Finite Group Databasebeta

← #25124982

Subgroups — #25124982

Order 11008.

1122 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×#14583521C211yesmaximal, characteristic
2C2×#14582997C211yesmaximal, characteristic, complemented
3#19137271C211yesmaximal, characteristic, complemented
4#19135921C211yesmaximal, characteristic, complemented
5#19135832C211yesmaximal, characteristic, complemented
6#19135796C211yesmaximal, characteristic, complemented
7#19135779C211yesmaximal, characteristic
8#19135734C211yesmaximal, characteristic, complemented
9#19135686C211yesmaximal, characteristic, complemented
10#19135602C211yesmaximal, characteristic, complemented
11#19135597C211yesmaximal, characteristic
12#19134425C211yesmaximal, characteristic, complemented
13C4×#13063247C211yesmaximal, characteristic, complemented
14#19134362C211yesmaximal, characteristic, complemented
15C2×C4×Q16×C43C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17#14583521—24no—
18#14583521—24no—
19C2×#13063324C2211yescharacteristic
20C2×#13063319—21no—
21C2×#13063314C2211yescharacteristic
22C2×#13063313—21no—
23C2×#13063310—21no—
24C2×#13063303—21no—
25C2×#13063301C2211yescharacteristic
26C2×#13063301C2211yescharacteristic
27C2×#13063300C2211yescharacteristic
28C2×C4×D172C2211yescharacteristic
29C2×#13063282C2211yescharacteristic
30#14582997—24no—
31C2×#13063258C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×(C2×D43)⋊C8C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×#13063236C2211yescharacteristic
41#14582806C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582794—21no—
44#14582790—21no—
45#14582789—21no—
46#14582783—21no—
47#14582756C2211yescharacteristic
48C4×C4⋊Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×Q16×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C4×Q16×C43—24no—
59C2×#107×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C22×Dic86—21no—
64C22×D172—21no—
65C22×D172C2311yescharacteristic
66C22×C4×D43—21no—
67C22×C4×D43C2311yescharacteristic
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063324—22no—
74#13063324—22no—
75#13063319—28no—
76#13063314—22no—
77#13063314—22no—
78#13063313—28no—
79#13063310—28no—
80#13063303—28no—
81#13063301—22no—
82#13063301—22no—
83#13063301—22no—
84#13063301—22no—
85#13063300—22no—
86#13063300—22no—
87C4×D172—22no—
88C4×D172D414yes—
89#13063282—22no—
90#13063282—22no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4D411yescharacteristic
99C2×Dic43⋊C4D411yescharacteristic
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
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)⋊C4D411yescharacteristic
108C2×(C2×D43)⋊C4D411yescharacteristic
109C2×C4×Dic43—21no—
110C2×C4×Dic43C2311yescharacteristic
111#13063258—22no—
112#13063249—22no—
113#13063249—22no—
114#13063249—22no—
115#13063247—22no—
116#13063247—22no—
117#13063245—22no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120#13063236—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C22×Q8×C43C2311yescharacteristic
127C22×Q8×C43C2311yescharacteristic
128C2×Q16×C43—22no—
129C2×Q16×C43—22no—
130C2×Q16×C43—22no—
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C4×Q8×C43—22no—
134C4×Q8×C43—22no—
135C4×Q8×C43—22no—
136C4×Q8×C43D414yes—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43—21no—
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C42×C43—21no—
142C2×C42×C43—21no—
143C2×C42×C43C2311yescharacteristic
144#107×C43—22no—
145#103×C43—22no—
146#103×C43—22no—
147C4×C8×C43—22no—
148C23×D43—21no—
149C23×D43C2×D411yescharacteristic
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43C2×D412yes—
161C2×Q8×C43#4112yes—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2411yescharacteristic
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175C2×D172—21no—
176C2×D172—24no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—81no—
182C2×D172—81no—
183C2×D172C2×D412yes—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—24no—
191C2×C4×D43—81no—
192C2×C4×D43—81no—
193C2×Dic86—24no—
194C2×Dic86—81no—
195C2×Dic86—81no—
196Q16×C43—28no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43#4112yes—
203C4⋊C4×C43—24no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—42no—
208C4⋊C4×C43C2×D412yes—
209C42×C43—24no—
210C42×C43—42no—
211C42×C43C2×D412yes—
212C42×C43C2×D412yes—
213#10621884—28no—
214(C2×D43)⋊C4—24no—
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—22no—
221(C2×D43)⋊C4—22no—
222(C2×D43)⋊C4—81no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43C2×D412yes—
228C4⋊Dic43#4112yes—
229Dic43⋊C4—24no—
230Dic43⋊C4—24no—
231Dic43⋊C4—24no—
232Dic43⋊C4—22no—
233Dic43⋊C4—22no—
234Dic43⋊C4—81no—
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#4112yes—
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—22no—
262Q8×C43—22no—
263Q8×C43—41no—
264Q8×C43—41no—
265Q8×C43—41no—
266Q8×C43—41no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
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—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43#12012yes—
284C2×C4×C43#12012yes—
285C2×C4×C43C22×D411yescharacteristic
286C2×C4×C43C22×D411yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—22no—
295C2×Dic43—21no—
296C2×Dic43—22no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309D172—22no—
310D172—22no—
311D172—41no—
312D172—41no—
313D172—84no—
314C4×D43—41no—
315C4×D43—41no—
316C4×D43—41no—
317C4×D43—41no—
318C4×D43—84no—
319Dic86—84no—
320C8×C43—22no—
321C8×C43—41no—
322C43⋊C8—22no—
323C43⋊C8—41no—
324#23585—431nomaximal, Sylow
325C22×C43C2×#12011yescharacteristic
326C22×C43#52511yescharacteristic
327C22×C43#53211yescharacteristic
328C22×C43#57611yescharacteristic
329C22×C43#57711yescharacteristic
330C22×C43#57811yescharacteristic
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#52511yescharacteristic
353C4×C43#52511yescharacteristic
354C4×C43#53211yescharacteristic
355C4×C43#53211yescharacteristic
356Dic43—42no—
357Dic43—41no—
358Dic43—41no—
359Dic43—41no—
360Dic43—42no—
361Dic43—81no—
362C2×#542—431no—
363C2×#440—431no—
364C2×C4×Q16D4311yescharacteristic, complemented
365#2323—431no—
366#2057—431no—
367#2042—431no—
368#2036—431no—
369#2033—431no—
370#2024—431no—
371#2015—431no—
372#2001—431no—
373#2000—431no—
374#1763—431no—
375C4×#102—431no—
376#1750—431no—
377C2×C43#238811yescharacteristic
378C2×C43#301111yescharacteristic
379C2×C43#301211yescharacteristic
380C2×C43#312111yescharacteristic
381C2×C43#312411yescharacteristic
382C2×C43#317511yescharacteristic
383C2×C43#317811yescharacteristic
384D43—81no—
385D43—82no—
386C22×Q16C2×D4311yescharacteristic
387C22×SD16—431no—
388#542—864no—
389#542—864no—
390C2×C4⋊Q8—431no—
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×Q8C2×D4311yescharacteristic
400C2×C4×Q8C2×D4311yescharacteristic
401C2×C4×D4—431no—
402C2×#117—431no—
403#440—864no—
404C4×Q16—24no—
405C2×#107—431no—
406C2×#107C2×D4311yescharacteristic
407C2×#103—431no—
408C2×#103—431no—
409C2×#103—431no—
410C2×#103C2×D4311yescharacteristic
411C2×#103C2×D4311yescharacteristic
412C2×#102—431no—
413C2×#102—431no—
414C2×#102—431no—
415C2×C22⋊C8—431no—
416C2×C22⋊C8—431no—
417C2×#97—431no—
418C2×C4×C8C2×D4311yescharacteristic
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#2358511yescharacteristic, complemented, Sylow
434C22×Q8—861no—
435C22×Q8C22×D4311yescharacteristic
436C22×Q8C22×D4311yescharacteristic
437C22×D4—431no—
438C22×D4—861no—
439C23×C4—431no—
440C23×C4—861no—
441C2×Q16—22no—
442C2×Q16—22no—
443C2×Q16—22no—
444C2×SD16—862no—
445C2×SD16—862no—
446C2×SD16—862no—
447C22×C8—431no—
448C22×C8—431no—
449C22×C8C22×D4311yescharacteristic
450C22×C8C22×D4311yescharacteristic
451C4⋊Q8—862no—
452C4⋊Q8—862no—
453#126—868no—
454#124—868no—
455#124—862no—
456#124—862no—
457#123—868no—
458C22⋊Q8—868no—
459C22⋊Q8—862no—
460C22⋊Q8—862no—
461C22⋊Q8—862no—
462C22⋊Q8—862no—
463#121—862no—
464#121—862no—
465C4×Q8—22no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8C22⋊D4314yes—
469C4×D4—434no—
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—431no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
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—21no—
497C2×C42—431no—
498C2×C42—861no—
499C2×C42C22×D4311yescharacteristic
500#107—22no—
501#107—862no—
502#103—22no—
503#103—22no—
504#103—862no—
505#103—862no—
506#103—862no—
507#102—862no—
508#102—862no—
509#102—862no—
510C22⋊C8—862no—
511C22⋊C8—862no—
512#97—862no—
513C4×C8—22no—
514#95—861no—
515#95—861no—
516#95—861no—
517#95—861no—
518#95—861no—
519C24—431no—
520C24—861no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—864no—
532C2×Q8—3441no—
533C2×Q8—3441no—
534C2×Q8#1062189812yes—
535C2×Q8C2×C22⋊D4312yes—
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—861no—
553C22×C4—861no—
554C22×C4—864no—
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—28no—
568SD16—868no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—432no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8#1062189812yes—
581C4⋊C4—24no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—42no—
586C4⋊C4—432no—
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—861no—
597C4⋊C4—3441no—
598C4⋊C4C2×C22⋊D4312yes—
599C22⋊C4—864no—
600C22⋊C4—864no—
601C22⋊C4—864no—
602C22⋊C4—864no—
603C22⋊C4—864no—
604C22⋊C4—862no—
605C22⋊C4—862no—
606C22⋊C4—864no—
607C22⋊C4—3441no—
608C42—24no—
609C42—42no—
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—22no—
633Q8—22no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—3444no—
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—861no—
662C2×C4—862no—
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×C4#41×D4311yescharacteristic
689C2×C4C2×#1062189811yescharacteristic
690C2×C4C2×#1062189811yescharacteristic
691C8—22no—
692C8—41no—
693C8—862no—
694C8—1721no—
695C22—3441no—
696C22—3441no—
697C22—3441no—
698C22—3441no—
699C22—1721no—
700C22—1722no—
701C22—1721no—
702C22—1721no—
703C22—1721no—
704C22—1721no—
705C22—1721no—
706C22—1722no—
707C22—1722no—
708C22—1721no—
709C22C2×#1306329311yescharacteristic
710C22#1458340811yescharacteristic
711C22#1458344611yescharacteristic
712C22#1458370111yescharacteristic
713C22#1458370611yescharacteristic
714C22#1458371211yescharacteristic
715C22#1458371211yescharacteristic
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—81no—
722C4—3441no—
723C4—1721no—
724C4—1722no—
725C4—1721no—
726C4—1721no—
727C4—1722no—
728C4#1458340811yescharacteristic
729C4#1458341011yescharacteristic
730C4#1458344511yescharacteristic
731C4#1458344611yescharacteristic
732C2—3442no—
733C2—3441no—
734C2#1913781011yescharacteristic
735C2#1914388611yescharacteristic
736C2#1914389511yescharacteristic
737C2#1914483011yescharacteristic
738C2#1914486311yescharacteristic
739C2#1914523611yescharacteristic
740C2#1914526711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C4×Q16×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenterC2×C4×Q16D43
hypocenterC43#23585
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#14582997C2semidirect
3. #19137271C2semidirect
4. #19135921C2semidirect
5. #19135832C2semidirect
6. #19135796C2semidirect
8. #19135734C2semidirect
9. #19135686C2semidirect
10. #19135602C2semidirect
12. #19134425C2semidirect
13. C4×#13063247C2semidirect
14. #19134362C2semidirect
15. C2×C4×Q16×C43C2semidirect
364. C2×C4×Q16D43semidirect
433. C43#23585semidirect

Maximal subgroups

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

subgroupindex
C2×#145835212
C2×#145829972
#191372712
#191359212
#191358322
#191357962
#191357792
#191357342
#191356862
#191356022
#191355972
#191344252
C4×#130632472
#191343622
C2×C4×Q16×C432
#2358543