Finite Group Databasebeta

← C31×#24882 #21481641

Subgroups — C31×#24882 #21481641

Order 7936.

1168 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#480C211yesmaximal, characteristic, complemented
2C2×C31×#418C211yesmaximal, characteristic, complemented
3C31×#2408C211yesmaximal, characteristic
4C31×#2352C211yesmaximal, characteristic, complemented
5C31×#2092C211yesmaximal, characteristic, complemented
6C31×#2073C211yesmaximal, characteristic, complemented
7C31×#2034C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic, complemented
9C31×#1926C211yesmaximal, characteristic, complemented
10C31×#1925C211yesmaximal, characteristic, complemented
11C31×#1874C211yesmaximal, characteristic, complemented
12C31×#1870C211yesmaximal, characteristic, complemented
13C31×#1854C211yesmaximal, characteristic, complemented
14C31×#1809C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×M16×C31C2211yescharacteristic
18C2×C31×#121C2211yescharacteristic
19C2×C31×#121C2211yescharacteristic
20C2×C31×#120—21no—
21C2×C4×D4×C31C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic, complemented
24C31×#480—24no—
25C2×C31×#107C2211yescharacteristic, complemented
26C2×C31×#107C2211yescharacteristic, complemented
27C2×C31×#106C2211yescharacteristic, complemented
28C2×C31×#106C2211yescharacteristic, complemented
29C31×#418—24no—
30C2×C31×#102C2211yescharacteristic
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic, complemented
40C2×C31×C22⋊C8C2211yescharacteristic, complemented
41C31×#394—21no—
42C31×#392—21no—
43C31×#390C2211yescharacteristic
44C31×#390C2211yescharacteristic
45C31×#388—21no—
46C31×#387—21no—
47C31×#386—21no—
48C31×#382C2211yescharacteristic, complemented
49C31×#380C2211yescharacteristic
50C31×#380C2211yescharacteristic
51C31×#380C2211yescharacteristic, complemented
52C31×#379—21no—
53C4×C4⋊C4×C31C2211yescharacteristic, complemented
54C4×C22⋊C4×C31—21no—
55C31×#340C2211yescharacteristic, complemented
56C31×#340C2211yescharacteristic, complemented
57C31×#340C2211yescharacteristic, complemented
58C31×#340C2211yescharacteristic, complemented
59C31×#336C2211yescharacteristic, complemented
60C31×#336C2211yescharacteristic, complemented
61C25×C31—21no—
62C22×D4×C31—22no—
63C22×D4×C31—22no—
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—41no—
70C22×D4×C31—41no—
71C22×D4×C31D411yescharacteristic
72C22×D4×C31C2311yescharacteristic
73C22×D4×C31C2311yescharacteristic
74C23×C4×C31—21no—
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C2×M16×C31—22no—
78C2×M16×C31—22no—
79C2×M16×C31—41no—
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C31×#121—22no—
85C31×#121—22no—
86C31×#121—41no—
87C31×#121—41no—
88C31×#120—44no—
89C4×D4×C31—22no—
90C4×D4×C31—22no—
91C31×#117—22no—
92C31×#117—41no—
93C2×C4⋊C4×C31—22no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—41no—
96C2×C4⋊C4×C31D411yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
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×C31D411yescharacteristic
114C2×C22⋊C4×C31D411yescharacteristic
115C2×C42×C31—21no—
116C2×C42×C31—21no—
117C2×C42×C31C2311yescharacteristic
118C31×#107—22no—
119C31×#107—22no—
120C31×#106—41no—
121C31×#106—41no—
122C31×#102—22no—
123C31×#102—22no—
124C31×#102—22no—
125C31×#102—22no—
126C31×#102—22no—
127C31×#102—41no—
128C31×#102—41no—
129C31×#102D414yescomplemented
130C31×C22⋊C8—22no—
131C31×C22⋊C8—22no—
132C31×C22⋊C8—41no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C24×C31—21no—
140C24×C31—21no—
141C24×C31—42no—
142C24×C31—42no—
143C24×C31—42no—
144C24×C31—42no—
145C24×C31—42no—
146C24×C31—81no—
147C24×C31—81no—
148C24×C31C2×D411yescharacteristic
149C24×C31C2×D411yescharacteristic
150C2×D4×C31—28no—
151C2×D4×C31—22no—
152C2×D4×C31—22no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—44no—
164C2×D4×C31—44no—
165C2×D4×C31—41no—
166C2×D4×C31—42no—
167C2×D4×C31—42no—
168C2×D4×C31—44no—
169C2×D4×C31—42no—
170C2×D4×C31—42no—
171C2×D4×C31—42no—
172C2×D4×C31—42no—
173C2×D4×C31—42no—
174C2×D4×C31—81no—
175C2×D4×C31—81no—
176C2×D4×C31C2×D412yes—
177C2×D4×C31#4112yes—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—42no—
195C22×C4×C31—42no—
196C22×C4×C31—81no—
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31#4112yes—
202C22×C4×C31#4112yes—
203C22×C4×C31C2411yescharacteristic
204M16×C31—44no—
205C2×C8×C31—21no—
206C2×C8×C31—21no—
207C2×C8×C31—21no—
208C2×C8×C31—21no—
209C2×C8×C31—21no—
210C2×C8×C31—21no—
211C2×C8×C31—21no—
212C2×C8×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31—21no—
215C2×C8×C31—21no—
216C2×C8×C31C2×D412yes—
217C4⋊C4×C31—22no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—42no—
230C4⋊C4×C31C2×D412yes—
231C22⋊C4×C31—22no—
232C22⋊C4×C31—22no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—42no—
236C22⋊C4×C31—42no—
237C22⋊C4×C31—42no—
238C22⋊C4×C31—42no—
239C22⋊C4×C31—42no—
240C22⋊C4×C31—81no—
241C22⋊C4×C31—81no—
242C22⋊C4×C31—81no—
243C42×C31—21no—
244C42×C31—21no—
245C42×C31—42no—
246C42×C31—81no—
247#24882C3111yesmaximal, characteristic, direct product factor, Sylow
248C23×C31—21no—
249C23×C31—21no—
250C23×C31—21no—
251C23×C31—21no—
252C23×C31—21no—
253C23×C31—21no—
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—22no—
261C23×C31—22no—
262C23×C31—48no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—84no—
276C23×C31—84no—
277C23×C31—84no—
278C23×C31—84no—
279C23×C31—84no—
280C23×C31—84no—
281C23×C31#12312yes—
282C23×C31AGL(1,ℤ/8)12yes—
283C23×C31C22×D411yescharacteristic
284D4×C31—22no—
285D4×C31—22no—
286D4×C31—22no—
287D4×C31—22no—
288D4×C31—48no—
289D4×C31—44no—
290D4×C31—41no—
291D4×C31—41no—
292D4×C31—41no—
293D4×C31—41no—
294D4×C31—84no—
295D4×C31—84no—
296C2×C4×C31—21no—
297C2×C4×C31—21no—
298C2×C4×C31—22no—
299C2×C4×C31—22no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—22no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—84no—
334C2×C4×C31#12312yes—
335C2×C4×C31C22×D411yescharacteristic
336C2×C4×C31C2×#4111yescharacteristic
337C2×C4×C31C2×#4111yescharacteristic
338C2×C4×C31C2×#4111yescharacteristic
339C2×C4×C31H(5,𝔽2)11yescharacteristic
340C2×C4×C31H(5,𝔽2)11yescharacteristic
341C8×C31—22no—
342C8×C31—41no—
343C8×C31—41no—
344C8×C31—41no—
345C2×#480C2×C3111yescharacteristic, complemented
346C2×#418C2×C3111yescharacteristic, complemented
347#2408C2×C3111yescharacteristic
348#2352C2×C3111yescharacteristic, complemented
349#2092C2×C3111yescharacteristic, complemented
350#2073C2×C3111yescharacteristic, complemented
351#2034C2×C3111yescharacteristic, complemented
352#2034C2×C3111yescharacteristic, complemented
353#1926C2×C3111yescharacteristic, complemented
354#1925C2×C3111yescharacteristic, complemented
355#1874C2×C3111yescharacteristic, complemented
356#1870C2×C3111yescharacteristic, complemented
357#1854C2×C3111yescharacteristic, complemented
358#1809C2×C3111yescharacteristic, complemented
359#1786C2×C3111yescharacteristic, complemented
360C22×C31—22no—
361C22×C31—22no—
362C22×C31—22no—
363C22×C31—22no—
364C22×C31—22no—
365C22×C31—22no—
366C22×C31—41no—
367C22×C31—41no—
368C22×C31—41no—
369C22×C31—41no—
370C22×C31—41no—
371C22×C31—41no—
372C22×C31—41no—
373C22×C31—41no—
374C22×C31—42no—
375C22×C31—42no—
376C22×C31—42no—
377C22×C31—42no—
378C22×C31—42no—
379C22×C31—42no—
380C22×C31—816no—
381C22×C31—81no—
382C22×C31—81no—
383C22×C31—81no—
384C22×C31—81no—
385C22×C31—81no—
386C22×C31—81no—
387C22×C31—81no—
388C22×C31—81no—
389C22×C31C2×#12311yescharacteristic
390C22×C31D4211yescharacteristic
391C22×C31#54611yescharacteristic
392C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
393C22×C31#57511yescharacteristic
394C22×C31#57611yescharacteristic
395C22×C31#57711yescharacteristic
396C4×C31—22no—
397C4×C31—41no—
398C4×C31—41no—
399C4×C31—41no—
400C4×C31—42no—
401C4×C31—81no—
402C4×C31—81no—
403C4×C31—81no—
404C4×C31—81no—
405C4×C31—81no—
406C4×C31#52511yescharacteristic
407C4×C31#53811yescharacteristic
408C4×C31#54611yescharacteristic
409C4×C31#55111yescharacteristic
410C23×D4C22×C3111yescharacteristic
411C22×M16C22×C3111yescharacteristic
412C2×#121C22×C3111yescharacteristic
413C2×#121C22×C3111yescharacteristic
414C2×#120—21no—
415C2×C4×D4C22×C3111yescharacteristic
416C2×#117C22×C3111yescharacteristic
417C22×C4⋊C4C22×C3111yescharacteristic, complemented
418#480—24no—
419C2×#107C22×C3111yescharacteristic, complemented
420C2×#107C22×C3111yescharacteristic, complemented
421C2×#106C22×C3111yescharacteristic, complemented
422C2×#106C22×C3111yescharacteristic, complemented
423#418—24no—
424C2×#102C22×C3111yescharacteristic
425C2×#102C22×C3111yescharacteristic
426C2×#102C22×C3111yescharacteristic
427C2×#102C22×C3111yescharacteristic
428C2×#102C22×C3111yescharacteristic
429C2×#102C22×C3111yescharacteristic
430C2×#102C22×C3111yescharacteristic
431C2×#102C22×C3111yescharacteristic
432C2×C22⋊C8C22×C3111yescharacteristic
433C2×C22⋊C8C22×C3111yescharacteristic, complemented
434C2×C22⋊C8C22×C3111yescharacteristic, complemented
435#394—21no—
436#392—21no—
437#390C22×C3111yescharacteristic
438#390C22×C3111yescharacteristic
439#388—21no—
440#387—21no—
441#386—21no—
442#382C22×C3111yescharacteristic, complemented
443#380C22×C3111yescharacteristic
444#380C22×C3111yescharacteristic
445#380C22×C3111yescharacteristic, complemented
446#379—21no—
447C4×C4⋊C4C22×C3111yescharacteristic, complemented
448C4×C22⋊C4—21no—
449#340C22×C3111yescharacteristic, complemented
450#340C22×C3111yescharacteristic, complemented
451#340C22×C3111yescharacteristic, complemented
452#340C22×C3111yescharacteristic, complemented
453#336C22×C3111yescharacteristic, complemented
454#336C22×C3111yescharacteristic, complemented
455C2×C31—42no—
456C2×C31—42no—
457C2×C31—82no—
458C2×C31—82no—
459C2×C31#241811yescharacteristic
460C2×C31#309411yescharacteristic
461C2×C31#309611yescharacteristic
462C2×C31#326411yescharacteristic
463C2×C31#327511yescharacteristic
464C2×C31#331011yescharacteristic
465C2×C31#332211yescharacteristic
466C25—21no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4D4×C3111yescharacteristic
477C22×D4C23×C3111yescharacteristic
478C22×D4C23×C3111yescharacteristic
479C23×C4—21no—
480C23×C4C23×C3111yescharacteristic
481C23×C4C23×C3111yescharacteristic
482C2×M16—22no—
483C2×M16—22no—
484C2×M16—41no—
485C22×C8C23×C3111yescharacteristic
486C22×C8C23×C3111yescharacteristic
487C22×C8C23×C3111yescharacteristic
488C22×C8C23×C3111yescharacteristic
489#121—22no—
490#121—22no—
491#121—41no—
492#121—41no—
493#120—44no—
494C4×D4—22no—
495C4×D4—22no—
496#117—22no—
497#117—41no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4D4×C3111yescharacteristic
502C2×C4⋊C4C23×C3111yescharacteristic
503C2×C4⋊C4C23×C3111yescharacteristic
504C2×C4⋊C4C23×C3111yescharacteristic
505C2×C4⋊C4C23×C3111yescharacteristic
506C2×C4⋊C4C23×C3111yescharacteristic
507C2×C4⋊C4C23×C3111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4D4×C3111yescharacteristic
519C2×C22⋊C4D4×C3111yescharacteristic
520C2×C42—21no—
521C2×C42—21no—
522C2×C42C23×C3111yescharacteristic
523#107—22no—
524#107—22no—
525#106—41no—
526#106—41no—
527#102—22no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—41no—
533#102—41no—
534#102D4×C3114yescomplemented
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—41no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544C31#2488211yescharacteristic, direct product factor, Sylow
545C24—21no—
546C24—21no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—81no—
553C24—81no—
554C24C2×D4×C3111yescharacteristic
555C24C2×D4×C3111yescharacteristic
556C2×D4—28no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—41no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4C2×D4×C3112yes—
583C2×D4#41×C3112yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
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—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—81no—
603C22×C4C2×D4×C3111yescharacteristic
604C22×C4C2×D4×C3111yescharacteristic
605C22×C4C2×D4×C3111yescharacteristic
606C22×C4C2×D4×C3111yescharacteristic
607C22×C4#41×C3112yes—
608C22×C4#41×C3112yes—
609C22×C4C24×C3111yescharacteristic
610M16—44no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8C2×D4×C3112yes—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—42no—
636C4⋊C4C2×D4×C3112yes—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—42no—
652C42—81no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—22no—
667C23—48no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23C31×#12312yes—
687C23C31×AGL(1,ℤ/8)12yes—
688C23C22×D4×C3111yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—44no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—84no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4C31×#12312yes—
740C2×C4C22×D4×C3111yescharacteristic
741C2×C4C2×#41×C3111yescharacteristic
742C2×C4C2×#41×C3111yescharacteristic
743C2×C4C2×#41×C3111yescharacteristic
744C2×C4C31×H(5,𝔽2)11yescharacteristic
745C2×C4C31×H(5,𝔽2)11yescharacteristic
746C8—22no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—816no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C2×C31×#12311yescharacteristic
780C22D42×C3111yescharacteristic
781C22C31×#54611yescharacteristic
782C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
783C22C31×#57511yescharacteristic
784C22C31×#57611yescharacteristic
785C22C31×#57711yescharacteristic
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—42no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C31×#52511yescharacteristic
797C4C31×#53811yescharacteristic
798C4C31×#54611yescharacteristic
799C4C31×#55111yescharacteristic
800C2—42no—
801C2—42no—
802C2—82no—
803C2—82no—
804C2C31×#241811yescharacteristic
805C2C31×#309411yescharacteristic
806C2C31×#309611yescharacteristic
807C2C31×#326411yescharacteristic
808C2C31×#327511yescharacteristic
809C2C31×#331011yescharacteristic
810C2C31×#332211yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2408C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#480C2semidirect
2. C2×C31×#418C2semidirect
4. C31×#2352C2semidirect
5. C31×#2092C2semidirect
6. C31×#2073C2semidirect
7. C31×#2034C2semidirect
8. C31×#2034C2semidirect
9. C31×#1926C2semidirect
10. C31×#1925C2semidirect
11. C31×#1874C2semidirect
12. C31×#1870C2semidirect
13. C31×#1854C2semidirect
14. C31×#1809C2semidirect
15. C31×#1786C2semidirect
23. C22×C4⋊C4×C31C22semidirect
25. C2×C31×#107C22semidirect
26. C2×C31×#107C22semidirect
27. C2×C31×#106C22semidirect
28. C2×C31×#106C22semidirect
39. C2×C31×C22⋊C8C22semidirect
40. C2×C31×C22⋊C8C22semidirect
48. C31×#382C22semidirect
51. C31×#380C22semidirect
53. C4×C4⋊C4×C31C22semidirect
55. C31×#340C22semidirect
56. C31×#340C22semidirect
57. C31×#340C22semidirect
58. C31×#340C22semidirect
59. C31×#336C22semidirect
60. C31×#336C22semidirect
129. C31×#102D4semidirect
247. #24882C31direct (N × H)
345. C2×#480C2×C31semidirect
346. C2×#418C2×C31semidirect
348. #2352C2×C31semidirect
349. #2092C2×C31semidirect
350. #2073C2×C31semidirect
351. #2034C2×C31semidirect
352. #2034C2×C31semidirect
353. #1926C2×C31semidirect
354. #1925C2×C31semidirect
355. #1874C2×C31semidirect
356. #1870C2×C31semidirect
357. #1854C2×C31semidirect
358. #1809C2×C31semidirect
359. #1786C2×C31semidirect
417. C22×C4⋊C4C22×C31semidirect
419. C2×#107C22×C31semidirect
420. C2×#107C22×C31semidirect
421. C2×#106C22×C31semidirect
422. C2×#106C22×C31semidirect
433. C2×C22⋊C8C22×C31semidirect
434. C2×C22⋊C8C22×C31semidirect
442. #382C22×C31semidirect
445. #380C22×C31semidirect
447. C4×C4⋊C4C22×C31semidirect
449. #340C22×C31semidirect
450. #340C22×C31semidirect
451. #340C22×C31semidirect
452. #340C22×C31semidirect
453. #336C22×C31semidirect
454. #336C22×C31semidirect
534. #102D4×C31semidirect
544. C31#24882direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4802
C2×C31×#4182
C31×#24082
C31×#23522
C31×#20922
C31×#20732
C31×#20342
C31×#19262
C31×#19252
C31×#18742
C31×#18702
C31×#18542
C31×#18092
C31×#17862
#2488231