Finite Group Databasebeta

← #27081074

Subgroups — #27081074

Order 12032.

2242 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×D47C211yesmaximal, characteristic
2#20252449C212yesmaximal, complemented
3#20252446C212yesmaximal, complemented
4#20252444C211yesmaximal, characteristic, complemented
5#20252442C212yesmaximal, complemented
6#20252437C214yesmaximal, complemented
7#20252430C214yesmaximal, complemented
8#20252121C214yesmaximal, complemented
9D4×#10625324C214yesmaximal, complemented
10#20252022C212yesmaximal, complemented
11#20251830C212yesmaximal, complemented
12C2×#15689085C212yesmaximal, complemented
13C47×#2977C211yesmaximal, characteristic, complemented
14C2×#41×D47C2211yescharacteristic
15C23×C4×D47C2211yescharacteristic
16C22×#10625324C2214yes—
17C22×#10625324C2212yescomplemented
18C2×M16×D47C2212yescomplemented
19#15689636C412yes—
20#15689635C2211yescharacteristic
21#15689634C2211yescharacteristic
22#15689633C412yes—
23#15689632C2214yes—
24#15689631C412yes—
25#15689630C2211yescharacteristic
26#15689629C412yes—
27#123×D47C412yes—
28C22⋊Q8×D47C412yes—
29#121×D47C412yes—
30#120×D47C412yes—
31C4×D4×D47C2214yes—
32#117×D47C2211yescharacteristic
33#15689202C2214yescomplemented
34#15689200C2214yescomplemented
35#15689199C2214yescomplemented
36#15689198C2214yescomplemented
37#15689196C2214yescomplemented
38#15689195C2214yescomplemented
39#15689194C2214yescomplemented
40#15689194C2214yescomplemented
41#15689193C2214yescomplemented
42#15689191C2214yescomplemented
43#15689191C2214yescomplemented
44D4×C47⋊C8C2214yescomplemented
45C8×C22⋊D47C2214yescomplemented
46(C22⋊D47)⋊C8C2214yescomplemented
47#15689185C2212yescomplemented
48#15689184C2212yescomplemented
49#15689183C2214yescomplemented
50#15689182C2212yescomplemented
51#15689181C2214yescomplemented
52#15689145C2214yescomplemented
53#15689091C2212yescomplemented
54#15689090C2212yescomplemented
55#15689089C2212yescomplemented
56#15689088C2214yescomplemented
57#15689088C2214yescomplemented
58#15689085C2214yes—
59#15689085C2212yes—
60#15689085C2212yes—
61#15689085C2212yescomplemented
62#15689085C2212yescomplemented
63#15689085C2214yescomplemented
64#15689085C2214yescomplemented
65C2×C22⋊(C47⋊C8)C2212yescomplemented
66C2×(C2×D47)⋊C8C2214yescomplemented
67#15689075C2212yescomplemented
68C4×#10625324C2212yescomplemented
69C47×#525C2211yescharacteristic
70C47×#435C2214yescomplemented
71C8×D4×C47C2214yescomplemented
72C47×#433C2212yescomplemented
73C47×#408C2212yescomplemented
74C2×C22⋊C8×C47C2212yescomplemented
75C24×D47C2×C411yescharacteristic
76C2×#10625354C2×C411yescharacteristic
77C2×#10625350C2311yescharacteristic
78C2×#10625350C2312yes—
79C2×#10625352C2×C412yes—
80C2×#10625352C2×C411yescharacteristic
81#41×D47—44no—
82C2×Q8×D47C2×C411yescharacteristic
83C2×D4×D47C2×C414yes—
84C2×D4×D47C2×C412yes—
85C2×D4×D47C2×C411yescharacteristic
86C23×Dic47C2×C411yescharacteristic
87C22×C4×D47—44no—
88C22×C4×D47C2×C412yes—
89C22×C4×D47C2×C411yescharacteristic
90C22×C4×D47C2×C411yescharacteristic
91C22×C4×D47C2×C412yes—
92C22×C4×D47C2311yescharacteristic
93C22×C4×D47C2312yes—
94C22×C4×D47C2312yes—
95C22×C4×D47C2312yes—
96C22×C4×D47C2311yescharacteristic
97C2×#10625329C2312yescomplemented
98C2×#10625324—48no—
99C2×#10625324—44no—
100C2×#10625324C2314yes—
101C2×#10625324C2314yes—
102C2×#10625324C2314yes—
103C2×#10625324C2314yes—
104C2×#10625324C2314yescomplemented
105M16×D47—44no—
106C22×C47⋊C8C2314yes—
107C22×C47⋊C8C2312yescomplemented
108C2×C8×D47C2314yescomplemented
109#13094009C2×C414yes—
110#13094008C2×C412yes—
111#13094007C2×C412yes—
112#13094006C2×C414yes—
113#13094005C2×C412yes—
114#13094004C2×C412yes—
115#13094003C2×C412yes—
116#13094002C2×C414yes—
117#13094001C2×C414yes—
118#13094000C2×C412yes—
119#13093999C2×C412yes—
120#13093998C2×C412yes—
121#13093997C2×C414yes—
122#13093996C2×C414yes—
123#13093995C2×C412yes—
124#13093994C2×C412yes—
125#13093994C2×C414yes—
126#13093993C2×C412yes—
127#13093992C2×C412yes—
128#13093992C2×C414yes—
129C4×D188C2314yes—
130D4×Dic47C2×C414yes—
131#13093986C2×C414yes—
132C4×C22⋊D47C2314yes—
133C4×C22⋊D47C2314yes—
134(C22⋊D47)⋊C4C2×C414yes—
135(C22⋊D47)⋊C4C2×C414yes—
136#13093983C2311yescharacteristic
137#13093982C2×C412yes—
138#13093981C2312yes—
139#13093980C2×C412yes—
140C4⋊C4×D47C2×C412yes—
141C4⋊C4×D47C2×C414yes—
142C22⋊C4×D47C2×C412yes—
143C22⋊C4×D47C2×C414yes—
144C22⋊C4×D47C2×C414yes—
145C42×D47C2312yes—
146C4⋊(C47⋊C8)C2314yescomplemented
147Dic47⋊C8C2314yescomplemented
148Dic47⋊C8C2314yescomplemented
149C22⋊(C47⋊C8)C2314yes—
150C22⋊(C47⋊C8)C2312yes—
151C22⋊(C47⋊C8)C2312yes—
152C22⋊(C47⋊C8)C2314yescomplemented
153(C2×D47)⋊C8C2314yes—
154(C2×D47)⋊C8C2314yes—
155(C2×D47)⋊C8C2314yes—
156(C2×D47)⋊C8C2314yes—
157(C2×D47)⋊C8C2314yescomplemented
158(C2×D47)⋊C8C2314yescomplemented
159#13093935C2312yescomplemented
160#13093934C2314yescomplemented
161C4×C47⋊C8C2312yescomplemented
162C8×Dic47C2314yescomplemented
163C2×#41×C47C2311yescharacteristic
164C23×C4×C47C2311yescharacteristic
165C2×M16×C47C2312yescomplemented
166C22×C8×C47C2314yes—
167C22×C8×C47C2312yescomplemented
168#123×C47C2×C412yes—
169C22⋊Q8×C47C2×C412yes—
170#121×C47C2×C412yes—
171#120×C47C2×C412yes—
172C4×D4×C47C2314yes—
173#117×C47C2311yescharacteristic
174C4⋊C8×C47C2314yescomplemented
175C22⋊C8×C47C2314yes—
176C22⋊C8×C47C2312yes—
177C22⋊C8×C47C2312yes—
178C22⋊C8×C47C2314yescomplemented
179#97×C47C2312yescomplemented
180C4×C8×C47C2312yescomplemented
181C24×C47C22×C411yescharacteristic
182C23×D47—42no—
183C23×D47—44no—
184C23×D47C22×C412yes—
185C23×D47C22×C411yescharacteristic
186C23×D47C22×C412yes—
187C23×D47C22×C412yes—
188C23×D47C22×C411yescharacteristic
189#41×C47—42no—
190C2×Q8×C47C22×C411yescharacteristic
191C2×D4×C47C22×C414yes—
192C2×D4×C47C22×C412yes—
193C2×D4×C47C22×C411yescharacteristic
194C22×C4×C47—42no—
195C22×C4×C47C22×C412yes—
196C22×C4×C47C22×C411yescharacteristic
197C22×C4×C47C2411yescharacteristic
198C22×C4×C47C2412yes—
199C22×C4×C47C2412yes—
200C2×C22⋊D47C22×C414yes—
201C2×C22⋊D47C22×C414yes—
202C2×C22⋊D47C22×C412yes—
203C2×C22⋊D47C22×C412yes—
204C2×C22⋊D47C22×C412yes—
205C22×Dic47—42no—
206C22×Dic47C22×C411yescharacteristic
207C22×Dic47C22×C412yes—
208C22×Dic47C22×C412yes—
209C22×Dic47C22×C412yes—
210C22×Dic47C22×C411yescharacteristic
211#10625354—42no—
212Q8×D47—42no—
213#10625352—42no—
214#10625352—44no—
215D4×D47—42no—
216D4×D47—44no—
217D4×D47—48no—
218#10625350—42no—
219#10625350—42no—
220#10625350—42no—
221C2×D188C22×C414yes—
222C2×D188C22×C412yes—
223C2×D188C22×C411yescharacteristic
224C2×C4×D47—24no—
225C2×C4×D47—28no—
226C2×C4×D47—24no—
227C2×C4×D47—24no—
228C2×C4×D47—42no—
229C2×C4×D47—44no—
230C2×C4×D47—42no—
231C2×C4×D47—44no—
232C2×C4×D47—42no—
233C2×C4×D47—44no—
234C2×C4×D47C22×C412yes—
235C2×C4×D47C22×C412yes—
236C2×C4×D47C22×C411yescharacteristic
237C2×C4×D47C22×C411yescharacteristic
238C2×C4×D47C22×C412yes—
239C2×C4×D47C22×C412yes—
240C2×C4×D47C22×C414yes—
241C2×C4×D47C22×C412yes—
242C2×C4×D47C22×C412yes—
243C2×C4×D47C22×C412yes—
244C2×C4×D47C2411yescharacteristic
245C2×C4×D47C2412yes—
246C2×C4×D47C2412yes—
247C2×C4×D47C2411yescharacteristic
248C2×Dic94C22×C412yes—
249C2×Dic94C22×C411yescharacteristic
250M16×C47—42no—
251C2×C8×C47—44no—
252C2×C8×C47—42no—
253C2×C8×C47C2414yes—
254C2×C8×C47C2414yes—
255C4⋊C4×C47C22×C412yes—
256C4⋊C4×C47C22×C414yes—
257C22⋊C4×C47C22×C412yes—
258C22⋊C4×C47C22×C414yes—
259C22⋊C4×C47C22×C414yes—
260C42×C47C2412yes—
261C22⋊Dic47C22×C412yes—
262C22⋊Dic47C22×C414yes—
263C22⋊Dic47C22×C414yes—
264(C2×D47)⋊C4C22×C414yes—
265(C2×D47)⋊C4C22×C414yes—
266(C2×D47)⋊C4C22×C414yes—
267(C2×D47)⋊C4C22×C414yes—
268(C2×D47)⋊C4C22×C414yes—
269C4⋊Dic47C22×C412yes—
270C4⋊Dic47C22×C414yes—
271Dic47⋊C4C22×C414yes—
272Dic47⋊C4C22×C414yes—
273Dic47⋊C4C22×C414yes—
274C4×Dic47C22×C414yes—
275C4×Dic47C2412yes—
276#10625329—42no—
277C2×C47⋊C8—44no—
278C2×C47⋊C8—42no—
279C2×C47⋊C8C2414yes—
280C2×C47⋊C8C2414yes—
281#10625324—28no—
282#10625324—28no—
283#10625324—44no—
284#10625324—44no—
285#10625324—44no—
286C8×D47—44no—
287C23×C47—24no—
288C23×C47—41no—
289C23×C47C23×C411yescharacteristic
290C23×C47C23×C412yes—
291C23×C47C23×C412yes—
292C22×D47—24no—
293C22×D47—24no—
294C22×D47—22no—
295C22×D47—24no—
296C22×D47—24no—
297C22×D47—42no—
298C22×D47—41no—
299C22×D47—42no—
300C22×D47—42no—
301C22×D47—42no—
302C22×D47—42no—
303C22×D47—44no—
304C22×D47—416no—
305C22×D47C23×C411yescharacteristic
306C22×D47C23×C412yes—
307C22×D47C23×C412yes—
308C22×D47C23×C411yescharacteristic
309Q8×C47—41no—
310D4×C47—28no—
311D4×C47—41no—
312D4×C47—42no—
313C2×C4×C47—24no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—42no—
318C2×C4×C47—41no—
319C2×C4×C47C23×C414yes—
320C2×C4×C47C23×C412yes—
321C2×C4×C47C23×C412yes—
322C2×C4×C47C23×C411yescharacteristic
323C2×C4×C47C2511yescharacteristic
324C22⋊D47—28no—
325C22⋊D47—42no—
326C22⋊D47—42no—
327C22⋊D47—42no—
328C22⋊D47—44no—
329C2×Dic47—22no—
330C2×Dic47—24no—
331C2×Dic47—24no—
332C2×Dic47—42no—
333C2×Dic47—41no—
334C2×Dic47C23×C414yes—
335C2×Dic47C23×C411yescharacteristic
336C2×Dic47C23×C412yes—
337C2×Dic47C23×C412yes—
338C2×Dic47C23×C411yescharacteristic
339D188—41no—
340D188—42no—
341D188—44no—
342C4×D47—24no—
343C4×D47—22no—
344C4×D47—24no—
345C4×D47—22no—
346C4×D47—24no—
347C4×D47—22no—
348C4×D47—22no—
349C4×D47—24no—
350C4×D47—22no—
351C4×D47—24no—
352C4×D47—42no—
353C4×D47—42no—
354C4×D47—42no—
355C4×D47—44no—
356C4×D47H(5,𝔽2)14yes—
357Dic94—42no—
358Dic94—41no—
359C8×C47—24no—
360C8×C47—24no—
361C47⋊C8—24no—
362C47⋊C8—24no—
363#60231—471nomaximal, Sylow
364C22×C47—22no—
365C22×C47—22no—
366C22×C47—21no—
367C22×C47—22no—
368C22×C47—24no—
369C22×C47—22no—
370C22×C47—44no—
371C22×C47#56814yes—
372C22×C47C24×C411yescharacteristic
373C2×D47—22no—
374C2×D47—21no—
375C2×D47—22no—
376C2×D47—22no—
377C2×D47—22no—
378C2×D47—24no—
379C2×D47—22no—
380C2×D47—22no—
381C2×D47—48no—
382C2×D47—44no—
383C2×D47—48no—
384C2×D47—44no—
385C2×D47—84no—
386C2×D47#51812yes—
387C4×C47—21no—
388C4×C47—22no—
389C4×C47—22no—
390C4×C47—24no—
391C4×C47C2×H(5,𝔽2)12yes—
392Dic47—21no—
393Dic47—22no—
394Dic47—22no—
395Dic47—24no—
396Dic47#51812yes—
397C2×#525—471no—
398#2978—472no—
399#2978—472no—
400#2977—472no—
401#2977—471no—
402#2977D4711yescharacteristic, complemented
403#2976—474no—
404#2976—474no—
405D4×M16—474no—
406D4×M16—474no—
407#2921—472no—
408#2879—472no—
409C2×#407—472no—
410C2×C47—24no—
411C2×C47—41no—
412C2×C47—42no—
413C2×C47C2×#51811yescharacteristic
414C2×C47C2×#56812yes—
415D47—22no—
416D47—41no—
417D47—42no—
418D47—42no—
419C22×#41—471no—
420C24×C4—471no—
421C22×M16—472no—
422C22×M16—474no—
423C22×M16—472no—
424#525—471no—
425#525—471no—
426#525—472no—
427#525—472no—
428#525—472no—
429#525—472no—
430#525—474no—
431#525—471no—
432#525C2×D4711yescharacteristic
433C2×#123—472no—
434C2×C22⋊Q8—472no—
435C2×#121—472no—
436C2×#120—472no—
437C2×C4×D4—474no—
438C2×#117—471no—
439#436—474no—
440#436—474no—
441#436—474no—
442#436—474no—
443#435—474no—
444#435—474no—
445#435—474no—
446#435—474no—
447#435—474no—
448#435—474no—
449#435—474no—
450#435C2×D4714yescomplemented
451C8×D4—474no—
452C8×D4—474no—
453C8×D4—474no—
454C8×D4C2×D4714yescomplemented
455#433—472no—
456#433—474no—
457#433—474no—
458#433—472no—
459#433—472no—
460#433C2×D4712yescomplemented
461#423—474no—
462#408—472no—
463#408—472no—
464#408—472no—
465#408—474no—
466#408—474no—
467#408C2×D4712yescomplemented
468#407—474no—
469#407—472no—
470#407—472no—
471#407—472no—
472#407—472no—
473#407—474no—
474#407—474no—
475C2×C22⋊C8—472no—
476C2×C22⋊C8—474no—
477C2×C22⋊C8C2×D4712yescomplemented
478C4×M16—472no—
479C4×M16—472no—
480C47#6023111yescharacteristic, complemented, Sylow
481C25—471no—
482C2×#41—471no—
483C2×#41—472no—
484C2×#41—471no—
485C2×#41—472no—
486C2×#41—471no—
487C2×#41—1884no—
488C2×#41C22×D4711yescharacteristic
489C22×Q8—471no—
490C22×D4—474no—
491C22×D4—472no—
492C22×D4—471no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—472no—
496C23×C4—472no—
497C23×C4—472no—
498C23×C4—471no—
499C23×C4—471no—
500C23×C4—472no—
501C23×C4—472no—
502C23×C4—471no—
503C23×C4—1884no—
504C23×C4C22×D4711yescharacteristic
505C2×M16—472no—
506C2×M16—474no—
507C2×M16—474no—
508C2×M16—474no—
509C2×M16—474no—
510C2×M16—474no—
511C2×M16—1888no—
512C2×M16—1884no—
513C2×M16—1884no—
514C2×M16C22×D4712yescomplemented
515C22×C8—474no—
516C22×C8—472no—
517C22×C8—474no—
518C22×C8C22×D4714yes—
519C22×C8C22×D4712yescomplemented
520#123—472no—
521#123—472no—
522#123—474no—
523#123—474no—
524#123—472no—
525#123C4×D4712yes—
526C22⋊Q8—472no—
527C22⋊Q8—472no—
528C22⋊Q8—474no—
529C22⋊Q8—472no—
530C22⋊Q8—474no—
531C22⋊Q8C4×D4712yes—
532#121—472no—
533#121—474no—
534#121—472no—
535#121—472no—
536#121—474no—
537#121C4×D4712yes—
538#120—472no—
539#120—472no—
540#120—474no—
541#120—474no—
542#120—472no—
543#120C4×D4712yes—
544C4×D4—474no—
545C4×D4—474no—
546C4×D4—474no—
547C4×D4—474no—
548C4×D4—474no—
549C4×D4—474no—
550C4×D4—474no—
551C4×D4C22×D4714yes—
552#117—471no—
553#117—472no—
554#117—472no—
555#117—472no—
556#117C22×D4711yescharacteristic
557C2×C4⋊C4—472no—
558C2×C4⋊C4—474no—
559C2×C22⋊C4—472no—
560C2×C22⋊C4—474no—
561C2×C22⋊C4—474no—
562C2×C42—472no—
563C4⋊C8—474no—
564C4⋊C8—474no—
565C4⋊C8—474no—
566C4⋊C8C22×D4714yescomplemented
567C22⋊C8—474no—
568C22⋊C8—472no—
569C22⋊C8—472no—
570C22⋊C8—474no—
571C22⋊C8—474no—
572C22⋊C8—474no—
573C22⋊C8—474no—
574C22⋊C8—474no—
575C22⋊C8—474no—
576C22⋊C8—474no—
577C22⋊C8C22×D4714yes—
578C22⋊C8C22×D4712yes—
579C22⋊C8C22×D4712yes—
580C22⋊C8C22×D4714yescomplemented
581#97—474no—
582#97—472no—
583#97C22×D4712yescomplemented
584C4×C8—474no—
585C4×C8—472no—
586C4×C8C22×D4712yescomplemented
587C24—472no—
588C24—471no—
589C24—472no—
590C24—472no—
591C24—471no—
592C24—1884no—
593C24—1882no—
594C24C2×C4×D4711yescharacteristic
595#41—42no—
596#41—1882no—
597#41—1882no—
598#41—1882no—
599#41—1882no—
600#41—1884no—
601#41—1882no—
602C2×Q8—471no—
603C2×Q8—472no—
604C2×Q8—1882no—
605C2×Q8C2×C4×D4711yescharacteristic
606C2×D4—474no—
607C2×D4—474no—
608C2×D4—472no—
609C2×D4—472no—
610C2×D4—472no—
611C2×D4—474no—
612C2×D4—472no—
613C2×D4—471no—
614C2×D4—1882no—
615C2×D4—1884no—
616C2×D4—1888no—
617C2×D4C2×C4×D4714yes—
618C2×D4C2×C4×D4712yes—
619C2×D4C2×C4×D4711yescharacteristic
620C22×C4—42no—
621C22×C4—471no—
622C22×C4—471no—
623C22×C4—472no—
624C22×C4—472no—
625C22×C4—472no—
626C22×C4—471no—
627C22×C4—472no—
628C22×C4—472no—
629C22×C4—471no—
630C22×C4—471no—
631C22×C4—472no—
632C22×C4—472no—
633C22×C4—471no—
634C22×C4—472no—
635C22×C4—472no—
636C22×C4—474no—
637C22×C4—472no—
638C22×C4—472no—
639C22×C4—472no—
640C22×C4—948no—
641C22×C4—944no—
642C22×C4—944no—
643C22×C4—944no—
644C22×C4—1884no—
645C22×C4—1882no—
646C22×C4—1882no—
647C22×C4—1884no—
648C22×C4—1882no—
649C22×C4—1884no—
650C22×C4—1882no—
651C22×C4C2×C4×D4712yes—
652C22×C4C2×C4×D4711yescharacteristic
653C22×C4C23×D4711yescharacteristic
654C22×C4C23×D4712yes—
655C22×C4C23×D4712yes—
656M16—42no—
657M16—948no—
658M16—948no—
659M16—1884no—
660M16—1884no—
661M16—1884no—
662M16—1882no—
663C2×C8—44no—
664C2×C8—42no—
665C2×C8—474no—
666C2×C8—474no—
667C2×C8—1884no—
668C2×C8—1884no—
669C2×C8—1882no—
670C2×C8C23×D4714yes—
671C2×C8C23×D4714yes—
672C4⋊C4—474no—
673C4⋊C4—474no—
674C4⋊C4—474no—
675C4⋊C4—472no—
676C4⋊C4—474no—
677C4⋊C4C2×C4×D4712yes—
678C4⋊C4C2×C4×D4714yes—
679C22⋊C4—472no—
680C22⋊C4—474no—
681C22⋊C4—474no—
682C22⋊C4—474no—
683C22⋊C4—474no—
684C22⋊C4—474no—
685C22⋊C4—474no—
686C22⋊C4—474no—
687C22⋊C4C2×C4×D4712yes—
688C22⋊C4C2×C4×D4714yes—
689C22⋊C4C2×C4×D4714yes—
690C42—474no—
691C42—472no—
692C42C23×D4712yes—
693C23—24no—
694C23—41no—
695C23—471no—
696C23—472no—
697C23—471no—
698C23—472no—
699C23—944no—
700C23—942no—
701C23—944no—
702C23—944no—
703C23—944no—
704C23—1884no—
705C23—1882no—
706C23—1881no—
707C23—1882no—
708C23—1882no—
709C23—1882no—
710C23—1882no—
711C23—18816no—
712C23C22×C4×D4711yescharacteristic
713C23C22×C4×D4712yes—
714C23C22×C4×D4712yes—
715Q8—41no—
716Q8—1881no—
717Q8—1882no—
718D4—28no—
719D4—41no—
720D4—42no—
721D4—948no—
722D4—1884no—
723D4—1881no—
724D4—1882no—
725D4—1884no—
726D4—1882no—
727D4—1882no—
728D4—1882no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—471no—
736C2×C4—474no—
737C2×C4—474no—
738C2×C4—472no—
739C2×C4—472no—
740C2×C4—471no—
741C2×C4—944no—
742C2×C4—942no—
743C2×C4—944no—
744C2×C4—944no—
745C2×C4—942no—
746C2×C4—944no—
747C2×C4—944no—
748C2×C4—942no—
749C2×C4—944no—
750C2×C4—942no—
751C2×C4—944no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—1882no—
755C2×C4—1882no—
756C2×C4—1882no—
757C2×C4—1884no—
758C2×C4—1882no—
759C2×C4—1881no—
760C2×C4C22×C4×D4714yes—
761C2×C4C22×C4×D4712yes—
762C2×C4C22×C4×D4712yes—
763C2×C4C22×C4×D4711yescharacteristic
764C2×C4C24×D4711yescharacteristic
765C8—24no—
766C8—24no—
767C8—944no—
768C8—944no—
769C22—22no—
770C22—22no—
771C22—24no—
772C22—22no—
773C22—21no—
774C22—22no—
775C22—44no—
776C22—472no—
777C22—942no—
778C22—944no—
779C22—942no—
780C22—942no—
781C22—942no—
782C22—941no—
783C22—942no—
784C22—942no—
785C22—3764no—
786C22—1888no—
787C22—1888no—
788C22—1884no—
789C22—1884no—
790C22#1568988814yes—
791C22C23×C4×D4711yescharacteristic
792C4—24no—
793C4—21no—
794C4—22no—
795C4—22no—
796C4—472no—
797C4—944no—
798C4—941no—
799C4—942no—
800C4—942no—
801C4H(5,𝔽2)×D4712yes—
802C2—24no—
803C2—41no—
804C2—42no—
805C2—942no—
806C2—1882no—
807C2—1882no—
808C2—1881no—
809C2#518×D4711yescharacteristic
810C2C2×#1568988812yes—
subgroupG/H
center, FrattiniC2×C4C24×D47
commutator, socleC22×C47C24×C4
FittingC47×#2977C2
prime radical#525×D47C2
cosocleC2×C4×C47C25
hypercenter#2977D47
hypocenterC47#60231
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #2977

Complements

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

NH ≅ G/Ntype
2. #20252449C2semidirect
3. #20252446C2semidirect
4. #20252444C2semidirect
5. #20252442C2semidirect
6. #20252437C2semidirect
7. #20252430C2semidirect
8. #20252121C2semidirect
9. D4×#10625324C2semidirect
10. #20252022C2semidirect
11. #20251830C2semidirect
12. C2×#15689085C2semidirect
13. C47×#2977C2semidirect
17. C22×#10625324C22semidirect
18. C2×M16×D47C22semidirect
33. #15689202C22semidirect
34. #15689200C22semidirect
35. #15689199C22semidirect
36. #15689198C22semidirect
37. #15689196C22semidirect
38. #15689195C22semidirect
39. #15689194C22semidirect
40. #15689194C22semidirect
41. #15689193C22semidirect
42. #15689191C22semidirect
43. #15689191C22semidirect
44. D4×C47⋊C8C22semidirect
45. C8×C22⋊D47C22semidirect
46. (C22⋊D47)⋊C8C22semidirect
47. #15689185C22semidirect
48. #15689184C22semidirect
49. #15689183C22semidirect
50. #15689182C22semidirect
51. #15689181C22semidirect
52. #15689145C22semidirect
53. #15689091C22semidirect
54. #15689090C22semidirect
55. #15689089C22semidirect
56. #15689088C22semidirect
57. #15689088C22semidirect
61. #15689085C22semidirect
62. #15689085C22semidirect
63. #15689085C22semidirect
64. #15689085C22semidirect
65. C2×C22⋊(C47⋊C8)C22semidirect
66. C2×(C2×D47)⋊C8C22semidirect
67. #15689075C22semidirect
68. C4×#10625324C22semidirect
70. C47×#435C22semidirect
71. C8×D4×C47C22semidirect
72. C47×#433C22semidirect
73. C47×#408C22semidirect
74. C2×C22⋊C8×C47C22semidirect
97. C2×#10625329C23semidirect
104. C2×#10625324C23semidirect
107. C22×C47⋊C8C23semidirect
108. C2×C8×D47C23semidirect
146. C4⋊(C47⋊C8)C23semidirect
147. Dic47⋊C8C23semidirect
148. Dic47⋊C8C23semidirect
152. C22⋊(C47⋊C8)C23semidirect
157. (C2×D47)⋊C8C23semidirect
158. (C2×D47)⋊C8C23semidirect
159. #13093935C23semidirect
160. #13093934C23semidirect
161. C4×C47⋊C8C23semidirect
162. C8×Dic47C23semidirect
165. C2×M16×C47C23semidirect
167. C22×C8×C47C23semidirect
174. C4⋊C8×C47C23semidirect
178. C22⋊C8×C47C23semidirect
179. #97×C47C23semidirect
180. C4×C8×C47C23semidirect
402. #2977D47semidirect
450. #435C2×D47semidirect
454. C8×D4C2×D47semidirect
460. #433C2×D47semidirect
467. #408C2×D47semidirect
477. C2×C22⋊C8C2×D47semidirect
480. C47#60231semidirect
514. C2×M16C22×D47semidirect
519. C22×C8C22×D47semidirect
566. C4⋊C8C22×D47semidirect
580. C22⋊C8C22×D47semidirect
583. #97C22×D47semidirect
586. C4×C8C22×D47semidirect

Maximal subgroups

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

subgroupindex
#525×D472
#202524492
#202524462
#202524442
#202524422
#202524372
#202524302
#202521212
D4×#106253242
#202520222
#202518302
C2×#156890852
C47×#29772
#6023147