Finite Group Databasebeta

← #25153691

Subgroups — #25153691

Order 11008.

1162 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583202C211yesmaximal, characteristic, complemented
2C22×#13063247C211yesmaximal, characteristic
3#19138320C211yesmaximal, characteristic, complemented
4#19137415C211yesmaximal, characteristic
5#19136113C211yesmaximal, characteristic, complemented
6#19135978C211yesmaximal, characteristic, complemented
7#19135970C211yesmaximal, characteristic, complemented
8#19135740C211yesmaximal, characteristic, complemented
9#19134857C211yesmaximal, characteristic, complemented
10#19134839C211yesmaximal, characteristic, complemented
11#19134787C211yesmaximal, characteristic, complemented
12#19134773C211yesmaximal, characteristic, complemented
13#19134604C211yesmaximal, characteristic, complemented
14#19134525C211yesmaximal, characteristic
15C43×#1808C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C2×#13063316C2211yescharacteristic, complemented
18C2×#13063287C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C2×C22⋊C4×D43—21no—
22#14583202—24no—
23C2×#13063256C2211yescharacteristic, complemented
24C2×#13063256C2211yescharacteristic, complemented
25C2×Dic43⋊C8C2211yescharacteristic, complemented
26C2×Dic43⋊C8C2211yescharacteristic, complemented
27C2×#13063247—24no—
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37#14582841—21no—
38#14582831—21no—
39#14582800C2211yescharacteristic
40#14582800C2211yescharacteristic
41#14582798C2211yescharacteristic, complemented
42#14582795C2211yescharacteristic, complemented
43#14582777—21no—
44#14582777—21no—
45#14582774—21no—
46#14582764C2211yescharacteristic, complemented
47#14582757—21no—
48#14582754—21no—
49C4×C22⋊Dic43C2211yescharacteristic
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54C23×C8×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic, complemented
56C2×#107×C43C2211yescharacteristic, complemented
57C43×#380C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C43×#340C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C24×D43—21no—
62C22×D172—22no—
63C22×D172—22no—
64C22×D172—21no—
65C22×D172—22no—
66C22×D172—41no—
67C22×D172—41no—
68C22×D172Q814yes—
69C22×D172C2311yescharacteristic
70C22×D172C2311yescharacteristic
71C23×Dic43—21no—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063316—22no—
77#13063316—41no—
78#13063287—22no—
79#13063287—22no—
80#13063287—41no—
81#13063287—41no—
82C2×C4⋊Dic43—22no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—41no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×C22⋊Dic43D411yescharacteristic
92C2×C22⋊Dic43D411yescharacteristic
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C22⋊C4×D43—44no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102#13063256—22no—
103#13063256—41no—
104Dic43⋊C8—22no—
105Dic43⋊C8—41no—
106#13063247—22no—
107#13063247—22no—
108#13063247—22no—
109#13063247D414yes—
110#13063245—22no—
111#13063245—22no—
112#13063245—41no—
113#13063245—41no—
114C22⋊(C43⋊C8)—22no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95D411yescharacteristic
120C43⋊#95D411yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C22×C8×C43—22no—
123C22×C8×C43—22no—
124C22×C8×C43—41no—
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133#107×C43—22no—
134#107×C43—41no—
135#95×C43—21no—
136#95×C43—21no—
137C24×C43C2×D411yescharacteristic
138C23×D43—21no—
139C23×D43—21no—
140C23×D43—24no—
141C23×D43—42no—
142C23×D43—42no—
143C23×D43—42no—
144C23×D43—42no—
145C23×D43—81no—
146C23×D43—81no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×Q812yes—
157C22×C4×C43#4112yes—
158C22×C4×C43C2411yescharacteristic
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—42no—
162C22×Dic43—42no—
163C22×Dic43—81no—
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—24no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—28no—
178C2×D172—42no—
179C2×D172—42no—
180C2×D172—44no—
181C2×D172—44no—
182C2×D172—44no—
183C2×D172C2×D412yes—
184C2×D172C2×Q812yes—
185C2×D172C2×Q812yes—
186C2×D172#4112yes—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43—42no—
191C2×C4×D43—81no—
192C2×C4×D43—81no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—44no—
199C2×C8×C43C2×D412yes—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C22⋊C4×C43—42no—
209C22⋊C4×C43—42no—
210C22⋊Dic43—22no—
211C22⋊Dic43—22no—
212(C2×D43)⋊C4—42no—
213(C2×D43)⋊C4—42no—
214(C2×D43)⋊C4—42no—
215(C2×D43)⋊C4—42no—
216(C2×D43)⋊C4—81no—
217(C2×D43)⋊C4—81no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—42no—
222C4⋊Dic43—42no—
223C4⋊Dic43—81no—
224C4⋊Dic43C2×D412yes—
225Dic43⋊C4—42no—
226Dic43⋊C4—81no—
227C4×Dic43—21no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43C22⋊Q812yes—
242C23×C43#13512yes—
243C23×C43AGL(1,ℤ/8)12yes—
244C23×C43C22×D411yescharacteristic
245C22×D43—22no—
246C22×D43—22no—
247C22×D43—22no—
248C22×D43—22no—
249C22×D43—48no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—48no—
261C22×D43—84no—
262C22×D43—84no—
263C22×D43—84no—
264C22×D43—84no—
265C22×D43—84no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
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—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43C22⋊Q812yes—
285C2×C4×C43C22×D411yescharacteristic
286C2×C4×C43C22×Q811yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43H(5,𝔽2)11yescharacteristic
290C2×C4×C43H(5,𝔽2)11yescharacteristic
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—22no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—84no—
310D172—22no—
311D172—22no—
312D172—22no—
313D172—22no—
314D172—22no—
315D172—48no—
316D172—41no—
317D172—41no—
318D172C22⋊Q814yes—
319C4×D43—84no—
320C4×D43—84no—
321C8×C43—22no—
322C8×C43—41no—
323C43⋊C8—41no—
324C43⋊C8—41no—
325#25952—431nomaximal, Sylow
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—22no—
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43#47814yescomplemented
333C22×C43C2×C22⋊Q811yescharacteristic
334C22×C43D4211yescharacteristic
335C22×C43#54611yescharacteristic
336C22×C43C2×#13511yescharacteristic
337C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C43#57611yescharacteristic
339C22×C43#57711yescharacteristic
340C2×D43—24no—
341C2×D43—42no—
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—816no—
351C2×D43—81no—
352C2×D43—81no—
353C2×D43—81no—
354C2×D43—81no—
355C4×C43—22no—
356C4×C43—81no—
357C4×C43—81no—
358C4×C43—81no—
359C4×C43—81no—
360C4×C43C2×C22⋊Q811yescharacteristic
361C4×C43#54311yescharacteristic
362C4×C43#54611yescharacteristic
363C4×C43#55111yescharacteristic
364Dic43—41no—
365Dic43—41no—
366Dic43—42no—
367Dic43—41no—
368Dic43—41no—
369Dic43—81no—
370C2×#478—431no—
371C22×#102—431no—
372#2442—431no—
373D4×C22⋊C4—431no—
374#2092—431no—
375#2067—431no—
376#2065—431no—
377#2025—431no—
378#1864—431no—
379#1862—431no—
380#1853—431no—
381#1850—431no—
382#1808D4311yescharacteristic, complemented
383#1804—431no—
384#1786—431no—
385C2×C43—24no—
386C2×C43#243711yescharacteristic
387C2×C43C2×#47811yescharacteristic
388C2×C43#308111yescharacteristic
389C2×C43#326511yescharacteristic
390C2×C43#328011yescharacteristic
391C2×C43#329611yescharacteristic
392C2×C43#331811yescharacteristic
393D43—44no—
394D43—82no—
395C23×D4—431no—
396C23×C8C2×D4311yescharacteristic
397C2×#125—431no—
398C2×C4×D4—431no—
399C2×C4×D4—431no—
400C22×C4⋊C4—431no—
401C22×C22⋊C4—861no—
402#478—864no—
403C2×#107C2×D4311yescharacteristic, complemented
404C2×#107C2×D4311yescharacteristic, complemented
405C2×#106—431no—
406C2×#106—431no—
407C2×C4⋊C8—431no—
408C2×C4⋊C8—431no—
409C2×#102—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×#102—431no—
415C2×#102—431no—
416C2×#102—431no—
417C2×#102—864no—
418C2×C22⋊C8—431no—
419#400—861no—
420#398—861no—
421#390—431no—
422#390—431no—
423#389—431no—
424#389—431no—
425#386—861no—
426#386—861no—
427#385—861no—
428#382—431no—
429#380—861no—
430#380C2×D4311yescharacteristic
431#380C2×D4311yescharacteristic
432#379—861no—
433C4×C22⋊C4—431no—
434#340—431no—
435#340—431no—
436#340C2×D4311yescharacteristic, complemented
437#340C2×D4311yescharacteristic, complemented
438#336—431no—
439#336—431no—
440C43#2595211yescharacteristic, complemented, Sylow
441C25—861no—
442C22×D4—434no—
443C22×D4—431no—
444C22×D4—431no—
445C22×D4—862no—
446C22×D4—862no—
447C22×D4—862no—
448C22×D4—861no—
449C22×D4—1721no—
450C22×D4—1721no—
451C23×C4—861no—
452C23×C4—861no—
453C23×C4—861no—
454C23×C4C22×D4311yescharacteristic
455C22×C8—22no—
456C22×C8—22no—
457C22×C8—41no—
458C22×C8—431no—
459C22×C8—431no—
460C22×C8C22×D4311yescharacteristic
461C22×C8C22×D4311yescharacteristic
462#125—862no—
463#125—1721no—
464C4×D4—862no—
465C4×D4—862no—
466C4×D4—1721no—
467C4×D4—1721no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—862no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—1721no—
477C2×C4⋊C4C22×D4311yescharacteristic
478C2×C4⋊C4C22×D4311yescharacteristic
479C2×C4⋊C4C22×D4311yescharacteristic
480C2×C4⋊C4C22×D4311yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—431no—
484C2×C22⋊C4—431no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—1724no—
492C2×C42—431no—
493C2×C42—431no—
494#107—22no—
495#107—41no—
496#106—862no—
497#106—1721no—
498C4⋊C8—862no—
499C4⋊C8—1721no—
500#102—434no—
501#102—862no—
502#102—862no—
503#102—862no—
504#102—862no—
505#102—862no—
506#102—1721no—
507#102—1721no—
508C22⋊C8—862no—
509#95—21no—
510#95—21no—
511#95—431no—
512#95—431no—
513#95—861no—
514#95—861no—
515#95—861no—
516#95—861no—
517C24—861no—
518C24—864no—
519C24—861no—
520C24—3441no—
521C24—3441no—
522C24—1722no—
523C24—1722no—
524C24—1722no—
525C24—1722no—
526C24D4×D4311yescharacteristic
527C2×D4—432no—
528C2×D4—432no—
529C2×D4—432no—
530C2×D4—432no—
531C2×D4—868no—
532C2×D4—864no—
533C2×D4—861no—
534C2×D4—861no—
535C2×D4—861no—
536C2×D4—861no—
537C2×D4—861no—
538C2×D4—861no—
539C2×D4—861no—
540C2×D4—861no—
541C2×D4—1724no—
542C2×D4—1724no—
543C2×D4—1724no—
544C2×D4—1722no—
545C2×D4—1722no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—431no—
555C22×C4—431no—
556C22×C4—431no—
557C22×C4—431no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—3441no—
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×C4#1062189812yes—
570C22×C4D4×D4311yescharacteristic
571C22×C4Q8×D4312yes—
572C22×C4C23×D4311yescharacteristic
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—44no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8D4×D4312yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—432no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—3441no—
599C4⋊C4—3441no—
600C4⋊C4—1722no—
601C4⋊C4—1722no—
602C4⋊C4—1722no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—862no—
606C22⋊C4—862no—
607C22⋊C4—3441no—
608C22⋊C4—3441no—
609C22⋊C4—1722no—
610C22⋊C4—1722no—
611C22⋊C4—1722no—
612C22⋊C4—1722no—
613C42—861no—
614C42—861no—
615C42—861no—
616C42—861no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—862no—
622C23—862no—
623C23—862no—
624C23—862no—
625C23—3444no—
626C23—3444no—
627C23—3444no—
628C23—3444no—
629C23—3444no—
630C23—1728no—
631C23—1721no—
632C23—1721no—
633C23—1721no—
634C23—1721no—
635C23—1728no—
636C23—1721no—
637C23—1721no—
638C23—1721no—
639C23—1721no—
640C23—1721no—
641C23—1721no—
642C23#1306330312yes—
643C23#1306334812yes—
644C23#1306334912yes—
645C23C2×D4×D4311yescharacteristic
646D4—434no—
647D4—862no—
648D4—862no—
649D4—862no—
650D4—862no—
651D4—862no—
652D4—1728no—
653D4—1721no—
654D4—1721no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—862no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—3444no—
687C2×C4—3444no—
688C2×C4—3444no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4#1306330312yes—
695C2×C4C2×D4×D4311yescharacteristic
696C2×C4C2×Q8×D4311yescharacteristic
697C2×C4#41×D4311yescharacteristic
698C2×C4C2×#1062189811yescharacteristic
699C2×C4#1306337011yescharacteristic
700C2×C4#1306337111yescharacteristic
701C8—22no—
702C8—41no—
703C8—1721no—
704C8—1721no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—864no—
712C22—34416no—
713C22—3441no—
714C22—3441no—
715C22—3441no—
716C22—3441no—
717C22—1722no—
718C22—1722no—
719C22—1722no—
720C22—1722no—
721C22—1722no—
722C22—1722no—
723C22—1722no—
724C22—1722no—
725C22—1722no—
726C22#1458320214yescomplemented
727C22C2×#1306330311yescharacteristic
728C22#1458353311yescharacteristic
729C22#1458353811yescharacteristic
730C22C2×#1306334811yescharacteristic
731C22C2×#1306334911yescharacteristic
732C22#1458370111yescharacteristic
733C22#1458370611yescharacteristic
734C4—22no—
735C4—81no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4—3441no—
740C4—1721no—
741C4—1722no—
742C4—1721no—
743C4—1721no—
744C4—1721no—
745C4C22⋊Q8×D4311yescharacteristic
746C4#1458352411yescharacteristic
747C4#1458353911yescharacteristic
748C4#1458357311yescharacteristic
749C2—24no—
750C2—3442no—
751C2—1724no—
752C2#1913826311yescharacteristic
753C2C2×#1458320211yescharacteristic
754C2#1914442911yescharacteristic
755C2#1914608711yescharacteristic
756C2#1914627711yescharacteristic
757C2#1914643611yescharacteristic
758C2#1914674211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1808C2
socleC23×C43C22×D4
prime radicalC23×D172C22
hypercenter#1808D43
hypocenterC43#25952
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
1. C2×#14583202C2semidirect
3. #19138320C2semidirect
5. #19136113C2semidirect
6. #19135978C2semidirect
7. #19135970C2semidirect
8. #19135740C2semidirect
9. #19134857C2semidirect
10. #19134839C2semidirect
11. #19134787C2semidirect
12. #19134773C2semidirect
13. #19134604C2semidirect
15. C43×#1808C2semidirect
17. C2×#13063316C22semidirect
23. C2×#13063256C22semidirect
24. C2×#13063256C22semidirect
25. C2×Dic43⋊C8C22semidirect
26. C2×Dic43⋊C8C22semidirect
41. #14582798C22semidirect
42. #14582795C22semidirect
46. #14582764C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582653C22semidirect
53. #14582653C22semidirect
55. C2×#107×C43C22semidirect
56. C2×#107×C43C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
332. C22×C43#478semidirect
382. #1808D43semidirect
403. C2×#107C2×D43semidirect
404. C2×#107C2×D43semidirect
436. #340C2×D43semidirect
437. #340C2×D43semidirect
440. C43#25952semidirect
726. C22#14583202semidirect

Maximal subgroups

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

subgroupindex
C2×#145832022
C22×#130632472
#191383202
#191374152
#191361132
#191359782
#191359702
#191357402
#191348572
#191348392
#191347872
#191347732
#191346042
#191345252
C43×#18082
#2595243