Finite Group Databasebeta

← #25113916

Subgroups — #25113916

Order 11008.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137480C211yesmaximal, characteristic, complemented
2D4×C22⋊Dic43C211yesmaximal, characteristic
3#19135294C211yesmaximal, characteristic, complemented
4#19135280C211yesmaximal, characteristic, complemented
5#19135224C211yesmaximal, characteristic, complemented
6#19135217C211yesmaximal, characteristic, complemented
7#19134858C211yesmaximal, characteristic, complemented
8#19134844C211yesmaximal, characteristic, complemented
9#19134690C211yesmaximal, characteristic, complemented
10#19134628C211yesmaximal, characteristic, complemented
11#19134526C211yesmaximal, characteristic
12#19134422C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic, complemented
14#19134376C211yesmaximal, characteristic, complemented
15C2×C43×#418C211yesmaximal, characteristic
16C2×D4×Dic43C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C22×C22⋊Dic43—21no—
19C2×#13063259C2211yescharacteristic, complemented
20C2×#13063257C2211yescharacteristic, complemented
21C2×#13063246C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063235C2211yescharacteristic, complemented
27C2×C8×Dic43C2211yescharacteristic, complemented
28#14582802C2211yescharacteristic
29#14582802C2211yescharacteristic
30#14582798C2211yescharacteristic, complemented
31#14582798C2211yescharacteristic, complemented
32#14582792—21no—
33#14582792—21no—
34#14582779—21no—
35#14582779—21no—
36#14582765—21no—
37#14582759C2211yescharacteristic
38#14582759C2211yescharacteristic
39#14582755—21no—
40C4⋊C4×Dic43C2211yescharacteristic, complemented
41C4⋊C4×Dic43C2211yescharacteristic, complemented
42C4×C22⋊Dic43C2211yescharacteristic
43#14582745—21no—
44#14582662C2211yescharacteristic, complemented
45#14582662C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582653C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52C23×D4×C43C2211yescharacteristic
53C22×M16×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C43×#418C418yescomplemented
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C23×Dic43—21no—
61C23×Dic43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64D4×Dic43—22no—
65D4×Dic43—22no—
66D4×Dic43—41no—
67D4×Dic43—41no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—44no—
83C2×C22⋊Dic43D411yescharacteristic
84C2×C22⋊Dic43D411yescharacteristic
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063259—41no—
90#13063257—41no—
91#13063246—22no—
92#13063246—22no—
93#13063246—41no—
94#13063246—41no—
95C22⋊(C43⋊C8)—22no—
96#13063235—41no—
97C8×Dic43—41no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C25×C43—21no—
107C22×D4×C43—22no—
108C22×D4×C43—22no—
109C22×D4×C43—21no—
110C22×D4×C43—22no—
111C22×D4×C43—41no—
112C22×D4×C43—41no—
113C22×D4×C43C2×C414yes—
114C22×D4×C43C2311yescharacteristic
115C22×D4×C43C2311yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C2×M16×C43—41no—
118C2×M16×C43—41no—
119C2×M16×C43C2×C414yescomplemented
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122#117×C43—22no—
123#117×C43C2×C414yescomplemented
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C42×C43—21no—
128#102×C43C2×C414yes—
129#102×C43C2×C414yes—
130#102×C43C2×C414yescomplemented
131#102×C43C2×C414yescomplemented
132C24×C43—21no—
133C24×C43—21no—
134C24×C43—24no—
135C24×C43—42no—
136C24×C43—42no—
137C24×C43—42no—
138C24×C43—42no—
139C24×C43—81no—
140C24×C43—81no—
141C24×C43C2×D411yescharacteristic
142C2×D4×C43—24no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—28no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—42no—
153C2×D4×C43—42no—
154C2×D4×C43—44no—
155C2×D4×C43—44no—
156C2×D4×C43—44no—
157C2×D4×C43C22×C412yes—
158C2×D4×C43C22×C412yes—
159C2×D4×C43#4112yes—
160C2×D4×C43#4112yes—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43C22×C412yes—
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43#4112yes—
170C22×C4×C43C2411yescharacteristic
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—42no—
176C22×Dic43—42no—
177C22×Dic43—42no—
178C22×Dic43—42no—
179C22×Dic43—81no—
180C22×Dic43—81no—
181C22×Dic43C2×D411yescharacteristic
182C22×Dic43C2×D411yescharacteristic
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185M16×C43—44no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43C22×C412yes—
191C2×C8×C43C22×C412yes—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43C22×C412yes—
195C4⋊C4×C43C22×C412yes—
196C22⋊C4×C43—24no—
197C42×C43—24no—
198C22⋊Dic43—22no—
199C22⋊Dic43—41no—
200C22⋊Dic43—42no—
201C22⋊Dic43—42no—
202C22⋊Dic43—42no—
203C22⋊Dic43—42no—
204C22⋊Dic43—42no—
205C22⋊Dic43—81no—
206C22⋊Dic43—81no—
207C22⋊Dic43—81no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—81no—
217C4⋊Dic43—81no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—42no—
223C4×Dic43—42no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C23×C43—22no—
231C23×C43—22no—
232C23×C43—22no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—22no—
240C23×C43—48no—
241C23×C43—48no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—84no—
253C23×C43—84no—
254C23×C43—84no—
255C23×C43—84no—
256C23×C43—84no—
257C23×C43C4×D412yes—
258C23×C43C22×D411yescharacteristic
259D4×C43—22no—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—22no—
263D4×C43—22no—
264D4×C43—48no—
265D4×C43—41no—
266D4×C43—41no—
267D4×C43#11714yes—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43C4×D412yes—
281C2×C4×C43C23×C411yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43H(5,𝔽2)11yescharacteristic
286C2×C4×C43H(5,𝔽2)11yescharacteristic
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
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—41no—
309C2×Dic43—41no—
310C2×Dic43—84no—
311C2×Dic43—84no—
312C2×Dic43AGL(1,ℤ/8)12yes—
313C8×C43—22no—
314C8×C43—22no—
315C43⋊C8—41no—
316C43⋊C8—41no—
317#22584—431nomaximal, Sylow
318C22×C43—24no—
319C22×C43—22no—
320C22×C43—22no—
321C22×C43—22no—
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—41no—
325C22×C43—42no—
326C22×C43—41no—
327C22×C43—42no—
328C22×C43—41no—
329C22×C43—42no—
330C22×C43—41no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—816no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43C2×C4×D411yescharacteristic
341C22×C43#54611yescharacteristic
342C22×C43#54611yescharacteristic
343C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C43#57511yescharacteristic
345C22×C43#57611yescharacteristic
346C22×C43#57711yescharacteristic
347C4×C43—22no—
348C4×C43—42no—
349C4×C43—42no—
350C4×C43C2×#11711yescharacteristic
351C4×C43#51811yescharacteristic
352C4×C43#55111yescharacteristic
353C4×C43#55111yescharacteristic
354Dic43—22no—
355Dic43—41no—
356Dic43—41no—
357Dic43—41no—
358Dic43—81no—
359Dic43—81no—
360Dic43—81no—
361Dic43—81no—
362C2×#418D4311yescharacteristic
363#2346—431no—
364D4×C22⋊C4—431no—
365#1936—431no—
366#1934—431no—
367#1926—431no—
368#1925—431no—
369#1864—431no—
370#1862—431no—
371#1825—431no—
372#1809—431no—
373#1786—431no—
374#1762—431no—
375C4×#102—431no—
376#1753—431no—
377C2×C43—42no—
378C2×C43—44no—
379C2×C43—82no—
380C2×C43#234211yescharacteristic
381C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
382C2×C43#294611yescharacteristic
383C2×C43#331011yescharacteristic
384C2×C43#331911yescharacteristic
385C2×C43#332311yescharacteristic
386C2×C43#332511yescharacteristic
387C23×D4C2×D4311yescharacteristic
388C22×M16C2×D4311yescharacteristic
389C2×C4×D4—431no—
390C2×C4×D4—431no—
391C2×#117C2×D4311yescharacteristic
392C22×C22⋊C4—861no—
393C2×#107—431no—
394C2×#106—431no—
395#418Dic4318yescomplemented
396C2×#102—431no—
397C2×#102—431no—
398C2×#102—431no—
399C2×#102—431no—
400C2×#102C2×D4311yescharacteristic
401C2×#102C2×D4311yescharacteristic
402C2×#102C2×D4311yescharacteristic
403C2×#102C2×D4311yescharacteristic
404C2×C22⋊C8—431no—
405C2×#97—431no—
406C2×C4×C8—431no—
407#390—431no—
408#390—431no—
409#389—431no—
410#389—431no—
411#388—861no—
412#388—861no—
413#386—861no—
414#386—861no—
415#382—861no—
416#380—431no—
417#380—431no—
418#379—861no—
419C4×C4⋊C4—431no—
420C4×C4⋊C4—431no—
421C4×C22⋊C4—431no—
422#376—861no—
423#340—431no—
424#340—431no—
425#340—431no—
426#340—431no—
427#340—431no—
428#340—431no—
429#336—431no—
430#336—431no—
431C43#2258411yescharacteristic, complemented, Sylow
432C25—21no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—21no—
436C22×D4—22no—
437C22×D4—41no—
438C22×D4—41no—
439C22×D4C2×Dic4314yes—
440C22×D4C22×D4311yescharacteristic
441C22×D4C22×D4311yescharacteristic
442C23×C4—861no—
443C23×C4—861no—
444C23×C4C22×D4311yescharacteristic
445C2×M16—41no—
446C2×M16—41no—
447C2×M16C2×Dic4314yescomplemented
448C22×C8—431no—
449C22×C8—431no—
450C22×C8C22×D4311yescharacteristic
451C22×C8C22×D4311yescharacteristic
452C4×D4—862no—
453C4×D4—862no—
454C4×D4—1721no—
455C4×D4—1721no—
456#117—22no—
457#117C2×Dic4314yescomplemented
458C2×C4⋊C4—431no—
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×C22⋊C4—21no—
467C2×C22⋊C4—431no—
468C2×C22⋊C4—431no—
469C2×C22⋊C4—861no—
470C2×C22⋊C4—861no—
471C2×C22⋊C4—861no—
472C2×C22⋊C4—861no—
473C2×C22⋊C4—861no—
474C2×C22⋊C4—861no—
475C2×C22⋊C4—861no—
476C2×C22⋊C4—861no—
477C2×C22⋊C4—1724no—
478C2×C42—21no—
479C2×C42—431no—
480C2×C42—431no—
481C2×C42—861no—
482C2×C42—861no—
483#107—1721no—
484#106—1721no—
485#102—862no—
486#102—862no—
487#102—1721no—
488#102—1721no—
489#102C2×Dic4314yes—
490#102C2×Dic4314yes—
491#102C2×Dic4314yescomplemented
492#102C2×Dic4314yescomplemented
493C22⋊C8—862no—
494#97—1721no—
495C4×C8—1721no—
496#95—431no—
497#95—431no—
498#95—861no—
499#95—861no—
500#95—861no—
501#95—861no—
502#95—861no—
503#95—861no—
504C24—21no—
505C24—21no—
506C24—24no—
507C24—42no—
508C24—42no—
509C24—42no—
510C24—42no—
511C24—81no—
512C24—81no—
513C24D4×D4311yescharacteristic
514C2×D4—28no—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4#1062189812yes—
530C2×D4#1062189812yes—
531C2×D4C22×Dic4312yes—
532C2×D4C22×Dic4312yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—431no—
540C22×C4—431no—
541C22×C4—431no—
542C22×C4—431no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—3441no—
548C22×C4—3441no—
549C22×C4—1722no—
550C22×C4—1722no—
551C22×C4—1722no—
552C22×C4—1722no—
553C22×C4D4×D4311yescharacteristic
554C22×C4#1062190012yes—
555C22×C4C22×Dic4312yes—
556C22×C4C23×D4311yescharacteristic
557M16—44no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—861no—
563C2×C8—861no—
564C2×C8—861no—
565C2×C8—861no—
566C2×C8—861no—
567C2×C8—861no—
568C2×C8C22×Dic4312yes—
569C2×C8C22×Dic4312yes—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—861no—
573C4⋊C4—861no—
574C4⋊C4—861no—
575C4⋊C4—861no—
576C4⋊C4—861no—
577C4⋊C4—861no—
578C4⋊C4—861no—
579C4⋊C4—861no—
580C4⋊C4—3441no—
581C4⋊C4—3441no—
582C4⋊C4C22×Dic4312yes—
583C4⋊C4C22×Dic4312yes—
584C22⋊C4—24no—
585C22⋊C4—862no—
586C22⋊C4—3441no—
587C22⋊C4—3441no—
588C22⋊C4—3441no—
589C22⋊C4—1722no—
590C22⋊C4—1721no—
591C22⋊C4—1722no—
592C22⋊C4—1722no—
593C22⋊C4—1722no—
594C22⋊C4—1722no—
595C42—24no—
596C42—861no—
597C42—861no—
598C42—861no—
599C42—861no—
600C42—1722no—
601C42—1722no—
602C23—22no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—22no—
608C23—22no—
609C23—21no—
610C23—21no—
611C23—22no—
612C23—48no—
613C23—48no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—84no—
625C23—84no—
626C23—84no—
627C23—84no—
628C23—84no—
629C23D4×Dic4312yes—
630C23C2×D4×D4311yescharacteristic
631D4—22no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639D4#1306328414yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—432no—
653C2×C4—861no—
654C2×C4—861no—
655C2×C4—861no—
656C2×C4—861no—
657C2×C4—861no—
658C2×C4—861no—
659C2×C4—861no—
660C2×C4—861no—
661C2×C4—861no—
662C2×C4—861no—
663C2×C4—861no—
664C2×C4—3444no—
665C2×C4—3444no—
666C2×C4—1721no—
667C2×C4—1721no—
668C2×C4—1721no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4D4×Dic4312yes—
679C2×C4C23×Dic4311yescharacteristic
680C2×C4C2×#1062190011yescharacteristic
681C2×C4C2×#1062189811yescharacteristic
682C2×C4C2×#1062189811yescharacteristic
683C2×C4#1306337011yescharacteristic
684C2×C4#1306337011yescharacteristic
685C8—22no—
686C8—22no—
687C8—1721no—
688C8—1721no—
689C22—22no—
690C22—22no—
691C22—24no—
692C22—22no—
693C22—41no—
694C22—42no—
695C22—42no—
696C22—41no—
697C22—42no—
698C22—42no—
699C22—41no—
700C22—42no—
701C22—41no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—816no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×D4×Dic4311yescharacteristic
712C22#1458353911yescharacteristic
713C22#1458353911yescharacteristic
714C22AGL(1,ℤ/8)×D4311yescharacteristic
715C22#1458369511yescharacteristic
716C22#1458370311yescharacteristic
717C22#1458370911yescharacteristic
718C4—22no—
719C4—42no—
720C4—42no—
721C4—862no—
722C4—3441no—
723C4—3441no—
724C4—3441no—
725C4—3441no—
726C4—1721no—
727C4—1721no—
728C4—1721no—
729C4C2×#1306328411yescharacteristic
730C4#1458337411yescharacteristic
731C4#1458357511yescharacteristic
732C4#1458357511yescharacteristic
733C2—42no—
734C2—44no—
735C2—82no—
736C2#1913744411yescharacteristic
737C2AGL(1,ℤ/8)×Dic4311yescharacteristic
738C2#1914342811yescharacteristic
739C2#1914661711yescharacteristic
740C2#1914675211yescharacteristic
741C2#1914680711yescharacteristic
742C2#1914683311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#418C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#418D43
hypocenterC43#22584
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
1. #19137480C2semidirect
3. #19135294C2semidirect
4. #19135280C2semidirect
5. #19135224C2semidirect
6. #19135217C2semidirect
7. #19134858C2semidirect
8. #19134844C2semidirect
9. #19134690C2semidirect
10. #19134628C2semidirect
12. #19134422C2semidirect
13. #102×Dic43C2semidirect
14. #19134376C2semidirect
19. C2×#13063259C22semidirect
20. C2×#13063257C22semidirect
26. C2×#13063235C22semidirect
27. C2×C8×Dic43C22semidirect
30. #14582798C22semidirect
31. #14582798C22semidirect
40. C4⋊C4×Dic43C22semidirect
41. C4⋊C4×Dic43C22semidirect
44. #14582662C22semidirect
45. #14582662C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582653C22semidirect
51. #14582653C22semidirect
55. C43×#418C4semidirect
119. C2×M16×C43C2×C4semidirect
123. #117×C43C2×C4semidirect
130. #102×C43C2×C4semidirect
131. #102×C43C2×C4semidirect
395. #418Dic43semidirect
431. C43#22584semidirect
447. C2×M16C2×Dic43semidirect
457. #117C2×Dic43semidirect
491. #102C2×Dic43semidirect
492. #102C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191374802
D4×C22⋊Dic432
#191352942
#191352802
#191352242
#191352172
#191348582
#191348442
#191346902
#191346282
#191345262
#191344222
#102×Dic432
#191343762
C2×C43×#4182
#2258443