Finite Group Databasebeta

← C31×#23881 #21480640

Subgroups — C31×#23881 #21480640

Order 7936.

1714 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#575C211yesmaximal, characteristic, complemented
2C31×#3489C211yesmaximal, characteristic, complemented
3C2×C31×#456C211yesmaximal, characteristic, complemented
4C2×C31×#454C211yesmaximal, characteristic, complemented
5C31×#3005C211yesmaximal, characteristic, complemented
6C31×#2432C211yesmaximal, characteristic, complemented
7C31×#2007C211yesmaximal, characteristic, complemented
8C31×#2006C211yesmaximal, characteristic, complemented
9C31×#2005C211yesmaximal, characteristic, complemented
10C31×#2003C211yesmaximal, characteristic, complemented
11C31×#1901C211yesmaximal, characteristic, complemented
12C31×#1883C211yesmaximal, characteristic, complemented
13C31×#1882C211yesmaximal, characteristic, complemented
14C31×#1871C211yesmaximal, characteristic, complemented
15C31×#1789C211yesmaximal, characteristic, complemented
16C2×C31×2−1+4C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C22×#41×C31C2211yescharacteristic
19C31×#575—24no—
20C31×#575—24no—
21C2×C31×#137—21no—
22C2×C31×#137C2211yescharacteristic
23C2×C31×#137C2211yescharacteristic
24C2×C31×#137C2211yescharacteristic, complemented
25C2×C31×AGL(1,ℤ/8)—21no—
26C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
27C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
28C2×C31×AGL(1,ℤ/8)C2211yescharacteristic, complemented
29C2×C31×#135—21no—
30C2×C31×#135—21no—
31C22×M16×C31C2211yescharacteristic
32D4×Q8×C31—21no—
33C31×#548—21no—
34C31×#547—21no—
35C31×#547—22no—
36C31×#546—21no—
37C31×#546—22no—
38C31×#537—21no—
39C31×#537C2211yescharacteristic
40C31×#536—21no—
41C31×#536C2211yescharacteristic
42C2×C31×C4⋊Q8C2211yescharacteristic, complemented
43C2×C31×#124C2211yescharacteristic, complemented
44C31×#525—21no—
45C31×#525C2211yescharacteristic
46C2×C31×C22⋊Q8—21no—
47C2×C31×C22⋊Q8C2211yescharacteristic
48C31×#520C2211yescharacteristic
49C31×#456—24no—
50C31×#454—24no—
51C31×#452—21no—
52C31×#452—21no—
53C31×#449—21no—
54C31×#449—21no—
55C2×C31×#104C2211yescharacteristic
56C2×C31×#104C2211yescharacteristic
57C2×C31×#104C2211yescharacteristic
58C2×C31×#104C2211yescharacteristic
59C2×C31×#104C2211yescharacteristic, complemented
60C2×C31×#104C2211yescharacteristic, complemented
61C31×#419C2211yescharacteristic, complemented
62C31×#418C2211yescharacteristic, complemented
63C2×C31×#101C2211yescharacteristic, complemented
64C2×C31×#101C2211yescharacteristic, complemented
65C31×#407C2211yescharacteristic
66C31×#394—22no—
67C31×#391C2211yescharacteristic, complemented
68C31×#390C2211yescharacteristic, complemented
69C31×#385—22no—
70C4×C22⋊C4×C31C2211yescharacteristic
71C31×#343C2211yescharacteristic, complemented
72C31×#343C2211yescharacteristic, complemented
73C31×#339C2211yescharacteristic, complemented
74C31×#339C2211yescharacteristic, complemented
75C31×2−1+4—22no—
76C31×2−1+4—22no—
77C31×2−1+4—41no—
78C31×2−1+4—41no—
79C2×#41×C31—21no—
80C2×#41×C31—21no—
81C2×#41×C31—21no—
82C2×#41×C31—22no—
83C2×#41×C31—21no—
84C2×#41×C31—22no—
85C2×#41×C31—22no—
86C2×#41×C31—22no—
87C2×#41×C31—22no—
88C2×#41×C31—21no—
89C2×#41×C31—21no—
90C2×#41×C31—21no—
91C2×#41×C31—21no—
92C2×#41×C31—41no—
93C2×#41×C31—41no—
94C2×#41×C31—41no—
95C2×#41×C31—41no—
96C2×#41×C31D411yescharacteristic
97C2×#41×C31D411yescharacteristic
98C2×#41×C31C2311yescharacteristic
99C2×#41×C31C2311yescharacteristic
100C2×#41×C31C2311yescharacteristic
101C22×Q8×C31—21no—
102C22×Q8×C31—21no—
103C22×Q8×C31D411yescharacteristic
104C22×Q8×C31C2311yescharacteristic
105C22×Q8×C31C2311yescharacteristic
106C22×D4×C31—21no—
107C22×D4×C31—21no—
108C22×D4×C31D411yescharacteristic
109C22×D4×C31C2311yescharacteristic
110C23×C4×C31—21no—
111C23×C4×C31—21no—
112C23×C4×C31C2311yescharacteristic
113C31×#137—28no—
114C31×#137—22no—
115C31×#137—22no—
116C31×#137—22no—
117C31×#137—22no—
118C31×#137—41no—
119C31×#137D414yescomplemented
120C31×AGL(1,ℤ/8)—28no—
121C31×AGL(1,ℤ/8)—22no—
122C31×AGL(1,ℤ/8)—22no—
123C31×AGL(1,ℤ/8)—22no—
124C31×AGL(1,ℤ/8)—22no—
125C31×AGL(1,ℤ/8)—41no—
126C31×AGL(1,ℤ/8)D414yescomplemented
127C31×#135—28no—
128C31×#135—28no—
129C2×Q16×C31—21no—
130C2×Q16×C31—21no—
131C2×Q16×C31—21no—
132C2×SD16×C31—21no—
133C2×SD16×C31—21no—
134C2×SD16×C31—21no—
135C2×SD16×C31—21no—
136C2×SD16×C31—21no—
137C2×SD16×C31—21no—
138C2×D8×C31—21no—
139C2×D8×C31—21no—
140C2×D8×C31—21no—
141C2×M16×C31—21no—
142C2×M16×C31—22no—
143C2×M16×C31—22no—
144C2×M16×C31C2311yescharacteristic
145C2×M16×C31C2311yescharacteristic
146C2×M16×C31C2311yescharacteristic
147C2×M16×C31C2311yescharacteristic
148C22×C8×C31—21no—
149C31×C4⋊Q8—22no—
150C31×C4⋊Q8—21no—
151C31×C4⋊Q8—22no—
152C31×C4⋊Q8—41no—
153C31×#124—22no—
154C31×#124—21no—
155C31×#124—22no—
156C31×#124—41no—
157C31×#123—22no—
158C31×#123—22no—
159C31×#123—22no—
160C31×#123—21no—
161C31×#123—22no—
162C31×C22⋊Q8—22no—
163C31×C22⋊Q8—22no—
164C31×C22⋊Q8—22no—
165C31×C22⋊Q8—21no—
166C31×C22⋊Q8—21no—
167C31×C22⋊Q8—21no—
168C31×C22⋊Q8—21no—
169C31×C22⋊Q8—21no—
170C31×C22⋊Q8—21no—
171C31×C22⋊Q8—21no—
172C31×C22⋊Q8—21no—
173C31×C22⋊Q8D411yescharacteristic
174C31×C22⋊Q8D411yescharacteristic
175C31×#121—22no—
176C31×#121—22no—
177C31×#121—22no—
178C31×#121—21no—
179C31×#121—21no—
180C31×#121—22no—
181C31×#121D411yescharacteristic
182C31×#121D411yescharacteristic
183C31×#120—22no—
184C31×#120—21no—
185C4×Q8×C31—21no—
186C4×D4×C31—22no—
187C4×D4×C31—22no—
188C4×D4×C31—21no—
189C4×D4×C31—22no—
190C4×D4×C31—21no—
191C4×D4×C31—21no—
192C31×#117—21no—
193C31×#117C2311yescharacteristic
194C2×C4⋊C4×C31—22no—
195C2×C4⋊C4×C31—21no—
196C2×C4⋊C4×C31—22no—
197C2×C4⋊C4×C31D412yes—
198C2×C4⋊C4×C31C2311yescharacteristic
199C2×C22⋊C4×C31—22no—
200C2×C22⋊C4×C31—21no—
201C2×C22⋊C4×C31—22no—
202C2×C22⋊C4×C31—22no—
203C2×C22⋊C4×C31D412yes—
204C2×C42×C31C2311yescharacteristic
205C2×C42×C31C2311yescharacteristic
206C31×#104—22no—
207C31×#104—22no—
208C31×#104—22no—
209C31×#104—22no—
210C31×#104—41no—
211C31×#104—41no—
212C31×#103—21no—
213C31×#103—21no—
214C31×#102—21no—
215C31×#102—21no—
216C31×#101—22no—
217C31×#101—22no—
218C31×C22⋊C8—21no—
219C31×C22⋊C8—21no—
220C31×#95—21no—
221C31×#95—22no—
222C24×C31—21no—
223C24×C31—21no—
224C24×C31C2×D411yescharacteristic
225#41×C31—21no—
226#41×C31—21no—
227#41×C31—24no—
228#41×C31—24no—
229#41×C31—22no—
230#41×C31—22no—
231#41×C31—21no—
232#41×C31—21no—
233#41×C31—21no—
234#41×C31—21no—
235#41×C31—21no—
236#41×C31—21no—
237#41×C31—21no—
238#41×C31—21no—
239#41×C31—42no—
240#41×C31—42no—
241#41×C31—41no—
242#41×C31—41no—
243#41×C31—42no—
244#41×C31—42no—
245#41×C31—42no—
246#41×C31—42no—
247#41×C31—42no—
248#41×C31—42no—
249#41×C31—44no—
250#41×C31—44no—
251#41×C31—42no—
252#41×C31—42no—
253#41×C31—42no—
254#41×C31—42no—
255#41×C31—42no—
256#41×C31—42no—
257#41×C31C2×D412yes—
258#41×C31C2×D412yes—
259C2×Q8×C31—22no—
260C2×Q8×C31—21no—
261C2×Q8×C31—21no—
262C2×Q8×C31—21no—
263C2×Q8×C31—21no—
264C2×Q8×C31—21no—
265C2×Q8×C31—21no—
266C2×Q8×C31—21no—
267C2×Q8×C31—21no—
268C2×Q8×C31—22no—
269C2×Q8×C31—21no—
270C2×Q8×C31—21no—
271C2×Q8×C31—21no—
272C2×Q8×C31—21no—
273C2×Q8×C31—41no—
274C2×Q8×C31—42no—
275C2×Q8×C31—42no—
276C2×Q8×C31—42no—
277C2×Q8×C31—42no—
278C2×Q8×C31C2×D411yescharacteristic
279C2×Q8×C31C2×D411yescharacteristic
280C2×Q8×C31C2×D412yes—
281C2×Q8×C31C2×D411yescharacteristic
282C2×D4×C31—21no—
283C2×D4×C31—22no—
284C2×D4×C31—22no—
285C2×D4×C31—21no—
286C2×D4×C31—21no—
287C2×D4×C31—21no—
288C2×D4×C31—21no—
289C2×D4×C31—21no—
290C2×D4×C31—22no—
291C2×D4×C31—21no—
292C2×D4×C31—21no—
293C2×D4×C31—21no—
294C2×D4×C31—21no—
295C2×D4×C31—21no—
296C2×D4×C31—21no—
297C2×D4×C31—21no—
298C2×D4×C31—41no—
299C2×D4×C31—42no—
300C2×D4×C31—42no—
301C2×D4×C31—42no—
302C2×D4×C31—42no—
303C2×D4×C31—41no—
304C2×D4×C31—41no—
305C2×D4×C31C2×D411yescharacteristic
306C2×D4×C31C2×D411yescharacteristic
307C2×D4×C31C2×D412yes—
308C2×D4×C31C2×D411yescharacteristic
309C22×C4×C31—21no—
310C22×C4×C31—21no—
311C22×C4×C31—21no—
312C22×C4×C31—21no—
313C22×C4×C31—21no—
314C22×C4×C31—22no—
315C22×C4×C31—22no—
316C22×C4×C31—21no—
317C22×C4×C31—21no—
318C22×C4×C31—21no—
319C22×C4×C31—22no—
320C22×C4×C31—21no—
321C22×C4×C31—21no—
322C22×C4×C31—21no—
323C22×C4×C31—21no—
324C22×C4×C31—21no—
325C22×C4×C31—42no—
326C22×C4×C31—42no—
327C22×C4×C31—42no—
328C22×C4×C31—42no—
329C22×C4×C31—41no—
330C22×C4×C31—41no—
331C22×C4×C31C2×D412yes—
332C22×C4×C31C2×D411yescharacteristic
333C22×C4×C31C2×D411yescharacteristic
334C22×C4×C31C2×D411yescharacteristic
335C22×C4×C31C2×D411yescharacteristic
336C22×C4×C31C2×D411yescharacteristic
337C22×C4×C31C2×D412yes—
338C22×C4×C31C2411yescharacteristic
339Q16×C31—24no—
340Q16×C31—24no—
341Q16×C31—42no—
342SD16×C31—24no—
343SD16×C31—24no—
344SD16×C31—24no—
345SD16×C31—24no—
346SD16×C31—42no—
347SD16×C31—42no—
348D8×C31—24no—
349D8×C31—24no—
350D8×C31—42no—
351M16×C31—24no—
352M16×C31—21no—
353M16×C31—21no—
354M16×C31—21no—
355M16×C31—21no—
356M16×C31—21no—
357M16×C31—21no—
358M16×C31C2×D412yes—
359M16×C31C2×D412yes—
360C2×C8×C31—24no—
361C2×C8×C31—21no—
362C2×C8×C31—21no—
363C2×C8×C31—21no—
364C2×C8×C31—21no—
365C4⋊C4×C31—22no—
366C4⋊C4×C31—22no—
367C4⋊C4×C31—22no—
368C4⋊C4×C31—22no—
369C4⋊C4×C31—21no—
370C4⋊C4×C31—22no—
371C4⋊C4×C31—22no—
372C4⋊C4×C31—21no—
373C4⋊C4×C31—21no—
374C4⋊C4×C31—21no—
375C4⋊C4×C31—44no—
376C4⋊C4×C31C2×D411yescharacteristic
377C4⋊C4×C31C2×D411yescharacteristic
378C22⋊C4×C31—22no—
379C22⋊C4×C31—22no—
380C22⋊C4×C31—22no—
381C22⋊C4×C31—22no—
382C22⋊C4×C31—22no—
383C22⋊C4×C31—21no—
384C22⋊C4×C31—22no—
385C22⋊C4×C31—22no—
386C22⋊C4×C31—21no—
387C22⋊C4×C31—21no—
388C22⋊C4×C31—21no—
389C22⋊C4×C31—21no—
390C22⋊C4×C31—44no—
391C22⋊C4×C31—44no—
392C22⋊C4×C31—42no—
393C42×C31—22no—
394C42×C31—21no—
395C42×C31—21no—
396C42×C31—21no—
397C42×C31—21no—
398C42×C31—21no—
399#23881C3111yesmaximal, characteristic, direct product factor, Sylow
400C23×C31—21no—
401C23×C31—21no—
402C23×C31—21no—
403C23×C31—21no—
404C23×C31—21no—
405C23×C31—22no—
406C23×C31—41no—
407C23×C31—41no—
408C23×C31—42no—
409C23×C31—42no—
410C23×C31—42no—
411C23×C31—42no—
412C23×C31—41no—
413C23×C31—41no—
414C23×C31—81no—
415C23×C31#12011yescharacteristic
416C23×C31#12011yescharacteristic
417C23×C31C22×D411yescharacteristic
418Q8×C31—21no—
419Q8×C31—21no—
420Q8×C31—22no—
421Q8×C31—21no—
422Q8×C31—21no—
423Q8×C31—22no—
424Q8×C31—21no—
425Q8×C31—42no—
426Q8×C31—44no—
427Q8×C31—41no—
428Q8×C31—41no—
429Q8×C31—41no—
430Q8×C31—41no—
431Q8×C31—41no—
432Q8×C31—41no—
433Q8×C31#12012yes—
434D4×C31—22no—
435D4×C31—22no—
436D4×C31—21no—
437D4×C31—22no—
438D4×C31—21no—
439D4×C31—21no—
440D4×C31—21no—
441D4×C31—22no—
442D4×C31—21no—
443D4×C31—42no—
444D4×C31—42no—
445D4×C31—42no—
446D4×C31—42no—
447D4×C31—44no—
448D4×C31—44no—
449D4×C31—44no—
450D4×C31—41no—
451D4×C31—41no—
452D4×C31—41no—
453D4×C31—41no—
454D4×C31—41no—
455D4×C31—41no—
456D4×C31—81no—
457D4×C31—82no—
458D4×C31#12012yes—
459C2×C4×C31—21no—
460C2×C4×C31—21no—
461C2×C4×C31—21no—
462C2×C4×C31—21no—
463C2×C4×C31—21no—
464C2×C4×C31—21no—
465C2×C4×C31—21no—
466C2×C4×C31—21no—
467C2×C4×C31—21no—
468C2×C4×C31—21no—
469C2×C4×C31—21no—
470C2×C4×C31—22no—
471C2×C4×C31—22no—
472C2×C4×C31—22no—
473C2×C4×C31—21no—
474C2×C4×C31—22no—
475C2×C4×C31—21no—
476C2×C4×C31—21no—
477C2×C4×C31—22no—
478C2×C4×C31—21no—
479C2×C4×C31—22no—
480C2×C4×C31—22no—
481C2×C4×C31—22no—
482C2×C4×C31—42no—
483C2×C4×C31—42no—
484C2×C4×C31—42no—
485C2×C4×C31—44no—
486C2×C4×C31—44no—
487C2×C4×C31—44no—
488C2×C4×C31—41no—
489C2×C4×C31—44no—
490C2×C4×C31—41no—
491C2×C4×C31—41no—
492C2×C4×C31—41no—
493C2×C4×C31—41no—
494C2×C4×C31—41no—
495C2×C4×C31—41no—
496C2×C4×C31—41no—
497C2×C4×C31—42no—
498C2×C4×C31—41no—
499C2×C4×C31—41no—
500C2×C4×C31—41no—
501C2×C4×C31—82no—
502C2×C4×C31#12011yescharacteristic
503C2×C4×C31#12011yescharacteristic
504C2×C4×C31C22×D411yescharacteristic
505C2×C4×C31C22×D411yescharacteristic
506C2×C4×C31C22×D411yescharacteristic
507C2×C4×C31C22×D411yescharacteristic
508C2×C4×C31H(5,𝔽2)11yescharacteristic
509C2×C4×C31H(5,𝔽2)11yescharacteristic
510C8×C31—22no—
511C8×C31—22no—
512C8×C31—41no—
513C8×C31—41no—
514C2×#575C2×C3111yescharacteristic, complemented
515#3489C2×C3111yescharacteristic, complemented
516C2×#456C2×C3111yescharacteristic, complemented
517C2×#454C2×C3111yescharacteristic, complemented
518#3005C2×C3111yescharacteristic, complemented
519#2432C2×C3111yescharacteristic, complemented
520#2007C2×C3111yescharacteristic, complemented
521#2006C2×C3111yescharacteristic, complemented
522#2005C2×C3111yescharacteristic, complemented
523#2003C2×C3111yescharacteristic, complemented
524#1901C2×C3111yescharacteristic, complemented
525#1883C2×C3111yescharacteristic, complemented
526#1882C2×C3111yescharacteristic, complemented
527#1871C2×C3111yescharacteristic, complemented
528#1789C2×C3111yescharacteristic, complemented
529C22×C31—21no—
530C22×C31—21no—
531C22×C31—21no—
532C22×C31—21no—
533C22×C31—22no—
534C22×C31—21no—
535C22×C31—21no—
536C22×C31—21no—
537C22×C31—21no—
538C22×C31—44no—
539C22×C31—41no—
540C22×C31—41no—
541C22×C31—41no—
542C22×C31—41no—
543C22×C31—42no—
544C22×C31—41no—
545C22×C31—41no—
546C22×C31—41no—
547C22×C31—41no—
548C22×C31—81no—
549C22×C31—81no—
550C22×C31—82no—
551C22×C31—84no—
552C22×C31—81no—
553C22×C31—81no—
554C22×C31C2×#12011yescharacteristic
555C22×C31D4211yescharacteristic
556C22×C31D4211yescharacteristic
557C4×C31—21no—
558C4×C31—21no—
559C4×C31—22no—
560C4×C31—42no—
561C4×C31—42no—
562C4×C31—41no—
563C4×C31—42no—
564C4×C31—41no—
565C4×C31—42no—
566C4×C31—41no—
567C4×C31—41no—
568C4×C31—81no—
569C4×C31C2×#12011yescharacteristic
570C4×C31#53411yescharacteristic
571C4×C31D4211yescharacteristic
572C4×C31D4211yescharacteristic
573C2×2−1+4C22×C3111yescharacteristic
574C22×#41C22×C3111yescharacteristic
575C22×#41C22×C3111yescharacteristic
576#575—24no—
577#575—24no—
578C2×#137—21no—
579C2×#137C22×C3111yescharacteristic
580C2×#137C22×C3111yescharacteristic
581C2×#137C22×C3111yescharacteristic, complemented
582C2×AGL(1,ℤ/8)—21no—
583C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
584C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
585C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
586C2×#135—21no—
587C2×#135—21no—
588C22×M16C22×C3111yescharacteristic
589D4×Q8—21no—
590#548—21no—
591#547—21no—
592#547—22no—
593#546—21no—
594#546—22no—
595#537—21no—
596#537C22×C3111yescharacteristic
597#536—21no—
598#536C22×C3111yescharacteristic
599C2×C4⋊Q8C22×C3111yescharacteristic, complemented
600C2×#124C22×C3111yescharacteristic, complemented
601#525—21no—
602#525C22×C3111yescharacteristic
603C2×C22⋊Q8—21no—
604C2×C22⋊Q8C22×C3111yescharacteristic
605#520C22×C3111yescharacteristic
606#456—24no—
607#454—24no—
608#452—21no—
609#452—21no—
610#449—21no—
611#449—21no—
612C2×#104C22×C3111yescharacteristic
613C2×#104C22×C3111yescharacteristic
614C2×#104C22×C3111yescharacteristic
615C2×#104C22×C3111yescharacteristic
616C2×#104C22×C3111yescharacteristic, complemented
617C2×#104C22×C3111yescharacteristic, complemented
618#419C22×C3111yescharacteristic, complemented
619#418C22×C3111yescharacteristic, complemented
620C2×#101C22×C3111yescharacteristic, complemented
621C2×#101C22×C3111yescharacteristic, complemented
622#407C22×C3111yescharacteristic
623#394—22no—
624#391C22×C3111yescharacteristic, complemented
625#390C22×C3111yescharacteristic, complemented
626#385—22no—
627C4×C22⋊C4C22×C3111yescharacteristic
628#343C22×C3111yescharacteristic, complemented
629#343C22×C3111yescharacteristic, complemented
630#339C22×C3111yescharacteristic, complemented
631#339C22×C3111yescharacteristic, complemented
632C2×C31—21no—
633C2×C31—21no—
634C2×C31—41no—
635C2×C31—41no—
636C2×C31—42no—
637C2×C31—81no—
638C2×C31—82no—
639C2×C31—81no—
640C2×C31#240311yescharacteristic
641C2×C31#301811yescharacteristic
642C2×C31#302011yescharacteristic
6432−1+4—22no—
6442−1+4—22no—
6452−1+4—41no—
6462−1+4—41no—
647C2×#41—21no—
648C2×#41—21no—
649C2×#41—21no—
650C2×#41—22no—
651C2×#41—21no—
652C2×#41—22no—
653C2×#41—22no—
654C2×#41—22no—
655C2×#41—22no—
656C2×#41—21no—
657C2×#41—21no—
658C2×#41—21no—
659C2×#41—21no—
660C2×#41—41no—
661C2×#41—41no—
662C2×#41—41no—
663C2×#41—41no—
664C2×#41D4×C3111yescharacteristic
665C2×#41D4×C3111yescharacteristic
666C2×#41C23×C3111yescharacteristic
667C2×#41C23×C3111yescharacteristic
668C2×#41C23×C3111yescharacteristic
669C22×Q8—21no—
670C22×Q8—21no—
671C22×Q8D4×C3111yescharacteristic
672C22×Q8C23×C3111yescharacteristic
673C22×Q8C23×C3111yescharacteristic
674C22×D4—21no—
675C22×D4—21no—
676C22×D4D4×C3111yescharacteristic
677C22×D4C23×C3111yescharacteristic
678C23×C4—21no—
679C23×C4—21no—
680C23×C4C23×C3111yescharacteristic
681#137—28no—
682#137—22no—
683#137—22no—
684#137—22no—
685#137—22no—
686#137—41no—
687#137D4×C3114yescomplemented
688AGL(1,ℤ/8)—28no—
689AGL(1,ℤ/8)—22no—
690AGL(1,ℤ/8)—22no—
691AGL(1,ℤ/8)—22no—
692AGL(1,ℤ/8)—22no—
693AGL(1,ℤ/8)—41no—
694AGL(1,ℤ/8)D4×C3114yescomplemented
695#135—28no—
696#135—28no—
697C2×Q16—21no—
698C2×Q16—21no—
699C2×Q16—21no—
700C2×SD16—21no—
701C2×SD16—21no—
702C2×SD16—21no—
703C2×SD16—21no—
704C2×SD16—21no—
705C2×SD16—21no—
706C2×D8—21no—
707C2×D8—21no—
708C2×D8—21no—
709C2×M16—21no—
710C2×M16—22no—
711C2×M16—22no—
712C2×M16C23×C3111yescharacteristic
713C2×M16C23×C3111yescharacteristic
714C2×M16C23×C3111yescharacteristic
715C2×M16C23×C3111yescharacteristic
716C22×C8—21no—
717C4⋊Q8—22no—
718C4⋊Q8—21no—
719C4⋊Q8—22no—
720C4⋊Q8—41no—
721#124—22no—
722#124—21no—
723#124—22no—
724#124—41no—
725#123—22no—
726#123—22no—
727#123—22no—
728#123—21no—
729#123—22no—
730C22⋊Q8—22no—
731C22⋊Q8—22no—
732C22⋊Q8—22no—
733C22⋊Q8—21no—
734C22⋊Q8—21no—
735C22⋊Q8—21no—
736C22⋊Q8—21no—
737C22⋊Q8—21no—
738C22⋊Q8—21no—
739C22⋊Q8—21no—
740C22⋊Q8—21no—
741C22⋊Q8D4×C3111yescharacteristic
742C22⋊Q8D4×C3111yescharacteristic
743#121—22no—
744#121—22no—
745#121—22no—
746#121—21no—
747#121—21no—
748#121—22no—
749#121D4×C3111yescharacteristic
750#121D4×C3111yescharacteristic
751#120—22no—
752#120—21no—
753C4×Q8—21no—
754C4×D4—22no—
755C4×D4—22no—
756C4×D4—21no—
757C4×D4—22no—
758C4×D4—21no—
759C4×D4—21no—
760#117—21no—
761#117C23×C3111yescharacteristic
762C2×C4⋊C4—22no—
763C2×C4⋊C4—21no—
764C2×C4⋊C4—22no—
765C2×C4⋊C4D4×C3112yes—
766C2×C4⋊C4C23×C3111yescharacteristic
767C2×C22⋊C4—22no—
768C2×C22⋊C4—21no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4D4×C3112yes—
772C2×C42C23×C3111yescharacteristic
773C2×C42C23×C3111yescharacteristic
774#104—22no—
775#104—22no—
776#104—22no—
777#104—22no—
778#104—41no—
779#104—41no—
780#103—21no—
781#103—21no—
782#102—21no—
783#102—21no—
784#101—22no—
785#101—22no—
786C22⋊C8—21no—
787C22⋊C8—21no—
788#95—21no—
789#95—22no—
790C31#2388111yescharacteristic, direct product factor, Sylow
791C24—21no—
792C24—21no—
793C24C2×D4×C3111yescharacteristic
794#41—21no—
795#41—21no—
796#41—24no—
797#41—24no—
798#41—22no—
799#41—22no—
800#41—21no—
801#41—21no—
802#41—21no—
803#41—21no—
804#41—21no—
805#41—21no—
806#41—21no—
807#41—21no—
808#41—42no—
809#41—42no—
810#41—41no—
811#41—41no—
812#41—42no—
813#41—42no—
814#41—42no—
815#41—42no—
816#41—42no—
817#41—42no—
818#41—44no—
819#41—44no—
820#41—42no—
821#41—42no—
822#41—42no—
823#41—42no—
824#41—42no—
825#41—42no—
826#41C2×D4×C3112yes—
827#41C2×D4×C3112yes—
828C2×Q8—22no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—22no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—41no—
843C2×Q8—42no—
844C2×Q8—42no—
845C2×Q8—42no—
846C2×Q8—42no—
847C2×Q8C2×D4×C3111yescharacteristic
848C2×Q8C2×D4×C3111yescharacteristic
849C2×Q8C2×D4×C3112yes—
850C2×Q8C2×D4×C3111yescharacteristic
851C2×D4—21no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—22no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4C2×D4×C3111yescharacteristic
875C2×D4C2×D4×C3111yescharacteristic
876C2×D4C2×D4×C3112yes—
877C2×D4C2×D4×C3111yescharacteristic
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—22no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4C2×D4×C3112yes—
901C22×C4C2×D4×C3111yescharacteristic
902C22×C4C2×D4×C3111yescharacteristic
903C22×C4C2×D4×C3111yescharacteristic
904C22×C4C2×D4×C3111yescharacteristic
905C22×C4C2×D4×C3111yescharacteristic
906C22×C4C2×D4×C3112yes—
907C22×C4C24×C3111yescharacteristic
908Q16—24no—
909Q16—24no—
910Q16—42no—
911SD16—24no—
912SD16—24no—
913SD16—24no—
914SD16—24no—
915SD16—42no—
916SD16—42no—
917D8—24no—
918D8—24no—
919D8—42no—
920M16—24no—
921M16—21no—
922M16—21no—
923M16—21no—
924M16—21no—
925M16—21no—
926M16—21no—
927M16C2×D4×C3112yes—
928M16C2×D4×C3112yes—
929C2×C8—24no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—21no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—44no—
945C4⋊C4C2×D4×C3111yescharacteristic
946C4⋊C4C2×D4×C3111yescharacteristic
947C22⋊C4—22no—
948C22⋊C4—22no—
949C22⋊C4—22no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—21no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—21no—
956C22⋊C4—21no—
957C22⋊C4—21no—
958C22⋊C4—21no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—42no—
962C42—22no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—22no—
974C23—41no—
975C23—41no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—41no—
981C23—41no—
982C23—81no—
983C23C31×#12011yescharacteristic
984C23C31×#12011yescharacteristic
985C23C22×D4×C3111yescharacteristic
986Q8—21no—
987Q8—21no—
988Q8—22no—
989Q8—21no—
990Q8—21no—
991Q8—22no—
992Q8—21no—
993Q8—42no—
994Q8—44no—
995Q8—41no—
996Q8—41no—
997Q8—41no—
998Q8—41no—
999Q8—41no—
1000Q8—41no—
1001Q8C31×#12012yes—
1002D4—22no—
1003D4—22no—
1004D4—21no—
1005D4—22no—
1006D4—21no—
1007D4—21no—
1008D4—21no—
1009D4—22no—
1010D4—21no—
1011D4—42no—
1012D4—42no—
1013D4—42no—
1014D4—42no—
1015D4—44no—
1016D4—44no—
1017D4—44no—
1018D4—41no—
1019D4—41no—
1020D4—41no—
1021D4—41no—
1022D4—41no—
1023D4—41no—
1024D4—81no—
1025D4—82no—
1026D4C31×#12012yes—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—41no—
1057C2×C4—44no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—42no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—82no—
1070C2×C4C31×#12011yescharacteristic
1071C2×C4C31×#12011yescharacteristic
1072C2×C4C22×D4×C3111yescharacteristic
1073C2×C4C22×D4×C3111yescharacteristic
1074C2×C4C22×D4×C3111yescharacteristic
1075C2×C4C22×D4×C3111yescharacteristic
1076C2×C4C31×H(5,𝔽2)11yescharacteristic
1077C2×C4C31×H(5,𝔽2)11yescharacteristic
1078C8—22no—
1079C8—22no—
1080C8—41no—
1081C8—41no—
1082C22—21no—
1083C22—21no—
1084C22—21no—
1085C22—21no—
1086C22—22no—
1087C22—21no—
1088C22—21no—
1089C22—21no—
1090C22—21no—
1091C22—44no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—81no—
1102C22—81no—
1103C22—82no—
1104C22—84no—
1105C22—81no—
1106C22—81no—
1107C22C2×C31×#12011yescharacteristic
1108C22D42×C3111yescharacteristic
1109C22D42×C3111yescharacteristic
1110C4—21no—
1111C4—21no—
1112C4—22no—
1113C4—42no—
1114C4—42no—
1115C4—41no—
1116C4—42no—
1117C4—41no—
1118C4—42no—
1119C4—41no—
1120C4—41no—
1121C4—81no—
1122C4C2×C31×#12011yescharacteristic
1123C4C31×#53411yescharacteristic
1124C4D42×C3111yescharacteristic
1125C4D42×C3111yescharacteristic
1126C2—21no—
1127C2—21no—
1128C2—41no—
1129C2—41no—
1130C2—42no—
1131C2—82no—
1132C2—81no—
1133C2—81no—
1134C2C31×#240311yescharacteristic
1135C2C31×#301811yescharacteristic
1136C2C31×#302011yescharacteristic
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. C2×C31×#575C2semidirect
2. C31×#3489C2semidirect
3. C2×C31×#456C2semidirect
4. C2×C31×#454C2semidirect
5. C31×#3005C2semidirect
6. C31×#2432C2semidirect
7. C31×#2007C2semidirect
8. C31×#2006C2semidirect
9. C31×#2005C2semidirect
10. C31×#2003C2semidirect
11. C31×#1901C2semidirect
12. C31×#1883C2semidirect
13. C31×#1882C2semidirect
14. C31×#1871C2semidirect
15. C31×#1789C2semidirect
24. C2×C31×#137C22semidirect
28. C2×C31×AGL(1,ℤ/8)C22semidirect
42. C2×C31×C4⋊Q8C22semidirect
43. C2×C31×#124C22semidirect
59. C2×C31×#104C22semidirect
60. C2×C31×#104C22semidirect
61. C31×#419C22semidirect
62. C31×#418C22semidirect
63. C2×C31×#101C22semidirect
64. C2×C31×#101C22semidirect
67. C31×#391C22semidirect
68. C31×#390C22semidirect
71. C31×#343C22semidirect
72. C31×#343C22semidirect
73. C31×#339C22semidirect
74. C31×#339C22semidirect
119. C31×#137D4semidirect
126. C31×AGL(1,ℤ/8)D4semidirect
399. #23881C31direct (N × H)
514. C2×#575C2×C31semidirect
515. #3489C2×C31semidirect
516. C2×#456C2×C31semidirect
517. C2×#454C2×C31semidirect
518. #3005C2×C31semidirect
519. #2432C2×C31semidirect
520. #2007C2×C31semidirect
521. #2006C2×C31semidirect
522. #2005C2×C31semidirect
523. #2003C2×C31semidirect
524. #1901C2×C31semidirect
525. #1883C2×C31semidirect
526. #1882C2×C31semidirect
527. #1871C2×C31semidirect
528. #1789C2×C31semidirect
581. C2×#137C22×C31semidirect
585. C2×AGL(1,ℤ/8)C22×C31semidirect
599. C2×C4⋊Q8C22×C31semidirect
600. C2×#124C22×C31semidirect
616. C2×#104C22×C31semidirect
617. C2×#104C22×C31semidirect
618. #419C22×C31semidirect
619. #418C22×C31semidirect
620. C2×#101C22×C31semidirect
621. C2×#101C22×C31semidirect
624. #391C22×C31semidirect
625. #390C22×C31semidirect
628. #343C22×C31semidirect
629. #343C22×C31semidirect
630. #339C22×C31semidirect
631. #339C22×C31semidirect
687. #137D4×C31semidirect
694. AGL(1,ℤ/8)D4×C31semidirect
790. C31#23881direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5752
C31×#34892
C2×C31×#4562
C2×C31×#4542
C31×#30052
C31×#24322
C31×#20072
C31×#20062
C31×#20052
C31×#20032
C31×#19012
C31×#18832
C31×#18822
C31×#18712
C31×#17892
#2388131