Finite Group Databasebeta

← C31×#25080 #21481839

Subgroups — C31×#25080 #21481839

Order 7936.

1356 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#465C211yesmaximal, characteristic, complemented
2C2×C31×#460C211yesmaximal, characteristic, complemented
3C2×C31×#450C211yesmaximal, characteristic, complemented
4C22×C31×#102C211yesmaximal, characteristic, complemented
5C31×#2433C211yesmaximal, characteristic
6C31×#2360C211yesmaximal, characteristic, complemented
7C31×#2065C211yesmaximal, characteristic, complemented
8C31×#2055C211yesmaximal, characteristic, complemented
9C31×#2041C211yesmaximal, characteristic, complemented
10C31×#2014C211yesmaximal, characteristic, complemented
11C31×#1982C211yesmaximal, characteristic, complemented
12C31×#1926C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic, complemented
14C31×#1874C211yesmaximal, characteristic, complemented
15C31×#1850C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic, complemented
20C23×C8×C31C2211yescharacteristic
21C2×C31×#127C2211yescharacteristic
22C2×C31×#127C2211yescharacteristic
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C31×#120—21no—
26C2×C31×#120—21no—
27C2×C4×Q8×C31C2211yescharacteristic, complemented
28C22×C4⋊C4×C31C2211yescharacteristic
29C31×#465—24no—
30C31×#460—24no—
31C31×#450—24no—
32C2×C31×#106C2211yescharacteristic, complemented
33C2×C31×C4⋊C8C2211yescharacteristic, complemented
34C2×C31×C4⋊C8C2211yescharacteristic, complemented
35C2×C31×#103C2211yescharacteristic, complemented
36C2×C31×#102—24no—
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic, complemented
44C2×C31×#102C2211yescharacteristic, complemented
45C2×C31×#102C2211yescharacteristic, complemented
46C2×C31×C22⋊C8C2211yescharacteristic
47C31×#392—21no—
48C31×#392—21no—
49C31×#391C2211yescharacteristic, complemented
50C31×#390C2211yescharacteristic
51C31×#390C2211yescharacteristic
52C31×#389—21no—
53C31×#389C2211yescharacteristic, complemented
54C31×#387—21no—
55C31×#385—21no—
56C4×C4⋊C4×C31C2211yescharacteristic, complemented
57C4×C22⋊C4×C31—21no—
58C4×C22⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#336C2211yescharacteristic, complemented
62C31×#336C2211yescharacteristic, complemented
63C25×C31—21no—
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—21no—
68C22×D4×C31—22no—
69C22×D4×C31—21no—
70C22×D4×C31—21no—
71C22×D4×C31—21no—
72C22×D4×C31—21no—
73C22×D4×C31—21no—
74C22×D4×C31—22no—
75C22×D4×C31—41no—
76C22×D4×C31—41no—
77C22×D4×C31C2311yescharacteristic
78C22×D4×C31C2311yescharacteristic
79C22×D4×C31C2311yescharacteristic
80C23×C4×C31—21no—
81C23×C4×C31C2311yescharacteristic
82C2×SD16×C31—22no—
83C2×SD16×C31—22no—
84C2×SD16×C31—22no—
85C2×SD16×C31—22no—
86C2×SD16×C31—22no—
87C2×SD16×C31—22no—
88C2×SD16×C31—41no—
89C2×SD16×C31—41no—
90C2×SD16×C31—41no—
91C22×C8×C31—22no—
92C22×C8×C31—22no—
93C22×C8×C31—41no—
94C22×C8×C31C2311yescharacteristic
95C22×C8×C31C2311yescharacteristic
96C22×C8×C31C2311yescharacteristic
97C22×C8×C31C2311yescharacteristic
98C31×#127—22no—
99C31×#127—22no—
100C31×#127—41no—
101C31×#127—41no—
102C31×C22⋊Q8—22no—
103C31×C22⋊Q8D414yescomplemented
104C31×#121—22no—
105C31×#121—22no—
106C31×#120—44no—
107C31×#120—44no—
108C4×Q8×C31—22no—
109C4×Q8×C31—41no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—22no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31—21no—
115C2×C4⋊C4×C31—41no—
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C4⋊C4×C31C2311yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31D411yescharacteristic
127C2×C22⋊C4×C31D411yescharacteristic
128C2×C42×C31—21no—
129C2×C42×C31—21no—
130C2×C42×C31C2311yescharacteristic
131C2×C42×C31C2311yescharacteristic
132C31×#106—22no—
133C31×C4⋊C8—22no—
134C31×C4⋊C8—41no—
135C31×#103—22no—
136C31×#102—22no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—41no—
144C31×#102D414yescomplemented
145C31×C22⋊C8—22no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95—21no—
149C31×#95—21no—
150C31×#95D411yescharacteristic
151C31×#95D411yescharacteristic
152C24×C31—21no—
153C24×C31—21no—
154C24×C31—21no—
155C24×C31—42no—
156C24×C31—42no—
157C24×C31—42no—
158C24×C31—42no—
159C24×C31—42no—
160C24×C31—81no—
161C24×C31—81no—
162C24×C31C2×D411yescharacteristic
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31C2×D412yes—
169C2×D4×C31—28no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—21no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—44no—
187C2×D4×C31—44no—
188C2×D4×C31—42no—
189C2×D4×C31—42no—
190C2×D4×C31—44no—
191C2×D4×C31—42no—
192C2×D4×C31—42no—
193C2×D4×C31—42no—
194C2×D4×C31—42no—
195C2×D4×C31—42no—
196C2×D4×C31—42no—
197C2×D4×C31—42no—
198C2×D4×C31—42no—
199C2×D4×C31—42no—
200C2×D4×C31—42no—
201C2×D4×C31—42no—
202C2×D4×C31—42no—
203C2×D4×C31—81no—
204C2×D4×C31—81no—
205C2×D4×C31—81no—
206C2×D4×C31—81no—
207C2×D4×C31C2×D412yes—
208C2×D4×C31#4112yes—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—42no—
219C22×C4×C31—42no—
220C22×C4×C31—81no—
221C22×C4×C31C2×D411yescharacteristic
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31C2×D411yescharacteristic
224C22×C4×C31C2×D412yes—
225C22×C4×C31C2×D411yescharacteristic
226C22×C4×C31C2×D411yescharacteristic
227C22×C4×C31#4112yes—
228C22×C4×C31C2411yescharacteristic
229SD16×C31—44no—
230SD16×C31—44no—
231SD16×C31—44no—
232C2×C8×C31—21no—
233C2×C8×C31—21no—
234C2×C8×C31—21no—
235C2×C8×C31—21no—
236C2×C8×C31—21no—
237C2×C8×C31—21no—
238C2×C8×C31—21no—
239C2×C8×C31—21no—
240C2×C8×C31—21no—
241C2×C8×C31—21no—
242C2×C8×C31—21no—
243C2×C8×C31—44no—
244C2×C8×C31C2×D412yes—
245C4⋊C4×C31—24no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31—21no—
248C4⋊C4×C31—21no—
249C4⋊C4×C31—21no—
250C4⋊C4×C31—21no—
251C4⋊C4×C31—21no—
252C4⋊C4×C31—42no—
253C4⋊C4×C31—42no—
254C4⋊C4×C31—81no—
255C4⋊C4×C31C2×D412yes—
256C4⋊C4×C31C2×D412yes—
257C22⋊C4×C31—24no—
258C22⋊C4×C31—22no—
259C22⋊C4×C31—42no—
260C22⋊C4×C31—42no—
261C22⋊C4×C31—42no—
262C22⋊C4×C31—42no—
263C22⋊C4×C31—42no—
264C22⋊C4×C31SD1614yescomplemented
265C42×C31—21no—
266C42×C31—21no—
267C42×C31—21no—
268C42×C31—21no—
269C42×C31—42no—
270C42×C31—81no—
271#25080C3111yesmaximal, characteristic, direct product factor, Sylow
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—21no—
275C23×C31—21no—
276C23×C31—22no—
277C23×C31—22no—
278C23×C31—48no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31—41no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—84no—
299C23×C31—84no—
300C23×C31—84no—
301C23×C31—84no—
302C23×C31—84no—
303C23×C31—84no—
304C23×C31#12112yes—
305C23×C31C2×SD1612yes—
306C23×C31AGL(1,ℤ/8)12yes—
307C23×C31C22×D411yescharacteristic
308Q8×C31—22no—
309Q8×C31—22no—
310Q8×C31—41no—
311Q8×C31—41no—
312D4×C31—22no—
313D4×C31—22no—
314D4×C31—22no—
315D4×C31—22no—
316D4×C31—48no—
317D4×C31—41no—
318D4×C31—41no—
319D4×C31—41no—
320D4×C31—41no—
321D4×C31—41no—
322D4×C31—41no—
323D4×C31—41no—
324D4×C31—41no—
325D4×C31—84no—
326D4×C31—84no—
327D4×C31—84no—
328D4×C31—84no—
329D4×C31—84no—
330C2×C4×C31—21no—
331C2×C4×C31—21no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—22no—
337C2×C4×C31—22no—
338C2×C4×C31—22no—
339C2×C4×C31—22no—
340C2×C4×C31—22no—
341C2×C4×C31—22no—
342C2×C4×C31—21no—
343C2×C4×C31—22no—
344C2×C4×C31—21no—
345C2×C4×C31—21no—
346C2×C4×C31—21no—
347C2×C4×C31—21no—
348C2×C4×C31—21no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
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—84no—
362C2×C4×C31#12112yes—
363C2×C4×C31C2×SD1612yes—
364C2×C4×C31C2×SD1612yes—
365C2×C4×C31C22×D411yescharacteristic
366C2×C4×C31C22×D411yescharacteristic
367C2×C4×C31C2×#4111yescharacteristic
368C2×C4×C31C2×#4111yescharacteristic
369C2×C4×C31H(5,𝔽2)11yescharacteristic
370C2×C4×C31H(5,𝔽2)11yescharacteristic
371C8×C31—22no—
372C8×C31—41no—
373C8×C31—41no—
374C8×C31—41no—
375C2×#465C2×C3111yescharacteristic, complemented
376C2×#460C2×C3111yescharacteristic, complemented
377C2×#450C2×C3111yescharacteristic, complemented
378C22×#102C2×C3111yescharacteristic, complemented
379#2433C2×C3111yescharacteristic
380#2360C2×C3111yescharacteristic, complemented
381#2065C2×C3111yescharacteristic, complemented
382#2055C2×C3111yescharacteristic, complemented
383#2041C2×C3111yescharacteristic, complemented
384#2014C2×C3111yescharacteristic, complemented
385#1982C2×C3111yescharacteristic, complemented
386#1926C2×C3111yescharacteristic, complemented
387#1880C2×C3111yescharacteristic, complemented
388#1874C2×C3111yescharacteristic, complemented
389#1850C2×C3111yescharacteristic, complemented
390C22×C31—22no—
391C22×C31—22no—
392C22×C31—22no—
393C22×C31—22no—
394C22×C31—22no—
395C22×C31—22no—
396C22×C31—42no—
397C22×C31—42no—
398C22×C31—42no—
399C22×C31—42no—
400C22×C31—42no—
401C22×C31—42no—
402C22×C31—816no—
403C22×C31—81no—
404C22×C31—81no—
405C22×C31—81no—
406C22×C31—81no—
407C22×C31—81no—
408C22×C31—81no—
409C22×C31—81no—
410C22×C31—81no—
411C22×C31—81no—
412C22×C31—81no—
413C22×C31—81no—
414C22×C31—81no—
415C22×C31—81no—
416C22×C31—81no—
417C22×C31—81no—
418C22×C31#46014yescomplemented
419C22×C31C2×#12111yescharacteristic
420C22×C31D4211yescharacteristic
421C22×C31#54611yescharacteristic
422C22×C31C22×SD1611yescharacteristic
423C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C31#57611yescharacteristic
425C22×C31#57711yescharacteristic
426C4×C31—22no—
427C4×C31—22no—
428C4×C31—22no—
429C4×C31—42no—
430C4×C31—41no—
431C4×C31—42no—
432C4×C31—42no—
433C4×C31—41no—
434C4×C31—81no—
435C4×C31—81no—
436C4×C31#52511yescharacteristic
437C4×C31#53811yescharacteristic
438C4×C31D4211yescharacteristic
439C4×C31#54611yescharacteristic
440C23×D4C22×C3111yescharacteristic
441C22×SD16C22×C3111yescharacteristic
442C22×SD16C22×C3111yescharacteristic
443C22×SD16C22×C3111yescharacteristic, complemented
444C23×C8C22×C3111yescharacteristic
445C2×#127C22×C3111yescharacteristic
446C2×#127C22×C3111yescharacteristic
447C2×C22⋊Q8C22×C3111yescharacteristic
448C2×#121C22×C3111yescharacteristic
449C2×#120—21no—
450C2×#120—21no—
451C2×C4×Q8C22×C3111yescharacteristic, complemented
452C22×C4⋊C4C22×C3111yescharacteristic
453#465—24no—
454#460—24no—
455#450—24no—
456C2×#106C22×C3111yescharacteristic, complemented
457C2×C4⋊C8C22×C3111yescharacteristic, complemented
458C2×C4⋊C8C22×C3111yescharacteristic, complemented
459C2×#103C22×C3111yescharacteristic, complemented
460C2×#102—24no—
461C2×#102C22×C3111yescharacteristic
462C2×#102C22×C3111yescharacteristic
463C2×#102C22×C3111yescharacteristic
464C2×#102C22×C3111yescharacteristic
465C2×#102C22×C3111yescharacteristic
466C2×#102C22×C3111yescharacteristic
467C2×#102C22×C3111yescharacteristic, complemented
468C2×#102C22×C3111yescharacteristic, complemented
469C2×#102C22×C3111yescharacteristic, complemented
470C2×C22⋊C8C22×C3111yescharacteristic
471#392—21no—
472#392—21no—
473#391C22×C3111yescharacteristic, complemented
474#390C22×C3111yescharacteristic
475#390C22×C3111yescharacteristic
476#389—21no—
477#389C22×C3111yescharacteristic, complemented
478#387—21no—
479#385—21no—
480C4×C4⋊C4C22×C3111yescharacteristic, complemented
481C4×C22⋊C4—21no—
482C4×C22⋊C4C22×C3111yescharacteristic
483#340C22×C3111yescharacteristic, complemented
484#340C22×C3111yescharacteristic, complemented
485#336C22×C3111yescharacteristic, complemented
486#336C22×C3111yescharacteristic, complemented
487C2×C31—24no—
488C2×C31—82no—
489C2×C31—82no—
490C2×C31—161no—
491C2×C31#242411yescharacteristic
492C2×C31C2×#46011yescharacteristic
493C2×C31#304511yescharacteristic
494C2×C31#326411yescharacteristic
495C2×C31D4×SD1611yescharacteristic
496C2×C31#329511yescharacteristic
497C2×C31#331011yescharacteristic
498C25—21no—
499C22×Q8C23×C3111yescharacteristic
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—22no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4C23×C3111yescharacteristic
513C22×D4C23×C3111yescharacteristic
514C22×D4C23×C3111yescharacteristic
515C23×C4—21no—
516C23×C4C23×C3111yescharacteristic
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C22×C8—22no—
527C22×C8—22no—
528C22×C8—41no—
529C22×C8C23×C3111yescharacteristic
530C22×C8C23×C3111yescharacteristic
531C22×C8C23×C3111yescharacteristic
532C22×C8C23×C3111yescharacteristic
533#127—22no—
534#127—22no—
535#127—41no—
536#127—41no—
537C22⋊Q8—22no—
538C22⋊Q8D4×C3114yescomplemented
539#121—22no—
540#121—22no—
541#120—44no—
542#120—44no—
543C4×Q8—22no—
544C4×Q8—41no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4C23×C3111yescharacteristic
552C2×C4⋊C4C23×C3111yescharacteristic
553C2×C4⋊C4C23×C3111yescharacteristic
554C2×C4⋊C4C23×C3111yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4D4×C3111yescharacteristic
562C2×C22⋊C4D4×C3111yescharacteristic
563C2×C42—21no—
564C2×C42—21no—
565C2×C42C23×C3111yescharacteristic
566C2×C42C23×C3111yescharacteristic
567#106—22no—
568C4⋊C8—22no—
569C4⋊C8—41no—
570#103—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—41no—
579#102D4×C3114yescomplemented
580C22⋊C8—22no—
581#95—21no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95D4×C3111yescharacteristic
586#95D4×C3111yescharacteristic
587C31#2508011yescharacteristic, direct product factor, Sylow
588C24—21no—
589C24—21no—
590C24—21no—
591C24—42no—
592C24—42no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—81no—
597C24—81no—
598C24C2×D4×C3111yescharacteristic
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8C2×D4×C3112yes—
605C2×D4—28no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—44no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—81no—
640C2×D4—81no—
641C2×D4—81no—
642C2×D4—81no—
643C2×D4C2×D4×C3112yes—
644C2×D4#41×C3112yes—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—81no—
657C22×C4C2×D4×C3111yescharacteristic
658C22×C4C2×D4×C3111yescharacteristic
659C22×C4C2×D4×C3111yescharacteristic
660C22×C4C2×D4×C3112yes—
661C22×C4C2×D4×C3111yescharacteristic
662C22×C4C2×D4×C3111yescharacteristic
663C22×C4#41×C3112yes—
664C22×C4C24×C3111yescharacteristic
665SD16—44no—
666SD16—44no—
667SD16—44no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—44no—
680C2×C8C2×D4×C3112yes—
681C4⋊C4—24no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—81no—
691C4⋊C4C2×D4×C3112yes—
692C4⋊C4C2×D4×C3112yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4SD16×C3114yescomplemented
701C42—21no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—42no—
706C42—81no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—22no—
712C23—22no—
713C23—48no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23—84no—
737C23—84no—
738C23—84no—
739C23C31×#12112yes—
740C23C2×SD16×C3112yes—
741C23C31×AGL(1,ℤ/8)12yes—
742C23C22×D4×C3111yescharacteristic
743Q8—22no—
744Q8—22no—
745Q8—41no—
746Q8—41no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4—84no—
762D4—84no—
763D4—84no—
764D4—84no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—41no—
785C2×C4—41no—
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—84no—
797C2×C4C31×#12112yes—
798C2×C4C2×SD16×C3112yes—
799C2×C4C2×SD16×C3112yes—
800C2×C4C22×D4×C3111yescharacteristic
801C2×C4C22×D4×C3111yescharacteristic
802C2×C4C2×#41×C3111yescharacteristic
803C2×C4C2×#41×C3111yescharacteristic
804C2×C4C31×H(5,𝔽2)11yescharacteristic
805C2×C4C31×H(5,𝔽2)11yescharacteristic
806C8—22no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—816no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22C31×#46014yescomplemented
839C22C2×C31×#12111yescharacteristic
840C22D42×C3111yescharacteristic
841C22C31×#54611yescharacteristic
842C22C22×SD16×C3111yescharacteristic
843C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
844C22C31×#57611yescharacteristic
845C22C31×#57711yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—41no—
851C4—42no—
852C4—42no—
853C4—41no—
854C4—81no—
855C4—81no—
856C4C31×#52511yescharacteristic
857C4C31×#53811yescharacteristic
858C4D42×C3111yescharacteristic
859C4C31×#54611yescharacteristic
860C2—24no—
861C2—82no—
862C2—82no—
863C2—161no—
864C2C31×#242411yescharacteristic
865C2C2×C31×#46011yescharacteristic
866C2C31×#304511yescharacteristic
867C2C31×#326411yescharacteristic
868C2D4×SD16×C3111yescharacteristic
869C2C31×#329511yescharacteristic
870C2C31×#331011yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2433C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#465C2semidirect
2. C2×C31×#460C2semidirect
3. C2×C31×#450C2semidirect
4. C22×C31×#102C2semidirect
6. C31×#2360C2semidirect
7. C31×#2065C2semidirect
8. C31×#2055C2semidirect
9. C31×#2041C2semidirect
10. C31×#2014C2semidirect
11. C31×#1982C2semidirect
12. C31×#1926C2semidirect
13. C31×#1880C2semidirect
14. C31×#1874C2semidirect
15. C31×#1850C2semidirect
19. C22×SD16×C31C22semidirect
27. C2×C4×Q8×C31C22semidirect
32. C2×C31×#106C22semidirect
33. C2×C31×C4⋊C8C22semidirect
34. C2×C31×C4⋊C8C22semidirect
35. C2×C31×#103C22semidirect
43. C2×C31×#102C22semidirect
44. C2×C31×#102C22semidirect
45. C2×C31×#102C22semidirect
49. C31×#391C22semidirect
53. C31×#389C22semidirect
56. C4×C4⋊C4×C31C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#336C22semidirect
62. C31×#336C22semidirect
103. C31×C22⋊Q8D4semidirect
144. C31×#102D4semidirect
264. C22⋊C4×C31SD16semidirect
271. #25080C31direct (N × H)
375. C2×#465C2×C31semidirect
376. C2×#460C2×C31semidirect
377. C2×#450C2×C31semidirect
378. C22×#102C2×C31semidirect
380. #2360C2×C31semidirect
381. #2065C2×C31semidirect
382. #2055C2×C31semidirect
383. #2041C2×C31semidirect
384. #2014C2×C31semidirect
385. #1982C2×C31semidirect
386. #1926C2×C31semidirect
387. #1880C2×C31semidirect
388. #1874C2×C31semidirect
389. #1850C2×C31semidirect
418. C22×C31#460semidirect
443. C22×SD16C22×C31semidirect
451. C2×C4×Q8C22×C31semidirect
456. C2×#106C22×C31semidirect
457. C2×C4⋊C8C22×C31semidirect
458. C2×C4⋊C8C22×C31semidirect
459. C2×#103C22×C31semidirect
467. C2×#102C22×C31semidirect
468. C2×#102C22×C31semidirect
469. C2×#102C22×C31semidirect
473. #391C22×C31semidirect
477. #389C22×C31semidirect
480. C4×C4⋊C4C22×C31semidirect
483. #340C22×C31semidirect
484. #340C22×C31semidirect
485. #336C22×C31semidirect
486. #336C22×C31semidirect
538. C22⋊Q8D4×C31semidirect
579. #102D4×C31semidirect
587. C31#25080direct (N × H)
700. C22⋊C4SD16×C31semidirect
838. C22C31×#460semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4652
C2×C31×#4602
C2×C31×#4502
C22×C31×#1022
C31×#24332
C31×#23602
C31×#20652
C31×#20552
C31×#20412
C31×#20142
C31×#19822
C31×#19262
C31×#18802
C31×#18742
C31×#18502
#2508031