Finite Group Databasebeta

← #25103817

Subgroups — #25103817

Order 11008.

960 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583223C211yesmaximal, characteristic
2#19137101C211yesmaximal, characteristic
3#117×Dic43C211yesmaximal, characteristic, complemented
4#19135220C211yesmaximal, characteristic, complemented
5#19135213C211yesmaximal, characteristic, complemented
6#19135171C211yesmaximal, characteristic, complemented
7#19135164C211yesmaximal, characteristic, complemented
8#19134915C211yesmaximal, characteristic
9#19134792C211yesmaximal, characteristic, complemented
10#19134491C211yesmaximal, characteristic, complemented
11#19134491C211yesmaximal, characteristic, complemented
12#19134419C211yesmaximal, characteristic, complemented
13#19134419C211yesmaximal, characteristic, complemented
14#19134359C211yesmaximal, characteristic, complemented
15C43×#1825C211yesmaximal, characteristic, complemented
16C2×#13063299C2211yescharacteristic
17C2×#13063287C2211yescharacteristic
18C2×(C22⋊D43)⋊C4—21no—
19C2×#13063284C2211yescharacteristic
20C22×C4×Dic43C2211yescharacteristic
21#14583223C418yescomplemented
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33#14582800C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582788—21no—
36#14582776—21no—
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C22⋊C4×Dic43—21no—
43C22⋊C4×Dic43—21no—
44#14582746—21no—
45#14582745—21no—
46C42×Dic43—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C43×#380C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C23×Dic43D411yescharacteristic
63C23×Dic43D411yescharacteristic
64C22×C4×D43—21no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063299—22no—
68#13063299C2×C414yes—
69#13063287—22no—
70#13063287—22no—
71(C22⋊D43)⋊C4—44no—
72#13063284—22no—
73#13063284—22no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—22no—
85C2×C4×Dic43—22no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063258—22no—
96#13063258C2×C414yescomplemented
97#13063256—22no—
98#13063256C2×C414yescomplemented
99#13063247—22no—
100#13063247—22no—
101#13063245C2×C414yescomplemented
102#13063245C2×C414yescomplemented
103C22⋊(C43⋊C8)C2×C414yescomplemented
104#13063235—22no—
105#13063235—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C23×C4×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115#117×C43—22no—
116#117×C43C2×C414yescomplemented
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C42×C43—21no—
124C22⋊C8×C43—22no—
125#95×C43—21no—
126C24×C43C2×D411yescharacteristic
127C23×D43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C22×C412yes—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43#4112yes—
139C22×C4×C43C2411yescharacteristic
140C2×C22⋊D43—24no—
141C2×C22⋊D43—42no—
142C2×C22⋊D43—42no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—41no—
150C22×Dic43—41no—
151C22×Dic43—41no—
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172C22×C412yes—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43C22×C412yes—
178C4⋊C4×C43C22×C412yes—
179C22⋊C4×C43—24no—
180C22⋊C4×C43—42no—
181C42×C43—24no—
182C22⋊Dic43—24no—
183(C2×D43)⋊C4—24no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—42no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C22×C412yes—
191C4⋊Dic43#4112yes—
192C4⋊Dic43#4112yes—
193Dic43⋊C4—42no—
194C4×Dic43—24no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—22no—
198C4×Dic43—22no—
199C4×Dic43—42no—
200C4×Dic43—42no—
201C4×Dic43—42no—
202C4×Dic43—42no—
203C4×Dic43—42no—
204C4×Dic43#4112yes—
205C4×Dic43#4112yes—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8C22×C412yes—
211C2×C43⋊C8C22×C412yes—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43C4×D412yes—
219C23×C43C22×D411yescharacteristic
220C22×D43—22no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43C4×D412yes—
246C2×C4×C43C23×C411yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C22⋊D43—48no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—22no—
260C2×Dic43—21no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—44no—
266C2×Dic43—44no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43#12312yes—
274C2×Dic43#12312yes—
275C2×Dic43AGL(1,ℤ/8)12yes—
276D172—22no—
277D172—22no—
278D172—41no—
279D172—41no—
280C4×D43—84no—
281C8×C43—41no—
282C8×C43—41no—
283C43⋊C8—22no—
284C43⋊C8—22no—
285#21582—431nomaximal, Sylow
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—22no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43C2×C4×D411yescharacteristic
294C22×C43C2×#12311yescharacteristic
295C22×C43#52511yescharacteristic
296C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C43#57511yescharacteristic
298C22×C43#57511yescharacteristic
299C22×C43#57511yescharacteristic
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C4×C43—22no—
308C4×C43—42no—
309C4×C43—42no—
310C4×C43—81no—
311C4×C43—81no—
312C4×C43C4×#4111yescharacteristic
313C4×C43C4×#4111yescharacteristic
314C4×C43#52911yescharacteristic
315C4×C43#52911yescharacteristic
316Dic43—22no—
317Dic43—22no—
318Dic43—22no—
319Dic43—41no—
320Dic43—42no—
321Dic43—42no—
322Dic43—42no—
323C2×#482—431no—
324C4×#121—431no—
325C4×#117—431no—
326#1926—431no—
327#1925—431no—
328#1919—431no—
329#1918—431no—
330#1875—431no—
331#1854—431no—
332#1825D4311yescharacteristic, complemented
333#1776—431no—
334#1776—431no—
335#1762—431no—
336#1762—431no—
337#1749—431no—
338C2×C43—42no—
339C2×C43C4×#12311yescharacteristic
340C2×C43#294311yescharacteristic
341C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
342C2×C43#309311yescharacteristic
343C2×C43#309411yescharacteristic
344C2×C43#311111yescharacteristic
345C2×C43#311511yescharacteristic
346D43—82no—
347C2×#121—431no—
348C2×C4×D4—431no—
349C2×C4×D4—861no—
350C2×#117—431no—
351C2×#117C2×D4311yescharacteristic
352C22×C42—431no—
353#482—438no—
354C2×#107—431no—
355C2×#107—431no—
356C2×#106—431no—
357C2×#106—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×#102—431no—
362C2×C22⋊C8—431no—
363C2×C22⋊C8C2×D4311yescharacteristic
364C2×#97—431no—
365C2×#97—431no—
366#390—431no—
367#389—431no—
368#388—861no—
369#386—861no—
370#380C2×D4311yescharacteristic
371C4×C4⋊C4—431no—
372C4×C4⋊C4—431no—
373C4×C4⋊C4—431no—
374C4×C4⋊C4—431no—
375C4×C4⋊C4—431no—
376C4×C22⋊C4—861no—
377C4×C22⋊C4—861no—
378C4×C22⋊C4—861no—
379#376—861no—
380C43—861no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340C2×D4311yescharacteristic
386#340C2×D4311yescharacteristic
387#340C2×D4311yescharacteristic
388#340C2×D4311yescharacteristic
389#336—431no—
390#336—431no—
391C43#2158211yescharacteristic, complemented, Sylow
392C22×D4—431no—
393C22×D4—861no—
394C23×C4—431no—
395C23×C4—431no—
396C23×C4—861no—
397C23×C4C22×D4311yescharacteristic
398C22×C8—431no—
399C22×C8—431no—
400C22×C8C22×D4311yescharacteristic
401C22×C8C22×D4311yescharacteristic
402#121—434no—
403#121—862no—
404C4×D4—862no—
405C4×D4—862no—
406C4×D4—1724no—
407#117—22no—
408#117—862no—
409#117—862no—
410#117C4×D4314yescomplemented
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C42—21no—
427C2×C42—431no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—431no—
431C2×C42—862no—
432C2×C42—862no—
433C2×C42—861no—
434C2×C42—861no—
435C2×C42—861no—
436C2×C42—861no—
437C2×C42—861no—
438C2×C42—861no—
439#107—434no—
440#107—862no—
441#106—434no—
442#106—862no—
443#102—434no—
444#102—434no—
445#102—862no—
446#102—862no—
447C22⋊C8—22no—
448C22⋊C8—434no—
449#97—862no—
450#97—862no—
451#95—21no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458C24—861no—
459C24D4×D4311yescharacteristic
460C2×D4—432no—
461C2×D4—864no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4—1722no—
468C2×D4—1722no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—1722no—
488C22×C4—1722no—
489C22×C4—1722no—
490C22×C4—1721no—
491C22×C4—1721no—
492C22×C4—1721no—
493C22×C4C2×C4×D4312yes—
494C22×C4D4×D4311yescharacteristic
495C22×C4#1062190012yes—
496C22×C4C23×D4311yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—432no—
504C2×C8—432no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—432no—
516C4⋊C4—432no—
517C4⋊C4—432no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—1722no—
522C4⋊C4C2×C4×D4312yes—
523C4⋊C4C2×C4×D4312yes—
524C22⋊C4—24no—
525C22⋊C4—42no—
526C22⋊C4—864no—
527C22⋊C4—864no—
528C22⋊C4—1722no—
529C22⋊C4—1722no—
530C22⋊C4—1722no—
531C42—24no—
532C42—432no—
533C42—432no—
534C42—862no—
535C42—862no—
536C42—864no—
537C42—861no—
538C42—861no—
539C42—1722no—
540C42—1722no—
541C42—1722no—
542C42—1722no—
543C42—1722no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—862no—
551C23—1721no—
552C23—1721no—
553C23—1721no—
554C23—1721no—
555C23—1721no—
556C23—1721no—
557C23(C22⋊D43)⋊C412yes—
558C23C2×D4×D4311yescharacteristic
559D4—862no—
560D4—862no—
561D4—1728no—
562D4—1721no—
563D4—1721no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—432no—
583C2×C4—432no—
584C2×C4—432no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—862no—
592C2×C4—861no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—3444no—
598C2×C4—1724no—
599C2×C4—1724no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4(C22⋊D43)⋊C412yes—
607C2×C4C22×C4×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4#41×D4311yescharacteristic
611C2×C4#41×D4311yescharacteristic
612C2×C4C2×#1062190011yescharacteristic
613C8—41no—
614C8—41no—
615C8—862no—
616C8—862no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—3441no—
625C22—3441no—
626C22—3441no—
627C22—3441no—
628C22—1722no—
629C22—1722no—
630C22—1722no—
631C22C2×(C22⋊D43)⋊C411yescharacteristic
632C22#123×D4311yescharacteristic
633C22#1458340711yescharacteristic
634C22AGL(1,ℤ/8)×D4311yescharacteristic
635C22#1458369611yescharacteristic
636C22#1458369611yescharacteristic
637C22#1458369811yescharacteristic
638C4—22no—
639C4—42no—
640C4—42no—
641C4—81no—
642C4—81no—
643C4—862no—
644C4—862no—
645C4—862no—
646C4—1722no—
647C4—1722no—
648C4—1721no—
649C4—1722no—
650C4#1458336711yescharacteristic
651C4#1458336711yescharacteristic
652C4#1458342611yescharacteristic
653C4#1458342611yescharacteristic
654C2—42no—
655C2—3442no—
656C2#1913711211yescharacteristic
657C2#1914339111yescharacteristic
658C2#1914340811yescharacteristic
659C2#1914452711yescharacteristic
660C2#1914453411yescharacteristic
661C2#1914470711yescharacteristic
662C2#1914474111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1825C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
cosocleC22×C4×C43C24
hypercenter#1825D43
hypocenterC43#21582
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
3. #117×Dic43C2semidirect
4. #19135220C2semidirect
5. #19135213C2semidirect
6. #19135171C2semidirect
7. #19135164C2semidirect
9. #19134792C2semidirect
10. #19134491C2semidirect
11. #19134491C2semidirect
12. #19134419C2semidirect
13. #19134419C2semidirect
14. #19134359C2semidirect
15. C43×#1825C2semidirect
21. #14583223C4semidirect
96. #13063258C2×C4semidirect
98. #13063256C2×C4semidirect
101. #13063245C2×C4semidirect
102. #13063245C2×C4semidirect
103. C22⋊(C43⋊C8)C2×C4semidirect
116. #117×C43C2×C4semidirect
332. #1825D43semidirect
391. C43#21582semidirect
410. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832232
#191371012
#117×Dic432
#191352202
#191352132
#191351712
#191351642
#191349152
#191347922
#191344912
#191344192
#191343592
C43×#18252
#2158243