Finite Group Databasebeta

← #25116968

Subgroups — #25116968

Order 11008.

1134 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×#14583058C211yesmaximal, characteristic
2C2×#14582897C211yesmaximal, characteristic
3#19137596C211yesmaximal, characteristic, complemented
4#19137420C211yesmaximal, characteristic
5#19135453C211yesmaximal, characteristic, complemented
6#19135285C211yesmaximal, characteristic, complemented
7#19135235C211yesmaximal, characteristic, complemented
8#19135025C211yesmaximal, characteristic, complemented
9#19134936C211yesmaximal, characteristic, complemented
10#19134931C211yesmaximal, characteristic, complemented
11#19134842C211yesmaximal, characteristic, complemented
12#19134781C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic, complemented
14#19134380C211yesmaximal, characteristic, complemented
15C2×C43×#440C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063301C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22#14583058C418yescomplemented
23C2×#13063258C2211yescharacteristic
24#14582897—24no—
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582805C2211yescharacteristic
35#14582804C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582794—21no—
38#14582783—21no—
39#14582778—21no—
40#14582776—21no—
41#14582770—21no—
42#14582760—21no—
43#14582756C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4×(C2×D43)⋊C4—21no—
46C4×(C2×D43)⋊C4C2211yescharacteristic
47C2×C43⋊#95—21no—
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#440—24no—
58C2×#107×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#97×C43C2211yescharacteristic
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—
71C23×Dic43—21no—
72C22×C4×D43—21no—
73C22×C4×D43C2311yescharacteristic
74C2×#10621885—41no—
75C2×#10621885—41no—
76C2×#10621885C2×C414yescomplemented
77C2×#10621872—22no—
78C2×#10621872—22no—
79C2×#10621872—41no—
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82#13063301—22no—
83#13063301C2×C414yescomplemented
84D4×Dic43—22no—
85D4×Dic43—41no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C4⋊C4×D43—22no—
93C4⋊C4×D43—41no—
94C2×C22⋊Dic43—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4D411yescharacteristic
98C2×(C2×D43)⋊C4D411yescharacteristic
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101#13063258—41no—
102#13063250—22no—
103#13063250C2×C414yescomplemented
104#13063249—41no—
105#13063248—22no—
106#13063246—22no—
107#13063246C2×C414yescomplemented
108(C2×D43)⋊C8C2×C414yescomplemented
109C8×Dic43—41no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95D411yescharacteristic
120C43⋊#95D411yescharacteristic
121C22×Q8×C43C2311yescharacteristic
122C22×D4×C43C2311yescharacteristic
123C23×C4×C43—21no—
124C2×SD16×C43—22no—
125C2×SD16×C43—22no—
126C2×SD16×C43C2×C414yescomplemented
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C4×Q8×C43—22no—
130C4×Q8×C43—41no—
131C4×D4×C43—22no—
132C4×D4×C43—41no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C42×C43—21no—
138C2×C42×C43C2311yescharacteristic
139#107×C43—22no—
140#103×C43—22no—
141#102×C43D414yes—
142#97×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×C43C22×C412yes—
155C2×D4×C43C2×D412yes—
156C2×D4×C43#4112yes—
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×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—24no—
167C2×C22⋊D43—42no—
168C2×C22⋊D43—42no—
169C22×Dic43—24no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—42no—
175C22×Dic43—42no—
176C22×Dic43—42no—
177C22×Dic43—42no—
178C22×Dic43—81no—
179C22×Dic43C2×D411yescharacteristic
180C22×Dic43C2×D411yescharacteristic
181C22×Dic43C2×D411yescharacteristic
182#10621900—28no—
183#10621900—44no—
184#10621900—44no—
185#10621900—44no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—42no—
191C2×C4×D43—42no—
192C2×C4×D43—81no—
193C2×C4×D43C22×C412yes—
194C2×C4×D43#4112yes—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86C22×C412yes—
201SD16×C43—28no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43C22×C412yes—
207C2×C8×C43C2×D412yes—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—42no—
212C4⋊C4×C43C2×D412yes—
213C22⋊C4×C43—42no—
214C42×C43—21no—
215C42×C43—21no—
216C42×C43—42no—
217C22⋊Dic43—42no—
218#10621885—44no—
219(C2×D43)⋊C4—22no—
220(C2×D43)⋊C4—24no—
221(C2×D43)⋊C4—41no—
222(C2×D43)⋊C4—81no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43C22×C412yes—
229Dic43⋊C4—24no—
230Dic43⋊C4—42no—
231Dic43⋊C4—81no—
232C4×Dic43—21no—
233C4×Dic43—21no—
234C4×Dic43—81no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8C22×C412yes—
241#10621872—44no—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—22no—
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—22no—
264D4×C43C4×D414yes—
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—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—84no—
281C2×C4×C43C23×C411yescharacteristic
282C2×C4×C43C22×D411yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43H(5,𝔽2)11yescharacteristic
286C2×C4×C43H(5,𝔽2)11yescharacteristic
287C22⋊D43—48no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—48no—
298C2×Dic43—41no—
299C2×Dic43—41no—
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×Dic43—84no—
309C2×Dic43C4×D412yes—
310C2×Dic43#13712yes—
311C4×D43—22no—
312C4×D43—22no—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—84no—
316Dic86—22no—
317Dic86—22no—
318Dic86—41no—
319Dic86—41no—
320C8×C43—22no—
321C8×C43—22no—
322C43⋊C8—22no—
323C43⋊C8—41no—
324#22862—431nomaximal, Sylow
325C22×C43—24no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43—42no—
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43C2×C4×D411yescharacteristic
333C22×C43D4211yescharacteristic
334C22×C43#54611yescharacteristic
335C22×C43C2×#13711yescharacteristic
336C22×C43#57511yescharacteristic
337C22×C43#57611yescharacteristic
338C22×C43#57811yescharacteristic
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—41no—
343C2×D43—41no—
344C2×D43—41no—
345C2×D43—41no—
346C4×C43—42no—
347C4×C43—42no—
348C4×C43—41no—
349C4×C43—41no—
350C4×C43—81no—
351C4×C43C2×C4×D411yescharacteristic
352C4×C43#51811yescharacteristic
353C4×C43#54611yescharacteristic
354C4×C43#55111yescharacteristic
355Dic43—22no—
356Dic43—22no—
357Dic43—42no—
358Dic43—42no—
359Dic43—41no—
360Dic43—81no—
361Dic43—81no—
362C2×#452—431no—
363C2×#440D4311yescharacteristic, complemented
364C2×#417—431no—
365#2360—431no—
366#2339—431no—
367#1969—431no—
368#1935—431no—
369#1928—431no—
370#1894—431no—
371#1878—431no—
372#1877—431no—
373#1862—431no—
374#1852—431no—
375C4×#102—431no—
376#1753—431no—
377C2×C43—44no—
378C2×C43#235811yescharacteristic
379C2×C43C4×#13711yescharacteristic
380C2×C43#295111yescharacteristic
381C2×C43#327311yescharacteristic
382C2×C43#327611yescharacteristic
383C2×C43#331411yescharacteristic
384C2×C43#331511yescharacteristic
385D43—42no—
386C22×#41—431no—
387C22×Q16—431no—
388C22×SD16C2×D4311yescharacteristic
389C22×M16—431no—
390C2×C22⋊Q8—431no—
391C2×C4×Q8C2×D4311yescharacteristic
392C2×C4×D4—431no—
393C2×C4×D4C2×D4311yescharacteristic
394C22×C4⋊C4—431no—
395#452—438no—
396#440—24no—
397C2×#107—431no—
398C2×#107C2×D4311yescharacteristic
399#417—864no—
400C2×#103—431no—
401C2×#103—431no—
402C2×#103—431no—
403C2×#103—431no—
404C2×#103C2×D4311yescharacteristic
405C2×#102—431no—
406C2×#102—431no—
407C2×#102C2×D4311yescharacteristic
408C2×C22⋊C8—431no—
409C2×#97C2×D4311yescharacteristic
410C2×C4×C8—431no—
411#391—431no—
412#391—431no—
413#391—431no—
414#389—431no—
415#389—861no—
416#387—861no—
417#386—861no—
418#386—861no—
419#385—861no—
420#381—861no—
421#380—431no—
422C4×C4⋊C4—431no—
423C4×C22⋊C4—431no—
424C4×C22⋊C4—861no—
425C2×#95—861no—
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#336—431no—
431#336—431no—
432C43#2286211yescharacteristic, complemented, Sylow
433C2×#41—434no—
434C2×#41—862no—
435C2×#41—862no—
436C2×#41—862no—
437C2×#41—1721no—
438C2×#41—1721no—
439C22×Q8—431no—
440C22×Q8C22×D4311yescharacteristic
441C22×D4—861no—
442C22×D4C22×D4311yescharacteristic
443C23×C4—21no—
444C23×C4—431no—
445C23×C4—861no—
446C23×C4—861no—
447C23×C4—861no—
448C2×Q16—434no—
449C2×Q16—1721no—
450C2×Q16—1721no—
451C2×SD16—22no—
452C2×SD16—22no—
453C2×SD16C4×D4314yescomplemented
454C2×M16—862no—
455C2×M16—862no—
456C2×M16—1721no—
457C22×C8—431no—
458C22×C8—431no—
459C22×C8C22×D4311yescharacteristic
460C22×C8C22×D4311yescharacteristic
461C22⋊Q8—434no—
462C22⋊Q8—862no—
463C4×Q8—22no—
464C4×Q8—41no—
465C4×D4—22no—
466C4×D4—41no—
467C4×D4—862no—
468C4×D4—1721no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—862no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—1721no—
478C2×C4⋊C4C22×D4311yescharacteristic
479C2×C4⋊C4C22×D4311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—431no—
482C2×C22⋊C4—431no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C42—21no—
487C2×C42—431no—
488C2×C42—861no—
489C2×C42C22×D4311yescharacteristic
490#107—22no—
491#107—1721no—
492#103—22no—
493#103—434no—
494#103—862no—
495#103—862no—
496#103—1721no—
497#102—434no—
498#102—862no—
499#102C22⋊D4314yes—
500C22⋊C8—434no—
501#97—22no—
502C4×C8—1721no—
503#95—431no—
504#95—431no—
505#95—861no—
506#95—861no—
507#95—861no—
508#95—861no—
509#95—861no—
510#95—861no—
511#95—861no—
512#95—861no—
513#95—861no—
514C24—21no—
515C24—431no—
516#41—868no—
517#41—1724no—
518#41—1724no—
519#41—1724no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—432no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8C2×C4×D4312yes—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—864no—
536C2×D4—1722no—
537C2×D4—1722no—
538C2×D4C2×C4×D4312yes—
539C2×D4#1062189812yes—
540C2×D4C2×C22⋊D4312yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—81no—
547C22×C4—431no—
548C22×C4—431no—
549C22×C4—432no—
550C22×C4—432no—
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—3441no—
562C22×C4—3441no—
563C22×C4—1722no—
564C22×C4—1722no—
565C22×C4—1722no—
566C22×C4—1722no—
567C22×C4—1722no—
568C22×C4—1722no—
569C22×C4D4×D4311yescharacteristic
570C22×C4D4×D4311yescharacteristic
571C22×C4C23×D4311yescharacteristic
572Q16—1724no—
573SD16—28no—
574M16—1724no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—432no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8C2×C4×D4312yes—
586C2×C8C2×C22⋊D4312yes—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—42no—
591C4⋊C4—432no—
592C4⋊C4—864no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—3441no—
599C4⋊C4—1722no—
600C4⋊C4C2×C22⋊D4312yes—
601C22⋊C4—42no—
602C22⋊C4—862no—
603C22⋊C4—864no—
604C22⋊C4—3441no—
605C22⋊C4—1721no—
606C22⋊C4—1722no—
607C42—21no—
608C42—21no—
609C42—42no—
610C42—861no—
611C42—861no—
612C42—3441no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—432no—
621C23—861no—
622C23—861no—
623C23—861no—
624C23—861no—
625C23—861no—
626C23—861no—
627C23C2×D4×D4311yescharacteristic
628Q8—22no—
629Q8—22no—
630Q8—41no—
631Q8—41no—
632Q8—862no—
633Q8—862no—
634Q8—1721no—
635Q8—1721no—
636D4—22no—
637D4—22no—
638D4—22no—
639D4—1728no—
640D4C4×C22⋊D4314yes—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—84no—
657C2×C4—432no—
658C2×C4—432no—
659C2×C4—861no—
660C2×C4—861no—
661C2×C4—861no—
662C2×C4—861no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—861no—
672C2×C4—3444no—
673C2×C4—3444no—
674C2×C4—1728no—
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—1721no—
684C2×C4—1721no—
685C2×C4C22×C4×D4311yescharacteristic
686C2×C4C22×C22⋊D4311yescharacteristic
687C2×C4#41×D4311yescharacteristic
688C2×C4C2×#1062189811yescharacteristic
689C2×C4#1306337011yescharacteristic
690C2×C4#1306337111yescharacteristic
691C8—22no—
692C8—22no—
693C8—862no—
694C8—1721no—
695C22—24no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—862no—
703C22—862no—
704C22—862no—
705C22—1721no—
706C22—1721no—
707C22—1721no—
708C22—1721no—
709C22C4×D4×D4311yescharacteristic
710C22D4×C22⋊D4311yescharacteristic
711C22#1458354511yescharacteristic
712C22#137×D4311yescharacteristic
713C22#1458369511yescharacteristic
714C22#1458370311yescharacteristic
715C22#1458371511yescharacteristic
716C4—42no—
717C4—41no—
718C4—42no—
719C4—41no—
720C4—81no—
721C4—862no—
722C4—862no—
723C4—3441no—
724C4—3441no—
725C4—1722no—
726C4—1722no—
727C4—1721no—
728C4C2×C4×C22⋊D4311yescharacteristic
729C4#1458337111yescharacteristic
730C4#1458353711yescharacteristic
731C4#1458357811yescharacteristic
732C2—44no—
733C2—1722no—
734C2#1913757211yescharacteristic
735C2#1914341711yescharacteristic
736C2#1914346711yescharacteristic
737C2#1914620011yescharacteristic
738C2#1914623511yescharacteristic
739C2#1914668111yescharacteristic
740C2#1914669611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
cosocleC22×C4×C43C24
hypercenterC2×#440D43
hypocenterC43#22862
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
3. #19137596C2semidirect
5. #19135453C2semidirect
6. #19135285C2semidirect
7. #19135235C2semidirect
8. #19135025C2semidirect
9. #19134936C2semidirect
10. #19134931C2semidirect
11. #19134842C2semidirect
12. #19134781C2semidirect
13. #102×Dic43C2semidirect
14. #19134380C2semidirect
15. C2×C43×#440C2semidirect
22. #14583058C4semidirect
76. C2×#10621885C2×C4semidirect
83. #13063301C2×C4semidirect
103. #13063250C2×C4semidirect
107. #13063246C2×C4semidirect
108. (C2×D43)⋊C8C2×C4semidirect
126. C2×SD16×C43C2×C4semidirect
363. C2×#440D43semidirect
432. C43#22862semidirect
453. 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×#145828972
#191375962
#191374202
#191354532
#191352852
#191352352
#191350252
#191349362
#191349312
#191348422
#191347812
#102×Dic432
#191343802
C2×C43×#4402
#2286243