Finite Group Databasebeta

← C31×#13993 #21470752

Subgroups — C31×#13993 #21470752

Order 7936.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#389C211yesmaximal, characteristic, complemented
2C2×C31×#380C211yesmaximal, characteristic
3C2×C31×#380C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
6C31×#1443C212yesmaximal, complemented
7C31×#1439C212yesmaximal
8C31×#1437C212yesmaximal
9C31×#1436C212yesmaximal, complemented
10C31×C4⋊#95C211yesmaximal, characteristic, complemented
11C31×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2212yes—
22C22×C42×C31C2211yescharacteristic
23C22×C42×C31C2211yescharacteristic
24C22×C42×C31C2212yes—
25C31×#389—24no—
26C31×#380—24no—
27C31×#380C418yescomplemented
28C4×C4⋊C4×C31—24no—
29C4×C22⋊C4×C31—24no—
30C2×C31×#95C2212yes—
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C25×C31C2311yescharacteristic
41C23×C4×C31—22no—
42C23×C4×C31—22no—
43C23×C4×C31—22no—
44C23×C4×C31—22no—
45C23×C4×C31—22no—
46C23×C4×C31—22no—
47C23×C4×C31C2×C414yes—
48C23×C4×C31C2312yes—
49C23×C4×C31C2312yes—
50C23×C4×C31C2312yes—
51C23×C4×C31C2311yescharacteristic
52C23×C4×C31C2312yes—
53C23×C4×C31C2311yescharacteristic
54C23×C4×C31C2311yescharacteristic
55C23×C4×C31C2311yescharacteristic
56C23×C4×C31C2311yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C2×C4⋊C4×C31—22no—
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—24no—
66C2×C4⋊C4×C31—24no—
67C2×C4⋊C4×C31—22no—
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31—42no—
70C2×C4⋊C4×C31C2×C414yes—
71C2×C4⋊C4×C31C2×C414yes—
72C2×C4⋊C4×C31D414yes—
73C2×C22⋊C4×C31—22no—
74C2×C22⋊C4×C31—22no—
75C2×C22⋊C4×C31—22no—
76C2×C22⋊C4×C31—22no—
77C2×C22⋊C4×C31—22no—
78C2×C22⋊C4×C31—24no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—42no—
81C2×C22⋊C4×C31—42no—
82C2×C22⋊C4×C31—42no—
83C2×C22⋊C4×C31C2×C418yes—
84C2×C22⋊C4×C31Q814yes—
85C2×C42×C31—22no—
86C2×C42×C31—22no—
87C2×C42×C31—22no—
88C2×C42×C31—24no—
89C2×C42×C31—22no—
90C2×C42×C31—22no—
91C2×C42×C31—42no—
92C2×C42×C31—42no—
93C2×C42×C31D414yes—
94C31×#95—22no—
95C31×#95—22no—
96C31×#95—24no—
97C31×#95—24no—
98C31×#95—24no—
99C31×#95—24no—
100C31×#95—42no—
101C31×#95—42no—
102C31×#95—42no—
103C31×#95C2×C418yes—
104C24×C31—21no—
105C24×C31—21no—
106C24×C31—21no—
107C24×C31—21no—
108C24×C31—21no—
109C24×C31—21no—
110C24×C31—21no—
111C24×C31—21no—
112C24×C31—21no—
113C24×C31—21no—
114C24×C31—21no—
115C24×C31—21no—
116C24×C31C22×C412yes—
117C24×C31C2×Q812yes—
118C24×C31#4112yes—
119C24×C31C2411yescharacteristic
120C22×C4×C31—21no—
121C22×C4×C31—21no—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—21no—
126C22×C4×C31—21no—
127C22×C4×C31—21no—
128C22×C4×C31—21no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—21no—
133C22×C4×C31—22no—
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—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
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—22no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—21no—
163C22×C4×C31—22no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—28no—
167C22×C4×C31—28no—
168C22×C4×C31—28no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—44no—
177C22×C4×C31—44no—
178C22×C4×C31—44no—
179C22×C4×C31—44no—
180C22×C4×C31C22×C412yes—
181C22×C4×C31C22×C414yes—
182C22×C4×C31C22×C414yes—
183C22×C4×C31C22×C412yes—
184C22×C4×C31C2×D412yes—
185C22×C4×C31C2×D414yes—
186C22×C4×C31C2×D412yes—
187C22×C4×C31C2×D412yes—
188C22×C4×C31C2×D412yes—
189C22×C4×C31C2×Q812yes—
190C22×C4×C31C2×Q812yes—
191C22×C4×C31#4112yes—
192C22×C4×C31#4112yes—
193C22×C4×C31#4112yes—
194C22×C4×C31#4112yes—
195C22×C4×C31#4112yes—
196C22×C4×C31#4112yes—
197C4⋊C4×C31—28no—
198C4⋊C4×C31—28no—
199C4⋊C4×C31—28no—
200C4⋊C4×C31—48no—
201C4⋊C4×C31—44no—
202C22⋊C4×C31—28no—
203C22⋊C4×C31—28no—
204C22⋊C4×C31—48no—
205C22⋊C4×C31—48no—
206C42×C31—28no—
207C42×C31—48no—
208C42×C31—44no—
209#13993C3111yesmaximal, characteristic, direct product factor, Sylow
210C23×C31—22no—
211C23×C31—22no—
212C23×C31—22no—
213C23×C31—22no—
214C23×C31—22no—
215C23×C31—22no—
216C23×C31—22no—
217C23×C31—22no—
218C23×C31—22no—
219C23×C31—22no—
220C23×C31—22no—
221C23×C31—22no—
222C23×C31—22no—
223C23×C31—22no—
224C23×C31—22no—
225C23×C31—22no—
226C23×C31—22no—
227C23×C31—22no—
228C23×C31—41no—
229C23×C31—41no—
230C23×C31—41no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31—41no—
241C23×C31—41no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31C4×Q814yes—
245C23×C31C23×C411yescharacteristic
246C23×C31C22×D411yescharacteristic
247C23×C31C22×D411yescharacteristic
248C23×C31C22×Q811yescharacteristic
249C23×C31C2×#4111yescharacteristic
250C23×C31C2×#4111yescharacteristic
251C23×C31C2×#4111yescharacteristic
252C23×C31C2×#4111yescharacteristic
253C23×C31C2×#4111yescharacteristic
254C23×C31C2×#4111yescharacteristic
255C23×C31C2×#4111yescharacteristic
256C23×C31H(5,𝔽2)11yescharacteristic
257C23×C31H(5,𝔽2)11yescharacteristic
258C23×C31H(5,𝔽2)11yescharacteristic
259C23×C312−1+411yescharacteristic
260C2×C4×C31—22no—
261C2×C4×C31—22no—
262C2×C4×C31—22no—
263C2×C4×C31—22no—
264C2×C4×C31—22no—
265C2×C4×C31—22no—
266C2×C4×C31—22no—
267C2×C4×C31—24no—
268C2×C4×C31—24no—
269C2×C4×C31—22no—
270C2×C4×C31—22no—
271C2×C4×C31—24no—
272C2×C4×C31—24no—
273C2×C4×C31—24no—
274C2×C4×C31—24no—
275C2×C4×C31—24no—
276C2×C4×C31—22no—
277C2×C4×C31—22no—
278C2×C4×C31—22no—
279C2×C4×C31—22no—
280C2×C4×C31—22no—
281C2×C4×C31—24no—
282C2×C4×C31—22no—
283C2×C4×C31—24no—
284C2×C4×C31—22no—
285C2×C4×C31—22no—
286C2×C4×C31—22no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—42no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—42no—
295C2×C4×C31—42no—
296C2×C4×C31—41no—
297C2×C4×C31—42no—
298C2×C4×C31—41no—
299C2×C4×C31—42no—
300C2×C4×C31—42no—
301C2×C4×C31—42no—
302C2×C4×C31—41no—
303C2×C4×C31—42no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—42no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—42no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—416no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31—42no—
322C2×C4×C31—42no—
323C2×C4×C31#11714yes—
324C2×C4×C31C4×D414yes—
325C2×C4×C31C4×D414yes—
326C2×C4×C31#12114yes—
327C2×C4×C31C22⋊Q814yes—
328C2×C4×C31#12314yes—
329C2×C4×C31#12414yes—
330C2×C4×C31#12614yes—
331C2×#389C2×C3111yescharacteristic, complemented
332C2×#380C2×C3111yescharacteristic
333C2×#380C2×C3111yescharacteristic
334C2×C4×C4⋊C4C2×C3111yescharacteristic, complemented
335C2×C4×C22⋊C4C2×C3111yescharacteristic
336#1443C2×C3112yescomplemented
337#1439C2×C3112yes—
338#1437C2×C3112yes—
339#1436C2×C3112yescomplemented
340C4⋊#95C2×C3111yescharacteristic, complemented
341C4⋊#95C2×C3111yescharacteristic, complemented
342C22×C31—24no—
343C22×C31—24no—
344C22×C31—24no—
345C22×C31—42no—
346C22×C31—42no—
347C22×C31—42no—
348C22×C31—42no—
349C22×C31—42no—
350C22×C31—42no—
351C22×C31—42no—
352C22×C31—42no—
353C22×C31—42no—
354C22×C31—42no—
355C22×C31—42no—
356C22×C31—42no—
357C22×C31C2×#11711yescharacteristic
358C22×C31C2×C4×D411yescharacteristic
359C22×C31C2×C4×D411yescharacteristic
360C22×C31C2×C4×Q811yescharacteristic
361C22×C31C4×#4111yescharacteristic
362C22×C31#51811yescharacteristic
363C22×C31#52011yescharacteristic
364C22×C31C2×#12111yescharacteristic
365C22×C31C2×C22⋊Q811yescharacteristic
366C22×C31C2×#12311yescharacteristic
367C22×C31#52511yescharacteristic
368C22×C31C2×#12411yescharacteristic
369C22×C31C2×#12611yescharacteristic
370C22×C31#52911yescharacteristic
371C22×C31#53311yescharacteristic
372C22×C31#53511yescharacteristic
373C22×C31#53711yescharacteristic
374C22×C31#54011yescharacteristic
375C22×C31#54211yescharacteristic
376C22×C31#54611yescharacteristic
377C22×C31#54611yescharacteristic
378C22×C31D4×Q811yescharacteristic
379C22×C31#55011yescharacteristic
380C22×C31#55211yescharacteristic
381C22×C31#55311yescharacteristic
382C22×C31#55311yescharacteristic
383C22×C31#55311yescharacteristic
384C22×C31#55311yescharacteristic
385C22×C31#55311yescharacteristic
386C22×C31#55411yescharacteristic
387C22×C31#55411yescharacteristic
388C22×C31#55411yescharacteristic
389C22×C31#55511yescharacteristic
390C22×C31#55611yescharacteristic
391C22×C31#55611yescharacteristic
392C4×C31—24no—
393C4×C31—44no—
394C4×C31—44no—
395C4×C31—42no—
396C4×C31—44no—
397C4×C31—42no—
398C4×C31—42no—
399C4×C31—42no—
400C4×C31—82no—
401C4×C31#38818yes—
402C24×C4C22×C3111yescharacteristic
403C22×C4⋊C4C22×C3111yescharacteristic
404C22×C4⋊C4C22×C3112yes—
405C22×C4⋊C4C22×C3111yescharacteristic
406C22×C4⋊C4C22×C3111yescharacteristic
407C22×C4⋊C4C22×C3111yescharacteristic
408C22×C22⋊C4C22×C3111yescharacteristic
409C22×C22⋊C4C22×C3112yes—
410C22×C22⋊C4C22×C3111yescharacteristic
411C22×C22⋊C4C22×C3112yes—
412C22×C42C22×C3111yescharacteristic
413C22×C42C22×C3111yescharacteristic
414C22×C42C22×C3112yes—
415#389—24no—
416#380—24no—
417#380C4×C3118yescomplemented
418C4×C4⋊C4—24no—
419C4×C22⋊C4—24no—
420C2×#95C22×C3112yes—
421C2×#95C22×C3111yescharacteristic
422C2×#95C22×C3112yes—
423C2×#95C22×C3112yes—
424C2×#95C22×C3112yes—
425C2×#95C22×C3111yescharacteristic
426C2×#95C22×C3112yes—
427C2×#95C22×C3112yes—
428C2×#95C22×C3112yes—
429C2×#95C22×C3112yes—
430C2×C31—44no—
431C2×C31C2×#38811yescharacteristic
432C2×C31C4×C22⋊Q811yescharacteristic
433C2×C31#232411yescharacteristic
434C2×C31#234511yescharacteristic
435C2×C31#234711yescharacteristic
436C2×C31#236011yescharacteristic
437C2×C31#236311yescharacteristic
438C2×C31#248511yescharacteristic
439C2×C31#248711yescharacteristic
440C2×C31#249011yescharacteristic
441C2×C31#249211yescharacteristic
442C2×C31#249411yescharacteristic
443C2×C31#249711yescharacteristic
444C2×C31#253511yescharacteristic
445C2×C31#253811yescharacteristic
446C25C23×C3111yescharacteristic
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4C2×C4×C3114yes—
454C23×C4C23×C3112yes—
455C23×C4C23×C3112yes—
456C23×C4C23×C3112yes—
457C23×C4C23×C3111yescharacteristic
458C23×C4C23×C3112yes—
459C23×C4C23×C3111yescharacteristic
460C23×C4C23×C3111yescharacteristic
461C23×C4C23×C3111yescharacteristic
462C23×C4C23×C3111yescharacteristic
463C23×C4C23×C3111yescharacteristic
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4C2×C4×C3114yes—
477C2×C4⋊C4C2×C4×C3114yes—
478C2×C4⋊C4D4×C3114yes—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4C2×C4×C3118yes—
490C2×C22⋊C4Q8×C3114yes—
491C2×C42—22no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—24no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—42no—
498C2×C42—42no—
499C2×C42D4×C3114yes—
500#95—22no—
501#95—22no—
502#95—24no—
503#95—24no—
504#95—24no—
505#95—24no—
506#95—42no—
507#95—42no—
508#95—42no—
509#95C2×C4×C3118yes—
510C31#1399311yescharacteristic, direct product factor, Sylow
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24C22×C4×C3112yes—
524C24C2×Q8×C3112yes—
525C24#41×C3112yes—
526C24C24×C3111yescharacteristic
527C22×C4—21no—
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—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4C22×C4×C3112yes—
588C22×C4C22×C4×C3114yes—
589C22×C4C22×C4×C3114yes—
590C22×C4C22×C4×C3112yes—
591C22×C4C2×D4×C3112yes—
592C22×C4C2×D4×C3114yes—
593C22×C4C2×D4×C3112yes—
594C22×C4C2×D4×C3112yes—
595C22×C4C2×D4×C3112yes—
596C22×C4C2×Q8×C3112yes—
597C22×C4C2×Q8×C3112yes—
598C22×C4#41×C3112yes—
599C22×C4#41×C3112yes—
600C22×C4#41×C3112yes—
601C22×C4#41×C3112yes—
602C22×C4#41×C3112yes—
603C22×C4#41×C3112yes—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—48no—
608C4⋊C4—44no—
609C22⋊C4—28no—
610C22⋊C4—28no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C42—28no—
614C42—48no—
615C42—44no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23C4×Q8×C3114yes—
651C23C23×C4×C3111yescharacteristic
652C23C22×D4×C3111yescharacteristic
653C23C22×D4×C3111yescharacteristic
654C23C22×Q8×C3111yescharacteristic
655C23C2×#41×C3111yescharacteristic
656C23C2×#41×C3111yescharacteristic
657C23C2×#41×C3111yescharacteristic
658C23C2×#41×C3111yescharacteristic
659C23C2×#41×C3111yescharacteristic
660C23C2×#41×C3111yescharacteristic
661C23C2×#41×C3111yescharacteristic
662C23C31×H(5,𝔽2)11yescharacteristic
663C23C31×H(5,𝔽2)11yescharacteristic
664C23C31×H(5,𝔽2)11yescharacteristic
665C23C31×2−1+411yescharacteristic
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—416no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4C31×#11714yes—
730C2×C4C4×D4×C3114yes—
731C2×C4C4×D4×C3114yes—
732C2×C4C31×#12114yes—
733C2×C4C31×C22⋊Q814yes—
734C2×C4C31×#12314yes—
735C2×C4C31×#12414yes—
736C2×C4C31×#12614yes—
737C22—24no—
738C22—24no—
739C22—24no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22C2×C31×#11711yescharacteristic
753C22C2×C4×D4×C3111yescharacteristic
754C22C2×C4×D4×C3111yescharacteristic
755C22C2×C4×Q8×C3111yescharacteristic
756C22C4×#41×C3111yescharacteristic
757C22C31×#51811yescharacteristic
758C22C31×#52011yescharacteristic
759C22C2×C31×#12111yescharacteristic
760C22C2×C31×C22⋊Q811yescharacteristic
761C22C2×C31×#12311yescharacteristic
762C22C31×#52511yescharacteristic
763C22C2×C31×#12411yescharacteristic
764C22C2×C31×#12611yescharacteristic
765C22C31×#52911yescharacteristic
766C22C31×#53311yescharacteristic
767C22C31×#53511yescharacteristic
768C22C31×#53711yescharacteristic
769C22C31×#54011yescharacteristic
770C22C31×#54211yescharacteristic
771C22C31×#54611yescharacteristic
772C22C31×#54611yescharacteristic
773C22D4×Q8×C3111yescharacteristic
774C22C31×#55011yescharacteristic
775C22C31×#55211yescharacteristic
776C22C31×#55311yescharacteristic
777C22C31×#55311yescharacteristic
778C22C31×#55311yescharacteristic
779C22C31×#55311yescharacteristic
780C22C31×#55311yescharacteristic
781C22C31×#55411yescharacteristic
782C22C31×#55411yescharacteristic
783C22C31×#55411yescharacteristic
784C22C31×#55511yescharacteristic
785C22C31×#55611yescharacteristic
786C22C31×#55611yescharacteristic
787C4—24no—
788C4—44no—
789C4—44no—
790C4—42no—
791C4—44no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—82no—
796C4C31×#38818yes—
797C2—44no—
798C2C2×C31×#38811yescharacteristic
799C2C4×C31×C22⋊Q811yescharacteristic
800C2C31×#232411yescharacteristic
801C2C31×#234511yescharacteristic
802C2C31×#234711yescharacteristic
803C2C31×#236011yescharacteristic
804C2C31×#236311yescharacteristic
805C2C31×#248511yescharacteristic
806C2C31×#248711yescharacteristic
807C2C31×#249011yescharacteristic
808C2C31×#249211yescharacteristic
809C2C31×#249411yescharacteristic
810C2C31×#249711yescharacteristic
811C2C31×#253511yescharacteristic
812C2C31×#253811yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#389C2semidirect
4. C2×C4×C4⋊C4×C31C2semidirect
6. C31×#1443C2semidirect
9. C31×#1436C2semidirect
10. C31×C4⋊#95C2semidirect
11. C31×C4⋊#95C2semidirect
27. C31×#380C4semidirect
209. #13993C31direct (N × H)
331. C2×#389C2×C31semidirect
334. C2×C4×C4⋊C4C2×C31semidirect
336. #1443C2×C31semidirect
339. #1436C2×C31semidirect
340. C4⋊#95C2×C31semidirect
341. C4⋊#95C2×C31semidirect
417. #380C4×C31semidirect
510. C31#13993direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3892
C2×C31×#3802
C2×C4×C4⋊C4×C312
C2×C4×C22⋊C4×C312
C31×#14432
C31×#14392
C31×#14372
C31×#14362
C31×C4⋊#952
#1399331