Finite Group Databasebeta

← C31×#23878 #21480637

Subgroups — C31×#23878 #21480637

Order 7936.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#575C211yesmaximal, characteristic, complemented
2C31×#3488C211yesmaximal, characteristic, complemented
3C2×C31×#455C211yesmaximal, characteristic, complemented
4C2×C31×#453C211yesmaximal, characteristic, complemented
5C31×#3005C211yesmaximal, characteristic, complemented
6C31×#2431C211yesmaximal, characteristic, complemented
7C31×#2007C211yesmaximal, characteristic, complemented
8C31×#2006C211yesmaximal, characteristic, complemented
9C31×#2004C211yesmaximal, characteristic, complemented
10C31×#2002C211yesmaximal, characteristic, complemented
11C31×#1900C211yesmaximal, characteristic, complemented
12C31×#1883C211yesmaximal, characteristic, complemented
13C31×#1882C211yesmaximal, characteristic, complemented
14C31×#1871C211yesmaximal, characteristic, complemented
15C31×#1789C211yesmaximal, characteristic, complemented
16C2×C31×H(5,𝔽2)C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C22×#41×C31C2211yescharacteristic, complemented
19C31×#575—24no—
20C31×#575—24no—
21C2×C31×#137—21no—
22C2×C31×#137C2211yescharacteristic
23C2×C31×#137C2211yescharacteristic, complemented
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, complemented
28C2×C31×AGL(1,ℤ/8)C2211yescharacteristic, complemented
29C2×C31×#135—21no—
30C2×C31×#135—21no—
31C22×M16×C31C2211yescharacteristic, complemented
32C31×#550—21no—
33C31×#548—21no—
34C31×#546—21no—
35C31×#546—22no—
36D42×C31—22no—
37D42×C31—21no—
38C31×#537—21no—
39C31×#537C2211yescharacteristic
40C31×#535—21no—
41C31×#535C2211yescharacteristic
42C2×C31×#127C2211yescharacteristic, complemented
43C2×C31×#124C2211yescharacteristic, complemented
44C31×#525—21no—
45C31×#525C2211yescharacteristic
46C2×C31×#121—21no—
47C2×C31×#121C2211yescharacteristic
48C31×#520C2211yescharacteristic
49C31×#455—24no—
50C31×#453—24no—
51C31×#452—21no—
52C31×#452—21no—
53C31×#449—21no—
54C31×#449—21no—
55C2×C31×#104C2211yescharacteristic
56C2×C31×#104C2211yescharacteristic
57C2×C31×#104C2211yescharacteristic, complemented
58C2×C31×#104C2211yescharacteristic, complemented
59C2×C31×#104C2211yescharacteristic, complemented
60C2×C31×#104C2211yescharacteristic, complemented
61C31×#419C2211yescharacteristic, complemented
62C31×#418C2211yescharacteristic, complemented
63C2×C31×#100C2211yescharacteristic, complemented
64C2×C31×#100C2211yescharacteristic, complemented
65C31×#407C2211yescharacteristic, complemented
66C31×#392—22no—
67C31×#391C2211yescharacteristic, complemented
68C31×#390C2211yescharacteristic, complemented
69C31×#386—22no—
70C4×C22⋊C4×C31C2211yescharacteristic, complemented
71C31×#343C2211yescharacteristic, complemented
72C31×#343C2211yescharacteristic, complemented
73C31×#339C2211yescharacteristic, complemented
74C31×#339C2211yescharacteristic, complemented
75C31×H(5,𝔽2)—22no—
76C31×H(5,𝔽2)—22no—
77C31×H(5,𝔽2)—41no—
78C31×H(5,𝔽2)—41no—
79C2×#41×C31—21no—
80C2×#41×C31—21no—
81C2×#41×C31—21no—
82C2×#41×C31—21no—
83C2×#41×C31—22no—
84C2×#41×C31—22no—
85C2×#41×C31—22no—
86C2×#41×C31—22no—
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×C31—41no—
94C2×#41×C31—41no—
95C2×#41×C31D411yescharacteristic, complemented
96C2×#41×C31D411yescharacteristic, complemented
97C2×#41×C31C2311yescharacteristic
98C2×#41×C31C2311yescharacteristic
99C2×#41×C31C2311yescharacteristic
100C22×Q8×C31D411yescharacteristic, complemented
101C22×Q8×C31C2311yescharacteristic
102C22×D4×C31—21no—
103C22×D4×C31—22no—
104C22×D4×C31—22no—
105C22×D4×C31—21no—
106C22×D4×C31—21no—
107C22×D4×C31—21no—
108C22×D4×C31—22no—
109C22×D4×C31D412yes—
110C22×D4×C31D411yescharacteristic, complemented
111C22×D4×C31C2311yescharacteristic
112C22×D4×C31C2311yescharacteristic
113C23×C4×C31—21no—
114C23×C4×C31—21no—
115C23×C4×C31C2311yescharacteristic
116C31×#137—28no—
117C31×#137—22no—
118C31×#137—22no—
119C31×#137—22no—
120C31×#137—22no—
121C31×#137—41no—
122C31×#137D414yescomplemented
123C31×AGL(1,ℤ/8)—28no—
124C31×AGL(1,ℤ/8)—22no—
125C31×AGL(1,ℤ/8)—22no—
126C31×AGL(1,ℤ/8)—22no—
127C31×AGL(1,ℤ/8)—22no—
128C31×AGL(1,ℤ/8)—41no—
129C31×AGL(1,ℤ/8)D414yescomplemented
130C31×#135—28no—
131C31×#135—28no—
132C2×Q16×C31—21no—
133C2×Q16×C31—21no—
134C2×Q16×C31—21no—
135C2×SD16×C31—21no—
136C2×SD16×C31—21no—
137C2×SD16×C31—21no—
138C2×SD16×C31—21no—
139C2×SD16×C31—21no—
140C2×SD16×C31—21no—
141C2×D8×C31—21no—
142C2×D8×C31—21no—
143C2×D8×C31—21no—
144C2×M16×C31—21no—
145C2×M16×C31—22no—
146C2×M16×C31—22no—
147C2×M16×C31C2311yescharacteristic
148C2×M16×C31C2311yescharacteristic
149C2×M16×C31C2311yescharacteristic
150C2×M16×C31C2311yescharacteristic
151C22×C8×C31—21no—
152C31×#127—22no—
153C31×#127—21no—
154C31×#127—22no—
155C31×#127—41no—
156C31×#124—22no—
157C31×#124—21no—
158C31×#124—22no—
159C31×#124—41no—
160C31×#123—22no—
161C31×#123—21no—
162C31×C22⋊Q8—22no—
163C31×C22⋊Q8—21no—
164C31×C22⋊Q8—21no—
165C31×C22⋊Q8D411yescharacteristic, complemented
166C31×C22⋊Q8D411yescharacteristic, complemented
167C31×#121—22no—
168C31×#121—22no—
169C31×#121—22no—
170C31×#121—22no—
171C31×#121—22no—
172C31×#121—21no—
173C31×#121—21no—
174C31×#121—21no—
175C31×#121—21no—
176C31×#121—21no—
177C31×#121—21no—
178C31×#121—22no—
179C31×#121—21no—
180C31×#121—21no—
181C31×#121D411yescharacteristic, complemented
182C31×#121D411yescharacteristic, complemented
183C31×#120—22no—
184C31×#120—22no—
185C31×#120—22no—
186C31×#120—21no—
187C31×#120—22no—
188C4×Q8×C31—21no—
189C4×D4×C31—22no—
190C4×D4×C31—22no—
191C4×D4×C31—21no—
192C4×D4×C31—22no—
193C4×D4×C31—21no—
194C4×D4×C31—21no—
195C31×#117—21no—
196C31×#117C2311yescharacteristic
197C2×C4⋊C4×C31—21no—
198C2×C4⋊C4×C31C2311yescharacteristic
199C2×C22⋊C4×C31—22no—
200C2×C22⋊C4×C31—22no—
201C2×C22⋊C4×C31—21no—
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×#100—22no—
217C31×#100—22no—
218C31×C22⋊C8—21no—
219C31×C22⋊C8—21no—
220C31×#95—21no—
221C31×#95—22no—
222C24×C31—22no—
223C24×C31—21no—
224C24×C31—21no—
225C24×C31C2×D412yes—
226C24×C31C2×D411yescharacteristic
227#41×C31—21no—
228#41×C31—21no—
229#41×C31—24no—
230#41×C31—24no—
231#41×C31—22no—
232#41×C31—22no—
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—21no—
240#41×C31—21no—
241#41×C31—42no—
242#41×C31—42no—
243#41×C31—41no—
244#41×C31—41no—
245#41×C31—42no—
246#41×C31—42no—
247#41×C31—42no—
248#41×C31—42no—
249#41×C31—42no—
250#41×C31—42no—
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—21no—
260C2×Q8×C31—21no—
261C2×Q8×C31—22no—
262C2×Q8×C31—21no—
263C2×Q8×C31—21no—
264C2×Q8×C31—21no—
265C2×Q8×C31—21no—
266C2×Q8×C31—41no—
267C2×Q8×C31C2×D411yescharacteristic
268C2×Q8×C31C2×D411yescharacteristic
269C2×Q8×C31C2×D411yescharacteristic
270C2×Q8×C31C2×D412yescomplemented
271C2×D4×C31—21no—
272C2×D4×C31—22no—
273C2×D4×C31—22no—
274C2×D4×C31—22no—
275C2×D4×C31—22no—
276C2×D4×C31—21no—
277C2×D4×C31—21no—
278C2×D4×C31—21no—
279C2×D4×C31—21no—
280C2×D4×C31—21no—
281C2×D4×C31—22no—
282C2×D4×C31—22no—
283C2×D4×C31—22no—
284C2×D4×C31—21no—
285C2×D4×C31—22no—
286C2×D4×C31—21no—
287C2×D4×C31—21no—
288C2×D4×C31—21no—
289C2×D4×C31—21no—
290C2×D4×C31—21no—
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—44no—
303C2×D4×C31—42no—
304C2×D4×C31—42no—
305C2×D4×C31—44no—
306C2×D4×C31—44no—
307C2×D4×C31—42no—
308C2×D4×C31—42no—
309C2×D4×C31—41no—
310C2×D4×C31—41no—
311C2×D4×C31—42no—
312C2×D4×C31—44no—
313C2×D4×C31—82no—
314C2×D4×C31—82no—
315C2×D4×C31—84no—
316C2×D4×C31C2×D411yescharacteristic
317C2×D4×C31C2×D411yescharacteristic
318C2×D4×C31C2×D411yescharacteristic
319C2×D4×C31C2×D412yescomplemented
320C22×C4×C31—21no—
321C22×C4×C31—21no—
322C22×C4×C31—21no—
323C22×C4×C31—21no—
324C22×C4×C31—21no—
325C22×C4×C31—22no—
326C22×C4×C31—21no—
327C22×C4×C31—21no—
328C22×C4×C31—21no—
329C22×C4×C31—22no—
330C22×C4×C31—21no—
331C22×C4×C31—21no—
332C22×C4×C31—21no—
333C22×C4×C31—21no—
334C22×C4×C31—21no—
335C22×C4×C31—42no—
336C22×C4×C31—42no—
337C22×C4×C31—42no—
338C22×C4×C31—42no—
339C22×C4×C31—41no—
340C22×C4×C31—41no—
341C22×C4×C31C2×D411yescharacteristic
342C22×C4×C31C2×D411yescharacteristic
343C22×C4×C31C2×D411yescharacteristic
344C22×C4×C31C2×D411yescharacteristic
345C22×C4×C31C2×D411yescharacteristic
346C22×C4×C31C2×D412yes—
347C22×C4×C31C2411yescharacteristic
348Q16×C31—24no—
349Q16×C31—24no—
350Q16×C31—42no—
351SD16×C31—24no—
352SD16×C31—24no—
353SD16×C31—24no—
354SD16×C31—24no—
355SD16×C31—42no—
356SD16×C31—42no—
357D8×C31—24no—
358D8×C31—24no—
359D8×C31—42no—
360M16×C31—24no—
361M16×C31—21no—
362M16×C31—21no—
363M16×C31—21no—
364M16×C31—21no—
365M16×C31—21no—
366M16×C31—21no—
367M16×C31C2×D412yescomplemented
368M16×C31C2×D412yescomplemented
369C2×C8×C31—24no—
370C2×C8×C31—21no—
371C2×C8×C31—21no—
372C2×C8×C31—21no—
373C2×C8×C31—21no—
374C4⋊C4×C31—22no—
375C4⋊C4×C31—22no—
376C4⋊C4×C31—21no—
377C4⋊C4×C31—21no—
378C4⋊C4×C31—21no—
379C4⋊C4×C31—21no—
380C4⋊C4×C31C2×D411yescharacteristic
381C4⋊C4×C31C2×D411yescharacteristic
382C22⋊C4×C31—22no—
383C22⋊C4×C31—22no—
384C22⋊C4×C31—22no—
385C22⋊C4×C31—22no—
386C22⋊C4×C31—22no—
387C22⋊C4×C31—21no—
388C22⋊C4×C31—21no—
389C22⋊C4×C31—21no—
390C22⋊C4×C31—21no—
391C22⋊C4×C31—22no—
392C22⋊C4×C31—22no—
393C22⋊C4×C31—21no—
394C22⋊C4×C31—44no—
395C22⋊C4×C31—42no—
396C22⋊C4×C31—82no—
397C42×C31—22no—
398C42×C31—21no—
399C42×C31—21no—
400C42×C31—21no—
401C42×C31—21no—
402C42×C31—21no—
403#23878C3111yesmaximal, characteristic, direct product factor, Sylow
404C23×C31—21no—
405C23×C31—21no—
406C23×C31—21no—
407C23×C31—22no—
408C23×C31—21no—
409C23×C31—21no—
410C23×C31—22no—
411C23×C31—22no—
412C23×C31—22no—
413C23×C31—41no—
414C23×C31—41no—
415C23×C31—42no—
416C23×C31—42no—
417C23×C31—42no—
418C23×C31—42no—
419C23×C31—44no—
420C23×C31—42no—
421C23×C31—42no—
422C23×C31—41no—
423C23×C31—41no—
424C23×C31—81no—
425C23×C31—82no—
426C23×C31—82no—
427C23×C31#12011yescharacteristic
428C23×C31#12011yescharacteristic
429C23×C31C22×D411yescharacteristic
430Q8×C31—21no—
431Q8×C31—21no—
432Q8×C31—22no—
433Q8×C31—21no—
434Q8×C31—21no—
435Q8×C31—22no—
436Q8×C31—21no—
437Q8×C31—42no—
438Q8×C31—41no—
439Q8×C31—41no—
440Q8×C31#12012yes—
441D4×C31—22no—
442D4×C31—22no—
443D4×C31—21no—
444D4×C31—22no—
445D4×C31—21no—
446D4×C31—21no—
447D4×C31—21no—
448D4×C31—22no—
449D4×C31—21no—
450D4×C31—42no—
451D4×C31—42no—
452D4×C31—44no—
453D4×C31—42no—
454D4×C31—44no—
455D4×C31—44no—
456D4×C31—42no—
457D4×C31—44no—
458D4×C31—44no—
459D4×C31—41no—
460D4×C31—41no—
461D4×C31—41no—
462D4×C31—41no—
463D4×C31—41no—
464D4×C31—41no—
465D4×C31—41no—
466D4×C31—41no—
467D4×C31—41no—
468D4×C31—41no—
469D4×C31—81no—
470D4×C31—82no—
471D4×C31—82no—
472D4×C31—82no—
473D4×C31—82no—
474D4×C31—88no—
475D4×C31#12012yes—
476C2×C4×C31—21no—
477C2×C4×C31—21no—
478C2×C4×C31—21no—
479C2×C4×C31—21no—
480C2×C4×C31—21no—
481C2×C4×C31—21no—
482C2×C4×C31—21no—
483C2×C4×C31—21no—
484C2×C4×C31—21no—
485C2×C4×C31—21no—
486C2×C4×C31—21no—
487C2×C4×C31—22no—
488C2×C4×C31—22no—
489C2×C4×C31—22no—
490C2×C4×C31—21no—
491C2×C4×C31—22no—
492C2×C4×C31—21no—
493C2×C4×C31—21no—
494C2×C4×C31—21no—
495C2×C4×C31—22no—
496C2×C4×C31—42no—
497C2×C4×C31—42no—
498C2×C4×C31—42no—
499C2×C4×C31—44no—
500C2×C4×C31—44no—
501C2×C4×C31—44no—
502C2×C4×C31—41no—
503C2×C4×C31—41no—
504C2×C4×C31—41no—
505C2×C4×C31—41no—
506C2×C4×C31—41no—
507C2×C4×C31—41no—
508C2×C4×C31—41no—
509C2×C4×C31—41no—
510C2×C4×C31—42no—
511C2×C4×C31—41no—
512C2×C4×C31—41no—
513C2×C4×C31—41no—
514C2×C4×C31—82no—
515C2×C4×C31#12011yescharacteristic
516C2×C4×C31#12011yescharacteristic
517C2×C4×C31C22×D411yescharacteristic
518C2×C4×C31C22×D411yescharacteristic
519C2×C4×C31C22×D411yescharacteristic
520C2×C4×C31C22×D411yescharacteristic
521C2×C4×C31H(5,𝔽2)11yescharacteristic
522C2×C4×C31H(5,𝔽2)11yescharacteristic
523C8×C31—22no—
524C8×C31—22no—
525C8×C31—41no—
526C8×C31—41no—
527C2×#575C2×C3111yescharacteristic, complemented
528#3488C2×C3111yescharacteristic, complemented
529C2×#455C2×C3111yescharacteristic, complemented
530C2×#453C2×C3111yescharacteristic, complemented
531#3005C2×C3111yescharacteristic, complemented
532#2431C2×C3111yescharacteristic, complemented
533#2007C2×C3111yescharacteristic, complemented
534#2006C2×C3111yescharacteristic, complemented
535#2004C2×C3111yescharacteristic, complemented
536#2002C2×C3111yescharacteristic, complemented
537#1900C2×C3111yescharacteristic, complemented
538#1883C2×C3111yescharacteristic, complemented
539#1882C2×C3111yescharacteristic, complemented
540#1871C2×C3111yescharacteristic, complemented
541#1789C2×C3111yescharacteristic, complemented
542C22×C31—21no—
543C22×C31—21no—
544C22×C31—21no—
545C22×C31—21no—
546C22×C31—22no—
547C22×C31—21no—
548C22×C31—21no—
549C22×C31—21no—
550C22×C31—21no—
551C22×C31—44no—
552C22×C31—41no—
553C22×C31—41no—
554C22×C31—41no—
555C22×C31—42no—
556C22×C31—41no—
557C22×C31—42no—
558C22×C31—41no—
559C22×C31—42no—
560C22×C31—41no—
561C22×C31—42no—
562C22×C31—41no—
563C22×C31—41no—
564C22×C31—81no—
565C22×C31—81no—
566C22×C31—82no—
567C22×C31—82no—
568C22×C31—82no—
569C22×C31—84no—
570C22×C31—81no—
571C22×C31—81no—
572C22×C31—164no—
573C22×C31C2×#12011yescharacteristic
574C22×C31D4211yescharacteristic
575C22×C31D4211yescharacteristic
576C4×C31—21no—
577C4×C31—21no—
578C4×C31—22no—
579C4×C31—42no—
580C4×C31—41no—
581C4×C31—41no—
582C4×C31—42no—
583C4×C31—41no—
584C4×C31—42no—
585C4×C31—41no—
586C4×C31—81no—
587C4×C31C2×#12011yescharacteristic
588C4×C31#53411yescharacteristic
589C4×C31D4211yescharacteristic
590C4×C31D4211yescharacteristic
591C2×H(5,𝔽2)C22×C3111yescharacteristic
592C22×#41C22×C3111yescharacteristic
593C22×#41C22×C3111yescharacteristic, complemented
594#575—24no—
595#575—24no—
596C2×#137—21no—
597C2×#137C22×C3111yescharacteristic
598C2×#137C22×C3111yescharacteristic, complemented
599C2×#137C22×C3111yescharacteristic, complemented
600C2×AGL(1,ℤ/8)—21no—
601C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
602C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
603C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
604C2×#135—21no—
605C2×#135—21no—
606C22×M16C22×C3111yescharacteristic, complemented
607#550—21no—
608#548—21no—
609#546—21no—
610#546—22no—
611D42—22no—
612D42—21no—
613#537—21no—
614#537C22×C3111yescharacteristic
615#535—21no—
616#535C22×C3111yescharacteristic
617C2×#127C22×C3111yescharacteristic, complemented
618C2×#124C22×C3111yescharacteristic, complemented
619#525—21no—
620#525C22×C3111yescharacteristic
621C2×#121—21no—
622C2×#121C22×C3111yescharacteristic
623#520C22×C3111yescharacteristic
624#455—24no—
625#453—24no—
626#452—21no—
627#452—21no—
628#449—21no—
629#449—21no—
630C2×#104C22×C3111yescharacteristic
631C2×#104C22×C3111yescharacteristic
632C2×#104C22×C3111yescharacteristic, complemented
633C2×#104C22×C3111yescharacteristic, complemented
634C2×#104C22×C3111yescharacteristic, complemented
635C2×#104C22×C3111yescharacteristic, complemented
636#419C22×C3111yescharacteristic, complemented
637#418C22×C3111yescharacteristic, complemented
638C2×#100C22×C3111yescharacteristic, complemented
639C2×#100C22×C3111yescharacteristic, complemented
640#407C22×C3111yescharacteristic, complemented
641#392—22no—
642#391C22×C3111yescharacteristic, complemented
643#390C22×C3111yescharacteristic, complemented
644#386—22no—
645C4×C22⋊C4C22×C3111yescharacteristic, complemented
646#343C22×C3111yescharacteristic, complemented
647#343C22×C3111yescharacteristic, complemented
648#339C22×C3111yescharacteristic, complemented
649#339C22×C3111yescharacteristic, complemented
650C2×C31—21no—
651C2×C31—21no—
652C2×C31—41no—
653C2×C31—41no—
654C2×C31—42no—
655C2×C31—82no—
656C2×C31—81no—
657C2×C31—82no—
658C2×C31—81no—
659C2×C31#240311yescharacteristic
660C2×C31#301811yescharacteristic
661C2×C31#301911yescharacteristic
662H(5,𝔽2)—22no—
663H(5,𝔽2)—22no—
664H(5,𝔽2)—41no—
665H(5,𝔽2)—41no—
666C2×#41—21no—
667C2×#41—21no—
668C2×#41—21no—
669C2×#41—21no—
670C2×#41—22no—
671C2×#41—22no—
672C2×#41—22no—
673C2×#41—22no—
674C2×#41—21no—
675C2×#41—21no—
676C2×#41—21no—
677C2×#41—21no—
678C2×#41—41no—
679C2×#41—41no—
680C2×#41—41no—
681C2×#41—41no—
682C2×#41D4×C3111yescharacteristic, complemented
683C2×#41D4×C3111yescharacteristic, complemented
684C2×#41C23×C3111yescharacteristic
685C2×#41C23×C3111yescharacteristic
686C2×#41C23×C3111yescharacteristic
687C22×Q8D4×C3111yescharacteristic, complemented
688C22×Q8C23×C3111yescharacteristic
689C22×D4—21no—
690C22×D4—22no—
691C22×D4—22no—
692C22×D4—21no—
693C22×D4—21no—
694C22×D4—21no—
695C22×D4—22no—
696C22×D4D4×C3112yes—
697C22×D4D4×C3111yescharacteristic, complemented
698C22×D4C23×C3111yescharacteristic
699C22×D4C23×C3111yescharacteristic
700C23×C4—21no—
701C23×C4—21no—
702C23×C4C23×C3111yescharacteristic
703#137—28no—
704#137—22no—
705#137—22no—
706#137—22no—
707#137—22no—
708#137—41no—
709#137D4×C3114yescomplemented
710AGL(1,ℤ/8)—28no—
711AGL(1,ℤ/8)—22no—
712AGL(1,ℤ/8)—22no—
713AGL(1,ℤ/8)—22no—
714AGL(1,ℤ/8)—22no—
715AGL(1,ℤ/8)—41no—
716AGL(1,ℤ/8)D4×C3114yescomplemented
717#135—28no—
718#135—28no—
719C2×Q16—21no—
720C2×Q16—21no—
721C2×Q16—21no—
722C2×SD16—21no—
723C2×SD16—21no—
724C2×SD16—21no—
725C2×SD16—21no—
726C2×SD16—21no—
727C2×SD16—21no—
728C2×D8—21no—
729C2×D8—21no—
730C2×D8—21no—
731C2×M16—21no—
732C2×M16—22no—
733C2×M16—22no—
734C2×M16C23×C3111yescharacteristic
735C2×M16C23×C3111yescharacteristic
736C2×M16C23×C3111yescharacteristic
737C2×M16C23×C3111yescharacteristic
738C22×C8—21no—
739#127—22no—
740#127—21no—
741#127—22no—
742#127—41no—
743#124—22no—
744#124—21no—
745#124—22no—
746#124—41no—
747#123—22no—
748#123—21no—
749C22⋊Q8—22no—
750C22⋊Q8—21no—
751C22⋊Q8—21no—
752C22⋊Q8D4×C3111yescharacteristic, complemented
753C22⋊Q8D4×C3111yescharacteristic, complemented
754#121—22no—
755#121—22no—
756#121—22no—
757#121—22no—
758#121—22no—
759#121—21no—
760#121—21no—
761#121—21no—
762#121—21no—
763#121—21no—
764#121—21no—
765#121—22no—
766#121—21no—
767#121—21no—
768#121D4×C3111yescharacteristic, complemented
769#121D4×C3111yescharacteristic, complemented
770#120—22no—
771#120—22no—
772#120—22no—
773#120—21no—
774#120—22no—
775C4×Q8—21no—
776C4×D4—22no—
777C4×D4—22no—
778C4×D4—21no—
779C4×D4—22no—
780C4×D4—21no—
781C4×D4—21no—
782#117—21no—
783#117C23×C3111yescharacteristic
784C2×C4⋊C4—21no—
785C2×C4⋊C4C23×C3111yescharacteristic
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—21no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4D4×C3112yes—
791C2×C42C23×C3111yescharacteristic
792C2×C42C23×C3111yescharacteristic
793#104—22no—
794#104—22no—
795#104—22no—
796#104—22no—
797#104—41no—
798#104—41no—
799#103—21no—
800#103—21no—
801#102—21no—
802#102—21no—
803#100—22no—
804#100—22no—
805C22⋊C8—21no—
806C22⋊C8—21no—
807#95—21no—
808#95—22no—
809C31#2387811yescharacteristic, direct product factor, Sylow
810C24—22no—
811C24—21no—
812C24—21no—
813C24C2×D4×C3112yes—
814C24C2×D4×C3111yescharacteristic
815#41—21no—
816#41—21no—
817#41—24no—
818#41—24no—
819#41—22no—
820#41—22no—
821#41—21no—
822#41—21no—
823#41—21no—
824#41—21no—
825#41—21no—
826#41—21no—
827#41—21no—
828#41—21no—
829#41—42no—
830#41—42no—
831#41—41no—
832#41—41no—
833#41—42no—
834#41—42no—
835#41—42no—
836#41—42no—
837#41—42no—
838#41—42no—
839#41—42no—
840#41—42no—
841#41—42no—
842#41—42no—
843#41—42no—
844#41—42no—
845#41C2×D4×C3112yes—
846#41C2×D4×C3112yes—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—22no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—41no—
855C2×Q8C2×D4×C3111yescharacteristic
856C2×Q8C2×D4×C3111yescharacteristic
857C2×Q8C2×D4×C3111yescharacteristic
858C2×Q8C2×D4×C3112yescomplemented
859C2×D4—21no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—21no—
873C2×D4—22no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—41no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—42no—
900C2×D4—44no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—84no—
904C2×D4C2×D4×C3111yescharacteristic
905C2×D4C2×D4×C3111yescharacteristic
906C2×D4C2×D4×C3111yescharacteristic
907C2×D4C2×D4×C3112yescomplemented
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—22no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—22no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4C2×D4×C3111yescharacteristic
930C22×C4C2×D4×C3111yescharacteristic
931C22×C4C2×D4×C3111yescharacteristic
932C22×C4C2×D4×C3111yescharacteristic
933C22×C4C2×D4×C3111yescharacteristic
934C22×C4C2×D4×C3112yes—
935C22×C4C24×C3111yescharacteristic
936Q16—24no—
937Q16—24no—
938Q16—42no—
939SD16—24no—
940SD16—24no—
941SD16—24no—
942SD16—24no—
943SD16—42no—
944SD16—42no—
945D8—24no—
946D8—24no—
947D8—42no—
948M16—24no—
949M16—21no—
950M16—21no—
951M16—21no—
952M16—21no—
953M16—21no—
954M16—21no—
955M16C2×D4×C3112yescomplemented
956M16C2×D4×C3112yescomplemented
957C2×C8—24no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4C2×D4×C3111yescharacteristic
969C4⋊C4C2×D4×C3111yescharacteristic
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—21no—
976C22⋊C4—21no—
977C22⋊C4—21no—
978C22⋊C4—21no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—21no—
982C22⋊C4—44no—
983C22⋊C4—42no—
984C22⋊C4—82no—
985C42—22no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—22no—
995C23—21no—
996C23—21no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—44no—
1007C23—42no—
1008C23—42no—
1009C23—41no—
1010C23—41no—
1011C23—81no—
1012C23—82no—
1013C23—82no—
1014C23C31×#12011yescharacteristic
1015C23C31×#12011yescharacteristic
1016C23C22×D4×C3111yescharacteristic
1017Q8—21no—
1018Q8—21no—
1019Q8—22no—
1020Q8—21no—
1021Q8—21no—
1022Q8—22no—
1023Q8—21no—
1024Q8—42no—
1025Q8—41no—
1026Q8—41no—
1027Q8C31×#12012yes—
1028D4—22no—
1029D4—22no—
1030D4—21no—
1031D4—22no—
1032D4—21no—
1033D4—21no—
1034D4—21no—
1035D4—22no—
1036D4—21no—
1037D4—42no—
1038D4—42no—
1039D4—44no—
1040D4—42no—
1041D4—44no—
1042D4—44no—
1043D4—42no—
1044D4—44no—
1045D4—44no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—81no—
1057D4—82no—
1058D4—82no—
1059D4—82no—
1060D4—82no—
1061D4—88no—
1062D4C31×#12012yes—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—42no—
1084C2×C4—42no—
1085C2×C4—42no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—42no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—82no—
1102C2×C4C31×#12011yescharacteristic
1103C2×C4C31×#12011yescharacteristic
1104C2×C4C22×D4×C3111yescharacteristic
1105C2×C4C22×D4×C3111yescharacteristic
1106C2×C4C22×D4×C3111yescharacteristic
1107C2×C4C22×D4×C3111yescharacteristic
1108C2×C4C31×H(5,𝔽2)11yescharacteristic
1109C2×C4C31×H(5,𝔽2)11yescharacteristic
1110C8—22no—
1111C8—22no—
1112C8—41no—
1113C8—41no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—22no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—44no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22—42no—
1130C22—41no—
1131C22—42no—
1132C22—41no—
1133C22—42no—
1134C22—41no—
1135C22—41no—
1136C22—81no—
1137C22—81no—
1138C22—82no—
1139C22—82no—
1140C22—82no—
1141C22—84no—
1142C22—81no—
1143C22—81no—
1144C22—164no—
1145C22C2×C31×#12011yescharacteristic
1146C22D42×C3111yescharacteristic
1147C22D42×C3111yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—22no—
1151C4—42no—
1152C4—41no—
1153C4—41no—
1154C4—42no—
1155C4—41no—
1156C4—42no—
1157C4—41no—
1158C4—81no—
1159C4C2×C31×#12011yescharacteristic
1160C4C31×#53411yescharacteristic
1161C4D42×C3111yescharacteristic
1162C4D42×C3111yescharacteristic
1163C2—21no—
1164C2—21no—
1165C2—41no—
1166C2—41no—
1167C2—42no—
1168C2—82no—
1169C2—81no—
1170C2—82no—
1171C2—81no—
1172C2C31×#240311yescharacteristic
1173C2C31×#301811yescharacteristic
1174C2C31×#301911yescharacteristic
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×#3488C2semidirect
3. C2×C31×#455C2semidirect
4. C2×C31×#453C2semidirect
5. C31×#3005C2semidirect
6. C31×#2431C2semidirect
7. C31×#2007C2semidirect
8. C31×#2006C2semidirect
9. C31×#2004C2semidirect
10. C31×#2002C2semidirect
11. C31×#1900C2semidirect
12. C31×#1883C2semidirect
13. C31×#1882C2semidirect
14. C31×#1871C2semidirect
15. C31×#1789C2semidirect
18. C22×#41×C31C22semidirect
23. C2×C31×#137C22semidirect
24. C2×C31×#137C22semidirect
27. C2×C31×AGL(1,ℤ/8)C22semidirect
28. C2×C31×AGL(1,ℤ/8)C22semidirect
31. C22×M16×C31C22semidirect
42. C2×C31×#127C22semidirect
43. C2×C31×#124C22semidirect
57. C2×C31×#104C22semidirect
58. C2×C31×#104C22semidirect
59. C2×C31×#104C22semidirect
60. C2×C31×#104C22semidirect
61. C31×#419C22semidirect
62. C31×#418C22semidirect
63. C2×C31×#100C22semidirect
64. C2×C31×#100C22semidirect
65. C31×#407C22semidirect
67. C31×#391C22semidirect
68. C31×#390C22semidirect
70. C4×C22⋊C4×C31C22semidirect
71. C31×#343C22semidirect
72. C31×#343C22semidirect
73. C31×#339C22semidirect
74. C31×#339C22semidirect
95. C2×#41×C31D4semidirect
96. C2×#41×C31D4semidirect
100. C22×Q8×C31D4semidirect
110. C22×D4×C31D4semidirect
122. C31×#137D4semidirect
129. C31×AGL(1,ℤ/8)D4semidirect
165. C31×C22⋊Q8D4semidirect
166. C31×C22⋊Q8D4semidirect
181. C31×#121D4semidirect
182. C31×#121D4semidirect
270. C2×Q8×C31C2×D4semidirect
319. C2×D4×C31C2×D4semidirect
367. M16×C31C2×D4semidirect
368. M16×C31C2×D4semidirect
403. #23878C31direct (N × H)
527. C2×#575C2×C31semidirect
528. #3488C2×C31semidirect
529. C2×#455C2×C31semidirect
530. C2×#453C2×C31semidirect
531. #3005C2×C31semidirect
532. #2431C2×C31semidirect
533. #2007C2×C31semidirect
534. #2006C2×C31semidirect
535. #2004C2×C31semidirect
536. #2002C2×C31semidirect
537. #1900C2×C31semidirect
538. #1883C2×C31semidirect
539. #1882C2×C31semidirect
540. #1871C2×C31semidirect
541. #1789C2×C31semidirect
593. C22×#41C22×C31semidirect
598. C2×#137C22×C31semidirect
599. C2×#137C22×C31semidirect
602. C2×AGL(1,ℤ/8)C22×C31semidirect
603. C2×AGL(1,ℤ/8)C22×C31semidirect
606. C22×M16C22×C31semidirect
617. C2×#127C22×C31semidirect
618. C2×#124C22×C31semidirect
632. C2×#104C22×C31semidirect
633. C2×#104C22×C31semidirect
634. C2×#104C22×C31semidirect
635. C2×#104C22×C31semidirect
636. #419C22×C31semidirect
637. #418C22×C31semidirect
638. C2×#100C22×C31semidirect
639. C2×#100C22×C31semidirect
640. #407C22×C31semidirect
642. #391C22×C31semidirect
643. #390C22×C31semidirect
645. C4×C22⋊C4C22×C31semidirect
646. #343C22×C31semidirect
647. #343C22×C31semidirect
648. #339C22×C31semidirect
649. #339C22×C31semidirect
682. C2×#41D4×C31semidirect
683. C2×#41D4×C31semidirect
687. C22×Q8D4×C31semidirect
697. C22×D4D4×C31semidirect
709. #137D4×C31semidirect
716. AGL(1,ℤ/8)D4×C31semidirect
752. C22⋊Q8D4×C31semidirect
753. C22⋊Q8D4×C31semidirect
768. #121D4×C31semidirect
769. #121D4×C31semidirect
809. C31#23878direct (N × H)
858. C2×Q8C2×D4×C31semidirect
907. C2×D4C2×D4×C31semidirect
955. M16C2×D4×C31semidirect
956. M16C2×D4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5752
C31×#34882
C2×C31×#4552
C2×C31×#4532
C31×#30052
C31×#24312
C31×#20072
C31×#20062
C31×#20042
C31×#20022
C31×#19002
C31×#18832
C31×#18822
C31×#18712
C31×#17892
#2387831