Finite Group Databasebeta

← #25118996

Subgroups — #25118996

Order 11008.

1122 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583094C211yesmaximal, characteristic
2C2×#14583008C211yesmaximal, characteristic, complemented
3C2×#14582979C211yesmaximal, characteristic, complemented
4#19137659C211yesmaximal, characteristic, complemented
5#19137505C211yesmaximal, characteristic, complemented
6#19135419C211yesmaximal, characteristic, complemented
7#19135363C211yesmaximal, characteristic, complemented
8#19135293C211yesmaximal, characteristic, complemented
9#19135279C211yesmaximal, characteristic, complemented
10#19134941C211yesmaximal, characteristic, complemented
11#19134941C211yesmaximal, characteristic, complemented
12#19134857C211yesmaximal, characteristic, complemented
13#19134843C211yesmaximal, characteristic, complemented
14#19134467C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063322C2211yescharacteristic
19C2×C4×D172—21no—
20C2×D4×Dic43C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23C2×#13063287C2211yescharacteristic
24#14583094C418yescomplemented
25#14583008—24no—
26#14582979—24no—
27C2×#13063258C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063235C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic
38#14582801—21no—
39#14582800C2211yescharacteristic
40#14582800C2211yescharacteristic
41#14582798C2211yescharacteristic
42#14582798C2211yescharacteristic
43#14582777—21no—
44#14582777—21no—
45#14582774—21no—
46#14582774—21no—
47#14582765C2211yescharacteristic
48#14582759—21no—
49C4×C4⋊Dic43C2211yescharacteristic
50C2×C43⋊#95—21no—
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×D172—21no—
63C22×D172—21no—
64C22×D172C2311yescharacteristic
65C22×D172C2311yescharacteristic
66C23×Dic43—21no—
67C23×Dic43—21no—
68C22×C4×D43—21no—
69C22×C4×D43—21no—
70C2×#10621882—22no—
71C2×#10621882—22no—
72C2×#10621882—22no—
73C2×#10621882—22no—
74C2×#10621882C2×C414yescomplemented
75C2×#10621882C2×C414yescomplemented
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063322—22no—
79#13063322C2×C414yescomplemented
80C4×D172—44no—
81D4×Dic43—22no—
82D4×Dic43—22no—
83D4×Dic43—41no—
84D4×Dic43—41no—
85#13063287—22no—
86#13063287—22no—
87#13063287—41no—
88#13063287—41no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43D411yescharacteristic
92C2×C4⋊Dic43D411yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×C4×Dic43C2311yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105#13063258—22no—
106#13063256—22no—
107C4⋊(C43⋊C8)C2×C414yescomplemented
108#13063247—22no—
109#13063247—22no—
110#13063247—41no—
111#13063247—41no—
112#13063245C2×C414yescomplemented
113#13063245C2×C414yescomplemented
114#13063235—22no—
115C8×Dic43—22no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95D411yescharacteristic
121C43⋊#95D411yescharacteristic
122C22×D4×C43C2311yescharacteristic
123C23×C4×C43—21no—
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C4×D4×C43—22no—
127C4×D4×C43C2×C414yescomplemented
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#102×C43—22no—
135#102×C43D414yescomplemented
136#97×C43—22no—
137#95×C43—21no—
138C24×C43—21no—
139C23×D43—21no—
140C23×D43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43C22×C412yes—
145C2×D4×C43C2×D412yes—
146C2×D4×C43#4112yes—
147C22×C4×C43—24no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—81no—
152C22×C4×C43—81no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—42no—
159C22×Dic43—42no—
160C22×Dic43—42no—
161C22×Dic43—42no—
162C22×Dic43—81no—
163C22×Dic43—81no—
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C2×D172—24no—
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—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—42no—
181C2×D172—42no—
182C2×D172—81no—
183C2×D172—81no—
184C2×D172C22×C412yes—
185C2×D172C22×C412yes—
186C2×C4×D43—42no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43—81no—
191C2×C4×D43—81no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43C2×D412yes—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43C22×C412yes—
203C4⋊C4×C43C2×D412yes—
204C22⋊C4×C43—24no—
205C42×C43—42no—
206C42×C43C22×C412yes—
207C42×C43#4112yes—
208C22⋊Dic43—42no—
209C22⋊Dic43—42no—
210#10621882—28no—
211#10621882—28no—
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—22no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—41no—
224C4⋊Dic43—81no—
225C4⋊Dic43—81no—
226C4×Dic43—21no—
227C4×Dic43—21no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8C22×C412yes—
235C2×C43⋊C8C22×C412yes—
236C23×C43—22no—
237C23×C43—22no—
238C23×C43—22no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43C22×D411yescharacteristic
244C22×D43—22no—
245C22×D43—22no—
246C22×D43—41no—
247C22×D43—41no—
248C22×D43—41no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258D4×C43—22no—
259D4×C43—22no—
260D4×C43—22no—
261D4×C43C4×D414yescomplemented
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—84no—
276C2×C4×C43C4×D412yes—
277C2×C4×C43C4×D412yes—
278C2×C4×C43C23×C411yescharacteristic
279C2×C4×C43C22×D411yescharacteristic
280C2×C4×C43C2×#4111yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
282C2×C4×C43H(5,𝔽2)11yescharacteristic
283C2×C4×C432−1+411yescharacteristic
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—21no—
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—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—84no—
302C2×Dic43—84no—
303C2×Dic43AGL(1,ℤ/8)12yes—
304D172—22no—
305D172—22no—
306D172—22no—
307D172—22no—
308D172—48no—
309D172—41no—
310D172—41no—
311D172—41no—
312D172—41no—
313D172—84no—
314C4×D43—84no—
315C4×D43—84no—
316C8×C43—22no—
317C8×C43—41no—
318C43⋊C8—22no—
319C43⋊C8—22no—
320#23008—431nomaximal, Sylow
321C22×C43—24no—
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—42no—
325C22×C43—42no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43C2×C4×D411yescharacteristic
329C22×C43D4211yescharacteristic
330C22×C43#54811yescharacteristic
331C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C43#57511yescharacteristic
333C22×C43#57611yescharacteristic
334C22×C43#57611yescharacteristic
335C2×D43—42no—
336C2×D43—42no—
337C2×D43—42no—
338C2×D43—42no—
339C2×D43—42no—
340C2×D43—42no—
341C2×D43—81no—
342C2×D43—81no—
343C2×D43—81no—
344C2×D43—81no—
345C2×D43—81no—
346C2×D43—81no—
347C2×D43—81no—
348C2×D43—81no—
349C4×C43—22no—
350C4×C43—22no—
351C4×C43—42no—
352C4×C43—42no—
353C4×C43—81no—
354C4×C43C2×C4×D411yescharacteristic
355C4×C43#52011yescharacteristic
356C4×C43#54711yescharacteristic
357C4×C43#55311yescharacteristic
358Dic43—22no—
359Dic43—41no—
360Dic43—41no—
361Dic43—41no—
362Dic43—81no—
363Dic43—81no—
364C2×#459—431no—
365C2×#442—431no—
366C2×C4×D8—431no—
367#2366—431no—
368#2349—431no—
369#1961—431no—
370#1949—431no—
371#1936—431no—
372#1934—431no—
373#1879—431no—
374#1879—431no—
375#1864—431no—
376#1862—431no—
377#1771—431no—
378#1762D4311yescharacteristic, complemented
379C2×C43—44no—
380C2×C43#236111yescharacteristic
381C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
382C2×C43#294811yescharacteristic
383C2×C43#326411yescharacteristic
384C2×C43#326811yescharacteristic
385C2×C43#336611yescharacteristic
386C2×C43#337011yescharacteristic
387D43—82no—
388D43—82no—
389C22×D8—431no—
390C22×D8—431no—
391C2×#127—431no—
392C2×C4×D4—431no—
393C2×C4×D4—431no—
394C2×C4×D4—431no—
395C2×C4×D4—431no—
396C2×C4×D4—861no—
397C2×C4×D4C2×D4311yescharacteristic
398#459—438no—
399#442—864no—
400C4×D8—864no—
401C2×#107—431no—
402C2×#106—431no—
403C2×C4⋊C8—431no—
404C2×#102—431no—
405C2×#102—431no—
406C2×#102—431no—
407C2×#102—431no—
408C2×#102—431no—
409C2×#102—431no—
410C2×#102C2×D4311yescharacteristic
411C2×#102C2×D4311yescharacteristic
412C2×#97—431no—
413C2×#97C2×D4311yescharacteristic
414C2×C4×C8—431no—
415#390—431no—
416#390—431no—
417#390—861no—
418#389—431no—
419#389—431no—
420#386—861no—
421#386—861no—
422#385—861no—
423#385—861no—
424#382—431no—
425#380—861no—
426C4×C4⋊C4—431no—
427C4×C4⋊C4C2×D4311yescharacteristic
428C2×#95—861no—
429#340—431no—
430#340—431no—
431#340C2×D4311yescharacteristic
432#340C2×D4311yescharacteristic
433#336—431no—
434#336—431no—
435C43#2300811yescharacteristic, complemented, Sylow
436C22×D4—431no—
437C22×D4—431no—
438C22×D4—861no—
439C22×D4—861no—
440C22×D4C22×D4311yescharacteristic
441C23×C4—21no—
442C23×C4—861no—
443C23×C4—861no—
444C23×C4—861no—
445C23×C4—861no—
446C2×D8—434no—
447C2×D8—434no—
448C2×D8—862no—
449C2×D8—862no—
450C2×D8—862no—
451C2×D8—862no—
452C22×C8—431no—
453C22×C8—431no—
454C22×C8C22×D4311yescharacteristic
455C22×C8C22×D4311yescharacteristic
456#127—434no—
457#127—862no—
458C4×D4—22no—
459C4×D4—862no—
460C4×D4—862no—
461C4×D4—862no—
462C4×D4—862no—
463C4×D4—1724no—
464C4×D4—1721no—
465C4×D4—1721no—
466C4×D4—1721no—
467C4×D4—1721no—
468C4×D4C4×D4314yescomplemented
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4C22×D4311yescharacteristic
476C2×C4⋊C4C22×D4311yescharacteristic
477C2×C4⋊C4C22×D4311yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—861no—
480C2×C22⋊C4—861no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C42—21no—
488C2×C42—431no—
489C2×C42—431no—
490C2×C42C22×D4311yescharacteristic
491#107—862no—
492#106—862no—
493C4⋊C8—434no—
494#102—22no—
495#102—434no—
496#102—434no—
497#102—862no—
498#102—862no—
499#102—1721no—
500#102—1721no—
501#102D17214yescomplemented
502#97—22no—
503#97—862no—
504C4×C8—862no—
505#95—21no—
506#95—431no—
507#95—431no—
508#95—861no—
509#95—861no—
510#95—861no—
511#95—861no—
512C24—21no—
513C24—861no—
514C24—861no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—432no—
519C2×D4—432no—
520C2×D4—864no—
521C2×D4—864no—
522C2×D4—861no—
523C2×D4—861no—
524C2×D4—861no—
525C2×D4—861no—
526C2×D4—861no—
527C2×D4—861no—
528C2×D4—861no—
529C2×D4—861no—
530C2×D4—861no—
531C2×D4—861no—
532C2×D4—3441no—
533C2×D4—3441no—
534C2×D4—1722no—
535C2×D4—1722no—
536C2×D4C2×C4×D4312yes—
537C2×D4C2×D17212yes—
538C2×D4#1062189812yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—431no—
546C22×C4—431no—
547C22×C4—431no—
548C22×C4—431no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—3441no—
552C22×C4—3441no—
553C22×C4—3441no—
554C22×C4—3441no—
555C22×C4—1722no—
556C22×C4—1722no—
557C22×C4—1722no—
558C22×C4—1722no—
559C22×C4—1722no—
560C22×C4—1722no—
561C22×C4—1722no—
562C22×C4—1722no—
563C22×C4D4×D4311yescharacteristic
564C22×C4D4×D4311yescharacteristic
565C22×C4C23×D4311yescharacteristic
566D8—868no—
567D8—868no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—432no—
574C2×C8—432no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8C2×D17212yes—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—862no—
585C4⋊C4—861no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—3441no—
590C4⋊C4—3441no—
591C4⋊C4—1721no—
592C4⋊C4C2×C4×D4312yes—
593C4⋊C4C2×D17212yes—
594C22⋊C4—24no—
595C22⋊C4—3441no—
596C22⋊C4—3441no—
597C22⋊C4—1722no—
598C22⋊C4—1722no—
599C22⋊C4—1722no—
600C22⋊C4—1722no—
601C22⋊C4—1722no—
602C22⋊C4—1722no—
603C42—42no—
604C42—861no—
605C42—861no—
606C42—861no—
607C42—861no—
608C42C2×C4×D4312yes—
609C42#1062190012yes—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—862no—
618C23—862no—
619C23—1721no—
620C23—1721no—
621C23—1721no—
622C23—1721no—
623C23—1721no—
624C23—1721no—
625C23—1721no—
626C23—1721no—
627C23—1721no—
628C23—1721no—
629C23—1721no—
630C23—1721no—
631C23C2×D4×D4311yescharacteristic
632D4—22no—
633D4—22no—
634D4—22no—
635D4—862no—
636D4—862no—
637D4—862no—
638D4—862no—
639D4—3444no—
640D4—1728no—
641D4—1721no—
642D4—1721no—
643D4—1721no—
644D4—1721no—
645D4C4×D17214yescomplemented
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—84no—
660C2×C4—432no—
661C2×C4—861no—
662C2×C4—861no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—861no—
672C2×C4—3444no—
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(C22⋊D43)⋊C412yes—
683C2×C4(C22⋊D43)⋊C412yes—
684C2×C4C22×C4×D4311yescharacteristic
685C2×C4C22×D17211yescharacteristic
686C2×C4C2×#1062190011yescharacteristic
687C2×C4C2×#1062189811yescharacteristic
688C2×C4#1306337111yescharacteristic
689C2×C4#1306337211yescharacteristic
690C8—22no—
691C8—41no—
692C8—862no—
693C8—862no—
694C22—24no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—3441no—
702C22—3441no—
703C22—3441no—
704C22—3441no—
705C22—3441no—
706C22—3441no—
707C22—3441no—
708C22—3441no—
709C22—1722no—
710C22—1722no—
711C22—1722no—
712C22—1722no—
713C22—1722no—
714C22—1722no—
715C22C2×(C22⋊D43)⋊C411yescharacteristic
716C22D4×D17211yescharacteristic
717C22#1458355811yescharacteristic
718C22AGL(1,ℤ/8)×D4311yescharacteristic
719C22#1458369811yescharacteristic
720C22#1458370311yescharacteristic
721C22#1458370311yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—81no—
727C4—862no—
728C4—3441no—
729C4—3441no—
730C4—1721no—
731C4—1721no—
732C4—1721no—
733C4C2×C4×D17211yescharacteristic
734C4#1458337911yescharacteristic
735C4#1458355311yescharacteristic
736C4#1458359511yescharacteristic
737C2—44no—
738C2—3442no—
739C2—3442no—
740C2#1913760911yescharacteristic
741C2#1914340811yescharacteristic
742C2#1914344311yescharacteristic
743C2#1914607711yescharacteristic
744C2#1914613711yescharacteristic
745C2#1914730311yescharacteristic
746C2#1914734911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1762C2
socleC23×C43C22×D4
prime radicalC2×#14583094C2
cosocleC22×C4×C43C24
hypercenter#1762D43
hypocenterC43#23008
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#14583008C2semidirect
3. C2×#14582979C2semidirect
4. #19137659C2semidirect
5. #19137505C2semidirect
6. #19135419C2semidirect
7. #19135363C2semidirect
8. #19135293C2semidirect
9. #19135279C2semidirect
10. #19134941C2semidirect
11. #19134941C2semidirect
12. #19134857C2semidirect
13. #19134843C2semidirect
14. #19134467C2semidirect
15. C43×#1762C2semidirect
24. #14583094C4semidirect
74. C2×#10621882C2×C4semidirect
75. C2×#10621882C2×C4semidirect
79. #13063322C2×C4semidirect
107. C4⋊(C43⋊C8)C2×C4semidirect
112. #13063245C2×C4semidirect
113. #13063245C2×C4semidirect
127. C4×D4×C43C2×C4semidirect
135. #102×C43D4semidirect
261. D4×C43C4×D4semidirect
378. #1762D43semidirect
435. C43#23008semidirect
468. C4×D4C4×D43semidirect
501. #102D172semidirect
645. D4C4×D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145830942
C2×#145830082
C2×#145829792
#191376592
#191375052
#191354192
#191353632
#191352932
#191352792
#191349412
#191348572
#191348432
#191344672
C43×#17622
#2300843