Finite Group Databasebeta

← #25169423

Subgroups — #25169423

Order 11008.

742 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139022C211yesmaximal, characteristic, complemented
2#19137632C211yesmaximal, characteristic
3#19136002C211yesmaximal, characteristic, complemented
4#19135984C211yesmaximal, characteristic, complemented
5#19135780C211yesmaximal, characteristic
6#19135779C211yesmaximal, characteristic
7#19135350C211yesmaximal, characteristic, complemented
8#19135325C211yesmaximal, characteristic, complemented
9#19135199C211yesmaximal, characteristic, complemented
10#19135172C211yesmaximal, characteristic, complemented
11#19134859C211yesmaximal, characteristic, complemented
12#19134795C211yesmaximal, characteristic, complemented
13#19134688C211yesmaximal, characteristic, complemented
14C4×#13063245C211yesmaximal, characteristic, complemented
15C43×#1921C211yesmaximal, characteristic, complemented
16C2×#13063300C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×#13063283C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30#14582840—21no—
31#14582823—21no—
32#14582800—21no—
33#14582800C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582790—21no—
37#14582789—21no—
38#14582783—21no—
39#14582777—21no—
40#14582768C2211yescharacteristic
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×(C2×D43)⋊C4C2211yescharacteristic
45#14582746—21no—
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172—21no—
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063300—22no—
66#13063300—22no—
67C4×D172—22no—
68C4×D172—41no—
69#13063283—22no—
70#13063283—41no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4D411yescharacteristic
86C2×(C2×D43)⋊C4D411yescharacteristic
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90#13063258—22no—
91#13063258—41no—
92#13063257—22no—
93Dic43⋊C8—22no—
94#13063247—22no—
95#13063247—41no—
96#13063245—22no—
97#13063245—22no—
98(C2×D43)⋊C8—22no—
99(C2×D43)⋊C8—41no—
100C4×C43⋊C8—41no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#107×C43—22no—
118#95×C43—21no—
119#95×C43—21no—
120C23×D43—21no—
121C23×D43C2×D411yescharacteristic
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2411yescharacteristic
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C2×D172—21no—
136C2×D172—24no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—81no—
142C2×D172—81no—
143C2×D172#4112yes—
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—42no—
151C2×C4×D43—42no—
152C2×C4×D43—81no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×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—21no—
166C4⋊C4×C43—81no—
167C4⋊C4×C43#4112yes—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—81no—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—22no—
173(C2×D43)⋊C4—22no—
174(C2×D43)⋊C4—42no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—81no—
178(C2×D43)⋊C4—81no—
179(C2×D43)⋊C4—81no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43#4112yes—
186Dic43⋊C4—42no—
187Dic43⋊C4—81no—
188Dic43⋊C4—81no—
189Dic43⋊C4—81no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—42no—
193C4×Dic43—81no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8#4112yes—
200C23×C43C22×D411yescharacteristic
201C22×D43—22no—
202C22×D43—21no—
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—22no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
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#13712yes—
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×C4×C432−1+411yescharacteristic
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—22no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43#13512yes—
257D172—22no—
258D172—22no—
259D172—41no—
260D172—41no—
261D172—84no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—84no—
267C8×C43—41no—
268C8×C43—41no—
269C43⋊C8—22no—
270C43⋊C8—41no—
271#27041—431nomaximal, Sylow
272C22×C43#52511yescharacteristic
273C22×C43#54611yescharacteristic
274C22×C43#54711yescharacteristic
275C22×C43C2×#13511yescharacteristic
276C22×C43C2×#13711yescharacteristic
277C22×C43#57611yescharacteristic
278C22×C43#57611yescharacteristic
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—42no—
283C2×D43—41no—
284C2×D43—42no—
285C2×D43—41no—
286C2×D43—42no—
287C2×D43—41no—
288C2×D43—41no—
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C4×C43—22no—
294C4×C43—42no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43#52911yescharacteristic
300C4×C43#53911yescharacteristic
301C4×C43#55311yescharacteristic
302C4×C43#55611yescharacteristic
303Dic43—22no—
304Dic43—41no—
305Dic43—41no—
306Dic43—42no—
307Dic43—81no—
308Dic43—81no—
309#2497—431no—
310#2363—431no—
311#2071—431no—
312#2067—431no—
313#2033—431no—
314#2033—431no—
315#1947—431no—
316#1942—431no—
317#1923—431no—
318#1921D4311yescharacteristic, complemented
319#1919—431no—
320#1864—431no—
321#1854—431no—
322#1825—431no—
323C4×#102—431no—
324C2×C43#246611yescharacteristic
325C2×C43#310711yescharacteristic
326C2×C43#312211yescharacteristic
327C2×C43#330511yescharacteristic
328C2×C43#331411yescharacteristic
329C2×C43#333911yescharacteristic
330C2×C43#335711yescharacteristic
331D43—81no—
332D43—82no—
333C2×#121—431no—
334C2×C4×D4—431no—
335C2×#117—431no—
336C2×#107—431no—
337C2×#107—431no—
338C2×#107C2×D4311yescharacteristic
339C2×#106—431no—
340C2×C4⋊C8—431no—
341C2×#102—431no—
342C2×#102—431no—
343C2×#102—431no—
344C2×#102—431no—
345C2×C22⋊C8—431no—
346C2×C22⋊C8—431no—
347C2×C4×C8—431no—
348#400—861no—
349#396—861no—
350#390—431no—
351#390—861no—
352#389—431no—
353#389—431no—
354#389C2×D4311yescharacteristic
355#388—861no—
356#388—861no—
357#387—861no—
358#386—861no—
359#384—431no—
360#380—431no—
361#380—431no—
362C4×C4⋊C4—431no—
363C4×C4⋊C4C2×D4311yescharacteristic
364C4×C22⋊C4—431no—
365C4×C22⋊C4—861no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#340C2×D4311yescharacteristic
372#340C2×D4311yescharacteristic
373#340C2×D4311yescharacteristic
374#336—431no—
375#336C2×D4311yescharacteristic
376C43#2704111yescharacteristic, complemented, Sylow
377C22×D4—431no—
378C22×D4—861no—
379C23×C4—431no—
380C23×C4—861no—
381C22×C8—431no—
382C22×C8—431no—
383C22×C8C22×D4311yescharacteristic
384C22×C8C22×D4311yescharacteristic
385#121—862no—
386#121—862no—
387C4×D4—862no—
388C4×D4—1721no—
389#117—862no—
390#117—1721no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—861no—
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—431no—
404C2×C22⋊C4—431no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C42—21no—
413C2×C42—431no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42C22×D4311yescharacteristic
417#107—22no—
418#107—862no—
419#107—1721no—
420#106—862no—
421C4⋊C8—862no—
422#102—862no—
423#102—862no—
424#102—862no—
425#102—1721no—
426C22⋊C8—862no—
427C22⋊C8—1721no—
428C4×C8—1721no—
429#95—21no—
430#95—21no—
431#95—431no—
432#95—431no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438C24—431no—
439C24—861no—
440C2×D4—432no—
441C2×D4—864no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—3441no—
448C2×D4—3441no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—3441no—
466C22×C4—1722no—
467C22×C4—1722no—
468C22×C4D4×D4311yescharacteristic
469C22×C4D4×D4311yescharacteristic
470C22×C4C23×D4311yescharacteristic
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—432no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—81no—
491C4⋊C4—432no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—3441no—
498C4⋊C4—3441no—
499C4⋊C4—3441no—
500C4⋊C4—1722no—
501C4⋊C4#1062189812yes—
502C22⋊C4—862no—
503C22⋊C4—864no—
504C22⋊C4—862no—
505C22⋊C4—3441no—
506C22⋊C4—3441no—
507C22⋊C4—3441no—
508C22⋊C4—1722no—
509C22⋊C4—1722no—
510C22⋊C4—1722no—
511C42—21no—
512C42—21no—
513C42—81no—
514C42—861no—
515C42—861no—
516C42—3441no—
517C42—1722no—
518C23—862no—
519C23—861no—
520C23—861no—
521C23—861no—
522C23—861no—
523C23—861no—
524C23—861no—
525C23—861no—
526C23—1721no—
527C23—1721no—
528C23—1721no—
529C23—1721no—
530C23—1721no—
531C23—1721no—
532C23C2×D4×D4311yescharacteristic
533D4—862no—
534D4—862no—
535D4—3444no—
536D4—1721no—
537D4—1721no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
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—432no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—862no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—3444no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4#1306335712yes—
579C2×C4#41×D4311yescharacteristic
580C2×C4#41×D4311yescharacteristic
581C2×C4#41×D4311yescharacteristic
582C2×C4C2×#1062189811yescharacteristic
583C2×C4#1306337111yescharacteristic
584C2×C4#1306337311yescharacteristic
585C8—41no—
586C8—41no—
587C8—862no—
588C8—1721no—
589C22—3441no—
590C22—3441no—
591C22—3441no—
592C22—3441no—
593C22—1721no—
594C22—1721no—
595C22—1722no—
596C22—1721no—
597C22—1722no—
598C22—1721no—
599C22—1721no—
600C22—1721no—
601C22—1722no—
602C22—1721no—
603C22#1458340811yescharacteristic
604C22#1458354111yescharacteristic
605C22#1458355111yescharacteristic
606C22#135×D4311yescharacteristic
607C22C2×#1306335711yescharacteristic
608C22#1458370311yescharacteristic
609C22#1458370311yescharacteristic
610C4—22no—
611C4—41no—
612C4—42no—
613C4—81no—
614C4—81no—
615C4—81no—
616C4—862no—
617C4—3441no—
618C4—3441no—
619C4—1721no—
620C4—1722no—
621C4—1721no—
622C4#1458343211yescharacteristic
623C4#1458349711yescharacteristic
624C4#1458359311yescharacteristic
625C4#1458362111yescharacteristic
626C2—3442no—
627C2—3441no—
628C2#1913863511yescharacteristic
629C2#1914466411yescharacteristic
630C2#1914483711yescharacteristic
631C2#1914654311yescharacteristic
632C2#1914667411yescharacteristic
633C2#1914699411yescharacteristic
634C2#1914721811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1921C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenter#1921D43
hypocenterC43#27041
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
1. #19139022C2semidirect
3. #19136002C2semidirect
4. #19135984C2semidirect
7. #19135350C2semidirect
8. #19135325C2semidirect
9. #19135199C2semidirect
10. #19135172C2semidirect
11. #19134859C2semidirect
12. #19134795C2semidirect
13. #19134688C2semidirect
14. C4×#13063245C2semidirect
15. C43×#1921C2semidirect
318. #1921D43semidirect
376. C43#27041semidirect

Maximal subgroups

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

subgroupindex
#191390222
#191376322
#191360022
#191359842
#191357802
#191357792
#191353502
#191353252
#191351992
#191351722
#191348592
#191347952
#191346882
C4×#130632452
C43×#19212
#2704143