Finite Group Databasebeta

← C2×#20253074 #27083520

Subgroups — C2×#20253074 #27083520

Order 12032.

2742 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094053C211yesmaximal, characteristic, complemented
2C22×#13094032C211yesmaximal, characteristic, complemented
3C2×#15689702C211yesmaximal, characteristic
4C2×#15689696C211yesmaximal, characteristic, complemented
5#20253074C2116yesmaximal, direct product factor
6C2×#15689381C211yesmaximal, characteristic, complemented
7C2×#15689380C211yesmaximal, characteristic, complemented
8C2×#15689368C211yesmaximal, characteristic, complemented
9C2×#15689365C211yesmaximal, characteristic, complemented
10C2×#15689362C211yesmaximal, characteristic, complemented
11C2×#15689350C211yesmaximal, characteristic, complemented
12C2×#15689349C211yesmaximal, characteristic, complemented
13C2×#15689164C211yesmaximal, characteristic, complemented
14C2×#15689116C211yesmaximal, characteristic, complemented
15C2×#103×D47C211yesmaximal, characteristic, complemented
16C2×C47×#468C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625352C2211yescharacteristic
19C22×Q8×D47C2211yescharacteristic
20C2×#13094053—28no—
21C2×#13094053C2218yescomplemented
22C22×Dic188C2211yescharacteristic
23C22×#10625337C2211yescharacteristic
24C22×#10625335C2211yescharacteristic
25C2×#13094032—28no—
26C2×#13094032C2218yescomplemented
27C22×#10625324C2211yescharacteristic
28C22×#10625324C2211yescharacteristic
29C23×C47⋊C8C2211yescharacteristic
30C22×C8×D47C2211yescharacteristic
31C22×C8×D47C2211yescharacteristic
32#15689702—24no—
33#15689702C2218yes—
34#15689696—24no—
35#15689696C2218yescomplemented
36C2×#13094023—21no—
37C2×#13094010—21no—
38C2×#13094009—21no—
39C2×#13094006—21no—
40C2×#13094004C2211yescharacteristic
41C2×#13094004C2211yescharacteristic
42C2×#13094003C2211yescharacteristic
43C2×#13094003C2211yescharacteristic
44C2×#13094001—21no—
45C2×#13094000C2211yescharacteristic
46C2×#13093997—21no—
47C2×#13093996—21no—
48C2×#13093995—21no—
49C2×#13093995C2211yescharacteristic
50C2×#13093982C2211yescharacteristic
51C2×C4⋊C4×D47C2211yescharacteristic
52#15689381C2218yescomplemented
53#15689380C2218yescomplemented
54#15689368C2218yescomplemented
55#15689365C2218yescomplemented
56#15689362C2218yescomplemented
57#15689350C2218yescomplemented
58#15689349C2218yescomplemented
59#15689164C2218yescomplemented
60C2×#13093957C2211yescharacteristic
61C2×#13093956C2211yescharacteristic
62C2×#13093955C2211yescharacteristic
63#15689116C2218yescomplemented
64C2×#13093949C2211yescharacteristic
65C2×#13093949C2211yescharacteristic
66C2×#13093948C2211yescharacteristic
67C2×#13093947C2211yescharacteristic
68C2×#13093947C2211yescharacteristic
69#103×D47C2218yescomplemented
70C2×#13093945C2211yescharacteristic
71C22×SD16×C47C2211yescharacteristic
72C22×M16×C47C2211yescharacteristic
73C2×C22⋊Q8×C47C2211yescharacteristic
74C2×#121×C47C2211yescharacteristic
75C47×#468C2218yescomplemented
76C2×#107×C47C2211yescharacteristic
77C2×#103×C47C2211yescharacteristic
78C2×#102×C47C2211yescharacteristic
79C2×#10625350—24no—
80C2×#10625350—24no—
81C2×#10625350D414yes—
82C2×#10625350C2314yes—
83C2×#10625352—24no—
84C2×#10625352—22no—
85C2×#10625352—24no—
86C2×#10625352C2314yes—
87C22×Dic94—21no—
88C22×Dic94D411yescharacteristic
89C22×Dic94C2311yescharacteristic
90C22×Dic94C2311yescharacteristic
91C2×Q8×D47—22no—
92C2×Q8×D47—24no—
93C2×Q8×D47—24no—
94C2×Q8×D47C2314yes—
95C22×D188D411yescharacteristic
96C22×C22⋊D47—21no—
97C22×C22⋊D47—21no—
98C22×C22⋊D47D411yescharacteristic
99C22×C22⋊D47D411yescharacteristic
100C23×Dic47—21no—
101C22×C4×D47—21no—
102C22×C4×D47—21no—
103C22×C4×D47C2311yescharacteristic
104C22×C4×D47C2311yescharacteristic
105#13094053—232no—
106C2×Dic188—24no—
107C2×Dic188C2314yes—
108C2×#10625337—24no—
109C2×#10625337C2314yes—
110C2×#10625335—24no—
111C2×#10625335C2314yes—
112#13094032—232no—
113C2×#10625324—24no—
114C2×#10625324D418yescomplemented
115C2×#10625324C2314yes—
116C2×#10625324C2314yes—
117C22×C47⋊C8—24no—
118C22×C47⋊C8C2314yes—
119C22×C47⋊C8C2311yescharacteristic
120C22×C47⋊C8C2311yescharacteristic
121C2×C8×D47—24no—
122C2×C8×D47—24no—
123C2×C8×D47C2314yes—
124C2×C8×D47C2314yes—
125#13094023—28no—
126#13094010—28no—
127#13094009—28no—
128#13094006—28no—
129#13094004—22no—
130#13094004—22no—
131#13094004C2314yes—
132#13094004C2314yes—
133#13094003—22no—
134#13094003—22no—
135#13094003C2314yes—
136#13094003C2314yes—
137#13094001—28no—
138#13094000—22no—
139#13094000C2314yes—
140#13093997—28no—
141#13093996—28no—
142#13093995—28no—
143#13093995—22no—
144#13093995C2314yes—
145#13093982—22no—
146#13093982C2314yes—
147C2×C4⋊Dic47—21no—
148C2×C4⋊Dic47—21no—
149C2×C4⋊Dic47C2311yescharacteristic
150C2×C4⋊Dic47C2311yescharacteristic
151C2×Dic47⋊C4—21no—
152C2×Dic47⋊C4—21no—
153C2×Dic47⋊C4—21no—
154C2×Dic47⋊C4—21no—
155C4⋊C4×D47—22no—
156C4⋊C4×D47C2314yes—
157C2×C22⋊Dic47—21no—
158C2×C22⋊Dic47—21no—
159C2×C22⋊Dic47—21no—
160C2×(C2×D47)⋊C4—21no—
161C2×(C2×D47)⋊C4—21no—
162C2×(C2×D47)⋊C4—21no—
163C2×(C2×D47)⋊C4—21no—
164C2×C4×Dic47—21no—
165#13093957C2314yes—
166#13093956C2314yes—
167#13093955C2314yes—
168#13093949C2314yes—
169#13093949C2314yes—
170#13093948C2314yes—
171#13093947C2314yes—
172#13093947C2314yes—
173#13093945C2314yes—
174C22×Q8×C47C2311yescharacteristic
175C22×D4×C47—21no—
176C22×D4×C47C2311yescharacteristic
177C23×C4×C47C2311yescharacteristic
178C2×SD16×C47—24no—
179C2×SD16×C47C2314yes—
180C2×M16×C47—24no—
181C2×M16×C47C2314yes—
182C22×C8×C47C2311yescharacteristic
183C22×C8×C47C2311yescharacteristic
184C22⋊Q8×C47—22no—
185C22⋊Q8×C47C2314yes—
186#121×C47—22no—
187#121×C47C2314yes—
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×C47C2314yes—
194#103×C47C2314yes—
195#102×C47C2314yes—
196C24×C47—21no—
197C24×C47C2×D411yescharacteristic
198C23×D47C2×D411yescharacteristic
199C23×D47C2×D411yescharacteristic
200C2×Q8×C47—21no—
201C2×Q8×C47—22no—
202C2×Q8×C47—22no—
203C2×Q8×C47C2412yes—
204C2×D4×C47—24no—
205C2×D4×C47—22no—
206C2×D4×C47—21no—
207C2×D4×C47—22no—
208C2×D4×C47—82no—
209C2×D4×C47C2412yes—
210C22×C4×C47—22no—
211C22×C4×C47—22no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D412yes—
217C22×C4×C47C2412yes—
218C22×C4×C47C2411yescharacteristic
219C2×C22⋊D47—24no—
220C2×C22⋊D47—24no—
221C2×C22⋊D47—24no—
222C2×C22⋊D47—24no—
223C2×C22⋊D47—44no—
224C2×C22⋊D47—82no—
225C2×C22⋊D47C2×D414yes—
226C2×C22⋊D47C2×D414yes—
227C22×Dic47—21no—
228C22×Dic47—21no—
229C22×Dic47—21no—
230C22×Dic47—21no—
231C22×Dic47—24no—
232C22×Dic47—44no—
233C22×Dic47C2×D411yescharacteristic
234C22×Dic47C2×D411yescharacteristic
235Q8×D47—28no—
236Q8×D47—28no—
237Q8×D47—48no—
238#10625352—28no—
239#10625352—28no—
240#10625352—48no—
241#10625350—216no—
242#10625350—28no—
243#10625350—28no—
244C2×D188—24no—
245C2×D188C2×D414yes—
246C2×C4×D47—22no—
247C2×C4×D47—22no—
248C2×C4×D47—24no—
249C2×C4×D47—24no—
250C2×C4×D47—44no—
251C2×C4×D47—82no—
252C2×C4×D47C2×D412yes—
253C2×C4×D47C2×D412yes—
254C2×C4×D47C2×D414yes—
255C2×C4×D47#4114yes—
256C2×C4×D47C2412yes—
257C2×C4×D47C2412yes—
258C2×Dic94—24no—
259C2×Dic94—22no—
260C2×Dic94—22no—
261C2×Dic94—22no—
262C2×Dic94—22no—
263C2×Dic94—21no—
264C2×Dic94—21no—
265C2×Dic94—24no—
266C2×Dic94—44no—
267C2×Dic94C2×D414yes—
268C2×Dic94C2412yes—
269C2×Dic94C2412yes—
270SD16×C47—28no—
271M16×C47—28no—
272C2×C8×C47—22no—
273C2×C8×C47C2×D414yes—
274C2×C8×C47C2412yes—
275C2×C8×C47C2412yes—
276C4⋊C4×C47—24no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47C2412yes—
280C4⋊C4×C47C2412yes—
281C22⋊C4×C47—24no—
282C22⋊C4×C47—24no—
283C22⋊Dic47—24no—
284C22⋊Dic47—24no—
285C22⋊Dic47—24no—
286#10625337—28no—
287#10625335—28no—
288(C2×D47)⋊C4—24no—
289(C2×D47)⋊C4—24no—
290(C2×D47)⋊C4—24no—
291(C2×D47)⋊C4—24no—
292C4⋊Dic47—21no—
293C4⋊Dic47—21no—
294C4⋊Dic47—24no—
295C4⋊Dic47—24no—
296C4⋊Dic47C2412yes—
297C4⋊Dic47C2412yes—
298Dic47⋊C4—24no—
299Dic47⋊C4—24no—
300Dic47⋊C4—24no—
301Dic47⋊C4—24no—
302C4×Dic47—24no—
303C2×C47⋊C8—22no—
304C2×C47⋊C8—28no—
305C2×C47⋊C8C2×D414yes—
306C2×C47⋊C8C2412yes—
307C2×C47⋊C8C2412yes—
308Dic188—28no—
309#10625324—28no—
310#10625324C2×D4116yescomplemented
311C8×D47—28no—
312C8×D47—28no—
313C23×C47—22no—
314C23×C47—22no—
315C23×C47—22no—
316C23×C47—22no—
317C23×C47—42no—
318C23×C47—42no—
319C23×C47—42no—
320C23×C47C22×D412yes—
321C23×C47C22×D411yescharacteristic
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—22no—
325C22×D47—22no—
326C22×D47—22no—
327C22×D47#12114yes—
328C22×D47C22×D412yes—
329C22×D47C22×D412yes—
330Q8×C47—22no—
331Q8×C47—22no—
332Q8×C47—42no—
333D4×C47—22no—
334D4×C47—22no—
335D4×C47—42no—
336D4×C47—84no—
337C2×C4×C47—22no—
338C2×C4×C47—24no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—42no—
345C2×C4×C47—42no—
346C2×C4×C47—42no—
347C2×C4×C47C22×D412yes—
348C2×C4×C47C22×D411yescharacteristic
349C2×C4×C47C22×D412yes—
350C2×C4×C47C2×#4112yes—
351C2×C4×C47C2511yescharacteristic
352C22⋊D47—28no—
353C22⋊D47—28no—
354C22⋊D47—48no—
355C22⋊D47—84no—
356C2×Dic47—22no—
357C2×Dic47—22no—
358C2×Dic47—22no—
359C2×Dic47—22no—
360C2×Dic47—22no—
361C2×Dic47—42no—
362C2×Dic47—42no—
363C2×Dic47—42no—
364C2×Dic47—42no—
365C2×Dic47—48no—
366C2×Dic47#12114yes—
367C2×Dic47C22×D412yes—
368C2×Dic47C22×D412yes—
369D188—28no—
370C4×D47—24no—
371C4×D47—22no—
372C4×D47—22no—
373C4×D47—48no—
374C4×D47—84no—
375C4×D47#12118yes—
376C4×D47C22×D414yes—
377C4×D47C2×#4114yes—
378Dic94—28no—
379Dic94—22no—
380Dic94—22no—
381Dic94—22no—
382Dic94—22no—
383Dic94—42no—
384Dic94—42no—
385Dic94—48no—
386C8×C47—22no—
387C8×C47C22×D414yes—
388C47⋊C8—22no—
389C47⋊C8C22×D414yes—
390C2×#3063—471nomaximal, Sylow
391C22×C47—22no—
392C22×C47—22no—
393C22×C47—22no—
394C22×C47—44no—
395C22×C47—42no—
396C22×C47—42no—
397C22×C47—42no—
398C22×C47—84no—
399C22×C47C2×#12112yes—
400C22×C47#57712yes—
401C22×C47#57812yes—
402C22×C47C23×D411yescharacteristic
403C2×D47—28no—
404C2×D47—22no—
405C2×D47—22no—
406C2×D47—22no—
407C2×D47—22no—
408C2×D47—22no—
409C2×D47—44no—
410C2×D47C2×#12114yes—
411C4×C47—22no—
412C4×C47—42no—
413C4×C47—42no—
414C4×C47—42no—
415C4×C47C2×#12112yes—
416C4×C47C23×D411yescharacteristic
417C4×C47C22×#4111yescharacteristic
418Dic47—22no—
419Dic47—42no—
420Dic47—42no—
421Dic47—42no—
422Dic47—42no—
423Dic47C2×#12114yes—
424C22×#137—471no—
425C22×#131—471no—
426C2×#537—471no—
427C2×#536—471no—
428#3063—4716no—
429C2×#470—471no—
430C2×#470—471no—
431C2×#468—471no—
432C2×#468D4711yescharacteristic, complemented
433C2×#467—471no—
434C2×#467—471no—
435C2×#465—471no—
436C2×#465—471no—
437C2×#428—471no—
438C2×#416—471no—
439C22×#103—471no—
440C2×C47—42no—
441C2×C47—82no—
442C2×C47#306314yescomplemented
443C2×C47C22×#12111yescharacteristic
444C2×C47C2×#57711yescharacteristic
445C2×C47C2×#57811yescharacteristic
446D47—24no—
447D47—42no—
448C22×#41—471no—
449C22×#41—471no—
450C23×Q8—471no—
451C2×#137—478no—
452C2×#137—948no—
453C22×Q16—471no—
454C22×Q16—471no—
455C22×SD16—471no—
456C22×SD16C2×D4711yescharacteristic
457C2×#131—478no—
458C2×#131—948no—
459C22×M16—471no—
460C22×M16—471no—
461C22×M16C2×D4711yescharacteristic
462C23×C8—471no—
463C23×C8—471no—
464C23×C8—471no—
465#537—478no—
466#537—944no—
467#536—478no—
468#536—944no—
469C2×C4⋊Q8—941no—
470C2×#124—941no—
471C2×#123—941no—
472C2×#123—941no—
473C2×C22⋊Q8—471no—
474C2×C22⋊Q8—471no—
475C2×C22⋊Q8—471no—
476C2×C22⋊Q8—471no—
477C2×C22⋊Q8—471no—
478C2×C22⋊Q8—941no—
479C2×C22⋊Q8C2×D4711yescharacteristic
480C2×#121—471no—
481C2×#121—941no—
482C2×#121—941no—
483C2×#121—941no—
484C2×#121C2×D4711yescharacteristic
485C2×#117—471no—
486C22×C4⋊C4—471no—
487#470—478no—
488#470—478no—
489#468—478no—
490#468C2×D4718yescomplemented
491#467—478no—
492#467—478no—
493#465—478no—
494#465—478no—
495#428—478no—
496C2×#107—471no—
497C2×#107C2×D4711yescharacteristic
498C2×#106—471no—
499C2×#106—471no—
500#416—478no—
501C2×#103—471no—
502C2×#103—471no—
503C2×#103—471no—
504C2×#103—471no—
505C2×#103—471no—
506C2×#103—478no—
507C2×#103C2×D4711yescharacteristic
508C2×#102—471no—
509C2×#102C2×D4711yescharacteristic
510C47C2×#306311yescharacteristic, complemented, Sylow
511C2×#41—474no—
512C2×#41—474no—
513C2×#41—474no—
514C2×#41—944no—
515C2×#41—944no—
516C2×#41—942no—
517C2×#41—944no—
518C2×#41—944no—
519C22×Q8—471no—
520C22×Q8—474no—
521C22×Q8—471no—
522C22×Q8—471no—
523C22×Q8—941no—
524C22×Q8—942no—
525C22×Q8—944no—
526C22×Q8—944no—
527C22×Q8C22×D4711yescharacteristic
528C22×D4—21no—
529C22×D4—471no—
530C22×D4—471no—
531C22×D4—471no—
532C22×D4—941no—
533C22×D4—941no—
534C22×D4C22×D4711yescharacteristic
535C23×C4—471no—
536C23×C4—471no—
537C23×C4—941no—
538C23×C4—941no—
539C23×C4—941no—
540C23×C4C22×D4711yescharacteristic
541#137—9432no—
542C2×Q16—474no—
543C2×Q16—474no—
544C2×Q16—944no—
545C2×Q16—944no—
546C2×SD16—24no—
547C2×SD16—474no—
548C2×SD16—944no—
549C2×SD16C22×D4714yes—
550#131—9432no—
551C2×M16—24no—
552C2×M16—478no—
553C2×M16—474no—
554C2×M16—474no—
555C2×M16—944no—
556C2×M16C22×D4714yes—
557C22×C8—471no—
558C22×C8—471no—
559C22×C8—474no—
560C22×C8—474no—
561C22×C8—474no—
562C22×C8—944no—
563C22×C8—944no—
564C22×C8—944no—
565C22×C8C22×D4711yescharacteristic
566C22×C8C22×D4711yescharacteristic
567C4⋊Q8—948no—
568#124—948no—
569#123—948no—
570#123—948no—
571C22⋊Q8—22no—
572C22⋊Q8—474no—
573C22⋊Q8—474no—
574C22⋊Q8—474no—
575C22⋊Q8—474no—
576C22⋊Q8—474no—
577C22⋊Q8—948no—
578C22⋊Q8—942no—
579C22⋊Q8—942no—
580C22⋊Q8—942no—
581C22⋊Q8—942no—
582C22⋊Q8—942no—
583C22⋊Q8C22×D4714yes—
584#121—22no—
585#121—474no—
586#121—948no—
587#121—942no—
588#121—948no—
589#121—948no—
590#121C22×D4714yes—
591#117—474no—
592#117—942no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—471no—
595C2×C4⋊C4—471no—
596C2×C4⋊C4—474no—
597C2×C4⋊C4—942no—
598C2×C4⋊C4—941no—
599C2×C4⋊C4—941no—
600C2×C4⋊C4—941no—
601C2×C4⋊C4—941no—
602C2×C4⋊C4—941no—
603C2×C4⋊C4—941no—
604C2×C4⋊C4C22×D4711yescharacteristic
605C2×C4⋊C4C22×D4711yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—941no—
609C2×C22⋊C4—941no—
610C2×C22⋊C4—941no—
611C2×C22⋊C4—941no—
612C2×C22⋊C4—941no—
613C2×C22⋊C4—941no—
614C2×C22⋊C4—941no—
615C2×C42—941no—
616#107—474no—
617#107C22×D4714yes—
618#106—474no—
619#106—474no—
620#103—474no—
621#103—474no—
622#103—474no—
623#103—474no—
624#103—474no—
625#103C22×D4714yes—
626#102—474no—
627#102C22×D4714yes—
628C24—21no—
629C24—471no—
630C24—471no—
631C24D4×D4711yescharacteristic
632#41—948no—
633#41—9416no—
634#41—948no—
635#41—948no—
636#41—948no—
637#41—1888no—
638C2×Q8—21no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—474no—
642C2×Q8—472no—
643C2×Q8—472no—
644C2×Q8—944no—
645C2×Q8—944no—
646C2×Q8—948no—
647C2×Q8—948no—
648C2×Q8—941no—
649C2×Q8—941no—
650C2×Q8—942no—
651C2×Q8—942no—
652C2×Q8—942no—
653C2×Q8—942no—
654C2×Q8—1884no—
655C2×Q8—1888no—
656C2×Q8C23×D4712yes—
657C2×D4—24no—
658C2×D4—22no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—82no—
662C2×D4—474no—
663C2×D4—474no—
664C2×D4—474no—
665C2×D4—944no—
666C2×D4—944no—
667C2×D4—944no—
668C2×D4—944no—
669C2×D4—944no—
670C2×D4—3762no—
671C2×D4—1884no—
672C2×D4C23×D4712yes—
673C22×C4—22no—
674C22×C4—22no—
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—471no—
684C22×C4—472no—
685C22×C4—472no—
686C22×C4—944no—
687C22×C4—944no—
688C22×C4—944no—
689C22×C4—942no—
690C22×C4—942no—
691C22×C4—941no—
692C22×C4—941no—
693C22×C4—941no—
694C22×C4—941no—
695C22×C4—3762no—
696C22×C4—1884no—
697C22×C4—1884no—
698C22×C4D4×D4712yes—
699C22×C4D4×D4711yescharacteristic
700C22×C4C23×D4712yes—
701C22×C4C23×D4711yescharacteristic
702Q16—948no—
703Q16—948no—
704SD16—28no—
705SD16—948no—
706M16—28no—
707M16—4716no—
708M16—948no—
709C2×C8—22no—
710C2×C8—474no—
711C2×C8—472no—
712C2×C8—472no—
713C2×C8—948no—
714C2×C8—948no—
715C2×C8—942no—
716C2×C8—948no—
717C2×C8D4×D4714yes—
718C2×C8C23×D4712yes—
719C2×C8C23×D4712yes—
720C4⋊C4—24no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—472no—
724C4⋊C4—472no—
725C4⋊C4—944no—
726C4⋊C4—944no—
727C4⋊C4—944no—
728C4⋊C4—944no—
729C4⋊C4—944no—
730C4⋊C4—944no—
731C4⋊C4—941no—
732C4⋊C4—941no—
733C4⋊C4C23×D4712yes—
734C4⋊C4C23×D4712yes—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—944no—
738C22⋊C4—944no—
739C22⋊C4—944no—
740C22⋊C4—944no—
741C22⋊C4—944no—
742C22⋊C4—944no—
743C22⋊C4—944no—
744C42—944no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—474no—
753C23—472no—
754C23—472no—
755C23—942no—
756C23—942no—
757C23—942no—
758C23—942no—
759C23—942no—
760C23C2×D4×D4712yes—
761C23C2×D4×D4711yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—42no—
765Q8—948no—
766Q8—942no—
767Q8—942no—
768Q8—942no—
769Q8—942no—
770Q8—1888no—
771Q8—1882no—
772Q8—1882no—
773D4—22no—
774D4—22no—
775D4—42no—
776D4—84no—
777D4—948no—
778D4—948no—
779D4—948no—
780D4—3764no—
781D4—1888no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—474no—
793C2×C4—472no—
794C2×C4—478no—
795C2×C4—474no—
796C2×C4—474no—
797C2×C4—472no—
798C2×C4—942no—
799C2×C4—944no—
800C2×C4—942no—
801C2×C4—942no—
802C2×C4—942no—
803C2×C4—942no—
804C2×C4—942no—
805C2×C4—942no—
806C2×C4—3764no—
807C2×C4—1888no—
808C2×C4—1888no—
809C2×C4—1882no—
810C2×C4—1882no—
811C2×C4—1882no—
812C2×C4—1882no—
813C2×C4C2×D4×D4712yes—
814C2×C4C2×D4×D4711yescharacteristic
815C2×C4C2×D4×D4712yes—
816C2×C4#41×D4712yes—
817C2×C4C24×D4711yescharacteristic
818C8—22no—
819C8—474no—
820C8—942no—
821C8C2×D4×D4714yes—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—84no—
830C22—474no—
831C22—942no—
832C22—942no—
833C22—948no—
834C22—942no—
835C22—942no—
836C22—942no—
837C22—1884no—
838C22#121×D4712yes—
839C22#1568993312yes—
840C22#1568993912yes—
841C22C22×D4×D4711yescharacteristic
842C4—22no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—474no—
847C4—942no—
848C4—1882no—
849C4—1882no—
850C4—1882no—
851C4—1882no—
852C4#121×D4712yes—
853C4C22×D4×D4711yescharacteristic
854C4C2×#41×D4711yescharacteristic
855C2—42no—
856C2—82no—
857C2—944no—
858C2—1882no—
859C2#2025307414yesdirect product factor
860C2C2×#121×D4711yescharacteristic
861C2C2×#1568993311yescharacteristic
862C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#468C2
socleC23×C47C22×D4
prime radicalC2×#15689702C2
hypercenterC2×#468D47
hypocenterC47C2×#3063
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C22×#13094053C2semidirect
2. C22×#13094032C2semidirect
4. C2×#15689696C2semidirect
5. #20253074C2direct (N × H)
6. C2×#15689381C2semidirect
7. C2×#15689380C2semidirect
8. C2×#15689368C2semidirect
9. C2×#15689365C2semidirect
10. C2×#15689362C2semidirect
11. C2×#15689350C2semidirect
12. C2×#15689349C2semidirect
13. C2×#15689164C2semidirect
14. C2×#15689116C2semidirect
15. C2×#103×D47C2semidirect
16. C2×C47×#468C2semidirect
21. C2×#13094053C22semidirect
26. C2×#13094032C22semidirect
35. #15689696C22semidirect
52. #15689381C22semidirect
53. #15689380C22semidirect
54. #15689368C22semidirect
55. #15689365C22semidirect
56. #15689362C22semidirect
57. #15689350C22semidirect
58. #15689349C22semidirect
59. #15689164C22semidirect
63. #15689116C22semidirect
69. #103×D47C22semidirect
75. C47×#468C22semidirect
114. C2×#10625324D4semidirect
310. #10625324C2×D4semidirect
432. C2×#468D47semidirect
442. C2×C47#3063semidirect
490. #468C2×D47semidirect
510. C47C2×#3063semidirect
859. C2#20253074direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940532
C22×#130940322
C2×#156897022
C2×#156896962
#202530742
C2×#156893812
C2×#156893802
C2×#156893682
C2×#156893652
C2×#156893622
C2×#156893502
C2×#156893492
C2×#156891642
C2×#156891162
C2×#103×D472
C2×C47×#4682
C2×#306347