Finite Group Databasebeta

← #25164575

Subgroups — #25164575

Order 11008.

772 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138362C211yesmaximal, characteristic
2#19137693C211yesmaximal, characteristic, complemented
3#19136096C211yesmaximal, characteristic, complemented
4#19135830C211yesmaximal, characteristic
5#19135740C211yesmaximal, characteristic, complemented
6#19135740C211yesmaximal, characteristic, complemented
7#19135522C211yesmaximal, characteristic
8#19135293C211yesmaximal, characteristic, complemented
9#19135220C211yesmaximal, characteristic, complemented
10#19135214C211yesmaximal, characteristic, complemented
11#19135214C211yesmaximal, characteristic, complemented
12#19135162C211yesmaximal, characteristic, complemented
13#19134857C211yesmaximal, characteristic, complemented
14#19134419C211yesmaximal, characteristic, complemented
15C43×#1918C211yesmaximal, characteristic, complemented
16C2×#13063322C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063310—21no—
19C2×#13063287C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×#13063247C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31#14582817—21no—
32#14582816—21no—
33#14582800C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582800C2211yescharacteristic
36#14582798C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582796—21no—
39#14582783—21no—
40#14582782—21no—
41#14582777—21no—
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×Dic43⋊C4C2211yescharacteristic
45C4×C4⋊Dic43—21no—
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172—21no—
60C22×D172—21no—
61C22×D172C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063322—22no—
67#13063322—41no—
68#13063316—22no—
69#13063316—22no—
70#13063310—44no—
71#13063287—22no—
72#13063287—41no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4D411yescharacteristic
80C2×Dic43⋊C4D411yescharacteristic
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43C2311yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92#13063256—41no—
93C4⋊(C43⋊C8)—41no—
94#13063247—22no—
95#13063247—22no—
96#13063247—22no—
97#13063247—41no—
98#13063245—22no—
99#13063245—22no—
100#13063245—22no—
101#13063245—22no—
102#13063235—41no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C42×C43—21no—
117C2×C42×C43C2311yescharacteristic
118#107×C43—22no—
119#95×C43—21no—
120#95×C43—21no—
121C23×D43—21no—
122C23×D43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2411yescharacteristic
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C22×Dic43C2×D411yescharacteristic
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—42no—
148C2×D172—42no—
149C2×D172—42no—
150C2×D172—42no—
151C2×D172—81no—
152C2×D172—81no—
153C2×D172#4112yes—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C4×D43—81no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—42no—
170C4⋊C4×C43#4112yes—
171C4⋊C4×C43#4112yes—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—42no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—42no—
178(C2×D43)⋊C4—42no—
179(C2×D43)⋊C4—81no—
180(C2×D43)⋊C4—81no—
181(C2×D43)⋊C4—81no—
182C4⋊Dic43—24no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—42no—
187C4⋊Dic43#4112yes—
188Dic43⋊C4—24no—
189Dic43⋊C4—22no—
190Dic43⋊C4—41no—
191Dic43⋊C4—81no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—81no—
197C4×Dic43—81no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C23×C43C22×D411yescharacteristic
205C22×D43—22no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—22no—
222C2×C4×C43—21no—
223C2×C4×C43—22no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43AGL(1,ℤ/8)12yes—
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C2×C4×C432−1+411yescharacteristic
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261D172—22no—
262D172—22no—
263D172—41no—
264D172—41no—
265D172—41no—
266D172—41no—
267D172—41no—
268D172—41no—
269D172—84no—
270D172—84no—
271C4×D43—84no—
272C8×C43—41no—
273C8×C43—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276#26716—431nomaximal, Sylow
277C22×C43#52511yescharacteristic
278C22×C43#54611yescharacteristic
279C22×C43#54811yescharacteristic
280C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C43#57511yescharacteristic
282C22×C43#57611yescharacteristic
283C22×C43#57711yescharacteristic
284C2×D43—42no—
285C2×D43—42no—
286C2×D43—42no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C4×C43—22no—
299C4×C43—42no—
300C4×C43—42no—
301C4×C43—41no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43#52911yescharacteristic
305C4×C43#54211yescharacteristic
306C4×C43#55211yescharacteristic
307C4×C43#55911yescharacteristic
308Dic43—41no—
309Dic43—41no—
310Dic43—42no—
311Dic43—41no—
312Dic43—41no—
313Dic43—81no—
314#2445—431no—
315#2370—431no—
316#2088—431no—
317#2041—431no—
318#2025—431no—
319#2025—431no—
320#1982—431no—
321#1936—431no—
322#1926—431no—
323#1925—431no—
324#1925—431no—
325#1918D4311yescharacteristic, complemented
326#1917—431no—
327#1864—431no—
328#1762—431no—
329C2×C43#245811yescharacteristic
330C2×C43#311511yescharacteristic
331C2×C43#311911yescharacteristic
332C2×C43#331011yescharacteristic
333C2×C43#332211yescharacteristic
334C2×C43#336611yescharacteristic
335C2×C43#337111yescharacteristic
336D43—82no—
337D43—161no—
338C2×#127—431no—
339C2×#125—431no—
340C2×#123—861no—
341C2×C4×D4—431no—
342C2×#107C2×D4311yescharacteristic
343C2×#106—431no—
344C2×C4⋊C8—431no—
345C2×#102—431no—
346C2×#102—431no—
347C2×#102—431no—
348C2×#102—431no—
349C2×#102—431no—
350C2×#102—431no—
351C2×#102—431no—
352C2×#102—431no—
353C2×#97—431no—
354#394—861no—
355#394—861no—
356#390—431no—
357#390—431no—
358#390—431no—
359#389—431no—
360#389—431no—
361#389—861no—
362#389C2×D4311yescharacteristic
363#387—861no—
364#387—861no—
365#386—861no—
366C4×C4⋊C4—431no—
367C4×C4⋊C4—431no—
368C4×C4⋊C4—431no—
369C4×C4⋊C4—861no—
370C4×C4⋊C4C2×D4311yescharacteristic
371#340—431no—
372#340—431no—
373#340—431no—
374#340C2×D4311yescharacteristic
375#340C2×D4311yescharacteristic
376#340C2×D4311yescharacteristic
377#336—431no—
378#336—431no—
379#336—431no—
380#336C2×D4311yescharacteristic
381C43#2671611yescharacteristic, complemented, Sylow
382C22×D4—431no—
383C22×D4—431no—
384C22×D4—861no—
385C22×D4—861no—
386C23×C4—861no—
387C22×C8—431no—
388C22×C8—431no—
389C22×C8C22×D4311yescharacteristic
390C22×C8C22×D4311yescharacteristic
391#127—862no—
392#127—1721no—
393#125—862no—
394#125—862no—
395#123—1724no—
396C4×D4—862no—
397C4×D4—1721no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C42—21no—
419C2×C42—431no—
420C2×C42—431no—
421C2×C42—861no—
422C2×C42—861no—
423C2×C42C22×D4311yescharacteristic
424#107—22no—
425#106—1721no—
426C4⋊C8—1721no—
427#102—862no—
428#102—862no—
429#102—862no—
430#102—862no—
431#102—862no—
432#102—862no—
433#102—862no—
434#102—1721no—
435#97—1721no—
436#95—21no—
437#95—21no—
438#95—431no—
439#95—431no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444C24—861no—
445C24—861no—
446C2×D4—432no—
447C2×D4—861no—
448C2×D4—861no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—3441no—
459C2×D4—3441no—
460C2×D4—1722no—
461C2×D4—1722no—
462C2×D4—1722no—
463C2×D4—1722no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—3441no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4D4×D4311yescharacteristic
478C22×C4D4×D4311yescharacteristic
479C22×C4C23×D4311yescharacteristic
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—42no—
499C4⋊C4—432no—
500C4⋊C4—864no—
501C4⋊C4—864no—
502C4⋊C4—862no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—3441no—
507C4⋊C4—1721no—
508C4⋊C4—1722no—
509C4⋊C4#1062189812yes—
510C4⋊C4#1062190212yes—
511C22⋊C4—3441no—
512C22⋊C4—3441no—
513C22⋊C4—3441no—
514C22⋊C4—1722no—
515C22⋊C4—1722no—
516C22⋊C4—1722no—
517C22⋊C4—1722no—
518C42—21no—
519C42—21no—
520C42—42no—
521C42—861no—
522C42—861no—
523C42—861no—
524C42—861no—
525C42—3441no—
526C42—3441no—
527C23—862no—
528C23—1721no—
529C23—1721no—
530C23—1721no—
531C23—1721no—
532C23—1721no—
533C23—1721no—
534C23—1721no—
535C23—1721no—
536C23—1721no—
537C23—1721no—
538C23—1721no—
539C23—1721no—
540C23—1721no—
541C23C2×D4×D4311yescharacteristic
542D4—862no—
543D4—862no—
544D4—3444no—
545D4—3444no—
546D4—1721no—
547D4—1721no—
548D4—1721no—
549D4—1721no—
550D4—1721no—
551D4—1721no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—862no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—3444no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4#1306334912yes—
589C2×C4#41×D4311yescharacteristic
590C2×C4#41×D4311yescharacteristic
591C2×C4C2×#1062189811yescharacteristic
592C2×C4C2×#1062190211yescharacteristic
593C2×C4#1306337111yescharacteristic
594C2×C4#1306337211yescharacteristic
595C8—41no—
596C8—41no—
597C8—1721no—
598C8—1721no—
599C22—3441no—
600C22—3441no—
601C22—3441no—
602C22—3441no—
603C22—3441no—
604C22—3441no—
605C22—3441no—
606C22—3441no—
607C22—3441no—
608C22—3441no—
609C22—3441no—
610C22—1722no—
611C22—1722no—
612C22—1722no—
613C22#1458341211yescharacteristic
614C22#1458354111yescharacteristic
615C22#1458355811yescharacteristic
616C22C2×#1306334911yescharacteristic
617C22#1458369811yescharacteristic
618C22#1458370111yescharacteristic
619C22#1458370811yescharacteristic
620C4—22no—
621C4—42no—
622C4—41no—
623C4—42no—
624C4—81no—
625C4—81no—
626C4—3441no—
627C4—1721no—
628C4—1721no—
629C4—1721no—
630C4—1722no—
631C4—1721no—
632C4#1458342711yescharacteristic
633C4#1458351511yescharacteristic
634C4#1458358711yescharacteristic
635C4#1458363411yescharacteristic
636C2—3442no—
637C2—6881no—
638C2#1913852411yescharacteristic
639C2#1914474811yescharacteristic
640C2#1914480111yescharacteristic
641C2#1914661411yescharacteristic
642C2#1914679411yescharacteristic
643C2#1914730011yescharacteristic
644C2#1914736411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1918C2
socleC23×C43C22×D4
prime radicalC2×#13063322C22
hypercenter#1918D43
hypocenterC43#26716
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
2. #19137693C2semidirect
3. #19136096C2semidirect
5. #19135740C2semidirect
6. #19135740C2semidirect
8. #19135293C2semidirect
9. #19135220C2semidirect
10. #19135214C2semidirect
11. #19135214C2semidirect
12. #19135162C2semidirect
13. #19134857C2semidirect
14. #19134419C2semidirect
15. C43×#1918C2semidirect
325. #1918D43semidirect
381. C43#26716semidirect

Maximal subgroups

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

subgroupindex
#191383622
#191376932
#191360962
#191358302
#191357402
#191355222
#191352932
#191352202
#191352142
#191351622
#191348572
#191344192
C43×#19182
#2671643