Finite Group Databasebeta

← C31×#24428 #21481187

Subgroups — C31×#24428 #21481187

Order 7936.

1632 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#546C211yesmaximal, characteristic, complemented
2C2×C31×#466C211yesmaximal, characteristic, complemented
3C2×C31×#449C211yesmaximal, characteristic, complemented
4C2×C31×#447C211yesmaximal, characteristic, complemented
5C2×C31×#416C211yesmaximal, characteristic, complemented
6C31×#2414C211yesmaximal, characteristic, complemented
7C31×#2042C211yesmaximal, characteristic, complemented
8C31×#2036C211yesmaximal, characteristic, complemented
9C31×#2012C211yesmaximal, characteristic, complemented
10C31×#2000C211yesmaximal, characteristic, complemented
11C31×#1879C211yesmaximal, characteristic, complemented
12C31×#1875C211yesmaximal, characteristic, complemented
13C31×#1869C211yesmaximal, characteristic, complemented
14C31×#1862C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic, complemented
19C22×D8×C31C2211yescharacteristic
20C22×D8×C31C2211yescharacteristic
21C23×C8×C31C2211yescharacteristic, complemented
22C31×#546—24no—
23C31×#546—24no—
24C2×C31×#124C2211yescharacteristic
25C2×C31×#123—21no—
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C31×#121—21no—
28C2×C31×#121C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic, complemented
31C2×C31×#120—21no—
32C2×C4×D4×C31C2211yescharacteristic
33C2×C4×D4×C31C2211yescharacteristic
34C2×C31×#117C2211yescharacteristic, complemented
35C22×C22⋊C4×C31—21no—
36C31×#466—24no—
37C31×#449—24no—
38C31×#447—24no—
39C2×C31×#107C2211yescharacteristic, complemented
40C31×#416—24no—
41C2×C31×#103C2211yescharacteristic, complemented
42C2×C31×#103C2211yescharacteristic, complemented
43C2×C31×#103C2211yescharacteristic, complemented
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×#102C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C2×C31×#102C2211yescharacteristic
50C2×C31×#102C2211yescharacteristic, complemented
51C2×C31×C22⋊C8C2211yescharacteristic
52C2×C31×C22⋊C8C2211yescharacteristic
53C2×C31×C22⋊C8C2211yescharacteristic, complemented
54C31×#394—21no—
55C31×#392—21no—
56C31×#390—21no—
57C31×#390C2211yescharacteristic, complemented
58C31×#389C2211yescharacteristic, complemented
59C31×#388—21no—
60C31×#380C2211yescharacteristic
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C31×#336C2211yescharacteristic, complemented
64C31×#336C2211yescharacteristic, complemented
65C25×C31—21no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—41no—
70C2×#41×C31—41no—
71C2×#41×C31D414yescomplemented
72C22×Q8×C31C2311yescharacteristic
73C22×D4×C31—21no—
74C22×D4×C31—21no—
75C22×D4×C31—22no—
76C22×D4×C31—22no—
77C22×D4×C31—22no—
78C22×D4×C31—22no—
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31—41no—
83C22×D4×C31—41no—
84C22×D4×C31D411yescharacteristic
85C22×D4×C31C2311yescharacteristic
86C22×D4×C31C2311yescharacteristic
87C22×D4×C31C2311yescharacteristic
88C23×C4×C31—21no—
89C23×C4×C31—21no—
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C2×SD16×C31—22no—
93C2×SD16×C31—41no—
94C2×SD16×C31—41no—
95C2×D8×C31—22no—
96C2×D8×C31—22no—
97C2×D8×C31—22no—
98C2×D8×C31—22no—
99C2×D8×C31—22no—
100C2×D8×C31—41no—
101C22×C8×C31—22no—
102C22×C8×C31—22no—
103C22×C8×C31—41no—
104C22×C8×C31C2311yescharacteristic
105C22×C8×C31C2311yescharacteristic
106C22×C8×C31C2311yescharacteristic
107C22×C8×C31C2311yescharacteristic
108C31×#124—22no—
109C31×#124—22no—
110C31×#123—28no—
111C31×C22⋊Q8—22no—
112C31×C22⋊Q8—22no—
113C31×#121—28no—
114C31×#121—22no—
115C31×#121—22no—
116C31×#121—22no—
117C31×#121—22no—
118C31×#121—41no—
119C31×#121D414yescomplemented
120C31×#120—28no—
121C4×D4×C31—22no—
122C4×D4×C31—22no—
123C4×D4×C31—22no—
124C4×D4×C31—22no—
125C31×#117—22no—
126C31×#117—41no—
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31—21no—
129C2×C4⋊C4×C31D411yescharacteristic
130C2×C4⋊C4×C31C2311yescharacteristic
131C2×C4⋊C4×C31C2311yescharacteristic
132C2×C4⋊C4×C31C2311yescharacteristic
133C2×C4⋊C4×C31C2311yescharacteristic
134C2×C22⋊C4×C31—28no—
135C2×C22⋊C4×C31—21no—
136C2×C22⋊C4×C31—21no—
137C2×C22⋊C4×C31—21no—
138C2×C22⋊C4×C31—21no—
139C2×C22⋊C4×C31—21no—
140C2×C22⋊C4×C31—21no—
141C2×C22⋊C4×C31—21no—
142C2×C22⋊C4×C31—21no—
143C2×C22⋊C4×C31—21no—
144C2×C22⋊C4×C31—21no—
145C2×C22⋊C4×C31—21no—
146C2×C22⋊C4×C31D411yescharacteristic
147C2×C22⋊C4×C31D411yescharacteristic
148C2×C42×C31—21no—
149C2×C42×C31C2311yescharacteristic
150C31×#107—22no—
151C31×#103—22no—
152C31×#103—22no—
153C31×#103—22no—
154C31×#102—22no—
155C31×#102—22no—
156C31×#102—22no—
157C31×#102—22no—
158C31×#102—22no—
159C31×#102—41no—
160C31×#102D414yescomplemented
161C31×C22⋊C8—22no—
162C31×C22⋊C8—22no—
163C31×C22⋊C8—41no—
164C31×#95—21no—
165C31×#95—21no—
166C24×C31—21no—
167C24×C31—24no—
168C24×C31—21no—
169C24×C31—21no—
170C24×C31—42no—
171C24×C31—42no—
172C24×C31—42no—
173C24×C31—42no—
174C24×C31—81no—
175C24×C31—81no—
176C24×C31C2×D411yescharacteristic
177C24×C31C2×D411yescharacteristic
178#41×C31—28no—
179#41×C31—44no—
180#41×C31—44no—
181#41×C31—44no—
182C2×Q8×C31—21no—
183C2×Q8×C31—21no—
184C2×Q8×C31—21no—
185C2×Q8×C31—21no—
186C2×Q8×C31—21no—
187C2×Q8×C31C2×D412yes—
188C2×D4×C31—24no—
189C2×D4×C31—22no—
190C2×D4×C31—24no—
191C2×D4×C31—22no—
192C2×D4×C31—24no—
193C2×D4×C31—21no—
194C2×D4×C31—21no—
195C2×D4×C31—21no—
196C2×D4×C31—21no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—21no—
207C2×D4×C31—41no—
208C2×D4×C31—42no—
209C2×D4×C31—42no—
210C2×D4×C31—42no—
211C2×D4×C31—44no—
212C2×D4×C31—44no—
213C2×D4×C31—44no—
214C2×D4×C31—42no—
215C2×D4×C31—42no—
216C2×D4×C31—44no—
217C2×D4×C31—42no—
218C2×D4×C31—42no—
219C2×D4×C31—81no—
220C2×D4×C31—81no—
221C2×D4×C31—81no—
222C2×D4×C31—81no—
223C2×D4×C31—81no—
224C2×D4×C31C2×D412yes—
225C2×D4×C31C2×D412yes—
226C2×D4×C31C2×D412yes—
227C2×D4×C31#4112yes—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—24no—
236C22×C4×C31—24no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—42no—
246C22×C4×C31—42no—
247C22×C4×C31—81no—
248C22×C4×C31—81no—
249C22×C4×C31C2×D411yescharacteristic
250C22×C4×C31C2×D411yescharacteristic
251C22×C4×C31C2×D411yescharacteristic
252C22×C4×C31C2×D411yescharacteristic
253C22×C4×C31C2×D412yes—
254C22×C4×C31C2×D412yes—
255C22×C4×C31C2411yescharacteristic
256SD16×C31—44no—
257D8×C31—44no—
258D8×C31—44no—
259C2×C8×C31—21no—
260C2×C8×C31—21no—
261C2×C8×C31—21no—
262C2×C8×C31—21no—
263C2×C8×C31—21no—
264C2×C8×C31—21no—
265C2×C8×C31—21no—
266C2×C8×C31—21no—
267C2×C8×C31—21no—
268C2×C8×C31—21no—
269C2×C8×C31—21no—
270C2×C8×C31—44no—
271C2×C8×C31C2×D412yes—
272C4⋊C4×C31—24no—
273C4⋊C4×C31—22no—
274C4⋊C4×C31—21no—
275C4⋊C4×C31—21no—
276C4⋊C4×C31—21no—
277C4⋊C4×C31—21no—
278C4⋊C4×C31—21no—
279C4⋊C4×C31—21no—
280C4⋊C4×C31—81no—
281C4⋊C4×C31C2×D412yes—
282C4⋊C4×C31C2×D412yes—
283C22⋊C4×C31—24no—
284C22⋊C4×C31—24no—
285C22⋊C4×C31—24no—
286C22⋊C4×C31—24no—
287C22⋊C4×C31—22no—
288C22⋊C4×C31—22no—
289C22⋊C4×C31—24no—
290C22⋊C4×C31—42no—
291C22⋊C4×C31—42no—
292C22⋊C4×C31—42no—
293C22⋊C4×C31—42no—
294C22⋊C4×C31—81no—
295C22⋊C4×C31—81no—
296C42×C31—21no—
297C42×C31—21no—
298C42×C31—42no—
299#24428C3111yesmaximal, characteristic, direct product factor, Sylow
300C23×C31—21no—
301C23×C31—22no—
302C23×C31—21no—
303C23×C31—21no—
304C23×C31—22no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—22no—
308C23×C31—21no—
309C23×C31—21no—
310C23×C31—21no—
311C23×C31—21no—
312C23×C31—21no—
313C23×C31—21no—
314C23×C31—21no—
315C23×C31—22no—
316C23×C31—48no—
317C23×C31—48no—
318C23×C31—41no—
319C23×C31—41no—
320C23×C31—41no—
321C23×C31—41no—
322C23×C31—41no—
323C23×C31—41no—
324C23×C31—41no—
325C23×C31—41no—
326C23×C31—41no—
327C23×C31—41no—
328C23×C31—41no—
329C23×C31—41no—
330C23×C31—41no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—41no—
334C23×C31—41no—
335C23×C31—84no—
336C23×C31—84no—
337C23×C31—84no—
338C23×C31—84no—
339C23×C31—84no—
340C23×C31#12012yes—
341C23×C31#13512yes—
342C23×C31C22×D411yescharacteristic
343Q8×C31—22no—
344Q8×C31—22no—
345Q8×C31—41no—
346Q8×C31—41no—
347D4×C31—22no—
348D4×C31—22no—
349D4×C31—22no—
350D4×C31—22no—
351D4×C31—22no—
352D4×C31—44no—
353D4×C31—48no—
354D4×C31—48no—
355D4×C31—41no—
356D4×C31—41no—
357D4×C31—41no—
358D4×C31—41no—
359D4×C31—41no—
360D4×C31—41no—
361D4×C31—84no—
362D4×C31—84no—
363D4×C31—84no—
364D4×C31#12114yes—
365C2×C4×C31—21no—
366C2×C4×C31—21no—
367C2×C4×C31—22no—
368C2×C4×C31—22no—
369C2×C4×C31—22no—
370C2×C4×C31—22no—
371C2×C4×C31—21no—
372C2×C4×C31—21no—
373C2×C4×C31—22no—
374C2×C4×C31—22no—
375C2×C4×C31—21no—
376C2×C4×C31—22no—
377C2×C4×C31—21no—
378C2×C4×C31—21no—
379C2×C4×C31—21no—
380C2×C4×C31—21no—
381C2×C4×C31—21no—
382C2×C4×C31—21no—
383C2×C4×C31—48no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—41no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—41no—
392C2×C4×C31—41no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31—41no—
397C2×C4×C31—41no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—84no—
401C2×C4×C31#12012yes—
402C2×C4×C31C22×D411yescharacteristic
403C2×C4×C31C22×D411yescharacteristic
404C2×C4×C31C22×D411yescharacteristic
405C2×C4×C31C2×#4111yescharacteristic
406C2×C4×C31H(5,𝔽2)11yescharacteristic
407C2×C4×C31H(5,𝔽2)11yescharacteristic
408C8×C31—22no—
409C8×C31—41no—
410C8×C31—41no—
411C8×C31—41no—
412C2×#546C2×C3111yescharacteristic, complemented
413C2×#466C2×C3111yescharacteristic, complemented
414C2×#449C2×C3111yescharacteristic, complemented
415C2×#447C2×C3111yescharacteristic, complemented
416C2×#416C2×C3111yescharacteristic, complemented
417#2414C2×C3111yescharacteristic, complemented
418#2042C2×C3111yescharacteristic, complemented
419#2036C2×C3111yescharacteristic, complemented
420#2012C2×C3111yescharacteristic, complemented
421#2000C2×C3111yescharacteristic, complemented
422#1879C2×C3111yescharacteristic, complemented
423#1875C2×C3111yescharacteristic, complemented
424#1869C2×C3111yescharacteristic, complemented
425#1862C2×C3111yescharacteristic, complemented
426#1786C2×C3111yescharacteristic, complemented
427C22×C31—22no—
428C22×C31—24no—
429C22×C31—22no—
430C22×C31—22no—
431C22×C31—22no—
432C22×C31—22no—
433C22×C31—22no—
434C22×C31—41no—
435C22×C31—42no—
436C22×C31—42no—
437C22×C31—41no—
438C22×C31—41no—
439C22×C31—41no—
440C22×C31—42no—
441C22×C31—41no—
442C22×C31—42no—
443C22×C31—41no—
444C22×C31—42no—
445C22×C31—41no—
446C22×C31—41no—
447C22×C31—42no—
448C22×C31—42no—
449C22×C31—42no—
450C22×C31—42no—
451C22×C31—816no—
452C22×C31—81no—
453C22×C31—81no—
454C22×C31—81no—
455C22×C31—81no—
456C22×C31—81no—
457C22×C31—81no—
458C22×C31—81no—
459C22×C31—81no—
460C22×C31—81no—
461C22×C31—81no—
462C22×C31—81no—
463C22×C31C2×#12011yescharacteristic
464C22×C31D4211yescharacteristic
465C22×C31#54611yescharacteristic
466C22×C31C2×#13511yescharacteristic
467C22×C31#57511yescharacteristic
468C22×C31#57611yescharacteristic
469C22×C31#57611yescharacteristic
470C4×C31—22no—
471C4×C31—41no—
472C4×C31—42no—
473C4×C31—41no—
474C4×C31—41no—
475C4×C31—42no—
476C4×C31—42no—
477C4×C31—81no—
478C4×C31—81no—
479C4×C31C2×#12111yescharacteristic
480C4×C31#53411yescharacteristic
481C4×C31D4211yescharacteristic
482C4×C31#54611yescharacteristic
483C22×#41C22×C3111yescharacteristic
484C23×D4C22×C3111yescharacteristic
485C22×SD16C22×C3111yescharacteristic, complemented
486C22×D8C22×C3111yescharacteristic
487C22×D8C22×C3111yescharacteristic
488C23×C8C22×C3111yescharacteristic, complemented
489#546—24no—
490#546—24no—
491C2×#124C22×C3111yescharacteristic
492C2×#123—21no—
493C2×C22⋊Q8C22×C3111yescharacteristic
494C2×#121—21no—
495C2×#121C22×C3111yescharacteristic
496C2×#121C22×C3111yescharacteristic
497C2×#121C22×C3111yescharacteristic, complemented
498C2×#120—21no—
499C2×C4×D4C22×C3111yescharacteristic
500C2×C4×D4C22×C3111yescharacteristic
501C2×#117C22×C3111yescharacteristic, complemented
502C22×C22⋊C4—21no—
503#466—24no—
504#449—24no—
505#447—24no—
506C2×#107C22×C3111yescharacteristic, complemented
507#416—24no—
508C2×#103C22×C3111yescharacteristic, complemented
509C2×#103C22×C3111yescharacteristic, complemented
510C2×#103C22×C3111yescharacteristic, complemented
511C2×#102C22×C3111yescharacteristic
512C2×#102C22×C3111yescharacteristic
513C2×#102C22×C3111yescharacteristic
514C2×#102C22×C3111yescharacteristic
515C2×#102C22×C3111yescharacteristic
516C2×#102C22×C3111yescharacteristic
517C2×#102C22×C3111yescharacteristic, complemented
518C2×C22⋊C8C22×C3111yescharacteristic
519C2×C22⋊C8C22×C3111yescharacteristic
520C2×C22⋊C8C22×C3111yescharacteristic, complemented
521#394—21no—
522#392—21no—
523#390—21no—
524#390C22×C3111yescharacteristic, complemented
525#389C22×C3111yescharacteristic, complemented
526#388—21no—
527#380C22×C3111yescharacteristic
528#340C22×C3111yescharacteristic, complemented
529#340C22×C3111yescharacteristic, complemented
530#336C22×C3111yescharacteristic, complemented
531#336C22×C3111yescharacteristic, complemented
532C2×C31—42no—
533C2×C31—42no—
534C2×C31—44no—
535C2×C31—82no—
536C2×C31—161no—
537C2×C31#241011yescharacteristic
538C2×C31#300211yescharacteristic
539C2×C31#300811yescharacteristic
540C2×C31#326811yescharacteristic
541C2×C31#328011yescharacteristic
542C2×C31#329711yescharacteristic
543C2×C31#331911yescharacteristic
544C25—21no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—41no—
549C2×#41—41no—
550C2×#41D4×C3114yescomplemented
551C22×Q8C23×C3111yescharacteristic
552C22×D4—21no—
553C22×D4—21no—
554C22×D4—22no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4D4×C3111yescharacteristic
564C22×D4C23×C3111yescharacteristic
565C22×D4C23×C3111yescharacteristic
566C22×D4C23×C3111yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C23×C3111yescharacteristic
570C23×C4C23×C3111yescharacteristic
571C2×SD16—22no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×D8—22no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—41no—
580C22×C8—22no—
581C22×C8—22no—
582C22×C8—41no—
583C22×C8C23×C3111yescharacteristic
584C22×C8C23×C3111yescharacteristic
585C22×C8C23×C3111yescharacteristic
586C22×C8C23×C3111yescharacteristic
587#124—22no—
588#124—22no—
589#123—28no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592#121—28no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—41no—
598#121D4×C3114yescomplemented
599#120—28no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604#117—22no—
605#117—41no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4D4×C3111yescharacteristic
609C2×C4⋊C4C23×C3111yescharacteristic
610C2×C4⋊C4C23×C3111yescharacteristic
611C2×C4⋊C4C23×C3111yescharacteristic
612C2×C4⋊C4C23×C3111yescharacteristic
613C2×C22⋊C4—28no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4D4×C3111yescharacteristic
626C2×C22⋊C4D4×C3111yescharacteristic
627C2×C42—21no—
628C2×C42C23×C3111yescharacteristic
629#107—22no—
630#103—22no—
631#103—22no—
632#103—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—41no—
639#102D4×C3114yescomplemented
640C22⋊C8—22no—
641C22⋊C8—22no—
642C22⋊C8—41no—
643#95—21no—
644#95—21no—
645C31#2442811yescharacteristic, direct product factor, Sylow
646C24—21no—
647C24—24no—
648C24—21no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C3111yescharacteristic
657C24C2×D4×C3111yescharacteristic
658#41—28no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C3112yes—
668C2×D4—24no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—22no—
672C2×D4—24no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—44no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4C2×D4×C3112yes—
705C2×D4C2×D4×C3112yes—
706C2×D4C2×D4×C3112yes—
707C2×D4#41×C3112yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—81no—
728C22×C4—81no—
729C22×C4C2×D4×C3111yescharacteristic
730C22×C4C2×D4×C3111yescharacteristic
731C22×C4C2×D4×C3111yescharacteristic
732C22×C4C2×D4×C3111yescharacteristic
733C22×C4C2×D4×C3112yes—
734C22×C4C2×D4×C3112yes—
735C22×C4C24×C3111yescharacteristic
736SD16—44no—
737D8—44no—
738D8—44no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—44no—
751C2×C8C2×D4×C3112yes—
752C4⋊C4—24no—
753C4⋊C4—22no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—81no—
761C4⋊C4C2×D4×C3112yes—
762C4⋊C4C2×D4×C3112yes—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—24no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42—21no—
777C42—21no—
778C42—42no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—48no—
796C23—48no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23C31×#12012yes—
820C23C31×#13512yes—
821C23C22×D4×C3111yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—41no—
825Q8—41no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—44no—
832D4—48no—
833D4—48no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—84no—
841D4—84no—
842D4—84no—
843D4C31×#12114yes—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—48no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—84no—
880C2×C4C31×#12012yes—
881C2×C4C22×D4×C3111yescharacteristic
882C2×C4C22×D4×C3111yescharacteristic
883C2×C4C22×D4×C3111yescharacteristic
884C2×C4C2×#41×C3111yescharacteristic
885C2×C4C31×H(5,𝔽2)11yescharacteristic
886C2×C4C31×H(5,𝔽2)11yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—22no—
892C22—24no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—41no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—816no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×C31×#12011yescharacteristic
928C22D42×C3111yescharacteristic
929C22C31×#54611yescharacteristic
930C22C2×C31×#13511yescharacteristic
931C22C31×#57511yescharacteristic
932C22C31×#57611yescharacteristic
933C22C31×#57611yescharacteristic
934C4—22no—
935C4—41no—
936C4—42no—
937C4—41no—
938C4—41no—
939C4—42no—
940C4—42no—
941C4—81no—
942C4—81no—
943C4C2×C31×#12111yescharacteristic
944C4C31×#53411yescharacteristic
945C4D42×C3111yescharacteristic
946C4C31×#54611yescharacteristic
947C2—42no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—161no—
952C2C31×#241011yescharacteristic
953C2C31×#300211yescharacteristic
954C2C31×#300811yescharacteristic
955C2C31×#326811yescharacteristic
956C2C31×#328011yescharacteristic
957C2C31×#329711yescharacteristic
958C2C31×#331911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
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×#546C2semidirect
2. C2×C31×#466C2semidirect
3. C2×C31×#449C2semidirect
4. C2×C31×#447C2semidirect
5. C2×C31×#416C2semidirect
6. C31×#2414C2semidirect
7. C31×#2042C2semidirect
8. C31×#2036C2semidirect
9. C31×#2012C2semidirect
10. C31×#2000C2semidirect
11. C31×#1879C2semidirect
12. C31×#1875C2semidirect
13. C31×#1869C2semidirect
14. C31×#1862C2semidirect
15. C31×#1786C2semidirect
18. C22×SD16×C31C22semidirect
21. C23×C8×C31C22semidirect
30. C2×C31×#121C22semidirect
34. C2×C31×#117C22semidirect
39. C2×C31×#107C22semidirect
41. C2×C31×#103C22semidirect
42. C2×C31×#103C22semidirect
43. C2×C31×#103C22semidirect
50. C2×C31×#102C22semidirect
53. C2×C31×C22⋊C8C22semidirect
57. C31×#390C22semidirect
58. C31×#389C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#336C22semidirect
64. C31×#336C22semidirect
71. C2×#41×C31D4semidirect
119. C31×#121D4semidirect
160. C31×#102D4semidirect
299. #24428C31direct (N × H)
412. C2×#546C2×C31semidirect
413. C2×#466C2×C31semidirect
414. C2×#449C2×C31semidirect
415. C2×#447C2×C31semidirect
416. C2×#416C2×C31semidirect
417. #2414C2×C31semidirect
418. #2042C2×C31semidirect
419. #2036C2×C31semidirect
420. #2012C2×C31semidirect
421. #2000C2×C31semidirect
422. #1879C2×C31semidirect
423. #1875C2×C31semidirect
424. #1869C2×C31semidirect
425. #1862C2×C31semidirect
426. #1786C2×C31semidirect
485. C22×SD16C22×C31semidirect
488. C23×C8C22×C31semidirect
497. C2×#121C22×C31semidirect
501. C2×#117C22×C31semidirect
506. C2×#107C22×C31semidirect
508. C2×#103C22×C31semidirect
509. C2×#103C22×C31semidirect
510. C2×#103C22×C31semidirect
517. C2×#102C22×C31semidirect
520. C2×C22⋊C8C22×C31semidirect
524. #390C22×C31semidirect
525. #389C22×C31semidirect
528. #340C22×C31semidirect
529. #340C22×C31semidirect
530. #336C22×C31semidirect
531. #336C22×C31semidirect
550. C2×#41D4×C31semidirect
598. #121D4×C31semidirect
639. #102D4×C31semidirect
645. C31#24428direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5462
C2×C31×#4662
C2×C31×#4492
C2×C31×#4472
C2×C31×#4162
C31×#24142
C31×#20422
C31×#20362
C31×#20122
C31×#20002
C31×#18792
C31×#18752
C31×#18692
C31×#18622
C31×#17862
#2442831