Finite Group Databasebeta

← C2×#20253015 #27083433

Subgroups — C2×#20253015 #27083433

Order 12032.

2898 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094056C211yesmaximal, characteristic, complemented
2C23×#10625324C211yesmaximal, characteristic, complemented
3C2×#15689636C211yesmaximal, characteristic
4C2×C22⋊Q8×D47C211yesmaximal, characteristic, complemented
5#20253015C2116yesmaximal, direct product factor
6C2×#15689380C211yesmaximal, characteristic, complemented
7C2×#15689378C211yesmaximal, characteristic, complemented
8C2×#15689372C211yesmaximal, characteristic, complemented
9C2×#15689370C211yesmaximal, characteristic, complemented
10C2×#15689362C211yesmaximal, characteristic, complemented
11C2×#15689354C211yesmaximal, characteristic, complemented
12C2×#15689352C211yesmaximal, characteristic, complemented
13C2×#15689164C211yesmaximal, characteristic, complemented
14C2×#15689123C211yesmaximal, characteristic, complemented
15C2×#15689130C211yesmaximal, characteristic, complemented
16C2×C47×#467C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C2×#13094056—28no—
21C2×#13094056C2218yescomplemented
22C22×#10625337C2211yescharacteristic, complemented
23C22×#10625325C2211yescharacteristic, complemented
24C22×#10625336C2211yescharacteristic, complemented
25C22×#10625324—28no—
26C22×#10625324C2211yescharacteristic
27C22×#10625324C2211yescharacteristic
28C22×#10625324C2211yescharacteristic
29C22×#10625324C2211yescharacteristic
30C22×#10625324C2218yescomplemented
31C23×C47⋊C8C2211yescharacteristic
32#15689636—24no—
33#15689636C2218yes—
34C2×#13094009—21no—
35C2×#13094004C2211yescharacteristic
36C2×#13094003C2211yescharacteristic
37C2×#13094002—21no—
38C2×#13094001—21no—
39C2×#13094000C2211yescharacteristic
40C2×#13094000C2211yescharacteristic
41C22⋊Q8×D47—24no—
42C22⋊Q8×D47C2218yescomplemented
43C2×#13093999C2211yescharacteristic
44C2×#13093998C2211yescharacteristic
45C2×#13093994—21no—
46C2×#13093986—21no—
47C2×(C22⋊D47)⋊C4—21no—
48C2×#13093982C2211yescharacteristic
49C2×C4⋊C4×D47—21no—
50C2×C4⋊C4×D47C2211yescharacteristic
51C2×C22⋊C4×D47—21no—
52#15689380C2218yescomplemented
53#15689378C2218yescomplemented
54#15689372C2218yescomplemented
55#15689370C2218yescomplemented
56#15689362C2218yescomplemented
57#15689354C2218yescomplemented
58#15689352C2218yescomplemented
59#15689164C2218yescomplemented
60C2×#13093957C2211yescharacteristic, complemented
61C2×#13093956C2211yescharacteristic, complemented
62C2×#13093955C2211yescharacteristic, complemented
63#15689130C2218yescomplemented
64#15689123C2218yescomplemented
65C2×#13093949C2211yescharacteristic, complemented
66C2×#13093948C2211yescharacteristic, complemented
67C2×#13093948C2211yescharacteristic, complemented
68C2×#13093947C2211yescharacteristic, complemented
69C2×#13093946C2211yescharacteristic, complemented
70C2×#13093944C2211yescharacteristic, complemented
71C22×Q16×C47C2211yescharacteristic, complemented
72C23×C8×C47C2211yescharacteristic
73C2×C22⋊Q8×C47C2211yescharacteristic
74C2×C22⋊Q8×C47C2211yescharacteristic
75C47×#467C2218yescomplemented
76C2×#107×C47C2211yescharacteristic, complemented
77C2×#103×C47C2211yescharacteristic, complemented
78C2×#103×C47C2211yescharacteristic, complemented
79C24×D47D411yescharacteristic
80C2×#10625354—22no—
81C2×#10625354—24no—
82C2×#10625354—24no—
83C2×#10625354C2314yes—
84C22×Dic94—21no—
85C22×Dic94C2311yescharacteristic
86C2×Q8×D47—22no—
87C2×Q8×D47—24no—
88C2×Q8×D47—24no—
89C2×Q8×D47C2314yes—
90C22×D188—21no—
91C22×D188—21no—
92C22×D188C2311yescharacteristic
93C22×C22⋊D47—21no—
94C23×Dic47D411yescharacteristic
95C22×C4×D47—24no—
96C22×C4×D47—24no—
97C22×C4×D47—21no—
98C22×C4×D47—21no—
99C22×C4×D47—21no—
100C22×C4×D47D411yescharacteristic
101C22×C4×D47D411yescharacteristic
102C22×C4×D47D414yes—
103C22×C4×D47C2311yescharacteristic
104C22×C4×D47C2314yes—
105C22×C4×D47C2311yescharacteristic
106#13094056—232no—
107C2×#10625337—24no—
108C2×#10625337C2314yescomplemented
109C2×#10625325—24no—
110C2×#10625325C2314yescomplemented
111C2×#10625336—24no—
112C2×#10625336C2314yescomplemented
113C2×#10625324—24no—
114C2×#10625324—24no—
115C2×#10625324—24no—
116C2×#10625324—232no—
117C2×#10625324D418yescomplemented
118C2×#10625324C2314yes—
119C2×#10625324C2314yes—
120C2×#10625324C2314yes—
121C2×#10625324C2314yes—
122C22×C47⋊C8—24no—
123C22×C47⋊C8C2314yes—
124C22×C47⋊C8C2311yescharacteristic
125C22×C47⋊C8C2311yescharacteristic
126#13094009—28no—
127#13094004—22no—
128#13094004C2314yes—
129#13094003—22no—
130#13094003C2314yes—
131#13094002—28no—
132#13094001—28no—
133#13094000—22no—
134#13094000—22no—
135#13094000C2314yes—
136#13094000C2314yes—
137#13093999—22no—
138#13093999C2314yes—
139#13093998—22no—
140#13093998C2314yes—
141#13093994—28no—
142#13093986—28no—
143(C22⋊D47)⋊C4—28no—
144#13093982—22no—
145#13093982C2314yes—
146C2×C4⋊Dic47—21no—
147C2×C4⋊Dic47C2311yescharacteristic
148C2×C4⋊Dic47C2311yescharacteristic
149C2×Dic47⋊C4—21no—
150C2×Dic47⋊C4—21no—
151C2×Dic47⋊C4—21no—
152C2×Dic47⋊C4—21no—
153C4⋊C4×D47—28no—
154C4⋊C4×D47—22no—
155C4⋊C4×D47C2314yes—
156C2×C22⋊Dic47—21no—
157C2×(C2×D47)⋊C4—21no—
158C2×(C2×D47)⋊C4—21no—
159C2×(C2×D47)⋊C4—21no—
160C2×(C2×D47)⋊C4—21no—
161C2×(C2×D47)⋊C4—21no—
162C2×(C2×D47)⋊C4—21no—
163C22⋊C4×D47—28no—
164C2×C4×Dic47—21no—
165#13093957C2314yescomplemented
166#13093956C2314yescomplemented
167#13093955C2314yescomplemented
168#13093949C2314yescomplemented
169#13093948C2314yescomplemented
170#13093948C2314yescomplemented
171#13093947C2314yescomplemented
172#13093946C2314yescomplemented
173#13093944C2314yescomplemented
174C22×Q8×C47C2311yescharacteristic
175C22×Q8×C47C2311yescharacteristic
176C23×C4×C47C2311yescharacteristic
177C2×Q16×C47—24no—
178C2×Q16×C47C2314yescomplemented
179C22×C8×C47—24no—
180C22×C8×C47C2314yes—
181C22×C8×C47C2311yescharacteristic
182C22×C8×C47C2311yescharacteristic
183C22⋊Q8×C47—22no—
184C22⋊Q8×C47—22no—
185C22⋊Q8×C47C2314yes—
186C22⋊Q8×C47C2314yes—
187C2×C4⋊C4×C47—21no—
188C2×C4⋊C4×C47—21no—
189C2×C4⋊C4×C47C2311yescharacteristic
190C2×C4⋊C4×C47C2311yescharacteristic
191C2×C22⋊C4×C47—21no—
192C2×C22⋊C4×C47—21no—
193#107×C47C2314yescomplemented
194#103×C47C2314yescomplemented
195#103×C47C2314yescomplemented
196C24×C47C2×D411yescharacteristic
197C23×D47—24no—
198C23×D47—24no—
199C23×D47—21no—
200C23×D47—42no—
201C23×D47C2×D411yescharacteristic
202C23×D47C2×D414yes—
203C23×D47C2×D411yescharacteristic
204C2×Q8×C47—21no—
205C2×Q8×C47—21no—
206C2×Q8×C47—22no—
207C2×Q8×C47—22no—
208C2×Q8×C47—22no—
209C2×Q8×C47—22no—
210C2×Q8×C47C2412yes—
211C2×Q8×C47C2412yes—
212C22×C4×C47—22no—
213C22×C4×C47—22no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D412yes—
220C22×C4×C47C2412yes—
221C22×C4×C47C2411yescharacteristic
222C2×C22⋊D47—24no—
223C2×C22⋊D47—44no—
224C22×Dic47—24no—
225C22×Dic47—21no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47C2×D411yescharacteristic
229C22×Dic47C2×D414yes—
230C22×Dic47C2×D411yescharacteristic
231#10625354—28no—
232#10625354—28no—
233#10625354—48no—
234Q8×D47—28no—
235Q8×D47—28no—
236Q8×D47—48no—
237C2×D188—22no—
238C2×D188—22no—
239C2×D188—24no—
240C2×D188—24no—
241C2×D188—21no—
242C2×D188—44no—
243C2×D188—44no—
244C2×D188C2412yes—
245C2×C4×D47—24no—
246C2×C4×D47—22no—
247C2×C4×D47—22no—
248C2×C4×D47—24no—
249C2×C4×D47—216no—
250C2×C4×D47—28no—
251C2×C4×D47—28no—
252C2×C4×D47—24no—
253C2×C4×D47—24no—
254C2×C4×D47—24no—
255C2×C4×D47—44no—
256C2×C4×D47—44no—
257C2×C4×D47—44no—
258C2×C4×D47C2×D414yes—
259C2×C4×D47C2×D414yes—
260C2×C4×D47C2×D412yes—
261C2×C4×D47C2×D412yes—
262C2×C4×D47C2×D414yes—
263C2×C4×D47#4114yes—
264C2×C4×D47C2412yes—
265C2×C4×D47C2412yes—
266C2×Dic94—22no—
267C2×Dic94—22no—
268C2×Dic94—21no—
269C2×Dic94—24no—
270C2×Dic94—44no—
271C2×Dic94C2412yes—
272Q16×C47—28no—
273C2×C8×C47—22no—
274C2×C8×C47—28no—
275C2×C8×C47C2×D414yes—
276C2×C8×C47C2412yes—
277C2×C8×C47C2412yes—
278C4⋊C4×C47—24no—
279C4⋊C4×C47—24no—
280C4⋊C4×C47—21no—
281C4⋊C4×C47—21no—
282C4⋊C4×C47C2412yes—
283C4⋊C4×C47C2412yes—
284C22⋊C4×C47—24no—
285C22⋊C4×C47—24no—
286C22⋊Dic47—24no—
287#10625337—28no—
288#10625336—28no—
289(C2×D47)⋊C4—24no—
290(C2×D47)⋊C4—24no—
291(C2×D47)⋊C4—24no—
292(C2×D47)⋊C4—24no—
293(C2×D47)⋊C4—24no—
294(C2×D47)⋊C4—24no—
295C4⋊Dic47—21no—
296C4⋊Dic47—21no—
297C4⋊Dic47—24no—
298C4⋊Dic47C2412yes—
299C4⋊Dic47C2412yes—
300Dic47⋊C4—24no—
301Dic47⋊C4—24no—
302Dic47⋊C4—24no—
303Dic47⋊C4—24no—
304C4×Dic47—24no—
305C2×C47⋊C8—22no—
306C2×C47⋊C8—28no—
307C2×C47⋊C8C2×D414yes—
308C2×C47⋊C8C2412yes—
309C2×C47⋊C8C2412yes—
310#10625325—28no—
311#10625324—28no—
312#10625324—28no—
313#10625324—28no—
314#10625324C2×D4116yescomplemented
315C23×C47—22no—
316C23×C47—22no—
317C23×C47#13714yescomplemented
318C23×C47C22×D412yes—
319C23×C47C22×D411yescharacteristic
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—28no—
325C22×D47—22no—
326C22×D47—28no—
327C22×D47—22no—
328C22×D47—44no—
329C22×D47—416no—
330C22×D47—42no—
331C22×D47—42no—
332C22×D47—42no—
333C22×D47#12114yes—
334C22×D47C22×D412yes—
335C22×D47C22×D412yes—
336Q8×C47—22no—
337Q8×C47—22no—
338Q8×C47—22no—
339Q8×C47—22no—
340Q8×C47—42no—
341Q8×C47—42no—
342C2×C4×C47—22no—
343C2×C4×C47—24no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—42no—
351C2×C4×C47—42no—
352C2×C4×C47—42no—
353C2×C4×C47—42no—
354C2×C4×C47C22×D412yes—
355C2×C4×C47C22×D411yescharacteristic
356C2×C4×C47C22×D412yes—
357C2×C4×C47C2×#4112yes—
358C2×C4×C47C2511yescharacteristic
359C22⋊D47—48no—
360C2×Dic47—22no—
361C2×Dic47—28no—
362C2×Dic47—22no—
363C2×Dic47—22no—
364C2×Dic47—22no—
365C2×Dic47—42no—
366C2×Dic47—42no—
367C2×Dic47—42no—
368C2×Dic47#12114yes—
369C2×Dic47C22×D412yes—
370C2×Dic47C22×D412yes—
371D188—22no—
372D188—22no—
373D188—48no—
374D188—48no—
375D188—42no—
376C4×D47—28no—
377C4×D47—24no—
378C4×D47—22no—
379C4×D47—22no—
380C4×D47—28no—
381C4×D47—48no—
382C4×D47—48no—
383C4×D47—48no—
384C4×D47#12118yes—
385C4×D47C22×D414yes—
386C4×D47C2×#4114yes—
387Dic94—22no—
388Dic94—22no—
389Dic94—42no—
390Dic94—48no—
391C8×C47—22no—
392C8×C47C22×D414yes—
393C47⋊C8—22no—
394C47⋊C8C22×D414yes—
395C2×#3056—471nomaximal, Sylow
396C22×C47—22no—
397C22×C47—28no—
398C22×C47—22no—
399C22×C47C2×#12112yes—
400C22×C47C2×#13712yes—
401C22×C47C2×#13714yescomplemented
402C22×C47#57512yes—
403C22×C47C23×D411yescharacteristic
404C2×D47—28no—
405C2×D47—22no—
406C2×D47—22no—
407C2×D47—22no—
408C2×D47—22no—
409C2×D47—22no—
410C2×D47—416no—
411C2×D47—44no—
412C2×D47—42no—
413C2×D47—42no—
414C2×D47—42no—
415C2×D47—84no—
416C2×D47C2×#12114yes—
417C4×C47—22no—
418C4×C47—42no—
419C4×C47—42no—
420C4×C47—42no—
421C4×C47—42no—
422C4×C47C2×#12112yes—
423C4×C47C23×D411yescharacteristic
424C4×C47C22×#4111yescharacteristic
425Dic47—22no—
426Dic47—42no—
427Dic47—42no—
428Dic47—42no—
429Dic47C2×#12114yes—
430C22×#137—471no—
431C23×M16—471no—
432C2×#525—471no—
433C22×C22⋊Q8—471no—
434#3056—4716no—
435C2×#470—471no—
436C2×#470—471no—
437C2×#468—471no—
438C2×#468—471no—
439C2×#467—471no—
440C2×#467D4711yescharacteristic, complemented
441C2×#465—471no—
442C2×#465—471no—
443C2×#428—471no—
444C2×#417—471no—
445C2×#419—471no—
446C2×C47—24no—
447C2×C47#305614yescomplemented
448C2×C47C22×#12111yescharacteristic
449C2×C47C22×#13711yescharacteristic
450C2×C47C2×#57511yescharacteristic
451D47—24no—
452D47—42no—
453D47—82no—
454C22×#41—471no—
455C23×Q8—471no—
456C24×C4—471no—
457C2×#137—478no—
458C2×#137—948no—
459C22×Q16—471no—
460C22×Q16C2×D4711yescharacteristic, complemented
461C22×SD16—471no—
462C22×SD16—471no—
463C22×M16—471no—
464C22×M16—471no—
465C22×M16—471no—
466C22×M16—471no—
467C22×M16—478no—
468C22×M16—948no—
469C23×C8—471no—
470C23×C8C2×D4711yescharacteristic
471#525—478no—
472#525—944no—
473C2×#123—941no—
474C2×C22⋊Q8—471no—
475C2×C22⋊Q8—471no—
476C2×C22⋊Q8—471no—
477C2×C22⋊Q8—478no—
478C2×C22⋊Q8—471no—
479C2×C22⋊Q8—941no—
480C2×C22⋊Q8—941no—
481C2×C22⋊Q8—944no—
482C2×C22⋊Q8C2×D4711yescharacteristic
483C2×C22⋊Q8C2×D4711yescharacteristic
484C2×#121—471no—
485C2×#121—471no—
486C2×#120—941no—
487C2×C4×D4—941no—
488C2×C4×D4—941no—
489C2×#117—471no—
490C22×C4⋊C4—471no—
491C22×C4⋊C4—941no—
492C22×C22⋊C4—941no—
493#470—478no—
494#470—478no—
495#468—478no—
496#468—478no—
497#467—478no—
498#467C2×D4718yescomplemented
499#465—478no—
500#465—478no—
501#428—478no—
502C2×#107—471no—
503C2×#107C2×D4711yescharacteristic, complemented
504C2×#106—471no—
505C2×#106—471no—
506#419—478no—
507#417—478no—
508C2×#103—471no—
509C2×#103—471no—
510C2×#103—471no—
511C2×#103—471no—
512C2×#103C2×D4711yescharacteristic, complemented
513C2×#103C2×D4711yescharacteristic, complemented
514C2×#102—471no—
515C2×#102—471no—
516C47C2×#305611yescharacteristic, complemented, Sylow
517C25—471no—
518C2×#41—474no—
519C2×#41—942no—
520C2×#41—944no—
521C2×#41—944no—
522C22×Q8—474no—
523C22×Q8—471no—
524C22×Q8—941no—
525C22×Q8—942no—
526C22×Q8—944no—
527C22×Q8—944no—
528C22×Q8C22×D4711yescharacteristic
529C22×Q8C22×D4711yescharacteristic
530C22×D4—471no—
531C22×D4—941no—
532C22×D4—941no—
533C22×D4—941no—
534C23×C4—471no—
535C23×C4—471no—
536C23×C4—471no—
537C23×C4—471no—
538C23×C4—474no—
539C23×C4—471no—
540C23×C4—474no—
541C23×C4—944no—
542C23×C4—944no—
543C23×C4—941no—
544C23×C4—941no—
545C23×C4—941no—
546C23×C4C22×D4711yescharacteristic
547#137—9432no—
548C2×Q16—24no—
549C2×Q16—474no—
550C2×Q16—944no—
551C2×Q16C22×D4714yescomplemented
552C2×SD16—474no—
553C2×SD16—474no—
554C2×SD16—944no—
555C2×SD16—944no—
556C2×M16—478no—
557C2×M16—474no—
558C2×M16—474no—
559C2×M16—474no—
560C2×M16—474no—
561C2×M16—944no—
562C2×M16—9432no—
563C2×M16—944no—
564C2×M16—944no—
565C22×C8—24no—
566C22×C8—471no—
567C22×C8—471no—
568C22×C8—474no—
569C22×C8—944no—
570C22×C8C22×D4711yescharacteristic
571C22×C8C22×D4714yes—
572C22×C8C22×D4711yescharacteristic
573#123—948no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—474no—
577C22⋊Q8—474no—
578C22⋊Q8—474no—
579C22⋊Q8—474no—
580C22⋊Q8—948no—
581C22⋊Q8—948no—
582C22⋊Q8—942no—
583C22⋊Q8—942no—
584C22⋊Q8—942no—
585C22⋊Q8—942no—
586C22⋊Q8C22×D4714yes—
587C22⋊Q8C22×D4714yes—
588#121—474no—
589#121—474no—
590#121—942no—
591#121—942no—
592#120—948no—
593C4×D4—948no—
594C4×D4—948no—
595#117—474no—
596#117—942no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—471no—
600C2×C4⋊C4—471no—
601C2×C4⋊C4—474no—
602C2×C4⋊C4—942no—
603C2×C4⋊C4—948no—
604C2×C4⋊C4—941no—
605C2×C4⋊C4—941no—
606C2×C4⋊C4—941no—
607C2×C4⋊C4—941no—
608C2×C4⋊C4—941no—
609C2×C4⋊C4C22×D4711yescharacteristic
610C2×C4⋊C4C22×D4711yescharacteristic
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—948no—
614C2×C22⋊C4—941no—
615C2×C22⋊C4—941no—
616C2×C22⋊C4—941no—
617C2×C22⋊C4—941no—
618C2×C22⋊C4—941no—
619C2×C22⋊C4—941no—
620C2×C22⋊C4—941no—
621C2×C42—941no—
622#107—474no—
623#107C22×D4714yescomplemented
624#106—474no—
625#106—474no—
626#103—474no—
627#103—474no—
628#103—474no—
629#103—474no—
630#103C22×D4714yescomplemented
631#103C22×D4714yescomplemented
632#102—474no—
633#102—474no—
634C24—471no—
635C24—471no—
636C24—474no—
637C24—944no—
638C24—944no—
639C24—941no—
640C24—1882no—
641C24D4×D4711yescharacteristic
642#41—948no—
643#41—948no—
644#41—1888no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—22no—
650C2×Q8—22no—
651C2×Q8—472no—
652C2×Q8—944no—
653C2×Q8—948no—
654C2×Q8—948no—
655C2×Q8—941no—
656C2×Q8—942no—
657C2×Q8—942no—
658C2×Q8—1884no—
659C2×Q8—1888no—
660C2×Q8C23×D4712yes—
661C2×Q8C23×D4712yes—
662C2×D4—472no—
663C2×D4—944no—
664C2×D4—944no—
665C2×D4—944no—
666C2×D4—942no—
667C2×D4—941no—
668C2×D4—942no—
669C2×D4—1884no—
670C2×D4—1884no—
671C2×D4—1884no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—471no—
679C22×C4—472no—
680C22×C4—474no—
681C22×C4—474no—
682C22×C4—472no—
683C22×C4—474no—
684C22×C4—471no—
685C22×C4—474no—
686C22×C4—474no—
687C22×C4—472no—
688C22×C4—472no—
689C22×C4—948no—
690C22×C4—944no—
691C22×C4—9416no—
692C22×C4—948no—
693C22×C4—944no—
694C22×C4—944no—
695C22×C4—944no—
696C22×C4—944no—
697C22×C4—944no—
698C22×C4—942no—
699C22×C4—942no—
700C22×C4—941no—
701C22×C4—941no—
702C22×C4—941no—
703C22×C4—1884no—
704C22×C4—1884no—
705C22×C4—1884no—
706C22×C4D4×D4712yes—
707C22×C4D4×D4711yescharacteristic
708C22×C4C23×D4712yes—
709C22×C4C23×D4711yescharacteristic
710Q16—28no—
711Q16—948no—
712SD16—948no—
713SD16—948no—
714M16—4716no—
715M16—948no—
716M16—948no—
717M16—948no—
718C2×C8—22no—
719C2×C8—28no—
720C2×C8—474no—
721C2×C8—472no—
722C2×C8—472no—
723C2×C8—948no—
724C2×C8—942no—
725C2×C8D4×D4714yes—
726C2×C8C23×D4712yes—
727C2×C8C23×D4712yes—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—472no—
733C4⋊C4—472no—
734C4⋊C4—944no—
735C4⋊C4—944no—
736C4⋊C4—944no—
737C4⋊C4—944no—
738C4⋊C4—944no—
739C4⋊C4—941no—
740C4⋊C4—941no—
741C4⋊C4C23×D4712yes—
742C4⋊C4C23×D4712yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—944no—
746C22⋊C4—944no—
747C22⋊C4—944no—
748C22⋊C4—944no—
749C22⋊C4—944no—
750C22⋊C4—944no—
751C22⋊C4—944no—
752C42—944no—
753C23—22no—
754C23—22no—
755C23—474no—
756C23—472no—
757C23—472no—
758C23—948no—
759C23—942no—
760C23—942no—
761C23—942no—
762C23—942no—
763C23—948no—
764C23—942no—
765C23—942no—
766C23—1884no—
767C23—18816no—
768C23—1882no—
769C23—1882no—
770C23—1882no—
771C23#1309405614yescomplemented
772C23C2×D4×D4712yes—
773C23C2×D4×D4711yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—22no—
777Q8—22no—
778Q8—42no—
779Q8—42no—
780Q8—942no—
781Q8—942no—
782Q8—1888no—
783Q8—1882no—
784D4—942no—
785D4—942no—
786D4—1888no—
787D4—1888no—
788D4—1888no—
789D4—1882no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—474no—
803C2×C4—472no—
804C2×C4—478no—
805C2×C4—474no—
806C2×C4—474no—
807C2×C4—472no—
808C2×C4—948no—
809C2×C4—948no—
810C2×C4—948no—
811C2×C4—942no—
812C2×C4—944no—
813C2×C4—942no—
814C2×C4—942no—
815C2×C4—942no—
816C2×C4—942no—
817C2×C4—942no—
818C2×C4—1888no—
819C2×C4—1888no—
820C2×C4—1888no—
821C2×C4—1882no—
822C2×C4—1882no—
823C2×C4—1882no—
824C2×C4C2×D4×D4712yes—
825C2×C4C2×D4×D4711yescharacteristic
826C2×C4C2×D4×D4712yes—
827C2×C4#41×D4712yes—
828C2×C4C24×D4711yescharacteristic
829C8—22no—
830C8—474no—
831C8—942no—
832C8C2×D4×D4714yes—
833C22—22no—
834C22—28no—
835C22—22no—
836C22—474no—
837C22—942no—
838C22—942no—
839C22—948no—
840C22—942no—
841C22—942no—
842C22—942no—
843C22—3764no—
844C22—18816no—
845C22—1882no—
846C22—1882no—
847C22—1882no—
848C22—1884no—
849C22#121×D4712yes—
850C22C2×#1309405612yes—
851C22C2×#1309405614yescomplemented
852C22#1568992012yes—
853C22C22×D4×D4711yescharacteristic
854C4—22no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—474no—
860C4—942no—
861C4—1882no—
862C4—1882no—
863C4—1882no—
864C4#121×D4712yes—
865C4C22×D4×D4711yescharacteristic
866C4C2×#41×D4711yescharacteristic
867C2—24no—
868C2—944no—
869C2—3762no—
870C2—1882no—
871C2#2025301514yesdirect product factor
872C2C2×#121×D4711yescharacteristic
873C2C22×#1309405611yescharacteristic
874C2C2×#1568992011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#467C2
socleC23×C47C22×D4
prime radicalC2×#15689636C2
hypercenterC2×#467D47
hypocenterC47C2×#3056
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C22×#13094056C2semidirect
2. C23×#10625324C2semidirect
4. C2×C22⋊Q8×D47C2semidirect
5. #20253015C2direct (N × H)
6. C2×#15689380C2semidirect
7. C2×#15689378C2semidirect
8. C2×#15689372C2semidirect
9. C2×#15689370C2semidirect
10. C2×#15689362C2semidirect
11. C2×#15689354C2semidirect
12. C2×#15689352C2semidirect
13. C2×#15689164C2semidirect
14. C2×#15689123C2semidirect
15. C2×#15689130C2semidirect
16. C2×C47×#467C2semidirect
21. C2×#13094056C22semidirect
22. C22×#10625337C22semidirect
23. C22×#10625325C22semidirect
24. C22×#10625336C22semidirect
30. C22×#10625324C22semidirect
42. C22⋊Q8×D47C22semidirect
52. #15689380C22semidirect
53. #15689378C22semidirect
54. #15689372C22semidirect
55. #15689370C22semidirect
56. #15689362C22semidirect
57. #15689354C22semidirect
58. #15689352C22semidirect
59. #15689164C22semidirect
60. C2×#13093957C22semidirect
61. C2×#13093956C22semidirect
62. C2×#13093955C22semidirect
63. #15689130C22semidirect
64. #15689123C22semidirect
65. C2×#13093949C22semidirect
66. C2×#13093948C22semidirect
67. C2×#13093948C22semidirect
68. C2×#13093947C22semidirect
69. C2×#13093946C22semidirect
70. C2×#13093944C22semidirect
71. C22×Q16×C47C22semidirect
75. C47×#467C22semidirect
76. C2×#107×C47C22semidirect
77. C2×#103×C47C22semidirect
78. C2×#103×C47C22semidirect
108. C2×#10625337C23semidirect
110. C2×#10625325C23semidirect
112. C2×#10625336C23semidirect
117. C2×#10625324D4semidirect
165. #13093957C23semidirect
166. #13093956C23semidirect
167. #13093955C23semidirect
168. #13093949C23semidirect
169. #13093948C23semidirect
170. #13093948C23semidirect
171. #13093947C23semidirect
172. #13093946C23semidirect
173. #13093944C23semidirect
178. C2×Q16×C47C23semidirect
193. #107×C47C23semidirect
194. #103×C47C23semidirect
195. #103×C47C23semidirect
314. #10625324C2×D4semidirect
317. C23×C47#137semidirect
401. C22×C47C2×#137semidirect
440. C2×#467D47semidirect
447. C2×C47#3056semidirect
460. C22×Q16C2×D47semidirect
498. #467C2×D47semidirect
503. C2×#107C2×D47semidirect
512. C2×#103C2×D47semidirect
513. C2×#103C2×D47semidirect
516. C47C2×#3056semidirect
551. C2×Q16C22×D47semidirect
623. #107C22×D47semidirect
630. #103C22×D47semidirect
631. #103C22×D47semidirect
771. C23#13094056semidirect
851. C22C2×#13094056semidirect
871. C2#20253015direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940562
C23×#106253242
C2×#156896362
C2×C22⋊Q8×D472
#202530152
C2×#156893802
C2×#156893782
C2×#156893722
C2×#156893702
C2×#156893622
C2×#156893542
C2×#156893522
C2×#156891642
C2×#156891232
C2×#156891302
C2×C47×#4672
C2×#305647