Finite Group Databasebeta

← C31×#24736 #21481495

Subgroups — C31×#24736 #21481495

Order 7936.

924 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#464C211yesmaximal, characteristic
2C2×C31×#464C211yesmaximal, characteristic
3C2×C31×#462C211yesmaximal, characteristic, complemented
4C2×C4×Q16×C31C211yesmaximal, characteristic, complemented
5C31×#2545C211yesmaximal, characteristic
6C31×#2351C211yesmaximal, characteristic, complemented
7C31×#2068C211yesmaximal, characteristic, complemented
8C31×#2067C211yesmaximal, characteristic
9C31×#2043C211yesmaximal, characteristic, complemented
10C31×#2042C211yesmaximal, characteristic
11C31×#1958C211yesmaximal, characteristic
12C31×#1939C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic
14C31×#1878C211yesmaximal, characteristic, complemented
15C31×#1805C211yesmaximal, characteristic, complemented
16C22×Q16×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C2×C31×C4⋊Q8C2211yescharacteristic
20C2×C31×#124C2211yescharacteristic
21C2×C31×#124C2211yescharacteristic
22C2×C4×Q8×C31C2211yescharacteristic
23C2×C4×Q8×C31C2211yescharacteristic
24C2×C4×Q8×C31C2211yescharacteristic
25C2×C4×Q8×C31C2211yescharacteristic
26C31×#464—24no—
27C31×#464—24no—
28C31×#462—24no—
29C4×Q16×C31—24no—
30C2×C31×#107C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×C4⋊C8C2211yescharacteristic
33C2×C31×C4⋊C8C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C4×C8×C31C2211yescharacteristic
45C31×#396—21no—
46C31×#396—21no—
47C31×#391C2211yescharacteristic
48C31×#390C2211yescharacteristic
49C31×#389—21no—
50C31×#389—21no—
51C31×#389C2211yescharacteristic
52C31×#389C2211yescharacteristic
53C31×#388—21no—
54C31×#388—21no—
55C31×#382—21no—
56C31×#382C2211yescharacteristic
57C4×C4⋊C4×C31—21no—
58C4×C4⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×Q8×C31C2311yescharacteristic
66C22×D4×C31C2311yescharacteristic
67C2×Q16×C31—22no—
68C2×Q16×C31—22no—
69C2×Q16×C31—22no—
70C2×Q16×C31—22no—
71C2×Q16×C31—22no—
72C2×Q16×C31D414yes—
73C2×SD16×C31—22no—
74C2×SD16×C31—22no—
75C2×SD16×C31—22no—
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C31×C4⋊Q8—22no—
81C31×C4⋊Q8—41no—
82C31×#124—22no—
83C31×#124—22no—
84C31×#124—22no—
85C31×#124—41no—
86C4×Q8×C31—22no—
87C4×Q8×C31—22no—
88C4×Q8×C31—22no—
89C4×Q8×C31—22no—
90C4×Q8×C31—22no—
91C4×Q8×C31—41no—
92C4×Q8×C31—41no—
93C4×Q8×C31D414yes—
94C2×C4⋊C4×C31—21no—
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×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C42×C31—21no—
115C2×C42×C31—21no—
116C2×C42×C31—21no—
117C2×C42×C31—21no—
118C2×C42×C31C2311yescharacteristic
119C2×C42×C31C2311yescharacteristic
120C2×C42×C31C2311yescharacteristic
121C31×#107—22no—
122C31×C4⋊C8—22no—
123C31×C4⋊C8—22no—
124C31×C4⋊C8—22no—
125C31×#103—22no—
126C31×#103—22no—
127C31×#103—22no—
128C31×#103—22no—
129C31×#103—22no—
130C31×#103—22no—
131C31×#103—41no—
132C31×#102—22no—
133C31×#102—22no—
134C31×#102—41no—
135C4×C8×C31—22no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95D411yescharacteristic
143C31×#95D411yescharacteristic
144C24×C31—21no—
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×C31C2×D412yes—
160C2×Q8×C31C2×D412yes—
161C2×Q8×C31C2×D412yes—
162C2×Q8×C31#4112yes—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×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×C31—21no—
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2×D411yescharacteristic
182C22×C4×C31C2411yescharacteristic
183Q16×C31—28no—
184Q16×C31—44no—
185SD16×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—21no—
197C2×C8×C31C2×D412yes—
198C4⋊C4×C31—24no—
199C4⋊C4×C31—22no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—41no—
208C4⋊C4×C31—42no—
209C4⋊C4×C31—42no—
210C4⋊C4×C31—42no—
211C4⋊C4×C31—42no—
212C4⋊C4×C31—42no—
213C4⋊C4×C31—42no—
214C4⋊C4×C31—42no—
215C4⋊C4×C31C2×D412yes—
216C22⋊C4×C31—42no—
217C22⋊C4×C31—42no—
218C22⋊C4×C31—42no—
219C22⋊C4×C31—42no—
220C22⋊C4×C31—42no—
221C22⋊C4×C31—42no—
222C42×C31—24no—
223C42×C31—21no—
224C42×C31—21no—
225C42×C31—21no—
226C42×C31—21no—
227C42×C31—42no—
228C42×C31—42no—
229C42×C31—42no—
230C42×C31C2×D412yes—
231C42×C31#4112yes—
232#24736C3111yesmaximal, characteristic, direct product factor, Sylow
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31C22×D411yescharacteristic
241Q8×C31—22no—
242Q8×C31—22no—
243Q8×C31—22no—
244Q8×C31—22no—
245Q8×C31—22no—
246Q8×C31—41no—
247Q8×C31—41no—
248Q8×C31—41no—
249Q8×C31—41no—
250Q8×C31—41no—
251Q8×C31—41no—
252Q8×C31#12114yes—
253D4×C31—41no—
254D4×C31—41no—
255D4×C31—41no—
256D4×C31—41no—
257C2×C4×C31—22no—
258C2×C4×C31—21no—
259C2×C4×C31—22no—
260C2×C4×C31—22no—
261C2×C4×C31—21no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—21no—
266C2×C4×C31—22no—
267C2×C4×C31—21no—
268C2×C4×C31—21no—
269C2×C4×C31—21no—
270C2×C4×C31—22no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—21no—
276C2×C4×C31—21no—
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—41no—
292C2×C4×C31—41no—
293C2×C4×C31#12112yes—
294C2×C4×C31#12112yes—
295C2×C4×C31#13512yes—
296C2×C4×C31C22×D411yescharacteristic
297C2×C4×C31C22×D411yescharacteristic
298C2×C4×C31C2×#4111yescharacteristic
299C2×C4×C31C2×#4111yescharacteristic
300C2×C4×C31H(5,𝔽2)11yescharacteristic
301C2×C4×C312−1+411yescharacteristic
302C8×C31—22no—
303C8×C31—41no—
304C8×C31—41no—
305C8×C31—41no—
306C2×#464C2×C3111yescharacteristic
307C2×#464C2×C3111yescharacteristic
308C2×#462C2×C3111yescharacteristic, complemented
309C2×C4×Q16C2×C3111yescharacteristic, complemented
310#2545C2×C3111yescharacteristic
311#2351C2×C3111yescharacteristic, complemented
312#2068C2×C3111yescharacteristic, complemented
313#2067C2×C3111yescharacteristic
314#2043C2×C3111yescharacteristic, complemented
315#2042C2×C3111yescharacteristic
316#1958C2×C3111yescharacteristic
317#1939C2×C3111yescharacteristic, complemented
318#1880C2×C3111yescharacteristic
319#1878C2×C3111yescharacteristic, complemented
320#1805C2×C3111yescharacteristic, complemented
321C22×C31—81no—
322C22×C31—81no—
323C22×C31—81no—
324C22×C31—81no—
325C22×C31—81no—
326C22×C31—81no—
327C22×C31—81no—
328C22×C31C2×#12111yescharacteristic
329C22×C31D4211yescharacteristic
330C22×C31#54811yescharacteristic
331C22×C31C2×#13511yescharacteristic
332C22×C31#57511yescharacteristic
333C22×C31#57811yescharacteristic
334C22×C31#57811yescharacteristic
335C4×C31—24no—
336C4×C31—22no—
337C4×C31—22no—
338C4×C31—22no—
339C4×C31—42no—
340C4×C31—41no—
341C4×C31—41no—
342C4×C31—41no—
343C4×C31—42no—
344C4×C31—81no—
345C4×C31—81no—
346C4×C31—81no—
347C4×C31—81no—
348C4×C31C2×#12111yescharacteristic
349C4×C31#53711yescharacteristic
350C4×C31#54711yescharacteristic
351C4×C31#55311yescharacteristic
352C22×Q16C22×C3111yescharacteristic
353C22×Q16C22×C3111yescharacteristic
354C22×SD16C22×C3111yescharacteristic
355C2×C4⋊Q8C22×C3111yescharacteristic
356C2×#124C22×C3111yescharacteristic
357C2×#124C22×C3111yescharacteristic
358C2×C4×Q8C22×C3111yescharacteristic
359C2×C4×Q8C22×C3111yescharacteristic
360C2×C4×Q8C22×C3111yescharacteristic
361C2×C4×Q8C22×C3111yescharacteristic
362#464—24no—
363#464—24no—
364#462—24no—
365C4×Q16—24no—
366C2×#107C22×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×#102C22×C3111yescharacteristic
378C2×#102C22×C3111yescharacteristic
379C2×#102C22×C3111yescharacteristic
380C2×C4×C8C22×C3111yescharacteristic
381#396—21no—
382#396—21no—
383#391C22×C3111yescharacteristic
384#390C22×C3111yescharacteristic
385#389—21no—
386#389—21no—
387#389C22×C3111yescharacteristic
388#389C22×C3111yescharacteristic
389#388—21no—
390#388—21no—
391#382—21no—
392#382C22×C3111yescharacteristic
393C4×C4⋊C4—21no—
394C4×C4⋊C4C22×C3111yescharacteristic
395#340C22×C3111yescharacteristic
396#340C22×C3111yescharacteristic
397#336C22×C3111yescharacteristic
398#336C22×C3111yescharacteristic
399C2×C31—161no—
400C2×C31#241611yescharacteristic
401C2×C31#303511yescharacteristic
402C2×C31#304411yescharacteristic
403C2×C31#327711yescharacteristic
404C2×C31#328511yescharacteristic
405C2×C31#336411yescharacteristic
406C2×C31#337711yescharacteristic
407C22×Q8C23×C3111yescharacteristic
408C22×Q8C23×C3111yescharacteristic
409C22×Q8C23×C3111yescharacteristic
410C22×D4C23×C3111yescharacteristic
411C2×Q16—22no—
412C2×Q16—22no—
413C2×Q16—22no—
414C2×Q16—22no—
415C2×Q16—22no—
416C2×Q16D4×C3114yes—
417C2×SD16—22no—
418C2×SD16—22no—
419C2×SD16—22no—
420C22×C8C23×C3111yescharacteristic
421C22×C8C23×C3111yescharacteristic
422C22×C8C23×C3111yescharacteristic
423C22×C8C23×C3111yescharacteristic
424C4⋊Q8—22no—
425C4⋊Q8—41no—
426#124—22no—
427#124—22no—
428#124—22no—
429#124—41no—
430C4×Q8—22no—
431C4×Q8—22no—
432C4×Q8—22no—
433C4×Q8—22no—
434C4×Q8—22no—
435C4×Q8—41no—
436C4×Q8—41no—
437C4×Q8D4×C3114yes—
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⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4D4×C3111yescharacteristic
447C2×C4⋊C4D4×C3111yescharacteristic
448C2×C4⋊C4C23×C3111yescharacteristic
449C2×C4⋊C4C23×C3111yescharacteristic
450C2×C4⋊C4C23×C3111yescharacteristic
451C2×C4⋊C4C23×C3111yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42C23×C3111yescharacteristic
463C2×C42C23×C3111yescharacteristic
464C2×C42C23×C3111yescharacteristic
465#107—22no—
466C4⋊C8—22no—
467C4⋊C8—22no—
468C4⋊C8—22no—
469#103—22no—
470#103—22no—
471#103—22no—
472#103—22no—
473#103—22no—
474#103—22no—
475#103—41no—
476#102—22no—
477#102—22no—
478#102—41no—
479C4×C8—22no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95D4×C3111yescharacteristic
487#95D4×C3111yescharacteristic
488C31#2473611yescharacteristic, direct product factor, Sylow
489C24—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×Q8C2×D4×C3112yes—
505C2×Q8C2×D4×C3112yes—
506C2×Q8C2×D4×C3112yes—
507C2×Q8#41×C3112yes—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4C2×D4×C3111yescharacteristic
522C22×C4C2×D4×C3111yescharacteristic
523C22×C4C2×D4×C3111yescharacteristic
524C22×C4C2×D4×C3111yescharacteristic
525C22×C4C2×D4×C3111yescharacteristic
526C22×C4C2×D4×C3111yescharacteristic
527C22×C4C24×C3111yescharacteristic
528Q16—28no—
529Q16—44no—
530SD16—44no—
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—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8C2×D4×C3112yes—
543C4⋊C4—24no—
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—41no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4C2×D4×C3112yes—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C42—24no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—42no—
573C42—42no—
574C42—42no—
575C42C2×D4×C3112yes—
576C42#41×C3112yes—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23C22×D4×C3111yescharacteristic
585Q8—22no—
586Q8—22no—
587Q8—22no—
588Q8—22no—
589Q8—22no—
590Q8—41no—
591Q8—41no—
592Q8—41no—
593Q8—41no—
594Q8—41no—
595Q8—41no—
596Q8C31×#12114yes—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—41no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
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×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4C31×#12112yes—
638C2×C4C31×#12112yes—
639C2×C4C31×#13512yes—
640C2×C4C22×D4×C3111yescharacteristic
641C2×C4C22×D4×C3111yescharacteristic
642C2×C4C2×#41×C3111yescharacteristic
643C2×C4C2×#41×C3111yescharacteristic
644C2×C4C31×H(5,𝔽2)11yescharacteristic
645C2×C4C31×2−1+411yescharacteristic
646C8—22no—
647C8—41no—
648C8—41no—
649C8—41no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22C2×C31×#12111yescharacteristic
658C22D42×C3111yescharacteristic
659C22C31×#54811yescharacteristic
660C22C2×C31×#13511yescharacteristic
661C22C31×#57511yescharacteristic
662C22C31×#57811yescharacteristic
663C22C31×#57811yescharacteristic
664C4—24no—
665C4—22no—
666C4—22no—
667C4—22no—
668C4—42no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—42no—
673C4—81no—
674C4—81no—
675C4—81no—
676C4—81no—
677C4C2×C31×#12111yescharacteristic
678C4C31×#53711yescharacteristic
679C4C31×#54711yescharacteristic
680C4C31×#55311yescharacteristic
681C2—161no—
682C2C31×#241611yescharacteristic
683C2C31×#303511yescharacteristic
684C2C31×#304411yescharacteristic
685C2C31×#327711yescharacteristic
686C2C31×#328511yescharacteristic
687C2C31×#336411yescharacteristic
688C2C31×#337711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31C23
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
3. C2×C31×#462C2semidirect
4. C2×C4×Q16×C31C2semidirect
6. C31×#2351C2semidirect
7. C31×#2068C2semidirect
9. C31×#2043C2semidirect
12. C31×#1939C2semidirect
14. C31×#1878C2semidirect
15. C31×#1805C2semidirect
232. #24736C31direct (N × H)
308. C2×#462C2×C31semidirect
309. C2×C4×Q16C2×C31semidirect
311. #2351C2×C31semidirect
312. #2068C2×C31semidirect
314. #2043C2×C31semidirect
317. #1939C2×C31semidirect
319. #1878C2×C31semidirect
320. #1805C2×C31semidirect
488. C31#24736direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4642
C2×C31×#4622
C2×C4×Q16×C312
C31×#25452
C31×#23512
C31×#20682
C31×#20672
C31×#20432
C31×#20422
C31×#19582
C31×#19392
C31×#18802
C31×#18782
C31×#18052
#2473631