Finite Group Databasebeta

← C31×#24455 #21481214

Subgroups — C31×#24455 #21481214

Order 7936.

1480 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#548C211yesmaximal, characteristic, complemented
2C2×C31×#469C211yesmaximal, characteristic, complemented
3C2×C31×#449C211yesmaximal, characteristic, complemented
4C2×C31×#448C211yesmaximal, characteristic, complemented
5C2×C31×#419C211yesmaximal, characteristic, complemented
6C31×#2414C211yesmaximal, characteristic, complemented
7C31×#2042C211yesmaximal, characteristic, complemented
8C31×#2035C211yesmaximal, characteristic, complemented
9C31×#2012C211yesmaximal, characteristic, complemented
10C31×#2000C211yesmaximal, characteristic, complemented
11C31×#1880C211yesmaximal, characteristic, complemented
12C31×#1875C211yesmaximal, characteristic, complemented
13C31×#1870C211yesmaximal, characteristic, complemented
14C31×#1865C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×Q8×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×D8×C31C2211yescharacteristic
21C22×M16×C31C2211yescharacteristic
22C31×#548—24no—
23C31×#548—24no—
24C2×C31×#124—21no—
25C2×C31×#124C2211yescharacteristic
26C2×C31×C22⋊Q8—21no—
27C2×C31×C22⋊Q8C2211yescharacteristic
28C2×C31×#121—21no—
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C31×#121C2211yescharacteristic
32C2×C4×Q8×C31C2211yescharacteristic
33C2×C4×D4×C31—21no—
34C2×C4×D4×C31C2211yescharacteristic
35C2×C31×#117C2211yescharacteristic
36C31×#469—24no—
37C31×#449—24no—
38C31×#448—24no—
39C2×C31×#106C2211yescharacteristic
40C31×#419—24no—
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#103C2211yescharacteristic
44C2×C31×#103C2211yescharacteristic
45C2×C31×#103C2211yescharacteristic
46C2×C31×#103C2211yescharacteristic
47C2×C31×#102C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C2×C31×#102C2211yescharacteristic
50C2×C31×#102C2211yescharacteristic
51C2×C31×C22⋊C8C2211yescharacteristic
52C2×C31×C22⋊C8C2211yescharacteristic
53C2×C31×C22⋊C8C2211yescharacteristic
54C31×#394—21no—
55C31×#392—21no—
56C31×#390—21no—
57C31×#390C2211yescharacteristic
58C31×#389C2211yescharacteristic
59C31×#388—21no—
60C31×#380C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C31×#336C2211yescharacteristic
64C31×#336C2211yescharacteristic
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—41no—
70C2×#41×C31—41no—
71C22×Q8×C31—21no—
72C22×Q8×C31—22no—
73C22×Q8×C31—22no—
74C22×Q8×C31—22no—
75C22×Q8×C31—41no—
76C22×Q8×C31—41no—
77C22×Q8×C31D414yescomplemented
78C22×Q8×C31C2311yescharacteristic
79C22×Q8×C31C2311yescharacteristic
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31—21no—
83C22×D4×C31—21no—
84C22×D4×C31D411yescharacteristic
85C22×D4×C31C2311yescharacteristic
86C22×D4×C31C2311yescharacteristic
87C23×C4×C31—21no—
88C23×C4×C31—21no—
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C2×SD16×C31—22no—
92C2×SD16×C31—22no—
93C2×SD16×C31—22no—
94C2×SD16×C31—22no—
95C2×SD16×C31—41no—
96C2×SD16×C31—41no—
97C2×D8×C31—22no—
98C2×D8×C31—22no—
99C2×D8×C31—41no—
100C2×M16×C31—22no—
101C2×M16×C31—22no—
102C2×M16×C31—41no—
103C22×C8×C31C2311yescharacteristic
104C22×C8×C31C2311yescharacteristic
105C22×C8×C31C2311yescharacteristic
106C22×C8×C31C2311yescharacteristic
107C31×#124—28no—
108C31×#124—22no—
109C31×#124—22no—
110C31×C22⋊Q8—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
120C4×Q8×C31—22no—
121C4×Q8×C31—22no—
122C4×D4×C31—28no—
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×C31—21no—
130C2×C4⋊C4×C31D411yescharacteristic
131C2×C4⋊C4×C31C2311yescharacteristic
132C2×C4⋊C4×C31C2311yescharacteristic
133C2×C4⋊C4×C31C2311yescharacteristic
134C2×C4⋊C4×C31C2311yescharacteristic
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×C31D411yescharacteristic
146C2×C22⋊C4×C31D411yescharacteristic
147C2×C42×C31—21no—
148C2×C42×C31—21no—
149C2×C42×C31C2311yescharacteristic
150C31×#106—22no—
151C31×#103—22no—
152C31×#103—22no—
153C31×#103—22no—
154C31×#103—22no—
155C31×#103—22no—
156C31×#103D414yescomplemented
157C31×#102—22no—
158C31×#102—22no—
159C31×#102—22no—
160C31×#102—41no—
161C31×C22⋊C8—22no—
162C31×C22⋊C8—22no—
163C31×C22⋊C8—41no—
164C31×#95—21no—
165C31×#95—21no—
166C24×C31—21no—
167C24×C31—21no—
168C24×C31C2×D411yescharacteristic
169C24×C31C2×D411yescharacteristic
170#41×C31—44no—
171#41×C31—44no—
172#41×C31—44no—
173#41×C31—44no—
174C2×Q8×C31—24no—
175C2×Q8×C31—21no—
176C2×Q8×C31—21no—
177C2×Q8×C31—21no—
178C2×Q8×C31—21no—
179C2×Q8×C31—28no—
180C2×Q8×C31—21no—
181C2×Q8×C31—21no—
182C2×Q8×C31—21no—
183C2×Q8×C31—21no—
184C2×Q8×C31—42no—
185C2×Q8×C31—42no—
186C2×Q8×C31—44no—
187C2×Q8×C31—44no—
188C2×Q8×C31—44no—
189C2×Q8×C31C2×D412yes—
190C2×Q8×C31C2×D412yes—
191C2×Q8×C31C2×D412yes—
192C2×Q8×C31#4112yes—
193C2×D4×C31—24no—
194C2×D4×C31—22no—
195C2×D4×C31—24no—
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—41no—
209C2×D4×C31—42no—
210C2×D4×C31—42no—
211C2×D4×C31—42no—
212C2×D4×C31—42no—
213C2×D4×C31—42no—
214C2×D4×C31—42no—
215C2×D4×C31—42no—
216C2×D4×C31—81no—
217C2×D4×C31—81no—
218C2×D4×C31—81no—
219C2×D4×C31C2×D412yes—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—24no—
226C22×C4×C31—24no—
227C22×C4×C31—21no—
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—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—42no—
239C22×C4×C31—42no—
240C22×C4×C31—42no—
241C22×C4×C31—42no—
242C22×C4×C31C2×D411yescharacteristic
243C22×C4×C31C2×D411yescharacteristic
244C22×C4×C31C2×D411yescharacteristic
245C22×C4×C31C2×D411yescharacteristic
246C22×C4×C31C2×D412yes—
247C22×C4×C31C2×D412yes—
248C22×C4×C31C2411yescharacteristic
249SD16×C31—44no—
250SD16×C31—44no—
251D8×C31—44no—
252M16×C31—44no—
253C2×C8×C31—21no—
254C2×C8×C31—21no—
255C2×C8×C31—21no—
256C2×C8×C31—21no—
257C2×C8×C31—21no—
258C2×C8×C31—21no—
259C2×C8×C31—21no—
260C2×C8×C31—21no—
261C2×C8×C31—21no—
262C2×C8×C31—21no—
263C2×C8×C31—21no—
264C2×C8×C31C2×D412yes—
265C4⋊C4×C31—24no—
266C4⋊C4×C31—24no—
267C4⋊C4×C31—22no—
268C4⋊C4×C31—21no—
269C4⋊C4×C31—21no—
270C4⋊C4×C31—21no—
271C4⋊C4×C31—21no—
272C4⋊C4×C31—21no—
273C4⋊C4×C31—21no—
274C4⋊C4×C31—81no—
275C4⋊C4×C31C2×D412yes—
276C4⋊C4×C31C2×D412yes—
277C22⋊C4×C31—24no—
278C22⋊C4×C31—24no—
279C22⋊C4×C31—24no—
280C22⋊C4×C31—22no—
281C22⋊C4×C31—24no—
282C22⋊C4×C31—22no—
283C22⋊C4×C31—42no—
284C22⋊C4×C31—42no—
285C22⋊C4×C31—42no—
286C22⋊C4×C31—42no—
287C22⋊C4×C31—81no—
288C22⋊C4×C31—81no—
289C42×C31—24no—
290C42×C31—21no—
291C42×C31—21no—
292C42×C31—42no—
293#24455C3111yesmaximal, characteristic, direct product factor, Sylow
294C23×C31—21no—
295C23×C31—21no—
296C23×C31—21no—
297C23×C31—21no—
298C23×C31—21no—
299C23×C31—21no—
300C23×C31—21no—
301C23×C31—22no—
302C23×C31—21no—
303C23×C31—21no—
304C23×C31—21no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—21no—
308C23×C31—41no—
309C23×C31—41no—
310C23×C31—41no—
311C23×C31—41no—
312C23×C31—41no—
313C23×C31—41no—
314C23×C31—41no—
315C23×C31—41no—
316C23×C31—41no—
317C23×C31—41no—
318C23×C31—41no—
319C23×C31—41no—
320C23×C31—41no—
321C23×C31#12012yes—
322C23×C31C22×D411yescharacteristic
323Q8×C31—22no—
324Q8×C31—22no—
325Q8×C31—22no—
326Q8×C31—22no—
327Q8×C31—22no—
328Q8×C31—48no—
329Q8×C31—41no—
330Q8×C31—41no—
331Q8×C31#12114yes—
332D4×C31—22no—
333D4×C31—22no—
334D4×C31—48no—
335D4×C31—44no—
336D4×C31—48no—
337D4×C31—41no—
338D4×C31—41no—
339D4×C31—41no—
340D4×C31—41no—
341D4×C31—41no—
342D4×C31—41no—
343D4×C31—84no—
344D4×C31—84no—
345C2×C4×C31—22no—
346C2×C4×C31—21no—
347C2×C4×C31—22no—
348C2×C4×C31—21no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—21no—
355C2×C4×C31—21no—
356C2×C4×C31—22no—
357C2×C4×C31—22no—
358C2×C4×C31—21no—
359C2×C4×C31—22no—
360C2×C4×C31—21no—
361C2×C4×C31—21no—
362C2×C4×C31—21no—
363C2×C4×C31—21no—
364C2×C4×C31—21no—
365C2×C4×C31—21no—
366C2×C4×C31—48no—
367C2×C4×C31—48no—
368C2×C4×C31—41no—
369C2×C4×C31—41no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—41no—
374C2×C4×C31—41no—
375C2×C4×C31—41no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—41no—
379C2×C4×C31—41no—
380C2×C4×C31—41no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31#12012yes—
385C2×C4×C31C22×D411yescharacteristic
386C2×C4×C31C22×D411yescharacteristic
387C2×C4×C31C22×D411yescharacteristic
388C2×C4×C31C2×#4111yescharacteristic
389C2×C4×C31H(5,𝔽2)11yescharacteristic
390C2×C4×C31H(5,𝔽2)11yescharacteristic
391C8×C31—22no—
392C8×C31—41no—
393C8×C31—41no—
394C8×C31—41no—
395C2×#548C2×C3111yescharacteristic, complemented
396C2×#469C2×C3111yescharacteristic, complemented
397C2×#449C2×C3111yescharacteristic, complemented
398C2×#448C2×C3111yescharacteristic, complemented
399C2×#419C2×C3111yescharacteristic, complemented
400#2414C2×C3111yescharacteristic, complemented
401#2042C2×C3111yescharacteristic, complemented
402#2035C2×C3111yescharacteristic, complemented
403#2012C2×C3111yescharacteristic, complemented
404#2000C2×C3111yescharacteristic, complemented
405#1880C2×C3111yescharacteristic, complemented
406#1875C2×C3111yescharacteristic, complemented
407#1870C2×C3111yescharacteristic, complemented
408#1865C2×C3111yescharacteristic, complemented
409#1788C2×C3111yescharacteristic, complemented
410C22×C31—22no—
411C22×C31—22no—
412C22×C31—22no—
413C22×C31—41no—
414C22×C31—41no—
415C22×C31—41no—
416C22×C31—41no—
417C22×C31—42no—
418C22×C31—41no—
419C22×C31—41no—
420C22×C31—42no—
421C22×C31—41no—
422C22×C31—42no—
423C22×C31—41no—
424C22×C31—41no—
425C22×C31—41no—
426C22×C31—41no—
427C22×C31—81no—
428C22×C31—81no—
429C22×C31—81no—
430C22×C31—81no—
431C22×C31—81no—
432C22×C31—81no—
433C22×C31—81no—
434C22×C31—81no—
435C22×C31—81no—
436C22×C31—81no—
437C22×C31—81no—
438C22×C31C2×#12011yescharacteristic
439C22×C31D4211yescharacteristic
440C22×C31#54611yescharacteristic
441C22×C31#57511yescharacteristic
442C22×C31#57511yescharacteristic
443C22×C31#57711yescharacteristic
444C22×C31#57711yescharacteristic
445C4×C31—22no—
446C4×C31—24no—
447C4×C31—41no—
448C4×C31—42no—
449C4×C31—41no—
450C4×C31—42no—
451C4×C31—41no—
452C4×C31—42no—
453C4×C31—81no—
454C4×C31—81no—
455C4×C31C2×#12111yescharacteristic
456C4×C31#53411yescharacteristic
457C4×C31D4211yescharacteristic
458C4×C31#54611yescharacteristic
459C22×#41C22×C3111yescharacteristic
460C23×Q8C22×C3111yescharacteristic
461C22×SD16C22×C3111yescharacteristic
462C22×SD16C22×C3111yescharacteristic
463C22×D8C22×C3111yescharacteristic
464C22×M16C22×C3111yescharacteristic
465#548—24no—
466#548—24no—
467C2×#124—21no—
468C2×#124C22×C3111yescharacteristic
469C2×C22⋊Q8—21no—
470C2×C22⋊Q8C22×C3111yescharacteristic
471C2×#121—21no—
472C2×#121C22×C3111yescharacteristic
473C2×#121C22×C3111yescharacteristic
474C2×#121C22×C3111yescharacteristic
475C2×C4×Q8C22×C3111yescharacteristic
476C2×C4×D4—21no—
477C2×C4×D4C22×C3111yescharacteristic
478C2×#117C22×C3111yescharacteristic
479#469—24no—
480#449—24no—
481#448—24no—
482C2×#106C22×C3111yescharacteristic
483#419—24no—
484C2×#103C22×C3111yescharacteristic
485C2×#103C22×C3111yescharacteristic
486C2×#103C22×C3111yescharacteristic
487C2×#103C22×C3111yescharacteristic
488C2×#103C22×C3111yescharacteristic
489C2×#103C22×C3111yescharacteristic
490C2×#102C22×C3111yescharacteristic
491C2×#102C22×C3111yescharacteristic
492C2×#102C22×C3111yescharacteristic
493C2×#102C22×C3111yescharacteristic
494C2×C22⋊C8C22×C3111yescharacteristic
495C2×C22⋊C8C22×C3111yescharacteristic
496C2×C22⋊C8C22×C3111yescharacteristic
497#394—21no—
498#392—21no—
499#390—21no—
500#390C22×C3111yescharacteristic
501#389C22×C3111yescharacteristic
502#388—21no—
503#380C22×C3111yescharacteristic
504#340C22×C3111yescharacteristic
505#340C22×C3111yescharacteristic
506#336C22×C3111yescharacteristic
507#336C22×C3111yescharacteristic
508C2×C31—42no—
509C2×C31—81no—
510C2×C31—82no—
511C2×C31—161no—
512C2×C31#241011yescharacteristic
513C2×C31#300511yescharacteristic
514C2×C31#301011yescharacteristic
515C2×C31#327111yescharacteristic
516C2×C31#327511yescharacteristic
517C2×C31#332111yescharacteristic
518C2×C31#332611yescharacteristic
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—41no—
524C2×#41—41no—
525C22×Q8—21no—
526C22×Q8—22no—
527C22×Q8—22no—
528C22×Q8—22no—
529C22×Q8—41no—
530C22×Q8—41no—
531C22×Q8D4×C3114yescomplemented
532C22×Q8C23×C3111yescharacteristic
533C22×Q8C23×C3111yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4D4×C3111yescharacteristic
539C22×D4C23×C3111yescharacteristic
540C22×D4C23×C3111yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4C23×C3111yescharacteristic
544C23×C4C23×C3111yescharacteristic
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—41no—
554C2×M16—22no—
555C2×M16—22no—
556C2×M16—41no—
557C22×C8C23×C3111yescharacteristic
558C22×C8C23×C3111yescharacteristic
559C22×C8C23×C3111yescharacteristic
560C22×C8C23×C3111yescharacteristic
561#124—28no—
562#124—22no—
563#124—22no—
564C22⋊Q8—28no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567#121—28no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—41no—
573#121D4×C3114yescomplemented
574C4×Q8—22no—
575C4×Q8—22no—
576C4×D4—28no—
577C4×D4—22no—
578C4×D4—22no—
579#117—22no—
580#117—41no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4D4×C3111yescharacteristic
585C2×C4⋊C4C23×C3111yescharacteristic
586C2×C4⋊C4C23×C3111yescharacteristic
587C2×C4⋊C4C23×C3111yescharacteristic
588C2×C4⋊C4C23×C3111yescharacteristic
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4D4×C3111yescharacteristic
600C2×C22⋊C4D4×C3111yescharacteristic
601C2×C42—21no—
602C2×C42—21no—
603C2×C42C23×C3111yescharacteristic
604#106—22no—
605#103—22no—
606#103—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103D4×C3114yescomplemented
611#102—22no—
612#102—22no—
613#102—22no—
614#102—41no—
615C22⋊C8—22no—
616C22⋊C8—22no—
617C22⋊C8—41no—
618#95—21no—
619#95—21no—
620C31#2445511yescharacteristic, direct product factor, Sylow
621C24—21no—
622C24—21no—
623C24C2×D4×C3111yescharacteristic
624C24C2×D4×C3111yescharacteristic
625#41—44no—
626#41—44no—
627#41—44no—
628#41—44no—
629C2×Q8—24no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—28no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—42no—
640C2×Q8—42no—
641C2×Q8—44no—
642C2×Q8—44no—
643C2×Q8—44no—
644C2×Q8C2×D4×C3112yes—
645C2×Q8C2×D4×C3112yes—
646C2×Q8C2×D4×C3112yes—
647C2×Q8#41×C3112yes—
648C2×D4—24no—
649C2×D4—22no—
650C2×D4—24no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—41no—
663C2×D4—41no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4—81no—
674C2×D4C2×D4×C3112yes—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4C2×D4×C3111yescharacteristic
698C22×C4C2×D4×C3111yescharacteristic
699C22×C4C2×D4×C3111yescharacteristic
700C22×C4C2×D4×C3111yescharacteristic
701C22×C4C2×D4×C3112yes—
702C22×C4C2×D4×C3112yes—
703C22×C4C24×C3111yescharacteristic
704SD16—44no—
705SD16—44no—
706D8—44no—
707M16—44no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8C2×D4×C3112yes—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—22no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—81no—
730C4⋊C4C2×D4×C3112yes—
731C4⋊C4C2×D4×C3112yes—
732C22⋊C4—24no—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—22no—
736C22⋊C4—24no—
737C22⋊C4—22no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—81no—
743C22⋊C4—81no—
744C42—24no—
745C42—21no—
746C42—21no—
747C42—42no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23C31×#12012yes—
776C23C22×D4×C3111yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—22no—
782Q8—48no—
783Q8—41no—
784Q8—41no—
785Q8C31×#12114yes—
786D4—22no—
787D4—22no—
788D4—48no—
789D4—44no—
790D4—48no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—84no—
798D4—84no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—48no—
821C2×C4—48no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4C31×#12012yes—
839C2×C4C22×D4×C3111yescharacteristic
840C2×C4C22×D4×C3111yescharacteristic
841C2×C4C22×D4×C3111yescharacteristic
842C2×C4C2×#41×C3111yescharacteristic
843C2×C4C31×H(5,𝔽2)11yescharacteristic
844C2×C4C31×H(5,𝔽2)11yescharacteristic
845C8—22no—
846C8—41no—
847C8—41no—
848C8—41no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—42no—
857C22—41no—
858C22—41no—
859C22—42no—
860C22—41no—
861C22—42no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22C2×C31×#12011yescharacteristic
878C22D42×C3111yescharacteristic
879C22C31×#54611yescharacteristic
880C22C31×#57511yescharacteristic
881C22C31×#57511yescharacteristic
882C22C31×#57711yescharacteristic
883C22C31×#57711yescharacteristic
884C4—22no—
885C4—24no—
886C4—41no—
887C4—42no—
888C4—41no—
889C4—42no—
890C4—41no—
891C4—42no—
892C4—81no—
893C4—81no—
894C4C2×C31×#12111yescharacteristic
895C4C31×#53411yescharacteristic
896C4D42×C3111yescharacteristic
897C4C31×#54611yescharacteristic
898C2—42no—
899C2—81no—
900C2—82no—
901C2—161no—
902C2C31×#241011yescharacteristic
903C2C31×#300511yescharacteristic
904C2C31×#301011yescharacteristic
905C2C31×#327111yescharacteristic
906C2C31×#327511yescharacteristic
907C2C31×#332111yescharacteristic
908C2C31×#332611yescharacteristic
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×#548C2semidirect
2. C2×C31×#469C2semidirect
3. C2×C31×#449C2semidirect
4. C2×C31×#448C2semidirect
5. C2×C31×#419C2semidirect
6. C31×#2414C2semidirect
7. C31×#2042C2semidirect
8. C31×#2035C2semidirect
9. C31×#2012C2semidirect
10. C31×#2000C2semidirect
11. C31×#1880C2semidirect
12. C31×#1875C2semidirect
13. C31×#1870C2semidirect
14. C31×#1865C2semidirect
15. C31×#1788C2semidirect
77. C22×Q8×C31D4semidirect
119. C31×#121D4semidirect
156. C31×#103D4semidirect
293. #24455C31direct (N × H)
395. C2×#548C2×C31semidirect
396. C2×#469C2×C31semidirect
397. C2×#449C2×C31semidirect
398. C2×#448C2×C31semidirect
399. C2×#419C2×C31semidirect
400. #2414C2×C31semidirect
401. #2042C2×C31semidirect
402. #2035C2×C31semidirect
403. #2012C2×C31semidirect
404. #2000C2×C31semidirect
405. #1880C2×C31semidirect
406. #1875C2×C31semidirect
407. #1870C2×C31semidirect
408. #1865C2×C31semidirect
409. #1788C2×C31semidirect
531. C22×Q8D4×C31semidirect
573. #121D4×C31semidirect
610. #103D4×C31semidirect
620. C31#24455direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5482
C2×C31×#4692
C2×C31×#4492
C2×C31×#4482
C2×C31×#4192
C31×#24142
C31×#20422
C31×#20352
C31×#20122
C31×#20002
C31×#18802
C31×#18752
C31×#18702
C31×#18652
C31×#17882
#2445531