Finite Group Databasebeta

← #25196519

Subgroups — #25196519

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137306C211yesmaximal, characteristic
2#19135743C211yesmaximal, characteristic, complemented
3#19135738C211yesmaximal, characteristic
4#19135733C211yesmaximal, characteristic, complemented
5#19135728C211yesmaximal, characteristic
6#19135409C211yesmaximal, characteristic
7#19135404C211yesmaximal, characteristic
8#19134728C211yesmaximal, characteristic, complemented
9#19134722C211yesmaximal, characteristic, complemented
10#19134607C211yesmaximal, characteristic, complemented
11#19134602C211yesmaximal, characteristic
12#19134597C211yesmaximal, characteristic, complemented
13#19134592C211yesmaximal, characteristic
14#19134452C211yesmaximal, characteristic, complemented
15C43×#2660C211yesmaximal, characteristic, complemented
16C2×#13063313C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063248C2211yescharacteristic
22C2×#13063248C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582805C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582791—21no—
34#14582791—21no—
35#14582773—21no—
36#14582773—21no—
37#14582769C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C4⋊Q8×C43C2211yescharacteristic
49C2×#125×C43C2211yescharacteristic
50C43×#398—21no—
51C43×#398—21no—
52C43×#395—21no—
53C43×#395—21no—
54C43×#384C2211yescharacteristic
55C43×#384C2211yescharacteristic
56C43×#382C2211yescharacteristic
57C43×#382C2211yescharacteristic
58C43×#376C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063313—22no—
67#13063313Q814yescomplemented
68C4×Dic86—22no—
69C4×Dic86—22no—
70C4×D172—22no—
71C4×D172—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×C4×Dic43—21no—
83C4⋊(C43⋊C8)—22no—
84C4⋊(C43⋊C8)—22no—
85#13063248—41no—
86#13063248—41no—
87#13063248—41no—
88#13063248—41no—
89#13063245—41no—
90#13063245—41no—
91#13063245—41no—
92#13063245—41no—
93#13063236—22no—
94C4×C43⋊C8—22no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C22×Q8×C43—21no—
98C4⋊Q8×C43—41no—
99C4⋊Q8×C43—41no—
100#125×C43—41no—
101#125×C43—41no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115C2×C42×C43C2311yescharacteristic
116#95×C43—21no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120#95×C43D411yescharacteristic
121#95×C43D411yescharacteristic
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124C23×D43—21no—
125C2×Q8×C43—42no—
126C2×Q8×C43—81no—
127C2×Q8×C43—81no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172C2×Q812yes—
148C2×C4×D43—42no—
149C2×C4×D43—81no—
150C2×C4×D43—81no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86C2×Q812yes—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—42no—
166C4⋊C4×C43—42no—
167C4⋊C4×C43—42no—
168C4⋊C4×C43—81no—
169C4⋊C4×C43—81no—
170C4⋊C4×C43—81no—
171C4⋊C4×C43—81no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43C2×Q812yes—
175C42×C43#4112yes—
176C42×C43#4112yes—
177C42×C43#4112yes—
178(C2×D43)⋊C4—24no—
179(C2×D43)⋊C4—24no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—81no—
182(C2×D43)⋊C4—81no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—81no—
188C4⋊Dic43—81no—
189Dic43⋊C4—42no—
190C4×Dic43—42no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C23×C43C22×D411yescharacteristic
204C22×D43—22no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211Q8×C43—84no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
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×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43C22⋊Q812yes—
239C2×C4×C43C22⋊Q812yes—
240C2×C4×C43#12412yes—
241C2×C4×C43#12412yes—
242C2×C4×C43C22×Q811yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C2×Dic43—22no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257D172—22no—
258D172—22no—
259D172—41no—
260D172—41no—
261C4×D43—84no—
262Dic86—22no—
263Dic86—22no—
264Dic86—41no—
265Dic86—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270#29151—431nomaximal, Sylow
271C22×C43C2×C22⋊Q811yescharacteristic
272C22×C43C2×#12411yescharacteristic
273C22×C43#53511yescharacteristic
274C22×C43#57611yescharacteristic
275C22×C43#57711yescharacteristic
276C22×C43#57711yescharacteristic
277C22×C43#57811yescharacteristic
278C2×D43—42no—
279C2×D43—42no—
280C2×D43—42no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C2×D43—81no—
285C4×C43—22no—
286C4×C43—22no—
287C4×C43—22no—
288C4×C43—22no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43#55411yescharacteristic
296C4×C43#55411yescharacteristic
297C4×C43#55511yescharacteristic
298C4×C43#55511yescharacteristic
299Dic43—42no—
300Dic43—81no—
301Dic43—81no—
302#2660D4311yescharacteristic, complemented
303#2326—431no—
304#2026—431no—
305#2025—431no—
306#2024—431no—
307#2023—431no—
308#1959—431no—
309#1958—431no—
310#1836—431no—
311#1834—431no—
312#1805—431no—
313#1804—431no—
314#1803—431no—
315#1802—431no—
316#1768—431no—
317C2×C43#256311yescharacteristic
318C2×C43#308311yescharacteristic
319C2×C43#308411yescharacteristic
320C2×C43#313611yescharacteristic
321C2×C43#313711yescharacteristic
322C2×C43#322411yescharacteristic
323C2×C43#322511yescharacteristic
324D43—82no—
325C2×C4⋊Q8C2×D4311yescharacteristic
326C2×#125C2×D4311yescharacteristic
327C2×#124—431no—
328C2×C4×Q8—431no—
329C2×C4×D4—431no—
330C2×C4⋊C8—431no—
331C2×C4⋊C8—431no—
332C2×#103—431no—
333C2×#103—431no—
334C2×#103—431no—
335C2×#103—431no—
336C2×#102—431no—
337C2×#102—431no—
338C2×#102—431no—
339C2×#102—431no—
340C2×#97—431no—
341C2×C4×C8—431no—
342#398—21no—
343#398—21no—
344#395—21no—
345#395—21no—
346#391—431no—
347#390—431no—
348#388—861no—
349#388—861no—
350#385—861no—
351#385—861no—
352#384—431no—
353#384C2×D4311yescharacteristic
354#384C2×D4311yescharacteristic
355#382C2×D4311yescharacteristic
356#382C2×D4311yescharacteristic
357#376C2×D4311yescharacteristic
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#336—431no—
367#336—431no—
368C43#2915111yescharacteristic, complemented, Sylow
369C22×Q8—21no—
370C22×Q8—431no—
371C22×D4—431no—
372C23×C4—861no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8—431no—
376C22×C8—431no—
377C4⋊Q8—41no—
378C4⋊Q8—41no—
379#125—41no—
380#125—41no—
381#124—434no—
382#124—862no—
383C4×Q8—862no—
384C4×Q8—862no—
385C4×D4—862no—
386C4×D4—862no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C42—861no—
409C2×C42C22×D4311yescharacteristic
410C2×C42C22×D4311yescharacteristic
411C2×C42C22×D4311yescharacteristic
412C4⋊C8—862no—
413C4⋊C8—862no—
414#103—1721no—
415#103—1721no—
416#103—1721no—
417#103—1721no—
418#102—1721no—
419#102—1721no—
420#102—1721no—
421#102—1721no—
422#97—862no—
423C4×C8—862no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—861no—
429#95—861no—
430#95C22⋊D4311yescharacteristic
431#95C22⋊D4311yescharacteristic
432#95C22⋊D4311yescharacteristic
433#95C22⋊D4311yescharacteristic
434C24—861no—
435C2×Q8—42no—
436C2×Q8—81no—
437C2×Q8—81no—
438C2×Q8—432no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×D4—432no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—861no—
449C2×D4—861no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—3441no—
458C22×C4—3441no—
459C22×C4—1722no—
460C22×C4C2×C22⋊D4311yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
462C22×C4C2×C22⋊D4311yescharacteristic
463C22×C4C2×C22⋊D4311yescharacteristic
464C22×C4C2×C22⋊D4311yescharacteristic
465C22×C4C2×C22⋊D4311yescharacteristic
466C22×C4C23×D4311yescharacteristic
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—81no—
491C4⋊C4—81no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—3441no—
499C4⋊C4—3441no—
500C4⋊C4—1722no—
501C22⋊C4—864no—
502C22⋊C4—864no—
503C22⋊C4—3441no—
504C22⋊C4—3441no—
505C22⋊C4—1722no—
506C42—21no—
507C42—21no—
508C42—1722no—
509C42Q8×D4312yes—
510C42#1062190212yes—
511C42#1062190212yes—
512C42#1062190212yes—
513C23—862no—
514C23—1721no—
515C23—1721no—
516C23—1721no—
517C23—1721no—
518C23—1721no—
519C23—1721no—
520C23C22×C22⋊D4311yescharacteristic
521Q8—84no—
522Q8—862no—
523Q8—862no—
524Q8—1721no—
525Q8—1721no—
526D4—862no—
527D4—862no—
528D4—1721no—
529D4—1721no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—862no—
557C2×C4—3444no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4#1306330112yes—
567C2×C4#1306330112yes—
568C2×C4#1306331412yes—
569C2×C4#1306331412yes—
570C2×C4C2×Q8×D4311yescharacteristic
571C2×C4C2×#1062190211yescharacteristic
572C2×C4C2×#1062190211yescharacteristic
573C2×C4C2×#1062190211yescharacteristic
574C2×C4#1306337011yescharacteristic
575C2×C4#1306337011yescharacteristic
576C8—1721no—
577C8—1721no—
578C8—1721no—
579C8—1721no—
580C22—3441no—
581C22—3441no—
582C22—3441no—
583C22—3441no—
584C22—1722no—
585C22—1722no—
586C22—1722no—
587C22C2×#1306330111yescharacteristic
588C22C2×#1306331411yescharacteristic
589C22#1458346611yescharacteristic
590C22#1458370211yescharacteristic
591C22#1458370711yescharacteristic
592C22#1458371011yescharacteristic
593C22#1458371411yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4—3441no—
605C4—3441no—
606C4—1722no—
607C4#1458361011yescharacteristic
608C4#1458361011yescharacteristic
609C4#1458361511yescharacteristic
610C4#1458361511yescharacteristic
611C2—3442no—
612C2#1913976911yescharacteristic
613C2#1914444211yescharacteristic
614C2#1914445311yescharacteristic
615C2#1914495411yescharacteristic
616C2#1914496511yescharacteristic
617C2#1914568911yescharacteristic
618C2#1914570411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2660C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2660D43
hypocenterC43#29151
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #2660

Complements

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

NH ≅ G/Ntype
2. #19135743C2semidirect
4. #19135733C2semidirect
8. #19134728C2semidirect
9. #19134722C2semidirect
10. #19134607C2semidirect
12. #19134597C2semidirect
14. #19134452C2semidirect
15. C43×#2660C2semidirect
67. #13063313Q8semidirect
302. #2660D43semidirect
368. C43#29151semidirect

Maximal subgroups

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

subgroupindex
#191373062
#191357432
#191357382
#191357332
#191357282
#191354092
#191354042
#191347282
#191347222
#191346072
#191346022
#191345972
#191345922
#191344522
C43×#26602
#2915143