Finite Group Databasebeta

← C31×#24764 #21481523

Subgroups — C31×#24764 #21481523

Order 7936.

904 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#470C211yesmaximal, characteristic
2C2×C31×#467C211yesmaximal, characteristic
3C2×C31×#462C211yesmaximal, characteristic, complemented
4C2×C31×#424C211yesmaximal, characteristic
5C31×#2621C211yesmaximal, characteristic
6C31×#2323C211yesmaximal, characteristic
7C31×#2068C211yesmaximal, characteristic, complemented
8C31×#2066C211yesmaximal, characteristic, complemented
9C31×#2056C211yesmaximal, characteristic, complemented
10C31×#2056C211yesmaximal, characteristic, complemented
11C31×#1981C211yesmaximal, characteristic, complemented
12C31×#1949C211yesmaximal, characteristic, complemented
13C31×#1894C211yesmaximal, characteristic
14C31×#1892C211yesmaximal, characteristic
15C31×#1805C211yesmaximal, characteristic, complemented
16C22×Q16×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C22×M16×C31C2211yescharacteristic
19C23×C8×C31C2211yescharacteristic
20C2×C31×C4⋊Q8C2211yescharacteristic
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C31×C22⋊Q8C2211yescharacteristic
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C4×Q8×C31C2211yescharacteristic
25C2×C31×#117C2211yescharacteristic
26C31×#470—24no—
27C31×#467—24no—
28C31×#462—24no—
29C2×C31×#107C2211yescharacteristic
30C2×C31×#106C2211yescharacteristic
31C31×#424—24no—
32C2×C31×C4⋊C8C2211yescharacteristic
33C2×C31×C4⋊C8C2211yescharacteristic
34C2×C31×C4⋊C8C2211yescharacteristic
35C2×C31×C4⋊C8C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#103C2211yescharacteristic
44C31×#398—21no—
45C31×#398—21no—
46C31×#397—21no—
47C31×#397—21no—
48C31×#391C2211yescharacteristic
49C31×#391C2211yescharacteristic
50C31×#391C2211yescharacteristic
51C31×#389—21no—
52C31×#389C2211yescharacteristic
53C31×#388—21no—
54C31×#388—21no—
55C31×#387—21no—
56C31×#382C2211yescharacteristic
57C31×#380C2211yescharacteristic
58C4×C4⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×Q8×C31C2311yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C2×Q16×C31—22no—
68C2×Q16×C31—22no—
69C2×Q16×C31—22no—
70C2×Q16×C31—22no—
71C2×Q16×C31—41no—
72C2×Q16×C31—41no—
73C2×M16×C31—22no—
74C2×M16×C31—22no—
75C2×M16×C31—41no—
76C22×C8×C31—22no—
77C22×C8×C31—22no—
78C22×C8×C31—41no—
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C31×C4⋊Q8—22no—
84C31×C4⋊Q8—22no—
85C31×C22⋊Q8—22no—
86C31×C22⋊Q8—22no—
87C31×C22⋊Q8—22no—
88C31×C22⋊Q8—22no—
89C31×C22⋊Q8—22no—
90C31×C22⋊Q8D414yes—
91C4×Q8×C31—22no—
92C4×Q8×C31—22no—
93C31×#117—22no—
94C31×#117—22no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31D411yescharacteristic
103C2×C4⋊C4×C31D411yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31D411yescharacteristic
114C2×C22⋊C4×C31D411yescharacteristic
115C2×C42×C31—21no—
116C2×C42×C31—21no—
117C2×C42×C31C2311yescharacteristic
118C2×C42×C31C2311yescharacteristic
119C31×#107—22no—
120C31×#106—22no—
121C31×C4⋊C8—22no—
122C31×C4⋊C8—22no—
123C31×C4⋊C8—22no—
124C31×C4⋊C8D414yes—
125C31×#103—22no—
126C31×#103—22no—
127C31×#103—22no—
128C31×#103—22no—
129C31×#103—22no—
130C31×#103—22no—
131C31×#103—41no—
132C31×#103—41no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95—21no—
143C31×#95—21no—
144C24×C31C2×D411yescharacteristic
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31—21no—
157C2×Q8×C31—21no—
158C2×Q8×C31—21no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31—21no—
162C2×Q8×C31C2×D412yes—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D412yes—
181C22×C4×C31#4112yes—
182C22×C4×C31C2411yescharacteristic
183Q16×C31—44no—
184Q16×C31—44no—
185M16×C31—44no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31—21no—
194C2×C8×C31—21no—
195C2×C8×C31—21no—
196C2×C8×C31—44no—
197C2×C8×C31C2×D412yes—
198C2×C8×C31C2×D412yes—
199C4⋊C4×C31—24no—
200C4⋊C4×C31—22no—
201C4⋊C4×C31—22no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—42no—
212C4⋊C4×C31—42no—
213C4⋊C4×C31—42no—
214C4⋊C4×C31—42no—
215C4⋊C4×C31—42no—
216C4⋊C4×C31—81no—
217C4⋊C4×C31C2×D412yes—
218C22⋊C4×C31—24no—
219C22⋊C4×C31—22no—
220C22⋊C4×C31—22no—
221C22⋊C4×C31—42no—
222C22⋊C4×C31—42no—
223C22⋊C4×C31—81no—
224C42×C31—21no—
225C42×C31—21no—
226C42×C31—42no—
227C42×C31—81no—
228C42×C31C2×D412yes—
229C42×C31#4112yes—
230#24764C3111yesmaximal, characteristic, direct product factor, Sylow
231C23×C31—21no—
232C23×C31—21no—
233C23×C31—21no—
234C23×C31—21no—
235C23×C31—21no—
236C23×C31—21no—
237C23×C31#12112yes—
238C23×C31C22×D411yescharacteristic
239Q8×C31—22no—
240Q8×C31—22no—
241Q8×C31—41no—
242Q8×C31—41no—
243Q8×C31—41no—
244Q8×C31—41no—
245Q8×C31—41no—
246Q8×C31—41no—
247Q8×C31—41no—
248Q8×C31—41no—
249Q8×C31—41no—
250Q8×C31—41no—
251C2×C4×C31—21no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—22no—
258C2×C4×C31—22no—
259C2×C4×C31—22no—
260C2×C4×C31—22no—
261C2×C4×C31—21no—
262C2×C4×C31—21no—
263C2×C4×C31—22no—
264C2×C4×C31—22no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—21no—
268C2×C4×C31—21no—
269C2×C4×C31—41no—
270C2×C4×C31—41no—
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—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31#12112yes—
292C2×C4×C31#12112yes—
293C2×C4×C31#12112yes—
294C2×C4×C31C22×D411yescharacteristic
295C2×C4×C31C22×D411yescharacteristic
296C2×C4×C31C2×#4111yescharacteristic
297C2×C4×C31C2×#4111yescharacteristic
298C2×C4×C31H(5,𝔽2)11yescharacteristic
299C2×C4×C312−1+411yescharacteristic
300C8×C31—22no—
301C8×C31—22no—
302C8×C31—41no—
303C8×C31—41no—
304C2×#470C2×C3111yescharacteristic
305C2×#467C2×C3111yescharacteristic
306C2×#462C2×C3111yescharacteristic, complemented
307C2×#424C2×C3111yescharacteristic
308#2621C2×C3111yescharacteristic
309#2323C2×C3111yescharacteristic
310#2068C2×C3111yescharacteristic, complemented
311#2066C2×C3111yescharacteristic, complemented
312#2056C2×C3111yescharacteristic, complemented
313#2056C2×C3111yescharacteristic, complemented
314#1981C2×C3111yescharacteristic, complemented
315#1949C2×C3111yescharacteristic, complemented
316#1894C2×C3111yescharacteristic
317#1892C2×C3111yescharacteristic
318#1805C2×C3111yescharacteristic, complemented
319C22×C31—22no—
320C22×C31—22no—
321C22×C31—22no—
322C22×C31—41no—
323C22×C31—41no—
324C22×C31—41no—
325C22×C31—41no—
326C22×C31C2×#12111yescharacteristic
327C22×C31C2×#12111yescharacteristic
328C22×C31#53711yescharacteristic
329C22×C31#57711yescharacteristic
330C22×C31#57811yescharacteristic
331C22×C31#57811yescharacteristic
332C22×C31#57811yescharacteristic
333C4×C31—22no—
334C4×C31—22no—
335C4×C31—22no—
336C4×C31—42no—
337C4×C31—42no—
338C4×C31—41no—
339C4×C31—41no—
340C4×C31—81no—
341C4×C31—81no—
342C4×C31—81no—
343C4×C31—81no—
344C4×C31—81no—
345C4×C31—81no—
346C4×C31D4211yescharacteristic
347C4×C31#54711yescharacteristic
348C4×C31#54811yescharacteristic
349C4×C31#55311yescharacteristic
350C22×Q16C22×C3111yescharacteristic
351C22×Q16C22×C3111yescharacteristic
352C22×M16C22×C3111yescharacteristic
353C23×C8C22×C3111yescharacteristic
354C2×C4⋊Q8C22×C3111yescharacteristic
355C2×C22⋊Q8C22×C3111yescharacteristic
356C2×C22⋊Q8C22×C3111yescharacteristic
357C2×C22⋊Q8C22×C3111yescharacteristic
358C2×C4×Q8C22×C3111yescharacteristic
359C2×#117C22×C3111yescharacteristic
360#470—24no—
361#467—24no—
362#462—24no—
363C2×#107C22×C3111yescharacteristic
364C2×#106C22×C3111yescharacteristic
365#424—24no—
366C2×C4⋊C8C22×C3111yescharacteristic
367C2×C4⋊C8C22×C3111yescharacteristic
368C2×C4⋊C8C22×C3111yescharacteristic
369C2×C4⋊C8C22×C3111yescharacteristic
370C2×#103C22×C3111yescharacteristic
371C2×#103C22×C3111yescharacteristic
372C2×#103C22×C3111yescharacteristic
373C2×#103C22×C3111yescharacteristic
374C2×#103C22×C3111yescharacteristic
375C2×#103C22×C3111yescharacteristic
376C2×#103C22×C3111yescharacteristic
377C2×#103C22×C3111yescharacteristic
378#398—21no—
379#398—21no—
380#397—21no—
381#397—21no—
382#391C22×C3111yescharacteristic
383#391C22×C3111yescharacteristic
384#391C22×C3111yescharacteristic
385#389—21no—
386#389C22×C3111yescharacteristic
387#388—21no—
388#388—21no—
389#387—21no—
390#382C22×C3111yescharacteristic
391#380C22×C3111yescharacteristic
392C4×C4⋊C4C22×C3111yescharacteristic
393#340C22×C3111yescharacteristic
394#340C22×C3111yescharacteristic
395#340C22×C3111yescharacteristic
396#340C22×C3111yescharacteristic
397C2×C31—42no—
398C2×C31#241611yescharacteristic
399C2×C31#304411yescharacteristic
400C2×C31#304611yescharacteristic
401C2×C31#305911yescharacteristic
402C2×C31#306311yescharacteristic
403C2×C31#325811yescharacteristic
404C2×C31#326111yescharacteristic
405C22×Q8C23×C3111yescharacteristic
406C22×Q8C23×C3111yescharacteristic
407C22×Q8C23×C3111yescharacteristic
408C23×C4C23×C3111yescharacteristic
409C2×Q16—22no—
410C2×Q16—22no—
411C2×Q16—22no—
412C2×Q16—22no—
413C2×Q16—41no—
414C2×Q16—41no—
415C2×M16—22no—
416C2×M16—22no—
417C2×M16—41no—
418C22×C8—22no—
419C22×C8—22no—
420C22×C8—41no—
421C22×C8C23×C3111yescharacteristic
422C22×C8C23×C3111yescharacteristic
423C22×C8C23×C3111yescharacteristic
424C22×C8C23×C3111yescharacteristic
425C4⋊Q8—22no—
426C4⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—22no—
429C22⋊Q8—22no—
430C22⋊Q8—22no—
431C22⋊Q8—22no—
432C22⋊Q8D4×C3114yes—
433C4×Q8—22no—
434C4×Q8—22no—
435#117—22no—
436#117—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4D4×C3111yescharacteristic
445C2×C4⋊C4D4×C3111yescharacteristic
446C2×C4⋊C4C23×C3111yescharacteristic
447C2×C4⋊C4C23×C3111yescharacteristic
448C2×C4⋊C4C23×C3111yescharacteristic
449C2×C4⋊C4C23×C3111yescharacteristic
450C2×C4⋊C4C23×C3111yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4D4×C3111yescharacteristic
456C2×C22⋊C4D4×C3111yescharacteristic
457C2×C42—21no—
458C2×C42—21no—
459C2×C42C23×C3111yescharacteristic
460C2×C42C23×C3111yescharacteristic
461#107—22no—
462#106—22no—
463C4⋊C8—22no—
464C4⋊C8—22no—
465C4⋊C8—22no—
466C4⋊C8D4×C3114yes—
467#103—22no—
468#103—22no—
469#103—22no—
470#103—22no—
471#103—22no—
472#103—22no—
473#103—41no—
474#103—41no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486C31#2476411yescharacteristic, direct product factor, Sylow
487C24C2×D4×C3111yescharacteristic
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8C2×D4×C3112yes—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4C2×D4×C3111yescharacteristic
519C22×C4C2×D4×C3111yescharacteristic
520C22×C4C2×D4×C3111yescharacteristic
521C22×C4C2×D4×C3111yescharacteristic
522C22×C4C2×D4×C3111yescharacteristic
523C22×C4C2×D4×C3112yes—
524C22×C4#41×C3112yes—
525C22×C4C24×C3111yescharacteristic
526Q16—44no—
527Q16—44no—
528M16—44no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—44no—
540C2×C8C2×D4×C3112yes—
541C2×C8C2×D4×C3112yes—
542C4⋊C4—24no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—81no—
560C4⋊C4C2×D4×C3112yes—
561C22⋊C4—24no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—81no—
567C42—21no—
568C42—21no—
569C42—42no—
570C42—81no—
571C42C2×D4×C3112yes—
572C42#41×C3112yes—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23C31×#12112yes—
580C23C22×D4×C3111yescharacteristic
581Q8—22no—
582Q8—22no—
583Q8—41no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591Q8—41no—
592Q8—41no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
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—41no—
632C2×C4—41no—
633C2×C4C31×#12112yes—
634C2×C4C31×#12112yes—
635C2×C4C31×#12112yes—
636C2×C4C22×D4×C3111yescharacteristic
637C2×C4C22×D4×C3111yescharacteristic
638C2×C4C2×#41×C3111yescharacteristic
639C2×C4C2×#41×C3111yescharacteristic
640C2×C4C31×H(5,𝔽2)11yescharacteristic
641C2×C4C31×2−1+411yescharacteristic
642C8—22no—
643C8—22no—
644C8—41no—
645C8—41no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22C2×C31×#12111yescharacteristic
654C22C2×C31×#12111yescharacteristic
655C22C31×#53711yescharacteristic
656C22C31×#57711yescharacteristic
657C22C31×#57811yescharacteristic
658C22C31×#57811yescharacteristic
659C22C31×#57811yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—42no—
664C4—42no—
665C4—41no—
666C4—41no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4D42×C3111yescharacteristic
674C4C31×#54711yescharacteristic
675C4C31×#54811yescharacteristic
676C4C31×#55311yescharacteristic
677C2—42no—
678C2C31×#241611yescharacteristic
679C2C31×#304411yescharacteristic
680C2C31×#304611yescharacteristic
681C2C31×#305911yescharacteristic
682C2C31×#306311yescharacteristic
683C2C31×#325811yescharacteristic
684C2C31×#326111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#462C2semidirect
7. C31×#2068C2semidirect
8. C31×#2066C2semidirect
9. C31×#2056C2semidirect
10. C31×#2056C2semidirect
11. C31×#1981C2semidirect
12. C31×#1949C2semidirect
15. C31×#1805C2semidirect
230. #24764C31direct (N × H)
306. C2×#462C2×C31semidirect
310. #2068C2×C31semidirect
311. #2066C2×C31semidirect
312. #2056C2×C31semidirect
313. #2056C2×C31semidirect
314. #1981C2×C31semidirect
315. #1949C2×C31semidirect
318. #1805C2×C31semidirect
486. C31#24764direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4702
C2×C31×#4672
C2×C31×#4622
C2×C31×#4242
C31×#26212
C31×#23232
C31×#20682
C31×#20662
C31×#20562
C31×#19812
C31×#19492
C31×#18942
C31×#18922
C31×#18052
#2476431