Finite Group Databasebeta

← #25117232

Subgroups — #25117232

Order 11008.

1106 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583058C211yesmaximal, characteristic
2C2×C4×#10621885C211yesmaximal, characteristic, complemented
3C2×#14582897C211yesmaximal, characteristic
4#19137596C211yesmaximal, characteristic, complemented
5#19137434C211yesmaximal, characteristic
6#19135478C211yesmaximal, characteristic, complemented
7#19135281C211yesmaximal, characteristic, complemented
8#19135218C211yesmaximal, characteristic, complemented
9#19135025C211yesmaximal, characteristic, complemented
10#19134933C211yesmaximal, characteristic, complemented
11#19134852C211yesmaximal, characteristic, complemented
12#19134784C211yesmaximal, characteristic, complemented
13#19134424C211yesmaximal, characteristic, complemented
14#19134375C211yesmaximal, characteristic, complemented
15C43×#1880C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063301C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14583058C418yescomplemented
24C4×#10621885—24no—
25C2×#13063259C2211yescharacteristic
26C2×#13063258C2211yescharacteristic
27#14582897—24no—
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C2×#13063235C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic
37#14582806C2211yescharacteristic
38#14582802C2211yescharacteristic
39#14582799—21no—
40#14582799—21no—
41#14582797C2211yescharacteristic
42#14582794—21no—
43#14582783—21no—
44#14582770—21no—
45#14582757—21no—
46#14582756C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48C22⋊C4×Dic43—21no—
49C4×(C2×D43)⋊C4—21no—
50C4×(C2×D43)⋊C4C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C2×#10621900—22no—
63C2×#10621900—22no—
64C2×#10621900—22no—
65C2×#10621900—41no—
66C2×#10621900—41no—
67C2×#10621900C2×C414yes—
68C22×Dic86C2311yescharacteristic
69C22×C22⋊D43—21no—
70C23×Dic43—21no—
71C22×C4×D43—21no—
72C22×C4×D43C2311yescharacteristic
73C2×#10621885—22no—
74C2×#10621885—22no—
75C2×#10621885C2×C414yescomplemented
76C2×#10621872—22no—
77C2×#10621872—22no—
78C2×#10621872—41no—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81#13063301—22no—
82#13063301C2×C414yes—
83C4×Dic86—22no—
84C4×Dic86—41no—
85#13063290—22no—
86#13063290—41no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C4⋊C4×D43—22no—
96C4⋊C4×D43—41no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4D411yescharacteristic
102C2×(C2×D43)⋊C4D411yescharacteristic
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43C2311yescharacteristic
107#13063259—41no—
108#13063258—22no—
109#13063250—22no—
110#13063250C2×C414yescomplemented
111#13063249—22no—
112#13063248D414yes—
113#13063246—22no—
114#13063246C2×C414yescomplemented
115(C2×D43)⋊C8C2×C414yes—
116#13063235—41no—
117C4×C43⋊C8—22no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95D411yescharacteristic
124C43⋊#95D411yescharacteristic
125C22×Q8×C43C2311yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C2×SD16×C43—41no—
128C2×SD16×C43—41no—
129C2×SD16×C43C2×C414yescomplemented
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C4×Q8×C43—22no—
133C4×Q8×C43—41no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C42×C43—21no—
140C2×C42×C43C2311yescharacteristic
141#103×C43—41no—
142#102×C43—22no—
143C24×C43—21no—
144C23×D43C2×D411yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43C22×C412yes—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43C22×C412yes—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C2×C22⋊D43—24no—
164C2×C22⋊D43—42no—
165C2×C22⋊D43—42no—
166C22×Dic43—24no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—42no—
172C22×Dic43—42no—
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176#10621900—28no—
177#10621900—44no—
178#10621900—44no—
179#10621900—44no—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—42no—
185C2×C4×D43—42no—
186C2×C4×D43—81no—
187C2×C4×D43C22×C412yes—
188C2×C4×D43#4112yes—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86C22×C412yes—
193C2×Dic86C2×D412yes—
194C2×Dic86#4112yes—
195SD16×C43—44no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43C22×C412yes—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—42no—
206C4⋊C4×C43C2×D412yes—
207C22⋊C4×C43—42no—
208C22⋊C4×C43—81no—
209C42×C43—21no—
210C42×C43—21no—
211C42×C43—42no—
212C22⋊Dic43—42no—
213C22⋊Dic43—81no—
214#10621885—28no—
215(C2×D43)⋊C4—22no—
216(C2×D43)⋊C4—24no—
217(C2×D43)⋊C4—41no—
218(C2×D43)⋊C4—81no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43C22×C412yes—
225Dic43⋊C4—24no—
226Dic43⋊C4—42no—
227Dic43⋊C4—42no—
228Dic43⋊C4—42no—
229Dic43⋊C4—81no—
230C4×Dic43—21no—
231C4×Dic43—21no—
232C4×Dic43—42no—
233C4×Dic43—42no—
234C4×Dic43—81no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8C22×C412yes—
240C2×C43⋊C8C2×D412yes—
241#10621872—44no—
242C23×C43—22no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43C22×D411yescharacteristic
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43C4×D412yes—
257Q8×C43—22no—
258Q8×C43—22no—
259Q8×C43—41no—
260Q8×C43—41no—
261D4×C43—22no—
262D4×C43—22no—
263D4×C43—41no—
264D4×C43—41no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—22no—
268C2×C4×C43—21no—
269C2×C4×C43—22no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
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#13712yes—
280C2×C4×C43C23×C411yescharacteristic
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43H(5,𝔽2)11yescharacteristic
285C2×C4×C43H(5,𝔽2)11yescharacteristic
286C22⋊D43—48no—
287C2×Dic43—22no—
288C2×Dic43—22no—
289C2×Dic43—21no—
290C2×Dic43—22no—
291C2×Dic43—21no—
292C2×Dic43—22no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—48no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43C4×D412yes—
309C4×D43—22no—
310C4×D43—22no—
311C4×D43—22no—
312C4×D43—22no—
313C4×D43—84no—
314Dic86—22no—
315Dic86—22no—
316Dic86—22no—
317Dic86C4×D414yes—
318C8×C43—22no—
319C8×C43—41no—
320C43⋊C8—22no—
321C43⋊C8—22no—
322#22879—431nomaximal, Sylow
323C22×C43—42no—
324C22×C43—42no—
325C22×C43—42no—
326C22×C43—81no—
327C22×C43—81no—
328C22×C43—81no—
329C22×C43—81no—
330C22×C43C2×C4×D411yescharacteristic
331C22×C43D4211yescharacteristic
332C22×C43#54611yescharacteristic
333C22×C43C2×#13711yescharacteristic
334C22×C43#57511yescharacteristic
335C22×C43#57611yescharacteristic
336C22×C43#57811yescharacteristic
337C2×D43—22no—
338C2×D43—22no—
339C2×D43—22no—
340C2×D43—41no—
341C2×D43—41no—
342C2×D43—41no—
343C2×D43—41no—
344C4×C43—22no—
345C4×C43—42no—
346C4×C43—42no—
347C4×C43—41no—
348C4×C43—81no—
349C4×C43C2×C4×D411yescharacteristic
350C4×C43#51811yescharacteristic
351C4×C43#54611yescharacteristic
352C4×C43#55111yescharacteristic
353Dic43—24no—
354Dic43—22no—
355Dic43—41no—
356Dic43—42no—
357Dic43—41no—
358Dic43—81no—
359Dic43—81no—
360C2×#452—431no—
361C2×C4×Q16—431no—
362C2×#417—431no—
363#2360—431no—
364#2341—431no—
365#1973—431no—
366#1934—431no—
367#1925—431no—
368#1894—431no—
369#1880D4311yescharacteristic, complemented
370#1878—431no—
371#1863—431no—
372#1852—431no—
373#1763—431no—
374#1753—431no—
375C2×C43—82no—
376C2×C43#235811yescharacteristic
377C2×C43C4×#13711yescharacteristic
378C2×C43#295111yescharacteristic
379C2×C43#326811yescharacteristic
380C2×C43#327011yescharacteristic
381C2×C43#332711yescharacteristic
382C2×C43#333311yescharacteristic
383D43—42no—
384C22×#41—431no—
385C22×Q16—431no—
386C22×SD16C2×D4311yescharacteristic
387C22×M16—431no—
388C2×C22⋊Q8—431no—
389C2×C4×Q8—431no—
390C2×C4×Q8—431no—
391C2×C4×Q8C2×D4311yescharacteristic
392C22×C4⋊C4—431no—
393#452—438no—
394C4×Q16—864no—
395C2×#107—431no—
396C2×#107—431no—
397#417—864no—
398C2×#103—431no—
399C2×#103—431no—
400C2×#103—431no—
401C2×#103—431no—
402C2×#103C2×D4311yescharacteristic
403C2×#102—431no—
404C2×#102—431no—
405C2×#102C2×D4311yescharacteristic
406C2×C22⋊C8—431no—
407C2×#97—431no—
408C2×C4×C8—431no—
409#391—431no—
410#390—431no—
411#390—861no—
412#390—861no—
413#390C2×D4311yescharacteristic
414#389—431no—
415#389—861no—
416#387—861no—
417#385—861no—
418#380—431no—
419#380—861no—
420C4×C4⋊C4—431no—
421C4×C22⋊C4—431no—
422C4×C22⋊C4—861no—
423C4×C22⋊C4—861no—
424#340—431no—
425#340—431no—
426#340—431no—
427#340C2×D4311yescharacteristic
428#336—431no—
429#336C2×D4311yescharacteristic
430C43#2287911yescharacteristic, complemented, Sylow
431C2×#41—434no—
432C2×#41—862no—
433C2×#41—862no—
434C2×#41—862no—
435C2×#41—1721no—
436C2×#41—1721no—
437C22×Q8—431no—
438C22×Q8C22×D4311yescharacteristic
439C22×D4—861no—
440C22×D4C22×D4311yescharacteristic
441C23×C4—431no—
442C23×C4—861no—
443C23×C4—861no—
444C2×Q16—434no—
445C2×Q16—862no—
446C2×Q16—862no—
447C2×SD16—41no—
448C2×SD16—41no—
449C2×SD16C4×D4314yescomplemented
450C2×M16—862no—
451C2×M16—862no—
452C2×M16—1721no—
453C22×C8—431no—
454C22×C8—431no—
455C22×C8C22×D4311yescharacteristic
456C22×C8C22×D4311yescharacteristic
457C22⋊Q8—434no—
458C22⋊Q8—862no—
459C4×Q8—22no—
460C4×Q8—41no—
461C4×Q8—862no—
462C4×Q8—862no—
463C4×Q8—1721no—
464C4×Q8—1721no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—431no—
467C2×C4⋊C4—431no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—861no—
470C2×C4⋊C4—862no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—1721no—
476C2×C4⋊C4C22×D4311yescharacteristic
477C2×C4⋊C4C22×D4311yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—431no—
481C2×C22⋊C4—431no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C42—21no—
487C2×C42—431no—
488C2×C42—861no—
489C2×C42—861no—
490C2×C42—861no—
491C2×C42C22×D4311yescharacteristic
492#107—862no—
493#107—1721no—
494#103—41no—
495#103—434no—
496#103—434no—
497#103—862no—
498#103—862no—
499#102—22no—
500#102—434no—
501#102—862no—
502C22⋊C8—434no—
503#97—1721no—
504C4×C8—862no—
505#95—431no—
506#95—431no—
507#95—861no—
508#95—861no—
509#95—861no—
510#95—861no—
511#95—861no—
512C24—21no—
513C24—431no—
514#41—868no—
515#41—1724no—
516#41—1724no—
517#41—1724no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—432no—
524C2×Q8—432no—
525C2×Q8—432no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8C2×C4×D4312yes—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—864no—
536C2×D4—1722no—
537C2×D4—1722no—
538C2×D4C2×C4×D4312yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—431no—
543C22×C4—432no—
544C22×C4—432no—
545C22×C4—431no—
546C22×C4—431no—
547C22×C4—864no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—3441no—
557C22×C4—1722no—
558C22×C4—1722no—
559C22×C4—1722no—
560C22×C4—1722no—
561C22×C4D4×D4311yescharacteristic
562C22×C4D4×D4311yescharacteristic
563C22×C4C23×D4311yescharacteristic
564Q16—868no—
565SD16—44no—
566M16—1724no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—432no—
573C2×C8—432no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8C2×C4×D4312yes—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—42no—
583C4⋊C4—432no—
584C4⋊C4—864no—
585C4⋊C4—861no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—3441no—
591C4⋊C4—1722no—
592C4⋊C4—1722no—
593C4⋊C4—1722no—
594C4⋊C4D4×D4312yes—
595C22⋊C4—42no—
596C22⋊C4—81no—
597C22⋊C4—864no—
598C22⋊C4—862no—
599C22⋊C4—3441no—
600C22⋊C4—3441no—
601C22⋊C4—1721no—
602C22⋊C4—1722no—
603C42—21no—
604C42—21no—
605C42—42no—
606C42—861no—
607C42—861no—
608C42—3441no—
609C42—1722no—
610C42—1722no—
611C23—22no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—432no—
619C23—861no—
620C23—861no—
621C23—861no—
622C23—861no—
623C23—861no—
624C23—861no—
625C23C2×D4×D4311yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—41no—
629Q8—41no—
630Q8—434no—
631Q8—862no—
632Q8—862no—
633Q8—862no—
634D4—22no—
635D4—22no—
636D4—41no—
637D4—41no—
638D4—1728no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—432no—
654C2×C4—862no—
655C2×C4—862no—
656C2×C4—861no—
657C2×C4—862no—
658C2×C4—861no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—861no—
670C2×C4—3444no—
671C2×C4—1728no—
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#1306335412yes—
681C2×C4C22×C4×D4311yescharacteristic
682C2×C4C2×D4×D4311yescharacteristic
683C2×C4#41×D4311yescharacteristic
684C2×C4#41×D4311yescharacteristic
685C2×C4#1306337011yescharacteristic
686C2×C4#1306337011yescharacteristic
687C8—22no—
688C8—41no—
689C8—862no—
690C8—862no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—862no—
699C22—862no—
700C22—862no—
701C22—1721no—
702C22—1721no—
703C22—1721no—
704C22—1721no—
705C22C4×D4×D4311yescharacteristic
706C22#1458353111yescharacteristic
707C22#1458354611yescharacteristic
708C22C2×#1306335411yescharacteristic
709C22#1458369611yescharacteristic
710C22#1458370311yescharacteristic
711C22#1458371511yescharacteristic
712C4—22no—
713C4—42no—
714C4—41no—
715C4—42no—
716C4—81no—
717C4—862no—
718C4—864no—
719C4—3441no—
720C4—3441no—
721C4—1722no—
722C4—1721no—
723C4—1721no—
724C4C4×D4×D4311yescharacteristic
725C4#1458337211yescharacteristic
726C4#1458354611yescharacteristic
727C4#1458357711yescharacteristic
728C2—82no—
729C2—1722no—
730C2#1913757811yescharacteristic
731C2C4×#1306335411yescharacteristic
732C2#1914346711yescharacteristic
733C2#1914613911yescharacteristic
734C2#1914615811yescharacteristic
735C2#1914687011yescharacteristic
736C2#1914693611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1880C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
cosocleC22×C4×C43C24
hypercenter#1880D43
hypocenterC43#22879
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621885C2semidirect
4. #19137596C2semidirect
6. #19135478C2semidirect
7. #19135281C2semidirect
8. #19135218C2semidirect
9. #19135025C2semidirect
10. #19134933C2semidirect
11. #19134852C2semidirect
12. #19134784C2semidirect
13. #19134424C2semidirect
14. #19134375C2semidirect
15. C43×#1880C2semidirect
23. #14583058C4semidirect
75. C2×#10621885C2×C4semidirect
110. #13063250C2×C4semidirect
114. #13063246C2×C4semidirect
129. C2×SD16×C43C2×C4semidirect
369. #1880D43semidirect
430. C43#22879semidirect
449. C2×SD16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830582
C2×C4×#106218852
C2×#145828972
#191375962
#191374342
#191354782
#191352812
#191352182
#191350252
#191349332
#191348522
#191347842
#191344242
#191343752
C43×#18802
#2287943