Finite Group Databasebeta

← C31×#23889 #21480648

Subgroups — C31×#23889 #21480648

Order 7936.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#578C211yesmaximal, characteristic, complemented
2C2×C31×#577C211yesmaximal, characteristic, complemented
3C2×C31×#454C211yesmaximal, characteristic, complemented
4C2×C31×#455C211yesmaximal, characteristic, complemented
5C31×#3013C211yesmaximal, characteristic, complemented
6C31×#3012C211yesmaximal, characteristic, complemented
7C31×#2020C211yesmaximal, characteristic, complemented
8C31×#2019C211yesmaximal, characteristic, complemented
9C31×#2015C211yesmaximal, characteristic, complemented
10C31×#2007C211yesmaximal, characteristic, complemented
11C31×#1908C211yesmaximal, characteristic, complemented
12C31×#1907C211yesmaximal, characteristic, complemented
13C31×#1876C211yesmaximal, characteristic, complemented
14C31×#1876C211yesmaximal, characteristic, complemented
15C31×#1793C211yesmaximal, characteristic, complemented
16C2×C31×2−1+4C2211yescharacteristic
17C2×C31×2−1+4C2211yescharacteristic, complemented
18C2×C31×H(5,𝔽2)C2211yescharacteristic
19C31×#578—24no—
20C31×#578—24no—
21C31×#577—24no—
22C31×#577—24no—
23C2×C31×#137—21no—
24C2×C31×#137—21no—
25C2×C31×#137—21no—
26C2×C31×#137C2211yescharacteristic
27C2×C31×#137C2211yescharacteristic
28C2×C31×#137C2211yescharacteristic
29C2×C31×#137C2211yescharacteristic, complemented
30C2×C31×AGL(1,ℤ/8)—21no—
31C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
32C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
33C2×C31×#135—21no—
34C2×C31×#135—21no—
35C2×C31×#135C2211yescharacteristic
36C2×C31×#135C2211yescharacteristic
37C22×Q16×C31—21no—
38C22×Q16×C31C2211yescharacteristic, complemented
39C22×SD16×C31—21no—
40C22×SD16×C31C2211yescharacteristic
41C2×C31×#131C2211yescharacteristic
42C2×C31×#131C2211yescharacteristic, complemented
43C31×#537C2211yescharacteristic
44C2×C31×#124C2211yescharacteristic
45C31×#455—24no—
46C31×#454—24no—
47C31×#452—21no—
48C31×#452—21no—
49C31×#451—21no—
50C31×#450—21no—
51C31×#449—21no—
52C31×#449—21no—
53C31×#448—21no—
54C31×#447—21no—
55C2×C31×#104C2211yescharacteristic
56C2×C31×#104C2211yescharacteristic
57C2×C31×#104C2211yescharacteristic, complemented
58C2×C31×#104C2211yescharacteristic, complemented
59C31×#417C2211yescharacteristic
60C31×#417C2211yescharacteristic, complemented
61C2×C31×#103C2211yescharacteristic, complemented
62C2×C31×#102C2211yescharacteristic
63C2×C31×#101C2211yescharacteristic, complemented
64C2×C31×#101C2211yescharacteristic, complemented
65C2×C31×#100C2211yescharacteristic
66C31×#408C2211yescharacteristic
67C31×#408C2211yescharacteristic, complemented
68C31×#391C2211yescharacteristic, complemented
69C31×#343C2211yescharacteristic, complemented
70C31×#341C2211yescharacteristic, complemented
71C31×#341C2211yescharacteristic, complemented
72C31×#336C2211yescharacteristic, complemented
73C31×2−1+4—22no—
74C31×2−1+4—22no—
75C31×2−1+4—22no—
76C31×2−1+4—22no—
77C31×2−1+4—22no—
78C31×2−1+4—41no—
79C31×2−1+4—41no—
80C31×2−1+4D414yescomplemented
81C31×H(5,𝔽2)—22no—
82C31×H(5,𝔽2)—22no—
83C31×H(5,𝔽2)—22no—
84C31×H(5,𝔽2)—41no—
85C2×#41×C31—21no—
86C2×#41×C31—21no—
87C2×#41×C31—21no—
88C2×#41×C31—21no—
89C2×#41×C31—21no—
90C2×#41×C31—21no—
91C2×#41×C31—41no—
92C2×#41×C31—41no—
93C2×#41×C31C2311yescharacteristic
94C2×#41×C31C2311yescharacteristic
95C2×#41×C31C2311yescharacteristic
96C2×#41×C31C2311yescharacteristic
97C22×Q8×C31—21no—
98C22×Q8×C31—21no—
99C22×Q8×C31—21no—
100C22×Q8×C31—21no—
101C22×Q8×C31C2311yescharacteristic
102C22×Q8×C31C2311yescharacteristic
103C22×D4×C31—21no—
104C22×D4×C31—21no—
105C22×D4×C31—41no—
106C22×D4×C31C2311yescharacteristic
107C31×#137—28no—
108C31×#137—28no—
109C31×#137—28no—
110C31×#137—22no—
111C31×#137—22no—
112C31×#137—22no—
113C31×#137—22no—
114C31×#137—22no—
115C31×#137—22no—
116C31×#137—41no—
117C31×#137D414yescomplemented
118C31×AGL(1,ℤ/8)—28no—
119C31×AGL(1,ℤ/8)—22no—
120C31×AGL(1,ℤ/8)—22no—
121C31×AGL(1,ℤ/8)—41no—
122C31×AGL(1,ℤ/8)D414yescomplemented
123C31×#135—28no—
124C31×#135—28no—
125C31×#135—22no—
126C31×#135—22no—
127C31×#135—22no—
128C31×#135—22no—
129C2×Q16×C31—28no—
130C2×Q16×C31—21no—
131C2×Q16×C31—21no—
132C2×Q16×C31—22no—
133C2×Q16×C31—22no—
134C2×Q16×C31—21no—
135C2×Q16×C31—21no—
136C2×Q16×C31—21no—
137C2×Q16×C31—21no—
138C2×Q16×C31D411yescharacteristic
139C2×Q16×C31D411yescharacteristic
140C2×SD16×C31—28no—
141C2×SD16×C31—21no—
142C2×SD16×C31—22no—
143C2×SD16×C31—21no—
144C2×SD16×C31—22no—
145C2×SD16×C31—21no—
146C2×SD16×C31—21no—
147C2×SD16×C31—21no—
148C2×SD16×C31—21no—
149C2×SD16×C31—21no—
150C2×SD16×C31—21no—
151C2×SD16×C31D411yescharacteristic
152C2×SD16×C31D411yescharacteristic
153C2×SD16×C31D411yescharacteristic
154C2×SD16×C31D411yescharacteristic
155C2×D8×C31—21no—
156C2×D8×C31—21no—
157C2×D8×C31D411yescharacteristic
158C2×D8×C31D411yescharacteristic
159C31×#131—22no—
160C31×#131—22no—
161C31×#131—22no—
162C31×#131—22no—
163C2×M16×C31—21no—
164C2×M16×C31—21no—
165C2×M16×C31C2311yescharacteristic
166C2×M16×C31C2311yescharacteristic
167C2×M16×C31C2311yescharacteristic
168C2×M16×C31C2311yescharacteristic
169C22×C8×C31—21no—
170C22×C8×C31—21no—
171C22×C8×C31C2311yescharacteristic
172C22×C8×C31C2311yescharacteristic
173C31×#124—22no—
174C31×#124—22no—
175C31×C22⋊Q8—21no—
176C31×C22⋊Q8—21no—
177C31×#121—21no—
178C31×#121—21no—
179C31×#121—41no—
180C2×C4⋊C4×C31C2311yescharacteristic
181C2×C22⋊C4×C31—41no—
182C2×C42×C31C2311yescharacteristic
183C31×#104—22no—
184C31×#104—22no—
185C31×#104—22no—
186C31×#104—22no—
187C31×#103—21no—
188C31×#103—21no—
189C31×#103—21no—
190C31×#103—21no—
191C31×#102—21no—
192C31×#102—21no—
193C31×#102—21no—
194C31×#102—21no—
195C31×#101—22no—
196C31×#101—41no—
197C31×#100—22no—
198C31×C22⋊C8—21no—
199C31×C22⋊C8—21no—
200C31×C22⋊C8—21no—
201C31×C22⋊C8—21no—
202C31×#95—41no—
203C24×C31—21no—
204C24×C31—41no—
205#41×C31—21no—
206#41×C31—21no—
207#41×C31—21no—
208#41×C31—21no—
209#41×C31—24no—
210#41×C31—24no—
211#41×C31—24no—
212#41×C31—24no—
213#41×C31—21no—
214#41×C31—21no—
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—44no—
222#41×C31—42no—
223#41×C31—42no—
224#41×C31—42no—
225#41×C31—44no—
226#41×C31—42no—
227#41×C31—44no—
228#41×C31—42no—
229#41×C31—42no—
230#41×C31—44no—
231#41×C31—42no—
232#41×C31—42no—
233#41×C31C2×D412yes—
234#41×C31C2×D412yes—
235#41×C31C2×D412yes—
236#41×C31C2×D412yes—
237C2×Q8×C31—21no—
238C2×Q8×C31—21no—
239C2×Q8×C31—24no—
240C2×Q8×C31—24no—
241C2×Q8×C31—24no—
242C2×Q8×C31—21no—
243C2×Q8×C31—21no—
244C2×Q8×C31—21no—
245C2×Q8×C31—21no—
246C2×Q8×C31—21no—
247C2×Q8×C31—21no—
248C2×Q8×C31—21no—
249C2×Q8×C31—21no—
250C2×Q8×C31—41no—
251C2×Q8×C31—41no—
252C2×Q8×C31—42no—
253C2×Q8×C31—42no—
254C2×Q8×C31—42no—
255C2×Q8×C31—42no—
256C2×Q8×C31—42no—
257C2×Q8×C31C2×D411yescharacteristic
258C2×Q8×C31C2×D411yescharacteristic
259C2×Q8×C31C2×D412yes—
260C2×Q8×C31C2×D412yes—
261C2×Q8×C31C2×D411yescharacteristic
262C2×Q8×C31C2×D411yescharacteristic
263C2×D4×C31—21no—
264C2×D4×C31—21no—
265C2×D4×C31—24no—
266C2×D4×C31—21no—
267C2×D4×C31—21no—
268C2×D4×C31—21no—
269C2×D4×C31—21no—
270C2×D4×C31—21no—
271C2×D4×C31—21no—
272C2×D4×C31—21no—
273C2×D4×C31—42no—
274C2×D4×C31—41no—
275C2×D4×C31—41no—
276C2×D4×C31—42no—
277C2×D4×C31—44no—
278C2×D4×C31—44no—
279C2×D4×C31—41no—
280C2×D4×C31—41no—
281C2×D4×C31—42no—
282C2×D4×C31—41no—
283C2×D4×C31C2×D411yescharacteristic
284C2×D4×C31C2×D411yescharacteristic
285C2×D4×C31C2×D412yes—
286C2×D4×C31C2×D411yescharacteristic
287C2×D4×C31C2×D411yescharacteristic
288C22×C4×C31—21no—
289C22×C4×C31—21no—
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—41no—
297C22×C4×C31—41no—
298C22×C4×C31—41no—
299C22×C4×C31—41no—
300C22×C4×C31—41no—
301C22×C4×C31C2411yescharacteristic
302Q16×C31—24no—
303Q16×C31—24no—
304Q16×C31—24no—
305Q16×C31—24no—
306Q16×C31—22no—
307Q16×C31—24no—
308Q16×C31—22no—
309Q16×C31—42no—
310SD16×C31—24no—
311SD16×C31—24no—
312SD16×C31—24no—
313SD16×C31—24no—
314SD16×C31—22no—
315SD16×C31—24no—
316SD16×C31—22no—
317SD16×C31—24no—
318SD16×C31—22no—
319SD16×C31—22no—
320SD16×C31—42no—
321SD16×C31—42no—
322D8×C31—24no—
323D8×C31—22no—
324D8×C31—22no—
325D8×C31—42no—
326M16×C31—24no—
327M16×C31—24no—
328M16×C31—21no—
329M16×C31—21no—
330M16×C31—21no—
331M16×C31—21no—
332M16×C31—21no—
333M16×C31—21no—
334M16×C31C2×D412yes—
335M16×C31C2×D412yes—
336C2×C8×C31—24no—
337C2×C8×C31—24no—
338C2×C8×C31—21no—
339C2×C8×C31—21no—
340C2×C8×C31—21no—
341C2×C8×C31—21no—
342C2×C8×C31—21no—
343C2×C8×C31—21no—
344C2×C8×C31—21no—
345C2×C8×C31—21no—
346C2×C8×C31C2×D411yescharacteristic
347C2×C8×C31C2×D411yescharacteristic
348C2×C8×C31C2×D411yescharacteristic
349C2×C8×C31C2×D411yescharacteristic
350C4⋊C4×C31—21no—
351C4⋊C4×C31—21no—
352C4⋊C4×C31—41no—
353C22⋊C4×C31—44no—
354C22⋊C4×C31—41no—
355C22⋊C4×C31—41no—
356C42×C31—21no—
357C42×C31—21no—
358#23889C3111yesmaximal, characteristic, direct product factor, Sylow
359C23×C31—21no—
360C23×C31—21no—
361C23×C31—21no—
362C23×C31—21no—
363C23×C31—22no—
364C23×C31—44no—
365C23×C31—41no—
366C23×C31—41no—
367C23×C31—81no—
368C23×C31—81no—
369C23×C31—161no—
370C23×C31—161no—
371C23×C31H(5,𝔽2)11yescharacteristic
372Q8×C31—21no—
373Q8×C31—21no—
374Q8×C31—22no—
375Q8×C31—22no—
376Q8×C31—22no—
377Q8×C31—21no—
378Q8×C31—21no—
379Q8×C31—21no—
380Q8×C31—22no—
381Q8×C31—21no—
382Q8×C31—44no—
383Q8×C31—44no—
384Q8×C31—41no—
385Q8×C31—41no—
386Q8×C31—41no—
387Q8×C31—41no—
388Q8×C31#12012yes—
389Q8×C31#12012yes—
390D4×C31—22no—
391D4×C31—22no—
392D4×C31—22no—
393D4×C31—22no—
394D4×C31—22no—
395D4×C31—21no—
396D4×C31—21no—
397D4×C31—21no—
398D4×C31—21no—
399D4×C31—21no—
400D4×C31—22no—
401D4×C31—21no—
402D4×C31—44no—
403D4×C31—44no—
404D4×C31—44no—
405D4×C31—44no—
406D4×C31—41no—
407D4×C31—41no—
408D4×C31—41no—
409D4×C31—41no—
410D4×C31—41no—
411D4×C31—41no—
412D4×C31—161no—
413D4×C31#12012yes—
414D4×C31#12012yes—
415C2×C4×C31—21no—
416C2×C4×C31—21no—
417C2×C4×C31—22no—
418C2×C4×C31—22no—
419C2×C4×C31—22no—
420C2×C4×C31—22no—
421C2×C4×C31—22no—
422C2×C4×C31—22no—
423C2×C4×C31—21no—
424C2×C4×C31—21no—
425C2×C4×C31—44no—
426C2×C4×C31—44no—
427C2×C4×C31—44no—
428C2×C4×C31—44no—
429C2×C4×C31—44no—
430C2×C4×C31—41no—
431C2×C4×C31—41no—
432C2×C4×C31—41no—
433C2×C4×C31—41no—
434C2×C4×C31—41no—
435C2×C4×C31—41no—
436C2×C4×C31—41no—
437C2×C4×C31—41no—
438C2×C4×C31—41no—
439C2×C4×C31—41no—
440C2×C4×C31—41no—
441C2×C4×C31—41no—
442C2×C4×C31—81no—
443C2×C4×C31C22×D411yescharacteristic
444C2×C4×C31C22×D411yescharacteristic
445C2×C4×C31C22×D411yescharacteristic
446C2×C4×C31C22×D411yescharacteristic
447C2×C4×C31C22×D411yescharacteristic
448C2×C4×C31H(5,𝔽2)11yescharacteristic
449C8×C31—21no—
450C8×C31—21no—
451C8×C31—22no—
452C8×C31—22no—
453C8×C31—21no—
454C8×C31—21no—
455C8×C31—41no—
456C8×C31—41no—
457C2×#578C2×C3111yescharacteristic, complemented
458C2×#577C2×C3111yescharacteristic, complemented
459C2×#454C2×C3111yescharacteristic, complemented
460C2×#455C2×C3111yescharacteristic, complemented
461#3013C2×C3111yescharacteristic, complemented
462#3012C2×C3111yescharacteristic, complemented
463#2020C2×C3111yescharacteristic, complemented
464#2019C2×C3111yescharacteristic, complemented
465#2015C2×C3111yescharacteristic, complemented
466#2007C2×C3111yescharacteristic, complemented
467#1908C2×C3111yescharacteristic, complemented
468#1907C2×C3111yescharacteristic, complemented
469#1876C2×C3111yescharacteristic, complemented
470#1876C2×C3111yescharacteristic, complemented
471#1793C2×C3111yescharacteristic, complemented
472C22×C31—21no—
473C22×C31—21no—
474C22×C31—22no—
475C22×C31—22no—
476C22×C31—41no—
477C22×C31—41no—
478C22×C31—41no—
479C22×C31—41no—
480C22×C31—41no—
481C22×C31—41no—
482C22×C31—42no—
483C22×C31—41no—
484C22×C31—41no—
485C22×C31—41no—
486C22×C31—41no—
487C22×C31—82no—
488C22×C31—81no—
489C22×C31—81no—
490C22×C31—161no—
491C22×C31—164no—
492C22×C31#53411yescharacteristic
493C22×C31D4211yescharacteristic
494C22×C31D4211yescharacteristic
495C4×C31—22no—
496C4×C31—22no—
497C4×C31—41no—
498C4×C31—42no—
499C4×C31—42no—
500C4×C31—41no—
501C4×C31—81no—
502C4×C31—81no—
503C4×C31C2×#12011yescharacteristic
504C4×C31C2×#12011yescharacteristic
505C4×C31D4211yescharacteristic
506C4×C31D4211yescharacteristic
507C2×2−1+4C22×C3111yescharacteristic
508C2×2−1+4C22×C3111yescharacteristic, complemented
509C2×H(5,𝔽2)C22×C3111yescharacteristic
510#578—24no—
511#578—24no—
512#577—24no—
513#577—24no—
514C2×#137—21no—
515C2×#137—21no—
516C2×#137—21no—
517C2×#137C22×C3111yescharacteristic
518C2×#137C22×C3111yescharacteristic
519C2×#137C22×C3111yescharacteristic
520C2×#137C22×C3111yescharacteristic, complemented
521C2×AGL(1,ℤ/8)—21no—
522C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
523C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
524C2×#135—21no—
525C2×#135—21no—
526C2×#135C22×C3111yescharacteristic
527C2×#135C22×C3111yescharacteristic
528C22×Q16—21no—
529C22×Q16C22×C3111yescharacteristic, complemented
530C22×SD16—21no—
531C22×SD16C22×C3111yescharacteristic
532C2×#131C22×C3111yescharacteristic
533C2×#131C22×C3111yescharacteristic, complemented
534#537C22×C3111yescharacteristic
535C2×#124C22×C3111yescharacteristic
536#455—24no—
537#454—24no—
538#452—21no—
539#452—21no—
540#451—21no—
541#450—21no—
542#449—21no—
543#449—21no—
544#448—21no—
545#447—21no—
546C2×#104C22×C3111yescharacteristic
547C2×#104C22×C3111yescharacteristic
548C2×#104C22×C3111yescharacteristic, complemented
549C2×#104C22×C3111yescharacteristic, complemented
550#417C22×C3111yescharacteristic
551#417C22×C3111yescharacteristic, complemented
552C2×#103C22×C3111yescharacteristic, complemented
553C2×#102C22×C3111yescharacteristic
554C2×#101C22×C3111yescharacteristic, complemented
555C2×#101C22×C3111yescharacteristic, complemented
556C2×#100C22×C3111yescharacteristic
557#408C22×C3111yescharacteristic
558#408C22×C3111yescharacteristic, complemented
559#391C22×C3111yescharacteristic, complemented
560#343C22×C3111yescharacteristic, complemented
561#341C22×C3111yescharacteristic, complemented
562#341C22×C3111yescharacteristic, complemented
563#336C22×C3111yescharacteristic, complemented
564C2×C31—21no—
565C2×C31—21no—
566C2×C31—42no—
567C2×C31—42no—
568C2×C31—81no—
569C2×C31—81no—
570C2×C31—82no—
571C2×C31#240311yescharacteristic
572C2×C31#328911yescharacteristic
573C2×C31#329011yescharacteristic
5742−1+4—22no—
5752−1+4—22no—
5762−1+4—22no—
5772−1+4—22no—
5782−1+4—22no—
5792−1+4—41no—
5802−1+4—41no—
5812−1+4D4×C3114yescomplemented
582H(5,𝔽2)—22no—
583H(5,𝔽2)—22no—
584H(5,𝔽2)—22no—
585H(5,𝔽2)—41no—
586C2×#41—21no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—41no—
593C2×#41—41no—
594C2×#41C23×C3111yescharacteristic
595C2×#41C23×C3111yescharacteristic
596C2×#41C23×C3111yescharacteristic
597C2×#41C23×C3111yescharacteristic
598C22×Q8—21no—
599C22×Q8—21no—
600C22×Q8—21no—
601C22×Q8—21no—
602C22×Q8C23×C3111yescharacteristic
603C22×Q8C23×C3111yescharacteristic
604C22×D4—21no—
605C22×D4—21no—
606C22×D4—41no—
607C22×D4C23×C3111yescharacteristic
608#137—28no—
609#137—28no—
610#137—28no—
611#137—22no—
612#137—22no—
613#137—22no—
614#137—22no—
615#137—22no—
616#137—22no—
617#137—41no—
618#137D4×C3114yescomplemented
619AGL(1,ℤ/8)—28no—
620AGL(1,ℤ/8)—22no—
621AGL(1,ℤ/8)—22no—
622AGL(1,ℤ/8)—41no—
623AGL(1,ℤ/8)D4×C3114yescomplemented
624#135—28no—
625#135—28no—
626#135—22no—
627#135—22no—
628#135—22no—
629#135—22no—
630C2×Q16—28no—
631C2×Q16—21no—
632C2×Q16—21no—
633C2×Q16—22no—
634C2×Q16—22no—
635C2×Q16—21no—
636C2×Q16—21no—
637C2×Q16—21no—
638C2×Q16—21no—
639C2×Q16D4×C3111yescharacteristic
640C2×Q16D4×C3111yescharacteristic
641C2×SD16—28no—
642C2×SD16—21no—
643C2×SD16—22no—
644C2×SD16—21no—
645C2×SD16—22no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16D4×C3111yescharacteristic
653C2×SD16D4×C3111yescharacteristic
654C2×SD16D4×C3111yescharacteristic
655C2×SD16D4×C3111yescharacteristic
656C2×D8—21no—
657C2×D8—21no—
658C2×D8D4×C3111yescharacteristic
659C2×D8D4×C3111yescharacteristic
660#131—22no—
661#131—22no—
662#131—22no—
663#131—22no—
664C2×M16—21no—
665C2×M16—21no—
666C2×M16C23×C3111yescharacteristic
667C2×M16C23×C3111yescharacteristic
668C2×M16C23×C3111yescharacteristic
669C2×M16C23×C3111yescharacteristic
670C22×C8—21no—
671C22×C8—21no—
672C22×C8C23×C3111yescharacteristic
673C22×C8C23×C3111yescharacteristic
674#124—22no—
675#124—22no—
676C22⋊Q8—21no—
677C22⋊Q8—21no—
678#121—21no—
679#121—21no—
680#121—41no—
681C2×C4⋊C4C23×C3111yescharacteristic
682C2×C22⋊C4—41no—
683C2×C42C23×C3111yescharacteristic
684#104—22no—
685#104—22no—
686#104—22no—
687#104—22no—
688#103—21no—
689#103—21no—
690#103—21no—
691#103—21no—
692#102—21no—
693#102—21no—
694#102—21no—
695#102—21no—
696#101—22no—
697#101—41no—
698#100—22no—
699C22⋊C8—21no—
700C22⋊C8—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703#95—41no—
704C31#2388911yescharacteristic, direct product factor, Sylow
705C24—21no—
706C24—41no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—24no—
712#41—24no—
713#41—24no—
714#41—24no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—44no—
724#41—42no—
725#41—42no—
726#41—42no—
727#41—44no—
728#41—42no—
729#41—44no—
730#41—42no—
731#41—42no—
732#41—44no—
733#41—42no—
734#41—42no—
735#41C2×D4×C3112yes—
736#41C2×D4×C3112yes—
737#41C2×D4×C3112yes—
738#41C2×D4×C3112yes—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—41no—
753C2×Q8—41no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—42no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8C2×D4×C3111yescharacteristic
760C2×Q8C2×D4×C3111yescharacteristic
761C2×Q8C2×D4×C3112yes—
762C2×Q8C2×D4×C3112yes—
763C2×Q8C2×D4×C3111yescharacteristic
764C2×Q8C2×D4×C3111yescharacteristic
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—42no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—41no—
782C2×D4—41no—
783C2×D4—42no—
784C2×D4—41no—
785C2×D4C2×D4×C3111yescharacteristic
786C2×D4C2×D4×C3111yescharacteristic
787C2×D4C2×D4×C3112yes—
788C2×D4C2×D4×C3111yescharacteristic
789C2×D4C2×D4×C3111yescharacteristic
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4C24×C3111yescharacteristic
804Q16—24no—
805Q16—24no—
806Q16—24no—
807Q16—24no—
808Q16—22no—
809Q16—24no—
810Q16—22no—
811Q16—42no—
812SD16—24no—
813SD16—24no—
814SD16—24no—
815SD16—24no—
816SD16—22no—
817SD16—24no—
818SD16—22no—
819SD16—24no—
820SD16—22no—
821SD16—22no—
822SD16—42no—
823SD16—42no—
824D8—24no—
825D8—22no—
826D8—22no—
827D8—42no—
828M16—24no—
829M16—24no—
830M16—21no—
831M16—21no—
832M16—21no—
833M16—21no—
834M16—21no—
835M16—21no—
836M16C2×D4×C3112yes—
837M16C2×D4×C3112yes—
838C2×C8—24no—
839C2×C8—24no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8C2×D4×C3111yescharacteristic
849C2×C8C2×D4×C3111yescharacteristic
850C2×C8C2×D4×C3111yescharacteristic
851C2×C8C2×D4×C3111yescharacteristic
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—41no—
855C22⋊C4—44no—
856C22⋊C4—41no—
857C22⋊C4—41no—
858C42—21no—
859C42—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—22no—
865C23—44no—
866C23—41no—
867C23—41no—
868C23—81no—
869C23—81no—
870C23—161no—
871C23—161no—
872C23C31×H(5,𝔽2)11yescharacteristic
873Q8—21no—
874Q8—21no—
875Q8—22no—
876Q8—22no—
877Q8—22no—
878Q8—21no—
879Q8—21no—
880Q8—21no—
881Q8—22no—
882Q8—21no—
883Q8—44no—
884Q8—44no—
885Q8—41no—
886Q8—41no—
887Q8—41no—
888Q8—41no—
889Q8C31×#12012yes—
890Q8C31×#12012yes—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—21no—
897D4—21no—
898D4—21no—
899D4—21no—
900D4—21no—
901D4—22no—
902D4—21no—
903D4—44no—
904D4—44no—
905D4—44no—
906D4—44no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—161no—
914D4C31×#12012yes—
915D4C31×#12012yes—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—81no—
944C2×C4C22×D4×C3111yescharacteristic
945C2×C4C22×D4×C3111yescharacteristic
946C2×C4C22×D4×C3111yescharacteristic
947C2×C4C22×D4×C3111yescharacteristic
948C2×C4C22×D4×C3111yescharacteristic
949C2×C4C31×H(5,𝔽2)11yescharacteristic
950C8—21no—
951C8—21no—
952C8—22no—
953C8—22no—
954C8—21no—
955C8—21no—
956C8—41no—
957C8—41no—
958C22—21no—
959C22—21no—
960C22—22no—
961C22—22no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—82no—
974C22—81no—
975C22—81no—
976C22—161no—
977C22—164no—
978C22C31×#53411yescharacteristic
979C22D42×C3111yescharacteristic
980C22D42×C3111yescharacteristic
981C4—22no—
982C4—22no—
983C4—41no—
984C4—42no—
985C4—42no—
986C4—41no—
987C4—81no—
988C4—81no—
989C4C2×C31×#12011yescharacteristic
990C4C2×C31×#12011yescharacteristic
991C4D42×C3111yescharacteristic
992C4D42×C3111yescharacteristic
993C2—21no—
994C2—21no—
995C2—42no—
996C2—42no—
997C2—81no—
998C2—81no—
999C2—82no—
1000C2C31×#240311yescharacteristic
1001C2C31×#328911yescharacteristic
1002C2C31×#329011yescharacteristic
subgroupG/H
center, socleC22×C31D42
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#578C2semidirect
2. C2×C31×#577C2semidirect
3. C2×C31×#454C2semidirect
4. C2×C31×#455C2semidirect
5. C31×#3013C2semidirect
6. C31×#3012C2semidirect
7. C31×#2020C2semidirect
8. C31×#2019C2semidirect
9. C31×#2015C2semidirect
10. C31×#2007C2semidirect
11. C31×#1908C2semidirect
12. C31×#1907C2semidirect
13. C31×#1876C2semidirect
14. C31×#1876C2semidirect
15. C31×#1793C2semidirect
17. C2×C31×2−1+4C22semidirect
29. C2×C31×#137C22semidirect
38. C22×Q16×C31C22semidirect
42. C2×C31×#131C22semidirect
57. C2×C31×#104C22semidirect
58. C2×C31×#104C22semidirect
60. C31×#417C22semidirect
61. C2×C31×#103C22semidirect
63. C2×C31×#101C22semidirect
64. C2×C31×#101C22semidirect
67. C31×#408C22semidirect
68. C31×#391C22semidirect
69. C31×#343C22semidirect
70. C31×#341C22semidirect
71. C31×#341C22semidirect
72. C31×#336C22semidirect
80. C31×2−1+4D4semidirect
117. C31×#137D4semidirect
122. C31×AGL(1,ℤ/8)D4semidirect
358. #23889C31direct (N × H)
457. C2×#578C2×C31semidirect
458. C2×#577C2×C31semidirect
459. C2×#454C2×C31semidirect
460. C2×#455C2×C31semidirect
461. #3013C2×C31semidirect
462. #3012C2×C31semidirect
463. #2020C2×C31semidirect
464. #2019C2×C31semidirect
465. #2015C2×C31semidirect
466. #2007C2×C31semidirect
467. #1908C2×C31semidirect
468. #1907C2×C31semidirect
469. #1876C2×C31semidirect
470. #1876C2×C31semidirect
471. #1793C2×C31semidirect
508. C2×2−1+4C22×C31semidirect
520. C2×#137C22×C31semidirect
529. C22×Q16C22×C31semidirect
533. C2×#131C22×C31semidirect
548. C2×#104C22×C31semidirect
549. C2×#104C22×C31semidirect
551. #417C22×C31semidirect
552. C2×#103C22×C31semidirect
554. C2×#101C22×C31semidirect
555. C2×#101C22×C31semidirect
558. #408C22×C31semidirect
559. #391C22×C31semidirect
560. #343C22×C31semidirect
561. #341C22×C31semidirect
562. #341C22×C31semidirect
563. #336C22×C31semidirect
581. 2−1+4D4×C31semidirect
618. #137D4×C31semidirect
623. AGL(1,ℤ/8)D4×C31semidirect
704. C31#23889direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5782
C2×C31×#5772
C2×C31×#4542
C2×C31×#4552
C31×#30132
C31×#30122
C31×#20202
C31×#20192
C31×#20152
C31×#20072
C31×#19082
C31×#19072
C31×#18762
C31×#17932
#2388931