Finite Group Databasebeta

← #25113777

Subgroups — #25113777

Order 11008.

1190 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#102×D43C211yesmaximal, characteristic
2#19137468C211yesmaximal, characteristic, complemented
3#19137416C211yesmaximal, characteristic
4#19135281C211yesmaximal, characteristic, complemented
5#19135275C211yesmaximal, characteristic, complemented
6#19135224C211yesmaximal, characteristic, complemented
7#19134859C211yesmaximal, characteristic, complemented
8#19134853C211yesmaximal, characteristic, complemented
9#19134684C211yesmaximal, characteristic, complemented
10#19134617C211yesmaximal, characteristic, complemented
11#19134524C211yesmaximal, characteristic
12C4×#13063245C211yesmaximal, characteristic, complemented
13#19134409C211yesmaximal, characteristic, complemented
14#19134365C211yesmaximal, characteristic, complemented
15C43×#1926C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×C4⋊C4×D43C2211yescharacteristic
21C2×C22⋊C4×D43—21no—
22C2×#13063257C2211yescharacteristic, complemented
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29#102×D43C418yescomplemented
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×C4×C43⋊C8C2211yescharacteristic, complemented
32C2×C8×Dic43C2211yescharacteristic, complemented
33#14582802C2211yescharacteristic
34#14582797C2211yescharacteristic, complemented
35#14582795C2211yescharacteristic, complemented
36#14582783—21no—
37#14582781—21no—
38#14582775—21no—
39#14582775—21no—
40#14582758—21no—
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43#14582754—21no—
44C4⋊C4×Dic43C2211yescharacteristic, complemented
45C4×(C2×D43)⋊C4—21no—
46C4×(C2×D43)⋊C4C2211yescharacteristic
47#14582662C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C2×#106×C43C2211yescharacteristic, complemented
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic, complemented
58C43×#340C2211yescharacteristic, complemented
59C43×#336C2211yescharacteristic, complemented
60C24×D43—21no—
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C2×D4×D43—22no—
64C2×D4×D43—22no—
65C2×D4×D43—22no—
66C2×D4×D43—41no—
67C2×D4×D43—41no—
68C2×D4×D43C2×C414yes—
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C2×C8×D43—41no—
76C2×C8×D43—41no—
77C2×C8×D43C2×C414yescomplemented
78C4×D172—22no—
79C4×D172—41no—
80#13063287—22no—
81#13063287—41no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C4⋊C4×D43—22no—
89C4⋊C4×D43C2×C414yescomplemented
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4D411yescharacteristic
97C2×(C2×D43)⋊C4D411yescharacteristic
98C22⋊C4×D43—44no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101#13063257—41no—
102#13063247—22no—
103#13063247C2×C414yes—
104#13063246—41no—
105#13063246C2×C414yescomplemented
106#13063245—22no—
107#13063245C2×C414yes—
108(C2×D43)⋊C8—22no—
109C4×C43⋊C8—41no—
110C8×Dic43—41no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95D411yescharacteristic
117C43⋊#95D411yescharacteristic
118C22×D4×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C42×C43—21no—
127C2×C42×C43C2311yescharacteristic
128#106×C43—41no—
129#102×C43—41no—
130#102×C43C2×C414yescomplemented
131#95×C43—21no—
132C24×C43—21no—
133C23×D43—21no—
134C23×D43—24no—
135C23×D43—42no—
136C23×D43—42no—
137C23×D43—42no—
138C23×D43—42no—
139C23×D43—81no—
140C23×D43—81no—
141C23×D43C2×D411yescharacteristic
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43C22×C412yes—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C2×C22⋊D43—24no—
155C2×C22⋊D43—42no—
156C2×C22⋊D43—42no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163D4×D43—28no—
164D4×D43—44no—
165D4×D43—44no—
166D4×D43—44no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172C22×C412yes—
171C2×D172#4112yes—
172C2×D172#4112yes—
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—24no—
178C2×C4×D43—42no—
179C2×C4×D43—42no—
180C2×C4×D43—42no—
181C2×C4×D43—42no—
182C2×C4×D43—81no—
183C2×C4×D43—81no—
184C2×C4×D43—81no—
185C2×C4×D43—81no—
186C2×C4×D43C22×C412yes—
187C2×C4×D43#4112yes—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43C22×C412yes—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43C22×C412yes—
200C22⋊C4×C43—42no—
201C22⋊C4×C43—81no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—81no—
205C22⋊Dic43—42no—
206C22⋊Dic43—81no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—42no—
209(C2×D43)⋊C4—42no—
210(C2×D43)⋊C4—42no—
211(C2×D43)⋊C4—42no—
212(C2×D43)⋊C4SD1614yes—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43C22×C412yes—
219Dic43⋊C4—24no—
220Dic43⋊C4—81no—
221Dic43⋊C4—81no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—81no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8C22×C412yes—
231C8×D43—44no—
232C23×C43—22no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43C22×D411yescharacteristic
240C22×D43—21no—
241C22×D43—21no—
242C22×D43—21no—
243C22×D43—21no—
244C22×D43—22no—
245C22×D43—22no—
246C22×D43—22no—
247C22×D43—48no—
248C22×D43—41no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—48no—
253C22×D43—84no—
254C22×D43—84no—
255C22×D43—84no—
256C22×D43—84no—
257C22×D43—84no—
258C22×D43C4×D412yes—
259C22×D43C2×SD1612yes—
260C22×D43#13512yes—
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—21no—
270C2×C4×C43—21no—
271C2×C4×C43—41no—
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×C43C2×SD1612yes—
280C2×C4×C43C23×C411yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
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—21no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—22no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43C4×D412yes—
304C2×Dic43C2×SD1612yes—
305D172—22no—
306D172—22no—
307D172—22no—
308D172#11714yes—
309C4×D43—22no—
310C4×D43—22no—
311C4×D43—22no—
312C4×D43—22no—
313C4×D43—84no—
314C4×D43—84no—
315C4×D43—84no—
316C8×C43—22no—
317C8×C43—41no—
318C43⋊C8—22no—
319C43⋊C8—41no—
320#22574—431nomaximal, Sylow
321C22×C43—42no—
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—81no—
325C22×C43—81no—
326C22×C43—81no—
327C22×C43—81no—
328C22×C43C2×C4×D411yescharacteristic
329C22×C43#54611yescharacteristic
330C22×C43#54611yescharacteristic
331C22×C43C22×SD1611yescharacteristic
332C22×C43C2×#13511yescharacteristic
333C22×C43#57611yescharacteristic
334C22×C43#57611yescharacteristic
335C2×D43—22no—
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—22no—
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—24no—
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—816no—
349C2×D43C4×SD1614yes—
350C4×C43—22no—
351C4×C43—42no—
352C4×C43—41no—
353C4×C43—81no—
354C4×C43—81no—
355C4×C43C2×#11711yescharacteristic
356C4×C43#51811yescharacteristic
357C4×C43#55111yescharacteristic
358C4×C43#55111yescharacteristic
359Dic43—22no—
360Dic43—22no—
361Dic43—42no—
362Dic43—41no—
363Dic43—81no—
364Dic43—81no—
365C22×#102—431no—
366#2345—431no—
367D4×C22⋊C4—431no—
368#1934—431no—
369#1934—431no—
370#1926—431no—
371#1926D4311yescharacteristic, complemented
372#1864—431no—
373#1864—431no—
374#1824—431no—
375#1807—431no—
376#1786—431no—
377C4×#102—431no—
378C4×#102—431no—
379C8×C22⋊C4—431no—
380C2×C43—82no—
381C2×C43#234211yescharacteristic
382C2×C43C2×C4×SD1611yescharacteristic
383C2×C43#294811yescharacteristic
384C2×C43#329511yescharacteristic
385C2×C43#329511yescharacteristic
386C2×C43#329711yescharacteristic
387C2×C43#329711yescharacteristic
388D43—24no—
389D43—44no—
390C23×D4—431no—
391C23×C8—431no—
392C2×C4×D4—431no—
393C2×C4×D4—431no—
394C22×C4⋊C4—431no—
395C22×C22⋊C4—861no—
396C2×#106—431no—
397C2×#106C2×D4311yescharacteristic, complemented
398C2×#102—431no—
399C2×#102—431no—
400C2×#102—431no—
401C2×#102—438no—
402C2×#102—431no—
403C2×#102—431no—
404C2×#102—431no—
405C2×#102C2×D4311yescharacteristic
406C2×#102C2×D4311yescharacteristic
407C2×C22⋊C8—431no—
408C2×C4×C8—431no—
409C2×C4×C8—431no—
410#390—431no—
411#390C2×D4311yescharacteristic
412#389—431no—
413#389—431no—
414#387—861no—
415#387—861no—
416#386—861no—
417#386—861no—
418#380—431no—
419#380—431no—
420#380—861no—
421#379—861no—
422C4×C4⋊C4—431no—
423C4×C4⋊C4C2×D4311yescharacteristic, complemented
424C4×C22⋊C4—431no—
425C4×C22⋊C4—861no—
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#340—431no—
431#340C2×D4311yescharacteristic, complemented
432#336—431no—
433#336C2×D4311yescharacteristic, complemented
434C43#2257411yescharacteristic, complemented, Sylow
435C25—861no—
436C22×D4—434no—
437C22×D4—431no—
438C22×D4—862no—
439C22×D4—861no—
440C22×D4—862no—
441C22×D4—862no—
442C22×D4—1721no—
443C22×D4—1721no—
444C22×D4C22×D4311yescharacteristic
445C23×C4—431no—
446C23×C4—861no—
447C23×C4—861no—
448C23×C4—861no—
449C22×C8—431no—
450C22×C8—434no—
451C22×C8—431no—
452C22×C8—1721no—
453C22×C8—1721no—
454C22×C8C22×D4311yescharacteristic
455C22×C8C22×D4311yescharacteristic
456C4×D4—862no—
457C4×D4—862no—
458C4×D4—1721no—
459C4×D4—1721no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4—434no—
462C2×C4⋊C4—431no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—862no—
465C2×C4⋊C4—861no—
466C2×C4⋊C4—861no—
467C2×C4⋊C4—861no—
468C2×C4⋊C4C22×D4311yescharacteristic
469C2×C4⋊C4C22×D4311yescharacteristic
470C2×C4⋊C4C22×D4311yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—431no—
474C2×C22⋊C4—431no—
475C2×C22⋊C4—861no—
476C2×C22⋊C4—861no—
477C2×C22⋊C4—861no—
478C2×C22⋊C4—861no—
479C2×C22⋊C4—861no—
480C2×C22⋊C4—861no—
481C2×C22⋊C4—1724no—
482C2×C42—21no—
483C2×C42—431no—
484C2×C42—861no—
485C2×C42C22×D4311yescharacteristic
486#106—41no—
487#106—1721no—
488#102—41no—
489#102—434no—
490#102—434no—
491#102—434no—
492#102—862no—
493#102—862no—
494#102—1721no—
495#102C4×D4314yescomplemented
496C22⋊C8—862no—
497C4×C8—1721no—
498C4×C8—1721no—
499#95—21no—
500#95—431no—
501#95—431no—
502#95—861no—
503#95—861no—
504#95—861no—
505#95—861no—
506#95—861no—
507C24—21no—
508C24—431no—
509C24—864no—
510C24—861no—
511C24—3441no—
512C24—3441no—
513C24—1722no—
514C24—1722no—
515C24—1722no—
516C24—1722no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—432no—
523C2×D4—432no—
524C2×D4—432no—
525C2×D4—864no—
526C2×D4—868no—
527C2×D4—861no—
528C2×D4—861no—
529C2×D4—861no—
530C2×D4—1724no—
531C2×D4—1724no—
532C2×D4—1724no—
533C2×D4—1722no—
534C2×D4—1722no—
535C2×D4C2×C4×D4312yes—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—431no—
540C22×C4—431no—
541C22×C4—432no—
542C22×C4—432no—
543C22×C4—431no—
544C22×C4—864no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—3441no—
553C22×C4—3441no—
554C22×C4—3441no—
555C22×C4—3441no—
556C22×C4—1722no—
557C22×C4—1722no—
558C22×C4—1722no—
559C22×C4—1722no—
560C22×C4D4×D4311yescharacteristic
561C22×C4D4×D4311yescharacteristic
562C22×C4C23×D4311yescharacteristic
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—432no—
569C2×C8—861no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—1724no—
575C2×C8C2×C4×D4312yes—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—432no—
582C4⋊C4—864no—
583C4⋊C4—861no—
584C4⋊C4—861no—
585C4⋊C4—861no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—3441no—
589C4⋊C4—3441no—
590C4⋊C4C2×C4×D4312yes—
591C22⋊C4—42no—
592C22⋊C4—81no—
593C22⋊C4—434no—
594C22⋊C4—862no—
595C22⋊C4—3441no—
596C22⋊C4—1722no—
597C22⋊C4—1722no—
598C22⋊C4—1722no—
599C22⋊C4—1722no—
600C22⋊C4—1722no—
601C42—21no—
602C42—21no—
603C42—81no—
604C42—861no—
605C42—861no—
606C42—3441no—
607C23—22no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—432no—
615C23—432no—
616C23—432no—
617C23—861no—
618C23—861no—
619C23—861no—
620C23—861no—
621C23—862no—
622C23—862no—
623C23—862no—
624C23—3444no—
625C23—3444no—
626C23—3444no—
627C23—3444no—
628C23—3444no—
629C23—1728no—
630C23—1728no—
631C23—1721no—
632C23—1721no—
633C23—1721no—
634C23—1721no—
635C23C2×D4×D4311yescharacteristic
636D4—22no—
637D4—22no—
638D4—41no—
639D4—41no—
640D4—434no—
641D4—862no—
642D4—862no—
643D4—862no—
644D4—1728no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
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—432no—
660C2×C4—432no—
661C2×C4—861no—
662C2×C4—861no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—861no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—3444no—
674C2×C4—3444no—
675C2×C4—3444no—
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×C4SD16×D4312yes—
685C2×C4C22×C4×D4311yescharacteristic
686C2×C4#41×D4311yescharacteristic
687C2×C4#41×D4311yescharacteristic
688C2×C4#41×D4311yescharacteristic
689C2×C4#1306337011yescharacteristic
690C2×C4#1306337111yescharacteristic
691C8—22no—
692C8—41no—
693C8—862no—
694C8—1721no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—434no—
703C22—862no—
704C22—862no—
705C22—862no—
706C22—862no—
707C22—862no—
708C22—862no—
709C22—864no—
710C22—34416no—
711C22—1722no—
712C22—1722no—
713C22—1722no—
714C22—1722no—
715C22—1722no—
716C22—1722no—
717C22C4×D4×D4311yescharacteristic
718C22#1458354111yescharacteristic
719C22#1458354611yescharacteristic
720C22C2×SD16×D4311yescharacteristic
721C22#135×D4311yescharacteristic
722C22#1458370311yescharacteristic
723C22#1458370311yescharacteristic
724C4—22no—
725C4—42no—
726C4—41no—
727C4—81no—
728C4—81no—
729C4—862no—
730C4—862no—
731C4—3441no—
732C4—3441no—
733C4—1722no—
734C4—1721no—
735C4#117×D4311yescharacteristic
736C4#1458337111yescharacteristic
737C4#1458357411yescharacteristic
738C4#1458357911yescharacteristic
739C2—82no—
740C2—864no—
741C2—1724no—
742C2#1913743911yescharacteristic
743C2C4×SD16×D4311yescharacteristic
744C2#1914344411yescharacteristic
745C2#1914641711yescharacteristic
746C2#1914642211yescharacteristic
747C2#1914644811yescharacteristic
748C2#1914645211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1926C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1926D43
hypocenterC43#22574
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
2. #19137468C2semidirect
4. #19135281C2semidirect
5. #19135275C2semidirect
6. #19135224C2semidirect
7. #19134859C2semidirect
8. #19134853C2semidirect
9. #19134684C2semidirect
10. #19134617C2semidirect
12. C4×#13063245C2semidirect
13. #19134409C2semidirect
14. #19134365C2semidirect
15. C43×#1926C2semidirect
22. C2×#13063257C22semidirect
29. #102×D43C4semidirect
31. C2×C4×C43⋊C8C22semidirect
32. C2×C8×Dic43C22semidirect
34. #14582797C22semidirect
35. #14582795C22semidirect
44. C4⋊C4×Dic43C22semidirect
47. #14582662C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582653C22semidirect
53. C2×#106×C43C22semidirect
57. C4×C4⋊C4×C43C22semidirect
58. C43×#340C22semidirect
59. C43×#336C22semidirect
77. C2×C8×D43C2×C4semidirect
89. C4⋊C4×D43C2×C4semidirect
105. #13063246C2×C4semidirect
130. #102×C43C2×C4semidirect
371. #1926D43semidirect
397. C2×#106C2×D43semidirect
423. C4×C4⋊C4C2×D43semidirect
431. #340C2×D43semidirect
433. #336C2×D43semidirect
434. C43#22574semidirect
495. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#102×D432
#191374682
#191374162
#191352812
#191352752
#191352242
#191348592
#191348532
#191346842
#191346172
#191345242
C4×#130632452
#191344092
#191343652
C43×#19262
#2257443