Finite Group Databasebeta

← C2×#20252607 #27082616

Subgroups — C2×#20252607 #27082616

Order 12032.

5130 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10625352C211yesmaximal, characteristic, complemented
2C22×#13094045C212yesmaximal, complemented
3C2×#15689636C211yesmaximal, characteristic, complemented
4#20252607C2116yesmaximal, direct product factor
5C2×#15689282C212yesmaximal, complemented
6C2×#15689269C212yesmaximal, complemented
7C2×#15689278C211yesmaximal, characteristic, complemented
8C2×#15689264C211yesmaximal, characteristic, complemented
9C2×#15689257C211yesmaximal, characteristic, complemented
10C2×#15689116C212yesmaximal, complemented
11C2×C22⋊C8×D47C211yesmaximal, characteristic, complemented
12C2×C47×#450C211yesmaximal, characteristic, complemented
13C22×#10625354C2211yescharacteristic, complemented
14C22×#10625352—216no—
15C22×#10625352—21no—
16C22×#10625352—21no—
17C22×#10625352—24no—
18C22×#10625352C2212yes—
19C22×#10625352C2212yes—
20C22×#10625352C2218yescomplemented
21C23×Dic94C2211yescharacteristic
22C23×C22⋊D47—21no—
23C24×Dic47—21no—
24C23×C4×D47C2211yescharacteristic
25C2×#13094045—216no—
26C2×#13094045C22116yescomplemented
27C22×#10625337C2212yescomplemented
28C22×#10625325C2212yescomplemented
29C22×#10625334C2212yescomplemented
30C22×C8×D47C2212yescomplemented
31#15689636—24no—
32#15689636C2218yescomplemented
33C2×#13094009—21no—
34C2×#13094000C2211yescharacteristic, complemented
35C2×#13093999C2211yescharacteristic, complemented
36C2×#13093998C2211yescharacteristic
37C2×#13093994—21no—
38C2×#13093986—21no—
39C2×(C22⋊D47)⋊C4—21no—
40C2×#13093982C2211yescharacteristic, complemented
41#15689282C22116yescomplemented
42#15689278C2218yescomplemented
43#15689269C22116yescomplemented
44#15689264C2218yescomplemented
45#15689257C2218yescomplemented
46#15689116C22116yescomplemented
47C2×#13093949C2212yescomplemented
48C2×#13093947C2212yescomplemented
49C2×#13093945C2212yescomplemented
50C2×C22⋊(C47⋊C8)C2211yescharacteristic
51C2×(C2×D47)⋊C8C2212yescomplemented
52C22⋊C8×D47C2218yescomplemented
53C23×D4×C47C2211yescharacteristic
54C22×SD16×C47C2212yescomplemented
55C2×C22⋊Q8×C47C2211yescharacteristic
56C47×#450C2218yescomplemented
57C2×#102×C47C2212yescomplemented
58C2×C22⋊C8×C47C2211yescharacteristic
59C24×D47D411yescharacteristic
60C2×#10625354—22no—
61C2×#10625354—28no—
62C2×#10625354C2314yescomplemented
63C2×#10625352—216no—
64C2×#10625352—216no—
65C2×#10625352—264no—
66C2×#10625352—28no—
67C2×#10625352—264no—
68C2×#10625352—24no—
69C2×#10625352—24no—
70C2×#10625352—28no—
71C2×#10625352—28no—
72C2×#10625352—28no—
73C2×#10625352—28no—
74C2×#10625352D4116yescomplemented
75C2×#10625352C2318yes—
76C2×#10625352C2318yes—
77C22×Dic94—21no—
78C22×Dic94—22no—
79C22×Dic94—28no—
80C22×Dic94C2314yes—
81C22×Dic94C2312yes—
82C22×D188—21no—
83C22×D188—21no—
84C22×D188C2311yescharacteristic
85C22×C22⋊D47—216no—
86C22×C22⋊D47—22no—
87C22×C22⋊D47—22no—
88C22×C22⋊D47—28no—
89C22×C22⋊D47—21no—
90C23×Dic47—216no—
91C23×Dic47—21no—
92C23×Dic47—22no—
93C23×Dic47—22no—
94C23×Dic47—28no—
95C23×Dic47D411yescharacteristic
96C22×C4×D47—28no—
97C22×C4×D47—21no—
98C22×C4×D47D411yescharacteristic
99C22×C4×D47D411yescharacteristic
100C22×C4×D47D414yes—
101C22×C4×D47C2314yes—
102C22×C4×D47C2311yescharacteristic
103C22×C4×D47C2311yescharacteristic
104#13094045—264no—
105C2×#10625337—28no—
106C2×#10625337C2318yescomplemented
107C2×#10625325—28no—
108C2×#10625325C2318yescomplemented
109C2×#10625334—28no—
110C2×#10625334C2318yescomplemented
111C22×C47⋊C8C2312yes—
112C2×C8×D47—28no—
113C2×C8×D47C2318yescomplemented
114#13094009—28no—
115#13094000—22no—
116#13094000C2314yescomplemented
117#13093999—22no—
118#13093999C2314yescomplemented
119#13093998—22no—
120#13093998C2314yes—
121#13093994—28no—
122#13093986—28no—
123(C22⋊D47)⋊C4—28no—
124#13093982—22no—
125#13093982C2314yescomplemented
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×(C2×D47)⋊C4—21no—
129C2×(C2×D47)⋊C4—21no—
130C2×(C2×D47)⋊C4—21no—
131C2×(C2×D47)⋊C4—21no—
132C2×C4×Dic47—21no—
133#13093949C2318yescomplemented
134#13093947C2318yescomplemented
135#13093945C2318yescomplemented
136C22⋊(C47⋊C8)C2314yes—
137(C2×D47)⋊C8C2318yescomplemented
138C25×C47—21no—
139C22×Q8×C47C2311yescharacteristic
140C22×D4×C47—28no—
141C22×D4×C47—21no—
142C22×D4×C47—22no—
143C22×D4×C47C2314yes—
144C22×D4×C47C2312yes—
145C23×C4×C47C2311yescharacteristic
146C2×SD16×C47—28no—
147C2×SD16×C47C2318yescomplemented
148C22×C8×C47C2312yes—
149C22⋊Q8×C47—22no—
150C22⋊Q8×C47C2314yes—
151C2×C4⋊C4×C47—21no—
152C2×C4⋊C4×C47C2311yescharacteristic
153C2×C22⋊C4×C47—21no—
154#102×C47C2318yescomplemented
155C22⋊C8×C47C2314yes—
156C24×C47—28no—
157C24×C47—24no—
158C24×C47—22no—
159C24×C47—44no—
160C24×C47—44no—
161C24×C47C2×D411yescharacteristic
162C23×D47—24no—
163C23×D47—24no—
164C23×D47—21no—
165C23×D47—42no—
166C23×D47C2×D411yescharacteristic
167C23×D47C2×D414yes—
168C23×D47C2×D411yescharacteristic
169C2×Q8×C47—21no—
170C2×Q8×C47—24no—
171C2×Q8×C47C2412yes—
172C2×D4×C47—28no—
173C2×D4×C47—216no—
174C2×D4×C47—216no—
175C2×D4×C47—24no—
176C2×D4×C47—22no—
177C2×D4×C47—24no—
178C2×D4×C47C2×D418yes—
179C2×D4×C47C2414yes—
180C22×C4×C47—24no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D412yes—
185C22×C4×C47C2412yes—
186C22×C4×C47C2411yescharacteristic
187C2×C22⋊D47—264no—
188C2×C22⋊D47—216no—
189C2×C22⋊D47—216no—
190C2×C22⋊D47—28no—
191C2×C22⋊D47—28no—
192C2×C22⋊D47—24no—
193C2×C22⋊D47—44no—
194C22×Dic47—28no—
195C22×Dic47—264no—
196C22×Dic47—216no—
197C22×Dic47—24no—
198C22×Dic47—22no—
199C22×Dic47—24no—
200C22×Dic47—216no—
201C22×Dic47—28no—
202C22×Dic47—28no—
203C22×Dic47—21no—
204C22×Dic47C2×D411yescharacteristic
205C22×Dic47C2×D414yes—
206C22×Dic47C2×D411yescharacteristic
207#10625354—216no—
208#10625354—48no—
209#10625352—264no—
210#10625352—264no—
211#10625352—232no—
212#10625352—216no—
213#10625352—232no—
214#10625352—216no—
215#10625352—216no—
216#10625352C2×D4132yescomplemented
217C2×D188—24no—
218C2×D188—24no—
219C2×D188—24no—
220C2×D188—21no—
221C2×D188—44no—
222C2×D188—44no—
223C2×D188C2412yes—
224C2×C4×D47—24no—
225C2×C4×D47—24no—
226C2×C4×D47—24no—
227C2×C4×D47—216no—
228C2×C4×D47—216no—
229C2×C4×D47—24no—
230C2×C4×D47—44no—
231C2×C4×D47C2×D414yes—
232C2×C4×D47C2×D412yes—
233C2×C4×D47C2×D414yes—
234C2×C4×D47C2×D412yes—
235C2×C4×D47C2×D418yes—
236C2×C4×D47C2412yes—
237C2×C4×D47C2412yes—
238C2×Dic94—28no—
239C2×Dic94—216no—
240C2×Dic94—24no—
241C2×Dic94—22no—
242C2×Dic94—24no—
243C2×Dic94—216no—
244C2×Dic94C2×D418yes—
245C2×Dic94C2414yes—
246SD16×C47—216no—
247C2×C8×C47—24no—
248C2×C8×C47C2414yes—
249C4⋊C4×C47—24no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47C2412yes—
252C22⋊C4×C47—24no—
253#10625337—216no—
254#10625334—216no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4—24no—
257(C2×D47)⋊C4—24no—
258(C2×D47)⋊C4—24no—
259C4⋊Dic47—21no—
260C4⋊Dic47C2412yes—
261Dic47⋊C4—24no—
262C4×Dic47—24no—
263C2×C47⋊C8—24no—
264C2×C47⋊C8C2414yes—
265#10625325—216no—
266C8×D47—216no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—216no—
270C23×C47—28no—
271C23×C47—24no—
272C23×C47—432no—
273C23×C47—48no—
274C23×C47—44no—
275C23×C47—48no—
276C23×C47—44no—
277C23×C47#13514yescomplemented
278C23×C47C22×D412yes—
279C23×C47C22×D411yescharacteristic
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—28no—
285C22×D47—22no—
286C22×D47—28no—
287C22×D47—22no—
288C22×D47—44no—
289C22×D47—416no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47—42no—
293C22×D47#12014yes—
294C22×D47C22×D412yes—
295C22×D47C22×D412yes—
296Q8×C47—24no—
297Q8×C47—42no—
298D4×C47—216no—
299D4×C47—28no—
300D4×C47—24no—
301D4×C47C22×D418yes—
302C2×C4×C47—22no—
303C2×C4×C47—24no—
304C2×C4×C47—24no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—42no—
308C2×C4×C47—42no—
309C2×C4×C47C22×D412yes—
310C2×C4×C47C22×D411yescharacteristic
311C2×C4×C47C22×D414yes—
312C2×C4×C47C2511yescharacteristic
313C22⋊D47—232no—
314C22⋊D47—232no—
315C22⋊D47—48no—
316C2×Dic47—216no—
317C2×Dic47—232no—
318C2×Dic47—28no—
319C2×Dic47—22no—
320C2×Dic47—24no—
321C2×Dic47—28no—
322C2×Dic47—232no—
323C2×Dic47—22no—
324C2×Dic47—42no—
325C2×Dic47#12014yes—
326C2×Dic47C22×D412yes—
327C2×Dic47C22×D412yes—
328D188—24no—
329D188—48no—
330D188—48no—
331D188—42no—
332C4×D47—28no—
333C4×D47—24no—
334C4×D47—24no—
335C4×D47—28no—
336C4×D47—48no—
337C4×D47#12018yes—
338C4×D47C22×D418yes—
339Dic94—216no—
340Dic94—28no—
341Dic94—24no—
342Dic94C22×D418yes—
343C8×C47—24no—
344C47⋊C8—24no—
345C2×#3002—471nomaximal, Sylow
346C22×C47—22no—
347C22×C47—28no—
348C22×C47—22no—
349C22×C47—28no—
350C22×C47—432no—
351C22×C47—416no—
352C22×C47—44no—
353C22×C47—44no—
354C22×C47C2×#12012yes—
355C22×C47C2×#13512yes—
356C22×C47C2×#13514yescomplemented
357C22×C47#57512yes—
358C22×C47C23×D411yescharacteristic
359C2×D47—28no—
360C2×D47—22no—
361C2×D47—22no—
362C2×D47—22no—
363C2×D47—22no—
364C2×D47—22no—
365C2×D47—416no—
366C2×D47—44no—
367C2×D47—42no—
368C2×D47—42no—
369C2×D47—42no—
370C2×D47—84no—
371C2×D47C2×#12014yes—
372C4×C47—22no—
373C4×C47—42no—
374C4×C47—42no—
375C4×C47C2×#12012yes—
376C4×C47C23×D412yes—
377Dic47—28no—
378Dic47—22no—
379Dic47—42no—
380Dic47C2×#12014yes—
381C23×#41—471no—
382C22×#135—472no—
383C2×#525—471no—
384#3002—4716no—
385C2×#452—472no—
386C2×#449—472no—
387C2×#451—471no—
388C2×#448—471no—
389C2×#450D4711yescharacteristic, complemented
390C2×#447—471no—
391C2×#416—472no—
392C22×C22⋊C8—471no—
393C2×C47—24no—
394C2×C47—48no—
395C2×C47#300214yescomplemented
396C2×C47C22×#12011yescharacteristic
397C2×C47C22×#13511yescharacteristic
398C2×C47C2×#57511yescharacteristic
399D47—24no—
400D47—42no—
401D47—82no—
402C22×#41—471no—
403C22×#41—472no—
404C22×#41—472no—
405C22×#41—478no—
406C22×#41—941no—
407C22×#41—941no—
408C22×#41—944no—
409C22×#41—9416no—
410C23×Q8—471no—
411C23×D4—941no—
412C23×D4C2×D4711yescharacteristic
413C24×C4—471no—
414C24×C4—941no—
415C2×#135—4716no—
416C2×#135—9416no—
417C22×Q16—472no—
418C22×SD16—472no—
419C22×SD16C2×D4712yescomplemented
420C22×D8—472no—
421C23×C8—472no—
422#525—478no—
423#525—944no—
424C2×#123—941no—
425C2×C22⋊Q8—471no—
426C2×C22⋊Q8C2×D4711yescharacteristic
427C2×#121—471no—
428C2×#121—471no—
429C2×#120—941no—
430C2×C4×D4—941no—
431C2×C4×D4—941no—
432C2×#117—471no—
433#452—4716no—
434#451—478no—
435#450C2×D4718yescomplemented
436#449—4716no—
437#448—478no—
438#447—478no—
439#416—4716no—
440C2×#103—472no—
441C2×#103—472no—
442C2×#102—472no—
443C2×#102C2×D4712yescomplemented
444C2×C22⋊C8—471no—
445C2×C22⋊C8—472no—
446C2×C22⋊C8—478no—
447C2×C22⋊C8C2×D4711yescharacteristic
448C47C2×#300211yescharacteristic, complemented, Sylow
449C25—21no—
450C25—471no—
451C2×#41—474no—
452C2×#41—4716no—
453C2×#41—478no—
454C2×#41—478no—
455C2×#41—944no—
456C2×#41—948no—
457C2×#41—948no—
458C2×#41—944no—
459C2×#41—948no—
460C2×#41—942no—
461C2×#41—948no—
462C2×#41—948no—
463C2×#41—9464no—
464C2×#41—9416no—
465C2×#41—9464no—
466C2×#41—9416no—
467C2×#41—948no—
468C22×Q8—472no—
469C22×Q8—474no—
470C22×Q8—948no—
471C22×Q8—942no—
472C22×Q8—941no—
473C22×Q8C22×D4711yescharacteristic
474C22×D4—28no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—471no—
478C22×D4—941no—
479C22×D4—941no—
480C22×D4—948no—
481C22×D4—942no—
482C22×D4—942no—
483C22×D4—9416no—
484C22×D4—941no—
485C22×D4C22×D4714yes—
486C22×D4C22×D4712yes—
487C23×C4—471no—
488C23×C4—471no—
489C23×C4—471no—
490C23×C4—471no—
491C23×C4—474no—
492C23×C4—471no—
493C23×C4—474no—
494C23×C4—948no—
495C23×C4—941no—
496C23×C4—942no—
497C23×C4—948no—
498C23×C4—942no—
499C23×C4—9416no—
500C23×C4—941no—
501C23×C4C22×D4711yescharacteristic
502#135—9464no—
503C2×Q16—478no—
504C2×Q16—948no—
505C2×SD16—28no—
506C2×SD16—478no—
507C2×SD16—948no—
508C2×SD16C22×D4718yescomplemented
509C2×D8—478no—
510C2×D8—948no—
511C22×C8—472no—
512C22×C8—478no—
513C22×C8—948no—
514C22×C8C22×D4712yes—
515#123—948no—
516C22⋊Q8—22no—
517C22⋊Q8—474no—
518C22⋊Q8—942no—
519C22⋊Q8C22×D4714yes—
520#121—474no—
521#121—474no—
522#121—942no—
523#121—942no—
524#120—948no—
525C4×D4—948no—
526C4×D4—948no—
527#117—474no—
528#117—942no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—471no—
531C2×C4⋊C4—941no—
532C2×C4⋊C4C22×D4711yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—941no—
535C2×C22⋊C4—941no—
536C2×C22⋊C4—941no—
537C2×C22⋊C4—941no—
538C2×C42—941no—
539#103—478no—
540#103—478no—
541#102—478no—
542#102C22×D4718yescomplemented
543C22⋊C8—474no—
544C22⋊C8—478no—
545C22⋊C8C22×D4714yes—
546C24—28no—
547C24—24no—
548C24—22no—
549C24—44no—
550C24—44no—
551C24—471no—
552C24—471no—
553C24—474no—
554C24—944no—
555C24—944no—
556C24—941no—
557C24—1882no—
558C24D4×D4711yescharacteristic
559#41—4732no—
560#41—9432no—
561#41—9416no—
562#41—9416no—
563#41—9416no—
564#41—9464no—
565#41—9464no—
566#41—9432no—
567#41—9416no—
568#41—1888no—
569C2×Q8—21no—
570C2×Q8—24no—
571C2×Q8—478no—
572C2×Q8—474no—
573C2×Q8—9416no—
574C2×Q8—948no—
575C2×Q8—9416no—
576C2×Q8—944no—
577C2×Q8—944no—
578C2×Q8—942no—
579C2×Q8C23×D4712yes—
580C2×D4—28no—
581C2×D4—216no—
582C2×D4—216no—
583C2×D4—24no—
584C2×D4—22no—
585C2×D4—24no—
586C2×D4—472no—
587C2×D4—944no—
588C2×D4—944no—
589C2×D4—9416no—
590C2×D4—948no—
591C2×D4—948no—
592C2×D4—9464no—
593C2×D4—9416no—
594C2×D4—944no—
595C2×D4—944no—
596C2×D4—941no—
597C2×D4—1884no—
598C2×D4—1884no—
599C2×D4—1884no—
600C2×D4D4×D4718yes—
601C2×D4C23×D4714yes—
602C22×C4—24no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—471no—
606C22×C4—472no—
607C22×C4—478no—
608C22×C4—472no—
609C22×C4—474no—
610C22×C4—471no—
611C22×C4—474no—
612C22×C4—472no—
613C22×C4—474no—
614C22×C4—472no—
615C22×C4—944no—
616C22×C4—9416no—
617C22×C4—9416no—
618C22×C4—944no—
619C22×C4—944no—
620C22×C4—944no—
621C22×C4—9416no—
622C22×C4—948no—
623C22×C4—948no—
624C22×C4—948no—
625C22×C4—9464no—
626C22×C4—9416no—
627C22×C4—944no—
628C22×C4—942no—
629C22×C4—944no—
630C22×C4—941no—
631C22×C4—1884no—
632C22×C4D4×D4712yes—
633C22×C4D4×D4711yescharacteristic
634C22×C4C23×D4712yes—
635C22×C4C23×D4711yescharacteristic
636Q16—9416no—
637SD16—216no—
638SD16—9416no—
639D8—9416no—
640C2×C8—24no—
641C2×C8—474no—
642C2×C8—9416no—
643C2×C8—944no—
644C2×C8C23×D4714yes—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—472no—
648C4⋊C4—944no—
649C4⋊C4—941no—
650C4⋊C4C23×D4712yes—
651C22⋊C4—24no—
652C22⋊C4—944no—
653C22⋊C4—944no—
654C22⋊C4—944no—
655C22⋊C4—944no—
656C42—944no—
657C23—22no—
658C23—22no—
659C23—216no—
660C23—28no—
661C23—24no—
662C23—48no—
663C23—432no—
664C23—44no—
665C23—48no—
666C23—44no—
667C23—474no—
668C23—472no—
669C23—472no—
670C23—948no—
671C23—942no—
672C23—942no—
673C23—942no—
674C23—942no—
675C23—948no—
676C23—942no—
677C23—942no—
678C23—1884no—
679C23—18816no—
680C23—1882no—
681C23—1882no—
682C23—1882no—
683C23#1309404514yescomplemented
684C23C2×D4×D4712yes—
685C23C2×D4×D4711yescharacteristic
686Q8—24no—
687Q8—42no—
688Q8—478no—
689Q8—9416no—
690Q8—948no—
691Q8—944no—
692D4—216no—
693D4—28no—
694D4—24no—
695D4—9432no—
696D4—9432no—
697D4—944no—
698D4—1888no—
699D4—1888no—
700D4—1888no—
701D4—1882no—
702D4C2×D4×D4718yes—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—474no—
711C2×C4—472no—
712C2×C4—478no—
713C2×C4—478no—
714C2×C4—472no—
715C2×C4—948no—
716C2×C4—948no—
717C2×C4—948no—
718C2×C4—9432no—
719C2×C4—9416no—
720C2×C4—9432no—
721C2×C4—942no—
722C2×C4—948no—
723C2×C4—944no—
724C2×C4—944no—
725C2×C4—944no—
726C2×C4—942no—
727C2×C4—1888no—
728C2×C4—1882no—
729C2×C4C2×D4×D4712yes—
730C2×C4C2×D4×D4711yescharacteristic
731C2×C4C2×D4×D4714yes—
732C2×C4C24×D4711yescharacteristic
733C8—24no—
734C8—944no—
735C22—22no—
736C22—22no—
737C22—28no—
738C22—28no—
739C22—432no—
740C22—44no—
741C22—44no—
742C22—416no—
743C22—474no—
744C22—942no—
745C22—942no—
746C22—948no—
747C22—942no—
748C22—942no—
749C22—942no—
750C22—3764no—
751C22—18816no—
752C22—1882no—
753C22—1882no—
754C22—1882no—
755C22—1884no—
756C22#120×D4712yes—
757C22C2×#1309404512yes—
758C22C2×#1309404514yescomplemented
759C22#1568991912yes—
760C22C22×D4×D4711yescharacteristic
761C4—22no—
762C4—42no—
763C4—42no—
764C4—474no—
765C4—942no—
766C4—948no—
767C4—1882no—
768C4#120×D4712yes—
769C4C22×D4×D4712yes—
770C2—24no—
771C2—48no—
772C2—944no—
773C2—3762no—
774C2—1882no—
775C2#2025260714yesdirect product factor
776C2C2×#120×D4711yescharacteristic
777C2C22×#1309404511yescharacteristic
778C2C2×#1568991911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#450C2
socleC23×C47C22×D4
hypercenterC2×#450D47
hypocenterC47C2×#3002
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C23×#10625352C2semidirect
2. C22×#13094045C2semidirect
3. C2×#15689636C2semidirect
4. #20252607C2direct (N × H)
5. C2×#15689282C2semidirect
6. C2×#15689269C2semidirect
7. C2×#15689278C2semidirect
8. C2×#15689264C2semidirect
9. C2×#15689257C2semidirect
10. C2×#15689116C2semidirect
11. C2×C22⋊C8×D47C2semidirect
12. C2×C47×#450C2semidirect
13. C22×#10625354C22semidirect
20. C22×#10625352C22semidirect
26. C2×#13094045C22semidirect
27. C22×#10625337C22semidirect
28. C22×#10625325C22semidirect
29. C22×#10625334C22semidirect
30. C22×C8×D47C22semidirect
32. #15689636C22semidirect
34. C2×#13094000C22semidirect
35. C2×#13093999C22semidirect
40. C2×#13093982C22semidirect
41. #15689282C22semidirect
42. #15689278C22semidirect
43. #15689269C22semidirect
44. #15689264C22semidirect
45. #15689257C22semidirect
46. #15689116C22semidirect
47. C2×#13093949C22semidirect
48. C2×#13093947C22semidirect
49. C2×#13093945C22semidirect
51. C2×(C2×D47)⋊C8C22semidirect
52. C22⋊C8×D47C22semidirect
54. C22×SD16×C47C22semidirect
56. C47×#450C22semidirect
57. C2×#102×C47C22semidirect
62. C2×#10625354C23semidirect
74. C2×#10625352D4semidirect
106. C2×#10625337C23semidirect
108. C2×#10625325C23semidirect
110. C2×#10625334C23semidirect
113. C2×C8×D47C23semidirect
116. #13094000C23semidirect
118. #13093999C23semidirect
125. #13093982C23semidirect
133. #13093949C23semidirect
134. #13093947C23semidirect
135. #13093945C23semidirect
137. (C2×D47)⋊C8C23semidirect
147. C2×SD16×C47C23semidirect
154. #102×C47C23semidirect
216. #10625352C2×D4semidirect
277. C23×C47#135semidirect
356. C22×C47C2×#135semidirect
389. C2×#450D47semidirect
395. C2×C47#3002semidirect
419. C22×SD16C2×D47semidirect
435. #450C2×D47semidirect
443. C2×#102C2×D47semidirect
448. C47C2×#3002semidirect
508. C2×SD16C22×D47semidirect
542. #102C22×D47semidirect
683. C23#13094045semidirect
758. C22C2×#13094045semidirect
775. C2#20252607direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106253522
C22×#130940452
C2×#156896362
#202526072
C2×#156892822
C2×#156892692
C2×#156892782
C2×#156892642
C2×#156892572
C2×#156891162
C2×C22⋊C8×D472
C2×C47×#4502
C2×#300247