Finite Group Databasebeta

← #25140477

Subgroups — #25140477

Order 11008.

932 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×#14583057C211yesmaximal, characteristic
2C2×C4×Dic172C211yesmaximal, characteristic, complemented
3#19138098C211yesmaximal, characteristic
4C22⋊C4×Dic86C211yesmaximal, characteristic
5#19136142C211yesmaximal, characteristic, complemented
6#19136018C211yesmaximal, characteristic
7#19135918C211yesmaximal, characteristic, complemented
8#19135792C211yesmaximal, characteristic
9#19135271C211yesmaximal, characteristic, complemented
10#19134935C211yesmaximal, characteristic, complemented
11#19134935C211yesmaximal, characteristic, complemented
12#19134866C211yesmaximal, characteristic, complemented
13#19134611C211yesmaximal, characteristic, complemented
14#19134531C211yesmaximal, characteristic
15C43×#1923C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C22×Dic172C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×C4×Dic86C2211yescharacteristic
23#14583057—24no—
24C4×Dic172—24no—
25C2×#13063259C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35#14582840—21no—
36#14582827—21no—
37#14582805C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582805C2211yescharacteristic
40#14582803—21no—
41#14582803—21no—
42#14582797C2211yescharacteristic
43#14582793—21no—
44#14582781—21no—
45#14582765C2211yescharacteristic
46#14582759C2211yescharacteristic
47#14582759C2211yescharacteristic
48#14582757—21no—
49C22⋊C4×Dic43—21no—
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C2×C22⋊C8×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86—22no—
63C22×Dic86—22no—
64C22×Dic86—22no—
65C22×Dic86—22no—
66C22×Dic86—41no—
67C22×Dic86—41no—
68C22×Dic86C2311yescharacteristic
69C22×Dic86C2311yescharacteristic
70C22×Dic86C2311yescharacteristic
71C23×Dic43—21no—
72C2×Dic172—22no—
73C2×Dic172—22no—
74C2×Dic172—22no—
75C2×Dic172—22no—
76C2×Dic172—41no—
77C2×Dic172D414yes—
78#13063304—22no—
79#13063304—41no—
80C4×Dic86—22no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×Dic86—41no—
84C4×Dic86—41no—
85C4×Dic86—41no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102#13063259—22no—
103#13063257—41no—
104#13063250—22no—
105#13063250—22no—
106#13063250—22no—
107#13063250—22no—
108#13063250—22no—
109#13063250—22no—
110#13063250—41no—
111#13063250—41no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C23×C4×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C2×C22⋊C4×C43D411yescharacteristic
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132C4⋊C8×C43—41no—
133C22⋊C8×C43—22no—
134C22⋊C8×C43—41no—
135C4×C8×C43—22no—
136#95×C43D411yescharacteristic
137#95×C43D411yescharacteristic
138C24×C43C2×D411yescharacteristic
139C22×C4×C43—21no—
140C22×C4×C43—21no—
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×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—24no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—42no—
161C22×Dic43—42no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—24no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—44no—
177C2×Dic86—44no—
178C2×Dic86—44no—
179C2×Dic86—42no—
180C2×Dic86—42no—
181C2×Dic86—44no—
182C2×Dic86C2×D412yes—
183C2×Dic86C2×D412yes—
184C2×Dic86#4112yes—
185C2×Dic86#4112yes—
186C2×Dic86#4112yes—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43C2×D412yes—
199C22⋊C4×C43—22no—
200C22⋊C4×C43—22no—
201C42×C43—21no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—21no—
205C22⋊Dic43—42no—
206C22⋊Dic43—42no—
207C22⋊Dic43—42no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218Dic43⋊C4—42no—
219Dic43⋊C4—42no—
220Dic43⋊C4—42no—
221Dic43⋊C4—42no—
222Dic43⋊C4—42no—
223C4×Dic43—42no—
224C4×Dic43—42no—
225C4×Dic43—42no—
226Dic172—28no—
227Dic172—44no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43#13512yes—
235C23×C43C22×D411yescharacteristic
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
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—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43#13712yes—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—48no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286Dic86—22no—
287Dic86—22no—
288Dic86—22no—
289Dic86—22no—
290Dic86—22no—
291Dic86—22no—
292Dic86—22no—
293Dic86—48no—
294Dic86—41no—
295Dic86—41no—
296Dic86—41no—
297Dic86—41no—
298Dic86#12314yes—
299C8×C43—22no—
300C8×C43—41no—
301C8×C43—41no—
302C8×C43—41no—
303#24902—431nomaximal, Sylow
304C22×C43—22no—
305C22×C43—22no—
306C22×C43—22no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43#52511yescharacteristic
312C22×C43D4211yescharacteristic
313C22×C43#54611yescharacteristic
314C22×C43C2×#13511yescharacteristic
315C22×C43C2×#13711yescharacteristic
316C22×C43#57811yescharacteristic
317C22×C43#57811yescharacteristic
318C4×C43—22no—
319C4×C43—41no—
320C4×C43—41no—
321C4×C43—41no—
322C4×C43—41no—
323C4×C43C2×#12311yescharacteristic
324C4×C43#53811yescharacteristic
325C4×C43#54611yescharacteristic
326C4×C43#55111yescharacteristic
327Dic43—24no—
328Dic43—42no—
329Dic43—42no—
330Dic43—81no—
331Dic43—81no—
332Dic43—81no—
333Dic43—81no—
334Dic43—81no—
335C2×#451—431no—
336C2×C4×Q16—431no—
337#2421—431no—
338Q8×C22⋊C4—431no—
339#2097—431no—
340#2075—431no—
341#2056—431no—
342#2035—431no—
343#1933—431no—
344#1923D4311yescharacteristic
345#1878—431no—
346#1878—431no—
347#1865—431no—
348#1805—431no—
349#1787—431no—
350C2×C43—42no—
351C2×C43#241811yescharacteristic
352C2×C43#310811yescharacteristic
353C2×C43#312711yescharacteristic
354C2×C43#327011yescharacteristic
355C2×C43#328511yescharacteristic
356C2×C43#330011yescharacteristic
357C2×C43#332811yescharacteristic
358C23×Q8—431no—
359C22×Q16—431no—
360C22×Q16—431no—
361C2×C22⋊Q8—431no—
362C2×C4×Q8—431no—
363C2×C4×Q8—431no—
364C2×C4×Q8—431no—
365#451—864no—
366C4×Q16—864no—
367C2×#107—431no—
368C2×#106—431no—
369C2×C4⋊C8C2×D4311yescharacteristic
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×#103—431no—
377C2×#103—431no—
378C2×C22⋊C8C2×D4311yescharacteristic
379C2×C22⋊C8C2×D4311yescharacteristic
380C2×C4×C8C2×D4311yescharacteristic
381#400—861no—
382#397—861no—
383#391—431no—
384#391—431no—
385#391—431no—
386#391—861no—
387#391—861no—
388#389—431no—
389#388—861no—
390#387—861no—
391#382—431no—
392#380—431no—
393#380—431no—
394#380—861no—
395C4×C22⋊C4—861no—
396C4×C22⋊C4C2×D4311yescharacteristic
397#340—431no—
398#340—431no—
399#340—431no—
400#340—431no—
401#336C2×D4311yescharacteristic
402#336C2×D4311yescharacteristic
403C43#2490211yescharacteristic, complemented, Sylow
404C22×Q8—431no—
405C22×Q8—431no—
406C22×Q8—431no—
407C22×Q8—862no—
408C22×Q8—862no—
409C22×Q8—862no—
410C22×Q8—862no—
411C22×Q8—861no—
412C22×Q8—1721no—
413C22×Q8—1721no—
414C23×C4—861no—
415C23×C4C22×D4311yescharacteristic
416C2×Q16—434no—
417C2×Q16—862no—
418C2×Q16—862no—
419C2×Q16—862no—
420C2×Q16—862no—
421C2×Q16—1721no—
422C22×C8C22×D4311yescharacteristic
423C22×C8C22×D4311yescharacteristic
424C22×C8C22×D4311yescharacteristic
425C22×C8C22×D4311yescharacteristic
426C22⋊Q8—862no—
427C22⋊Q8—1721no—
428C4×Q8—862no—
429C4×Q8—862no—
430C4×Q8—862no—
431C4×Q8—1721no—
432C4×Q8—1721no—
433C4×Q8—1721no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4D17211yescharacteristic
448C2×C22⋊C4D17211yescharacteristic
449C2×C42—861no—
450C2×C42—861no—
451C2×C42—861no—
452C2×C42C22×D4311yescharacteristic
453C2×C42C22×D4311yescharacteristic
454#107—862no—
455#106—1721no—
456C4⋊C8—41no—
457#103—862no—
458#103—862no—
459#103—862no—
460#103—862no—
461#103—862no—
462#103—862no—
463#103—1721no—
464#103—1721no—
465C22⋊C8—22no—
466C22⋊C8—41no—
467C4×C8—22no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479#95D17211yescharacteristic
480#95D17211yescharacteristic
481C24C2×D17211yescharacteristic
482C2×Q8—432no—
483C2×Q8—432no—
484C2×Q8—432no—
485C2×Q8—432no—
486C2×Q8—432no—
487C2×Q8—864no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×Q8—861no—
492C2×Q8—861no—
493C2×Q8—861no—
494C2×Q8—861no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8—861no—
500C2×Q8—861no—
501C2×Q8—1722no—
502C2×Q8—1722no—
503C2×Q8—1724no—
504C2×Q8—1724no—
505C2×Q8—1724no—
506C2×Q8—1724no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—861no—
514C22×C4—864no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—1722no—
523C22×C4—1722no—
524C22×C4C2×D17211yescharacteristic
525C22×C4C2×D17211yescharacteristic
526C22×C4C2×D17211yescharacteristic
527C22×C4C2×D17211yescharacteristic
528C22×C4C2×D17211yescharacteristic
529C22×C4C23×D4311yescharacteristic
530Q16—868no—
531Q16—1724no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8D4×D4312yes—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—1722no—
555C4⋊C4—1722no—
556C4⋊C4—1722no—
557C4⋊C4—1722no—
558C4⋊C4—1722no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—1722no—
562C22⋊C4—1722no—
563C22⋊C4—1722no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—1722no—
569C42—1722no—
570C42—1722no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23#1306334712yes—
578C23C22×D17211yescharacteristic
579Q8—434no—
580Q8—862no—
581Q8—862no—
582Q8—862no—
583Q8—862no—
584Q8—862no—
585Q8—862no—
586Q8—862no—
587Q8—1728no—
588Q8—1721no—
589Q8—1721no—
590Q8—1721no—
591Q8—1721no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—1728no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4#1306335812yes—
636C2×C4C2×D4×D4311yescharacteristic
637C2×C4#41×D4311yescharacteristic
638C2×C4#41×D4311yescharacteristic
639C2×C4#41×D4311yescharacteristic
640C2×C4#1306337011yescharacteristic
641C2×C4#1306337111yescharacteristic
642C8—22no—
643C8—41no—
644C8—41no—
645C8—41no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22#1458341111yescharacteristic
654C22D4×D17211yescharacteristic
655C22#1458354411yescharacteristic
656C22C2×#1306334711yescharacteristic
657C22C2×#1306335811yescharacteristic
658C22#1458371611yescharacteristic
659C22#1458371611yescharacteristic
660C4—22no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—864no—
666C4—3441no—
667C4—3441no—
668C4—3441no—
669C4—3441no—
670C4—3441no—
671C4—1722no—
672C4—1722no—
673C4#123×D4311yescharacteristic
674C4#1458348311yescharacteristic
675C4#1458354611yescharacteristic
676C4#1458357411yescharacteristic
677C2—42no—
678C2#1913806211yescharacteristic
679C2#1914467711yescharacteristic
680C2#1914489611yescharacteristic
681C2#1914617011yescharacteristic
682C2#1914633811yescharacteristic
683C2#1914648411yescharacteristic
684C2#1914687911yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1923C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1923D43
hypocenterC43#24902
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic172C2semidirect
5. #19136142C2semidirect
7. #19135918C2semidirect
9. #19135271C2semidirect
10. #19134935C2semidirect
11. #19134935C2semidirect
12. #19134866C2semidirect
13. #19134611C2semidirect
403. C43#24902semidirect

Maximal subgroups

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

subgroupindex
C2×#145830572
C2×C4×Dic1722
#191380982
C22⋊C4×Dic862
#191361422
#191360182
#191359182
#191357922
#191352712
#191349352
#191348662
#191346112
#191345312
C43×#19232
#2490243