Finite Group Databasebeta

← #25156727

Subgroups — #25156727

Order 11008.

894 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583113C211yesmaximal, characteristic
2C2×#14582986C211yesmaximal, characteristic, complemented
3#19138396C211yesmaximal, characteristic, complemented
4#19137503C211yesmaximal, characteristic, complemented
5#19136094C211yesmaximal, characteristic, complemented
6#19136014C211yesmaximal, characteristic, complemented
7#19135834C211yesmaximal, characteristic, complemented
8#19135275C211yesmaximal, characteristic, complemented
9#19135153C211yesmaximal, characteristic, complemented
10#19134946C211yesmaximal, characteristic
11#19134940C211yesmaximal, characteristic
12#19134928C211yesmaximal, characteristic, complemented
13#19134846C211yesmaximal, characteristic, complemented
14#19134839C211yesmaximal, characteristic, complemented
15C43×#2092C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063312C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23#14583113—24no—
24#14582986—24no—
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582835—21no—
34#14582827—21no—
35#14582805C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582795C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582793—21no—
41#14582792—21no—
42#14582773—21no—
43#14582773—21no—
44#14582758—21no—
45C4×C4⋊Dic43C2211yescharacteristic
46#95×D43—21no—
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#382C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C2×#10621873—22no—
67C2×#10621873—22no—
68C2×#10621873D414yes—
69C2×#10621882—22no—
70C2×#10621882—22no—
71C2×#10621882—22no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063312—22no—
75#13063312—41no—
76#13063290—22no—
77#13063290—41no—
78C4×D172—22no—
79C4×D172—22no—
80#13063287—22no—
81#13063287—22no—
82#13063287—41no—
83#13063287—41no—
84C2×C4⋊Dic43D411yescharacteristic
85C2×C4⋊Dic43D411yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102Dic43⋊C8—22no—
103#13063250—22no—
104#13063248—22no—
105#13063248—22no—
106#13063247—22no—
107#13063246—22no—
108#13063245—22no—
109C8×Dic43—22no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C22×D4×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C42×C43C2311yescharacteristic
126#107×C43—41no—
127#106×C43—22no—
128#102×C43—22no—
129#102×C43—41no—
130#95×C43—21no—
131#95×C43—21no—
132C24×C43—21no—
133C23×D43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172C2×D412yes—
157C2×D172#4112yes—
158C2×D172#4112yes—
159C2×C4×D43—24no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43—81no—
165C2×C4×D43—81no—
166C2×C4×D43—81no—
167C2×C4×D43—81no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86C2×D412yes—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C2×D412yes—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C22⋊C4×C43—42no—
187C22⋊C4×C43—81no—
188C42×C43—21no—
189C42×C43—21no—
190C22⋊Dic43—42no—
191C22⋊Dic43—42no—
192C22⋊Dic43—42no—
193C22⋊Dic43—81no—
194#10621882—44no—
195(C2×D43)⋊C4—24no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—42no—
198C4⋊Dic43—21no—
199C4⋊Dic43—22no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—41no—
203C4⋊Dic43#4112yes—
204Dic43⋊C4—42no—
205Dic43⋊C4—81no—
206Dic43⋊C4—81no—
207Dic43⋊C4—81no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—42no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219#10621873—28no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43C22×D411yescharacteristic
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×C4×C432−1+411yescharacteristic
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—22no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43#13512yes—
281D172—22no—
282D172—22no—
283D172—22no—
284D172#12314yes—
285C4×D43—84no—
286C4×D43—84no—
287C4×D43—84no—
288Dic86—22no—
289Dic86—22no—
290Dic86—41no—
291Dic86—41no—
292C8×C43—22no—
293C8×C43—41no—
294C43⋊C8—41no—
295C43⋊C8—41no—
296#26168—431nomaximal, Sylow
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43#52511yescharacteristic
305C22×C43D4211yescharacteristic
306C22×C43#54811yescharacteristic
307C22×C43C2×#13511yescharacteristic
308C22×C43#57511yescharacteristic
309C22×C43#57611yescharacteristic
310C22×C43#57711yescharacteristic
311C2×D43—24no—
312C2×D43—42no—
313C2×D43—42no—
314C2×D43—42no—
315C2×D43—42no—
316C2×D43—42no—
317C2×D43—42no—
318C4×C43—41no—
319C4×C43—41no—
320C4×C43—81no—
321C4×C43—81no—
322C4×C43—81no—
323C4×C43C2×#12311yescharacteristic
324C4×C43#53911yescharacteristic
325C4×C43#54711yescharacteristic
326C4×C43#55311yescharacteristic
327Dic43—22no—
328Dic43—42no—
329Dic43—42no—
330Dic43—41no—
331Dic43—41no—
332Dic43—41no—
333Dic43—81no—
334C2×#463—431no—
335C2×C4×SD16—431no—
336#2448—431no—
337#2349—431no—
338#2092D4311yescharacteristic, complemented
339#2088—431no—
340#2074—431no—
341#2042—431no—
342#1934—431no—
343#1916—431no—
344#1879—431no—
345#1879—431no—
346#1877—431no—
347#1863—431no—
348#1862—431no—
349C2×C43—161no—
350C2×C43#244311yescharacteristic
351C2×C43#310211yescharacteristic
352C2×C43#311811yescharacteristic
353C2×C43#326811yescharacteristic
354C2×C43#328211yescharacteristic
355C2×C43#336111yescharacteristic
356C2×C43#337611yescharacteristic
357D43—44no—
358C22×SD16—431no—
359C22×D8—431no—
360C2×#124—431no—
361C2×C4×Q8—431no—
362C2×C4×D4—431no—
363C2×C4×D4—431no—
364C2×C4×D4—431no—
365#463—864no—
366C4×SD16—864no—
367C2×#107C2×D4311yescharacteristic
368C2×#106C2×D4311yescharacteristic
369C2×C4⋊C8—431no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102C2×D4311yescharacteristic
377C2×#102C2×D4311yescharacteristic
378C2×C4×C8—431no—
379#399—861no—
380#397—861no—
381#391—431no—
382#390—431no—
383#390C2×D4311yescharacteristic
384#389—431no—
385#389—431no—
386#389—431no—
387#388—861no—
388#388—861no—
389#385—861no—
390#385—861no—
391#382C2×D4311yescharacteristic
392#380—861no—
393C4×C4⋊C4—431no—
394C2×#95—861no—
395#340—431no—
396#340—431no—
397#340—431no—
398#340—431no—
399#336—431no—
400#336—431no—
401#336—431no—
402#336C2×D4311yescharacteristic
403C43#2616811yescharacteristic, complemented, Sylow
404C22×Q8—431no—
405C22×D4—431no—
406C22×D4C22×D4311yescharacteristic
407C23×C4—861no—
408C23×C4—861no—
409C23×C4—861no—
410C2×SD16—434no—
411C2×SD16—862no—
412C2×SD16—862no—
413C2×D8—862no—
414C2×D8—862no—
415C2×D8—862no—
416C22×C8—431no—
417C22×C8—431no—
418C22×C8C22×D4311yescharacteristic
419C22×C8C22×D4311yescharacteristic
420#124—862no—
421#124—1721no—
422C4×Q8—862no—
423C4×Q8—1721no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—862no—
428C4×D4—1721no—
429C4×D4—1721no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C4⋊C4C22×D4311yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C42—431no—
451C2×C42—431no—
452C2×C42—861no—
453C2×C42C22×D4311yescharacteristic
454#107—41no—
455#106—22no—
456C4⋊C8—862no—
457#103—862no—
458#103—862no—
459#103—862no—
460#102—22no—
461#102—41no—
462#102—862no—
463#102—862no—
464#102—862no—
465C4×C8—862no—
466#95—21no—
467#95—21no—
468#95—431no—
469#95—431no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475C24—21no—
476C24—861no—
477C2×Q8—432no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8—861no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—432no—
490C2×D4—432no—
491C2×D4—432no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—864no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—3441no—
507C22×C4—3441no—
508C22×C4—3441no—
509C22×C4—3441no—
510C22×C4—1722no—
511C22×C4—1722no—
512C22×C4—1722no—
513C22×C4—1722no—
514C22×C4D4×D4311yescharacteristic
515C22×C4D4×D4311yescharacteristic
516C22×C4C23×D4311yescharacteristic
517SD16—868no—
518D8—1724no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8D4×D4312yes—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—432no—
538C4⋊C4—862no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—3441no—
543C4⋊C4—3441no—
544C4⋊C4—3441no—
545C4⋊C4—1721no—
546C4⋊C4—1722no—
547C22⋊C4—42no—
548C22⋊C4—81no—
549C22⋊C4—864no—
550C22⋊C4—3441no—
551C22⋊C4—1722no—
552C22⋊C4—1722no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C22⋊C4—1722no—
556C42—21no—
557C42—21no—
558C42—861no—
559C42—861no—
560C42—861no—
561C42—861no—
562C42—1722no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—862no—
571C23—862no—
572C23—862no—
573C23—1721no—
574C23—1721no—
575C23—1721no—
576C23—1721no—
577C23C2×D4×D4311yescharacteristic
578Q8—862no—
579Q8—862no—
580Q8—1721no—
581Q8—1721no—
582D4—41no—
583D4—41no—
584D4—41no—
585D4—41no—
586D4—434no—
587D4—862no—
588D4—862no—
589D4—862no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—432no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—862no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—862no—
619C2×C4—3444no—
620C2×C4—3444no—
621C2×C4—3444no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4C2×D4×D4311yescharacteristic
630C2×C4#41×D4311yescharacteristic
631C2×C4#41×D4311yescharacteristic
632C2×C4#41×D4311yescharacteristic
633C2×C4#1306337011yescharacteristic
634C2×C4#1306337311yescharacteristic
635C8—22no—
636C8—41no—
637C8—1721no—
638C8—1721no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—864no—
647C22—1722no—
648C22—1722no—
649C22—1722no—
650C22—1722no—
651C22—1722no—
652C22—1722no—
653C22#1458340711yescharacteristic
654C22#1458353411yescharacteristic
655C22#1458355911yescharacteristic
656C22#135×D4311yescharacteristic
657C22#1458369511yescharacteristic
658C22#1458370311yescharacteristic
659C22#1458370611yescharacteristic
660C4—41no—
661C4—41no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—862no—
666C4—3441no—
667C4—1722no—
668C4—1721no—
669C4—1722no—
670C4—1721no—
671C4—1721no—
672C4#123×D4311yescharacteristic
673C4#1458349511yescharacteristic
674C4#1458355111yescharacteristic
675C4#1458359411yescharacteristic
676C2—161no—
677C2—1724no—
678C2#1913833311yescharacteristic
679C2#1914460811yescharacteristic
680C2#1914477411yescharacteristic
681C2#1914613411yescharacteristic
682C2#1914630111yescharacteristic
683C2#1914725811yescharacteristic
684C2#1914742511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2092C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenter#2092D43
hypocenterC43#26168
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2092

Complements

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

NH ≅ G/Ntype
2. C2×#14582986C2semidirect
3. #19138396C2semidirect
4. #19137503C2semidirect
5. #19136094C2semidirect
6. #19136014C2semidirect
7. #19135834C2semidirect
8. #19135275C2semidirect
9. #19135153C2semidirect
12. #19134928C2semidirect
13. #19134846C2semidirect
14. #19134839C2semidirect
15. C43×#2092C2semidirect
338. #2092D43semidirect
403. C43#26168semidirect

Maximal subgroups

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

subgroupindex
C2×#145831132
C2×#145829862
#191383962
#191375032
#191360942
#191360142
#191358342
#191352752
#191351532
#191349462
#191349402
#191349282
#191348462
#191348392
C43×#20922
#2616843