Finite Group Databasebeta

← C31×#17577 #21474336

Subgroups — C31×#17577 #21474336

Order 7936.

1762 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic
2C2×C31×#407C211yesmaximal, characteristic, complemented
3C31×#2280C211yesmaximal, characteristic, complemented
4C31×#1519C214yesmaximal, complemented
5C31×#1510C214yesmaximal, complemented
6C31×#1507C214yesmaximal, complemented
7C23×D4×C31—21no—
8C23×D4×C31C411yescharacteristic, complemented
9C24×C4×C31C2211yescharacteristic
10C22×M16×C31—21no—
11C2×C31×#121—21no—
12C2×C31×#121—21no—
13C2×C31×#121—21no—
14C2×C31×#121—21no—
15C2×C31×#121—21no—
16C2×C31×#121—21no—
17C2×C31×#121C412yescomplemented
18C2×C31×#121C412yescomplemented
19C2×C31×#121C412yescomplemented
20C2×C31×#121C2212yes—
21C2×C31×#121C2212yes—
22C2×C31×#121C2212yes—
23C2×C31×#117—21no—
24C22×C4⋊C4×C31C411yescharacteristic, complemented
25C22×C22⋊C4×C31—21no—
26C31×#407—21no—
27C31×#407—21no—
28C31×#407C2212yescomplemented
29C31×#407C2212yescomplemented
30C2×C31×C22⋊C8—21no—
31C2×C31×C22⋊C8C2212yescomplemented
32C31×#381C2212yescomplemented
33C31×#380—21no—
34C31×#380C2212yescomplemented
35C31×#379—21no—
36C4×C22⋊C4×C31—21no—
37C4×C22⋊C4×C31C2212yescomplemented
38C31×#327C22116yescomplemented
39C25×C31—21no—
40C25×C31D411yescharacteristic
41C22×D4×C31—22no—
42C22×D4×C31—22no—
43C22×D4×C31—22no—
44C22×D4×C31—22no—
45C22×D4×C31—22no—
46C22×D4×C31—22no—
47C22×D4×C31—21no—
48C22×D4×C31—21no—
49C22×D4×C31—21no—
50C22×D4×C31—44no—
51C22×D4×C31—48no—
52C22×D4×C31C2×C412yes—
53C22×D4×C31C2×C412yes—
54C22×D4×C31C2×C412yes—
55C23×C4×C31—21no—
56C23×C4×C31—44no—
57C23×C4×C31C2×C411yescharacteristic
58C23×C4×C31C2×C411yescharacteristic
59C23×C4×C31C2×C411yescharacteristic
60C23×C4×C31C2×C411yescharacteristic
61C23×C4×C31D411yescharacteristic
62C23×C4×C31D411yescharacteristic
63C23×C4×C31D411yescharacteristic
64C23×C4×C31D411yescharacteristic
65C23×C4×C31D411yescharacteristic
66C23×C4×C31D411yescharacteristic
67C23×C4×C31D411yescharacteristic
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C2×M16×C31—22no—
72C2×M16×C31—22no—
73C2×M16×C31—44no—
74C22×C8×C31—22no—
75C31×#121—22no—
76C31×#121—22no—
77C31×#121—22no—
78C31×#121—22no—
79C31×#121—22no—
80C31×#121—22no—
81C31×#121—22no—
82C31×#121—22no—
83C31×#121—22no—
84C31×#121—22no—
85C31×#121—22no—
86C31×#121—22no—
87C31×#121C2×C414yes—
88C31×#121C2×C414yes—
89C31×#121C2×C414yes—
90C31×#121C2314yes—
91C31×#117—44no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—22no—
96C2×C4⋊C4×C31C2×C412yes—
97C2×C4⋊C4×C31C2×C412yes—
98C2×C4⋊C4×C31C2×C412yes—
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—22no—
106C2×C22⋊C4×C31—22no—
107C2×C22⋊C4×C31—22no—
108C2×C42×C31—22no—
109C31×C22⋊C8—22no—
110C31×C22⋊C8—22no—
111C31×C22⋊C8—22no—
112C31×C22⋊C8C2314yescomplemented
113C31×#95—22no—
114C31×#95C2314yescomplemented
115C24×C31—24no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31—42no—
120C24×C31—42no—
121C24×C31—44no—
122C24×C31—44no—
123C24×C31—44no—
124C24×C31C22⋊C411yescharacteristic
125C24×C31C22⋊C411yescharacteristic
126C24×C31C22⋊C411yescharacteristic
127C24×C31C22⋊C411yescharacteristic
128C24×C31C2×D411yescharacteristic
129C24×C31C2×D411yescharacteristic
130C24×C31C2×D411yescharacteristic
131C2×D4×C31—24no—
132C2×D4×C31—24no—
133C2×D4×C31—24no—
134C2×D4×C31—24no—
135C2×D4×C31—22no—
136C2×D4×C31—22no—
137C2×D4×C31—22no—
138C2×D4×C31—44no—
139C2×D4×C31—44no—
140C2×D4×C31—44no—
141C2×D4×C31—44no—
142C2×D4×C31—44no—
143C2×D4×C31—48no—
144C2×D4×C31—48no—
145C2×D4×C31—48no—
146C2×D4×C31—48no—
147C2×D4×C31—48no—
148C2×D4×C31—48no—
149C2×D4×C31—44no—
150C2×D4×C31C22×C414yes—
151C22×C4×C31—24no—
152C22×C4×C31—24no—
153C22×C4×C31—24no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—24no—
158C22×C4×C31—42no—
159C22×C4×C31—42no—
160C22×C4×C31—42no—
161C22×C4×C31—42no—
162C22×C4×C31—42no—
163C22×C4×C31—42no—
164C22×C4×C31—42no—
165C22×C4×C31—42no—
166C22×C4×C31—42no—
167C22×C4×C31—42no—
168C22×C4×C31—42no—
169C22×C4×C31—44no—
170C22×C4×C31C22⋊C411yescharacteristic
171C22×C4×C31C22⋊C411yescharacteristic
172C22×C4×C31C22⋊C411yescharacteristic
173C22×C4×C31C22⋊C411yescharacteristic
174C22×C4×C31C22⋊C411yescharacteristic
175C22×C4×C31C22⋊C411yescharacteristic
176C22×C4×C31C22⋊C411yescharacteristic
177C22×C4×C31C22⋊C411yescharacteristic
178C22×C4×C31C22⋊C411yescharacteristic
179C22×C4×C31C22⋊C411yescharacteristic
180C22×C4×C31C22⋊C411yescharacteristic
181C22×C4×C31C22⋊C411yescharacteristic
182C22×C4×C31C22×C411yescharacteristic
183C22×C4×C31C22×C411yescharacteristic
184C22×C4×C31C22×C411yescharacteristic
185C22×C4×C31C22×C411yescharacteristic
186C22×C4×C31C22×C411yescharacteristic
187C22×C4×C31C22×C411yescharacteristic
188C22×C4×C31C2×D411yescharacteristic
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31C2×D411yescharacteristic
191C22×C4×C31C2×D411yescharacteristic
192C22×C4×C31C2×D411yescharacteristic
193C22×C4×C31C2×D411yescharacteristic
194C22×C4×C31C2×D411yescharacteristic
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2411yescharacteristic
198M16×C31—44no—
199M16×C31—44no—
200C2×C8×C31—24no—
201C2×C8×C31—44no—
202C4⋊C4×C31—22no—
203C4⋊C4×C31—22no—
204C4⋊C4×C31—22no—
205C4⋊C4×C31—44no—
206C4⋊C4×C31C22×C414yes—
207C22⋊C4×C31—24no—
208C22⋊C4×C31—24no—
209C22⋊C4×C31—24no—
210C22⋊C4×C31—24no—
211C22⋊C4×C31—44no—
212C22⋊C4×C31—44no—
213C22⋊C4×C31—44no—
214C42×C31—44no—
215#17577C3111yesmaximal, characteristic, direct product factor, Sylow
216C23×C31—22no—
217C23×C31—22no—
218C23×C31—22no—
219C23×C31—22no—
220C23×C31—22no—
221C23×C31—22no—
222C23×C31—22no—
223C23×C31—22no—
224C23×C31—22no—
225C23×C31—22no—
226C23×C31—22no—
227C23×C31—22no—
228C23×C31—24no—
229C23×C31—41no—
230C23×C31—41no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—416no—
238C23×C31—44no—
239C23×C31—44no—
240C23×C31—44no—
241C23×C31—44no—
242C23×C31—44no—
243C23×C31—44no—
244C23×C31—44no—
245C23×C31—44no—
246C23×C31—44no—
247C23×C31—816no—
248C23×C31C2×C22⋊C411yescharacteristic
249C23×C31C2×C22⋊C411yescharacteristic
250C23×C31C2×C22⋊C411yescharacteristic
251C23×C31C2×C22⋊C411yescharacteristic
252C23×C31C2×C22⋊C411yescharacteristic
253C23×C31C2×C22⋊C411yescharacteristic
254C23×C31AGL(1,ℤ/8)14yes—
255C23×C31C22×D411yescharacteristic
256D4×C31—44no—
257D4×C31—44no—
258D4×C31—48no—
259D4×C31—48no—
260D4×C31—48no—
261D4×C31—48no—
262D4×C31—44no—
263D4×C31—44no—
264C2×C4×C31—22no—
265C2×C4×C31—22no—
266C2×C4×C31—22no—
267C2×C4×C31—22no—
268C2×C4×C31—22no—
269C2×C4×C31—22no—
270C2×C4×C31—22no—
271C2×C4×C31—22no—
272C2×C4×C31—22no—
273C2×C4×C31—22no—
274C2×C4×C31—22no—
275C2×C4×C31—22no—
276C2×C4×C31—22no—
277C2×C4×C31—22no—
278C2×C4×C31—22no—
279C2×C4×C31—24no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—44no—
293C2×C4×C31—44no—
294C2×C4×C31—44no—
295C2×C4×C31—44no—
296C2×C4×C31—44no—
297C2×C4×C31—44no—
298C2×C4×C31#9914yes—
299C2×C4×C31C2×C22⋊C411yescharacteristic
300C2×C4×C31C2×C22⋊C411yescharacteristic
301C2×C4×C31C2×C22⋊C411yescharacteristic
302C2×C4×C31C2×C22⋊C411yescharacteristic
303C2×C4×C31C2×C22⋊C411yescharacteristic
304C2×C4×C31C2×C22⋊C411yescharacteristic
305C2×C4×C31C23×C411yescharacteristic
306C2×C4×C31C22×D411yescharacteristic
307C8×C31—44no—
308C22×#121C2×C3111yescharacteristic
309C2×#407C2×C3111yescharacteristic, complemented
310#2280C2×C3111yescharacteristic, complemented
311#1519C2×C3114yescomplemented
312#1510C2×C3114yescomplemented
313#1507C2×C3114yescomplemented
314C22×C31—28no—
315C22×C31—21no—
316C22×C31—21no—
317C22×C31—21no—
318C22×C31—21no—
319C22×C31—21no—
320C22×C31—21no—
321C22×C31—21no—
322C22×C31—21no—
323C22×C31—21no—
324C22×C31—21no—
325C22×C31—21no—
326C22×C31—21no—
327C22×C31—21no—
328C22×C31—21no—
329C22×C31—21no—
330C22×C31—21no—
331C22×C31—44no—
332C22×C31—44no—
333C22×C31—44no—
334C22×C31—44no—
335C22×C31—44no—
336C22×C31—44no—
337C22×C31—44no—
338C22×C31—44no—
339C22×C31—44no—
340C22×C31—88no—
341C22×C31—88no—
342C22×C31—88no—
343C22×C31C2×#9912yes—
344C22×C31#41812yes—
345C22×C31#41812yes—
346C22×C31#42112yes—
347C22×C31C22×C22⋊C411yescharacteristic
348C22×C31C2×AGL(1,ℤ/8)12yes—
349C4×C31—21no—
350C4×C31—21no—
351C4×C31—21no—
352C4×C31—21no—
353C4×C31—21no—
354C4×C31—21no—
355C4×C31—44no—
356C4×C31—84no—
357C4×C31C2×#9912yes—
358C4×C31C2×#9912yes—
359C23×D4—21no—
360C23×D4C4×C3111yescharacteristic, complemented
361C24×C4C22×C3111yescharacteristic
362C22×M16—21no—
363C2×#121—21no—
364C2×#121—21no—
365C2×#121—21no—
366C2×#121—21no—
367C2×#121—21no—
368C2×#121—21no—
369C2×#121C4×C3112yescomplemented
370C2×#121C4×C3112yescomplemented
371C2×#121C4×C3112yescomplemented
372C2×#121C22×C3112yes—
373C2×#121C22×C3112yes—
374C2×#121C22×C3112yes—
375C2×#117—21no—
376C22×C4⋊C4C4×C3111yescharacteristic, complemented
377C22×C22⋊C4—21no—
378#407—21no—
379#407—21no—
380#407C22×C3112yescomplemented
381#407C22×C3112yescomplemented
382C2×C22⋊C8—21no—
383C2×C22⋊C8C22×C3112yescomplemented
384#381C22×C3112yescomplemented
385#380—21no—
386#380C22×C3112yescomplemented
387#379—21no—
388C4×C22⋊C4—21no—
389C4×C22⋊C4C22×C3112yescomplemented
390#327C22×C31116yescomplemented
391C2×C31—22no—
392C2×C31—22no—
393C2×C31—22no—
394C2×C31—22no—
395C2×C31—22no—
396C2×C31—41no—
397C2×C31—41no—
398C2×C31—84no—
399C2×C31C22×#9911yescharacteristic
400C2×C31C2×#41811yescharacteristic
401C2×C31C2×#42111yescharacteristic
402C25—21no—
403C25D4×C3111yescharacteristic
404C22×D4—22no—
405C22×D4—22no—
406C22×D4—22no—
407C22×D4—22no—
408C22×D4—22no—
409C22×D4—22no—
410C22×D4—21no—
411C22×D4—21no—
412C22×D4—21no—
413C22×D4—44no—
414C22×D4—48no—
415C22×D4C2×C4×C3112yes—
416C22×D4C2×C4×C3112yes—
417C22×D4C2×C4×C3112yes—
418C23×C4—21no—
419C23×C4—44no—
420C23×C4C2×C4×C3111yescharacteristic
421C23×C4C2×C4×C3111yescharacteristic
422C23×C4C2×C4×C3111yescharacteristic
423C23×C4C2×C4×C3111yescharacteristic
424C23×C4D4×C3111yescharacteristic
425C23×C4D4×C3111yescharacteristic
426C23×C4D4×C3111yescharacteristic
427C23×C4D4×C3111yescharacteristic
428C23×C4D4×C3111yescharacteristic
429C23×C4D4×C3111yescharacteristic
430C23×C4D4×C3111yescharacteristic
431C23×C4C23×C3111yescharacteristic
432C23×C4C23×C3111yescharacteristic
433C23×C4C23×C3111yescharacteristic
434C2×M16—22no—
435C2×M16—22no—
436C2×M16—44no—
437C22×C8—22no—
438#121—22no—
439#121—22no—
440#121—22no—
441#121—22no—
442#121—22no—
443#121—22no—
444#121—22no—
445#121—22no—
446#121—22no—
447#121—22no—
448#121—22no—
449#121—22no—
450#121C2×C4×C3114yes—
451#121C2×C4×C3114yes—
452#121C2×C4×C3114yes—
453#121C23×C3114yes—
454#117—44no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4C2×C4×C3112yes—
460C2×C4⋊C4C2×C4×C3112yes—
461C2×C4⋊C4C2×C4×C3112yes—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C42—22no—
472C22⋊C8—22no—
473C22⋊C8—22no—
474C22⋊C8—22no—
475C22⋊C8C23×C3114yescomplemented
476#95—22no—
477#95C23×C3114yescomplemented
478C31#1757711yescharacteristic, direct product factor, Sylow
479C24—24no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—42no—
484C24—42no—
485C24—44no—
486C24—44no—
487C24—44no—
488C24C22⋊C4×C3111yescharacteristic
489C24C22⋊C4×C3111yescharacteristic
490C24C22⋊C4×C3111yescharacteristic
491C24C22⋊C4×C3111yescharacteristic
492C24C2×D4×C3111yescharacteristic
493C24C2×D4×C3111yescharacteristic
494C24C2×D4×C3111yescharacteristic
495C2×D4—24no—
496C2×D4—24no—
497C2×D4—24no—
498C2×D4—24no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—44no—
514C2×D4C22×C4×C3114yes—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—44no—
534C22×C4C22⋊C4×C3111yescharacteristic
535C22×C4C22⋊C4×C3111yescharacteristic
536C22×C4C22⋊C4×C3111yescharacteristic
537C22×C4C22⋊C4×C3111yescharacteristic
538C22×C4C22⋊C4×C3111yescharacteristic
539C22×C4C22⋊C4×C3111yescharacteristic
540C22×C4C22⋊C4×C3111yescharacteristic
541C22×C4C22⋊C4×C3111yescharacteristic
542C22×C4C22⋊C4×C3111yescharacteristic
543C22×C4C22⋊C4×C3111yescharacteristic
544C22×C4C22⋊C4×C3111yescharacteristic
545C22×C4C22⋊C4×C3111yescharacteristic
546C22×C4C22×C4×C3111yescharacteristic
547C22×C4C22×C4×C3111yescharacteristic
548C22×C4C22×C4×C3111yescharacteristic
549C22×C4C22×C4×C3111yescharacteristic
550C22×C4C22×C4×C3111yescharacteristic
551C22×C4C22×C4×C3111yescharacteristic
552C22×C4C2×D4×C3111yescharacteristic
553C22×C4C2×D4×C3111yescharacteristic
554C22×C4C2×D4×C3111yescharacteristic
555C22×C4C2×D4×C3111yescharacteristic
556C22×C4C2×D4×C3111yescharacteristic
557C22×C4C2×D4×C3111yescharacteristic
558C22×C4C2×D4×C3111yescharacteristic
559C22×C4C2×D4×C3111yescharacteristic
560C22×C4C2×D4×C3111yescharacteristic
561C22×C4C24×C3111yescharacteristic
562M16—44no—
563M16—44no—
564C2×C8—24no—
565C2×C8—44no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—44no—
570C4⋊C4C22×C4×C3114yes—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—44no—
576C22⋊C4—44no—
577C22⋊C4—44no—
578C42—44no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—24no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—416no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23—816no—
611C23C2×C22⋊C4×C3111yescharacteristic
612C23C2×C22⋊C4×C3111yescharacteristic
613C23C2×C22⋊C4×C3111yescharacteristic
614C23C2×C22⋊C4×C3111yescharacteristic
615C23C2×C22⋊C4×C3111yescharacteristic
616C23C2×C22⋊C4×C3111yescharacteristic
617C23C31×AGL(1,ℤ/8)14yes—
618C23C22×D4×C3111yescharacteristic
619D4—44no—
620D4—44no—
621D4—48no—
622D4—48no—
623D4—48no—
624D4—48no—
625D4—44no—
626D4—44no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—44no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4C31×#9914yes—
662C2×C4C2×C22⋊C4×C3111yescharacteristic
663C2×C4C2×C22⋊C4×C3111yescharacteristic
664C2×C4C2×C22⋊C4×C3111yescharacteristic
665C2×C4C2×C22⋊C4×C3111yescharacteristic
666C2×C4C2×C22⋊C4×C3111yescharacteristic
667C2×C4C2×C22⋊C4×C3111yescharacteristic
668C2×C4C23×C4×C3111yescharacteristic
669C2×C4C22×D4×C3111yescharacteristic
670C8—44no—
671C22—28no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—21no—
681C22—21no—
682C22—21no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—21no—
687C22—21no—
688C22—44no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—44no—
697C22—88no—
698C22—88no—
699C22—88no—
700C22C2×C31×#9912yes—
701C22C31×#41812yes—
702C22C31×#41812yes—
703C22C31×#42112yes—
704C22C22×C22⋊C4×C3111yescharacteristic
705C22C2×C31×AGL(1,ℤ/8)12yes—
706C4—21no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—44no—
713C4—84no—
714C4C2×C31×#9912yes—
715C4C2×C31×#9912yes—
716C2—22no—
717C2—22no—
718C2—22no—
719C2—22no—
720C2—22no—
721C2—41no—
722C2—41no—
723C2—84no—
724C2C22×C31×#9911yescharacteristic
725C2C2×C31×#41811yescharacteristic
726C2C2×C31×#42111yescharacteristic
subgroupG/H
center, socleC22×C31C22×C22⋊C4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC22×C31×#121C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#407C2semidirect
3. C31×#2280C2semidirect
4. C31×#1519C2semidirect
5. C31×#1510C2semidirect
6. C31×#1507C2semidirect
8. C23×D4×C31C4semidirect
17. C2×C31×#121C4semidirect
18. C2×C31×#121C4semidirect
19. C2×C31×#121C4semidirect
24. C22×C4⋊C4×C31C4semidirect
28. C31×#407C22semidirect
29. C31×#407C22semidirect
31. C2×C31×C22⋊C8C22semidirect
32. C31×#381C22semidirect
34. C31×#380C22semidirect
37. C4×C22⋊C4×C31C22semidirect
38. C31×#327C22semidirect
112. C31×C22⋊C8C23semidirect
114. C31×#95C23semidirect
215. #17577C31direct (N × H)
309. C2×#407C2×C31semidirect
310. #2280C2×C31semidirect
311. #1519C2×C31semidirect
312. #1510C2×C31semidirect
313. #1507C2×C31semidirect
360. C23×D4C4×C31semidirect
369. C2×#121C4×C31semidirect
370. C2×#121C4×C31semidirect
371. C2×#121C4×C31semidirect
376. C22×C4⋊C4C4×C31semidirect
380. #407C22×C31semidirect
381. #407C22×C31semidirect
383. C2×C22⋊C8C22×C31semidirect
384. #381C22×C31semidirect
386. #380C22×C31semidirect
389. C4×C22⋊C4C22×C31semidirect
390. #327C22×C31semidirect
475. C22⋊C8C23×C31semidirect
477. #95C23×C31semidirect
478. C31#17577direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C2×C31×#4072
C31×#22802
C31×#15192
C31×#15102
C31×#15072
#1757731