418C22semidirect
59. C31×#417C22semidirect
60. C31×#417C22semidirect
61. C2×C31×#100C22semidirect
62. C2×C31×#100C22semidirect
63. C31×#407C22semidirect
66. C31×#390C22semidirect
67. C31×#390C22semidirect
68. C31×#382C22semidirect
69. C31×#343C22semidirect
70. C31×#343C22semidirect
71. C31×#339C22semidirect
72. C31×#339C22semidirect
85. C2×#41×C31D4semidirect
86. C2×#41×C31D4semidirect
90. C22×Q8×C31D4semidirect
99. C22×D4×C31D4semidirect
135. C31×C22⋊Q8D4semidirect
136. C31×C22⋊Q8D4semidirect
155. C31×#121D4semidirect
156. C31×#121D4semidirect
192. C31×#104D4semidirect
327. M16×C31C2×D4semidirect
366. C42×C31C2×D4semidirect
367. #24468C31direct (N × H)
484. #3488C2×C31semidirect
485. #3055C2×C31semidirect
486. C2×#453C2×C31semidirect
487. #3006C2×C31semidirect
488. C2×#421C2×C31semidirect
489. #2619C2×C31semidirect
490. #2040C2×C31semidirect
491. #2037C2×C31semidirect
492. #2006C2×C31semidirect
493. #2002C2×C31semidirect
494. #1900C2×C31semidirect
495. #1897C2×C31semidirect
496. #1883C2×C31semidirect
497. #1860C2×C31semidirect
498. #1792C2×C31semidirect
551. C2×AGL(1,ℤ/8)C22×C31semidirect
552. C2×AGL(1,ℤ/8)C22×C31semidirect
553. C22×M16C22×C31semidirect
564. C2×#127C22×C31semidirect
569. C2×#121C22×C31semidirect
571. C2×#117C22×C31semidirect
581. #428C22×C31semidirect
585. C2×#104C22×C31semidirect
586. C2×#104C22×C31semidirect
587. C2×#104C22×C31semidirect
588. C2×#104C22×C31semidirect
589. #418C22×C31semidirect
591. #417C22×C31semidirect
592. #417C22×C31semidirect
593. C2×#100C22×C31semidirect
594. C2×#100C22×C31semidirect
595. #407C22×C31semidirect
598. #390C22×C31semidirect
599. #390C22×C31semidirect
600. #382C22×C31semidirect
601. #343C22×C31semidirect
602. #343C22×C31semidirect
603. #339C22×C31semidirect
604. #339C22×C31semidirect
629. C2×#41D4×C31semidirect
630. C2×#41D4×C31semidirect
634. C22×Q8D4×C31semidirect
643. C22×D4D4×C31semidirect
679. C22⋊Q8D4×C31semidirect
680. C22⋊Q8D4×C31semidirect
699. #121D4×C31semidirect
700. #121D4×C31semidirect
736. #104D4×C31semidirect
750. C31#24468direct (N × H)
872. M16C2×D4×C31semidirect
911. C42C2×D4×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#34882
C31×#30552
C2×C31×#4532
C31×#30062
C2×C31×#4212
C31×#26192
C31×#20402
C31×#20372
C31×#20062
C31×#20022
C31×#19002
C31×#18972
C31×#18832
C31×#18602
C31×#17922
#2446831