Finite Group Databasebeta

← C31×#25093 #21481852

Subgroups — C31×#25093 #21481852

Order 7936.

1322 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#468C211yesmaximal, characteristic, complemented
2C2×C31×#460C211yesmaximal, characteristic, complemented
3C2×C31×#450C211yesmaximal, characteristic, complemented
4C2×C31×#418C211yesmaximal, characteristic, complemented
5C31×#2433C211yesmaximal, characteristic
6C31×#2362C211yesmaximal, characteristic, complemented
7C31×#2067C211yesmaximal, characteristic, complemented
8C31×#2055C211yesmaximal, characteristic, complemented
9C31×#2041C211yesmaximal, characteristic, complemented
10C31×#2014C211yesmaximal, characteristic, complemented
11C31×#1982C211yesmaximal, characteristic, complemented
12C31×#1925C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic, complemented
14C31×#1875C211yesmaximal, characteristic, complemented
15C31×#1851C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic, complemented
20C22×M16×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
28C2×C31×#117C2211yescharacteristic
29C31×#468—24no—
30C31×#460—24no—
31C31×#450—24no—
32C2×C31×#107C2211yescharacteristic, complemented
33C2×C31×C4⋊C8C2211yescharacteristic, complemented
34C2×C31×C4⋊C8C2211yescharacteristic, complemented
35C31×#418—24no—
36C2×C31×#103C2211yescharacteristic, complemented
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×#389C2211yescharacteristic, complemented
53C31×#388—21no—
54C31×#388—21no—
55C31×#387—21no—
56C4×C4⋊C4×C31—21no—
57C4×C4⋊C4×C31C2211yescharacteristic, complemented
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×C31C2311yescharacteristic
81C2×SD16×C31—22no—
82C2×SD16×C31—22no—
83C2×SD16×C31—22no—
84C2×SD16×C31—22no—
85C2×SD16×C31—22no—
86C2×SD16×C31—22no—
87C2×SD16×C31—41no—
88C2×SD16×C31—41no—
89C2×SD16×C31—41no—
90C2×M16×C31—22no—
91C2×M16×C31—22no—
92C2×M16×C31—41no—
93C22×C8×C31C2311yescharacteristic
94C22×C8×C31C2311yescharacteristic
95C22×C8×C31C2311yescharacteristic
96C22×C8×C31C2311yescharacteristic
97C31×#127—22no—
98C31×#127—22no—
99C31×#127—41no—
100C31×#127—41no—
101C31×C22⋊Q8—22no—
102C31×C22⋊Q8D414yescomplemented
103C31×#121—22no—
104C31×#121—22no—
105C31×#120—44no—
106C31×#120—44no—
107C4×Q8×C31—22no—
108C4×Q8×C31—41no—
109C31×#117—22no—
110C31×#117—41no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
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×C31D411yescharacteristic
126C2×C22⋊C4×C31D411yescharacteristic
127C2×C42×C31—21no—
128C2×C42×C31—21no—
129C2×C42×C31—21no—
130C2×C42×C31C2311yescharacteristic
131C2×C42×C31C2311yescharacteristic
132C31×#107—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×C31C2×D411yescharacteristic
219C22×C4×C31C2×D411yescharacteristic
220C22×C4×C31C2×D411yescharacteristic
221C22×C4×C31C2×D412yes—
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31C2×D411yescharacteristic
224C22×C4×C31#4112yes—
225C22×C4×C31C2411yescharacteristic
226SD16×C31—44no—
227SD16×C31—44no—
228SD16×C31—44no—
229M16×C31—44no—
230C2×C8×C31—21no—
231C2×C8×C31—21no—
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×C31C2×D412yes—
242C4⋊C4×C31—24no—
243C4⋊C4×C31—21no—
244C4⋊C4×C31—21no—
245C4⋊C4×C31—21no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31—21no—
248C4⋊C4×C31—21no—
249C4⋊C4×C31—42no—
250C4⋊C4×C31—42no—
251C4⋊C4×C31C2×D412yes—
252C4⋊C4×C31C2×D412yes—
253C22⋊C4×C31—24no—
254C22⋊C4×C31—22no—
255C22⋊C4×C31—22no—
256C22⋊C4×C31—42no—
257C22⋊C4×C31—42no—
258C22⋊C4×C31—42no—
259C22⋊C4×C31—42no—
260C22⋊C4×C31—42no—
261C22⋊C4×C31—42no—
262C42×C31—21no—
263C42×C31—21no—
264C42×C31—21no—
265C42×C31—21no—
266C42×C31—42no—
267C42×C31—42no—
268C42×C31—42no—
269#25093C3111yesmaximal, characteristic, direct product factor, Sylow
270C23×C31—21no—
271C23×C31—21no—
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×C31C22×D411yescharacteristic
306Q8×C31—22no—
307Q8×C31—22no—
308Q8×C31—41no—
309Q8×C31—41no—
310D4×C31—22no—
311D4×C31—22no—
312D4×C31—22no—
313D4×C31—22no—
314D4×C31—48no—
315D4×C31—41no—
316D4×C31—41no—
317D4×C31—41no—
318D4×C31—41no—
319D4×C31—41no—
320D4×C31—41no—
321D4×C31—41no—
322D4×C31—41no—
323D4×C31—84no—
324D4×C31—84no—
325D4×C31—84no—
326D4×C31—84no—
327D4×C31—84no—
328C2×C4×C31—21no—
329C2×C4×C31—21no—
330C2×C4×C31—21no—
331C2×C4×C31—21no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—22no—
335C2×C4×C31—22no—
336C2×C4×C31—22no—
337C2×C4×C31—22no—
338C2×C4×C31—22no—
339C2×C4×C31—22no—
340C2×C4×C31—21no—
341C2×C4×C31—22no—
342C2×C4×C31—21no—
343C2×C4×C31—21no—
344C2×C4×C31—21no—
345C2×C4×C31—21no—
346C2×C4×C31—21no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
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#12112yes—
360C2×C4×C31AGL(1,ℤ/8)12yes—
361C2×C4×C31AGL(1,ℤ/8)12yes—
362C2×C4×C31C22×D411yescharacteristic
363C2×C4×C31C22×D411yescharacteristic
364C2×C4×C31C2×#4111yescharacteristic
365C2×C4×C31C2×#4111yescharacteristic
366C2×C4×C31H(5,𝔽2)11yescharacteristic
367C2×C4×C31H(5,𝔽2)11yescharacteristic
368C8×C31—22no—
369C8×C31—41no—
370C8×C31—41no—
371C8×C31—41no—
372C2×#468C2×C3111yescharacteristic, complemented
373C2×#460C2×C3111yescharacteristic, complemented
374C2×#450C2×C3111yescharacteristic, complemented
375C2×#418C2×C3111yescharacteristic, complemented
376#2433C2×C3111yescharacteristic
377#2362C2×C3111yescharacteristic, complemented
378#2067C2×C3111yescharacteristic, complemented
379#2055C2×C3111yescharacteristic, complemented
380#2041C2×C3111yescharacteristic, complemented
381#2014C2×C3111yescharacteristic, complemented
382#1982C2×C3111yescharacteristic, complemented
383#1925C2×C3111yescharacteristic, complemented
384#1880C2×C3111yescharacteristic, complemented
385#1875C2×C3111yescharacteristic, complemented
386#1851C2×C3111yescharacteristic, complemented
387C22×C31—22no—
388C22×C31—22no—
389C22×C31—22no—
390C22×C31—41no—
391C22×C31—41no—
392C22×C31—41no—
393C22×C31—41no—
394C22×C31—42no—
395C22×C31—42no—
396C22×C31—42no—
397C22×C31—42no—
398C22×C31—42no—
399C22×C31—42no—
400C22×C31—816no—
401C22×C31—81no—
402C22×C31—81no—
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×C31C2×#12111yescharacteristic
417C22×C31D4211yescharacteristic
418C22×C31#54611yescharacteristic
419C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
420C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
421C22×C31#57711yescharacteristic
422C22×C31#57711yescharacteristic
423C4×C31—22no—
424C4×C31—22no—
425C4×C31—22no—
426C4×C31—42no—
427C4×C31—41no—
428C4×C31—42no—
429C4×C31—42no—
430C4×C31—41no—
431C4×C31—81no—
432C4×C31—81no—
433C4×C31#52511yescharacteristic
434C4×C31#53811yescharacteristic
435C4×C31D4211yescharacteristic
436C4×C31#54611yescharacteristic
437C23×D4C22×C3111yescharacteristic
438C22×SD16C22×C3111yescharacteristic
439C22×SD16C22×C3111yescharacteristic
440C22×SD16C22×C3111yescharacteristic, complemented
441C22×M16C22×C3111yescharacteristic
442C2×#127C22×C3111yescharacteristic
443C2×#127C22×C3111yescharacteristic
444C2×C22⋊Q8C22×C3111yescharacteristic
445C2×#121C22×C3111yescharacteristic
446C2×#120—21no—
447C2×#120—21no—
448C2×C4×Q8C22×C3111yescharacteristic, complemented
449C2×#117C22×C3111yescharacteristic
450#468—24no—
451#460—24no—
452#450—24no—
453C2×#107C22×C3111yescharacteristic, complemented
454C2×C4⋊C8C22×C3111yescharacteristic, complemented
455C2×C4⋊C8C22×C3111yescharacteristic, complemented
456#418—24no—
457C2×#103C22×C3111yescharacteristic, complemented
458C2×#102C22×C3111yescharacteristic
459C2×#102C22×C3111yescharacteristic
460C2×#102C22×C3111yescharacteristic
461C2×#102C22×C3111yescharacteristic
462C2×#102C22×C3111yescharacteristic
463C2×#102C22×C3111yescharacteristic
464C2×#102C22×C3111yescharacteristic, complemented
465C2×#102C22×C3111yescharacteristic, complemented
466C2×#102C22×C3111yescharacteristic, complemented
467C2×C22⋊C8C22×C3111yescharacteristic
468#392—21no—
469#392—21no—
470#391C22×C3111yescharacteristic, complemented
471#390C22×C3111yescharacteristic
472#390C22×C3111yescharacteristic
473#389C22×C3111yescharacteristic, complemented
474#388—21no—
475#388—21no—
476#387—21no—
477C4×C4⋊C4—21no—
478C4×C4⋊C4C22×C3111yescharacteristic, complemented
479C4×C22⋊C4C22×C3111yescharacteristic
480#340C22×C3111yescharacteristic, complemented
481#340C22×C3111yescharacteristic, complemented
482#336C22×C3111yescharacteristic, complemented
483#336C22×C3111yescharacteristic, complemented
484C2×C31—42no—
485C2×C31—82no—
486C2×C31—82no—
487C2×C31—161no—
488C2×C31#242411yescharacteristic
489C2×C31#303811yescharacteristic
490C2×C31#304311yescharacteristic
491C2×C31#326511yescharacteristic
492C2×C31#327211yescharacteristic
493C2×C31#331011yescharacteristic
494C2×C31#332411yescharacteristic
495C25—21no—
496C22×Q8C23×C3111yescharacteristic
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—22no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4C23×C3111yescharacteristic
510C22×D4C23×C3111yescharacteristic
511C22×D4C23×C3111yescharacteristic
512C23×C4C23×C3111yescharacteristic
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×M16—22no—
523C2×M16—22no—
524C2×M16—41no—
525C22×C8C23×C3111yescharacteristic
526C22×C8C23×C3111yescharacteristic
527C22×C8C23×C3111yescharacteristic
528C22×C8C23×C3111yescharacteristic
529#127—22no—
530#127—22no—
531#127—41no—
532#127—41no—
533C22⋊Q8—22no—
534C22⋊Q8D4×C3114yescomplemented
535#121—22no—
536#121—22no—
537#120—44no—
538#120—44no—
539C4×Q8—22no—
540C4×Q8—41no—
541#117—22no—
542#117—41no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4C23×C3111yescharacteristic
547C2×C4⋊C4C23×C3111yescharacteristic
548C2×C4⋊C4C23×C3111yescharacteristic
549C2×C4⋊C4C23×C3111yescharacteristic
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4D4×C3111yescharacteristic
558C2×C22⋊C4D4×C3111yescharacteristic
559C2×C42—21no—
560C2×C42—21no—
561C2×C42—21no—
562C2×C42C23×C3111yescharacteristic
563C2×C42C23×C3111yescharacteristic
564#107—22no—
565C4⋊C8—22no—
566C4⋊C8—41no—
567#103—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—41no—
576#102D4×C3114yescomplemented
577C22⋊C8—22no—
578#95—21no—
579#95—21no—
580#95—21no—
581#95—21no—
582#95D4×C3111yescharacteristic
583#95D4×C3111yescharacteristic
584C31#2509311yescharacteristic, direct product factor, Sylow
585C24—21no—
586C24—21no—
587C24—21no—
588C24—42no—
589C24—42no—
590C24—42no—
591C24—42no—
592C24—42no—
593C24—81no—
594C24—81no—
595C24C2×D4×C3111yescharacteristic
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C3112yes—
602C2×D4—28no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
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—44no—
620C2×D4—44no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
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—81no—
637C2×D4—81no—
638C2×D4—81no—
639C2×D4—81no—
640C2×D4C2×D4×C3112yes—
641C2×D4#41×C3112yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4C2×D4×C3111yescharacteristic
652C22×C4C2×D4×C3111yescharacteristic
653C22×C4C2×D4×C3111yescharacteristic
654C22×C4C2×D4×C3112yes—
655C22×C4C2×D4×C3111yescharacteristic
656C22×C4C2×D4×C3111yescharacteristic
657C22×C4#41×C3112yes—
658C22×C4C24×C3111yescharacteristic
659SD16—44no—
660SD16—44no—
661SD16—44no—
662M16—44no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8C2×D4×C3112yes—
675C4⋊C4—24no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4C2×D4×C3112yes—
685C4⋊C4C2×D4×C3112yes—
686C22⋊C4—24no—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—42no—
700C42—42no—
701C42—42no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—22no—
710C23—48no—
711C23—41no—
712C23—41no—
713C23—41no—
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—84no—
731C23—84no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23C31×#12112yes—
737C23C22×D4×C3111yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—41no—
741Q8—41no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—48no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—84no—
756D4—84no—
757D4—84no—
758D4—84no—
759D4—84no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4C31×#12112yes—
792C2×C4C31×AGL(1,ℤ/8)12yes—
793C2×C4C31×AGL(1,ℤ/8)12yes—
794C2×C4C22×D4×C3111yescharacteristic
795C2×C4C22×D4×C3111yescharacteristic
796C2×C4C2×#41×C3111yescharacteristic
797C2×C4C2×#41×C3111yescharacteristic
798C2×C4C31×H(5,𝔽2)11yescharacteristic
799C2×C4C31×H(5,𝔽2)11yescharacteristic
800C8—22no—
801C8—41no—
802C8—41no—
803C8—41no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—816no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22C2×C31×#12111yescharacteristic
834C22D42×C3111yescharacteristic
835C22C31×#54611yescharacteristic
836C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
837C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
838C22C31×#57711yescharacteristic
839C22C31×#57711yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—42no—
844C4—41no—
845C4—42no—
846C4—42no—
847C4—41no—
848C4—81no—
849C4—81no—
850C4C31×#52511yescharacteristic
851C4C31×#53811yescharacteristic
852C4D42×C3111yescharacteristic
853C4C31×#54611yescharacteristic
854C2—42no—
855C2—82no—
856C2—82no—
857C2—161no—
858C2C31×#242411yescharacteristic
859C2C31×#303811yescharacteristic
860C2C31×#304311yescharacteristic
861C2C31×#326511yescharacteristic
862C2C31×#327211yescharacteristic
863C2C31×#331011yescharacteristic
864C2C31×#332411yescharacteristic
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×#468C2semidirect
2. C2×C31×#460C2semidirect
3. C2×C31×#450C2semidirect
4. C2×C31×#418C2semidirect
6. C31×#2362C2semidirect
7. C31×#2067C2semidirect
8. C31×#2055C2semidirect
9. C31×#2041C2semidirect
10. C31×#2014C2semidirect
11. C31×#1982C2semidirect
12. C31×#1925C2semidirect
13. C31×#1880C2semidirect
14. C31×#1875C2semidirect
15. C31×#1851C2semidirect
19. C22×SD16×C31C22semidirect
27. C2×C4×Q8×C31C22semidirect
32. C2×C31×#107C22semidirect
33. C2×C31×C4⋊C8C22semidirect
34. C2×C31×C4⋊C8C22semidirect
36. C2×C31×#103C22semidirect
43. C2×C31×#102C22semidirect
44. C2×C31×#102C22semidirect
45. C2×C31×#102C22semidirect
49. C31×#391C22semidirect
52. C31×#389C22semidirect
57. C4×C4⋊C4×C31C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#336C22semidirect
62. C31×#336C22semidirect
102. C31×C22⋊Q8D4semidirect
144. C31×#102D4semidirect
269. #25093C31direct (N × H)
372. C2×#468C2×C31semidirect
373. C2×#460C2×C31semidirect
374. C2×#450C2×C31semidirect
375. C2×#418C2×C31semidirect
377. #2362C2×C31semidirect
378. #2067C2×C31semidirect
379. #2055C2×C31semidirect
380. #2041C2×C31semidirect
381. #2014C2×C31semidirect
382. #1982C2×C31semidirect
383. #1925C2×C31semidirect
384. #1880C2×C31semidirect
385. #1875C2×C31semidirect
386. #1851C2×C31semidirect
440. C22×SD16C22×C31semidirect
448. C2×C4×Q8C22×C31semidirect
453. C2×#107C22×C31semidirect
454. C2×C4⋊C8C22×C31semidirect
455. C2×C4⋊C8C22×C31semidirect
457. C2×#103C22×C31semidirect
464. C2×#102C22×C31semidirect
465. C2×#102C22×C31semidirect
466. C2×#102C22×C31semidirect
470. #391C22×C31semidirect
473. #389C22×C31semidirect
478. C4×C4⋊C4C22×C31semidirect
480. #340C22×C31semidirect
481. #340C22×C31semidirect
482. #336C22×C31semidirect
483. #336C22×C31semidirect
534. C22⋊Q8D4×C31semidirect
576. #102D4×C31semidirect
584. C31#25093direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4682
C2×C31×#4602
C2×C31×#4502
C2×C31×#4182
C31×#24332
C31×#23622
C31×#20672
C31×#20552
C31×#20412
C31×#20142
C31×#19822
C31×#19252
C31×#18802
C31×#18752
C31×#18512
#2509331