Finite Group Databasebeta

← C31×#14022 #21470781

Subgroups — C31×#14022 #21470781

Order 7936.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#390C211yesmaximal, characteristic
2C2×C31×#390C211yesmaximal, characteristic
3C2×C31×#390C211yesmaximal, characteristic
4C2×C31×#388C212yesmaximal, complemented
5C2×C4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
6C2×C4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#1440C212yesmaximal, complemented
8C31×#1439C212yesmaximal, complemented
9C31×#1437C212yesmaximal, complemented
10C31×C4⋊#95C211yesmaximal, characteristic, complemented
11C31×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C42×C31C2211yescharacteristic
25C22×C42×C31C2212yes—
26C22×C42×C31C2211yescharacteristic
27C22×C42×C31C2211yescharacteristic
28C31×#390—24no—
29C31×#390—24no—
30C31×#390C418yescomplemented
31C31×#388—28no—
32C4×C4⋊C4×C31—24no—
33C4×C4⋊C4×C31—24no—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2212yes—
38C2×C31×#95C2211yescharacteristic
39C2×C31×#95C2212yes—
40C2×C31×#95C2212yes—
41C25×C31C2312yes—
42C22×D4×C31—22no—
43C22×D4×C31—22no—
44C22×D4×C31—22no—
45C22×D4×C31—22no—
46C22×D4×C31—22no—
47C22×D4×C31—22no—
48C22×D4×C31C2×C414yes—
49C23×C4×C31C2312yes—
50C23×C4×C31C2312yes—
51C23×C4×C31C2311yescharacteristic
52C23×C4×C31C2311yescharacteristic
53C23×C4×C31C2312yes—
54C23×C4×C31C2311yescharacteristic
55C23×C4×C31C2311yescharacteristic
56C23×C4×C31C2311yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2311yescharacteristic
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—22no—
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31—22no—
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31—22no—
65C2×C4⋊C4×C31—22no—
66C2×C4⋊C4×C31—22no—
67C2×C4⋊C4×C31—22no—
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31—22no—
70C2×C4⋊C4×C31—22no—
71C2×C4⋊C4×C31C2×C414yes—
72C2×C4⋊C4×C31D414yes—
73C2×C4⋊C4×C31D414yescomplemented
74C2×C22⋊C4×C31—24no—
75C2×C22⋊C4×C31—24no—
76C2×C22⋊C4×C31—24no—
77C2×C22⋊C4×C31—24no—
78C2×C22⋊C4×C31—24no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—24no—
81C2×C22⋊C4×C31—24no—
82C2×C22⋊C4×C31—24no—
83C2×C22⋊C4×C31—24no—
84C2×C22⋊C4×C31—42no—
85C2×C22⋊C4×C31—42no—
86C2×C22⋊C4×C31—42no—
87C2×C22⋊C4×C31—42no—
88C2×C22⋊C4×C31—42no—
89C2×C22⋊C4×C31—42no—
90C2×C22⋊C4×C31C2×C418yes—
91C2×C22⋊C4×C31C2×C418yes—
92C2×C42×C31—22no—
93C2×C42×C31—22no—
94C2×C42×C31—22no—
95C2×C42×C31—22no—
96C2×C42×C31—24no—
97C2×C42×C31—22no—
98C2×C42×C31—24no—
99C2×C42×C31—22no—
100C2×C42×C31—22no—
101C2×C42×C31—42no—
102C2×C42×C31C2×C414yes—
103C2×C42×C31D414yes—
104C31×#95—24no—
105C31×#95—22no—
106C31×#95—22no—
107C31×#95—24no—
108C31×#95—24no—
109C31×#95—42no—
110C31×#95—42no—
111C24×C31—22no—
112C24×C31—22no—
113C24×C31—22no—
114C24×C31—22no—
115C24×C31—22no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31—22no—
122C24×C31—22no—
123C24×C31—22no—
124C24×C31—22no—
125C24×C31C22×C414yes—
126C24×C31C2411yescharacteristic
127C2×D4×C31—28no—
128C2×D4×C31—28no—
129C2×D4×C31—28no—
130C2×D4×C31—44no—
131C2×D4×C31—44no—
132C2×D4×C31—44no—
133C2×D4×C31—44no—
134C22×C4×C31—21no—
135C22×C4×C31—21no—
136C22×C4×C31—21no—
137C22×C4×C31—21no—
138C22×C4×C31—21no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—21no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
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×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—22no—
181C22×C4×C31—22no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—22no—
185C22×C4×C31C22×C412yes—
186C22×C4×C31C22×C414yes—
187C22×C4×C31C22×C412yes—
188C22×C4×C31C22×C412yes—
189C22×C4×C31C2×D412yes—
190C22×C4×C31C2×D414yes—
191C22×C4×C31C2×D412yes—
192C22×C4×C31C2×D412yes—
193C22×C4×C31C2×D412yes—
194C22×C4×C31C2×D412yes—
195C22×C4×C31C2×D412yes—
196C22×C4×C31C2×D412yes—
197C22×C4×C31#4112yes—
198C22×C4×C31#4112yes—
199C22×C4×C31#4112yes—
200C22×C4×C31#4112yes—
201C22×C4×C31#4112yes—
202C22×C4×C31#4112yes—
203C22×C4×C31#4112yes—
204C4⋊C4×C31—28no—
205C4⋊C4×C31—28no—
206C4⋊C4×C31—28no—
207C4⋊C4×C31—28no—
208C4⋊C4×C31—44no—
209C22⋊C4×C31—216no—
210C22⋊C4×C31—48no—
211C22⋊C4×C31—48no—
212C22⋊C4×C31—48no—
213C22⋊C4×C31—48no—
214C22⋊C4×C31—48no—
215C42×C31—28no—
216C42×C31—28no—
217C42×C31—48no—
218C42×C31—44no—
219#14022C3111yesmaximal, characteristic, direct product factor, Sylow
220C23×C31—24no—
221C23×C31—24no—
222C23×C31—24no—
223C23×C31—24no—
224C23×C31—24no—
225C23×C31—24no—
226C23×C31—24no—
227C23×C31—42no—
228C23×C31—42no—
229C23×C31—42no—
230C23×C31—42no—
231C23×C31—42no—
232C23×C31—42no—
233C23×C31—42no—
234C23×C31—42no—
235C23×C31—42no—
236C23×C31—42no—
237C23×C31—42no—
238C23×C31—42no—
239C23×C31—42no—
240C23×C31—42no—
241C23×C31—42no—
242C23×C31—42no—
243C23×C31—42no—
244C23×C31—42no—
245C23×C31—42no—
246C23×C31—42no—
247C23×C31—42no—
248C23×C31—42no—
249C23×C31—42no—
250C23×C31—42no—
251C23×C31—42no—
252C23×C31—42no—
253C23×C31—42no—
254C23×C31—42no—
255C23×C31C23×C411yescharacteristic
256C23×C31C22×D411yescharacteristic
257C23×C31C22×D411yescharacteristic
258C23×C31C22×D411yescharacteristic
259C23×C31C2×#4111yescharacteristic
260C23×C31C2×#4111yescharacteristic
261C23×C31C2×#4111yescharacteristic
262C23×C31C2×#4111yescharacteristic
263C23×C31C2×#4111yescharacteristic
264C23×C31C2×#4111yescharacteristic
265C23×C31C2×#4111yescharacteristic
266C23×C31H(5,𝔽2)11yescharacteristic
267C23×C31H(5,𝔽2)11yescharacteristic
268C23×C31H(5,𝔽2)11yescharacteristic
269C23×C312−1+411yescharacteristic
270D4×C31—416no—
271C2×C4×C31—22no—
272C2×C4×C31—22no—
273C2×C4×C31—22no—
274C2×C4×C31—22no—
275C2×C4×C31—22no—
276C2×C4×C31—22no—
277C2×C4×C31—22no—
278C2×C4×C31—22no—
279C2×C4×C31—22no—
280C2×C4×C31—22no—
281C2×C4×C31—22no—
282C2×C4×C31—22no—
283C2×C4×C31—22no—
284C2×C4×C31—24no—
285C2×C4×C31—24no—
286C2×C4×C31—22no—
287C2×C4×C31—24no—
288C2×C4×C31—22no—
289C2×C4×C31—22no—
290C2×C4×C31—22no—
291C2×C4×C31—24no—
292C2×C4×C31—22no—
293C2×C4×C31—22no—
294C2×C4×C31—22no—
295C2×C4×C31—24no—
296C2×C4×C31—22no—
297C2×C4×C31—22no—
298C2×C4×C31—24no—
299C2×C4×C31—22no—
300C2×C4×C31—22no—
301C2×C4×C31—41no—
302C2×C4×C31—41no—
303C2×C4×C31—42no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—42no—
310C2×C4×C31—41no—
311C2×C4×C31—42no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—42no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—42no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—42no—
331C2×C4×C31—42no—
332C2×C4×C31#11714yes—
333C2×C4×C31C4×D414yes—
334C2×C4×C31C4×D414yes—
335C2×C4×C31C4×D414yes—
336C2×C4×C31#12114yes—
337C2×C4×C31#12114yes—
338C2×C4×C31#12314yes—
339C2×C4×C31#12414yes—
340C2×C4×C31#12614yes—
341C2×#390C2×C3111yescharacteristic
342C2×#390C2×C3111yescharacteristic
343C2×#390C2×C3111yescharacteristic
344C2×#388C2×C3112yescomplemented
345C2×C4×C4⋊C4C2×C3111yescharacteristic, complemented
346C2×C4×C4⋊C4C2×C3111yescharacteristic, complemented
347#1440C2×C3112yescomplemented
348#1439C2×C3112yescomplemented
349#1437C2×C3112yescomplemented
350C4⋊#95C2×C3111yescharacteristic, complemented
351C4⋊#95C2×C3111yescharacteristic, complemented
352C22×C31—44no—
353C22×C31—44no—
354C22×C31—44no—
355C22×C31—44no—
356C22×C31—44no—
357C22×C31—44no—
358C22×C31—44no—
359C22×C31—82no—
360C22×C31—82no—
361C22×C31—82no—
362C22×C31—82no—
363C22×C31—82no—
364C22×C31—82no—
365C22×C31—82no—
366C22×C31—82no—
367C22×C31C2×#11711yescharacteristic
368C22×C31C2×C4×D411yescharacteristic
369C22×C31C2×C4×D411yescharacteristic
370C22×C31C2×C4×D411yescharacteristic
371C22×C31C4×#4111yescharacteristic
372C22×C31#51811yescharacteristic
373C22×C31#52011yescharacteristic
374C22×C31C2×#12111yescharacteristic
375C22×C31C2×#12111yescharacteristic
376C22×C31C2×#12311yescharacteristic
377C22×C31#52511yescharacteristic
378C22×C31C2×#12411yescharacteristic
379C22×C31C2×#12611yescharacteristic
380C22×C31#52911yescharacteristic
381C22×C31#53211yescharacteristic
382C22×C31#53511yescharacteristic
383C22×C31#53711yescharacteristic
384C22×C31#54011yescharacteristic
385C22×C31#54211yescharacteristic
386C22×C31D4211yescharacteristic
387C22×C31#54611yescharacteristic
388C22×C31#54711yescharacteristic
389C22×C31#54811yescharacteristic
390C22×C31#55011yescharacteristic
391C22×C31#55011yescharacteristic
392C22×C31#55011yescharacteristic
393C22×C31#55311yescharacteristic
394C22×C31#55311yescharacteristic
395C22×C31#55511yescharacteristic
396C22×C31#55611yescharacteristic
397C22×C31#55611yescharacteristic
398C22×C31#55911yescharacteristic
399C22×C31#55911yescharacteristic
400C22×C31#55911yescharacteristic
401C22×C31#55911yescharacteristic
402C4×C31—24no—
403C4×C31—24no—
404C4×C31—42no—
405C4×C31—44no—
406C4×C31—42no—
407C4×C31—42no—
408C4×C31—42no—
409C4×C31—44no—
410C4×C31—82no—
411C4×C31#38818yescomplemented
412C23×D4C22×C3111yescharacteristic
413C22×C4⋊C4C22×C3111yescharacteristic
414C22×C4⋊C4C22×C3111yescharacteristic
415C22×C4⋊C4C22×C3111yescharacteristic
416C22×C4⋊C4C22×C3111yescharacteristic
417C22×C4⋊C4C22×C3111yescharacteristic
418C22×C22⋊C4C22×C3112yes—
419C22×C22⋊C4C22×C3112yes—
420C22×C22⋊C4C22×C3112yes—
421C22×C22⋊C4C22×C3112yes—
422C22×C22⋊C4C22×C3112yes—
423C22×C22⋊C4C22×C3112yes—
424C22×C42C22×C3111yescharacteristic
425C22×C42C22×C3112yes—
426C22×C42C22×C3111yescharacteristic
427C22×C42C22×C3111yescharacteristic
428#390—24no—
429#390—24no—
430#390C4×C3118yescomplemented
431#388—28no—
432C4×C4⋊C4—24no—
433C4×C4⋊C4—24no—
434C2×#95C22×C3112yes—
435C2×#95C22×C3112yes—
436C2×#95C22×C3111yescharacteristic
437C2×#95C22×C3112yes—
438C2×#95C22×C3111yescharacteristic
439C2×#95C22×C3112yes—
440C2×#95C22×C3112yes—
441C2×C31—84no—
442C2×C31C2×#38811yescharacteristic
443C2×C31C4×#12111yescharacteristic
444C2×C31#232411yescharacteristic
445C2×C31#235411yescharacteristic
446C2×C31#235711yescharacteristic
447C2×C31#236611yescharacteristic
448C2×C31#236711yescharacteristic
449C2×C31#241411yescharacteristic
450C2×C31#241611yescharacteristic
451C2×C31#244511yescharacteristic
452C2×C31#244811yescharacteristic
453C2×C31#251211yescharacteristic
454C2×C31#251311yescharacteristic
455C2×C31#254811yescharacteristic
456C2×C31#259211yescharacteristic
457C25C23×C3112yes—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4C2×C4×C3114yes—
465C23×C4C23×C3112yes—
466C23×C4C23×C3112yes—
467C23×C4C23×C3111yescharacteristic
468C23×C4C23×C3111yescharacteristic
469C23×C4C23×C3112yes—
470C23×C4C23×C3111yescharacteristic
471C23×C4C23×C3111yescharacteristic
472C23×C4C23×C3111yescharacteristic
473C23×C4C23×C3111yescharacteristic
474C23×C4C23×C3111yescharacteristic
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4C2×C4×C3114yes—
488C2×C4⋊C4D4×C3114yes—
489C2×C4⋊C4D4×C3114yescomplemented
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4C2×C4×C3118yes—
507C2×C22⋊C4C2×C4×C3118yes—
508C2×C42—22no—
509C2×C42—22no—
510C2×C42—22no—
511C2×C42—22no—
512C2×C42—24no—
513C2×C42—22no—
514C2×C42—24no—
515C2×C42—22no—
516C2×C42—22no—
517C2×C42—42no—
518C2×C42C2×C4×C3114yes—
519C2×C42D4×C3114yes—
520#95—24no—
521#95—22no—
522#95—22no—
523#95—24no—
524#95—24no—
525#95—42no—
526#95—42no—
527C31#1402211yescharacteristic, direct product factor, Sylow
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24C22×C4×C3114yes—
543C24C24×C3111yescharacteristic
544C2×D4—28no—
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—44no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4C22×C4×C3112yes—
603C22×C4C22×C4×C3114yes—
604C22×C4C22×C4×C3112yes—
605C22×C4C22×C4×C3112yes—
606C22×C4C2×D4×C3112yes—
607C22×C4C2×D4×C3114yes—
608C22×C4C2×D4×C3112yes—
609C22×C4C2×D4×C3112yes—
610C22×C4C2×D4×C3112yes—
611C22×C4C2×D4×C3112yes—
612C22×C4C2×D4×C3112yes—
613C22×C4C2×D4×C3112yes—
614C22×C4#41×C3112yes—
615C22×C4#41×C3112yes—
616C22×C4#41×C3112yes—
617C22×C4#41×C3112yes—
618C22×C4#41×C3112yes—
619C22×C4#41×C3112yes—
620C22×C4#41×C3112yes—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—44no—
626C22⋊C4—216no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C42—28no—
633C42—28no—
634C42—48no—
635C42—44no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23C23×C4×C3111yescharacteristic
672C23C22×D4×C3111yescharacteristic
673C23C22×D4×C3111yescharacteristic
674C23C22×D4×C3111yescharacteristic
675C23C2×#41×C3111yescharacteristic
676C23C2×#41×C3111yescharacteristic
677C23C2×#41×C3111yescharacteristic
678C23C2×#41×C3111yescharacteristic
679C23C2×#41×C3111yescharacteristic
680C23C2×#41×C3111yescharacteristic
681C23C2×#41×C3111yescharacteristic
682C23C31×H(5,𝔽2)11yescharacteristic
683C23C31×H(5,𝔽2)11yescharacteristic
684C23C31×H(5,𝔽2)11yescharacteristic
685C23C31×2−1+411yescharacteristic
686D4—416no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4C31×#11714yes—
749C2×C4C4×D4×C3114yes—
750C2×C4C4×D4×C3114yes—
751C2×C4C4×D4×C3114yes—
752C2×C4C31×#12114yes—
753C2×C4C31×#12114yes—
754C2×C4C31×#12314yes—
755C2×C4C31×#12414yes—
756C2×C4C31×#12614yes—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22C2×C31×#11711yescharacteristic
773C22C2×C4×D4×C3111yescharacteristic
774C22C2×C4×D4×C3111yescharacteristic
775C22C2×C4×D4×C3111yescharacteristic
776C22C4×#41×C3111yescharacteristic
777C22C31×#51811yescharacteristic
778C22C31×#52011yescharacteristic
779C22C2×C31×#12111yescharacteristic
780C22C2×C31×#12111yescharacteristic
781C22C2×C31×#12311yescharacteristic
782C22C31×#52511yescharacteristic
783C22C2×C31×#12411yescharacteristic
784C22C2×C31×#12611yescharacteristic
785C22C31×#52911yescharacteristic
786C22C31×#53211yescharacteristic
787C22C31×#53511yescharacteristic
788C22C31×#53711yescharacteristic
789C22C31×#54011yescharacteristic
790C22C31×#54211yescharacteristic
791C22D42×C3111yescharacteristic
792C22C31×#54611yescharacteristic
793C22C31×#54711yescharacteristic
794C22C31×#54811yescharacteristic
795C22C31×#55011yescharacteristic
796C22C31×#55011yescharacteristic
797C22C31×#55011yescharacteristic
798C22C31×#55311yescharacteristic
799C22C31×#55311yescharacteristic
800C22C31×#55511yescharacteristic
801C22C31×#55611yescharacteristic
802C22C31×#55611yescharacteristic
803C22C31×#55911yescharacteristic
804C22C31×#55911yescharacteristic
805C22C31×#55911yescharacteristic
806C22C31×#55911yescharacteristic
807C4—24no—
808C4—24no—
809C4—42no—
810C4—44no—
811C4—42no—
812C4—42no—
813C4—42no—
814C4—44no—
815C4—82no—
816C4C31×#38818yescomplemented
817C2—84no—
818C2C2×C31×#38811yescharacteristic
819C2C4×C31×#12111yescharacteristic
820C2C31×#232411yescharacteristic
821C2C31×#235411yescharacteristic
822C2C31×#235711yescharacteristic
823C2C31×#236611yescharacteristic
824C2C31×#236711yescharacteristic
825C2C31×#241411yescharacteristic
826C2C31×#241611yescharacteristic
827C2C31×#244511yescharacteristic
828C2C31×#244811yescharacteristic
829C2C31×#251211yescharacteristic
830C2C31×#251311yescharacteristic
831C2C31×#254811yescharacteristic
832C2C31×#259211yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C31×#388C2semidirect
5. C2×C4×C4⋊C4×C31C2semidirect
6. C2×C4×C4⋊C4×C31C2semidirect
7. C31×#1440C2semidirect
8. C31×#1439C2semidirect
9. C31×#1437C2semidirect
10. C31×C4⋊#95C2semidirect
11. C31×C4⋊#95C2semidirect
30. C31×#390C4semidirect
73. C2×C4⋊C4×C31D4semidirect
219. #14022C31direct (N × H)
344. C2×#388C2×C31semidirect
345. C2×C4×C4⋊C4C2×C31semidirect
346. C2×C4×C4⋊C4C2×C31semidirect
347. #1440C2×C31semidirect
348. #1439C2×C31semidirect
349. #1437C2×C31semidirect
350. C4⋊#95C2×C31semidirect
351. C4⋊#95C2×C31semidirect
411. C4×C31#388semidirect
430. #390C4×C31semidirect
489. C2×C4⋊C4D4×C31semidirect
527. C31#14022direct (N × H)
816. C4C31×#388semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3902
C2×C31×#3882
C2×C4×C4⋊C4×C312
C31×#14402
C31×#14392
C31×#14372
C31×C4⋊#952
#1402231