Finite Group Databasebeta

← C31×#24739 #21481498

Subgroups — C31×#24739 #21481498

Order 7936.

990 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#464C211yesmaximal, characteristic, complemented
2C2×C31×#464C211yesmaximal, characteristic, complemented
3C2×C31×#460C211yesmaximal, characteristic
4C2×C31×#440C211yesmaximal, characteristic, complemented
5C31×#2544C211yesmaximal, characteristic
6Q8×C4⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#2068C211yesmaximal, characteristic, complemented
8C31×#2067C211yesmaximal, characteristic, complemented
9C31×#2042C211yesmaximal, characteristic, complemented
10C31×#2041C211yesmaximal, characteristic
11C31×#1959C211yesmaximal, characteristic, complemented
12C31×#1940C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic, complemented
14C31×#1878C211yesmaximal, characteristic, complemented
15C31×#1802C211yesmaximal, characteristic, complemented
16C22×Q16×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C2×C31×#127C2211yescharacteristic
20C2×C31×#124C2211yescharacteristic
21C2×C31×#124C2211yescharacteristic
22C2×C4×Q8×C31C2211yescharacteristic
23C2×C4×Q8×C31C2211yescharacteristic
24C2×C4×Q8×C31C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C31×#464—24no—
27C31×#464—24no—
28C31×#460—24no—
29C31×#440—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×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#97C2211yescharacteristic
45C31×#394—21no—
46C31×#394—21no—
47C31×#391C2211yescharacteristic
48C31×#390C2211yescharacteristic
49C31×#389—21no—
50C31×#389—21no—
51C31×#389C2211yescharacteristic
52C31×#389C2211yescharacteristic
53C31×#386—21no—
54C31×#386—21no—
55C31×#384—21no—
56C31×#384C2211yescharacteristic
57C4×C4⋊C4×C31—21no—
58C4×C4⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31C2311yescharacteristic
68C22×D4×C31C2311yescharacteristic
69C23×C4×C31—21no—
70C2×Q16×C31—22no—
71C2×Q16×C31—22no—
72C2×Q16×C31—22no—
73C2×SD16×C31—22no—
74C2×SD16×C31—22no—
75C2×SD16×C31—22no—
76C2×SD16×C31—22no—
77C2×SD16×C31—22no—
78C2×SD16×C31D414yes—
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C31×#127—22no—
84C31×#127—41no—
85C31×#124—22no—
86C31×#124—22no—
87C31×#124—22no—
88C31×#124—41no—
89C4×Q8×C31—22no—
90C4×Q8×C31—22no—
91C4×Q8×C31—22no—
92C4×Q8×C31—41no—
93C4×Q8×C31—41no—
94C4×Q8×C31D414yescomplemented
95C4×D4×C31—22no—
96C4×D4×C31—22no—
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×C31—21no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31D411yescharacteristic
105C2×C4⋊C4×C31D411yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C42×C31—21no—
118C2×C42×C31—21no—
119C2×C42×C31—21no—
120C2×C42×C31C2311yescharacteristic
121C2×C42×C31C2311yescharacteristic
122C2×C42×C31C2311yescharacteristic
123C31×#107—22no—
124C31×C4⋊C8—22no—
125C31×C4⋊C8—22no—
126C31×C4⋊C8—22no—
127C31×#103—22no—
128C31×#103—22no—
129C31×#103—22no—
130C31×#103—41no—
131C31×#102—22no—
132C31×#102—22no—
133C31×#102—22no—
134C31×#102—22no—
135C31×#102—22no—
136C31×#102—41no—
137C31×#97—22no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95D411yescharacteristic
143C31×#95D411yescharacteristic
144C24×C31—21no—
145C24×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×C31C2×D412yes—
156C2×Q8×C31C2×D412yes—
157C2×Q8×C31#4112yes—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—42no—
170C2×D4×C31—42no—
171C2×D4×C31—42no—
172C2×D4×C31—42no—
173C2×D4×C31—81no—
174C2×D4×C31—81no—
175C2×D4×C31C2×D412yes—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—42no—
183C22×C4×C31—81no—
184C22×C4×C31—81no—
185C22×C4×C31C2×D411yescharacteristic
186C22×C4×C31C2×D411yescharacteristic
187C22×C4×C31C2×D411yescharacteristic
188C22×C4×C31C2×D411yescharacteristic
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31C2×D411yescharacteristic
191C22×C4×C31C2411yescharacteristic
192Q16×C31—44no—
193SD16×C31—28no—
194SD16×C31—44no—
195C2×C8×C31—21no—
196C2×C8×C31—21no—
197C2×C8×C31—21no—
198C2×C8×C31—21no—
199C2×C8×C31—21no—
200C2×C8×C31—21no—
201C2×C8×C31—21no—
202C2×C8×C31—21no—
203C2×C8×C31—21no—
204C2×C8×C31—21no—
205C2×C8×C31—21no—
206C2×C8×C31C2×D412yes—
207C4⋊C4×C31—24no—
208C4⋊C4×C31—22no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—41no—
217C4⋊C4×C31—42no—
218C4⋊C4×C31—42no—
219C4⋊C4×C31—42no—
220C4⋊C4×C31—81no—
221C4⋊C4×C31—81no—
222C4⋊C4×C31—81no—
223C4⋊C4×C31C2×D412yes—
224C22⋊C4×C31—42no—
225C22⋊C4×C31—42no—
226C22⋊C4×C31—42no—
227C22⋊C4×C31—42no—
228C22⋊C4×C31—42no—
229C22⋊C4×C31—81no—
230C22⋊C4×C31—81no—
231C42×C31—24no—
232C42×C31—21no—
233C42×C31—21no—
234C42×C31—21no—
235C42×C31—21no—
236C42×C31—42no—
237C42×C31—42no—
238C42×C31C2×D412yes—
239C42×C31#4112yes—
240#24739C3111yesmaximal, characteristic, direct product factor, Sylow
241C23×C31—22no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31—41no—
250C23×C31—41no—
251C23×C31—41no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31C22×D411yescharacteristic
256Q8×C31—22no—
257Q8×C31—22no—
258Q8×C31—22no—
259Q8×C31—41no—
260Q8×C31—41no—
261Q8×C31—41no—
262Q8×C31—41no—
263Q8×C31#12114yes—
264D4×C31—22no—
265D4×C31—22no—
266D4×C31—41no—
267D4×C31—41no—
268D4×C31—41no—
269D4×C31—41no—
270D4×C31—41no—
271D4×C31—41no—
272D4×C31—84no—
273D4×C31—84no—
274C2×C4×C31—22no—
275C2×C4×C31—21no—
276C2×C4×C31—22no—
277C2×C4×C31—22no—
278C2×C4×C31—21no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
283C2×C4×C31—22no—
284C2×C4×C31—21no—
285C2×C4×C31—21no—
286C2×C4×C31—21no—
287C2×C4×C31—21no—
288C2×C4×C31—21no—
289C2×C4×C31—21no—
290C2×C4×C31—21no—
291C2×C4×C31—21no—
292C2×C4×C31—21no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—41no—
299C2×C4×C31—41no—
300C2×C4×C31—41no—
301C2×C4×C31—41no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
307C2×C4×C31—84no—
308C2×C4×C31#12112yes—
309C2×C4×C31#12112yes—
310C2×C4×C31#13712yes—
311C2×C4×C31C22×D411yescharacteristic
312C2×C4×C31C22×D411yescharacteristic
313C2×C4×C31C2×#4111yescharacteristic
314C2×C4×C31C2×#4111yescharacteristic
315C2×C4×C31H(5,𝔽2)11yescharacteristic
316C2×C4×C312−1+411yescharacteristic
317C8×C31—22no—
318C8×C31—41no—
319C8×C31—41no—
320C8×C31—41no—
321C2×#464C2×C3111yescharacteristic, complemented
322C2×#464C2×C3111yescharacteristic, complemented
323C2×#460C2×C3111yescharacteristic
324C2×#440C2×C3111yescharacteristic, complemented
325#2544C2×C3111yescharacteristic
326Q8×C4⋊C4C2×C3111yescharacteristic, complemented
327#2068C2×C3111yescharacteristic, complemented
328#2067C2×C3111yescharacteristic, complemented
329#2042C2×C3111yescharacteristic, complemented
330#2041C2×C3111yescharacteristic
331#1959C2×C3111yescharacteristic, complemented
332#1940C2×C3111yescharacteristic, complemented
333#1880C2×C3111yescharacteristic, complemented
334#1878C2×C3111yescharacteristic, complemented
335#1802C2×C3111yescharacteristic, complemented
336C22×C31—42no—
337C22×C31—42no—
338C22×C31—42no—
339C22×C31—81no—
340C22×C31—81no—
341C22×C31—81no—
342C22×C31—81no—
343C22×C31—81no—
344C22×C31—81no—
345C22×C31—81no—
346C22×C31—81no—
347C22×C31—81no—
348C22×C31—81no—
349C22×C31—81no—
350C22×C31C2×#12111yescharacteristic
351C22×C31D4211yescharacteristic
352C22×C31#54811yescharacteristic
353C22×C31C2×#13711yescharacteristic
354C22×C31#57511yescharacteristic
355C22×C31#57611yescharacteristic
356C22×C31#57711yescharacteristic
357C4×C31—24no—
358C4×C31—22no—
359C4×C31—22no—
360C4×C31—22no—
361C4×C31—41no—
362C4×C31—41no—
363C4×C31—41no—
364C4×C31—42no—
365C4×C31—81no—
366C4×C31—81no—
367C4×C31—81no—
368C4×C31—81no—
369C4×C31C2×#12111yescharacteristic
370C4×C31#53711yescharacteristic
371C4×C31#54711yescharacteristic
372C4×C31#55311yescharacteristic
373C22×Q16C22×C3111yescharacteristic
374C22×SD16C22×C3111yescharacteristic
375C22×SD16C22×C3111yescharacteristic
376C2×#127C22×C3111yescharacteristic
377C2×#124C22×C3111yescharacteristic
378C2×#124C22×C3111yescharacteristic
379C2×C4×Q8C22×C3111yescharacteristic
380C2×C4×Q8C22×C3111yescharacteristic
381C2×C4×Q8C22×C3111yescharacteristic
382C2×C4×D4C22×C3111yescharacteristic
383#464—24no—
384#464—24no—
385#460—24no—
386#440—24no—
387C2×#107C22×C3111yescharacteristic
388C2×C4⋊C8C22×C3111yescharacteristic
389C2×C4⋊C8C22×C3111yescharacteristic
390C2×C4⋊C8C22×C3111yescharacteristic
391C2×#103C22×C3111yescharacteristic
392C2×#103C22×C3111yescharacteristic
393C2×#103C22×C3111yescharacteristic
394C2×#103C22×C3111yescharacteristic
395C2×#102C22×C3111yescharacteristic
396C2×#102C22×C3111yescharacteristic
397C2×#102C22×C3111yescharacteristic
398C2×#102C22×C3111yescharacteristic
399C2×#102C22×C3111yescharacteristic
400C2×#102C22×C3111yescharacteristic
401C2×#97C22×C3111yescharacteristic
402#394—21no—
403#394—21no—
404#391C22×C3111yescharacteristic
405#390C22×C3111yescharacteristic
406#389—21no—
407#389—21no—
408#389C22×C3111yescharacteristic
409#389C22×C3111yescharacteristic
410#386—21no—
411#386—21no—
412#384—21no—
413#384C22×C3111yescharacteristic
414C4×C4⋊C4—21no—
415C4×C4⋊C4C22×C3111yescharacteristic
416#340C22×C3111yescharacteristic
417#340C22×C3111yescharacteristic
418#336C22×C3111yescharacteristic
419#336C22×C3111yescharacteristic
420C2×C31—82no—
421C2×C31—161no—
422C2×C31#241611yescharacteristic
423C2×C31#303711yescharacteristic
424C2×C31#304511yescharacteristic
425C2×C31#326611yescharacteristic
426C2×C31#326811yescharacteristic
427C2×C31#337111yescharacteristic
428C2×C31#337511yescharacteristic
429C22×Q8C23×C3111yescharacteristic
430C22×Q8C23×C3111yescharacteristic
431C22×D4—21no—
432C22×D4—21no—
433C22×D4C23×C3111yescharacteristic
434C22×D4C23×C3111yescharacteristic
435C23×C4—21no—
436C2×Q16—22no—
437C2×Q16—22no—
438C2×Q16—22no—
439C2×SD16—22no—
440C2×SD16—22no—
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16—22no—
444C2×SD16D4×C3114yes—
445C22×C8C23×C3111yescharacteristic
446C22×C8C23×C3111yescharacteristic
447C22×C8C23×C3111yescharacteristic
448C22×C8C23×C3111yescharacteristic
449#127—22no—
450#127—41no—
451#124—22no—
452#124—22no—
453#124—22no—
454#124—41no—
455C4×Q8—22no—
456C4×Q8—22no—
457C4×Q8—22no—
458C4×Q8—41no—
459C4×Q8—41no—
460C4×Q8D4×C3114yescomplemented
461C4×D4—22no—
462C4×D4—22no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4D4×C3111yescharacteristic
471C2×C4⋊C4D4×C3111yescharacteristic
472C2×C4⋊C4C23×C3111yescharacteristic
473C2×C4⋊C4C23×C3111yescharacteristic
474C2×C4⋊C4C23×C3111yescharacteristic
475C2×C4⋊C4C23×C3111yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—21no—
486C2×C42C23×C3111yescharacteristic
487C2×C42C23×C3111yescharacteristic
488C2×C42C23×C3111yescharacteristic
489#107—22no—
490C4⋊C8—22no—
491C4⋊C8—22no—
492C4⋊C8—22no—
493#103—22no—
494#103—22no—
495#103—22no—
496#103—41no—
497#102—22no—
498#102—22no—
499#102—22no—
500#102—22no—
501#102—22no—
502#102—41no—
503#97—22no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95D4×C3111yescharacteristic
509#95D4×C3111yescharacteristic
510C31#2473911yescharacteristic, direct product factor, Sylow
511C24—21no—
512C24—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8C2×D4×C3112yes—
523C2×Q8C2×D4×C3112yes—
524C2×Q8#41×C3112yes—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—81no—
541C2×D4—81no—
542C2×D4C2×D4×C3112yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—42no—
550C22×C4—81no—
551C22×C4—81no—
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×C4C24×C3111yescharacteristic
559Q16—44no—
560SD16—28no—
561SD16—44no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8C2×D4×C3112yes—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—41no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—81no—
588C4⋊C4—81no—
589C4⋊C4—81no—
590C4⋊C4C2×D4×C3112yes—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C42—24no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—42no—
604C42—42no—
605C42C2×D4×C3112yes—
606C42#41×C3112yes—
607C23—22no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23C22×D4×C3111yescharacteristic
622Q8—22no—
623Q8—22no—
624Q8—22no—
625Q8—41no—
626Q8—41no—
627Q8—41no—
628Q8—41no—
629Q8C31×#12114yes—
630D4—22no—
631D4—22no—
632D4—41no—
633D4—41no—
634D4—41no—
635D4—41no—
636D4—41no—
637D4—41no—
638D4—84no—
639D4—84no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—84no—
674C2×C4C31×#12112yes—
675C2×C4C31×#12112yes—
676C2×C4C31×#13712yes—
677C2×C4C22×D4×C3111yescharacteristic
678C2×C4C22×D4×C3111yescharacteristic
679C2×C4C2×#41×C3111yescharacteristic
680C2×C4C2×#41×C3111yescharacteristic
681C2×C4C31×H(5,𝔽2)11yescharacteristic
682C2×C4C31×2−1+411yescharacteristic
683C8—22no—
684C8—41no—
685C8—41no—
686C8—41no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22C2×C31×#12111yescharacteristic
702C22D42×C3111yescharacteristic
703C22C31×#54811yescharacteristic
704C22C2×C31×#13711yescharacteristic
705C22C31×#57511yescharacteristic
706C22C31×#57611yescharacteristic
707C22C31×#57711yescharacteristic
708C4—24no—
709C4—22no—
710C4—22no—
711C4—22no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4—42no—
716C4—81no—
717C4—81no—
718C4—81no—
719C4—81no—
720C4C2×C31×#12111yescharacteristic
721C4C31×#53711yescharacteristic
722C4C31×#54711yescharacteristic
723C4C31×#55311yescharacteristic
724C2—82no—
725C2—161no—
726C2C31×#241611yescharacteristic
727C2C31×#303711yescharacteristic
728C2C31×#304511yescharacteristic
729C2C31×#326611yescharacteristic
730C2C31×#326811yescharacteristic
731C2C31×#337111yescharacteristic
732C2C31×#337511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#127C22
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×#464C2semidirect
2. C2×C31×#464C2semidirect
4. C2×C31×#440C2semidirect
6. Q8×C4⋊C4×C31C2semidirect
7. C31×#2068C2semidirect
8. C31×#2067C2semidirect
9. C31×#2042C2semidirect
11. C31×#1959C2semidirect
12. C31×#1940C2semidirect
13. C31×#1880C2semidirect
14. C31×#1878C2semidirect
15. C31×#1802C2semidirect
94. C4×Q8×C31D4semidirect
240. #24739C31direct (N × H)
321. C2×#464C2×C31semidirect
322. C2×#464C2×C31semidirect
324. C2×#440C2×C31semidirect
326. Q8×C4⋊C4C2×C31semidirect
327. #2068C2×C31semidirect
328. #2067C2×C31semidirect
329. #2042C2×C31semidirect
331. #1959C2×C31semidirect
332. #1940C2×C31semidirect
333. #1880C2×C31semidirect
334. #1878C2×C31semidirect
335. #1802C2×C31semidirect
460. C4×Q8D4×C31semidirect
510. C31#24739direct (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×#4602
C2×C31×#4402
C31×#25442
Q8×C4⋊C4×C312
C31×#20682
C31×#20672
C31×#20422
C31×#20412
C31×#19592
C31×#19402
C31×#18802
C31×#18782
C31×#18022
#2473931