Finite Group Databasebeta

← C31×#24464 #21481223

Subgroups — C31×#24464 #21481223

Order 7936.

1600 conjugacy classes of subgroups.

The subgroup lattice has 1100 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
5C22×C31×#104C211yesmaximal, characteristic, complemented
6C31×#2856C211yesmaximal, characteristic, complemented
7C31×#2039C211yesmaximal, characteristic, complemented
8C31×#2037C211yesmaximal, characteristic, complemented
9C31×#2006C211yesmaximal, characteristic, complemented
10C31×#2002C211yesmaximal, characteristic, complemented
11C31×#1900C211yesmaximal, characteristic, complemented
12C31×#1896C211yesmaximal, characteristic, complemented
13C31×#1883C211yesmaximal, characteristic, complemented
14C31×#1859C211yesmaximal, 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×#121—22no—
37C2×C31×#121C2211yescharacteristic
38C2×C31×#121C2211yescharacteristic, complemented
39C31×#520C2211yescharacteristic
40C22×C42×C31C2211yescharacteristic, complemented
41C31×#469—21no—
42C31×#468—21no—
43C31×#466—21no—
44C31×#465—21no—
45C31×#453—24no—
46C31×#449—21no—
47C31×#449—21no—
48C31×#448—21no—
49C31×#447—21no—
50C31×#428C2211yescharacteristic, complemented
51C2×C31×#104—24no—
52C2×C31×#104C2211yescharacteristic
53C2×C31×#104C2211yescharacteristic
54C2×C31×#104C2211yescharacteristic, complemented
55C2×C31×#104C2211yescharacteristic, complemented
56C2×C31×#104C2211yescharacteristic, complemented
57C2×C31×#104C2211yescharacteristic, complemented
58C31×#418C2211yescharacteristic, complemented
59C31×#417C2211yescharacteristic
60C31×#417C2211yescharacteristic, complemented
61C31×#417C2211yescharacteristic, complemented
62C2×C31×#100C2211yescharacteristic, complemented
63C2×C31×#100C2211yescharacteristic, complemented
64C31×#407C2211yescharacteristic, complemented
65C31×#390—22no—
66C31×#390C2211yescharacteristic, complemented
67C31×#390C2211yescharacteristic, complemented
68C31×#384C2211yescharacteristic, 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×C31—21no—
104C23×C4×C31C2311yescharacteristic
105C31×AGL(1,ℤ/8)—22no—
106C31×AGL(1,ℤ/8)—22no—
107C31×AGL(1,ℤ/8)—22no—
108C31×AGL(1,ℤ/8)—41no—
109C31×AGL(1,ℤ/8)—41no—
110C31×AGL(1,ℤ/8)—41no—
111C2×SD16×C31—21no—
112C2×SD16×C31—21no—
113C2×SD16×C31—21no—
114C2×D8×C31—21no—
115C2×D8×C31—21no—
116C2×D8×C31—21no—
117C2×M16×C31—21no—
118C2×M16×C31—22no—
119C2×M16×C31—41no—
120C2×M16×C31C2311yescharacteristic
121C2×M16×C31C2311yescharacteristic
122C2×M16×C31C2311yescharacteristic
123C2×M16×C31C2311yescharacteristic
124C22×C8×C31—21no—
125C31×#127—22no—
126C31×#127—21no—
127C31×#127—22no—
128C31×#127—41no—
129C31×#124—22no—
130C31×#124—21no—
131C31×#123—22no—
132C31×#123—21no—
133C31×C22⋊Q8—22no—
134C31×C22⋊Q8—21no—
135C31×C22⋊Q8—21no—
136C31×C22⋊Q8D411yescharacteristic, complemented
137C31×C22⋊Q8D411yescharacteristic, complemented
138C31×#121—22no—
139C31×#121—22no—
140C31×#121—22no—
141C31×#121—22no—
142C31×#121—22no—
143C31×#121—21no—
144C31×#121—21no—
145C31×#121—21no—
146C31×#121—21no—
147C31×#121—21no—
148C31×#121—21no—
149C31×#121—22no—
150C31×#121—21no—
151C31×#121—21no—
152C31×#121—21no—
153C31×#121—21no—
154C31×#121—21no—
155C31×#121—21no—
156C31×#121—48no—
157C31×#121D411yescharacteristic, complemented
158C31×#121D411yescharacteristic, complemented
159C31×#120—22no—
160C31×#120—22no—
161C31×#120—22no—
162C31×#120—21no—
163C31×#120—22no—
164C4×Q8×C31—21no—
165C4×D4×C31—22no—
166C4×D4×C31—22no—
167C4×D4×C31—21no—
168C4×D4×C31—22no—
169C4×D4×C31—21no—
170C4×D4×C31—21no—
171C31×#117—21no—
172C31×#117C2311yescharacteristic
173C2×C4⋊C4×C31—21no—
174C2×C4⋊C4×C31—22no—
175C2×C4⋊C4×C31C2311yescharacteristic
176C2×C4⋊C4×C31C2311yescharacteristic
177C2×C22⋊C4×C31—22no—
178C2×C22⋊C4×C31—22no—
179C2×C22⋊C4×C31—22no—
180C2×C22⋊C4×C31—21no—
181C2×C22⋊C4×C31D412yes—
182C2×C42×C31—22no—
183C2×C42×C31—21no—
184C2×C42×C31—41no—
185C2×C42×C31C2311yescharacteristic
186C2×C42×C31C2311yescharacteristic
187C31×#107—21no—
188C31×#106—21no—
189C31×#104—22no—
190C31×#104—22no—
191C31×#104—22no—
192C31×#104—22no—
193C31×#104—41no—
194C31×#104D414yescomplemented
195C31×#103—21no—
196C31×#103—21no—
197C31×#103—21no—
198C31×#102—21no—
199C31×#102—21no—
200C31×#102—21no—
201C31×#102—21no—
202C31×#102—21no—
203C31×#100—22no—
204C31×#100—41no—
205C31×C22⋊C8—21no—
206C31×C22⋊C8—21no—
207C24×C31—22no—
208C24×C31—21no—
209C24×C31—21no—
210C24×C31C2×D411yescharacteristic
211C24×C31C2×D412yes—
212#41×C31—21no—
213#41×C31—21no—
214#41×C31—22no—
215#41×C31—22no—
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—21no—
224#41×C31—42no—
225#41×C31—42no—
226#41×C31—41no—
227#41×C31—41no—
228#41×C31—42no—
229#41×C31—42no—
230#41×C31—42no—
231#41×C31—42no—
232#41×C31—42no—
233#41×C31—42no—
234#41×C31C2×D412yes—
235#41×C31#4112yes—
236C2×Q8×C31—21no—
237C2×Q8×C31—22no—
238C2×Q8×C31—41no—
239C2×Q8×C31C2×D411yescharacteristic
240C2×Q8×C31C2×D411yescharacteristic
241C2×Q8×C31C2×D411yescharacteristic
242C2×D4×C31—21no—
243C2×D4×C31—22no—
244C2×D4×C31—22no—
245C2×D4×C31—22no—
246C2×D4×C31—22no—
247C2×D4×C31—21no—
248C2×D4×C31—21no—
249C2×D4×C31—21no—
250C2×D4×C31—21no—
251C2×D4×C31—21no—
252C2×D4×C31—22no—
253C2×D4×C31—22no—
254C2×D4×C31—22no—
255C2×D4×C31—21no—
256C2×D4×C31—22no—
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—21no—
270C2×D4×C31—41no—
271C2×D4×C31—42no—
272C2×D4×C31—42no—
273C2×D4×C31—44no—
274C2×D4×C31—44no—
275C2×D4×C31—44no—
276C2×D4×C31—42no—
277C2×D4×C31—42no—
278C2×D4×C31—44no—
279C2×D4×C31—44no—
280C2×D4×C31—42no—
281C2×D4×C31—42no—
282C2×D4×C31—44no—
283C2×D4×C31—44no—
284C2×D4×C31—41no—
285C2×D4×C31—41no—
286C2×D4×C31—84no—
287C2×D4×C31C2×D411yescharacteristic
288C2×D4×C31C2×D411yescharacteristic
289C2×D4×C31C2×D411yescharacteristic
290C22×C4×C31—21no—
291C22×C4×C31—21no—
292C22×C4×C31—21no—
293C22×C4×C31—21no—
294C22×C4×C31—21no—
295C22×C4×C31—21no—
296C22×C4×C31—22no—
297C22×C4×C31—24no—
298C22×C4×C31—21no—
299C22×C4×C31—21no—
300C22×C4×C31—22no—
301C22×C4×C31—21no—
302C22×C4×C31—21no—
303C22×C4×C31—21no—
304C22×C4×C31—21no—
305C22×C4×C31—21no—
306C22×C4×C31—42no—
307C22×C4×C31—42no—
308C22×C4×C31—42no—
309C22×C4×C31—42no—
310C22×C4×C31C2×D411yescharacteristic
311C22×C4×C31C2×D411yescharacteristic
312C22×C4×C31C2×D411yescharacteristic
313C22×C4×C31C2×D411yescharacteristic
314C22×C4×C31C2×D411yescharacteristic
315C22×C4×C31C2×D412yes—
316C22×C4×C31C2411yescharacteristic
317SD16×C31—42no—
318SD16×C31—42no—
319SD16×C31—42no—
320D8×C31—42no—
321D8×C31—42no—
322D8×C31—42no—
323M16×C31—21no—
324M16×C31—21no—
325M16×C31—21no—
326M16×C31—21no—
327M16×C31—21no—
328M16×C31—21no—
329M16×C31—21no—
330M16×C31—42no—
331M16×C31C2×D412yescomplemented
332C2×C8×C31—21no—
333C2×C8×C31—21no—
334C2×C8×C31—21no—
335C2×C8×C31—21no—
336C2×C8×C31—42no—
337C4⋊C4×C31—22no—
338C4⋊C4×C31—22no—
339C4⋊C4×C31—21no—
340C4⋊C4×C31—21no—
341C4⋊C4×C31—21no—
342C4⋊C4×C31—21no—
343C4⋊C4×C31—21no—
344C4⋊C4×C31—21no—
345C4⋊C4×C31—44no—
346C4⋊C4×C31C2×D411yescharacteristic
347C4⋊C4×C31C2×D411yescharacteristic
348C22⋊C4×C31—22no—
349C22⋊C4×C31—22no—
350C22⋊C4×C31—22no—
351C22⋊C4×C31—22no—
352C22⋊C4×C31—22no—
353C22⋊C4×C31—21no—
354C22⋊C4×C31—21no—
355C22⋊C4×C31—21no—
356C22⋊C4×C31—21no—
357C22⋊C4×C31—22no—
358C22⋊C4×C31—22no—
359C22⋊C4×C31—21no—
360C22⋊C4×C31—44no—
361C22⋊C4×C31—44no—
362C22⋊C4×C31—41no—
363C22⋊C4×C31—41no—
364C42×C31—22no—
365C42×C31—21no—
366C42×C31—21no—
367C42×C31—21no—
368C42×C31—21no—
369C42×C31—42no—
370C42×C31C2×D412yescomplemented
371#24464C3111yesmaximal, characteristic, direct product factor, Sylow
372C23×C31—21no—
373C23×C31—21no—
374C23×C31—21no—
375C23×C31—22no—
376C23×C31—22no—
377C23×C31—21no—
378C23×C31—21no—
379C23×C31—22no—
380C23×C31—22no—
381C23×C31—41no—
382C23×C31—42no—
383C23×C31—44no—
384C23×C31—42no—
385C23×C31—42no—
386C23×C31—42no—
387C23×C31—42no—
388C23×C31—42no—
389C23×C31—41no—
390C23×C31—41no—
391C23×C31—41no—
392C23×C31—81no—
393C23×C31—82no—
394C23×C31—82no—
395C23×C31#12011yescharacteristic
396C23×C31#12011yescharacteristic
397C23×C31C22×D411yescharacteristic
398Q8×C31—21no—
399Q8×C31—21no—
400Q8×C31—21no—
401Q8×C31—21no—
402Q8×C31—21no—
403Q8×C31—42no—
404Q8×C31#12112yescomplemented
405D4×C31—22no—
406D4×C31—22no—
407D4×C31—21no—
408D4×C31—21no—
409D4×C31—21no—
410D4×C31—21no—
411D4×C31—21no—
412D4×C31—42no—
413D4×C31—42no—
414D4×C31—44no—
415D4×C31—42no—
416D4×C31—44no—
417D4×C31—41no—
418D4×C31—41no—
419D4×C31—41no—
420D4×C31—41no—
421D4×C31—44no—
422D4×C31—42no—
423D4×C31—41no—
424D4×C31—41no—
425D4×C31—41no—
426D4×C31—41no—
427D4×C31—41no—
428D4×C31—41no—
429D4×C31—41no—
430D4×C31—41no—
431D4×C31—88no—
432D4×C31—81no—
433D4×C31—82no—
434D4×C31—82no—
435D4×C31—82no—
436D4×C31—82no—
437D4×C31—82no—
438D4×C31—82no—
439D4×C31#12112yescomplemented
440C2×C4×C31—22no—
441C2×C4×C31—22no—
442C2×C4×C31—21no—
443C2×C4×C31—22no—
444C2×C4×C31—21no—
445C2×C4×C31—21no—
446C2×C4×C31—21no—
447C2×C4×C31—21no—
448C2×C4×C31—21no—
449C2×C4×C31—21no—
450C2×C4×C31—21no—
451C2×C4×C31—21no—
452C2×C4×C31—22no—
453C2×C4×C31—21no—
454C2×C4×C31—21no—
455C2×C4×C31—22no—
456C2×C4×C31—22no—
457C2×C4×C31—21no—
458C2×C4×C31—22no—
459C2×C4×C31—21no—
460C2×C4×C31—21no—
461C2×C4×C31—21no—
462C2×C4×C31—42no—
463C2×C4×C31—42no—
464C2×C4×C31—42no—
465C2×C4×C31—48no—
466C2×C4×C31—44no—
467C2×C4×C31—41no—
468C2×C4×C31—41no—
469C2×C4×C31—41no—
470C2×C4×C31—41no—
471C2×C4×C31—41no—
472C2×C4×C31—41no—
473C2×C4×C31—42no—
474C2×C4×C31—42no—
475C2×C4×C31—41no—
476C2×C4×C31—82no—
477C2×C4×C31#12011yescharacteristic
478C2×C4×C31#12011yescharacteristic
479C2×C4×C31C22×D411yescharacteristic
480C2×C4×C31C22×D411yescharacteristic
481C2×C4×C31C22×D411yescharacteristic
482C2×C4×C31C2×#4111yescharacteristic
483C2×C4×C31H(5,𝔽2)11yescharacteristic
484C2×C4×C31H(5,𝔽2)11yescharacteristic
485C8×C31—22no—
486C8×C31—41no—
487C8×C31—41no—
488C8×C31—41no—
489#3488C2×C3111yescharacteristic, complemented
490#3055C2×C3111yescharacteristic, complemented
491C2×#453C2×C3111yescharacteristic, complemented
492#3006C2×C3111yescharacteristic, complemented
493C22×#104C2×C3111yescharacteristic, complemented
494#2856C2×C3111yescharacteristic, complemented
495#2039C2×C3111yescharacteristic, complemented
496#2037C2×C3111yescharacteristic, complemented
497#2006C2×C3111yescharacteristic, complemented
498#2002C2×C3111yescharacteristic, complemented
499#1900C2×C3111yescharacteristic, complemented
500#1896C2×C3111yescharacteristic, complemented
501#1883C2×C3111yescharacteristic, complemented
502#1859C2×C3111yescharacteristic, complemented
503#1792C2×C3111yescharacteristic, complemented
504C22×C31—21no—
505C22×C31—21no—
506C22×C31—21no—
507C22×C31—21no—
508C22×C31—21no—
509C22×C31—22no—
510C22×C31—21no—
511C22×C31—21no—
512C22×C31—42no—
513C22×C31—42no—
514C22×C31—41no—
515C22×C31—41no—
516C22×C31—41no—
517C22×C31—41no—
518C22×C31—42no—
519C22×C31—42no—
520C22×C31—41no—
521C22×C31—41no—
522C22×C31—41no—
523C22×C31—42no—
524C22×C31—41no—
525C22×C31—84no—
526C22×C31—82no—
527C22×C31—82no—
528C22×C31—82no—
529C22×C31—82no—
530C22×C31—81no—
531C22×C31—81no—
532C22×C31—81no—
533C22×C31—164no—
534C22×C31#45312yescomplemented
535C22×C31C2×#12011yescharacteristic
536C22×C31D4211yescharacteristic
537C22×C31#54611yescharacteristic
538C4×C31—24no—
539C4×C31—21no—
540C4×C31—21no—
541C4×C31—22no—
542C4×C31—42no—
543C4×C31—41no—
544C4×C31—41no—
545C4×C31—42no—
546C4×C31—41no—
547C4×C31—41no—
548C4×C31—81no—
549C4×C31C2×#12111yescharacteristic
550C4×C31#53411yescharacteristic
551C4×C31D4211yescharacteristic
552C4×C31#54611yescharacteristic
553C2×H(5,𝔽2)C22×C3111yescharacteristic
554C22×#41C22×C3111yescharacteristic
555C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
556C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
557C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
558C22×M16C22×C3111yescharacteristic, complemented
559#550—21no—
560#548—21no—
561#546—21no—
562#546—22no—
563D42—22no—
564D42—21no—
565#537—21no—
566#537C22×C3111yescharacteristic
567#535—21no—
568#535C22×C3111yescharacteristic
569C2×#127C22×C3111yescharacteristic, complemented
570#525—21no—
571#525C22×C3111yescharacteristic
572C2×#121—21no—
573C2×#121—22no—
574C2×#121C22×C3111yescharacteristic
575C2×#121C22×C3111yescharacteristic, complemented
576#520C22×C3111yescharacteristic
577C22×C42C22×C3111yescharacteristic, complemented
578#469—21no—
579#468—21no—
580#466—21no—
581#465—21no—
582#453—24no—
583#449—21no—
584#449—21no—
585#448—21no—
586#447—21no—
587#428C22×C3111yescharacteristic, complemented
588C2×#104—24no—
589C2×#104C22×C3111yescharacteristic
590C2×#104C22×C3111yescharacteristic
591C2×#104C22×C3111yescharacteristic, complemented
592C2×#104C22×C3111yescharacteristic, complemented
593C2×#104C22×C3111yescharacteristic, complemented
594C2×#104C22×C3111yescharacteristic, complemented
595#418C22×C3111yescharacteristic, complemented
596#417C22×C3111yescharacteristic
597#417C22×C3111yescharacteristic, complemented
598#417C22×C3111yescharacteristic, complemented
599C2×#100C22×C3111yescharacteristic, complemented
600C2×#100C22×C3111yescharacteristic, complemented
601#407C22×C3111yescharacteristic, complemented
602#390—22no—
603#390C22×C3111yescharacteristic, complemented
604#390C22×C3111yescharacteristic, complemented
605#384C22×C3111yescharacteristic, complemented
606#343C22×C3111yescharacteristic, complemented
607#343C22×C3111yescharacteristic, complemented
608#339C22×C3111yescharacteristic, complemented
609#339C22×C3111yescharacteristic, complemented
610C2×C31—21no—
611C2×C31—21no—
612C2×C31—22no—
613C2×C31—41no—
614C2×C31—42no—
615C2×C31—81no—
616C2×C31—82no—
617C2×C31—81no—
618C2×C31—161no—
619C2×C31#241011yescharacteristic
620C2×C31C2×#45311yescharacteristic
621C2×C31#301811yescharacteristic
622H(5,𝔽2)—22no—
623H(5,𝔽2)—22no—
624H(5,𝔽2)—41no—
625H(5,𝔽2)—41no—
626C2×#41—21no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—22no—
631C2×#41—22no—
632C2×#41—41no—
633C2×#41—41no—
634C2×#41D4×C3111yescharacteristic, complemented
635C2×#41D4×C3111yescharacteristic, complemented
636C2×#41C23×C3111yescharacteristic
637C2×#41C23×C3111yescharacteristic
638C2×#41C23×C3111yescharacteristic
639C22×Q8D4×C3111yescharacteristic, complemented
640C22×D4—21no—
641C22×D4—22no—
642C22×D4—22no—
643C22×D4—21no—
644C22×D4—21no—
645C22×D4—21no—
646C22×D4—22no—
647C22×D4D4×C3112yes—
648C22×D4D4×C3111yescharacteristic, complemented
649C22×D4C23×C3111yescharacteristic
650C22×D4C23×C3111yescharacteristic
651C23×C4—21no—
652C23×C4—21no—
653C23×C4C23×C3111yescharacteristic
654AGL(1,ℤ/8)—22no—
655AGL(1,ℤ/8)—22no—
656AGL(1,ℤ/8)—22no—
657AGL(1,ℤ/8)—41no—
658AGL(1,ℤ/8)—41no—
659AGL(1,ℤ/8)—41no—
660C2×SD16—21no—
661C2×SD16—21no—
662C2×SD16—21no—
663C2×D8—21no—
664C2×D8—21no—
665C2×D8—21no—
666C2×M16—21no—
667C2×M16—22no—
668C2×M16—41no—
669C2×M16C23×C3111yescharacteristic
670C2×M16C23×C3111yescharacteristic
671C2×M16C23×C3111yescharacteristic
672C2×M16C23×C3111yescharacteristic
673C22×C8—21no—
674#127—22no—
675#127—21no—
676#127—22no—
677#127—41no—
678#124—22no—
679#124—21no—
680#123—22no—
681#123—21no—
682C22⋊Q8—22no—
683C22⋊Q8—21no—
684C22⋊Q8—21no—
685C22⋊Q8D4×C3111yescharacteristic, complemented
686C22⋊Q8D4×C3111yescharacteristic, complemented
687#121—22no—
688#121—22no—
689#121—22no—
690#121—22no—
691#121—22no—
692#121—21no—
693#121—21no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—22no—
699#121—21no—
700#121—21no—
701#121—21no—
702#121—21no—
703#121—21no—
704#121—21no—
705#121—48no—
706#121D4×C3111yescharacteristic, complemented
707#121D4×C3111yescharacteristic, complemented
708#120—22no—
709#120—22no—
710#120—22no—
711#120—21no—
712#120—22no—
713C4×Q8—21no—
714C4×D4—22no—
715C4×D4—22no—
716C4×D4—21no—
717C4×D4—22no—
718C4×D4—21no—
719C4×D4—21no—
720#117—21no—
721#117C23×C3111yescharacteristic
722C2×C4⋊C4—21no—
723C2×C4⋊C4—22no—
724C2×C4⋊C4C23×C3111yescharacteristic
725C2×C4⋊C4C23×C3111yescharacteristic
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4D4×C3112yes—
731C2×C42—22no—
732C2×C42—21no—
733C2×C42—41no—
734C2×C42C23×C3111yescharacteristic
735C2×C42C23×C3111yescharacteristic
736#107—21no—
737#106—21no—
738#104—22no—
739#104—22no—
740#104—22no—
741#104—22no—
742#104—41no—
743#104D4×C3114yescomplemented
744#103—21no—
745#103—21no—
746#103—21no—
747#102—21no—
748#102—21no—
749#102—21no—
750#102—21no—
751#102—21no—
752#100—22no—
753#100—41no—
754C22⋊C8—21no—
755C22⋊C8—21no—
756C31#2446411yescharacteristic, direct product factor, Sylow
757C24—22no—
758C24—21no—
759C24—21no—
760C24C2×D4×C3111yescharacteristic
761C24C2×D4×C3112yes—
762#41—21no—
763#41—21no—
764#41—22no—
765#41—22no—
766#41—21no—
767#41—21no—
768#41—21no—
769#41—21no—
770#41—21no—
771#41—21no—
772#41—21no—
773#41—21no—
774#41—42no—
775#41—42no—
776#41—41no—
777#41—41no—
778#41—42no—
779#41—42no—
780#41—42no—
781#41—42no—
782#41—42no—
783#41—42no—
784#41C2×D4×C3112yes—
785#41#41×C3112yes—
786C2×Q8—21no—
787C2×Q8—22no—
788C2×Q8—41no—
789C2×Q8C2×D4×C3111yescharacteristic
790C2×Q8C2×D4×C3111yescharacteristic
791C2×Q8C2×D4×C3111yescharacteristic
792C2×D4—21no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—21no—
806C2×D4—22no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—41no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—41no—
835C2×D4—41no—
836C2×D4—84no—
837C2×D4C2×D4×C3111yescharacteristic
838C2×D4C2×D4×C3111yescharacteristic
839C2×D4C2×D4×C3111yescharacteristic
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—24no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4C2×D4×C3111yescharacteristic
861C22×C4C2×D4×C3111yescharacteristic
862C22×C4C2×D4×C3111yescharacteristic
863C22×C4C2×D4×C3111yescharacteristic
864C22×C4C2×D4×C3111yescharacteristic
865C22×C4C2×D4×C3112yes—
866C22×C4C24×C3111yescharacteristic
867SD16—42no—
868SD16—42no—
869SD16—42no—
870D8—42no—
871D8—42no—
872D8—42no—
873M16—21no—
874M16—21no—
875M16—21no—
876M16—21no—
877M16—21no—
878M16—21no—
879M16—21no—
880M16—42no—
881M16C2×D4×C3112yescomplemented
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—42no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—44no—
896C4⋊C4C2×D4×C3111yescharacteristic
897C4⋊C4C2×D4×C3111yescharacteristic
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—22no—
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—21no—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—21no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—41no—
913C22⋊C4—41no—
914C42—22no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—42no—
920C42C2×D4×C3112yescomplemented
921C23—22no—
922C23—21no—
923C23—21no—
924C23—21no—
925C23—22no—
926C23—21no—
927C23—21no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—42no—
932C23—44no—
933C23—42no—
934C23—42no—
935C23—42no—
936C23—42no—
937C23—42no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—81no—
942C23—82no—
943C23—82no—
944C23C31×#12011yescharacteristic
945C23C31×#12011yescharacteristic
946C23C22×D4×C3111yescharacteristic
947Q8—21no—
948Q8—21no—
949Q8—21no—
950Q8—21no—
951Q8—21no—
952Q8—42no—
953Q8C31×#12112yescomplemented
954D4—22no—
955D4—22no—
956D4—21no—
957D4—21no—
958D4—21no—
959D4—21no—
960D4—21no—
961D4—42no—
962D4—42no—
963D4—44no—
964D4—42no—
965D4—44no—
966D4—44no—
967D4—42no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—41no—
972D4—41no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—41no—
977D4—41no—
978D4—41no—
979D4—41no—
980D4—88no—
981D4—81no—
982D4—82no—
983D4—82no—
984D4—82no—
985D4—82no—
986D4—82no—
987D4—82no—
988D4C31×#12112yescomplemented
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—48no—
1015C2×C4—44no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—41no—
1025C2×C4—82no—
1026C2×C4C31×#12011yescharacteristic
1027C2×C4C31×#12011yescharacteristic
1028C2×C4C22×D4×C3111yescharacteristic
1029C2×C4C22×D4×C3111yescharacteristic
1030C2×C4C22×D4×C3111yescharacteristic
1031C2×C4C2×#41×C3111yescharacteristic
1032C2×C4C31×H(5,𝔽2)11yescharacteristic
1033C2×C4C31×H(5,𝔽2)11yescharacteristic
1034C8—22no—
1035C8—41no—
1036C8—41no—
1037C8—41no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—22no—
1044C22—21no—
1045C22—21no—
1046C22—42no—
1047C22—42no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—42no—
1053C22—42no—
1054C22—41no—
1055C22—41no—
1056C22—41no—
1057C22—42no—
1058C22—41no—
1059C22—84no—
1060C22—82no—
1061C22—82no—
1062C22—82no—
1063C22—82no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—164no—
1068C22C31×#45312yescomplemented
1069C22C2×C31×#12011yescharacteristic
1070C22D42×C3111yescharacteristic
1071C22C31×#54611yescharacteristic
1072C4—24no—
1073C4—21no—
1074C4—21no—
1075C4—22no—
1076C4—42no—
1077C4—41no—
1078C4—41no—
1079C4—42no—
1080C4—41no—
1081C4—41no—
1082C4—81no—
1083C4C2×C31×#12111yescharacteristic
1084C4C31×#53411yescharacteristic
1085C4D42×C3111yescharacteristic
1086C4C31×#54611yescharacteristic
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—82no—
1094C2—81no—
1095C2—161no—
1096C2C31×#241011yescharacteristic
1097C2C2×C31×#45311yescharacteristic
1098C2C31×#301811yescharacteristic
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. C22×C31×#104C2semidirect
6. C31×#2856C2semidirect
7. C31×#2039C2semidirect
8. C31×#2037C2semidirect
9. C31×#2006C2semidirect
10. C31×#2002C2semidirect
11. C31×#1900C2semidirect
12. C31×#1896C2semidirect
13. C31×#1883C2semidirect
14. C31×#1859C2semidirect
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
38. C2×C31×#121C22semidirect
40. C22×C42×C31C22semidirect
50. C31×#428C22semidirect
54. C2×C31×#104C22semidirect
55. C2×C31×#104C22semidirect
56. C2×C31×#104C22semidirect
57. C2×C31×#104C22semidirect
58. C31×#418C22semidirect
60. C31×#417C22semidirect
61. C31×#417C22semidirect
62. C2×C31×#100C22semidirect
63. C2×C31×#100C22semidirect
64. C31×#407C22semidirect
66. C31×#390C22semidirect
67. C31×#390C22semidirect
68. C31×#384C22semidirect
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
136. C31×C22⋊Q8D4semidirect
137. C31×C22⋊Q8D4semidirect
157. C31×#121D4semidirect
158. C31×#121D4semidirect
194. C31×#104D4semidirect
331. M16×C31C2×D4semidirect
370. C42×C31C2×D4semidirect
371. #24464C31direct (N × H)
404. Q8×C31#121semidirect
439. D4×C31#121semidirect
489. #3488C2×C31semidirect
490. #3055C2×C31semidirect
491. C2×#453C2×C31semidirect
492. #3006C2×C31semidirect
493. C22×#104C2×C31semidirect
494. #2856C2×C31semidirect
495. #2039C2×C31semidirect
496. #2037C2×C31semidirect
497. #2006C2×C31semidirect
498. #2002C2×C31semidirect
499. #1900C2×C31semidirect
500. #1896C2×C31semidirect
501. #1883C2×C31semidirect
502. #1859C2×C31semidirect
503. #1792C2×C31semidirect
534. C22×C31#453semidirect
556. C2×AGL(1,ℤ/8)C22×C31semidirect
557. C2×AGL(1,ℤ/8)C22×C31semidirect
558. C22×M16C22×C31semidirect
569. C2×#127C22×C31semidirect
575. C2×#121C22×C31semidirect
577. C22×C42C22×C31semidirect
587. #428C22×C31semidirect
591. C2×#104C22×C31semidirect
592. C2×#104C22×C31semidirect
593. C2×#104C22×C31semidirect
594. C2×#104C22×C31semidirect
595. #418C22×C31semidirect
597. #417C22×C31semidirect
598. #417C22×C31semidirect
599. C2×#100C22×C31semidirect
600. C2×#100C22×C31semidirect
601. #407C22×C31semidirect
603. #390C22×C31semidirect
604. #390C22×C31semidirect
605. #384C22×C31semidirect
606. #343C22×C31semidirect
607. #343C22×C31semidirect
608. #339C22×C31semidirect
609. #339C22×C31semidirect
634. C2×#41D4×C31semidirect
635. C2×#41D4×C31semidirect
639. C22×Q8D4×C31semidirect
648. C22×D4D4×C31semidirect
685. C22⋊Q8D4×C31semidirect
686. C22⋊Q8D4×C31semidirect
706. #121D4×C31semidirect
707. #121D4×C31semidirect
743. #104D4×C31semidirect
756. C31#24464direct (N × H)
881. M16C2×D4×C31semidirect
920. C42C2×D4×C31semidirect
953. Q8C31×#121semidirect
988. D4C31×#121semidirect
1068. C22C31×#453semidirect

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
C22×C31×#1042
C31×#28562
C31×#20392
C31×#20372
C31×#20062
C31×#20022
C31×#19002
C31×#18962
C31×#18832
C31×#18592
C31×#17922
#2446431