Finite Group Databasebeta

← C31×#26890 #21483649

Subgroups — C31×#26890 #21483649

Order 7936.

912 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#477C211yesmaximal, characteristic, complemented
2C2×C4×D8×C31C211yesmaximal, characteristic
3C31×#2452C211yesmaximal, characteristic, complemented
4C31×#2367C211yesmaximal, characteristic, complemented
5C31×#2054C211yesmaximal, characteristic
6C31×#2042C211yesmaximal, characteristic, complemented
7C31×#2023C211yesmaximal, characteristic, complemented
8C31×#2012C211yesmaximal, characteristic
9C31×#1933C211yesmaximal, characteristic, complemented
10C31×#1925C211yesmaximal, characteristic, complemented
11C31×#1921C211yesmaximal, characteristic, complemented
12C31×#1916C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic, complemented
14C31×#1877C211yesmaximal, characteristic, complemented
15C31×#1862C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C2×C31×C4⋊Q8C2211yescharacteristic
19C2×C31×#124C2211yescharacteristic
20C2×C31×C22⋊Q8—21no—
21C2×C4×Q8×C31C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C31×#477—24no—
25C4×D8×C31—24no—
26C2×C31×#107C2211yescharacteristic
27C2×C31×#107C2211yescharacteristic
28C2×C31×C4⋊C8C2211yescharacteristic
29C2×C31×#103C2211yescharacteristic
30C2×C31×#103C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C4×C8×C31C2211yescharacteristic
38C31×#396—21no—
39C31×#393—21no—
40C31×#391C2211yescharacteristic
41C31×#390C2211yescharacteristic
42C31×#390C2211yescharacteristic
43C31×#390C2211yescharacteristic
44C31×#389C2211yescharacteristic
45C31×#389C2211yescharacteristic
46C31×#388—21no—
47C31×#388—21no—
48C31×#385—21no—
49C31×#385—21no—
50C4×C4⋊C4×C31C2211yescharacteristic
51C4×C4⋊C4×C31C2211yescharacteristic
52C4×C22⋊C4×C31—21no—
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#336C2211yescharacteristic
58C31×#336C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×Q8×C31—21no—
62C22×Q8×C31C2311yescharacteristic
63C22×D4×C31C2311yescharacteristic
64C22×D4×C31C2311yescharacteristic
65C23×C4×C31—21no—
66C23×C4×C31—21no—
67C2×SD16×C31—22no—
68C2×SD16×C31—22no—
69C2×SD16×C31—41no—
70C2×D8×C31—22no—
71C2×D8×C31—22no—
72C2×D8×C31—22no—
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C31×C4⋊Q8—22no—
78C31×C4⋊Q8—41no—
79C31×#124—22no—
80C31×#124—22no—
81C31×C22⋊Q8—44no—
82C4×Q8×C31—22no—
83C4×Q8×C31—41no—
84C4×D4×C31—22no—
85C4×D4×C31—22no—
86C4×D4×C31—41no—
87C4×D4×C31—41no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31D411yescharacteristic
93C2×C4⋊C4×C31D411yescharacteristic
94C2×C4⋊C4×C31C2311yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—21no—
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C42×C31—21no—
110C2×C42×C31—21no—
111C2×C42×C31C2311yescharacteristic
112C2×C42×C31C2311yescharacteristic
113C2×C42×C31C2311yescharacteristic
114C31×#107—22no—
115C31×#107D414yes—
116C31×C4⋊C8—22no—
117C31×#103—22no—
118C31×#103—22no—
119C31×#103—22no—
120C31×#102—22no—
121C31×#102—22no—
122C31×#102—22no—
123C31×#102—22no—
124C31×#102—41no—
125C4×C8×C31—22no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95D411yescharacteristic
132C31×#95D411yescharacteristic
133C24×C31—21no—
134C24×C31—21no—
135C2×Q8×C31—21no—
136C2×Q8×C31—21no—
137C2×Q8×C31—21no—
138C2×Q8×C31—21no—
139C2×Q8×C31—21no—
140C2×Q8×C31—42no—
141C2×Q8×C31—42no—
142C2×Q8×C31—81no—
143C2×Q8×C31#4112yes—
144C2×D4×C31—21no—
145C2×D4×C31—21no—
146C2×D4×C31—21no—
147C2×D4×C31—21no—
148C2×D4×C31—21no—
149C2×D4×C31—21no—
150C2×D4×C31—21no—
151C2×D4×C31—21no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31#4112yes—
155C2×D4×C31#4112yes—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—42no—
163C22×C4×C31—42no—
164C22×C4×C31—42no—
165C22×C4×C31—42no—
166C22×C4×C31—81no—
167C22×C4×C31—81no—
168C22×C4×C31C2×D411yescharacteristic
169C22×C4×C31C2×D411yescharacteristic
170C22×C4×C31C2×D411yescharacteristic
171C22×C4×C31C2×D411yescharacteristic
172C22×C4×C31C2×D411yescharacteristic
173C22×C4×C31C2×D411yescharacteristic
174C22×C4×C31C2411yescharacteristic
175SD16×C31—44no—
176D8×C31—28no—
177C2×C8×C31—21no—
178C2×C8×C31—21no—
179C2×C8×C31—21no—
180C2×C8×C31—21no—
181C2×C8×C31—21no—
182C2×C8×C31—21no—
183C2×C8×C31—21no—
184C2×C8×C31—21no—
185C2×C8×C31—21no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31C2×D412yes—
189C4⋊C4×C31—22no—
190C4⋊C4×C31—22no—
191C4⋊C4×C31—21no—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—42no—
200C4⋊C4×C31—42no—
201C4⋊C4×C31—42no—
202C4⋊C4×C31—42no—
203C4⋊C4×C31C2×D412yes—
204C4⋊C4×C31C2×D412yes—
205C22⋊C4×C31—24no—
206C22⋊C4×C31—24no—
207C22⋊C4×C31—42no—
208C22⋊C4×C31—42no—
209C22⋊C4×C31—42no—
210C22⋊C4×C31—42no—
211C22⋊C4×C31—42no—
212C22⋊C4×C31—42no—
213C22⋊C4×C31—81no—
214C22⋊C4×C31—81no—
215C42×C31—21no—
216C42×C31—21no—
217C42×C31—21no—
218C42×C31—21no—
219C42×C31—21no—
220C42×C31—21no—
221C42×C31—42no—
222C42×C31—81no—
223#26890C3111yesmaximal, characteristic, direct product factor, Sylow
224C23×C31—22no—
225C23×C31—22no—
226C23×C31—41no—
227C23×C31—41no—
228C23×C31—41no—
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—41no—
238C23×C31C22×D411yescharacteristic
239Q8×C31—22no—
240Q8×C31—22no—
241Q8×C31—41no—
242Q8×C31—41no—
243Q8×C31—84no—
244D4×C31—22no—
245D4×C31—22no—
246D4×C31—22no—
247D4×C31—22no—
248D4×C31—41no—
249D4×C31—41no—
250D4×C31—41no—
251D4×C31—41no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—21no—
258C2×C4×C31—22no—
259C2×C4×C31—21no—
260C2×C4×C31—21no—
261C2×C4×C31—22no—
262C2×C4×C31—22no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—21no—
268C2×C4×C31—21no—
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—41no—
272C2×C4×C31—41no—
273C2×C4×C31—41no—
274C2×C4×C31—41no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—41no—
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—84no—
287C2×C4×C31—84no—
288C2×C4×C31#13512yes—
289C2×C4×C31AGL(1,ℤ/8)12yes—
290C2×C4×C31C22×D411yescharacteristic
291C2×C4×C31C2×#4111yescharacteristic
292C2×C4×C31C2×#4111yescharacteristic
293C2×C4×C31C2×#4111yescharacteristic
294C2×C4×C31H(5,𝔽2)11yescharacteristic
295C2×C4×C312−1+411yescharacteristic
296C8×C31—22no—
297C8×C31—41no—
298C8×C31—41no—
299C8×C31—41no—
300C2×#477C2×C3111yescharacteristic, complemented
301C2×C4×D8C2×C3111yescharacteristic
302#2452C2×C3111yescharacteristic, complemented
303#2367C2×C3111yescharacteristic, complemented
304#2054C2×C3111yescharacteristic
305#2042C2×C3111yescharacteristic, complemented
306#2023C2×C3111yescharacteristic, complemented
307#2012C2×C3111yescharacteristic
308#1933C2×C3111yescharacteristic, complemented
309#1925C2×C3111yescharacteristic, complemented
310#1921C2×C3111yescharacteristic, complemented
311#1916C2×C3111yescharacteristic, complemented
312#1880C2×C3111yescharacteristic, complemented
313#1877C2×C3111yescharacteristic, complemented
314#1862C2×C3111yescharacteristic, complemented
315C22×C31—42no—
316C22×C31—42no—
317C22×C31—42no—
318C22×C31—42no—
319C22×C31—42no—
320C22×C31—42no—
321C22×C31—81no—
322C22×C31—81no—
323C22×C31—81no—
324C22×C31—81no—
325C22×C31—81no—
326C22×C31—81no—
327C22×C31—81no—
328C22×C31—81no—
329C22×C31#52511yescharacteristic
330C22×C31D4211yescharacteristic
331C22×C31#54811yescharacteristic
332C22×C31C2×#13511yescharacteristic
333C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C31#57611yescharacteristic
335C22×C31#57811yescharacteristic
336C4×C31—22no—
337C4×C31—22no—
338C4×C31—41no—
339C4×C31—41no—
340C4×C31—42no—
341C4×C31—41no—
342C4×C31—42no—
343C4×C31—42no—
344C4×C31—41no—
345C4×C31—81no—
346C4×C31—81no—
347C4×C31—81no—
348C4×C31#52511yescharacteristic
349C4×C31#53911yescharacteristic
350C4×C31#54811yescharacteristic
351C4×C31#55111yescharacteristic
352C22×SD16C22×C3111yescharacteristic
353C22×D8C22×C3111yescharacteristic
354C2×C4⋊Q8C22×C3111yescharacteristic
355C2×#124C22×C3111yescharacteristic
356C2×C22⋊Q8—21no—
357C2×C4×Q8C22×C3111yescharacteristic
358C2×C4×D4C22×C3111yescharacteristic
359C2×C4×D4C22×C3111yescharacteristic
360#477—24no—
361C4×D8—24no—
362C2×#107C22×C3111yescharacteristic
363C2×#107C22×C3111yescharacteristic
364C2×C4⋊C8C22×C3111yescharacteristic
365C2×#103C22×C3111yescharacteristic
366C2×#103C22×C3111yescharacteristic
367C2×#103C22×C3111yescharacteristic
368C2×#102C22×C3111yescharacteristic
369C2×#102C22×C3111yescharacteristic
370C2×#102C22×C3111yescharacteristic
371C2×#102C22×C3111yescharacteristic
372C2×#102C22×C3111yescharacteristic
373C2×C4×C8C22×C3111yescharacteristic
374#396—21no—
375#393—21no—
376#391C22×C3111yescharacteristic
377#390C22×C3111yescharacteristic
378#390C22×C3111yescharacteristic
379#390C22×C3111yescharacteristic
380#389C22×C3111yescharacteristic
381#389C22×C3111yescharacteristic
382#388—21no—
383#388—21no—
384#385—21no—
385#385—21no—
386C4×C4⋊C4C22×C3111yescharacteristic
387C4×C4⋊C4C22×C3111yescharacteristic
388C4×C22⋊C4—21no—
389#340C22×C3111yescharacteristic
390#340C22×C3111yescharacteristic
391#340C22×C3111yescharacteristic
392#340C22×C3111yescharacteristic
393#336C22×C3111yescharacteristic
394#336C22×C3111yescharacteristic
395#336C22×C3111yescharacteristic
396#336C22×C3111yescharacteristic
397C2×C31—82no—
398C2×C31—82no—
399C2×C31#246311yescharacteristic
400C2×C31#310611yescharacteristic
401C2×C31#312411yescharacteristic
402C2×C31#326411yescharacteristic
403C2×C31#328511yescharacteristic
404C2×C31#336111yescharacteristic
405C2×C31#336711yescharacteristic
406C22×Q8—21no—
407C22×Q8C23×C3111yescharacteristic
408C22×D4C23×C3111yescharacteristic
409C22×D4C23×C3111yescharacteristic
410C23×C4—21no—
411C23×C4—21no—
412C2×SD16—22no—
413C2×SD16—22no—
414C2×SD16—41no—
415C2×D8—22no—
416C2×D8—22no—
417C2×D8—22no—
418C22×C8C23×C3111yescharacteristic
419C22×C8C23×C3111yescharacteristic
420C22×C8C23×C3111yescharacteristic
421C22×C8C23×C3111yescharacteristic
422C4⋊Q8—22no—
423C4⋊Q8—41no—
424#124—22no—
425#124—22no—
426C22⋊Q8—44no—
427C4×Q8—22no—
428C4×Q8—41no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—41no—
432C4×D4—41no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4D4×C3111yescharacteristic
438C2×C4⋊C4D4×C3111yescharacteristic
439C2×C4⋊C4C23×C3111yescharacteristic
440C2×C4⋊C4C23×C3111yescharacteristic
441C2×C4⋊C4C23×C3111yescharacteristic
442C2×C4⋊C4C23×C3111yescharacteristic
443C2×C4⋊C4C23×C3111yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42C23×C3111yescharacteristic
457C2×C42C23×C3111yescharacteristic
458C2×C42C23×C3111yescharacteristic
459#107—22no—
460#107D4×C3114yes—
461C4⋊C8—22no—
462#103—22no—
463#103—22no—
464#103—22no—
465#102—22no—
466#102—22no—
467#102—22no—
468#102—22no—
469#102—41no—
470C4×C8—22no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95D4×C3111yescharacteristic
477#95D4×C3111yescharacteristic
478C31#2689011yescharacteristic, direct product factor, Sylow
479C24—21no—
480C24—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—81no—
489C2×Q8#41×C3112yes—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4#41×C3112yes—
501C2×D4#41×C3112yes—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—81no—
513C22×C4—81no—
514C22×C4C2×D4×C3111yescharacteristic
515C22×C4C2×D4×C3111yescharacteristic
516C22×C4C2×D4×C3111yescharacteristic
517C22×C4C2×D4×C3111yescharacteristic
518C22×C4C2×D4×C3111yescharacteristic
519C22×C4C2×D4×C3111yescharacteristic
520C22×C4C24×C3111yescharacteristic
521SD16—44no—
522D8—28no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8C2×D4×C3112yes—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4C2×D4×C3112yes—
550C4⋊C4C2×D4×C3112yes—
551C22⋊C4—24no—
552C22⋊C4—24no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—42no—
568C42—81no—
569C23—22no—
570C23—22no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23C22×D4×C3111yescharacteristic
584Q8—22no—
585Q8—22no—
586Q8—41no—
587Q8—41no—
588Q8—84no—
589D4—22no—
590D4—22no—
591D4—22no—
592D4—22no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—41no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—84no—
632C2×C4—84no—
633C2×C4C31×#13512yes—
634C2×C4C31×AGL(1,ℤ/8)12yes—
635C2×C4C22×D4×C3111yescharacteristic
636C2×C4C2×#41×C3111yescharacteristic
637C2×C4C2×#41×C3111yescharacteristic
638C2×C4C2×#41×C3111yescharacteristic
639C2×C4C31×H(5,𝔽2)11yescharacteristic
640C2×C4C31×2−1+411yescharacteristic
641C8—22no—
642C8—41no—
643C8—41no—
644C8—41no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22C31×#52511yescharacteristic
660C22D42×C3111yescharacteristic
661C22C31×#54811yescharacteristic
662C22C2×C31×#13511yescharacteristic
663C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
664C22C31×#57611yescharacteristic
665C22C31×#57811yescharacteristic
666C4—22no—
667C4—22no—
668C4—41no—
669C4—41no—
670C4—42no—
671C4—41no—
672C4—42no—
673C4—42no—
674C4—41no—
675C4—81no—
676C4—81no—
677C4—81no—
678C4C31×#52511yescharacteristic
679C4C31×#53911yescharacteristic
680C4C31×#54811yescharacteristic
681C4C31×#55111yescharacteristic
682C2—82no—
683C2—82no—
684C2C31×#246311yescharacteristic
685C2C31×#310611yescharacteristic
686C2C31×#312411yescharacteristic
687C2C31×#326411yescharacteristic
688C2C31×#328511yescharacteristic
689C2C31×#336111yescharacteristic
690C2C31×#336711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D8×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#477C2semidirect
3. C31×#2452C2semidirect
4. C31×#2367C2semidirect
6. C31×#2042C2semidirect
7. C31×#2023C2semidirect
9. C31×#1933C2semidirect
10. C31×#1925C2semidirect
11. C31×#1921C2semidirect
12. C31×#1916C2semidirect
13. C31×#1880C2semidirect
14. C31×#1877C2semidirect
15. C31×#1862C2semidirect
223. #26890C31direct (N × H)
300. C2×#477C2×C31semidirect
302. #2452C2×C31semidirect
303. #2367C2×C31semidirect
305. #2042C2×C31semidirect
306. #2023C2×C31semidirect
308. #1933C2×C31semidirect
309. #1925C2×C31semidirect
310. #1921C2×C31semidirect
311. #1916C2×C31semidirect
312. #1880C2×C31semidirect
313. #1877C2×C31semidirect
314. #1862C2×C31semidirect
478. C31#26890direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4772
C2×C4×D8×C312
C31×#24522
C31×#23672
C31×#20542
C31×#20422
C31×#20232
C31×#20122
C31×#19332
C31×#19252
C31×#19212
C31×#19162
C31×#18802
C31×#18772
C31×#18622
#2689031