Finite Group Databasebeta

← #25113918

Subgroups — #25113918

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
1C2×#14582902C211yesmaximal, characteristic
2#19137476C211yesmaximal, characteristic, complemented
3D4×(C2×D43)⋊C4C211yesmaximal, characteristic
4#19135290C211yesmaximal, characteristic, complemented
5#19135278C211yesmaximal, characteristic, complemented
6#19135220C211yesmaximal, characteristic, complemented
7#19135215C211yesmaximal, characteristic, complemented
8#19134856C211yesmaximal, characteristic, complemented
9#19134840C211yesmaximal, characteristic, complemented
10#19134689C211yesmaximal, characteristic, complemented
11#19134627C211yesmaximal, characteristic, complemented
12#19134524C211yesmaximal, characteristic
13#19134422C211yesmaximal, characteristic, complemented
14#19134378C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C22×(C2×D43)⋊C4—21no—
21C2×#13063258C2211yescharacteristic, complemented
22C2×#13063256C2211yescharacteristic, complemented
23#14582902C418yescomplemented
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×#13063235C2211yescharacteristic, complemented
32#14582801C2211yescharacteristic
33#14582800C2211yescharacteristic
34#14582797C2211yescharacteristic, complemented
35#14582795C2211yescharacteristic, complemented
36#14582790—21no—
37#14582788—21no—
38#14582778—21no—
39#14582776—21no—
40#14582763—21no—
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43#14582754—21no—
44C4⋊C4×Dic43C2211yescharacteristic, complemented
45C4×(C2×D43)⋊C4C2211yescharacteristic
46#14582745—21no—
47#14582662C2211yescharacteristic, complemented
48#14582662C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C2×C4×D4×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic, complemented
57C4×C4⋊C4×C43C2211yescharacteristic, complemented
58C43×#340C2211yescharacteristic, complemented
59C43×#340C2211yescharacteristic, 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—
69C23×Dic43—21no—
70C22×C4×D43C2311yescharacteristic
71C2×#10621872—41no—
72C2×#10621872—41no—
73C2×#10621872C2×C414yescomplemented
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76D4×Dic43—22no—
77D4×Dic43—41no—
78#13063283—22no—
79#13063283C2×C414yescomplemented
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×C22⋊Dic43—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—44no—
94C2×(C2×D43)⋊C4D411yescharacteristic
95C2×(C2×D43)⋊C4D411yescharacteristic
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99#13063258—41no—
100#13063256—41no—
101#13063247—41no—
102#13063247C2×C414yescomplemented
103#13063246—22no—
104#13063246C2×C414yes—
105#13063245—41no—
106#13063245C2×C414yescomplemented
107(C2×D43)⋊C8—22no—
108#13063235—41no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95D411yescharacteristic
115C43⋊#95D411yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C4×D4×C43—22no—
121C4×D4×C43—41no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C42×C43—21no—
127C2×C42×C43C2311yescharacteristic
128#102×C43—22no—
129#102×C43C2×C414yes—
130C4×C8×C43—41no—
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×C43C22×C412yes—
146C2×D4×C43#4112yes—
147C2×D4×C43#4112yes—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—42no—
152C22×C4×C43—42no—
153C22×C4×C43—81no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C2×C22⋊D43—24no—
158C2×C22⋊D43—42no—
159C2×C22⋊D43—42no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—42no—
164C22×Dic43—42no—
165C22×Dic43—81no—
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169D4×D43—28no—
170D4×D43—44no—
171D4×D43—44no—
172D4×D43—44no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172C22×C412yes—
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43C22×C412yes—
184C2×C4×D43#4112yes—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43C22×C412yes—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43C22×C412yes—
197C22⋊C4×C43—42no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—42no—
201C22⋊Dic43—42no—
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—24no—
204(C2×D43)⋊C4—41no—
205(C2×D43)⋊C4—42no—
206(C2×D43)⋊C4—42no—
207(C2×D43)⋊C4—42no—
208(C2×D43)⋊C4—81no—
209(C2×D43)⋊C4—81no—
210(C2×D43)⋊C4—81no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43C22×C412yes—
217Dic43⋊C4—81no—
218Dic43⋊C4—81no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—24no—
222C4×Dic43—42no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8C22×C412yes—
229#10621872—44no—
230C23×C43—22no—
231C23×C43—22no—
232C23×C43—22no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43C22×D411yescharacteristic
238C22×D43—21no—
239C22×D43—21no—
240C22×D43—21no—
241C22×D43—21no—
242C22×D43—21no—
243C22×D43—21no—
244C22×D43—22no—
245C22×D43—48no—
246C22×D43—48no—
247C22×D43—41no—
248C22×D43—41no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—84no—
254C22×D43—84no—
255C22×D43—84no—
256C22×D43—84no—
257C22×D43—84no—
258C22×D43C4×D412yes—
259D4×C43—22no—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43#11714yes—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—22no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
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—41no—
276C2×C4×C43—41no—
277C2×C4×C43—84no—
278C2×C4×C43AGL(1,ℤ/8)12yes—
279C2×C4×C43C23×C411yescharacteristic
280C2×C4×C43C2×#4111yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43H(5,𝔽2)11yescharacteristic
284C2×C4×C43H(5,𝔽2)11yescharacteristic
285C22⋊D43—48no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—22no—
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—41no—
302C2×Dic43—41no—
303C2×Dic43—84no—
304C2×Dic43C4×D412yes—
305D172—22no—
306D172—22no—
307D172—41no—
308D172—41no—
309C4×D43—22no—
310C4×D43—22no—
311C4×D43—22no—
312C4×D43—22no—
313C8×C43—22no—
314C8×C43—41no—
315C43⋊C8—22no—
316C43⋊C8—41no—
317#22584—431nomaximal, Sylow
318C22×C43—24no—
319C22×C43—42no—
320C22×C43—42no—
321C22×C43—42no—
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—42no—
325C22×C43C2×C4×D411yescharacteristic
326C22×C43#54611yescharacteristic
327C22×C43#54611yescharacteristic
328C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C43#57511yescharacteristic
330C22×C43#57611yescharacteristic
331C22×C43#57711yescharacteristic
332C2×D43—22no—
333C2×D43—22no—
334C2×D43—22no—
335C2×D43—41no—
336C2×D43—41no—
337C2×D43—41no—
338C2×D43—41no—
339C2×D43—42no—
340C2×D43—42no—
341C2×D43—42no—
342C2×D43—816no—
343C2×D43—81no—
344C2×D43—81no—
345C2×D43—81no—
346C2×D43—81no—
347C4×C43—22no—
348C4×C43—42no—
349C4×C43—41no—
350C4×C43—81no—
351C4×C43—81no—
352C4×C43C2×#11711yescharacteristic
353C4×C43#51811yescharacteristic
354C4×C43#55111yescharacteristic
355C4×C43#55111yescharacteristic
356Dic43—22no—
357Dic43—42no—
358Dic43—41no—
359Dic43—41no—
360Dic43—81no—
361Dic43—81no—
362C2×#418—431no—
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×#102D4311yescharacteristic, complemented
376#1753—431no—
377C2×C43—44no—
378C2×C43#234211yescharacteristic
379C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
380C2×C43#294611yescharacteristic
381C2×C43#331011yescharacteristic
382C2×C43#331911yescharacteristic
383C2×C43#332311yescharacteristic
384C2×C43#332511yescharacteristic
385D43—42no—
386D43—82no—
387C23×D4—431no—
388C22×M16—431no—
389C2×C4×D4—431no—
390C2×C4×D4C2×D4311yescharacteristic
391C2×#117—431no—
392C22×C22⋊C4—861no—
393C2×#107—431no—
394C2×#106—431no—
395#418—438no—
396C2×#102—431no—
397C2×#102—431no—
398C2×#102—431no—
399C2×#102—431no—
400C2×#102—431no—
401C2×#102—431no—
402C2×#102C2×D4311yescharacteristic
403C2×#102C2×D4311yescharacteristic
404C2×C22⋊C8—431no—
405C2×#97—431no—
406C2×C4×C8C2×D4311yescharacteristic, complemented
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⋊C4C2×D4311yescharacteristic, complemented
421C4×C22⋊C4—431no—
422#376—861no—
423#340—431no—
424#340—431no—
425#340—431no—
426#340—431no—
427#340C2×D4311yescharacteristic, complemented
428#340C2×D4311yescharacteristic, complemented
429#336—431no—
430#336—431no—
431C43#2258411yescharacteristic, complemented, Sylow
432C25—861no—
433C22×D4—434no—
434C22×D4—431no—
435C22×D4—862no—
436C22×D4—861no—
437C22×D4—862no—
438C22×D4—862no—
439C22×D4—1721no—
440C22×D4—1721no—
441C22×D4C22×D4311yescharacteristic
442C23×C4—21no—
443C23×C4—431no—
444C23×C4—861no—
445C2×M16—434no—
446C2×M16—1721no—
447C2×M16—1721no—
448C22×C8—431no—
449C22×C8—431no—
450C22×C8C22×D4311yescharacteristic
451C22×C8C22×D4311yescharacteristic
452C4×D4—22no—
453C4×D4—41no—
454C4×D4—862no—
455C4×D4—1721no—
456#117—434no—
457#117—862no—
458C2×C4⋊C4—431no—
459C2×C4⋊C4—431no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4—861no—
462C2×C4⋊C4—861no—
463C2×C4⋊C4C22×D4311yescharacteristic
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—861no—
481C2×C42—861no—
482C2×C42C22×D4311yescharacteristic
483#107—1721no—
484#106—1721no—
485#102—22no—
486#102—434no—
487#102—434no—
488#102—434no—
489#102—862no—
490#102—1721no—
491#102—1721no—
492#102C4×D4314yes—
493C22⋊C8—862no—
494#97—1721no—
495C4×C8—41no—
496#95—21no—
497#95—431no—
498#95—431no—
499#95—861no—
500#95—861no—
501#95—861no—
502#95—861no—
503#95—861no—
504C24—21no—
505C24—431no—
506C24—864no—
507C24—861no—
508C24—3441no—
509C24—3441no—
510C24—1722no—
511C24—1722no—
512C24—1722no—
513C24—1722no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—432no—
518C2×D4—864no—
519C2×D4—868no—
520C2×D4—861no—
521C2×D4—861no—
522C2×D4—861no—
523C2×D4—861no—
524C2×D4—861no—
525C2×D4—1724no—
526C2×D4—1724no—
527C2×D4—1724no—
528C2×D4—1722no—
529C2×D4—1722no—
530C2×D4C2×C4×D4312yes—
531C2×D4#1062189812yes—
532C2×D4#1062189812yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—81no—
539C22×C4—431no—
540C22×C4—432no—
541C22×C4—432no—
542C22×C4—431no—
543C22×C4—431no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—3441no—
552C22×C4—1722no—
553C22×C4—1722no—
554C22×C4D4×D4311yescharacteristic
555C22×C4D4×D4311yescharacteristic
556C22×C4C23×D4311yescharacteristic
557M16—1724no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—432no—
564C2×C8—861no—
565C2×C8—861no—
566C2×C8—861no—
567C2×C8—861no—
568C2×C8—861no—
569C2×C8C2×C4×D4312yes—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—432no—
576C4⋊C4—861no—
577C4⋊C4—861no—
578C4⋊C4—861no—
579C4⋊C4—861no—
580C4⋊C4—861no—
581C4⋊C4—3441no—
582C4⋊C4—3441no—
583C4⋊C4C2×C4×D4312yes—
584C22⋊C4—42no—
585C22⋊C4—864no—
586C22⋊C4—862no—
587C22⋊C4—3441no—
588C22⋊C4—3441no—
589C22⋊C4—3441no—
590C22⋊C4—1721no—
591C22⋊C4—1722no—
592C22⋊C4—1722no—
593C22⋊C4—1722no—
594C22⋊C4—1722no—
595C42—21no—
596C42—21no—
597C42—42no—
598C42—864no—
599C42—861no—
600C42—861no—
601C42—1722no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—432no—
610C23—861no—
611C23—861no—
612C23—861no—
613C23—861no—
614C23—861no—
615C23—861no—
616C23—862no—
617C23—3444no—
618C23—3444no—
619C23—3444no—
620C23—3444no—
621C23—3444no—
622C23—1728no—
623C23—1728no—
624C23—1721no—
625C23—1721no—
626C23—1721no—
627C23—1721no—
628C23—1721no—
629C23—1721no—
630C23C2×D4×D4311yescharacteristic
631D4—22no—
632D4—22no—
633D4—22no—
634D4—862no—
635D4—862no—
636D4—1728no—
637D4—1721no—
638D4—1721no—
639D4#1306328214yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—84no—
655C2×C4—432no—
656C2×C4—861no—
657C2×C4—861no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—3444no—
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×C4#1306334912yes—
679C2×C4C22×C4×D4311yescharacteristic
680C2×C4#41×D4311yescharacteristic
681C2×C4C2×#1062189811yescharacteristic
682C2×C4C2×#1062189811yescharacteristic
683C2×C4#1306337011yescharacteristic
684C2×C4#1306337111yescharacteristic
685C8—22no—
686C8—41no—
687C8—862no—
688C8—1721no—
689C22—24no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—862no—
697C22—862no—
698C22—862no—
699C22—34416no—
700C22—3441no—
701C22—3441no—
702C22—3441no—
703C22—3441no—
704C22—1722no—
705C22—1722no—
706C22—1722no—
707C22—1721no—
708C22—1721no—
709C22—1721no—
710C22—1721no—
711C22C4×D4×D4311yescharacteristic
712C22#1458353911yescharacteristic
713C22#1458354511yescharacteristic
714C22C2×#1306334911yescharacteristic
715C22#1458369611yescharacteristic
716C22#1458370111yescharacteristic
717C22#1458370511yescharacteristic
718C4—22no—
719C4—42no—
720C4—41no—
721C4—81no—
722C4—81no—
723C4—862no—
724C4—3441no—
725C4—3441no—
726C4—1721no—
727C4—1721no—
728C4—1722no—
729C4C2×#1306328211yescharacteristic
730C4#1458337111yescharacteristic
731C4#1458357311yescharacteristic
732C4#1458357811yescharacteristic
733C2—44no—
734C2—3442no—
735C2—1722no—
736C2#1913743811yescharacteristic
737C2C4×#1306334911yescharacteristic
738C2#1914342211yescharacteristic
739C2#1914661211yescharacteristic
740C2#1914674711yescharacteristic
741C2#1914681611yescharacteristic
742C2#1914683911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenterC4×#102D43
hypocenterC43#22584
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. #19137476C2semidirect
4. #19135290C2semidirect
5. #19135278C2semidirect
6. #19135220C2semidirect
7. #19135215C2semidirect
8. #19134856C2semidirect
9. #19134840C2semidirect
10. #19134689C2semidirect
11. #19134627C2semidirect
13. #19134422C2semidirect
14. #19134378C2semidirect
15. C4×#102×C43C2semidirect
21. C2×#13063258C22semidirect
22. C2×#13063256C22semidirect
23. #14582902C4semidirect
31. C2×#13063235C22semidirect
34. #14582797C22semidirect
35. #14582795C22semidirect
44. C4⋊C4×Dic43C22semidirect
47. #14582662C22semidirect
48. #14582662C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582654C22semidirect
52. #14582653C22semidirect
56. C2×C4×C8×C43C22semidirect
57. C4×C4⋊C4×C43C22semidirect
58. C43×#340C22semidirect
59. C43×#340C22semidirect
73. C2×#10621872C2×C4semidirect
79. #13063283C2×C4semidirect
102. #13063247C2×C4semidirect
106. #13063245C2×C4semidirect
375. C4×#102D43semidirect
406. C2×C4×C8C2×D43semidirect
420. C4×C4⋊C4C2×D43semidirect
427. #340C2×D43semidirect
428. #340C2×D43semidirect
431. C43#22584semidirect

Maximal subgroups

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

subgroupindex
C2×#145829022
#191374762
D4×(C2×D43)⋊C42
#191352902
#191352782
#191352202
#191352152
#191348562
#191348402
#191346892
#191346272
#191345242
#191344222
#191343782
C4×#102×C432
#2258443