Finite Group Databasebeta

← #25131161

Subgroups — #25131161

Order 11008.

1086 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583523C211yesmaximal, characteristic
2C2×#14583121C211yesmaximal, characteristic, complemented
3#19137271C211yesmaximal, characteristic, complemented
4#19135793C211yesmaximal, characteristic, complemented
5#19135786C211yesmaximal, characteristic
6#19135604C211yesmaximal, characteristic, complemented
7#19135597C211yesmaximal, characteristic
8#19135544C211yesmaximal, characteristic, complemented
9#19135525C211yesmaximal, characteristic, complemented
10#19134933C211yesmaximal, characteristic, complemented
11#19134926C211yesmaximal, characteristic, complemented
12#19134860C211yesmaximal, characteristic, complemented
13#19134853C211yesmaximal, characteristic, complemented
14#19134576C211yesmaximal, characteristic, complemented
15C2×C43×#475C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18#14583523—24no—
19#14583523—24no—
20C2×#13063320—21no—
21C2×#13063314—21no—
22C2×#13063313C2211yescharacteristic
23C2×#13063310—21no—
24C2×#13063305C2211yescharacteristic
25C2×#13063301—21no—
26C2×#13063301C2211yescharacteristic
27C2×#13063300C2211yescharacteristic
28C2×#13063290C2211yescharacteristic
29C2×#13063287C2211yescharacteristic
30C2×#13063282C2211yescharacteristic
31#14583121—24no—
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41#14582806C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582794—21no—
44#14582790—21no—
45#14582789—21no—
46#14582783—21no—
47#14582756C2211yescharacteristic
48C4×C4⋊Dic43C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×C4⋊Q8×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C43×#475—24no—
58C2×#106×C43C2211yescharacteristic
59C2×#106×C43C2211yescharacteristic
60C2×C4⋊C8×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172—21no—
65C22×D172C2311yescharacteristic
66C22×C4×D43—21no—
67C22×C4×D43C2311yescharacteristic
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621885—41no—
71C2×#10621884—22no—
72C2×#10621884—22no—
73C2×#10621884—41no—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063320—28no—
77#13063314—28no—
78#13063313—22no—
79#13063313D414yes—
80#13063310—28no—
81#13063305—22no—
82#13063305—22no—
83#13063301—28no—
84#13063301—22no—
85#13063301—22no—
86#13063300—22no—
87#13063300—22no—
88#13063290—22no—
89#13063290—22no—
90#13063287—22no—
91#13063287—22no—
92#13063282—22no—
93#13063282—22no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4D411yescharacteristic
101C2×Dic43⋊C4D411yescharacteristic
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4D411yescharacteristic
110C2×(C2×D43)⋊C4D411yescharacteristic
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43C2311yescharacteristic
114C4⋊(C43⋊C8)—22no—
115#13063250—22no—
116#13063250—41no—
117#13063248—22no—
118#13063247—22no—
119#13063247—41no—
120#13063245—22no—
121(C2×D43)⋊C8—41no—
122(C2×D43)⋊C8—41no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C22×Q8×C43—21no—
129C22×Q8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C4⋊Q8×C43—22no—
133C4⋊Q8×C43D414yes—
134C4×Q8×C43—22no—
135C4×Q8×C43—22no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C42×C43—21no—
142C2×C42×C43C2311yescharacteristic
143#106×C43—22no—
144#106×C43—22no—
145C4⋊C8×C43—22no—
146#103×C43—22no—
147#103×C43—22no—
148C23×D43—21no—
149C23×D43C2×D411yescharacteristic
150C2×Q8×C43—24no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—81no—
157C2×Q8×C43—81no—
158C2×Q8×C43#4112yes—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2411yescharacteristic
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C2×D172—21no—
173C2×D172—24no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—81no—
179C2×D172—81no—
180C2×D172C2×D412yes—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—24no—
188C2×C4×D43—81no—
189C2×C4×D43—81no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86C2×D412yes—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C4⋊C4×C43—24no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—42no—
208C4⋊C4×C43C2×D412yes—
209C4⋊C4×C43C2×D412yes—
210C42×C43—42no—
211C42×C43C2×D412yes—
212C42×C43C2×D412yes—
213#10621885—44no—
214#10621884—44no—
215(C2×D43)⋊C4—24no—
216(C2×D43)⋊C4—24no—
217(C2×D43)⋊C4—24no—
218(C2×D43)⋊C4—24no—
219(C2×D43)⋊C4—24no—
220(C2×D43)⋊C4—24no—
221(C2×D43)⋊C4—22no—
222(C2×D43)⋊C4—22no—
223(C2×D43)⋊C4—81no—
224C4⋊Dic43—24no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43#4112yes—
229Dic43⋊C4—24no—
230Dic43⋊C4—24no—
231Dic43⋊C4—22no—
232Dic43⋊C4—22no—
233Dic43⋊C4—81no—
234C4×Dic43—24no—
235C4×Dic43—21no—
236C4×Dic43—21no—
237C4×Dic43—81no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C23×C43C22×D411yescharacteristic
245C22×D43—21no—
246C22×D43—22no—
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259Q8×C43—22no—
260Q8×C43—22no—
261Q8×C43—41no—
262Q8×C43—41no—
263Q8×C43—84no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43#12012yes—
281C2×C4×C43#12012yes—
282C2×C4×C43C22×D411yescharacteristic
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43H(5,𝔽2)11yescharacteristic
287C2×C4×C432−1+411yescharacteristic
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—22no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—22no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306D172—22no—
307D172—22no—
308D172—41no—
309D172—41no—
310D172—84no—
311C4×D43—41no—
312C4×D43—41no—
313C4×D43—41no—
314C4×D43—41no—
315C4×D43—84no—
316Dic86—22no—
317Dic86—22no—
318Dic86—41no—
319Dic86—41no—
320C8×C43—41no—
321C8×C43—41no—
322C43⋊C8—41no—
323C43⋊C8—41no—
324#24169—431nomaximal, Sylow
325C22×C43C2×#12011yescharacteristic
326C22×C43#52511yescharacteristic
327C22×C43#53711yescharacteristic
328C22×C43#57711yescharacteristic
329C22×C43#57711yescharacteristic
330C22×C43#57711yescharacteristic
331C22×C43#57811yescharacteristic
332C2×D43—41no—
333C2×D43—41no—
334C2×D43—41no—
335C2×D43—42no—
336C2×D43—41no—
337C2×D43—41no—
338C2×D43—41no—
339C2×D43—42no—
340C2×D43—41no—
341C2×D43—42no—
342C2×D43—81no—
343C2×D43—81no—
344C2×D43—81no—
345C2×D43—81no—
346C4×C43—22no—
347C4×C43—22no—
348C4×C43—42no—
349C4×C43—42no—
350C4×C43—42no—
351C4×C43—81no—
352C4×C43#54611yescharacteristic
353C4×C43#54711yescharacteristic
354C4×C43#54811yescharacteristic
355C4×C43#55011yescharacteristic
356Dic43—42no—
357Dic43—42no—
358Dic43—41no—
359Dic43—41no—
360Dic43—41no—
361Dic43—81no—
362C2×#542—431no—
363C2×#475D4311yescharacteristic, complemented
364C2×#464—431no—
365#2323—431no—
366#2035—431no—
367#2034—431no—
368#2001—431no—
369#2000—431no—
370#1987—431no—
371#1983—431no—
372#1878—431no—
373#1877—431no—
374#1865—431no—
375#1864—431no—
376#1798—431no—
377C2×C43#240711yescharacteristic
378C2×C43#300911yescharacteristic
379C2×C43#301311yescharacteristic
380C2×C43#312111yescharacteristic
381C2×C43#312511yescharacteristic
382C2×C43#325811yescharacteristic
383C2×C43#326311yescharacteristic
384D43—81no—
385D43—82no—
386C22×Q16—431no—
387C22×SD16—431no—
388#542—864no—
389#542—864no—
390C2×C4⋊Q8C2×D4311yescharacteristic
391C2×#126—861no—
392C2×#124—431no—
393C2×#124—861no—
394C2×#123—861no—
395C2×C22⋊Q8—431no—
396C2×C22⋊Q8—431no—
397C2×C22⋊Q8—861no—
398C2×#121—431no—
399C2×C4×Q8—431no—
400C2×C4×Q8C2×D4311yescharacteristic
401C2×C4×D4—431no—
402C2×#117—431no—
403#475—24no—
404#464—864no—
405C2×#106C2×D4311yescharacteristic
406C2×#106C2×D4311yescharacteristic
407C2×C4⋊C8—431no—
408C2×C4⋊C8C2×D4311yescharacteristic
409C2×#103—431no—
410C2×#103—431no—
411C2×#103—431no—
412C2×#103C2×D4311yescharacteristic
413C2×#103C2×D4311yescharacteristic
414C2×#102—431no—
415C2×#102—431no—
416C2×#102—431no—
417C2×C22⋊C8—431no—
418C2×C22⋊C8—431no—
419#391—431no—
420#389—431no—
421#389—861no—
422#388—861no—
423#388—861no—
424#387—861no—
425#380—431no—
426C4×C4⋊C4—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#340—431no—
431#336—431no—
432#336—431no—
433C43#2416911yescharacteristic, complemented, Sylow
434C22×Q8—21no—
435C22×Q8—431no—
436C22×Q8C22×D4311yescharacteristic
437C22×D4—431no—
438C22×D4—861no—
439C23×C4—431no—
440C23×C4—861no—
441C2×Q16—862no—
442C2×Q16—862no—
443C2×Q16—1721no—
444C2×SD16—862no—
445C2×SD16—862no—
446C2×SD16—1721no—
447C22×C8—431no—
448C22×C8—431no—
449C22×C8C22×D4311yescharacteristic
450C22×C8C22×D4311yescharacteristic
451C4⋊Q8—22no—
452C4⋊Q8C22⋊D4314yes—
453#126—868no—
454#124—434no—
455#124—868no—
456#124—862no—
457#123—868no—
458C22⋊Q8—862no—
459C22⋊Q8—862no—
460C22⋊Q8—868no—
461C22⋊Q8—862no—
462C22⋊Q8—862no—
463#121—862no—
464#121—862no—
465C4×Q8—22no—
466C4×Q8—22no—
467C4×Q8—862no—
468C4×Q8—862no—
469C4×D4—862no—
470C4×D4—862no—
471#117—862no—
472#117—862no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4C22×D4311yescharacteristic
484C2×C4⋊C4C22×D4311yescharacteristic
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C22⋊C4—431no—
487C2×C22⋊C4—431no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C42—21no—
496C2×C42—431no—
497C2×C42—861no—
498C2×C42—861no—
499C2×C42C22×D4311yescharacteristic
500#106—22no—
501#106—22no—
502C4⋊C8—22no—
503C4⋊C8—862no—
504#103—22no—
505#103—22no—
506#103—862no—
507#103—862no—
508#103—1721no—
509#102—862no—
510#102—862no—
511#102—1721no—
512C22⋊C8—1721no—
513C22⋊C8—1721no—
514#95—861no—
515#95—861no—
516#95—861no—
517#95—861no—
518#95—861no—
519C24—431no—
520C24—861no—
521C2×Q8—24no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—81no—
528C2×Q8—81no—
529C2×Q8—432no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8#1062190212yes—
536C2×D4—432no—
537C2×D4—864no—
538C2×D4—861no—
539C2×D4—861no—
540C2×D4—861no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—3441no—
544C2×D4—3441no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—431no—
550C22×C4—431no—
551C22×C4—431no—
552C22×C4—864no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—3441no—
563C22×C4—3441no—
564C22×C4D4×D4311yescharacteristic
565C22×C4D4×D4311yescharacteristic
566C22×C4C23×D4311yescharacteristic
567Q16—1724no—
568SD16—1724no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C4⋊C4—24no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—42no—
587C4⋊C4—432no—
588C4⋊C4—864no—
589C4⋊C4—864no—
590C4⋊C4—864no—
591C4⋊C4—862no—
592C4⋊C4—862no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—3441no—
597C4⋊C4C2×C22⋊D4312yes—
598C4⋊C4C2×C22⋊D4312yes—
599C22⋊C4—864no—
600C22⋊C4—864no—
601C22⋊C4—864no—
602C22⋊C4—864no—
603C22⋊C4—862no—
604C22⋊C4—862no—
605C22⋊C4—864no—
606C22⋊C4—864no—
607C22⋊C4—3441no—
608C42—42no—
609C42—864no—
610C42—861no—
611C42—861no—
612C42—3441no—
613C42D4×D4312yes—
614C42C2×C22⋊D4312yes—
615C23—862no—
616C23—861no—
617C23—861no—
618C23—861no—
619C23—861no—
620C23—861no—
621C23—861no—
622C23—861no—
623C23—1721no—
624C23—1721no—
625C23—1721no—
626C23—1721no—
627C23—1721no—
628C23—1721no—
629C23C2×D4×D4311yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—41no—
633Q8—41no—
634Q8—84no—
635Q8—862no—
636Q8—862no—
637Q8—1721no—
638Q8—1721no—
639D4—862no—
640D4—862no—
641D4—3444no—
642D4—1721no—
643D4—1721no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—861no—
661C2×C4—862no—
662C2×C4—861no—
663C2×C4—861no—
664C2×C4—862no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—3444no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4#1306329312yes—
684C2×C4#1306329312yes—
685C2×C4C2×D4×D4311yescharacteristic
686C2×C4C22×C22⋊D4311yescharacteristic
687C2×C4#41×D4311yescharacteristic
688C2×C4C2×#1062190211yescharacteristic
689C2×C4#1306337111yescharacteristic
690C2×C4#1306337311yescharacteristic
691C8—41no—
692C8—41no—
693C8—1721no—
694C8—1721no—
695C22—3441no—
696C22—3441no—
697C22—3441no—
698C22—3441no—
699C22—1721no—
700C22—1721no—
701C22—1721no—
702C22—1721no—
703C22—1722no—
704C22—1721no—
705C22—1722no—
706C22—1721no—
707C22—1721no—
708C22—1722no—
709C22C2×#1306329311yescharacteristic
710C22#1458341211yescharacteristic
711C22#1458347911yescharacteristic
712C22#1458370511yescharacteristic
713C22#1458370511yescharacteristic
714C22#1458370811yescharacteristic
715C22#1458371511yescharacteristic
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—81no—
722C4—3441no—
723C4—1721no—
724C4—1722no—
725C4—1722no—
726C4—1721no—
727C4—1721no—
728C4#1458354011yescharacteristic
729C4#1458355111yescharacteristic
730C4#1458356011yescharacteristic
731C4#1458356811yescharacteristic
732C2—3442no—
733C2—3441no—
734C2#1913794211yescharacteristic
735C2#1914386811yescharacteristic
736C2#1914390911yescharacteristic
737C2#1914483111yescharacteristic
738C2#1914487911yescharacteristic
739C2#1914602811yescharacteristic
740C2#1914606411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#475C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenterC2×#475D43
hypocenterC43#24169
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
2. C2×#14583121C2semidirect
3. #19137271C2semidirect
4. #19135793C2semidirect
6. #19135604C2semidirect
8. #19135544C2semidirect
9. #19135525C2semidirect
10. #19134933C2semidirect
11. #19134926C2semidirect
12. #19134860C2semidirect
13. #19134853C2semidirect
14. #19134576C2semidirect
15. C2×C43×#475C2semidirect
363. C2×#475D43semidirect
433. C43#24169semidirect

Maximal subgroups

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

subgroupindex
C2×#145835232
C2×#145831212
#191372712
#191357932
#191357862
#191356042
#191355972
#191355442
#191355252
#191349332
#191349262
#191348602
#191348532
#191345762
C2×C43×#4752
#2416943