Finite Group Databasebeta

← #25133065

Subgroups — #25133065

Order 11008.

1118 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583196C211yesmaximal, characteristic, complemented
2C2×C4×#10621882C211yesmaximal, characteristic
3#19139953C211yesmaximal, characteristic, complemented
4#19135930C211yesmaximal, characteristic, complemented
5#19135920C211yesmaximal, characteristic, complemented
6#19135738C211yesmaximal, characteristic, complemented
7#19135728C211yesmaximal, characteristic, complemented
8#19135561C211yesmaximal, characteristic, complemented
9#19135532C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic
11#19134943C211yesmaximal, characteristic
12#19134856C211yesmaximal, characteristic, complemented
13#19134842C211yesmaximal, characteristic, complemented
14#19134605C211yesmaximal, characteristic, complemented
15C2×C43×#554C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18#14583196—24no—
19C4×#10621882—24no—
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582834—21no—
32#14582810—21no—
33#14582801C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582770—21no—
38#14582770—21no—
39#14582765C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C43×#554—24no—
51C43×#554—24no—
52C2×C4⋊Q8×C43C2211yescharacteristic
53C2×#125×C43C2211yescharacteristic
54C2×#125×C43C2211yescharacteristic
55C2×C22⋊Q8×C43—21no—
56C2×C22⋊Q8×C43—21no—
57C2×C22⋊Q8×C43—21no—
58C2×C4×Q8×C43C2211yescharacteristic
59C2×C4×D4×C43C2211yescharacteristic
60C2×C4×D4×C43C2211yescharacteristic
61C2×C4×D4×C43C2211yescharacteristic
62C22×C4⋊C4×C43—21no—
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C2×#10621882—22no—
66C2×#10621882—22no—
67C2×#10621882Q814yescomplemented
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C4×D172—22no—
73C4×D172—22no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84#13063258—22no—
85#13063258—22no—
86#13063256—22no—
87C4⋊(C43⋊C8)—22no—
88#13063246—22no—
89#13063246—22no—
90#13063246—22no—
91#13063245—22no—
92#13063245—22no—
93#13063245—22no—
94C4×C43⋊C8—22no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C22×Q8×C43—21no—
100C22×Q8×C43D411yescharacteristic
101C22×D4×C43C2311yescharacteristic
102C23×C4×C43—21no—
103C23×C4×C43—21no—
104C23×C4×C43—21no—
105C4⋊Q8×C43—22no—
106C4⋊Q8×C43—22no—
107#125×C43—22no—
108#125×C43—22no—
109#125×C43—22no—
110#125×C43D414yes—
111C22⋊Q8×C43—28no—
112C22⋊Q8×C43—28no—
113C22⋊Q8×C43—28no—
114C4×Q8×C43—22no—
115C4×Q8×C43—22no—
116C4×D4×C43—22no—
117C4×D4×C43—22no—
118C4×D4×C43—22no—
119C4×D4×C43—22no—
120C4×D4×C43—22no—
121C4×D4×C43D414yes—
122C2×C4⋊C4×C43—28no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43D411yescharacteristic
129C2×C4⋊C4×C43D411yescharacteristic
130C2×C4⋊C4×C43D411yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C2×C42×C43C2311yescharacteristic
139C2×C42×C43C2311yescharacteristic
140C24×C43—21no—
141C23×D43—21no—
142C2×Q8×C43—24no—
143C2×Q8×C43—22no—
144C2×Q8×C43—22no—
145C2×Q8×C43—41no—
146C2×Q8×C43—81no—
147C2×Q8×C43—81no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43C2×D412yes—
152C2×D4×C43C2×Q812yes—
153C2×D4×C43#4112yes—
154C22×C4×C43—24no—
155C22×C4×C43—24no—
156C22×C4×C43—24no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—42no—
161C22×C4×C43—42no—
162C22×C4×C43—81no—
163C22×C4×C43—81no—
164C22×C4×C43—81no—
165C22×C4×C43—81no—
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2411yescharacteristic
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172C2×Q812yes—
182C2×C4×D43—42no—
183C2×C4×D43—81no—
184C2×C4×D43—81no—
185C4⋊C4×C43—24no—
186C4⋊C4×C43—24no—
187C4⋊C4×C43—24no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—24no—
190C4⋊C4×C43—24no—
191C4⋊C4×C43—22no—
192C4⋊C4×C43—22no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43C2×D412yes—
197C4⋊C4×C43C2×D412yes—
198C4⋊C4×C43C2×D412yes—
199C22⋊C4×C43—24no—
200C22⋊C4×C43—24no—
201C22⋊C4×C43—24no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43—21no—
206C42×C43C2×D412yes—
207C42×C43C2×D412yes—
208#10621882—28no—
209(C2×D43)⋊C4—42no—
210(C2×D43)⋊C4—42no—
211(C2×D43)⋊C4—42no—
212(C2×D43)⋊C4—81no—
213(C2×D43)⋊C4—81no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220Dic43⋊C4—81no—
221Dic43⋊C4—81no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8C2×Q812yes—
234C23×C43—22no—
235C23×C43—22no—
236C23×C43—22no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43C22×D411yescharacteristic
242C22×D43—22no—
243C22×D43—41no—
244C22×D43—41no—
245C22×D43—41no—
246C22×D43—41no—
247C22×D43—41no—
248C22×D43—41no—
249Q8×C43—44no—
250Q8×C43—84no—
251D4×C43—22no—
252D4×C43—22no—
253D4×C43—22no—
254D4×C43C22⋊Q814yes—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—48no—
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—84no—
281C2×C4×C43—84no—
282C2×C4×C43#12012yes—
283C2×C4×C43#12012yes—
284C2×C4×C43#13512yes—
285C2×C4×C43C22×D411yescharacteristic
286C2×C4×C43C22×D411yescharacteristic
287C2×C4×C43C22×Q811yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C432−1+411yescharacteristic
290C2×C4×C432−1+411yescharacteristic
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300D172—22no—
301D172—22no—
302D172—41no—
303D172—41no—
304C4×D43—84no—
305C43⋊C8—22no—
306C43⋊C8—41no—
307C43⋊C8—41no—
308C43⋊C8—41no—
309#24335—431nomaximal, Sylow
310C22×C43—24no—
311C22×C43—42no—
312C22×C43—42no—
313C22×C43—42no—
314C22×C43—42no—
315C22×C43—42no—
316C22×C43—42no—
317C22×C43C2×#12011yescharacteristic
318C22×C43#54811yescharacteristic
319C22×C43D4×Q811yescharacteristic
320C22×C43C2×#13511yescharacteristic
321C22×C43#57511yescharacteristic
322C22×C43#57611yescharacteristic
323C22×C43#57611yescharacteristic
324C2×D43—42no—
325C2×D43—42no—
326C2×D43—42no—
327C2×D43—81no—
328C2×D43—81no—
329C2×D43—81no—
330C2×D43—81no—
331C4×C43—22no—
332C4×C43—22no—
333C4×C43—22no—
334C4×C43—41no—
335C4×C43—42no—
336C4×C43—41no—
337C4×C43—41no—
338C4×C43—42no—
339C4×C43—42no—
340C4×C43C2×C22⋊Q811yescharacteristic
341C4×C43#53611yescharacteristic
342C4×C43#54811yescharacteristic
343C4×C43D4×Q811yescharacteristic
344Dic43—81no—
345Dic43—81no—
346Dic43—81no—
347C2×#554D4311yescharacteristic, complemented
348C2×#478—431no—
349C2×C4×D8—431no—
350#2580—431no—
351#2059—431no—
352#2057—431no—
353#2025—431no—
354#2023—431no—
355#1991—431no—
356#1984—431no—
357#1879—431no—
358#1879—431no—
359#1864—431no—
360#1862—431no—
361#1804—431no—
362C2×C43—44no—
363C2×C43#240911yescharacteristic
364C2×C43#300211yescharacteristic
365C2×C43#300811yescharacteristic
366C2×C43#336111yescharacteristic
367C2×C43#337011yescharacteristic
368C2×C43#338011yescharacteristic
369C2×C43#338911yescharacteristic
370D43—82no—
371C22×D8—431no—
372#554—24no—
373#554—24no—
374C2×C4⋊Q8C2×D4311yescharacteristic
375C2×#125C2×D4311yescharacteristic
376C2×#125C2×D4311yescharacteristic
377C2×C22⋊Q8—21no—
378C2×C22⋊Q8—21no—
379C2×C22⋊Q8—21no—
380C2×C4×Q8C2×D4311yescharacteristic
381C2×C4×D4—431no—
382C2×C4×D4C2×D4311yescharacteristic
383C2×C4×D4C2×D4311yescharacteristic
384C2×C4×D4C2×D4311yescharacteristic
385C22×C4⋊C4—21no—
386#478—864no—
387C4×D8—864no—
388C2×#107—431no—
389C2×#107—431no—
390C2×#106—431no—
391C2×C4⋊C8—431no—
392C2×#102—431no—
393C2×#102—431no—
394C2×#102—431no—
395C2×#102—431no—
396C2×#102—431no—
397C2×#102—431no—
398C2×C4×C8—431no—
399#399—861no—
400#393—861no—
401#390—431no—
402#390—431no—
403#389—431no—
404#389—431no—
405#385—861no—
406#385—861no—
407#382—431no—
408#340—431no—
409#340—431no—
410#340—431no—
411#340—431no—
412#340—431no—
413#340—431no—
414#336—431no—
415#336—431no—
416#336—431no—
417#336—431no—
418C43#2433511yescharacteristic, complemented, Sylow
419C22×Q8—21no—
420C22×Q8C22⋊D4311yescharacteristic
421C22×D4—431no—
422C22×D4C22×D4311yescharacteristic
423C23×C4—21no—
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—861no—
427C2×D8—434no—
428C2×D8—862no—
429C2×D8—862no—
430C22×C8—431no—
431C22×C8—431no—
432C22×C8—431no—
433C22×C8—431no—
434C4⋊Q8—22no—
435C4⋊Q8—22no—
436#125—22no—
437#125—22no—
438#125—22no—
439#125C22⋊D4314yes—
440C22⋊Q8—28no—
441C22⋊Q8—28no—
442C22⋊Q8—28no—
443C4×Q8—22no—
444C4×Q8—22no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—862no—
451C4×D4—862no—
452C4×D4C22⋊D4314yes—
453C2×C4⋊C4—28no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—431no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4—431no—
462C2×C4⋊C4—861no—
463C2×C4⋊C4—861no—
464C2×C4⋊C4C22⋊D4311yescharacteristic
465C2×C4⋊C4C22⋊D4311yescharacteristic
466C2×C4⋊C4C22⋊D4311yescharacteristic
467C2×C4⋊C4C22×D4311yescharacteristic
468C2×C4⋊C4C22×D4311yescharacteristic
469C2×C4⋊C4C22×D4311yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—861no—
474C2×C22⋊C4—861no—
475C2×C22⋊C4—861no—
476C2×C22⋊C4—861no—
477C2×C22⋊C4—861no—
478C2×C42C22×D4311yescharacteristic
479C2×C42C22×D4311yescharacteristic
480C2×C42C22×D4311yescharacteristic
481#107—862no—
482#107—862no—
483#106—862no—
484C4⋊C8—862no—
485#102—862no—
486#102—862no—
487#102—862no—
488#102—862no—
489#102—862no—
490#102—862no—
491C4×C8—862no—
492#95—861no—
493#95—861no—
494#95—861no—
495#95—861no—
496C24—21no—
497C24—861no—
498C2×Q8—24no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—41no—
502C2×Q8—81no—
503C2×Q8—81no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—432no—
508C2×D4—861no—
509C2×D4—861no—
510C2×D4—861no—
511C2×D4—861no—
512C2×D4—861no—
513C2×D4Q8×D4312yes—
514C2×D4#1062190212yes—
515C2×D4C2×C22⋊D4312yes—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—861no—
531C22×C4—3441no—
532C22×C4—3441no—
533C22×C4—1722no—
534C22×C4C2×C22⋊D4311yescharacteristic
535C22×C4C2×C22⋊D4311yescharacteristic
536C22×C4C2×C22⋊D4311yescharacteristic
537C22×C4C2×C22⋊D4311yescharacteristic
538C22×C4C2×C22⋊D4311yescharacteristic
539C22×C4C2×C22⋊D4311yescharacteristic
540C22×C4C23×D4311yescharacteristic
541D8—868no—
542C2×C8—432no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—861no—
552C2×C8—861no—
553C2×C8—861no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—861no—
566C4⋊C4—861no—
567C4⋊C4—861no—
568C4⋊C4—861no—
569C4⋊C4—861no—
570C4⋊C4—861no—
571C4⋊C4—3441no—
572C4⋊C4—3441no—
573C4⋊C4C2×C22⋊D4312yes—
574C4⋊C4C2×C22⋊D4312yes—
575C4⋊C4C2×C22⋊D4312yes—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—3441no—
580C22⋊C4—3441no—
581C22⋊C4—1722no—
582C22⋊C4—1722no—
583C22⋊C4—1722no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42C2×C22⋊D4312yes—
589C42C2×C22⋊D4312yes—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—862no—
598C23—1721no—
599C23—1721no—
600C23—1721no—
601C23—1721no—
602C23—1721no—
603C23—1721no—
604C23C22×C22⋊D4311yescharacteristic
605Q8—44no—
606Q8—84no—
607D4—22no—
608D4—22no—
609D4—22no—
610D4—862no—
611D4—862no—
612D4—1721no—
613D4—1721no—
614D4#1306330114yes—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—48no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—84no—
641C2×C4—84no—
642C2×C4—3444no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1721no—
647C2×C4—1721no—
648C2×C4—1721no—
649C2×C4—1721no—
650C2×C4—1721no—
651C2×C4—1721no—
652C2×C4#1306329412yes—
653C2×C4#1306329412yes—
654C2×C4#1306334512yes—
655C2×C4C22×C22⋊D4311yescharacteristic
656C2×C4C22×C22⋊D4311yescharacteristic
657C2×C4C2×Q8×D4311yescharacteristic
658C2×C4C2×#1062190211yescharacteristic
659C2×C4#1306337311yescharacteristic
660C2×C4#1306337311yescharacteristic
661C8—862no—
662C8—1721no—
663C8—1721no—
664C8—1721no—
665C22—24no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—3441no—
673C22—3441no—
674C22—3441no—
675C22—3441no—
676C22—1722no—
677C22—1722no—
678C22—1722no—
679C22C2×#1306329411yescharacteristic
680C22#1458356011yescharacteristic
681C22Q8×C22⋊D4311yescharacteristic
682C22C2×#1306334511yescharacteristic
683C22#1458369711yescharacteristic
684C22#1458370211yescharacteristic
685C22#1458370211yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—41no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—42no—
694C4—42no—
695C4—3441no—
696C4—3441no—
697C4—3441no—
698C4C2×#1306330111yescharacteristic
699C4#1458347311yescharacteristic
700C4#1458356011yescharacteristic
701C4Q8×C22⋊D4311yescharacteristic
702C2—44no—
703C2—3442no—
704C2#1913795411yescharacteristic
705C2#1914381311yescharacteristic
706C2#1914386311yescharacteristic
707C2#1914725511yescharacteristic
708C2#1914734811yescharacteristic
709C2#1914745811yescharacteristic
710C2#1914754911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#554C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenterC2×#554D43
hypocenterC43#24335
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#14583196C2semidirect
3. #19139953C2semidirect
4. #19135930C2semidirect
5. #19135920C2semidirect
6. #19135738C2semidirect
7. #19135728C2semidirect
8. #19135561C2semidirect
9. #19135532C2semidirect
12. #19134856C2semidirect
13. #19134842C2semidirect
14. #19134605C2semidirect
15. C2×C43×#554C2semidirect
67. C2×#10621882Q8semidirect
347. C2×#554D43semidirect
418. C43#24335semidirect

Maximal subgroups

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

subgroupindex
C2×#145831962
C2×C4×#106218822
#191399532
#191359302
#191359202
#191357382
#191357282
#191355612
#191355322
#191349432
#191348562
#191348422
#191346052
C2×C43×#5542
#2433543