Finite Group Databasebeta

← C2×#20255022 #27091411

Subgroups — C2×#20255022 #27091411

Order 12032.

2902 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094055C211yesmaximal, characteristic, complemented
2C22×#13094051C211yesmaximal, characteristic, complemented
3C2×#15689784C211yesmaximal, characteristic, complemented
4C2×#15689770C211yesmaximal, characteristic, complemented
5#20255022C2116yesmaximal, direct product factor
6C2×#15689504C211yesmaximal, characteristic, complemented
7C2×#15689380C211yesmaximal, characteristic, complemented
8C2×#15689374C211yesmaximal, characteristic, complemented
9C2×#15689343C211yesmaximal, characteristic, complemented
10C2×#15689341C211yesmaximal, characteristic, complemented
11C2×#15689288C211yesmaximal, characteristic, complemented
12C2×#15689270C211yesmaximal, characteristic, complemented
13C2×#15689272C211yesmaximal, characteristic, complemented
14C2×#15689208C211yesmaximal, characteristic, complemented
15C2×#15689198C211yesmaximal, characteristic, complemented
16C2×C47×#448C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625350C2211yescharacteristic
19C22×D4×D47C2211yescharacteristic
20C2×#13094055—28no—
21C2×#13094055C2218yescomplemented
22C2×#13094051—28no—
23C2×#13094051C2218yescomplemented
24C22×#10625337C2211yescharacteristic, complemented
25C22×#10625337C2211yescharacteristic, complemented
26C22×#10625325C2211yescharacteristic, complemented
27C22×#10625336C2211yescharacteristic
28C22×#10625336C2211yescharacteristic
29C22×D376C2211yescharacteristic
30C22×#10625334C2211yescharacteristic
31C22×#10625329C2211yescharacteristic, complemented
32C22×#10625324C2211yescharacteristic
33#15689784—24no—
34#15689784C2218yescomplemented
35#15689770—24no—
36#15689770C2218yescomplemented
37C2×#13094013—21no—
38C2×#13094013C2211yescharacteristic, complemented
39C2×#13094011C2211yescharacteristic
40C2×#13094006—21no—
41C2×#13094004C2211yescharacteristic
42C2×#13094000—21no—
43C2×#13094000C2211yescharacteristic
44C2×#13093998—21no—
45C2×#13093998C2211yescharacteristic, complemented
46C2×#13093995—21no—
47C2×#13093992—21no—
48C2×Q8×Dic47C2211yescharacteristic, complemented
49C2×#13093986C2211yescharacteristic
50C2×C4×C22⋊D47—21no—
51C2×C4×C22⋊D47C2211yescharacteristic
52C2×C22⋊C4×D47—21no—
53#15689504C2218yescomplemented
54#15689380C2218yescomplemented
55#15689374C2218yescomplemented
56#15689343C2218yescomplemented
57#15689341C2218yescomplemented
58#15689288C2218yescomplemented
59#15689272C2218yescomplemented
60#15689270C2218yescomplemented
61#15689208C2218yescomplemented
62#15689198C2218yescomplemented
63C2×#13093955C2211yescharacteristic, complemented
64C2×Dic47⋊C8C2211yescharacteristic, complemented
65C2×#13093949C2211yescharacteristic, complemented
66C2×#13093946C2211yescharacteristic
67C2×#13093945C2211yescharacteristic
68C2×#13093944C2211yescharacteristic, complemented
69C2×(C2×D47)⋊C8C2211yescharacteristic
70C2×C8×Dic47C2211yescharacteristic, complemented
71C23×Q8×C47C2211yescharacteristic, complemented
72C22×SD16×C47C2211yescharacteristic
73C22×SD16×C47C2211yescharacteristic
74C2×#121×C47C2211yescharacteristic
75C47×#448C2218yescomplemented
76C2×#103×C47C2211yescharacteristic, complemented
77C2×#103×C47C2211yescharacteristic, complemented
78C2×C22⋊C8×C47C2211yescharacteristic, complemented
79C24×D47—21no—
80C2×#10625354—22no—
81C2×#10625354—24no—
82C2×#10625354—42no—
83C2×#10625354C2314yes—
84C2×#10625350—22no—
85C2×#10625350—24no—
86C2×#10625350—42no—
87C2×#10625350C2314yes—
88C22×Dic94C2311yescharacteristic
89C22×D188—21no—
90C22×D188C2311yescharacteristic
91C22×D188C2311yescharacteristic
92C22×C22⋊D47—21no—
93C22×C22⋊D47—21no—
94C22×C22⋊D47—21no—
95C22×C22⋊D47D411yescharacteristic
96C2×D4×D47—24no—
97C2×D4×D47—22no—
98C2×D4×D47—42no—
99C2×D4×D47C2314yes—
100C22×C4×D47—21no—
101C22×C4×D47—21no—
102C22×C4×D47—21no—
103C22×C4×D47C2311yescharacteristic
104#13094055—232no—
105#13094051—232no—
106C2×#10625337—24no—
107C2×#10625337—24no—
108C2×#10625337C2314yescomplemented
109C2×#10625337C2314yescomplemented
110C2×#10625325—42no—
111C2×#10625325C2314yescomplemented
112C2×#10625336—24no—
113C2×#10625336D418yescomplemented
114C2×#10625336C2314yes—
115C2×#10625336C2314yes—
116C2×D376—24no—
117C2×D376C2314yes—
118C2×#10625334—24no—
119C2×#10625334C2314yes—
120C2×#10625329—24no—
121C2×#10625329C2314yescomplemented
122C2×#10625324—24no—
123C2×#10625324C2314yes—
124C22×C47⋊C8C2311yescharacteristic
125C22×C47⋊C8C2311yescharacteristic
126#13094013—28no—
127#13094013—22no—
128#13094013C2314yescomplemented
129#13094011—22no—
130#13094011C2314yes—
131#13094006—28no—
132#13094004—22no—
133#13094004C2314yes—
134#13094000—22no—
135#13094000—28no—
136#13094000C2314yes—
137#13093998—22no—
138#13093998—28no—
139#13093998C2314yescomplemented
140#13093995—28no—
141#13093992—28no—
142Q8×Dic47—22no—
143Q8×Dic47C2314yescomplemented
144#13093986—22no—
145#13093986C2314yes—
146C4×C22⋊D47—28no—
147C4×C22⋊D47D414yes—
148C4×C22⋊D47C2314yes—
149C2×C4⋊Dic47—21no—
150C2×C4⋊Dic47—21no—
151C2×C4⋊Dic47C2311yescharacteristic
152C2×Dic47⋊C4—21no—
153C2×Dic47⋊C4D411yescharacteristic
154C2×C22⋊Dic47—21no—
155C2×C22⋊Dic47—21no—
156C2×C22⋊Dic47D411yescharacteristic
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×(C2×D47)⋊C4D411yescharacteristic
164C22⋊C4×D47—28no—
165C2×C4×Dic47—21no—
166C2×C4×Dic47C2311yescharacteristic
167#13093955C2314yescomplemented
168Dic47⋊C8C2314yescomplemented
169#13093949C2314yescomplemented
170#13093946C2314yes—
171#13093945C2314yes—
172#13093944C2314yescomplemented
173(C2×D47)⋊C8C2314yes—
174C8×Dic47C2314yescomplemented
175C22×Q8×C47—22no—
176C22×Q8×C47—21no—
177C22×Q8×C47—24no—
178C22×Q8×C47—42no—
179C22×Q8×C47C2311yescharacteristic
180C22×Q8×C47C2311yescharacteristic
181C22×Q8×C47C2314yescomplemented
182C22×D4×C47—21no—
183C22×D4×C47C2311yescharacteristic
184C23×C4×C47—21no—
185C23×C4×C47C2311yescharacteristic
186C2×SD16×C47—24no—
187C2×SD16×C47—42no—
188C2×SD16×C47C2314yes—
189C2×SD16×C47C2314yes—
190C22×C8×C47C2311yescharacteristic
191C22×C8×C47C2311yescharacteristic
192#121×C47—22no—
193#121×C47C2314yes—
194C2×C4⋊C4×C47C2311yescharacteristic
195C2×C22⋊C4×C47—21no—
196#103×C47C2314yescomplemented
197#103×C47C2314yescomplemented
198C22⋊C8×C47C2314yescomplemented
199C24×C47—21no—
200C24×C47C2×D411yescharacteristic
201C23×D47—21no—
202C23×D47—21no—
203C23×D47—24no—
204C23×D47—44no—
205C23×D47—44no—
206C23×D47—82no—
207C23×D47C2×D411yescharacteristic
208C2×Q8×C47—21no—
209C2×Q8×C47—21no—
210C2×Q8×C47—24no—
211C2×Q8×C47—22no—
212C2×Q8×C47—28no—
213C2×Q8×C47—22no—
214C2×Q8×C47—22no—
215C2×Q8×C47—44no—
216C2×Q8×C47—44no—
217C2×Q8×C47—48no—
218C2×Q8×C47C2×D414yes—
219C2×Q8×C47C2412yes—
220C2×Q8×C47C2412yes—
221C2×D4×C47—24no—
222C2×D4×C47—22no—
223C2×D4×C47—21no—
224C2×D4×C47—22no—
225C2×D4×C47—82no—
226C2×D4×C47C2412yes—
227C22×C4×C47—21no—
228C22×C4×C47—22no—
229C22×C4×C47—22no—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47—24no—
233C22×C4×C47—44no—
234C22×C4×C47C2×D411yescharacteristic
235C22×C4×C47C2×D412yes—
236C22×C4×C47C2412yes—
237C22×C4×C47C2411yescharacteristic
238C2×C22⋊D47—24no—
239C2×C22⋊D47—24no—
240C2×C22⋊D47—24no—
241C2×C22⋊D47—42no—
242C2×C22⋊D47—44no—
243C2×C22⋊D47—44no—
244C2×C22⋊D47—44no—
245C2×C22⋊D47C2×D414yes—
246C22×Dic47—21no—
247C22×Dic47—21no—
248C22×Dic47C2×D411yescharacteristic
249C22×Dic47C2×D411yescharacteristic
250C22×Dic47C2×D411yescharacteristic
251#10625354—28no—
252#10625354—44no—
253#10625354—48no—
254D4×D47—28no—
255D4×D47—44no—
256D4×D47—48no—
257#10625350—28no—
258#10625350—44no—
259#10625350—48no—
260C2×D188—21no—
261C2×D188—22no—
262C2×D188—22no—
263C2×D188—22no—
264C2×D188—24no—
265C2×D188—21no—
266C2×D188—44no—
267C2×D188C2×D414yes—
268C2×D188C2412yes—
269C2×D188C2412yes—
270C2×C4×D47—22no—
271C2×C4×D47—22no—
272C2×C4×D47—24no—
273C2×C4×D47—24no—
274C2×C4×D47—24no—
275C2×C4×D47—44no—
276C2×C4×D47—44no—
277C2×C4×D47—82no—
278C2×C4×D47C2×D412yes—
279C2×C4×D47C2412yes—
280C2×Dic94—22no—
281C2×Dic94—22no—
282C2×Dic94—21no—
283C2×Dic94C2412yes—
284SD16×C47—28no—
285SD16×C47—44no—
286C2×C8×C47—22no—
287C2×C8×C47—22no—
288C2×C8×C47C2412yes—
289C2×C8×C47C2412yes—
290C4⋊C4×C47—21no—
291C4⋊C4×C47C2412yes—
292C22⋊C4×C47—24no—
293C22⋊Dic47—24no—
294C22⋊Dic47—24no—
295C22⋊Dic47C2×D414yes—
296#10625337—28no—
297#10625337—28no—
298#10625336—28no—
299#10625336C2×D4116yescomplemented
300#10625334—28no—
301(C2×D47)⋊C4—24no—
302(C2×D47)⋊C4—24no—
303(C2×D47)⋊C4—24no—
304(C2×D47)⋊C4—24no—
305(C2×D47)⋊C4—24no—
306(C2×D47)⋊C4—24no—
307(C2×D47)⋊C4C2×D414yes—
308C4⋊Dic47—21no—
309C4⋊Dic47—24no—
310C4⋊Dic47—24no—
311C4⋊Dic47C2412yes—
312Dic47⋊C4—24no—
313Dic47⋊C4C2×D414yes—
314C4×Dic47—24no—
315C4×Dic47C2×D412yes—
316C4×Dic47C2412yes—
317#10625329—28no—
318C2×C47⋊C8—22no—
319C2×C47⋊C8C2×D414yes—
320C2×C47⋊C8C2412yes—
321C2×C47⋊C8C2412yes—
322D376—28no—
323#10625325—44no—
324#10625324—28no—
325C23×C47—22no—
326C23×C47—22no—
327C23×C47—22no—
328C23×C47—22no—
329C23×C47—42no—
330C23×C47—42no—
331C23×C47—42no—
332C23×C47C22×D412yes—
333C23×C47C22×D411yescharacteristic
334C22×D47—22no—
335C22×D47—24no—
336C22×D47—22no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—48no—
341C22×D47—48no—
342C22×D47—42no—
343C22×D47—42no—
344C22×D47—42no—
345C22×D47—42no—
346C22×D47—42no—
347C22×D47—84no—
348C22×D47—816no—
349C22×D47C22×D412yes—
350Q8×C47—24no—
351Q8×C47—22no—
352Q8×C47—22no—
353Q8×C47—22no—
354Q8×C47—48no—
355Q8×C47—42no—
356Q8×C47C22×D414yes—
357D4×C47—22no—
358D4×C47—22no—
359D4×C47—42no—
360D4×C47—84no—
361C2×C4×C47—22no—
362C2×C4×C47—24no—
363C2×C4×C47—22no—
364C2×C4×C47—24no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—48no—
370C2×C4×C47—42no—
371C2×C4×C47—42no—
372C2×C4×C47C22×D412yes—
373C2×C4×C47C22×D411yescharacteristic
374C2×C4×C47C22×D412yes—
375C2×C4×C47H(5,𝔽2)12yes—
376C2×C4×C47C2511yescharacteristic
377C22⋊D47—44no—
378C22⋊D47—48no—
379C22⋊D47—48no—
380C22⋊D47—48no—
381C2×Dic47—22no—
382C2×Dic47—22no—
383C2×Dic47—22no—
384C2×Dic47—22no—
385C2×Dic47—22no—
386C2×Dic47—42no—
387C2×Dic47—42no—
388C2×Dic47C22×D412yes—
389C2×Dic47C22×D412yes—
390C2×Dic47C22×D412yes—
391D188—24no—
392D188—22no—
393D188—22no—
394D188—22no—
395D188—48no—
396D188—42no—
397D188C22×D414yes—
398C4×D47—24no—
399C4×D47—22no—
400C4×D47—22no—
401C4×D47—48no—
402C4×D47—48no—
403C4×D47—84no—
404Dic94—22no—
405Dic94—22no—
406Dic94—42no—
407C8×C47—22no—
408C8×C47—22no—
409C47⋊C8—22no—
410C47⋊C8C22×D414yes—
411C2×#3275—471nomaximal, Sylow
412C22×C47—22no—
413C22×C47—22no—
414C22×C47—22no—
415C22×C47—44no—
416C22×C47—42no—
417C22×C47—42no—
418C22×C47—42no—
419C22×C47—84no—
420C22×C47D4212yes—
421C22×C47#57512yes—
422C22×C47#57712yes—
423C22×C47C23×D411yescharacteristic
424C2×D47—22no—
425C2×D47—24no—
426C2×D47—22no—
427C2×D47—22no—
428C2×D47—44no—
429C2×D47—48no—
430C2×D47—42no—
431C2×D47—42no—
432C2×D47—42no—
433C2×D47—42no—
434C2×D47—42no—
435C2×D47—816no—
436C2×D47—84no—
437C4×C47—22no—
438C4×C47—24no—
439C4×C47—42no—
440C4×C47—42no—
441C4×C47D4212yes—
442C4×C47C23×D411yescharacteristic
443C4×C47C2×H(5,𝔽2)11yescharacteristic
444Dic47—22no—
445Dic47—22no—
446Dic47—22no—
447Dic47—42no—
448Dic47—42no—
449C22×#137—471no—
450C22×AGL(1,ℤ/8)—471no—
451C2×#548—471no—
452C2×#546—471no—
453#3275—4716no—
454C2×#495—471no—
455C2×#470—471no—
456C2×#469—471no—
457C2×#464—471no—
458C2×#463—471no—
459C2×#452—471no—
460C2×#449—471no—
461C2×#448D4711yescharacteristic, complemented
462C2×#450—471no—
463C2×C4×SD16—471no—
464C2×#436—471no—
465C2×C47—42no—
466C2×C47—82no—
467C2×C47#327514yescomplemented
468C2×C47C2×D4211yescharacteristic
469C2×C47C2×#57511yescharacteristic
470C2×C47C2×#57711yescharacteristic
471D47—42no—
472D47—44no—
473D47—82no—
474C22×#41—471no—
475C22×#41—471no—
476C23×Q8C2×D4711yescharacteristic, complemented
477C23×D4—471no—
478C2×#137—478no—
479C2×#137—948no—
480C2×AGL(1,ℤ/8)—478no—
481C2×AGL(1,ℤ/8)—948no—
482C22×Q16—471no—
483C22×Q16—471no—
484C22×SD16—471no—
485C22×SD16—471no—
486C22×SD16—471no—
487C22×SD16C2×D4711yescharacteristic
488C22×SD16C2×D4711yescharacteristic
489C22×D8—471no—
490C22×D8—471no—
491C22×M16—471no—
492C22×M16—471no—
493#548—478no—
494#548—944no—
495#546—478no—
496#546—944no—
497C2×#124—471no—
498C2×#124—471no—
499C2×#124—941no—
500C2×#123—941no—
501C2×C22⋊Q8—471no—
502C2×C22⋊Q8—471no—
503C2×C22⋊Q8—941no—
504C2×#121—471no—
505C2×#121—941no—
506C2×#121—941no—
507C2×#121C2×D4711yescharacteristic
508C2×#120—941no—
509C2×C4×Q8—471no—
510C2×C4×D4—471no—
511C2×C4×D4—471no—
512C2×C4×D4—941no—
513C22×C22⋊C4—941no—
514#495—478no—
515#470—478no—
516#469—478no—
517#464—478no—
518#463—478no—
519#452—478no—
520#450—478no—
521#449—478no—
522#448C2×D4718yescomplemented
523C4×SD16—478no—
524#436—478no—
525C2×#106—471no—
526C2×C4⋊C8—471no—
527C2×#103—471no—
528C2×#103C2×D4711yescharacteristic, complemented
529C2×#103C2×D4711yescharacteristic, complemented
530C2×#102—471no—
531C2×#102—471no—
532C2×#102—471no—
533C2×C22⋊C8—471no—
534C2×C22⋊C8C2×D4711yescharacteristic, complemented
535C2×C4×C8—471no—
536C47C2×#327511yescharacteristic, complemented, Sylow
537C25—941no—
538C2×#41—474no—
539C2×#41—474no—
540C2×#41—944no—
541C2×#41—942no—
542C2×#41—942no—
543C2×#41—944no—
544C2×#41—1882no—
545C2×#41—1882no—
546C22×Q8—21no—
547C22×Q8—22no—
548C22×Q8—24no—
549C22×Q8—42no—
550C22×Q8—471no—
551C22×Q8C22×D4711yescharacteristic
552C22×Q8C22×D4711yescharacteristic
553C22×Q8C22×D4714yescomplemented
554C22×D4—21no—
555C22×D4—471no—
556C22×D4—474no—
557C22×D4—471no—
558C22×D4—471no—
559C22×D4—941no—
560C22×D4—942no—
561C22×D4—941no—
562C22×D4—944no—
563C22×D4—941no—
564C22×D4—941no—
565C22×D4—1882no—
566C22×D4C22×D4711yescharacteristic
567C23×C4—21no—
568C23×C4—471no—
569C23×C4—941no—
570C23×C4—941no—
571C23×C4—941no—
572C23×C4C22×D4711yescharacteristic
573#137—9432no—
574AGL(1,ℤ/8)—9432no—
575C2×Q16—474no—
576C2×Q16—474no—
577C2×Q16—944no—
578C2×Q16—944no—
579C2×SD16—24no—
580C2×SD16—42no—
581C2×SD16—478no—
582C2×SD16—474no—
583C2×SD16—474no—
584C2×SD16—474no—
585C2×SD16—944no—
586C2×SD16—1882no—
587C2×SD16C22×D4714yes—
588C2×SD16C22×D4714yes—
589C2×D8—474no—
590C2×D8—474no—
591C2×D8—944no—
592C2×D8—944no—
593C2×M16—474no—
594C2×M16—474no—
595C2×M16—944no—
596C2×M16—944no—
597C22×C8—471no—
598C22×C8—471no—
599C22×C8C22×D4711yescharacteristic
600C22×C8C22×D4711yescharacteristic
601#124—474no—
602#124—474no—
603#124—942no—
604#124—942no—
605#124—948no—
606#123—948no—
607C22⋊Q8—474no—
608C22⋊Q8—474no—
609C22⋊Q8—942no—
610C22⋊Q8—948no—
611C22⋊Q8—942no—
612#121—22no—
613#121—474no—
614#121—948no—
615#121—948no—
616#121—942no—
617#121C22×D4714yes—
618#120—948no—
619C4×Q8—474no—
620C4×Q8—942no—
621C4×D4—474no—
622C4×D4—474no—
623C4×D4—474no—
624C4×D4—942no—
625C4×D4—948no—
626C2×C4⋊C4—471no—
627C2×C4⋊C4—471no—
628C2×C4⋊C4—941no—
629C2×C4⋊C4—941no—
630C2×C4⋊C4—941no—
631C2×C4⋊C4C22×D4711yescharacteristic
632C2×C22⋊C4—21no—
633C2×C22⋊C4—471no—
634C2×C22⋊C4—471no—
635C2×C22⋊C4—948no—
636C2×C22⋊C4—941no—
637C2×C22⋊C4—941no—
638C2×C22⋊C4—941no—
639C2×C22⋊C4—941no—
640C2×C22⋊C4—941no—
641C2×C22⋊C4—941no—
642C2×C22⋊C4—941no—
643C2×C22⋊C4—941no—
644C2×C42—471no—
645C2×C42—941no—
646#106—474no—
647C4⋊C8—474no—
648#103—474no—
649#103C22×D4714yescomplemented
650#103C22×D4714yescomplemented
651#102—474no—
652#102—474no—
653#102—474no—
654C22⋊C8—474no—
655C22⋊C8C22×D4714yescomplemented
656C4×C8—474no—
657C24—21no—
658C24—471no—
659C24—944no—
660C24—941no—
661C24—941no—
662C24—3762no—
663C24—1884no—
664C24—1884no—
665C24D4×D4711yescharacteristic
666#41—948no—
667#41—948no—
668#41—1884no—
669#41—1888no—
670#41—1884no—
671#41—1888no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—24no—
675C2×Q8—22no—
676C2×Q8—28no—
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—48no—
682C2×Q8—472no—
683C2×Q8—941no—
684C2×Q8—942no—
685C2×Q8—942no—
686C2×Q8D4×D4714yes—
687C2×Q8C23×D4712yes—
688C2×Q8C23×D4712yes—
689C2×D4—24no—
690C2×D4—22no—
691C2×D4—21no—
692C2×D4—22no—
693C2×D4—82no—
694C2×D4—474no—
695C2×D4—474no—
696C2×D4—472no—
697C2×D4—472no—
698C2×D4—944no—
699C2×D4—944no—
700C2×D4—948no—
701C2×D4—944no—
702C2×D4—944no—
703C2×D4—941no—
704C2×D4—942no—
705C2×D4—941no—
706C2×D4—942no—
707C2×D4—942no—
708C2×D4—1884no—
709C2×D4—1884no—
710C2×D4—1888no—
711C2×D4—1882no—
712C2×D4—1884no—
713C2×D4—1884no—
714C2×D4—1884no—
715C2×D4C23×D4712yes—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—24no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—44no—
723C22×C4—471no—
724C22×C4—471no—
725C22×C4—471no—
726C22×C4—472no—
727C22×C4—472no—
728C22×C4—944no—
729C22×C4—944no—
730C22×C4—942no—
731C22×C4—942no—
732C22×C4—941no—
733C22×C4—941no—
734C22×C4—944no—
735C22×C4—3762no—
736C22×C4—1884no—
737C22×C4—1884no—
738C22×C4D4×D4712yes—
739C22×C4D4×D4711yescharacteristic
740C22×C4C23×D4712yes—
741C22×C4C23×D4711yescharacteristic
742Q16—948no—
743Q16—948no—
744SD16—28no—
745SD16—44no—
746SD16—4716no—
747SD16—948no—
748SD16—1884no—
749D8—948no—
750D8—948no—
751M16—948no—
752M16—948no—
753C2×C8—22no—
754C2×C8—22no—
755C2×C8—474no—
756C2×C8—472no—
757C2×C8—472no—
758C2×C8—942no—
759C2×C8C23×D4712yes—
760C2×C8C23×D4712yes—
761C4⋊C4—21no—
762C4⋊C4—474no—
763C4⋊C4—472no—
764C4⋊C4—944no—
765C4⋊C4—944no—
766C4⋊C4—944no—
767C4⋊C4—941no—
768C4⋊C4C23×D4712yes—
769C22⋊C4—24no—
770C22⋊C4—474no—
771C22⋊C4—474no—
772C22⋊C4—944no—
773C22⋊C4—944no—
774C22⋊C4—944no—
775C22⋊C4—944no—
776C22⋊C4—944no—
777C22⋊C4—944no—
778C22⋊C4—944no—
779C22⋊C4—944no—
780C42—472no—
781C42—472no—
782C42—944no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—472no—
791C23—942no—
792C23—944no—
793C23—942no—
794C23—942no—
795C23—942no—
796C23—942no—
797C23—3764no—
798C23—37616no—
799C23—1888no—
800C23—1888no—
801C23—1882no—
802C23—1882no—
803C23—1882no—
804C23—1882no—
805C23—1882no—
806C23C2×D4×D4712yes—
807C23C2×D4×D4711yescharacteristic
808Q8—24no—
809Q8—22no—
810Q8—22no—
811Q8—22no—
812Q8—48no—
813Q8—42no—
814Q8—942no—
815Q8—942no—
816Q8—1882no—
817Q8C2×D4×D4714yes—
818D4—22no—
819D4—22no—
820D4—42no—
821D4—84no—
822D4—474no—
823D4—944no—
824D4—942no—
825D4—942no—
826D4—942no—
827D4—1888no—
828D4—1884no—
829D4—1888no—
830D4—1888no—
831D4—1888no—
832D4—1882no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—48no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—472no—
845C2×C4—472no—
846C2×C4—472no—
847C2×C4—942no—
848C2×C4—942no—
849C2×C4—942no—
850C2×C4—944no—
851C2×C4—942no—
852C2×C4—942no—
853C2×C4—942no—
854C2×C4—942no—
855C2×C4—3764no—
856C2×C4—1888no—
857C2×C4—1888no—
858C2×C4—1882no—
859C2×C4—1882no—
860C2×C4C2×D4×D4712yes—
861C2×C4C2×D4×D4711yescharacteristic
862C2×C4C2×D4×D4712yes—
863C2×C4#1309406912yes—
864C2×C4C24×D4711yescharacteristic
865C8—22no—
866C8—22no—
867C8—474no—
868C8—942no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—44no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—84no—
877C22—942no—
878C22—944no—
879C22—942no—
880C22—942no—
881C22—37616no—
882C22—3764no—
883C22—1882no—
884C22—1882no—
885C22—1882no—
886C22—1884no—
887C22—1888no—
888C22—1882no—
889C22—1882no—
890C22#1568975512yes—
891C22#1568992212yes—
892C22#1568992912yes—
893C22C22×D4×D4711yescharacteristic
894C4—22no—
895C4—24no—
896C4—42no—
897C4—42no—
898C4—942no—
899C4—942no—
900C4—942no—
901C4—1882no—
902C4—1882no—
903C4#1568975512yes—
904C4C22×D4×D4711yescharacteristic
905C4C2×#1309406911yescharacteristic
906C2—42no—
907C2—82no—
908C2—3762no—
909C2—1882no—
910C2—1884no—
911C2#2025502214yesdirect product factor
912C2C2×#1568975511yescharacteristic
913C2C2×#1568992211yescharacteristic
914C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#448C2
socleC23×C47C22×D4
hypercenterC2×#448D47
hypocenterC47C2×#3275
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C22×#13094055C2semidirect
2. C22×#13094051C2semidirect
3. C2×#15689784C2semidirect
4. C2×#15689770C2semidirect
5. #20255022C2direct (N × H)
6. C2×#15689504C2semidirect
7. C2×#15689380C2semidirect
8. C2×#15689374C2semidirect
9. C2×#15689343C2semidirect
10. C2×#15689341C2semidirect
11. C2×#15689288C2semidirect
12. C2×#15689270C2semidirect
13. C2×#15689272C2semidirect
14. C2×#15689208C2semidirect
15. C2×#15689198C2semidirect
16. C2×C47×#448C2semidirect
21. C2×#13094055C22semidirect
23. C2×#13094051C22semidirect
24. C22×#10625337C22semidirect
25. C22×#10625337C22semidirect
26. C22×#10625325C22semidirect
31. C22×#10625329C22semidirect
34. #15689784C22semidirect
36. #15689770C22semidirect
38. C2×#13094013C22semidirect
45. C2×#13093998C22semidirect
48. C2×Q8×Dic47C22semidirect
53. #15689504C22semidirect
54. #15689380C22semidirect
55. #15689374C22semidirect
56. #15689343C22semidirect
57. #15689341C22semidirect
58. #15689288C22semidirect
59. #15689272C22semidirect
60. #15689270C22semidirect
61. #15689208C22semidirect
62. #15689198C22semidirect
63. C2×#13093955C22semidirect
64. C2×Dic47⋊C8C22semidirect
65. C2×#13093949C22semidirect
68. C2×#13093944C22semidirect
70. C2×C8×Dic47C22semidirect
71. C23×Q8×C47C22semidirect
75. C47×#448C22semidirect
76. C2×#103×C47C22semidirect
77. C2×#103×C47C22semidirect
78. C2×C22⋊C8×C47C22semidirect
108. C2×#10625337C23semidirect
109. C2×#10625337C23semidirect
111. C2×#10625325C23semidirect
113. C2×#10625336D4semidirect
121. C2×#10625329C23semidirect
128. #13094013C23semidirect
139. #13093998C23semidirect
143. Q8×Dic47C23semidirect
167. #13093955C23semidirect
168. Dic47⋊C8C23semidirect
169. #13093949C23semidirect
172. #13093944C23semidirect
174. C8×Dic47C23semidirect
181. C22×Q8×C47C23semidirect
196. #103×C47C23semidirect
197. #103×C47C23semidirect
198. C22⋊C8×C47C23semidirect
299. #10625336C2×D4semidirect
461. C2×#448D47semidirect
467. C2×C47#3275semidirect
476. C23×Q8C2×D47semidirect
522. #448C2×D47semidirect
528. C2×#103C2×D47semidirect
529. C2×#103C2×D47semidirect
534. C2×C22⋊C8C2×D47semidirect
536. C47C2×#3275semidirect
553. C22×Q8C22×D47semidirect
649. #103C22×D47semidirect
650. #103C22×D47semidirect
655. C22⋊C8C22×D47semidirect
911. C2#20255022direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940552
C22×#130940512
C2×#156897842
C2×#156897702
#202550222
C2×#156895042
C2×#156893802
C2×#156893742
C2×#156893432
C2×#156893412
C2×#156892882
C2×#156892702
C2×#156892722
C2×#156892082
C2×#156891982
C2×C47×#4482
C2×#327547