Finite Group Databasebeta

← #25098233

Subgroups — #25098233

Order 11008.

1998 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583466C211yesmaximal, characteristic
2#19147796C211yesmaximal, characteristic, complemented
3C2×#14582872C211yesmaximal, characteristic, complemented
4#19137177C211yesmaximal, characteristic, complemented
5#19135000C218yesmaximal, complemented
6#19134328C211yesmaximal, characteristic, complemented
7#19134327C211yesmaximal, characteristic, complemented
8C43×#2309C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10#14583466—24no—
11#14583466C418yescomplemented
12C2×#13063321—21no—
13C2×#13063312—21no—
14C2×#13063296—22no—
15C2×#13063294C2214yes—
16#14583380—22no—
17#14583379—22no—
18#14583376—21no—
19#14583373—21no—
20#14583372C2214yes—
21C4×#10621898—22no—
22#14583367—22no—
23C2×#13063284C2211yescharacteristic
24C2×#13063284C2211yescharacteristic
25C2×#13063284C2211yescharacteristic
26#117×D43—22no—
27#14582872—24no—
28C2×#13063239C2214yes—
29#14582802—22no—
30#14582802—22no—
31#14582755C2214yes—
32#14582666C2214yes—
33#14582665C2214yes—
34C23×D4×C43C2211yescharacteristic
35C2×#117×C43C2211yescharacteristic
36C2×#117×C43C2211yescharacteristic
37C43×#390—22no—
38C43×#390—22no—
39C43×#379C2214yes—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898—21no—
44C2×#10621898—22no—
45C2×#10621898—22no—
46C2×#10621898C2×C414yes—
47C2×#10621898D414yes—
48C22×Dic86D411yescharacteristic
49C22×D172D411yescharacteristic
50C22×C22⋊D43—24no—
51C22×C22⋊D43C2312yes—
52C22×C4×D43D412yes—
53#13063321—28no—
54#13063312—28no—
55#13063296—216no—
56#13063294—28no—
57#13063294C2×C4116yescomplemented
58C4×Dic86—24no—
59#13063290—24no—
60C4×D172—24no—
61#13063287—24no—
62C4×C22⋊D43—28no—
63(C22⋊D43)⋊C4—28no—
64#13063284—21no—
65#13063284—21no—
66#13063284—21no—
67#13063284—21no—
68#13063284—22no—
69#13063284—22no—
70#13063284—22no—
71#13063284C2×C414yescomplemented
72#13063283—24no—
73#13063282—24no—
74#13063281—24no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43D412yescomplemented
78C4⋊C4×D43—24no—
79C2×C22⋊Dic43—24no—
80C2×C22⋊Dic43—28no—
81C2×C22⋊Dic43C2312yes—
82C2×C22⋊Dic43C2312yes—
83C2×C22⋊Dic43C2312yes—
84C22⋊C4×D43—24no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43D412yescomplemented
88C42×D43—24no—
89#13063239—28no—
90C25×C43C2312yes—
91C22×D4×C43—21no—
92C22×D4×C43—21no—
93C22×D4×C43—21no—
94C22×D4×C43—21no—
95C22×D4×C43—21no—
96C22×D4×C43—21no—
97C22×D4×C43—22no—
98C22×D4×C43—22no—
99C22×D4×C43—22no—
100C22×D4×C43C2×C414yescomplemented
101C23×C4×C43C2311yescharacteristic
102#117×C43—21no—
103#117×C43—21no—
104#117×C43—21no—
105#117×C43—21no—
106#117×C43—22no—
107#117×C43—22no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43D412yescomplemented
110C2×C22⋊C4×C43—28no—
111C2×C22⋊C4×C43C2312yes—
112C2×C22⋊C4×C43C2312yes—
113C2×C42×C43—21no—
114C2×C42×C43D412yescomplemented
115C24×C43—22no—
116C24×C43—22no—
117C24×C43—22no—
118C24×C43—22no—
119C24×C43—22no—
120C24×C43—22no—
121C24×C43—84no—
122C24×C43C22×C414yes—
123C24×C43C2411yescharacteristic
124C23×D43C2×D412yes—
125C2×D4×C43—24no—
126C2×D4×C43—24no—
127C2×D4×C43—24no—
128C2×D4×C43—24no—
129C2×D4×C43—24no—
130C2×D4×C43—24no—
131C2×D4×C43—41no—
132C2×D4×C43—41no—
133C2×D4×C43—41no—
134C2×D4×C43—41no—
135C2×D4×C43—42no—
136C2×D4×C43—42no—
137C2×D4×C43—42no—
138C2×D4×C43—42no—
139C2×D4×C43—42no—
140C2×D4×C43—42no—
141C22×C4×C43—22no—
142C22×C4×C43C22×C412yes—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D412yes—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D414yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43#4112yes—
152C22×C4×C43#4112yes—
153C2×C22⋊D43—22no—
154C2×C22⋊D43—22no—
155C2×C22⋊D43—22no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—216no—
158C2×C22⋊D43—88no—
159C2×C22⋊D43C22×C414yes—
160C2×C22⋊D43C2×D414yes—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43C2×D412yes—
164C22×Dic43C2×D414yes—
165#10621898—24no—
166#10621898—24no—
167#10621898—24no—
168#10621898—24no—
169#10621898—24no—
170#10621898—24no—
171#10621898—24no—
172#10621898—24no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—22no—
176C2×D172C22⋊C414yescomplemented
177C2×C4×D43—22no—
178C2×C4×D43—22no—
179C2×C4×D43—24no—
180C2×C4×D43—28no—
181C2×C4×D43C22⋊C418yescomplemented
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—22no—
185C2×Dic86C22⋊C414yescomplemented
186C4⋊C4×C43—22no—
187C4⋊C4×C43—22no—
188C4⋊C4×C43—42no—
189C22⋊C4×C43—22no—
190C22⋊C4×C43—22no—
191C22⋊C4×C43—22no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—88no—
194C42×C43—22no—
195C42×C43—22no—
196C42×C43—42no—
197C22⋊Dic43—216no—
198C22⋊Dic43—22no—
199C22⋊Dic43—22no—
200C22⋊Dic43—22no—
201C22⋊Dic43—22no—
202C22⋊Dic43—22no—
203C22⋊Dic43—88no—
204C22⋊Dic43C22×C414yes—
205(C2×D43)⋊C4—28no—
206C4⋊Dic43—24no—
207C4⋊Dic43—22no—
208C4⋊Dic43—22no—
209C4⋊Dic43—42no—
210Dic43⋊C4—28no—
211C4×Dic43—28no—
212C4×Dic43—24no—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43—42no—
216C23×C43—24no—
217C23×C43—24no—
218C23×C43—24no—
219C23×C43—42no—
220C23×C43—48no—
221C23×C43—48no—
222C23×C43—48no—
223C23×C43—42no—
224C23×C43—42no—
225C23×C43—42no—
226C23×C43—42no—
227C23×C43—84no—
228C23×C43—84no—
229C23×C43—84no—
230C23×C43—84no—
231C23×C43C23×C411yescharacteristic
232C23×C43C22×D411yescharacteristic
233C23×C43C22×D411yescharacteristic
234C23×C43C22×D411yescharacteristic
235C23×C43C22×D411yescharacteristic
236C23×C43C2×#4111yescharacteristic
237C23×C43C2×#4111yescharacteristic
238C22×D43—22no—
239C22×D43—22no—
240C22×D43—44no—
241C22×D43C2×C22⋊C414yes—
242D4×C43—44no—
243D4×C43—44no—
244D4×C43—44no—
245D4×C43—44no—
246C2×C4×C43—24no—
247C2×C4×C43—44no—
248C2×C4×C43—44no—
249C2×C4×C43—42no—
250C2×C4×C43C2×C22⋊C412yes—
251C2×C4×C43C2×C22⋊C412yes—
252C2×C4×C43C4×D412yes—
253C2×C4×C43C4×D412yes—
254C2×C4×C43C4×D412yes—
255C2×C4×C43C4×D412yes—
256C2×C4×C43#12011yescharacteristic
257C2×C4×C43#12011yescharacteristic
258C2×C4×C43#12011yescharacteristic
259C2×C4×C43#12011yescharacteristic
260C2×C4×C43#12112yes—
261C2×C4×C43#12112yes—
262C2×C4×C43#12112yes—
263C2×C4×C43#12112yes—
264C2×C4×C43#12312yes—
265C2×C4×C43#12312yes—
266C22⋊D43—24no—
267C22⋊D43—24no—
268C22⋊D43—24no—
269C22⋊D43—24no—
270C22⋊D43—816no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—24no—
274C2×Dic43—24no—
275C2×Dic43—44no—
276C2×Dic43—44no—
277C2×Dic43—44no—
278C2×Dic43—42no—
279C2×Dic43C2×C22⋊C414yes—
280D172—24no—
281D172—24no—
282C4×D43—28no—
283C4×D43—28no—
284C4×D43—88no—
285Dic86—24no—
286Dic86—24no—
287#20961—431nomaximal, Sylow
288C22×C43—22no—
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—48no—
296C22×C43—48no—
297C22×C43—48no—
298C22×C43—44no—
299C22×C43—84no—
300C22×C43—84no—
301C22×C43—84no—
302C22×C43—84no—
303C22×C43C22×C22⋊C411yescharacteristic
304C22×C43C2×C4×D411yescharacteristic
305C22×C43C2×C4×D411yescharacteristic
306C22×C43C2×#12011yescharacteristic
307C22×C43C2×#12111yescharacteristic
308C22×C43C2×#12111yescharacteristic
309C22×C43C2×#12311yescharacteristic
310C2×D43—24no—
311C2×D43—44no—
312C2×D43—44no—
313C2×D43—82no—
314C4×C43—44no—
315C4×C43—82no—
316C4×C43#38612yes—
317C4×C43#38612yes—
318C4×C43#38612yes—
319C4×C43#38612yes—
320Dic43—24no—
321Dic43—44no—
322Dic43—44no—
323Dic43—82no—
324C2×#535—431no—
325#3428—431no—
326C2×#410—431no—
327#2309—431no—
328#2309D4311yescharacteristic, complemented
329#1889—438no—
330#1740—431no—
331#1740—431no—
332C2×C43—21no—
333C2×C43—21no—
334C2×C43—21no—
335C2×C43—21no—
336C2×C43—21no—
337C2×C43—21no—
338C2×C43—84no—
339C2×C43C2×#38611yescharacteristic
340C2×C43#302712yes—
341D43—44no—
342C22×#41—431no—
343C23×D4C2×D4311yescharacteristic
344#535—438no—
345#535—864no—
346C2×#127—861no—
347C2×#124—861no—
348C2×#121—862no—
349C2×#120—434no—
350#520—862no—
351#520—862no—
352#519—861no—
353#518—434no—
354#518—861no—
355C4×#41—862no—
356C4×#41—862no—
357C2×#117—431no—
358C2×#117—431no—
359C2×#117—431no—
360C2×#117—862no—
361C2×#117C2×D4311yescharacteristic
362C2×#117C2×D4311yescharacteristic
363#410—864no—
364C2×#99—434no—
365#390—22no—
366#390—22no—
367#390—862no—
368#390—862no—
369#379—434no—
370#379C2×D4314yes—
371#342—434no—
372#342—434no—
373C43#2096111yescharacteristic, complemented, Sylow
374C25C22×D4312yes—
375C2×#41—434no—
376C2×#41—434no—
377C2×#41—862no—
378C2×#41—861no—
379C2×#41—861no—
380C2×#41—862no—
381C2×#41—861no—
382C2×#41—861no—
383C22×Q8—431no—
384C22×D4—22no—
385C22×D4—21no—
386C22×D4—21no—
387C22×D4—22no—
388C22×D4—21no—
389C22×D4—21no—
390C22×D4—22no—
391C22×D4—21no—
392C22×D4—21no—
393C22×D4—432no—
394C22×D4—431no—
395C22×D4—864no—
396C22×D4C4×D4314yescomplemented
397C23×C4—432no—
398C23×C4C22×D4311yescharacteristic
399#127—868no—
400#124—868no—
401#121—8616no—
402#120—4316no—
403#120—868no—
404C4×Q8—864no—
405C4×Q8—864no—
406C4×D4—864no—
407C4×D4—868no—
408C4×D4—864no—
409C4×D4—868no—
410#117—21no—
411#117—21no—
412#117—21no—
413#117—21no—
414#117—22no—
415#117—22no—
416#117—434no—
417#117—864no—
418#117—864no—
419#117—864no—
420#117—861no—
421#117—861no—
422#117—862no—
423#117—861no—
424#117—861no—
425#117—862no—
426#117—862no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—432no—
429C2×C4⋊C4—864no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4C22⋊D4312yescomplemented
433C2×C22⋊C4—28no—
434C2×C22⋊C4—432no—
435C2×C22⋊C4—432no—
436C2×C22⋊C4—432no—
437C2×C22⋊C4—864no—
438C2×C22⋊C4—864no—
439C2×C22⋊C4—868no—
440C2×C22⋊C4C22×D4312yes—
441C2×C22⋊C4C22×D4312yes—
442C2×C42—21no—
443C2×C42—432no—
444C2×C42—864no—
445C2×C42—861no—
446C2×C42—861no—
447C2×C42C22⋊D4312yescomplemented
448#99—868no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—84no—
456C24—432no—
457C24C2×C4×D4314yes—
458C24C23×D4311yescharacteristic
459#41—864no—
460#41—864no—
461#41—864no—
462#41—864no—
463#41—864no—
464#41—864no—
465#41—864no—
466#41—864no—
467C2×Q8—434no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—862no—
471C2×D4—24no—
472C2×D4—24no—
473C2×D4—24no—
474C2×D4—24no—
475C2×D4—24no—
476C2×D4—24no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—42no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—434no—
488C2×D4—434no—
489C2×D4—434no—
490C2×D4—862no—
491C2×D4—862no—
492C2×D4—862no—
493C2×D4—862no—
494C2×D4—8616no—
495C2×D4—861no—
496C2×D4—861no—
497C2×D4—862no—
498C2×D4—3448no—
499C22×C4—22no—
500C22×C4—432no—
501C22×C4—438no—
502C22×C4—434no—
503C22×C4—868no—
504C22×C4—862no—
505C22×C4—862no—
506C22×C4—864no—
507C22×C4—862no—
508C22×C4—862no—
509C22×C4C2×C4×D4312yes—
510C22×C4#1062189812yes—
511C22×C4D4×D4311yescharacteristic
512C22×C4D4×D4311yescharacteristic
513C22×C4D4×D4312yes—
514C22×C4D4×D4311yescharacteristic
515C22×C4D4×D4311yescharacteristic
516C22×C4#1062190012yes—
517C22×C4C2×C22⋊D4314yes—
518C22×C4C2×C22⋊D4311yescharacteristic
519C22×C4C2×C22⋊D4311yescharacteristic
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—42no—
523C4⋊C4—868no—
524C4⋊C4—864no—
525C4⋊C4—862no—
526C4⋊C4—862no—
527C4⋊C4—1722no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—88no—
533C22⋊C4—434no—
534C22⋊C4—868no—
535C22⋊C4—8616no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4—862no—
539C22⋊C4—862no—
540C22⋊C4—862no—
541C22⋊C4—3448no—
542C42—22no—
543C42—22no—
544C42—42no—
545C42—868no—
546C42—864no—
547C42—862no—
548C42—862no—
549C42—1722no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—42no—
554C23—48no—
555C23—48no—
556C23—48no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—84no—
562C23—84no—
563C23—84no—
564C23—84no—
565C23—434no—
566C23—862no—
567C23—862no—
568C23—1724no—
569C23C22×C4×D4311yescharacteristic
570C23C2×D4×D4311yescharacteristic
571C23C2×D4×D4311yescharacteristic
572C23C2×D4×D4311yescharacteristic
573C23C22×C22⋊D4311yescharacteristic
574C23C2×#1062190011yescharacteristic
575C23C2×#1062189811yescharacteristic
576Q8—864no—
577Q8—864no—
578D4—44no—
579D4—44no—
580D4—44no—
581D4—44no—
582D4—864no—
583D4—864no—
584D4—864no—
585D4—864no—
586D4—864no—
587D4—864no—
588D4—34416no—
589C2×C4—24no—
590C2×C4—44no—
591C2×C4—44no—
592C2×C4—42no—
593C2×C4—434no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—868no—
597C2×C4—868no—
598C2×C4—864no—
599C2×C4—864no—
600C2×C4—3448no—
601C2×C4—1724no—
602C2×C4—1722no—
603C2×C4—1724no—
604C2×C4—1724no—
605C2×C4C22⋊C4×D4312yes—
606C2×C4C22⋊C4×D4312yes—
607C2×C4(C22⋊D43)⋊C412yes—
608C2×C4(C22⋊D43)⋊C412yes—
609C2×C4C4×C22⋊D4312yes—
610C2×C4C4×C22⋊D4312yes—
611C2×C4#1306329311yescharacteristic
612C2×C4#1306329311yescharacteristic
613C2×C4#1306329311yescharacteristic
614C2×C4#1306329311yescharacteristic
615C2×C4#1306329612yes—
616C2×C4#1306329612yes—
617C2×C4#1306329812yes—
618C2×C4#1306329812yes—
619C2×C4#1306330712yes—
620C2×C4#1306330712yes—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—48no—
629C22—48no—
630C22—48no—
631C22—44no—
632C22—84no—
633C22—84no—
634C22—84no—
635C22—84no—
636C22—864no—
637C22—3442no—
638C22—1724no—
639C22—1724no—
640C22C2×C22⋊C4×D4311yescharacteristic
641C22C2×(C22⋊D43)⋊C411yescharacteristic
642C22C2×C4×C22⋊D4311yescharacteristic
643C22C2×#1306329311yescharacteristic
644C22C2×#1306329611yescharacteristic
645C22C2×#1306329811yescharacteristic
646C22C2×#1306330711yescharacteristic
647C4—44no—
648C4—82no—
649C4—864no—
650C4—3442no—
651C4—1724no—
652C4—1724no—
653C4#1458277512yes—
654C4#1458277512yes—
655C4#1458277512yes—
656C4#1458277512yes—
657C2—21no—
658C2—21no—
659C2—21no—
660C2—21no—
661C2—21no—
662C2—21no—
663C2—84no—
664C2—1724no—
665C2C2×#1458277511yescharacteristic
666C2#1914399612yes—
subgroupG/H
centerC22C2×#13063293
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#2309C2
socleC22×C43C2×#120
prime radicalC2×#14583466C2
cosocleC24×C43C24
hypercenter#2309D43
hypocenterC43#20961
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. #19147796C2semidirect
3. C2×#14582872C2semidirect
4. #19137177C2semidirect
5. #19135000C2semidirect
6. #19134328C2semidirect
7. #19134327C2semidirect
8. C43×#2309C2semidirect
11. #14583466C4semidirect
57. #13063294C2×C4semidirect
71. #13063284C2×C4semidirect
77. C2×C4⋊Dic43D4semidirect
87. C2×C4×Dic43D4semidirect
100. C22×D4×C43C2×C4semidirect
109. C2×C4⋊C4×C43D4semidirect
114. C2×C42×C43D4semidirect
176. C2×D172C22⋊C4semidirect
181. C2×C4×D43C22⋊C4semidirect
185. C2×Dic86C22⋊C4semidirect
328. #2309D43semidirect
373. C43#20961semidirect
396. C22×D4C4×D43semidirect
432. C2×C4⋊C4C22⋊D43semidirect
447. C2×C42C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834662
#191477962
C2×#145828722
#191371772
#191350002
#191343282
#191343272
C43×#23092
#2096143