Finite Group Databasebeta

← C31×#24174 #21480933

Subgroups — C31×#24174 #21480933

Order 7936.

1078 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3512C211yesmaximal, characteristic, complemented
2C31×#3036C211yesmaximal, characteristic, complemented
3C4×C31×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4C31×#2566C211yesmaximal, characteristic, complemented
5C31×#2040C211yesmaximal, characteristic, complemented
6C31×#2039C211yesmaximal, characteristic, complemented
7C31×#2006C211yesmaximal, characteristic, complemented
8C31×#2006C211yesmaximal, characteristic, complemented
9C31×#1998C211yesmaximal, characteristic, complemented
10C31×#1980C211yesmaximal, characteristic, complemented
11C31×#1883C211yesmaximal, characteristic, complemented
12C31×#1883C211yesmaximal, characteristic, complemented
13C31×#1860C211yesmaximal, characteristic, complemented
14C31×#1859C211yesmaximal, characteristic, complemented
15C31×#1806C211yesmaximal, characteristic, complemented
16C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
17C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
18C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
19C31×#553—21no—
20C31×#553—21no—
21C31×#553—22no—
22C31×#553—22no—
23C31×#552—21no—
24C31×#552—21no—
25C31×#541—21no—
26C31×#540—21no—
27C31×#537C2211yescharacteristic
28C31×#537C2211yescharacteristic
29C31×#532C2211yescharacteristic
30C31×#529—21no—
31C31×#529—21no—
32C2×C31×#125C2211yescharacteristic
33C31×#520C2211yescharacteristic
34C31×#520C2211yescharacteristic
35C4×#41×C31C2211yescharacteristic
36C2×C4×D4×C31C2211yescharacteristic
37C31×#463—21no—
38C31×#463—21no—
39C31×#461—21no—
40C31×#459—21no—
41C31×#442—21no—
42C31×#440—21no—
43C4×SD16×C31—21no—
44C4×D8×C31—21no—
45C31×#428C2211yescharacteristic
46C31×#423C2211yescharacteristic
47C2×C31×#104C2211yescharacteristic
48C2×C31×#104C2211yescharacteristic
49C2×C31×#104C2211yescharacteristic
50C2×C31×#104C2211yescharacteristic
51C2×C31×#104C2211yescharacteristic
52C2×C31×#104C2211yescharacteristic
53C31×#418C2211yescharacteristic
54C31×#417C2211yescharacteristic
55C31×#417C2211yescharacteristic
56C31×#417C2211yescharacteristic
57C4×M16×C31C2211yescharacteristic
58C31×#396—22no—
59C31×#390C2211yescharacteristic
60C31×#390C2211yescharacteristic
61C31×#385—22no—
62C31×#384C2211yescharacteristic
63C31×#382C2211yescharacteristic
64C4×C4⋊C4×C31C2211yescharacteristic
65C31×#343C2211yescharacteristic
66C31×#343C2211yescharacteristic
67C31×#343C2211yescharacteristic
68C31×#343C2211yescharacteristic
69C31×#339C2211yescharacteristic
70C31×#339C2211yescharacteristic
71C2×#41×C31C2311yescharacteristic
72C2×#41×C31C2311yescharacteristic
73C2×#41×C31C2311yescharacteristic
74C22×D4×C31C2311yescharacteristic
75C23×C4×C31—21no—
76C31×AGL(1,ℤ/8)—22no—
77C31×AGL(1,ℤ/8)—22no—
78C31×AGL(1,ℤ/8)—22no—
79C31×AGL(1,ℤ/8)—22no—
80C31×AGL(1,ℤ/8)—41no—
81C31×AGL(1,ℤ/8)—41no—
82C2×SD16×C31—21no—
83C2×SD16×C31—21no—
84C2×SD16×C31—21no—
85C2×D8×C31—21no—
86C2×D8×C31—21no—
87C2×D8×C31—21no—
88C2×M16×C31C2311yescharacteristic
89C2×M16×C31C2311yescharacteristic
90C2×M16×C31C2311yescharacteristic
91C2×M16×C31C2311yescharacteristic
92C31×C4⋊Q8D411yescharacteristic
93C31×#127D411yescharacteristic
94C31×#126—22no—
95C31×#126—22no—
96C31×#126—22no—
97C31×#126—22no—
98C31×#125—22no—
99C31×#125—22no—
100C31×#125—21no—
101C31×#125—21no—
102C31×#125—21no—
103C31×#125—21no—
104C31×#124D411yescharacteristic
105C31×#124D411yescharacteristic
106C31×#123—22no—
107C31×#123—22no—
108C31×#123—22no—
109C31×#123—22no—
110C31×C22⋊Q8—21no—
111C31×C22⋊Q8—21no—
112C31×C22⋊Q8—21no—
113C31×C22⋊Q8—21no—
114C31×#121—22no—
115C31×#121—22no—
116C31×#121—21no—
117C31×#121—21no—
118C31×#121—21no—
119C31×#121—21no—
120C31×#121—21no—
121C31×#121—21no—
122C31×#121—22no—
123C31×#121—22no—
124C4×Q8×C31—21no—
125C4×Q8×C31—21no—
126C4×Q8×C31D411yescharacteristic
127C4×Q8×C31D411yescharacteristic
128C4×D4×C31—22no—
129C4×D4×C31—22no—
130C4×D4×C31—21no—
131C4×D4×C31—21no—
132C4×D4×C31—21no—
133C4×D4×C31—21no—
134C4×D4×C31—22no—
135C4×D4×C31—22no—
136C4×D4×C31—21no—
137C4×D4×C31—21no—
138C4×D4×C31—21no—
139C4×D4×C31—21no—
140C4×D4×C31—21no—
141C4×D4×C31—21no—
142C4×D4×C31D411yescharacteristic
143C4×D4×C31D411yescharacteristic
144C31×#117—22no—
145C31×#117—22no—
146C31×#117—21no—
147C31×#117—21no—
148C31×#117—21no—
149C31×#117C2311yescharacteristic
150C2×C4⋊C4×C31—21no—
151C2×C4⋊C4×C31—21no—
152C2×C4⋊C4×C31—21no—
153C2×C4⋊C4×C31—22no—
154C2×C4⋊C4×C31D412yes—
155C2×C4⋊C4×C31D412yes—
156C2×C4⋊C4×C31C2311yescharacteristic
157C2×C4⋊C4×C31C2311yescharacteristic
158C2×C4⋊C4×C31C2311yescharacteristic
159C2×C22⋊C4×C31—21no—
160C2×C22⋊C4×C31—22no—
161C2×C22⋊C4×C31—22no—
162C2×C42×C31—21no—
163C2×C42×C31C2311yescharacteristic
164C2×C42×C31C2311yescharacteristic
165C2×C42×C31C2311yescharacteristic
166C31×#107—21no—
167C31×#106—21no—
168C31×C4⋊C8—21no—
169C31×C4⋊C8—21no—
170C31×#104—22no—
171C31×#104—22no—
172C31×#104—41no—
173C31×#104—41no—
174C31×#104—41no—
175C31×#104—41no—
176C31×#103—21no—
177C31×#103—21no—
178C31×#103—21no—
179C31×#102—21no—
180C31×#102—21no—
181C31×#102—21no—
182C31×#102—21no—
183C31×#102—21no—
184C31×#97—21no—
185C4×C8×C31—21no—
186C31×#95—22no—
187C31×#95—21no—
188C24×C31—21no—
189#41×C31—21no—
190#41×C31—21no—
191#41×C31—21no—
192#41×C31—21no—
193#41×C31—21no—
194#41×C31—21no—
195#41×C31—21no—
196#41×C31—21no—
197#41×C31—21no—
198#41×C31—21no—
199#41×C31—21no—
200#41×C31—21no—
201C2×Q8×C31C2×D411yescharacteristic
202C2×Q8×C31C2×D411yescharacteristic
203C2×Q8×C31C2×D411yescharacteristic
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—21no—
207C2×D4×C31—22no—
208C2×D4×C31—22no—
209C2×D4×C31—21no—
210C2×D4×C31—21no—
211C2×D4×C31—21no—
212C2×D4×C31—21no—
213C2×D4×C31—21no—
214C2×D4×C31—21no—
215C2×D4×C31—21no—
216C2×D4×C31C2×D411yescharacteristic
217C2×D4×C31C2×D411yescharacteristic
218C2×D4×C31C2×D411yescharacteristic
219C2×D4×C31#4112yes—
220C22×C4×C31—21no—
221C22×C4×C31—22no—
222C22×C4×C31—22no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—41no—
231C22×C4×C31—41no—
232C22×C4×C31—82no—
233C22×C4×C31C2×D412yes—
234C22×C4×C31C2×D412yes—
235C22×C4×C31C2×D411yescharacteristic
236C22×C4×C31C2×D411yescharacteristic
237C22×C4×C31C2411yescharacteristic
238SD16×C31—24no—
239SD16×C31—42no—
240SD16×C31—42no—
241D8×C31—24no—
242D8×C31—42no—
243D8×C31—42no—
244M16×C31—21no—
245M16×C31—21no—
246M16×C31—21no—
247M16×C31—21no—
248M16×C31—21no—
249M16×C31—21no—
250M16×C31—21no—
251M16×C31#4112yes—
252C2×C8×C31—21no—
253C2×C8×C31—21no—
254C2×C8×C31—21no—
255C2×C8×C31—21no—
256C4⋊C4×C31—22no—
257C4⋊C4×C31—22no—
258C4⋊C4×C31—22no—
259C4⋊C4×C31—22no—
260C4⋊C4×C31—22no—
261C4⋊C4×C31—22no—
262C4⋊C4×C31—22no—
263C4⋊C4×C31—22no—
264C4⋊C4×C31—21no—
265C4⋊C4×C31—21no—
266C4⋊C4×C31—21no—
267C4⋊C4×C31—21no—
268C4⋊C4×C31—21no—
269C4⋊C4×C31—21no—
270C4⋊C4×C31—21no—
271C4⋊C4×C31—21no—
272C4⋊C4×C31—21no—
273C4⋊C4×C31—21no—
274C4⋊C4×C31—42no—
275C4⋊C4×C31—82no—
276C4⋊C4×C31C2×D411yescharacteristic
277C4⋊C4×C31C2×D411yescharacteristic
278C22⋊C4×C31—22no—
279C22⋊C4×C31—22no—
280C22⋊C4×C31—22no—
281C22⋊C4×C31—22no—
282C22⋊C4×C31—22no—
283C22⋊C4×C31—22no—
284C22⋊C4×C31—21no—
285C22⋊C4×C31—21no—
286C22⋊C4×C31—21no—
287C22⋊C4×C31—21no—
288C22⋊C4×C31—21no—
289C22⋊C4×C31—21no—
290C22⋊C4×C31—21no—
291C22⋊C4×C31—44no—
292C22⋊C4×C31—41no—
293C22⋊C4×C31—41no—
294C22⋊C4×C31—82no—
295C42×C31—22no—
296C42×C31—22no—
297C42×C31—21no—
298C42×C31—21no—
299C42×C31—21no—
300C42×C31—21no—
301C42×C31—21no—
302C42×C31—21no—
303C42×C31—21no—
304C42×C31C2×D411yescharacteristic
305C42×C31C2×D411yescharacteristic
306C42×C31C2×D411yescharacteristic
307C42×C31C2×D411yescharacteristic
308#24174C3111yesmaximal, characteristic, direct product factor, Sylow
309C23×C31—21no—
310C23×C31—21no—
311C23×C31—21no—
312C23×C31—22no—
313C23×C31—42no—
314C23×C31—42no—
315C23×C31—41no—
316C23×C31—41no—
317C23×C31C22×D411yescharacteristic
318Q8×C31—21no—
319Q8×C31—21no—
320Q8×C31—21no—
321Q8×C31—21no—
322Q8×C31—21no—
323Q8×C31—21no—
324D4×C31—21no—
325D4×C31—22no—
326D4×C31—21no—
327D4×C31—22no—
328D4×C31—21no—
329D4×C31—21no—
330D4×C31—21no—
331D4×C31—21no—
332D4×C31—41no—
333D4×C31—41no—
334D4×C31—41no—
335D4×C31—41no—
336D4×C31—41no—
337D4×C31—41no—
338D4×C31—41no—
339D4×C31—41no—
340D4×C31—81no—
341D4×C31—81no—
342D4×C31—82no—
343D4×C31—82no—
344C2×C4×C31—22no—
345C2×C4×C31—21no—
346C2×C4×C31—21no—
347C2×C4×C31—21no—
348C2×C4×C31—21no—
349C2×C4×C31—21no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—41no—
357C2×C4×C31—41no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—41no—
362C2×C4×C31—42no—
363C2×C4×C31—42no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—42no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—81no—
370C2×C4×C31—81no—
371C2×C4×C31—82no—
372C2×C4×C31—82no—
373C2×C4×C31—82no—
374C2×C4×C31—82no—
375C2×C4×C31#12011yescharacteristic
376C2×C4×C31#12011yescharacteristic
377C2×C4×C31#12011yescharacteristic
378C2×C4×C31#12011yescharacteristic
379C2×C4×C31C22×D411yescharacteristic
380C2×C4×C31C22×D411yescharacteristic
381C2×C4×C31C2×#4111yescharacteristic
382C2×C4×C31C2×#4111yescharacteristic
383C2×C4×C31H(5,𝔽2)11yescharacteristic
384C2×C4×C312−1+411yescharacteristic
385C8×C31—22no—
386C8×C31—41no—
387C8×C31—41no—
388C8×C31—41no—
389#3512C2×C3111yescharacteristic, complemented
390#3036C2×C3111yescharacteristic, complemented
391C4×AGL(1,ℤ/8)C2×C3111yescharacteristic, complemented
392#2566C2×C3111yescharacteristic, complemented
393#2040C2×C3111yescharacteristic, complemented
394#2039C2×C3111yescharacteristic, complemented
395#2006C2×C3111yescharacteristic, complemented
396#2006C2×C3111yescharacteristic, complemented
397#1998C2×C3111yescharacteristic, complemented
398#1980C2×C3111yescharacteristic, complemented
399#1883C2×C3111yescharacteristic, complemented
400#1883C2×C3111yescharacteristic, complemented
401#1860C2×C3111yescharacteristic, complemented
402#1859C2×C3111yescharacteristic, complemented
403#1806C2×C3111yescharacteristic, complemented
404C22×C31—21no—
405C22×C31—21no—
406C22×C31—44no—
407C22×C31—41no—
408C22×C31—41no—
409C22×C31—41no—
410C22×C31—42no—
411C22×C31—41no—
412C22×C31—41no—
413C22×C31—41no—
414C22×C31—41no—
415C22×C31—41no—
416C22×C31—41no—
417C22×C31—82no—
418C22×C31—81no—
419C22×C31—81no—
420C22×C31C2×#12011yescharacteristic
421C22×C31#54811yescharacteristic
422C22×C31#55011yescharacteristic
423C4×C31—21no—
424C4×C31—21no—
425C4×C31—21no—
426C4×C31—21no—
427C4×C31—42no—
428C4×C31—41no—
429C4×C31—41no—
430C4×C31—41no—
431C4×C31—42no—
432C4×C31—41no—
433C4×C31—42no—
434C4×C31—41no—
435C4×C31—81no—
436C4×C31—81no—
437C4×C31#52511yescharacteristic
438C4×C31#53711yescharacteristic
439C4×C31#54611yescharacteristic
440C4×C31#54711yescharacteristic
441C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
442C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
443C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
444#553—21no—
445#553—21no—
446#553—22no—
447#553—22no—
448#552—21no—
449#552—21no—
450#541—21no—
451#540—21no—
452#537C22×C3111yescharacteristic
453#537C22×C3111yescharacteristic
454#532C22×C3111yescharacteristic
455#529—21no—
456#529—21no—
457C2×#125C22×C3111yescharacteristic
458#520C22×C3111yescharacteristic
459#520C22×C3111yescharacteristic
460C4×#41C22×C3111yescharacteristic
461C2×C4×D4C22×C3111yescharacteristic
462#463—21no—
463#463—21no—
464#461—21no—
465#459—21no—
466#442—21no—
467#440—21no—
468C4×SD16—21no—
469C4×D8—21no—
470#428C22×C3111yescharacteristic
471#423C22×C3111yescharacteristic
472C2×#104C22×C3111yescharacteristic
473C2×#104C22×C3111yescharacteristic
474C2×#104C22×C3111yescharacteristic
475C2×#104C22×C3111yescharacteristic
476C2×#104C22×C3111yescharacteristic
477C2×#104C22×C3111yescharacteristic
478#418C22×C3111yescharacteristic
479#417C22×C3111yescharacteristic
480#417C22×C3111yescharacteristic
481#417C22×C3111yescharacteristic
482C4×M16C22×C3111yescharacteristic
483#396—22no—
484#390C22×C3111yescharacteristic
485#390C22×C3111yescharacteristic
486#385—22no—
487#384C22×C3111yescharacteristic
488#382C22×C3111yescharacteristic
489C4×C4⋊C4C22×C3111yescharacteristic
490#343C22×C3111yescharacteristic
491#343C22×C3111yescharacteristic
492#343C22×C3111yescharacteristic
493#343C22×C3111yescharacteristic
494#339C22×C3111yescharacteristic
495#339C22×C3111yescharacteristic
496C2×C31—21no—
497C2×C31—21no—
498C2×C31—81no—
499C2×C31—81no—
500C2×C31—81no—
501C2×C31—82no—
502C2×C31#240711yescharacteristic
503C2×C31#301811yescharacteristic
504C2×C31#302111yescharacteristic
505C2×#41C23×C3111yescharacteristic
506C2×#41C23×C3111yescharacteristic
507C2×#41C23×C3111yescharacteristic
508C22×D4C23×C3111yescharacteristic
509C23×C4—21no—
510AGL(1,ℤ/8)—22no—
511AGL(1,ℤ/8)—22no—
512AGL(1,ℤ/8)—22no—
513AGL(1,ℤ/8)—22no—
514AGL(1,ℤ/8)—41no—
515AGL(1,ℤ/8)—41no—
516C2×SD16—21no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×D8—21no—
520C2×D8—21no—
521C2×D8—21no—
522C2×M16C23×C3111yescharacteristic
523C2×M16C23×C3111yescharacteristic
524C2×M16C23×C3111yescharacteristic
525C2×M16C23×C3111yescharacteristic
526C4⋊Q8D4×C3111yescharacteristic
527#127D4×C3111yescharacteristic
528#126—22no—
529#126—22no—
530#126—22no—
531#126—22no—
532#125—22no—
533#125—22no—
534#125—21no—
535#125—21no—
536#125—21no—
537#125—21no—
538#124D4×C3111yescharacteristic
539#124D4×C3111yescharacteristic
540#123—22no—
541#123—22no—
542#123—22no—
543#123—22no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548#121—22no—
549#121—22no—
550#121—21no—
551#121—21no—
552#121—21no—
553#121—21no—
554#121—21no—
555#121—21no—
556#121—22no—
557#121—22no—
558C4×Q8—21no—
559C4×Q8—21no—
560C4×Q8D4×C3111yescharacteristic
561C4×Q8D4×C3111yescharacteristic
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—21no—
565C4×D4—21no—
566C4×D4—21no—
567C4×D4—21no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—21no—
571C4×D4—21no—
572C4×D4—21no—
573C4×D4—21no—
574C4×D4—21no—
575C4×D4—21no—
576C4×D4D4×C3111yescharacteristic
577C4×D4D4×C3111yescharacteristic
578#117—22no—
579#117—22no—
580#117—21no—
581#117—21no—
582#117—21no—
583#117C23×C3111yescharacteristic
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4D4×C3112yes—
589C2×C4⋊C4D4×C3112yes—
590C2×C4⋊C4C23×C3111yescharacteristic
591C2×C4⋊C4C23×C3111yescharacteristic
592C2×C4⋊C4C23×C3111yescharacteristic
593C2×C22⋊C4—21no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C42—21no—
597C2×C42C23×C3111yescharacteristic
598C2×C42C23×C3111yescharacteristic
599C2×C42C23×C3111yescharacteristic
600#107—21no—
601#106—21no—
602C4⋊C8—21no—
603C4⋊C8—21no—
604#104—22no—
605#104—22no—
606#104—41no—
607#104—41no—
608#104—41no—
609#104—41no—
610#103—21no—
611#103—21no—
612#103—21no—
613#102—21no—
614#102—21no—
615#102—21no—
616#102—21no—
617#102—21no—
618#97—21no—
619C4×C8—21no—
620#95—21no—
621#95—22no—
622C31#2417411yescharacteristic, direct product factor, Sylow
623C24—21no—
624#41—21no—
625#41—21no—
626#41—21no—
627#41—21no—
628#41—21no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—21no—
634#41—21no—
635#41—21no—
636C2×Q8C2×D4×C3111yescharacteristic
637C2×Q8C2×D4×C3111yescharacteristic
638C2×Q8C2×D4×C3111yescharacteristic
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4C2×D4×C3111yescharacteristic
652C2×D4C2×D4×C3111yescharacteristic
653C2×D4C2×D4×C3111yescharacteristic
654C2×D4#41×C3112yes—
655C22×C4—21no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—82no—
668C22×C4C2×D4×C3112yes—
669C22×C4C2×D4×C3112yes—
670C22×C4C2×D4×C3111yescharacteristic
671C22×C4C2×D4×C3111yescharacteristic
672C22×C4C24×C3111yescharacteristic
673SD16—24no—
674SD16—42no—
675SD16—42no—
676D8—24no—
677D8—42no—
678D8—42no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16#41×C3112yes—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—42no—
710C4⋊C4—82no—
711C4⋊C4C2×D4×C3111yescharacteristic
712C4⋊C4C2×D4×C3111yescharacteristic
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—44no—
727C22⋊C4—41no—
728C22⋊C4—41no—
729C22⋊C4—82no—
730C42—22no—
731C42—22no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—21no—
739C42C2×D4×C3111yescharacteristic
740C42C2×D4×C3111yescharacteristic
741C42C2×D4×C3111yescharacteristic
742C42C2×D4×C3111yescharacteristic
743C23—21no—
744C23—21no—
745C23—21no—
746C23—22no—
747C23—42no—
748C23—42no—
749C23—41no—
750C23—41no—
751C23C22×D4×C3111yescharacteristic
752Q8—21no—
753Q8—21no—
754Q8—21no—
755Q8—21no—
756Q8—21no—
757Q8—21no—
758D4—21no—
759D4—22no—
760D4—21no—
761D4—22no—
762D4—21no—
763D4—21no—
764D4—21no—
765D4—21no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—81no—
775D4—81no—
776D4—82no—
777D4—82no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—82no—
806C2×C4—82no—
807C2×C4—82no—
808C2×C4—82no—
809C2×C4C31×#12011yescharacteristic
810C2×C4C31×#12011yescharacteristic
811C2×C4C31×#12011yescharacteristic
812C2×C4C31×#12011yescharacteristic
813C2×C4C22×D4×C3111yescharacteristic
814C2×C4C22×D4×C3111yescharacteristic
815C2×C4C2×#41×C3111yescharacteristic
816C2×C4C2×#41×C3111yescharacteristic
817C2×C4C31×H(5,𝔽2)11yescharacteristic
818C2×C4C31×2−1+411yescharacteristic
819C8—22no—
820C8—41no—
821C8—41no—
822C8—41no—
823C22—21no—
824C22—21no—
825C22—44no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—82no—
837C22—81no—
838C22—81no—
839C22C2×C31×#12011yescharacteristic
840C22C31×#54811yescharacteristic
841C22C31×#55011yescharacteristic
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—42no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—42no—
853C4—41no—
854C4—81no—
855C4—81no—
856C4C31×#52511yescharacteristic
857C4C31×#53711yescharacteristic
858C4C31×#54611yescharacteristic
859C4C31×#54711yescharacteristic
860C2—21no—
861C2—21no—
862C2—82no—
863C2—81no—
864C2—81no—
865C2—81no—
866C2C31×#240711yescharacteristic
867C2C31×#301811yescharacteristic
868C2C31×#302111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3512C2semidirect
2. C31×#3036C2semidirect
3. C4×C31×AGL(1,ℤ/8)C2semidirect
4. C31×#2566C2semidirect
5. C31×#2040C2semidirect
6. C31×#2039C2semidirect
7. C31×#2006C2semidirect
8. C31×#2006C2semidirect
9. C31×#1998C2semidirect
10. C31×#1980C2semidirect
11. C31×#1883C2semidirect
12. C31×#1883C2semidirect
13. C31×#1860C2semidirect
14. C31×#1859C2semidirect
15. C31×#1806C2semidirect
308. #24174C31direct (N × H)
389. #3512C2×C31semidirect
390. #3036C2×C31semidirect
391. C4×AGL(1,ℤ/8)C2×C31semidirect
392. #2566C2×C31semidirect
393. #2040C2×C31semidirect
394. #2039C2×C31semidirect
395. #2006C2×C31semidirect
396. #2006C2×C31semidirect
397. #1998C2×C31semidirect
398. #1980C2×C31semidirect
399. #1883C2×C31semidirect
400. #1883C2×C31semidirect
401. #1860C2×C31semidirect
402. #1859C2×C31semidirect
403. #1806C2×C31semidirect
622. C31#24174direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35122
C31×#30362
C4×C31×AGL(1,ℤ/8)2
C31×#25662
C31×#20402
C31×#20392
C31×#20062
C31×#19982
C31×#19802
C31×#18832
C31×#18602
C31×#18592
C31×#18062
#2417431