Finite Group Databasebeta

← C2×C31×#1904 #21477755

Subgroups — C2×C31×#1904 #21477755

Order 7936.

1894 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C2×C31×#518C211yesmaximal, characteristic, complemented
3C2×C31×#421C211yesmaximal, characteristic, complemented
4C2×C31×#418C211yesmaximal, characteristic, complemented
5C2×C31×#410C211yesmaximal, characteristic, complemented
6C31×#1904C218yesmaximal, direct product factor
7C2×C31×#344C211yesmaximal, characteristic, complemented
8C2×C31×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#41×C31C2211yescharacteristic
10C23×D4×C31C2211yescharacteristic
11C2×C31×AGL(1,ℤ/8)—22no—
12C2×C31×AGL(1,ℤ/8)—22no—
13C2×C31×AGL(1,ℤ/8)—22no—
14C2×C31×AGL(1,ℤ/8)—22no—
15C2×C31×AGL(1,ℤ/8)C414yescomplemented
16C2×C31×AGL(1,ℤ/8)C2214yes—
17C22×SD16×C31C412yescomplemented
18C22×D8×C31C412yescomplemented
19C22×M16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C31×#518—22no—
22C31×#518—22no—
23C31×#518—22no—
24C31×#518C2214yescomplemented
25C2×C4×D4×C31—22no—
26C2×C4×D4×C31—22no—
27C2×C31×#117C2211yescharacteristic
28C2×C31×#117C2211yescharacteristic
29C2×C31×#117C2211yescharacteristic
30C22×C22⋊C4×C31—22no—
31C31×#421—22no—
32C31×#421C2214yescomplemented
33C2×C31×#104—22no—
34C31×#418—22no—
35C31×#418C2214yescomplemented
36C2×C31×#102—22no—
37C31×#410—22no—
38C31×#410C2214yescomplemented
39C2×C31×#99—22no—
40C31×#344C2214yescomplemented
41C31×H(3,ℤ/4)C2214yescomplemented
42C25×C31—21no—
43C2×#41×C31—21no—
44C2×#41×C31—21no—
45C2×#41×C31—21no—
46C2×#41×C31—21no—
47C2×#41×C31—21no—
48C2×#41×C31—21no—
49C2×#41×C31—21no—
50C2×#41×C31—21no—
51C2×#41×C31—21no—
52C2×#41×C31—21no—
53C2×#41×C31C2×C412yescomplemented
54C2×#41×C31C2312yes—
55C22×Q8×C31C2×C411yescharacteristic, complemented
56C22×D4×C31—21no—
57C22×D4×C31—21no—
58C22×D4×C31—21no—
59C22×D4×C31—21no—
60C22×D4×C31—21no—
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31C2×C412yes—
65C22×D4×C31C2×C412yes—
66C22×D4×C31C2×C411yescharacteristic, complemented
67C22×D4×C31D412yes—
68C22×D4×C31D412yes—
69C22×D4×C31D412yes—
70C22×D4×C31D412yes—
71C22×D4×C31C2312yes—
72C23×C4×C31—24no—
73C23×C4×C31—21no—
74C23×C4×C31C2311yescharacteristic
75C31×AGL(1,ℤ/8)—28no—
76C31×AGL(1,ℤ/8)—28no—
77C31×AGL(1,ℤ/8)—28no—
78C31×AGL(1,ℤ/8)—28no—
79C2×SD16×C31—24no—
80C2×SD16×C31—24no—
81C2×SD16×C31C2×C418yescomplemented
82C2×D8×C31—24no—
83C2×D8×C31—24no—
84C2×D8×C31C2×C418yescomplemented
85C2×M16×C31—21no—
86C2×M16×C31—21no—
87C2×M16×C31—21no—
88C2×M16×C31—21no—
89C2×M16×C31—21no—
90C2×M16×C31—21no—
91C2×M16×C31—21no—
92C2×M16×C31—21no—
93C2×M16×C31—21no—
94C2×M16×C31C2×C412yescomplemented
95C2×M16×C31C2312yes—
96C2×M16×C31C2312yes—
97C22×C8×C31—21no—
98C22×C8×C31C2×C412yescomplemented
99C4×D4×C31—28no—
100C4×D4×C31—28no—
101C4×D4×C31—28no—
102C4×D4×C31—28no—
103C31×#117—21no—
104C31×#117—21no—
105C31×#117—21no—
106C31×#117—21no—
107C31×#117—21no—
108C31×#117—21no—
109C31×#117—21no—
110C31×#117D412yes—
111C31×#117D412yes—
112C31×#117C2312yes—
113C31×#117C2312yes—
114C31×#117C2312yes—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31—21no—
117C2×C4⋊C4×C31—21no—
118C2×C22⋊C4×C31—24no—
119C2×C22⋊C4×C31—28no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—28no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31D412yes—
124C2×C42×C31—21no—
125C2×C42×C31—21no—
126C2×C42×C31D412yes—
127C31×#104—28no—
128C31×#102—28no—
129C31×#99—28no—
130C24×C31—22no—
131C24×C31—22no—
132C24×C31—22no—
133C24×C31—22no—
134C24×C31—22no—
135C24×C31—22no—
136C24×C31—22no—
137C24×C31—21no—
138C24×C31—84no—
139C24×C31C2×D411yescharacteristic
140#41×C31—22no—
141#41×C31—22no—
142#41×C31—22no—
143#41×C31—22no—
144#41×C31—22no—
145#41×C31—22no—
146#41×C31—22no—
147#41×C31—22no—
148#41×C31—41no—
149#41×C31—41no—
150#41×C31—41no—
151#41×C31—41no—
152#41×C31—41no—
153#41×C31—41no—
154#41×C31—41no—
155#41×C31—41no—
156C2×Q8×C31—21no—
157C2×Q8×C31—21no—
158C2×Q8×C31—21no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31C22×C412yescomplemented
162C2×D4×C31—22no—
163C2×D4×C31—22no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—22no—
167C2×D4×C31—22no—
168C2×D4×C31—22no—
169C2×D4×C31—22no—
170C2×D4×C31—22no—
171C2×D4×C31—22no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—22no—
176C2×D4×C31—22no—
177C2×D4×C31—22no—
178C2×D4×C31—22no—
179C2×D4×C31—22no—
180C2×D4×C31—22no—
181C2×D4×C31—22no—
182C2×D4×C31—22no—
183C2×D4×C31—22no—
184C2×D4×C31—22no—
185C2×D4×C31—22no—
186C2×D4×C31—22no—
187C2×D4×C31—22no—
188C2×D4×C31—22no—
189C2×D4×C31—22no—
190C2×D4×C31—41no—
191C2×D4×C31—41no—
192C2×D4×C31—41no—
193C2×D4×C31—41no—
194C2×D4×C31C22⋊C414yes—
195C2×D4×C31C22⋊C414yes—
196C2×D4×C31C22⋊C414yes—
197C2×D4×C31C22⋊C414yes—
198C2×D4×C31C22×C414yes—
199C2×D4×C31C22×C412yescomplemented
200C2×D4×C31C2×D414yes—
201C2×D4×C31C2×D414yes—
202C22×C4×C31—21no—
203C22×C4×C31—22no—
204C22×C4×C31—22no—
205C22×C4×C31—216no—
206C22×C4×C31—22no—
207C22×C4×C31—22no—
208C22×C4×C31—41no—
209C22×C4×C31—41no—
210C22×C4×C31—41no—
211C22×C4×C31—41no—
212C22×C4×C31—41no—
213C22×C4×C31—88no—
214C22×C4×C31C22×C411yescharacteristic
215C22×C4×C31C22×C411yescharacteristic
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219C22×C4×C31C2×D411yescharacteristic
220C22×C4×C31C2×D411yescharacteristic
221C22×C4×C31C2×D411yescharacteristic
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31#4111yescharacteristic
224C22×C4×C31#4111yescharacteristic
225C22×C4×C31#4111yescharacteristic
226C22×C4×C31#4111yescharacteristic
227C22×C4×C31C2411yescharacteristic
228SD16×C31—216no—
229D8×C31—216no—
230M16×C31—22no—
231M16×C31—22no—
232M16×C31—22no—
233M16×C31—22no—
234M16×C31—22no—
235M16×C31—22no—
236M16×C31—41no—
237M16×C31—41no—
238C2×C8×C31—22no—
239C2×C8×C31—22no—
240C2×C8×C31—22no—
241C2×C8×C31—41no—
242C2×C8×C31—41no—
243C2×C8×C31C22×C414yescomplemented
244C4⋊C4×C31—22no—
245C4⋊C4×C31—22no—
246C4⋊C4×C31—22no—
247C4⋊C4×C31—22no—
248C4⋊C4×C31—22no—
249C4⋊C4×C31—41no—
250C22⋊C4×C31—216no—
251C22⋊C4×C31—22no—
252C22⋊C4×C31—22no—
253C22⋊C4×C31—22no—
254C22⋊C4×C31—22no—
255C22⋊C4×C31—41no—
256C22⋊C4×C31C2×D414yes—
257C42×C31—22no—
258C42×C31—22no—
259C42×C31—22no—
260C42×C31—22no—
261C42×C31—41no—
262C42×C31C2×D414yes—
263C2×#1904C3111yesmaximal, characteristic, direct product factor, Sylow
264C23×C31—24no—
265C23×C31—24no—
266C23×C31—24no—
267C23×C31—24no—
268C23×C31—24no—
269C23×C31—24no—
270C23×C31—24no—
271C23×C31—22no—
272C23×C31—42no—
273C23×C31—48no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—84no—
277C23×C31—84no—
278C23×C31—82no—
279C23×C31—84no—
280C23×C31—84no—
281C23×C31—84no—
282C23×C31—84no—
283C23×C31C4×D411yescharacteristic
284C23×C31C4×D411yescharacteristic
285C23×C31#12011yescharacteristic
286C23×C31#12011yescharacteristic
287C23×C31#12111yescharacteristic
288C23×C31#12111yescharacteristic
289C23×C31C22×D411yescharacteristic
290Q8×C31—22no—
291Q8×C31—22no—
292Q8×C31—41no—
293Q8×C31—41no—
294D4×C31—22no—
295D4×C31—24no—
296D4×C31—22no—
297D4×C31—24no—
298D4×C31—24no—
299D4×C31—24no—
300D4×C31—24no—
301D4×C31—24no—
302D4×C31—24no—
303D4×C31—42no—
304D4×C31—42no—
305D4×C31—42no—
306D4×C31—42no—
307D4×C31—41no—
308D4×C31—41no—
309D4×C31C2×C22⋊C418yes—
310C2×C4×C31—22no—
311C2×C4×C31—24no—
312C2×C4×C31—24no—
313C2×C4×C31—44no—
314C2×C4×C31—44no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31—42no—
322C2×C4×C31—816no—
323C2×C4×C31—82no—
324C2×C4×C31C2×C22⋊C411yescharacteristic
325C2×C4×C31C2×C22⋊C411yescharacteristic
326C2×C4×C31C2×C22⋊C411yescharacteristic
327C2×C4×C31C2×C22⋊C411yescharacteristic
328C2×C4×C31C4×D411yescharacteristic
329C2×C4×C31C4×D411yescharacteristic
330C2×C4×C31C4×D411yescharacteristic
331C2×C4×C31C4×D411yescharacteristic
332C2×C4×C31C4×D411yescharacteristic
333C2×C4×C31C4×D411yescharacteristic
334C2×C4×C31#12011yescharacteristic
335C2×C4×C31#12011yescharacteristic
336C2×C4×C31#12111yescharacteristic
337C2×C4×C31#12111yescharacteristic
338C2×C4×C31#12111yescharacteristic
339C2×C4×C31#12111yescharacteristic
340C2×C4×C31#12111yescharacteristic
341C2×C4×C31#12111yescharacteristic
342C2×C4×C31#12311yescharacteristic
343C2×C4×C31#12311yescharacteristic
344C2×C4×C31#12311yescharacteristic
345C2×C4×C31#12311yescharacteristic
346C2×C4×C31C23×C411yescharacteristic
347C2×C4×C31C22×D411yescharacteristic
348C2×C4×C31C22×D411yescharacteristic
349C2×C4×C31C22×D411yescharacteristic
350C2×C4×C31C2×#4111yescharacteristic
351C2×C4×C31C2×#4111yescharacteristic
352C8×C31—24no—
353C8×C31—42no—
354C22×AGL(1,ℤ/8)C2×C3111yescharacteristic
355C2×#518C2×C3111yescharacteristic, complemented
356C2×#421C2×C3111yescharacteristic, complemented
357C2×#418C2×C3111yescharacteristic, complemented
358C2×#410C2×C3111yescharacteristic, complemented
359#1904C2×C3118yesdirect product factor
360C2×#344C2×C3111yescharacteristic, complemented
361C2×H(3,ℤ/4)C2×C3111yescharacteristic, complemented
362C22×C31—22no—
363C22×C31—22no—
364C22×C31—22no—
365C22×C31—28no—
366C22×C31—41no—
367C22×C31—41no—
368C22×C31—41no—
369C22×C31—41no—
370C22×C31—48no—
371C22×C31—48no—
372C22×C31—48no—
373C22×C31—42no—
374C22×C31—84no—
375C22×C31—84no—
376C22×C31—84no—
377C22×C31—84no—
378C22×C31—82no—
379C22×C31—82no—
380C22×C31—82no—
381C22×C31#38611yescharacteristic
382C22×C31#38611yescharacteristic
383C22×C31#38611yescharacteristic
384C22×C31#38611yescharacteristic
385C22×C31C2×C4×D411yescharacteristic
386C22×C31C2×#12011yescharacteristic
387C22×C31C2×#12111yescharacteristic
388C4×C31—44no—
389C4×C31—44no—
390C4×C31—42no—
391C4×C31—82no—
392C4×C31#38611yescharacteristic
393C4×C31#38611yescharacteristic
394C4×C31#38611yescharacteristic
395C4×C31#38611yescharacteristic
396C4×C31C22×C22⋊C411yescharacteristic
397C4×C31C2×C4×D411yescharacteristic
398C4×C31C2×#12111yescharacteristic
399C4×C31C2×#12311yescharacteristic
400C22×#41C22×C3111yescharacteristic
401C23×D4C22×C3111yescharacteristic
402C2×AGL(1,ℤ/8)—22no—
403C2×AGL(1,ℤ/8)—22no—
404C2×AGL(1,ℤ/8)—22no—
405C2×AGL(1,ℤ/8)—22no—
406C2×AGL(1,ℤ/8)C4×C3114yescomplemented
407C2×AGL(1,ℤ/8)C22×C3114yes—
408C22×SD16C4×C3112yescomplemented
409C22×D8C4×C3112yescomplemented
410C22×M16C22×C3111yescharacteristic
411C22×M16C22×C3111yescharacteristic
412#518—22no—
413#518—22no—
414#518—22no—
415#518C22×C3114yescomplemented
416C2×C4×D4—22no—
417C2×C4×D4—22no—
418C2×#117C22×C3111yescharacteristic
419C2×#117C22×C3111yescharacteristic
420C2×#117C22×C3111yescharacteristic
421C22×C22⋊C4—22no—
422#421—22no—
423#421C22×C3114yescomplemented
424C2×#104—22no—
425#418—22no—
426#418C22×C3114yescomplemented
427C2×#102—22no—
428#410—22no—
429#410C22×C3114yescomplemented
430C2×#99—22no—
431#344C22×C3114yescomplemented
432H(3,ℤ/4)C22×C3114yescomplemented
433C2×C31—21no—
434C2×C31—21no—
435C2×C31—21no—
436C2×C31—21no—
437C2×C31—21no—
438C2×C31—21no—
439C2×C31—48no—
440C2×C31—82no—
441C2×C31#190412yesdirect product factor
442C2×C31C2×#38611yescharacteristic
443C25—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41C2×C4×C3112yescomplemented
455C2×#41C23×C3112yes—
456C22×Q8C2×C4×C3111yescharacteristic, complemented
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4C2×C4×C3112yes—
466C22×D4C2×C4×C3112yes—
467C22×D4C2×C4×C3111yescharacteristic, complemented
468C22×D4D4×C3112yes—
469C22×D4D4×C3112yes—
470C22×D4D4×C3112yes—
471C22×D4D4×C3112yes—
472C22×D4C23×C3112yes—
473C23×C4—24no—
474C23×C4—21no—
475C23×C4C23×C3111yescharacteristic
476AGL(1,ℤ/8)—28no—
477AGL(1,ℤ/8)—28no—
478AGL(1,ℤ/8)—28no—
479AGL(1,ℤ/8)—28no—
480C2×SD16—24no—
481C2×SD16—24no—
482C2×SD16C2×C4×C3118yescomplemented
483C2×D8—24no—
484C2×D8—24no—
485C2×D8C2×C4×C3118yescomplemented
486C2×M16—21no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—21no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16C2×C4×C3112yescomplemented
496C2×M16C23×C3112yes—
497C2×M16C23×C3112yes—
498C22×C8—21no—
499C22×C8C2×C4×C3112yescomplemented
500C4×D4—28no—
501C4×D4—28no—
502C4×D4—28no—
503C4×D4—28no—
504#117—21no—
505#117—21no—
506#117—21no—
507#117—21no—
508#117—21no—
509#117—21no—
510#117—21no—
511#117D4×C3112yes—
512#117D4×C3112yes—
513#117C23×C3112yes—
514#117C23×C3112yes—
515#117C23×C3112yes—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—28no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—28no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4D4×C3112yes—
525C2×C42—21no—
526C2×C42—21no—
527C2×C42D4×C3112yes—
528#104—28no—
529#102—28no—
530#99—28no—
531C31C2×#190411yescharacteristic, direct product factor, Sylow
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—21no—
540C24—84no—
541C24C2×D4×C3111yescharacteristic
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8C22×C4×C3112yescomplemented
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4C22⋊C4×C3114yes—
597C2×D4C22⋊C4×C3114yes—
598C2×D4C22⋊C4×C3114yes—
599C2×D4C22⋊C4×C3114yes—
600C2×D4C22×C4×C3114yes—
601C2×D4C22×C4×C3112yescomplemented
602C2×D4C2×D4×C3114yes—
603C2×D4C2×D4×C3114yes—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—216no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—88no—
616C22×C4C22×C4×C3111yescharacteristic
617C22×C4C22×C4×C3111yescharacteristic
618C22×C4C2×D4×C3111yescharacteristic
619C22×C4C2×D4×C3111yescharacteristic
620C22×C4C2×D4×C3111yescharacteristic
621C22×C4C2×D4×C3111yescharacteristic
622C22×C4C2×D4×C3111yescharacteristic
623C22×C4C2×D4×C3111yescharacteristic
624C22×C4C2×D4×C3111yescharacteristic
625C22×C4#41×C3111yescharacteristic
626C22×C4#41×C3111yescharacteristic
627C22×C4#41×C3111yescharacteristic
628C22×C4#41×C3111yescharacteristic
629C22×C4C24×C3111yescharacteristic
630SD16—216no—
631D8—216no—
632M16—22no—
633M16—22no—
634M16—22no—
635M16—22no—
636M16—22no—
637M16—22no—
638M16—41no—
639M16—41no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8C22×C4×C3114yescomplemented
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—41no—
652C22⋊C4—216no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—41no—
658C22⋊C4C2×D4×C3114yes—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—41no—
664C42C2×D4×C3114yes—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—22no—
673C23—42no—
674C23—48no—
675C23—41no—
676C23—41no—
677C23—84no—
678C23—84no—
679C23—82no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23C4×D4×C3111yescharacteristic
685C23C4×D4×C3111yescharacteristic
686C23C31×#12011yescharacteristic
687C23C31×#12011yescharacteristic
688C23C31×#12111yescharacteristic
689C23C31×#12111yescharacteristic
690C23C22×D4×C3111yescharacteristic
691Q8—22no—
692Q8—22no—
693Q8—41no—
694Q8—41no—
695D4—22no—
696D4—24no—
697D4—22no—
698D4—24no—
699D4—24no—
700D4—24no—
701D4—24no—
702D4—24no—
703D4—24no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—41no—
709D4—41no—
710D4C2×C22⋊C4×C3118yes—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—816no—
724C2×C4—82no—
725C2×C4C2×C22⋊C4×C3111yescharacteristic
726C2×C4C2×C22⋊C4×C3111yescharacteristic
727C2×C4C2×C22⋊C4×C3111yescharacteristic
728C2×C4C2×C22⋊C4×C3111yescharacteristic
729C2×C4C4×D4×C3111yescharacteristic
730C2×C4C4×D4×C3111yescharacteristic
731C2×C4C4×D4×C3111yescharacteristic
732C2×C4C4×D4×C3111yescharacteristic
733C2×C4C4×D4×C3111yescharacteristic
734C2×C4C4×D4×C3111yescharacteristic
735C2×C4C31×#12011yescharacteristic
736C2×C4C31×#12011yescharacteristic
737C2×C4C31×#12111yescharacteristic
738C2×C4C31×#12111yescharacteristic
739C2×C4C31×#12111yescharacteristic
740C2×C4C31×#12111yescharacteristic
741C2×C4C31×#12111yescharacteristic
742C2×C4C31×#12111yescharacteristic
743C2×C4C31×#12311yescharacteristic
744C2×C4C31×#12311yescharacteristic
745C2×C4C31×#12311yescharacteristic
746C2×C4C31×#12311yescharacteristic
747C2×C4C23×C4×C3111yescharacteristic
748C2×C4C22×D4×C3111yescharacteristic
749C2×C4C22×D4×C3111yescharacteristic
750C2×C4C22×D4×C3111yescharacteristic
751C2×C4C2×#41×C3111yescharacteristic
752C2×C4C2×#41×C3111yescharacteristic
753C8—24no—
754C8—42no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—28no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—48no—
764C22—48no—
765C22—48no—
766C22—42no—
767C22—84no—
768C22—84no—
769C22—84no—
770C22—84no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22C31×#38611yescharacteristic
775C22C31×#38611yescharacteristic
776C22C31×#38611yescharacteristic
777C22C31×#38611yescharacteristic
778C22C2×C4×D4×C3111yescharacteristic
779C22C2×C31×#12011yescharacteristic
780C22C2×C31×#12111yescharacteristic
781C4—44no—
782C4—44no—
783C4—42no—
784C4—82no—
785C4C31×#38611yescharacteristic
786C4C31×#38611yescharacteristic
787C4C31×#38611yescharacteristic
788C4C31×#38611yescharacteristic
789C4C22×C22⋊C4×C3111yescharacteristic
790C4C2×C4×D4×C3111yescharacteristic
791C4C2×C31×#12111yescharacteristic
792C4C2×C31×#12311yescharacteristic
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—48no—
800C2—82no—
801C2C31×#190412yesdirect product factor
802C2C2×C31×#38611yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC22×C31×AGL(1,ℤ/8)C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#518C2semidirect
3. C2×C31×#421C2semidirect
4. C2×C31×#418C2semidirect
5. C2×C31×#410C2semidirect
6. C31×#1904C2direct (N × H)
7. C2×C31×#344C2semidirect
8. C2×C31×H(3,ℤ/4)C2semidirect
15. C2×C31×AGL(1,ℤ/8)C4semidirect
17. C22×SD16×C31C4semidirect
18. C22×D8×C31C4semidirect
24. C31×#518C22semidirect
32. C31×#421C22semidirect
35. C31×#418C22semidirect
38. C31×#410C22semidirect
40. C31×#344C22semidirect
41. C31×H(3,ℤ/4)C22semidirect
53. C2×#41×C31C2×C4semidirect
55. C22×Q8×C31C2×C4semidirect
66. C22×D4×C31C2×C4semidirect
81. C2×SD16×C31C2×C4semidirect
84. C2×D8×C31C2×C4semidirect
94. C2×M16×C31C2×C4semidirect
98. C22×C8×C31C2×C4semidirect
161. C2×Q8×C31C22×C4semidirect
199. C2×D4×C31C22×C4semidirect
243. C2×C8×C31C22×C4semidirect
263. C2×#1904C31direct (N × H)
355. C2×#518C2×C31semidirect
356. C2×#421C2×C31semidirect
357. C2×#418C2×C31semidirect
358. C2×#410C2×C31semidirect
359. #1904C2×C31direct (N × H)
360. C2×#344C2×C31semidirect
361. C2×H(3,ℤ/4)C2×C31semidirect
406. C2×AGL(1,ℤ/8)C4×C31semidirect
408. C22×SD16C4×C31semidirect
409. C22×D8C4×C31semidirect
415. #518C22×C31semidirect
423. #421C22×C31semidirect
426. #418C22×C31semidirect
429. #410C22×C31semidirect
431. #344C22×C31semidirect
432. H(3,ℤ/4)C22×C31semidirect
441. C2×C31#1904direct (N × H)
454. C2×#41C2×C4×C31semidirect
456. C22×Q8C2×C4×C31semidirect
467. C22×D4C2×C4×C31semidirect
482. C2×SD16C2×C4×C31semidirect
485. C2×D8C2×C4×C31semidirect
495. C2×M16C2×C4×C31semidirect
499. C22×C8C2×C4×C31semidirect
531. C31C2×#1904direct (N × H)
563. C2×Q8C22×C4×C31semidirect
601. C2×D4C22×C4×C31semidirect
645. C2×C8C22×C4×C31semidirect
801. C2C31×#1904direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×AGL(1,ℤ/8)2
C2×C31×#5182
C2×C31×#4212
C2×C31×#4182
C2×C31×#4102
C31×#19042
C2×C31×#3442
C2×C31×H(3,ℤ/4)2
C2×#190431