Finite Group Databasebeta

← #25156653

Subgroups — #25156653

Order 11008.

918 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583099C211yesmaximal, characteristic
2C2×#14582984C211yesmaximal, characteristic, complemented
3#19138362C211yesmaximal, characteristic
4Q8×Dic43⋊C4C211yesmaximal, characteristic, complemented
5#19136125C211yesmaximal, characteristic, complemented
6#19136096C211yesmaximal, characteristic, complemented
7#19136002C211yesmaximal, characteristic, complemented
8#19135830C211yesmaximal, characteristic
9#19135276C211yesmaximal, characteristic, complemented
10#19135155C211yesmaximal, characteristic, complemented
11#19134948C211yesmaximal, characteristic, complemented
12#19134948C211yesmaximal, characteristic, complemented
13#19134948C211yesmaximal, characteristic, complemented
14#19134853C211yesmaximal, characteristic, complemented
15C43×#1865C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063322C2211yescharacteristic
19C2×#13063310—21no—
20C2×Q8×Dic43C2211yescharacteristic
21C2×Q8×Dic43C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23#14583099—24no—
24#14582984—24no—
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582817—21no—
35#14582816—21no—
36#14582800C2211yescharacteristic
37#14582800C2211yescharacteristic
38#14582800C2211yescharacteristic
39#14582797—21no—
40#14582797C2211yescharacteristic
41#14582795—21no—
42#14582795C2211yescharacteristic
43#14582777—21no—
44#14582768—21no—
45#14582768C2211yescharacteristic
46C4×Dic43⋊C4—21no—
47C4×Dic43⋊C4C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×D172—21no—
62C22×D172—21no—
63C22×D172C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C4×D43—21no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C2×#10621884D414yes—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063322—22no—
75#13063322—41no—
76#13063310—44no—
77Q8×Dic43—22no—
78Q8×Dic43—22no—
79Q8×Dic43—22no—
80Q8×Dic43—41no—
81#13063287—22no—
82#13063287—41no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4D411yescharacteristic
92C2×Dic43⋊C4D411yescharacteristic
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—
99C2×(C2×D43)⋊C4—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43C2311yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104#13063256—22no—
105C4⋊(C43⋊C8)—22no—
106#13063247—22no—
107#13063247—22no—
108#13063247—22no—
109#13063247—41no—
110#13063245—22no—
111#13063245—22no—
112C8×Dic43—22no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C22×Q8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C4×Q8×C43—22no—
121C4×Q8×C43—41no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C42×C43—21no—
128C2×C42×C43C2311yescharacteristic
129#106×C43—41no—
130#103×C43—22no—
131#103×C43—22no—
132#95×C43—21no—
133C23×D43—21no—
134C23×D43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43C2×D412yes—
139C2×Q8×C43#4112yes—
140C2×Q8×C43#4112yes—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—42no—
166C2×D172—42no—
167C2×D172—42no—
168C2×D172—42no—
169C2×D172—81no—
170C2×D172—81no—
171C2×D172C2×D412yes—
172C2×C4×D43—42no—
173C2×C4×D43—42no—
174C2×C4×D43—81no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—42no—
188C4⋊C4×C43—42no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—42no—
192#10621884—28no—
193#10621884—44no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—42no—
198(C2×D43)⋊C4—81no—
199(C2×D43)⋊C4—81no—
200(C2×D43)⋊C4—81no—
201C4⋊Dic43—24no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—42no—
206C4⋊Dic43#4112yes—
207Dic43⋊C4—41no—
208Dic43⋊C4—42no—
209Dic43⋊C4—81no—
210Dic43⋊C4—81no—
211Dic43⋊C4—81no—
212Dic43⋊C4SD1614yescomplemented
213C4×Dic43—24no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—42no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8C2×D412yes—
225C23×C43C22×D411yescharacteristic
226C22×D43—22no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—41no—
240Q8×C43—22no—
241Q8×C43—22no—
242Q8×C43—22no—
243Q8×C43#12314yescomplemented
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—21no—
247C2×C4×C43—22no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43C2×SD1612yes—
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×C4×C432−1+411yescharacteristic
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—22no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43C2×SD1612yes—
285C2×Dic43C2×SD1612yes—
286D172—22no—
287D172—22no—
288D172—41no—
289D172—41no—
290D172—41no—
291D172—41no—
292D172—41no—
293D172—41no—
294D172—84no—
295D172—84no—
296C4×D43—84no—
297C8×C43—41no—
298C8×C43—41no—
299C43⋊C8—22no—
300C43⋊C8—41no—
301#26163—431nomaximal, Sylow
302C22×C43#52511yescharacteristic
303C22×C43D4211yescharacteristic
304C22×C43#54811yescharacteristic
305C22×C43C22×SD1611yescharacteristic
306C22×C43#57511yescharacteristic
307C22×C43#57611yescharacteristic
308C22×C43#57711yescharacteristic
309C2×D43—42no—
310C2×D43—42no—
311C2×D43—42no—
312C2×D43—81no—
313C2×D43—81no—
314C2×D43—81no—
315C2×D43—81no—
316C2×D43—81no—
317C2×D43—81no—
318C2×D43—81no—
319C2×D43—81no—
320C2×D43—81no—
321C2×D43—81no—
322C2×D43—81no—
323C4×C43—24no—
324C4×C43—22no—
325C4×C43—41no—
326C4×C43—81no—
327C4×C43—81no—
328C4×C43—81no—
329C4×C43C2×#12311yescharacteristic
330C4×C43#53911yescharacteristic
331C4×C43#54711yescharacteristic
332C4×C43#55311yescharacteristic
333Dic43—22no—
334Dic43—22no—
335Dic43—41no—
336Dic43—42no—
337Dic43—41no—
338Dic43—81no—
339C2×#460—431no—
340C2×C4×SD16—431no—
341#2445—431no—
342Q8×C4⋊C4—431no—
343#2094—431no—
344#2088—431no—
345#2071—431no—
346#2041—431no—
347#1934—431no—
348#1916—431no—
349#1880—431no—
350#1880—431no—
351#1880—431no—
352#1865D4311yescharacteristic, complemented
353#1864—431no—
354C2×C43#244311yescharacteristic
355C2×C43#310311yescharacteristic
356C2×C43#311911yescharacteristic
357C2×C43#326811yescharacteristic
358C2×C43D4×SD1611yescharacteristic
359C2×C43#336211yescharacteristic
360C2×C43#337111yescharacteristic
361D43—82no—
362D43—161no—
363C22×SD16—431no—
364C22×SD16—431no—
365C2×#127—431no—
366C2×#123—861no—
367C2×C4×Q8—431no—
368C2×C4×Q8—431no—
369C2×C4×Q8C2×D4311yescharacteristic
370C2×C4×D4—431no—
371#460—864no—
372C4×SD16—864no—
373C2×#106—431no—
374C2×#106C2×D4311yescharacteristic
375C2×C4⋊C8—431no—
376C2×#103C2×D4311yescharacteristic
377C2×#103C2×D4311yescharacteristic
378C2×#102—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×#102—431no—
382C2×#102—431no—
383C2×#102—431no—
384C2×C4×C8—431no—
385#394—861no—
386#394—861no—
387#390—431no—
388#390—431no—
389#390—431no—
390#389—431no—
391#389—431no—
392#389—861no—
393#389—861no—
394#389C2×D4311yescharacteristic
395#386—861no—
396#384—431no—
397#384—861no—
398C4×C4⋊C4—431no—
399C4×C4⋊C4—861no—
400#340—431no—
401#340—431no—
402#340—431no—
403#340C2×D4311yescharacteristic
404#336—431no—
405#336—431no—
406#336—431no—
407#336C2×D4311yescharacteristic
408C43#2616311yescharacteristic, complemented, Sylow
409C22×Q8C22×D4311yescharacteristic
410C22×D4—431no—
411C22×D4—431no—
412C22×D4—861no—
413C22×D4—861no—
414C23×C4—861no—
415C2×SD16—434no—
416C2×SD16—862no—
417C2×SD16—862no—
418C2×SD16—862no—
419C2×SD16—862no—
420C2×SD16—862no—
421C22×C8—431no—
422C22×C8—431no—
423C22×C8C22×D4311yescharacteristic
424C22×C8C22×D4311yescharacteristic
425#127—862no—
426#127—1721no—
427#123—1724no—
428C4×Q8—22no—
429C4×Q8—41no—
430C4×Q8—862no—
431C4×Q8—862no—
432C4×Q8—862no—
433C4×Q8—1721no—
434C4×D4—862no—
435C4×D4—1721no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4C22×D4311yescharacteristic
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C4⋊C4C22×D4311yescharacteristic
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C42—21no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—861no—
462C2×C42—861no—
463C2×C42C22×D4311yescharacteristic
464#106—41no—
465#106—862no—
466C4⋊C8—862no—
467#103—22no—
468#103—22no—
469#102—862no—
470#102—862no—
471#102—862no—
472#102—862no—
473#102—862no—
474#102—1721no—
475C4×C8—862no—
476#95—21no—
477#95—431no—
478#95—431no—
479#95—861no—
480#95—861no—
481C24—861no—
482C24—861no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8#1062189812yes—
487C2×Q8D4×D4312yes—
488C2×Q8#1062190212yes—
489C2×D4—432no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C2×D4—861no—
496C2×D4—861no—
497C2×D4—861no—
498C2×D4—861no—
499C2×D4—861no—
500C2×D4—861no—
501C2×D4—3441no—
502C2×D4—3441no—
503C2×D4—1722no—
504C2×D4—1722no—
505C2×D4—1722no—
506C2×D4—1722no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—3441no—
518C22×C4—1722no—
519C22×C4—1722no—
520C22×C4D4×D4311yescharacteristic
521C22×C4D4×D4311yescharacteristic
522C22×C4C23×D4311yescharacteristic
523SD16—868no—
524SD16—1724no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—432no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—861no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—434no—
546C4⋊C4—432no—
547C4⋊C4—864no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—3441no—
552C4⋊C4—3441no—
553C4⋊C4—3441no—
554C4⋊C4—1721no—
555C4⋊C4—1722no—
556C4⋊C4—1722no—
557C22⋊C4—3441no—
558C22⋊C4—3441no—
559C22⋊C4—3441no—
560C22⋊C4—1722no—
561C22⋊C4—1722no—
562C22⋊C4—1722no—
563C22⋊C4—1722no—
564C42—21no—
565C42—21no—
566C42—42no—
567C42—864no—
568C42—861no—
569C42—861no—
570C42—861no—
571C42—861no—
572C42—1722no—
573C23—862no—
574C23—1721no—
575C23—1721no—
576C23—1721no—
577C23—1721no—
578C23—1721no—
579C23—1721no—
580C23—1721no—
581C23—1721no—
582C23—1721no—
583C23—1721no—
584C23—1721no—
585C23—1721no—
586C23—1721no—
587C23C2×D4×D4311yescharacteristic
588Q8—22no—
589Q8—22no—
590Q8—22no—
591Q8#1306331014yescomplemented
592D4—862no—
593D4—862no—
594D4—3444no—
595D4—3444no—
596D4—1721no—
597D4—1721no—
598D4—1721no—
599D4—1721no—
600D4—1721no—
601D4—1721no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—432no—
620C2×C4—432no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—862no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—3444no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4SD16×D4312yes—
639C2×C4C2×D4×D4311yescharacteristic
640C2×C4#41×D4311yescharacteristic
641C2×C4C2×#1062189811yescharacteristic
642C2×C4C2×#1062190211yescharacteristic
643C2×C4#1306337011yescharacteristic
644C2×C4#1306337211yescharacteristic
645C8—41no—
646C8—41no—
647C8—862no—
648C8—1721no—
649C22—3441no—
650C22—3441no—
651C22—3441no—
652C22—3441no—
653C22—3441no—
654C22—3441no—
655C22—3441no—
656C22—3441no—
657C22—3441no—
658C22—3441no—
659C22—3441no—
660C22—1722no—
661C22—1722no—
662C22—1722no—
663C22#1458341211yescharacteristic
664C22#1458353111yescharacteristic
665C22#1458355811yescharacteristic
666C22C2×SD16×D4311yescharacteristic
667C22#1458369811yescharacteristic
668C22#1458370111yescharacteristic
669C22#1458370811yescharacteristic
670C4—24no—
671C4—22no—
672C4—41no—
673C4—81no—
674C4—81no—
675C4—81no—
676C4—862no—
677C4—862no—
678C4—3441no—
679C4—1721no—
680C4—1722no—
681C4—1721no—
682C4C2×#1306331011yescharacteristic
683C4#1458349811yescharacteristic
684C4#1458354711yescharacteristic
685C4#1458359811yescharacteristic
686C2—3442no—
687C2—6881no—
688C2#1913833411yescharacteristic
689C2#1914462811yescharacteristic
690C2#1914480111yescharacteristic
691C2#1914613811yescharacteristic
692C2#1914628411yescharacteristic
693C2#1914726411yescharacteristic
694C2#1914736411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1865C2
socleC23×C43C22×D4
prime radicalC2×#13063322C22
hypercenter#1865D43
hypocenterC43#26163
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
2. C2×#14582984C2semidirect
4. Q8×Dic43⋊C4C2semidirect
5. #19136125C2semidirect
6. #19136096C2semidirect
7. #19136002C2semidirect
9. #19135276C2semidirect
10. #19135155C2semidirect
11. #19134948C2semidirect
12. #19134948C2semidirect
13. #19134948C2semidirect
14. #19134853C2semidirect
15. C43×#1865C2semidirect
212. Dic43⋊C4SD16semidirect
243. Q8×C43#123semidirect
352. #1865D43semidirect
408. C43#26163semidirect
591. Q8#13063310semidirect

Maximal subgroups

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

subgroupindex
C2×#145830992
C2×#145829842
#191383622
Q8×Dic43⋊C42
#191361252
#191360962
#191360022
#191358302
#191352762
#191351552
#191349482
#191348532
C43×#18652
#2616343