Finite Group Databasebeta

← C2×#20252992 #27083408

Subgroups — C2×#20252992 #27083408

Order 12032.

2918 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094045C211yesmaximal, characteristic, complemented
2C22×M16×D47C211yesmaximal, characteristic, complemented
3C2×#15689636C211yesmaximal, characteristic, complemented
4C2×#15689633C211yesmaximal, characteristic, complemented
5#20252992C2116yesmaximal, direct product factor
6C2×#15689380C211yesmaximal, characteristic, complemented
7C2×#15689379C211yesmaximal, characteristic, complemented
8C2×#15689375C211yesmaximal, characteristic, complemented
9C2×#15689374C211yesmaximal, characteristic, complemented
10C2×#15689370C211yesmaximal, characteristic, complemented
11C2×#15689369C211yesmaximal, characteristic, complemented
12C2×#15689366C211yesmaximal, characteristic, complemented
13C2×#15689160C211yesmaximal, characteristic, complemented
14C2×#15689118C211yesmaximal, characteristic, complemented
15C2×#15689116C211yesmaximal, characteristic, complemented
16C2×C47×#468C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625352C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C2×#13094045—28no—
21C2×#13094045C2218yescomplemented
22C22×#10625337C2211yescharacteristic, complemented
23C22×#10625325C2211yescharacteristic, complemented
24C22×#10625334C2211yescharacteristic, complemented
25C22×#10625329C2211yescharacteristic
26C22×#10625324C2211yescharacteristic
27C22×#10625324C2211yescharacteristic
28C2×M16×D47—28no—
29C2×M16×D47C2218yescomplemented
30C22×C8×D47C2211yescharacteristic
31C22×C8×D47C2211yescharacteristic
32#15689636—24no—
33#15689636C2218yescomplemented
34#15689633—24no—
35#15689633C2218yescomplemented
36C2×#13094009—21no—
37C2×#13094006—21no—
38C2×#13094004C2211yescharacteristic
39C2×#13094003C2211yescharacteristic
40C2×#13094000C2211yescharacteristic
41C2×#13093999C2211yescharacteristic
42C2×#13093998C2211yescharacteristic
43C2×#13093995C2211yescharacteristic
44C2×#13093994—21no—
45C2×#13093992—21no—
46C2×D4×Dic47—21no—
47C2×#13093986—21no—
48C2×(C22⋊D47)⋊C4—21no—
49C2×(C22⋊D47)⋊C4—21no—
50C2×#13093982C2211yescharacteristic
51C2×#13093982C2211yescharacteristic
52#15689380C2218yescomplemented
53#15689379C2218yescomplemented
54#15689375C2218yescomplemented
55#15689374C2218yescomplemented
56#15689370C2218yescomplemented
57#15689369C2218yescomplemented
58#15689366C2218yescomplemented
59#15689160C2218yescomplemented
60C2×#13093958C2211yescharacteristic, complemented
61C2×#13093955C2211yescharacteristic, complemented
62C2×#13093955C2211yescharacteristic, complemented
63#15689118C2218yescomplemented
64#15689116C2218yescomplemented
65C2×#13093949C2211yescharacteristic, complemented
66C2×#13093948C2211yescharacteristic, complemented
67C2×#13093947C2211yescharacteristic, complemented
68C2×#13093946C2211yescharacteristic, complemented
69C2×#13093945C2211yescharacteristic, complemented
70C2×#13093944C2211yescharacteristic, complemented
71C22×SD16×C47C2211yescharacteristic, complemented
72C22×M16×C47C2211yescharacteristic
73C2×C22⋊Q8×C47C2211yescharacteristic
74C2×#121×C47C2211yescharacteristic
75C47×#468C2218yescomplemented
76C2×#107×C47C2211yescharacteristic, complemented
77C2×#103×C47C2211yescharacteristic, complemented
78C2×#102×C47C2211yescharacteristic, complemented
79C24×D47D411yescharacteristic
80C2×#10625354—22no—
81C2×#10625354—24no—
82C2×#10625354—24no—
83C2×#10625354C2314yes—
84C2×#10625352—24no—
85C2×#10625352—22no—
86C2×#10625352—24no—
87C2×#10625352C2314yes—
88C22×Dic94C2311yescharacteristic
89C22×D188—21no—
90C22×D188—21no—
91C22×D188C2311yescharacteristic
92C22×C22⋊D47—21no—
93C22×C22⋊D47—21no—
94C22×C22⋊D47—21no—
95C23×Dic47—21no—
96C23×Dic47D411yescharacteristic
97C22×C4×D47—24no—
98C22×C4×D47—24no—
99C22×C4×D47—21no—
100C22×C4×D47D411yescharacteristic
101C22×C4×D47D411yescharacteristic
102C22×C4×D47D414yes—
103C22×C4×D47C2311yescharacteristic
104C22×C4×D47C2314yes—
105C22×C4×D47C2311yescharacteristic
106#13094045—232no—
107C2×#10625337—24no—
108C2×#10625337C2314yescomplemented
109C2×#10625325—24no—
110C2×#10625325C2314yescomplemented
111C2×#10625334—24no—
112C2×#10625334C2314yescomplemented
113C2×#10625329—24no—
114C2×#10625329C2314yes—
115C2×#10625324—24no—
116C2×#10625324—24no—
117C2×#10625324C2314yes—
118C2×#10625324C2314yes—
119M16×D47—232no—
120C22×C47⋊C8C2311yescharacteristic
121C22×C47⋊C8C2311yescharacteristic
122C2×C8×D47—24no—
123C2×C8×D47D418yescomplemented
124C2×C8×D47C2314yes—
125C2×C8×D47C2314yes—
126#13094009—28no—
127#13094006—28no—
128#13094004—22no—
129#13094004C2314yes—
130#13094003—22no—
131#13094003C2314yes—
132#13094000—22no—
133#13094000C2314yes—
134#13093999—22no—
135#13093999C2314yes—
136#13093998—22no—
137#13093998C2314yes—
138#13093995—22no—
139#13093995C2314yes—
140#13093994—28no—
141#13093992—28no—
142D4×Dic47—28no—
143#13093986—28no—
144(C22⋊D47)⋊C4—28no—
145(C22⋊D47)⋊C4—28no—
146#13093982—22no—
147#13093982—22no—
148#13093982C2314yes—
149#13093982C2314yes—
150C2×C4⋊Dic47—21no—
151C2×C4⋊Dic47C2311yescharacteristic
152C2×C4⋊Dic47C2311yescharacteristic
153C2×Dic47⋊C4—21no—
154C2×Dic47⋊C4—21no—
155C2×C22⋊Dic47—21no—
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—
163C2×C4×Dic47—21no—
164C2×C4×Dic47—21no—
165#13093958C2314yescomplemented
166#13093955C2314yescomplemented
167#13093955C2314yescomplemented
168#13093949C2314yescomplemented
169#13093948C2314yescomplemented
170#13093947C2314yescomplemented
171#13093946C2314yescomplemented
172#13093945C2314yescomplemented
173#13093944C2314yescomplemented
174C22×Q8×C47C2311yescharacteristic
175C22×D4×C47—21no—
176C22×D4×C47C2311yescharacteristic
177C23×C4×C47C2311yescharacteristic
178C2×SD16×C47—24no—
179C2×SD16×C47C2314yescomplemented
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×C47C2314yescomplemented
194#103×C47C2314yescomplemented
195#102×C47C2314yescomplemented
196C24×C47—21no—
197C24×C47C2×D411yescharacteristic
198C23×D47—24no—
199C23×D47—21no—
200C23×D47—42no—
201C23×D47—42no—
202C23×D47C2×D411yescharacteristic
203C23×D47C2×D411yescharacteristic
204C23×D47C2×D414yes—
205C2×Q8×C47—21no—
206C2×Q8×C47—22no—
207C2×Q8×C47—22no—
208C2×Q8×C47C2412yes—
209C2×D4×C47—24no—
210C2×D4×C47—22no—
211C2×D4×C47—21no—
212C2×D4×C47—22no—
213C2×D4×C47—44no—
214C2×D4×C47C2412yes—
215C22×C4×C47—22no—
216C22×C4×C47—22no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D412yes—
222C22×C4×C47C2412yes—
223C22×C4×C47C2411yescharacteristic
224C2×C22⋊D47—24no—
225C2×C22⋊D47—24no—
226C2×C22⋊D47—24no—
227C2×C22⋊D47—44no—
228C2×C22⋊D47—44no—
229C2×C22⋊D47—44no—
230C22×Dic47—24no—
231C22×Dic47—21no—
232C22×Dic47—21no—
233C22×Dic47—21no—
234C22×Dic47—24no—
235C22×Dic47—44no—
236C22×Dic47C2×D411yescharacteristic
237C22×Dic47C2×D414yes—
238C22×Dic47C2×D411yescharacteristic
239#10625354—28no—
240#10625354—28no—
241#10625354—48no—
242#10625352—28no—
243#10625352—28no—
244#10625352—48no—
245C2×D188—22no—
246C2×D188—22no—
247C2×D188—24no—
248C2×D188—24no—
249C2×D188—21no—
250C2×D188—44no—
251C2×D188—44no—
252C2×D188C2412yes—
253C2×C4×D47—24no—
254C2×C4×D47—22no—
255C2×C4×D47—22no—
256C2×C4×D47—24no—
257C2×C4×D47—216no—
258C2×C4×D47—28no—
259C2×C4×D47—28no—
260C2×C4×D47—24no—
261C2×C4×D47—44no—
262C2×C4×D47C2×D414yes—
263C2×C4×D47C2×D412yes—
264C2×C4×D47C2×D414yes—
265C2×C4×D47C2×D412yes—
266C2×C4×D47C2×D414yes—
267C2×C4×D47#4114yes—
268C2×C4×D47C2412yes—
269C2×C4×D47C2412yes—
270C2×Dic94—22no—
271C2×Dic94—22no—
272C2×Dic94—21no—
273C2×Dic94C2412yes—
274SD16×C47—28no—
275M16×C47—28no—
276C2×C8×C47—22no—
277C2×C8×C47C2×D414yes—
278C2×C8×C47C2412yes—
279C2×C8×C47C2412yes—
280C4⋊C4×C47—24no—
281C4⋊C4×C47—21no—
282C4⋊C4×C47—21no—
283C4⋊C4×C47C2412yes—
284C4⋊C4×C47C2412yes—
285C22⋊C4×C47—24no—
286C22⋊C4×C47—24no—
287C22⋊Dic47—24no—
288C22⋊Dic47—24no—
289#10625337—28no—
290#10625334—28no—
291(C2×D47)⋊C4—24no—
292(C2×D47)⋊C4—24no—
293(C2×D47)⋊C4—24no—
294(C2×D47)⋊C4—24no—
295(C2×D47)⋊C4—24no—
296(C2×D47)⋊C4—24no—
297C4⋊Dic47—21no—
298C4⋊Dic47—21no—
299C4⋊Dic47—24no—
300C4⋊Dic47C2412yes—
301C4⋊Dic47C2412yes—
302Dic47⋊C4—24no—
303Dic47⋊C4—24no—
304C4×Dic47—24no—
305C4×Dic47—24no—
306#10625329—28no—
307C2×C47⋊C8—22no—
308C2×C47⋊C8C2×D414yes—
309C2×C47⋊C8C2412yes—
310C2×C47⋊C8C2412yes—
311#10625325—28no—
312#10625324—28no—
313#10625324—28no—
314C8×D47—28no—
315C8×D47C2×D4116yescomplemented
316C23×C47—22no—
317C23×C47—22no—
318C23×C47—22no—
319C23×C47—22no—
320C23×C47—42no—
321C23×C47—42no—
322C23×C47—42no—
323C23×C47C22×D412yes—
324C23×C47C22×D411yescharacteristic
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—28no—
331C22×D47—22no—
332C22×D47—44no—
333C22×D47—44no—
334C22×D47—416no—
335C22×D47—42no—
336C22×D47—42no—
337C22×D47—42no—
338C22×D47#12114yes—
339C22×D47C22×D412yes—
340C22×D47C22×D412yes—
341Q8×C47—22no—
342Q8×C47—22no—
343Q8×C47—42no—
344D4×C47—22no—
345D4×C47—22no—
346D4×C47—48no—
347D4×C47—42no—
348C2×C4×C47—22no—
349C2×C4×C47—24no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—42no—
356C2×C4×C47—42no—
357C2×C4×C47—42no—
358C2×C4×C47C22×D412yes—
359C2×C4×C47C22×D411yescharacteristic
360C2×C4×C47C22×D412yes—
361C2×C4×C47C2×#4112yes—
362C2×C4×C47C2511yescharacteristic
363C22⋊D47—48no—
364C22⋊D47—48no—
365C22⋊D47—48no—
366C2×Dic47—22no—
367C2×Dic47—28no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—42no—
372C2×Dic47—42no—
373C2×Dic47—42no—
374C2×Dic47—48no—
375C2×Dic47#12114yes—
376C2×Dic47C22×D412yes—
377C2×Dic47C22×D412yes—
378D188—22no—
379D188—22no—
380D188—48no—
381D188—48no—
382D188—42no—
383C4×D47—28no—
384C4×D47—24no—
385C4×D47—22no—
386C4×D47—22no—
387C4×D47—28no—
388C4×D47—48no—
389C4×D47#12118yes—
390C4×D47C22×D414yes—
391C4×D47C2×#4114yes—
392Dic94—22no—
393Dic94—22no—
394Dic94—42no—
395C8×C47—22no—
396C8×C47C22×D414yes—
397C47⋊C8—22no—
398C47⋊C8C22×D414yes—
399C2×#3054—471nomaximal, Sylow
400C22×C47—22no—
401C22×C47—22no—
402C22×C47—22no—
403C22×C47—44no—
404C22×C47—42no—
405C22×C47—42no—
406C22×C47—42no—
407C22×C47—84no—
408C22×C47C2×#12112yes—
409C22×C47#57512yes—
410C22×C47#57512yes—
411C22×C47C23×D411yescharacteristic
412C2×D47—28no—
413C2×D47—22no—
414C2×D47—22no—
415C2×D47—22no—
416C2×D47—22no—
417C2×D47—22no—
418C2×D47—416no—
419C2×D47—44no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47—42no—
423C2×D47—84no—
424C2×D47C2×#12114yes—
425C4×C47—22no—
426C4×C47—42no—
427C4×C47—42no—
428C4×C47—42no—
429C4×C47C2×#12112yes—
430C4×C47C23×D411yescharacteristic
431C4×C47C22×#4111yescharacteristic
432Dic47—22no—
433Dic47—42no—
434Dic47—42no—
435Dic47—42no—
436Dic47C2×#12114yes—
437C22×#135—471no—
438C23×M16—471no—
439C2×#525—471no—
440C2×#525—471no—
441#3054—4716no—
442C2×#470—471no—
443C2×#470—471no—
444C2×#469—471no—
445C2×#469—471no—
446C2×#468—471no—
447C2×#468—471no—
448C2×#468—471no—
449C2×#468D4711yescharacteristic, complemented
450C2×#427—471no—
451C2×#416—471no—
452C2×#416—471no—
453C2×C47—42no—
454C2×C47—82no—
455C2×C47#305414yescomplemented
456C2×C47C22×#12111yescharacteristic
457C2×C47C2×#57511yescharacteristic
458C2×C47C2×#57511yescharacteristic
459D47—24no—
460D47—42no—
461D47—82no—
462C22×#41—471no—
463C22×#41—471no—
464C24×C4—471no—
465C2×#135—478no—
466C2×#135—948no—
467C22×Q16—471no—
468C22×SD16—471no—
469C22×SD16C2×D4711yescharacteristic, complemented
470C22×D8—471no—
471C22×M16—471no—
472C22×M16—478no—
473C22×M16—471no—
474C22×M16—471no—
475C22×M16—948no—
476C22×M16C2×D4711yescharacteristic
477C23×C8—471no—
478C23×C8—471no—
479#525—478no—
480#525—478no—
481#525—944no—
482#525—944no—
483C2×#123—941no—
484C2×#123—941no—
485C2×C22⋊Q8—471no—
486C2×C22⋊Q8—471no—
487C2×C22⋊Q8—471no—
488C2×C22⋊Q8C2×D4711yescharacteristic
489C2×#121—471no—
490C2×#121—471no—
491C2×#121—471no—
492C2×#121C2×D4711yescharacteristic
493C2×#120—941no—
494C2×#120—941no—
495C2×C4×D4—941no—
496C2×C4×D4—941no—
497C2×C4×D4—941no—
498C2×C4×D4—941no—
499C2×#117—471no—
500C2×#117—471no—
501#470—478no—
502#470—478no—
503#469—478no—
504#469—478no—
505#468—478no—
506#468—478no—
507#468—478no—
508#468C2×D4718yescomplemented
509#427—478no—
510C2×#107—471no—
511C2×#107C2×D4711yescharacteristic, complemented
512C2×#106—471no—
513C2×#106—471no—
514#416—478no—
515#416—478no—
516C2×#103—471no—
517C2×#103—471no—
518C2×#103—471no—
519C2×#103C2×D4711yescharacteristic, complemented
520C2×#102—471no—
521C2×#102—471no—
522C2×#102—471no—
523C2×#102C2×D4711yescharacteristic, complemented
524C47C2×#305411yescharacteristic, complemented, Sylow
525C25—471no—
526C2×#41—474no—
527C2×#41—474no—
528C2×#41—942no—
529C2×#41—942no—
530C2×#41—944no—
531C2×#41—944no—
532C2×#41—944no—
533C2×#41—944no—
534C22×Q8—471no—
535C22×Q8C22×D4711yescharacteristic
536C22×D4—21no—
537C22×D4—471no—
538C22×D4—941no—
539C22×D4—941no—
540C22×D4—941no—
541C22×D4—941no—
542C22×D4—941no—
543C22×D4C22×D4711yescharacteristic
544C23×C4—471no—
545C23×C4—471no—
546C23×C4—471no—
547C23×C4—471no—
548C23×C4—474no—
549C23×C4—471no—
550C23×C4—474no—
551C23×C4—944no—
552C23×C4—944no—
553C23×C4—941no—
554C23×C4—941no—
555C23×C4C22×D4711yescharacteristic
556#135—9432no—
557C2×Q16—474no—
558C2×Q16—944no—
559C2×SD16—24no—
560C2×SD16—474no—
561C2×SD16—944no—
562C2×SD16C22×D4714yescomplemented
563C2×D8—474no—
564C2×D8—944no—
565C2×M16—24no—
566C2×M16—474no—
567C2×M16—474no—
568C2×M16—474no—
569C2×M16—944no—
570C2×M16—9432no—
571C2×M16—944no—
572C2×M16—944no—
573C2×M16C22×D4714yes—
574C22×C8—471no—
575C22×C8—478no—
576C22×C8—474no—
577C22×C8—471no—
578C22×C8—474no—
579C22×C8—944no—
580C22×C8C22×D4711yescharacteristic
581C22×C8C22×D4711yescharacteristic
582#123—948no—
583#123—948no—
584C22⋊Q8—22no—
585C22⋊Q8—474no—
586C22⋊Q8—474no—
587C22⋊Q8—474no—
588C22⋊Q8—942no—
589C22⋊Q8—942no—
590C22⋊Q8—942no—
591C22⋊Q8C22×D4714yes—
592#121—22no—
593#121—474no—
594#121—474no—
595#121—474no—
596#121—942no—
597#121—942no—
598#121—942no—
599#121C22×D4714yes—
600#120—948no—
601#120—948no—
602C4×D4—948no—
603C4×D4—948no—
604C4×D4—948no—
605C4×D4—948no—
606#117—474no—
607#117—474no—
608#117—942no—
609#117—942no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—471no—
612C2×C4⋊C4—471no—
613C2×C4⋊C4—941no—
614C2×C4⋊C4—941no—
615C2×C4⋊C4—941no—
616C2×C4⋊C4C22×D4711yescharacteristic
617C2×C4⋊C4C22×D4711yescharacteristic
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—941no—
621C2×C22⋊C4—941no—
622C2×C22⋊C4—941no—
623C2×C22⋊C4—941no—
624C2×C22⋊C4—941no—
625C2×C22⋊C4—941no—
626C2×C22⋊C4—941no—
627C2×C22⋊C4—941no—
628C2×C42—941no—
629C2×C42—941no—
630#107—474no—
631#107C22×D4714yescomplemented
632#106—474no—
633#106—474no—
634#103—474no—
635#103—474no—
636#103—474no—
637#103C22×D4714yescomplemented
638#102—474no—
639#102—474no—
640#102—474no—
641#102C22×D4714yescomplemented
642C24—21no—
643C24—471no—
644C24—471no—
645C24—474no—
646C24—944no—
647C24—941no—
648C24—1882no—
649C24—1882no—
650C24D4×D4711yescharacteristic
651#41—948no—
652#41—948no—
653#41—948no—
654#41—948no—
655#41—1888no—
656#41—1888no—
657C2×Q8—21no—
658C2×Q8—22no—
659C2×Q8—22no—
660C2×Q8—472no—
661C2×Q8—941no—
662C2×Q8—942no—
663C2×Q8—942no—
664C2×Q8C23×D4712yes—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—44no—
670C2×D4—472no—
671C2×D4—944no—
672C2×D4—944no—
673C2×D4—944no—
674C2×D4—944no—
675C2×D4—944no—
676C2×D4—942no—
677C2×D4—941no—
678C2×D4—942no—
679C2×D4—1884no—
680C2×D4—1884no—
681C2×D4—1884no—
682C2×D4—1884no—
683C2×D4—1884no—
684C2×D4C23×D4712yes—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—471no—
691C22×C4—472no—
692C22×C4—474no—
693C22×C4—474no—
694C22×C4—472no—
695C22×C4—474no—
696C22×C4—471no—
697C22×C4—474no—
698C22×C4—472no—
699C22×C4—474no—
700C22×C4—472no—
701C22×C4—948no—
702C22×C4—944no—
703C22×C4—9416no—
704C22×C4—948no—
705C22×C4—944no—
706C22×C4—944no—
707C22×C4—944no—
708C22×C4—944no—
709C22×C4—942no—
710C22×C4—942no—
711C22×C4—941no—
712C22×C4—941no—
713C22×C4—941no—
714C22×C4—1884no—
715C22×C4—1884no—
716C22×C4D4×D4712yes—
717C22×C4D4×D4711yescharacteristic
718C22×C4C23×D4712yes—
719C22×C4C23×D4711yescharacteristic
720Q16—948no—
721SD16—28no—
722SD16—948no—
723D8—948no—
724M16—28no—
725M16—948no—
726M16—948no—
727M16—948no—
728C2×C8—22no—
729C2×C8—474no—
730C2×C8—472no—
731C2×C8—4716no—
732C2×C8—472no—
733C2×C8—948no—
734C2×C8—942no—
735C2×C8D4×D4714yes—
736C2×C8C23×D4712yes—
737C2×C8C23×D4712yes—
738C4⋊C4—24no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—472no—
742C4⋊C4—472no—
743C4⋊C4—944no—
744C4⋊C4—944no—
745C4⋊C4—944no—
746C4⋊C4—941no—
747C4⋊C4—941no—
748C4⋊C4C23×D4712yes—
749C4⋊C4C23×D4712yes—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—944no—
753C22⋊C4—944no—
754C22⋊C4—944no—
755C22⋊C4—944no—
756C22⋊C4—944no—
757C22⋊C4—944no—
758C22⋊C4—944no—
759C22⋊C4—944no—
760C42—944no—
761C42—944no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—474no—
770C23—472no—
771C23—472no—
772C23—948no—
773C23—942no—
774C23—942no—
775C23—942no—
776C23—942no—
777C23—942no—
778C23—942no—
779C23—1884no—
780C23—1884no—
781C23—18816no—
782C23—1882no—
783C23—1882no—
784C23—1882no—
785C23C2×D4×D4712yes—
786C23C2×D4×D4711yescharacteristic
787Q8—22no—
788Q8—22no—
789Q8—42no—
790Q8—942no—
791Q8—942no—
792Q8—1882no—
793D4—22no—
794D4—22no—
795D4—48no—
796D4—42no—
797D4—942no—
798D4—942no—
799D4—1888no—
800D4—1888no—
801D4—1888no—
802D4—1888no—
803D4—1888no—
804D4—1882no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—474no—
816C2×C4—472no—
817C2×C4—478no—
818C2×C4—474no—
819C2×C4—474no—
820C2×C4—472no—
821C2×C4—948no—
822C2×C4—948no—
823C2×C4—948no—
824C2×C4—942no—
825C2×C4—944no—
826C2×C4—942no—
827C2×C4—942no—
828C2×C4—942no—
829C2×C4—942no—
830C2×C4—942no—
831C2×C4—1888no—
832C2×C4—1888no—
833C2×C4—1882no—
834C2×C4—1882no—
835C2×C4—1882no—
836C2×C4C2×D4×D4712yes—
837C2×C4C2×D4×D4711yescharacteristic
838C2×C4C2×D4×D4712yes—
839C2×C4#41×D4712yes—
840C2×C4C24×D4711yescharacteristic
841C8—22no—
842C8—474no—
843C8—942no—
844C8C2×D4×D4714yes—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—44no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—84no—
853C22—474no—
854C22—948no—
855C22—942no—
856C22—942no—
857C22—942no—
858C22—942no—
859C22—942no—
860C22—3764no—
861C22—18816no—
862C22—1882no—
863C22—1882no—
864C22—1882no—
865C22—1884no—
866C22#121×D4712yes—
867C22#1568991912yes—
868C22#1568992212yes—
869C22C22×D4×D4711yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—474no—
875C4—942no—
876C4—1882no—
877C4—1882no—
878C4—1882no—
879C4#121×D4712yes—
880C4C22×D4×D4711yescharacteristic
881C4C2×#41×D4711yescharacteristic
882C2—42no—
883C2—82no—
884C2—944no—
885C2—3762no—
886C2—1882no—
887C2#2025299214yesdirect product factor
888C2C2×#121×D4711yescharacteristic
889C2C2×#1568991911yescharacteristic
890C2C2×#1568992211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#468C2
socleC23×C47C22×D4
hypercenterC2×#468D47
hypocenterC47C2×#3054
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×#13094045C2semidirect
2. C22×M16×D47C2semidirect
3. C2×#15689636C2semidirect
4. C2×#15689633C2semidirect
5. #20252992C2direct (N × H)
6. C2×#15689380C2semidirect
7. C2×#15689379C2semidirect
8. C2×#15689375C2semidirect
9. C2×#15689374C2semidirect
10. C2×#15689370C2semidirect
11. C2×#15689369C2semidirect
12. C2×#15689366C2semidirect
13. C2×#15689160C2semidirect
14. C2×#15689118C2semidirect
15. C2×#15689116C2semidirect
16. C2×C47×#468C2semidirect
21. C2×#13094045C22semidirect
22. C22×#10625337C22semidirect
23. C22×#10625325C22semidirect
24. C22×#10625334C22semidirect
29. C2×M16×D47C22semidirect
33. #15689636C22semidirect
35. #15689633C22semidirect
52. #15689380C22semidirect
53. #15689379C22semidirect
54. #15689375C22semidirect
55. #15689374C22semidirect
56. #15689370C22semidirect
57. #15689369C22semidirect
58. #15689366C22semidirect
59. #15689160C22semidirect
60. C2×#13093958C22semidirect
61. C2×#13093955C22semidirect
62. C2×#13093955C22semidirect
63. #15689118C22semidirect
64. #15689116C22semidirect
65. C2×#13093949C22semidirect
66. C2×#13093948C22semidirect
67. C2×#13093947C22semidirect
68. C2×#13093946C22semidirect
69. C2×#13093945C22semidirect
70. C2×#13093944C22semidirect
71. C22×SD16×C47C22semidirect
75. C47×#468C22semidirect
76. C2×#107×C47C22semidirect
77. C2×#103×C47C22semidirect
78. C2×#102×C47C22semidirect
108. C2×#10625337C23semidirect
110. C2×#10625325C23semidirect
112. C2×#10625334C23semidirect
123. C2×C8×D47D4semidirect
165. #13093958C23semidirect
166. #13093955C23semidirect
167. #13093955C23semidirect
168. #13093949C23semidirect
169. #13093948C23semidirect
170. #13093947C23semidirect
171. #13093946C23semidirect
172. #13093945C23semidirect
173. #13093944C23semidirect
179. C2×SD16×C47C23semidirect
193. #107×C47C23semidirect
194. #103×C47C23semidirect
195. #102×C47C23semidirect
315. C8×D47C2×D4semidirect
449. C2×#468D47semidirect
455. C2×C47#3054semidirect
469. C22×SD16C2×D47semidirect
508. #468C2×D47semidirect
511. C2×#107C2×D47semidirect
519. C2×#103C2×D47semidirect
523. C2×#102C2×D47semidirect
524. C47C2×#3054semidirect
562. C2×SD16C22×D47semidirect
631. #107C22×D47semidirect
637. #103C22×D47semidirect
641. #102C22×D47semidirect
887. C2#20252992direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940452
C22×M16×D472
C2×#156896362
C2×#156896332
#202529922
C2×#156893802
C2×#156893792
C2×#156893752
C2×#156893742
C2×#156893702
C2×#156893692
C2×#156893662
C2×#156891602
C2×#156891182
C2×#156891162
C2×C47×#4682
C2×#305447