Finite Group Databasebeta

← C31×#24769 #21481528

Subgroups — C31×#24769 #21481528

Order 7936.

946 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#470C211yesmaximal, characteristic, complemented
2C2×C31×#465C211yesmaximal, characteristic
3C2×C31×#464C211yesmaximal, characteristic, complemented
4C2×C31×#424C211yesmaximal, characteristic, complemented
5C31×#2620C211yesmaximal, characteristic
6C31×#2323C211yesmaximal, characteristic, complemented
7C31×#2066C211yesmaximal, characteristic, complemented
8C31×#2065C211yesmaximal, characteristic, complemented
9C31×#2056C211yesmaximal, characteristic, complemented
10C31×#2055C211yesmaximal, characteristic, complemented
11C31×#1983C211yesmaximal, characteristic, complemented
12C31×#1948C211yesmaximal, characteristic, complemented
13C31×#1895C211yesmaximal, characteristic
14C31×#1892C211yesmaximal, characteristic, complemented
15C31×#1803C211yesmaximal, characteristic, complemented
16C22×Q16×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×M16×C31C2211yescharacteristic
19C23×C8×C31C2211yescharacteristic
20C2×C31×#124C2211yescharacteristic
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C31×C22⋊Q8C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C4×Q8×C31C2211yescharacteristic
25C2×C31×#117C2211yescharacteristic
26C31×#470—24no—
27C31×#465—24no—
28C31×#464—24no—
29C2×C31×#106C2211yescharacteristic
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×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C31×#396—21no—
45C31×#396—21no—
46C31×#394—21no—
47C31×#394—21no—
48C31×#391C2211yescharacteristic
49C31×#391C2211yescharacteristic
50C31×#390C2211yescharacteristic
51C31×#389—21no—
52C31×#389C2211yescharacteristic
53C31×#388—21no—
54C31×#388—21no—
55C31×#387—21no—
56C31×#384C2211yescharacteristic
57C31×#380C2211yescharacteristic
58C4×C4⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31—21no—
66C22×D4×C31C2311yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C2×Q16×C31—22no—
69C2×Q16×C31—22no—
70C2×Q16×C31—41no—
71C2×SD16×C31—22no—
72C2×SD16×C31—22no—
73C2×SD16×C31—41no—
74C2×M16×C31—22no—
75C2×M16×C31—22no—
76C2×M16×C31—41no—
77C22×C8×C31—22no—
78C22×C8×C31—22no—
79C22×C8×C31—41no—
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C31×#124—22no—
85C31×#124—22no—
86C31×C22⋊Q8—22no—
87C31×C22⋊Q8—22no—
88C31×C22⋊Q8—22no—
89C31×C22⋊Q8D414yes—
90C31×#121—22no—
91C31×#121—22no—
92C4×Q8×C31—22no—
93C4×Q8×C31—22no—
94C31×#117—22no—
95C31×#117—22no—
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×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31D411yescharacteristic
118C2×C22⋊C4×C31D411yescharacteristic
119C2×C42×C31—21no—
120C2×C42×C31—21no—
121C2×C42×C31C2311yescharacteristic
122C2×C42×C31C2311yescharacteristic
123C31×#106—22no—
124C31×#106—22no—
125C31×C4⋊C8—22no—
126C31×C4⋊C8—22no—
127C31×C4⋊C8—22no—
128C31×C4⋊C8D414yescomplemented
129C31×#103—22no—
130C31×#103—22no—
131C31×#103—22no—
132C31×#103—22no—
133C31×#103—41no—
134C31×#102—22no—
135C31×#102—22no—
136C31×#102—41no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95—21no—
143C31×#95—21no—
144C24×C31—21no—
145C24×C31C2×D411yescharacteristic
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×C31C2×D412yes—
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—42no—
165C2×D4×C31—81no—
166C2×D4×C31—81no—
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×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2×D411yescharacteristic
182C22×C4×C31C2×D411yescharacteristic
183C22×C4×C31C2×D412yes—
184C22×C4×C31#4112yes—
185C22×C4×C31C2411yescharacteristic
186Q16×C31—44no—
187SD16×C31—44no—
188M16×C31—44no—
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×C31—21no—
198C2×C8×C31—21no—
199C2×C8×C31—44no—
200C2×C8×C31C2×D412yes—
201C2×C8×C31C2×D412yes—
202C4⋊C4×C31—24no—
203C4⋊C4×C31—22no—
204C4⋊C4×C31—22no—
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—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—42no—
215C4⋊C4×C31—42no—
216C4⋊C4×C31—81no—
217C4⋊C4×C31—81no—
218C4⋊C4×C31—81no—
219C4⋊C4×C31C2×D412yes—
220C22⋊C4×C31—24no—
221C22⋊C4×C31—22no—
222C22⋊C4×C31—22no—
223C22⋊C4×C31—42no—
224C22⋊C4×C31—42no—
225C22⋊C4×C31—42no—
226C22⋊C4×C31—42no—
227C22⋊C4×C31—81no—
228C22⋊C4×C31—81no—
229C22⋊C4×C31—81no—
230C42×C31—21no—
231C42×C31—21no—
232C42×C31—42no—
233C42×C31—81no—
234C42×C31C2×D412yes—
235C42×C31#4112yes—
236#24769C3111yesmaximal, characteristic, direct product factor, Sylow
237C23×C31—21no—
238C23×C31—21no—
239C23×C31—21no—
240C23×C31—21no—
241C23×C31—21no—
242C23×C31—21no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31—41no—
250C23×C31#12112yes—
251C23×C31C22×D411yescharacteristic
252Q8×C31—22no—
253Q8×C31—22no—
254Q8×C31—41no—
255Q8×C31—41no—
256Q8×C31—41no—
257Q8×C31—41no—
258Q8×C31—41no—
259Q8×C31—41no—
260D4×C31—41no—
261D4×C31—41no—
262D4×C31—41no—
263D4×C31—41no—
264D4×C31—84no—
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—22no—
272C2×C4×C31—22no—
273C2×C4×C31—22no—
274C2×C4×C31—22no—
275C2×C4×C31—21no—
276C2×C4×C31—21no—
277C2×C4×C31—22no—
278C2×C4×C31—22no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
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—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#12112yes—
303C2×C4×C31#12112yes—
304C2×C4×C31#12112yes—
305C2×C4×C31C22×D411yescharacteristic
306C2×C4×C31C22×D411yescharacteristic
307C2×C4×C31C2×#4111yescharacteristic
308C2×C4×C31C2×#4111yescharacteristic
309C2×C4×C31H(5,𝔽2)11yescharacteristic
310C2×C4×C312−1+411yescharacteristic
311C8×C31—22no—
312C8×C31—22no—
313C8×C31—41no—
314C8×C31—41no—
315C2×#470C2×C3111yescharacteristic, complemented
316C2×#465C2×C3111yescharacteristic
317C2×#464C2×C3111yescharacteristic, complemented
318C2×#424C2×C3111yescharacteristic, complemented
319#2620C2×C3111yescharacteristic
320#2323C2×C3111yescharacteristic, complemented
321#2066C2×C3111yescharacteristic, complemented
322#2065C2×C3111yescharacteristic, complemented
323#2056C2×C3111yescharacteristic, complemented
324#2055C2×C3111yescharacteristic, complemented
325#1983C2×C3111yescharacteristic, complemented
326#1948C2×C3111yescharacteristic, complemented
327#1895C2×C3111yescharacteristic
328#1892C2×C3111yescharacteristic, complemented
329#1803C2×C3111yescharacteristic, complemented
330C22×C31—22no—
331C22×C31—22no—
332C22×C31—22no—
333C22×C31—41no—
334C22×C31—41no—
335C22×C31—41no—
336C22×C31—41no—
337C22×C31—81no—
338C22×C31—81no—
339C22×C31—81no—
340C22×C31—81no—
341C22×C31—81no—
342C22×C31—81no—
343C22×C31—81no—
344C22×C31C2×#12111yescharacteristic
345C22×C31C2×#12111yescharacteristic
346C22×C31#53711yescharacteristic
347C22×C31#57711yescharacteristic
348C22×C31#57711yescharacteristic
349C22×C31#57711yescharacteristic
350C22×C31#57811yescharacteristic
351C4×C31—22no—
352C4×C31—22no—
353C4×C31—22no—
354C4×C31—42no—
355C4×C31—42no—
356C4×C31—41no—
357C4×C31—41no—
358C4×C31—81no—
359C4×C31—81no—
360C4×C31—81no—
361C4×C31—81no—
362C4×C31—81no—
363C4×C31D4211yescharacteristic
364C4×C31#54711yescharacteristic
365C4×C31#54811yescharacteristic
366C4×C31#55311yescharacteristic
367C22×Q16C22×C3111yescharacteristic
368C22×SD16C22×C3111yescharacteristic
369C22×M16C22×C3111yescharacteristic
370C23×C8C22×C3111yescharacteristic
371C2×#124C22×C3111yescharacteristic
372C2×C22⋊Q8C22×C3111yescharacteristic
373C2×C22⋊Q8C22×C3111yescharacteristic
374C2×#121C22×C3111yescharacteristic
375C2×C4×Q8C22×C3111yescharacteristic
376C2×#117C22×C3111yescharacteristic
377#470—24no—
378#465—24no—
379#464—24no—
380C2×#106C22×C3111yescharacteristic
381C2×#106C22×C3111yescharacteristic
382#424—24no—
383C2×C4⋊C8C22×C3111yescharacteristic
384C2×C4⋊C8C22×C3111yescharacteristic
385C2×C4⋊C8C22×C3111yescharacteristic
386C2×C4⋊C8C22×C3111yescharacteristic
387C2×#103C22×C3111yescharacteristic
388C2×#103C22×C3111yescharacteristic
389C2×#103C22×C3111yescharacteristic
390C2×#103C22×C3111yescharacteristic
391C2×#103C22×C3111yescharacteristic
392C2×#102C22×C3111yescharacteristic
393C2×#102C22×C3111yescharacteristic
394C2×#102C22×C3111yescharacteristic
395#396—21no—
396#396—21no—
397#394—21no—
398#394—21no—
399#391C22×C3111yescharacteristic
400#391C22×C3111yescharacteristic
401#390C22×C3111yescharacteristic
402#389—21no—
403#389C22×C3111yescharacteristic
404#388—21no—
405#388—21no—
406#387—21no—
407#384C22×C3111yescharacteristic
408#380C22×C3111yescharacteristic
409C4×C4⋊C4C22×C3111yescharacteristic
410#340C22×C3111yescharacteristic
411#340C22×C3111yescharacteristic
412#340C22×C3111yescharacteristic
413#340C22×C3111yescharacteristic
414C2×C31—42no—
415C2×C31—161no—
416C2×C31#241611yescharacteristic
417C2×C31#304311yescharacteristic
418C2×C31#304611yescharacteristic
419C2×C31#306011yescharacteristic
420C2×C31#306311yescharacteristic
421C2×C31#325811yescharacteristic
422C2×C31#326311yescharacteristic
423C22×Q8C23×C3111yescharacteristic
424C22×Q8C23×C3111yescharacteristic
425C22×D4—21no—
426C22×D4C23×C3111yescharacteristic
427C23×C4C23×C3111yescharacteristic
428C2×Q16—22no—
429C2×Q16—22no—
430C2×Q16—41no—
431C2×SD16—22no—
432C2×SD16—22no—
433C2×SD16—41no—
434C2×M16—22no—
435C2×M16—22no—
436C2×M16—41no—
437C22×C8—22no—
438C22×C8—22no—
439C22×C8—41no—
440C22×C8C23×C3111yescharacteristic
441C22×C8C23×C3111yescharacteristic
442C22×C8C23×C3111yescharacteristic
443C22×C8C23×C3111yescharacteristic
444#124—22no—
445#124—22no—
446C22⋊Q8—22no—
447C22⋊Q8—22no—
448C22⋊Q8—22no—
449C22⋊Q8D4×C3114yes—
450#121—22no—
451#121—22no—
452C4×Q8—22no—
453C4×Q8—22no—
454#117—22no—
455#117—22no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4D4×C3111yescharacteristic
463C2×C4⋊C4D4×C3111yescharacteristic
464C2×C4⋊C4C23×C3111yescharacteristic
465C2×C4⋊C4C23×C3111yescharacteristic
466C2×C4⋊C4C23×C3111yescharacteristic
467C2×C4⋊C4C23×C3111yescharacteristic
468C2×C4⋊C4C23×C3111yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4D4×C3111yescharacteristic
478C2×C22⋊C4D4×C3111yescharacteristic
479C2×C42—21no—
480C2×C42—21no—
481C2×C42C23×C3111yescharacteristic
482C2×C42C23×C3111yescharacteristic
483#106—22no—
484#106—22no—
485C4⋊C8—22no—
486C4⋊C8—22no—
487C4⋊C8—22no—
488C4⋊C8D4×C3114yescomplemented
489#103—22no—
490#103—22no—
491#103—22no—
492#103—22no—
493#103—41no—
494#102—22no—
495#102—22no—
496#102—41no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504C31#2476911yescharacteristic, direct product factor, Sylow
505C24—21no—
506C24C2×D4×C3111yescharacteristic
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8C2×D4×C3112yes—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—42no—
526C2×D4—81no—
527C2×D4—81no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4C2×D4×C3111yescharacteristic
540C22×C4C2×D4×C3111yescharacteristic
541C22×C4C2×D4×C3111yescharacteristic
542C22×C4C2×D4×C3111yescharacteristic
543C22×C4C2×D4×C3111yescharacteristic
544C22×C4C2×D4×C3112yes—
545C22×C4#41×C3112yes—
546C22×C4C24×C3111yescharacteristic
547Q16—44no—
548SD16—44no—
549M16—44no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—44no—
561C2×C8C2×D4×C3112yes—
562C2×C8C2×D4×C3112yes—
563C4⋊C4—24no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—81no—
578C4⋊C4—81no—
579C4⋊C4—81no—
580C4⋊C4C2×D4×C3112yes—
581C22⋊C4—24no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C22⋊C4—81no—
591C42—21no—
592C42—21no—
593C42—42no—
594C42—81no—
595C42C2×D4×C3112yes—
596C42#41×C3112yes—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23C31×#12112yes—
611C23C22×D4×C3111yescharacteristic
612Q8—22no—
613Q8—22no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—41no—
624D4—84no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
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—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4C31×#12112yes—
663C2×C4C31×#12112yes—
664C2×C4C31×#12112yes—
665C2×C4C22×D4×C3111yescharacteristic
666C2×C4C22×D4×C3111yescharacteristic
667C2×C4C2×#41×C3111yescharacteristic
668C2×C4C2×#41×C3111yescharacteristic
669C2×C4C31×H(5,𝔽2)11yescharacteristic
670C2×C4C31×2−1+411yescharacteristic
671C8—22no—
672C8—22no—
673C8—41no—
674C8—41no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×C31×#12111yescharacteristic
690C22C2×C31×#12111yescharacteristic
691C22C31×#53711yescharacteristic
692C22C31×#57711yescharacteristic
693C22C31×#57711yescharacteristic
694C22C31×#57711yescharacteristic
695C22C31×#57811yescharacteristic
696C4—22no—
697C4—22no—
698C4—22no—
699C4—42no—
700C4—42no—
701C4—41no—
702C4—41no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4D42×C3111yescharacteristic
709C4C31×#54711yescharacteristic
710C4C31×#54811yescharacteristic
711C4C31×#55311yescharacteristic
712C2—42no—
713C2—161no—
714C2C31×#241611yescharacteristic
715C2C31×#304311yescharacteristic
716C2C31×#304611yescharacteristic
717C2C31×#306011yescharacteristic
718C2C31×#306311yescharacteristic
719C2C31×#325811yescharacteristic
720C2C31×#326311yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
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
1. C2×C31×#470C2semidirect
3. C2×C31×#464C2semidirect
4. C2×C31×#424C2semidirect
6. C31×#2323C2semidirect
7. C31×#2066C2semidirect
8. C31×#2065C2semidirect
9. C31×#2056C2semidirect
10. C31×#2055C2semidirect
11. C31×#1983C2semidirect
12. C31×#1948C2semidirect
14. C31×#1892C2semidirect
15. C31×#1803C2semidirect
128. C31×C4⋊C8D4semidirect
236. #24769C31direct (N × H)
315. C2×#470C2×C31semidirect
317. C2×#464C2×C31semidirect
318. C2×#424C2×C31semidirect
320. #2323C2×C31semidirect
321. #2066C2×C31semidirect
322. #2065C2×C31semidirect
323. #2056C2×C31semidirect
324. #2055C2×C31semidirect
325. #1983C2×C31semidirect
326. #1948C2×C31semidirect
328. #1892C2×C31semidirect
329. #1803C2×C31semidirect
488. C4⋊C8D4×C31semidirect
504. C31#24769direct (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×#4652
C2×C31×#4642
C2×C31×#4242
C31×#26202
C31×#23232
C31×#20662
C31×#20652
C31×#20562
C31×#20552
C31×#19832
C31×#19482
C31×#18952
C31×#18922
C31×#18032
#2476931