Finite Group Databasebeta

← #25164774

Subgroups — #25164774

Order 11008.

824 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137631C211yesmaximal, characteristic, complemented
2#19135905C211yesmaximal, characteristic, complemented
3#19135777C211yesmaximal, characteristic, complemented
4#19135738C211yesmaximal, characteristic, complemented
5#19135591C211yesmaximal, characteristic
6#19135553C211yesmaximal, characteristic, complemented
7#19135281C211yesmaximal, characteristic, complemented
8#19135212C211yesmaximal, characteristic, complemented
9#19135203C211yesmaximal, characteristic, complemented
10#19135187C211yesmaximal, characteristic, complemented
11#19134946C211yesmaximal, characteristic, complemented
12#19134918C211yesmaximal, characteristic, complemented
13#19134687C211yesmaximal, characteristic, complemented
14C4×#13063245C211yesmaximal, characteristic, complemented
15C43×#2490C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582801C2211yescharacteristic
32#14582799—21no—
33#14582797C2211yescharacteristic
34#14582788—21no—
35#14582775—21no—
36C4×C4⋊Dic43C2211yescharacteristic
37#14582746—21no—
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×#125×C43C2211yescharacteristic
49C2×#121×C43C2211yescharacteristic
50C43×#397—21no—
51C43×#394—21no—
52C43×#390—21no—
53C43×#390C2211yescharacteristic
54C43×#390C2211yescharacteristic
55C43×#388—21no—
56C43×#380C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C22⋊D43—21no—
61C22×C4×D43—21no—
62C2×#10621882—22no—
63C2×#10621882—41no—
64C2×#10621882—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063299—22no—
70#13063299—22no—
71C4×D172—22no—
72C4×D172—41no—
73#13063284—22no—
74#13063284—41no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86#13063258—22no—
87C4⋊(C43⋊C8)—41no—
88#13063246—22no—
89#13063246—22no—
90#13063246—41no—
91#13063245—22no—
92#13063245—22no—
93#13063245—41no—
94C22⋊(C43⋊C8)—41no—
95C22⋊(C43⋊C8)—41no—
96C4×C43⋊C8—41no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C22×D4×C43—21no—
100C22×D4×C43C2311yescharacteristic
101C23×C4×C43C2311yescharacteristic
102#125×C43—22no—
103#125×C43—41no—
104#121×C43—22no—
105#121×C43—41no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43D411yescharacteristic
118C2×C22⋊C4×C43D411yescharacteristic
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122#95×C43—21no—
123#95×C43—21no—
124#95×C43D411yescharacteristic
125#95×C43D411yescharacteristic
126C24×C43—21no—
127C24×C43C2×D411yescharacteristic
128C23×D43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—42no—
136C2×D4×C43—42no—
137C2×D4×C43—81no—
138C22×C4×C43—21no—
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×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C2×C22⋊D43—24no—
154C2×C22⋊D43—81no—
155C2×C22⋊D43—81no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172#4112yes—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×C4×D43—81no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—42no—
174C4⋊C4×C43—42no—
175C4⋊C4×C43#4112yes—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—42no—
179C22⋊C4×C43—42no—
180C22⋊C4×C43—81no—
181C22⋊C4×C43—81no—
182C22⋊C4×C43—81no—
183C22⋊C4×C43—81no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—81no—
189C22⋊Dic43—42no—
190#10621882—44no—
191(C2×D43)⋊C4—24no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—81no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43#4112yes—
200C4⋊Dic43#4112yes—
201Dic43⋊C4—81no—
202C4×Dic43—42no—
203C4×Dic43—81no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43C22×D411yescharacteristic
231C22×D43—22no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—84no—
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—21no—
251C2×C4×C43—22no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43#13512yes—
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43H(5,𝔽2)11yescharacteristic
276C2×C4×C43H(5,𝔽2)11yescharacteristic
277C22⋊D43—84no—
278C2×Dic43—22no—
279C2×Dic43—22no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287D172—22no—
288D172—22no—
289D172—41no—
290D172—41no—
291C4×D43—84no—
292C43⋊C8—41no—
293C43⋊C8—41no—
294C43⋊C8—41no—
295C43⋊C8—41no—
296#26730—431nomaximal, Sylow
297C22×C43—41no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43—41no—
303C22×C43—41no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43#52511yescharacteristic
312C22×C43#54611yescharacteristic
313C22×C43#54611yescharacteristic
314C22×C43C2×#13511yescharacteristic
315C22×C43#57511yescharacteristic
316C22×C43#57611yescharacteristic
317C22×C43#57611yescharacteristic
318C2×D43—42no—
319C2×D43—42no—
320C2×D43—42no—
321C2×D43—81no—
322C2×D43—81no—
323C2×D43—81no—
324C2×D43—81no—
325C4×C43—22no—
326C4×C43—41no—
327C4×C43—41no—
328C4×C43—41no—
329C4×C43—41no—
330C4×C43—42no—
331C4×C43—81no—
332C4×C43—81no—
333C4×C43#52911yescharacteristic
334C4×C43#53811yescharacteristic
335C4×C43#55511yescharacteristic
336C4×C43#55911yescharacteristic
337Dic43—42no—
338Dic43—42no—
339Dic43—81no—
340#2490D4311yescharacteristic, complemented
341#2363—431no—
342#2054—431no—
343#2033—431no—
344#2025—431no—
345#1999—431no—
346#1989—431no—
347#1934—431no—
348#1925—431no—
349#1923—431no—
350#1921—431no—
351#1879—431no—
352#1875—431no—
353#1825—431no—
354C4×#102—431no—
355C2×C43—81no—
356C2×C43—161no—
357C2×C43#245911yescharacteristic
358C2×C43#310211yescharacteristic
359C2×C43#312211yescharacteristic
360C2×C43#329711yescharacteristic
361C2×C43#330511yescharacteristic
362C2×C43#330911yescharacteristic
363C2×C43#332211yescharacteristic
364D43—82no—
365C22×D8—431no—
366C2×#125C2×D4311yescharacteristic
367C2×#121—431no—
368C2×#121C2×D4311yescharacteristic
369C2×C4×D4—431no—
370C2×#117—431no—
371C2×#107—431no—
372C2×C4⋊C8—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×#102—431no—
379C2×C22⋊C8—431no—
380C2×C22⋊C8—431no—
381C2×C4×C8—431no—
382#397—21no—
383#394—21no—
384#390—21no—
385#390—431no—
386#390—861no—
387#390C2×D4311yescharacteristic
388#390C2×D4311yescharacteristic
389#389—431no—
390#388—21no—
391#388—861no—
392#386—861no—
393#380C2×D4311yescharacteristic
394C4×C4⋊C4—431no—
395C4×C4⋊C4C2×D4311yescharacteristic
396C4×C22⋊C4—861no—
397C4×C22⋊C4C2×D4311yescharacteristic
398#340—431no—
399#340—431no—
400#340—431no—
401#340—431no—
402#340—431no—
403#340—431no—
404#340—431no—
405#340—431no—
406#336—431no—
407#336—431no—
408C43#2673011yescharacteristic, complemented, Sylow
409C22×D4—21no—
410C22×D4—431no—
411C22×D4—861no—
412C22×D4C22×D4311yescharacteristic
413C23×C4—861no—
414C23×C4C22×D4311yescharacteristic
415C2×D8—862no—
416C2×D8—1721no—
417C2×D8—1721no—
418C22×C8—431no—
419C22×C8—431no—
420C22×C8—431no—
421C22×C8—431no—
422#125—22no—
423#125—41no—
424#121—22no—
425#121—41no—
426#121—862no—
427#121—862no—
428C4×D4—862no—
429C4×D4—1721no—
430#117—862no—
431#117—1721no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
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—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4C22⋊D4311yescharacteristic
453C2×C22⋊C4C22⋊D4311yescharacteristic
454C2×C42—21no—
455C2×C42—861no—
456C2×C42—861no—
457C2×C42C22×D4311yescharacteristic
458C2×C42C22×D4311yescharacteristic
459#107—862no—
460C4⋊C8—1721no—
461#102—862no—
462#102—862no—
463#102—862no—
464#102—862no—
465#102—1721no—
466#102—1721no—
467C22⋊C8—1721no—
468C22⋊C8—1721no—
469C4×C8—1721no—
470#95—21no—
471#95—21no—
472#95—861no—
473#95—861no—
474#95C22⋊D4311yescharacteristic
475#95C22⋊D4311yescharacteristic
476C24—21no—
477C24—861no—
478C24C2×C22⋊D4311yescharacteristic
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—81no—
488C2×D4—432no—
489C2×D4—864no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C2×D4—3441no—
496C2×D4—3441no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—3441no—
510C22×C4—1722no—
511C22×C4—1722no—
512C22×C4C2×C22⋊D4311yescharacteristic
513C22×C4C2×C22⋊D4311yescharacteristic
514C22×C4C2×C22⋊D4311yescharacteristic
515C22×C4C2×C22⋊D4311yescharacteristic
516C22×C4C2×C22⋊D4311yescharacteristic
517C22×C4C23×D4311yescharacteristic
518D8—1724no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—432no—
539C4⋊C4—432no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—3441no—
545C4⋊C4#1062190012yes—
546C22⋊C4—22no—
547C22⋊C4—41no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—81no—
551C22⋊C4—81no—
552C22⋊C4—81no—
553C22⋊C4—81no—
554C22⋊C4—864no—
555C22⋊C4—3441no—
556C22⋊C4—1722no—
557C22⋊C4—1722no—
558C22⋊C4—1722no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—81no—
564C42—3441no—
565C42—1722no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—862no—
581C23—1721no—
582C23—1721no—
583C23—1721no—
584C23—1721no—
585C23—1721no—
586C23—1721no—
587C23C22×C22⋊D4311yescharacteristic
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—84no—
593D4—862no—
594D4—862no—
595D4—3444no—
596D4—1721no—
597D4—1721no—
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—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—862no—
626C2×C4—862no—
627C2×C4—3444no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4#1306334512yes—
636C2×C4#41×D4311yescharacteristic
637C2×C4#41×D4311yescharacteristic
638C2×C4#41×D4311yescharacteristic
639C2×C4C2×#1062190011yescharacteristic
640C2×C4#1306337011yescharacteristic
641C2×C4#1306337111yescharacteristic
642C8—1721no—
643C8—1721no—
644C8—1721no—
645C8—1721no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—3441no—
661C22—3441no—
662C22—3441no—
663C22—3441no—
664C22—1722no—
665C22—1722no—
666C22—1722no—
667C22#1458340611yescharacteristic
668C22#1458353711yescharacteristic
669C22#1458354311yescharacteristic
670C22C2×#1306334511yescharacteristic
671C22#1458369711yescharacteristic
672C22#1458370211yescharacteristic
673C22#1458370211yescharacteristic
674C4—22no—
675C4—41no—
676C4—42no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—81no—
681C4—81no—
682C4—3441no—
683C4—1722no—
684C4—1722no—
685C4#1458342811yescharacteristic
686C4#1458348311yescharacteristic
687C4#1458361111yescharacteristic
688C4#1458363111yescharacteristic
689C2—81no—
690C2—161no—
691C2—3442no—
692C2#1913852811yescharacteristic
693C2#1914460711yescharacteristic
694C2#1914483311yescharacteristic
695C2#1914643911yescharacteristic
696C2#1914654511yescharacteristic
697C2#1914659511yescharacteristic
698C2#1914679611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2490C2
socleC23×C43C22×D4
prime radical#19135591C2
hypercenter#2490D43
hypocenterC43#26730
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2490

Complements

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

NH ≅ G/Ntype
1. #19137631C2semidirect
2. #19135905C2semidirect
3. #19135777C2semidirect
4. #19135738C2semidirect
6. #19135553C2semidirect
7. #19135281C2semidirect
8. #19135212C2semidirect
9. #19135203C2semidirect
10. #19135187C2semidirect
11. #19134946C2semidirect
12. #19134918C2semidirect
13. #19134687C2semidirect
14. C4×#13063245C2semidirect
15. C43×#2490C2semidirect
340. #2490D43semidirect
408. C43#26730semidirect

Maximal subgroups

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

subgroupindex
#191376312
#191359052
#191357772
#191357382
#191355912
#191355532
#191352812
#191352122
#191352032
#191351872
#191349462
#191349182
#191346872
C4×#130632452
C43×#24902
#2673043