Finite Group Databasebeta

← #25169417

Subgroups — #25169417

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#19139028C211yesmaximal, characteristic, complemented
2#19137631C211yesmaximal, characteristic
3#19136000C211yesmaximal, characteristic, complemented
4#19135982C211yesmaximal, characteristic, complemented
5#19135778C211yesmaximal, characteristic
6#19135778C211yesmaximal, characteristic
7#19135354C211yesmaximal, characteristic, complemented
8#19135328C211yesmaximal, characteristic, complemented
9#19135188C211yesmaximal, characteristic, complemented
10#19135174C211yesmaximal, characteristic, complemented
11#19134859C211yesmaximal, characteristic, complemented
12#19134796C211yesmaximal, characteristic, complemented
13#19134691C211yesmaximal, characteristic, complemented
14C4×#13063247C211yesmaximal, characteristic, complemented
15C43×#1923C211yesmaximal, characteristic, complemented
16C2×#13063299C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27#14582841—21no—
28#14582822—21no—
29#14582801C2211yescharacteristic
30#14582799—21no—
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582792—21no—
35#14582788—21no—
36#14582786—21no—
37#14582775—21no—
38#14582769C2211yescharacteristic
39#14582759C2211yescharacteristic
40#14582759C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43#14582746—21no—
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C22⋊C4×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C22⋊D43—21no—
61C22×C4×D43—21no—
62#13063299—22no—
63#13063299—22no—
64C4×D172—22no—
65C4×D172—41no—
66#13063284—22no—
67#13063284—41no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90#13063259—22no—
91#13063259—22no—
92#13063259—41no—
93#13063257—22no—
94#13063247—22no—
95#13063247—22no—
96#13063247—22no—
97#13063247—41no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C23×C4×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C22⋊C4×C43D411yescharacteristic
111C2×C22⋊C4×C43D411yescharacteristic
112C2×C42×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114C4⋊C8×C43—22no—
115C22⋊C8×C43—22no—
116C22⋊C8×C43—41no—
117C4×C8×C43—41no—
118#95×C43D411yescharacteristic
119#95×C43D411yescharacteristic
120C24×C43C2×D411yescharacteristic
121C23×D43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C2×C22⋊D43—24no—
135C2×C22⋊D43—81no—
136C2×C22⋊D43—81no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172#4112yes—
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—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43#4112yes—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—21no—
171C22⋊Dic43—42no—
172C22⋊Dic43—81no—
173C22⋊Dic43—81no—
174(C2×D43)⋊C4—24no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—81no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—81no—
191C4⋊Dic43—81no—
192C4⋊Dic43#4112yes—
193C4⋊Dic43#4112yes—
194Dic43⋊C4—42no—
195Dic43⋊C4—81no—
196Dic43⋊C4—81no—
197C4×Dic43—42no—
198C4×Dic43—81no—
199C4×Dic43—81no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43C22×D411yescharacteristic
208C22×D43—22no—
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—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—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43#13512yes—
233C2×C4×C43#13712yes—
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C2×C4×C432−1+411yescharacteristic
240C22⋊D43—84no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
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—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262D172—22no—
263D172—22no—
264D172—41no—
265D172—41no—
266C4×D43—84no—
267C8×C43—22no—
268C8×C43—41no—
269C8×C43—41no—
270C8×C43—41no—
271#27041—431nomaximal, Sylow
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43#52511yescharacteristic
280C22×C43#54611yescharacteristic
281C22×C43#54711yescharacteristic
282C22×C43C2×#13511yescharacteristic
283C22×C43C2×#13711yescharacteristic
284C22×C43#57611yescharacteristic
285C22×C43#57611yescharacteristic
286C2×D43—42no—
287C2×D43—42no—
288C2×D43—42no—
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C4×C43—22no—
294C4×C43—22no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43#52911yescharacteristic
299C4×C43#53911yescharacteristic
300C4×C43#55311yescharacteristic
301C4×C43#55611yescharacteristic
302Dic43—42no—
303Dic43—42no—
304Dic43—81no—
305Dic43—81no—
306Dic43—81no—
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#1923D4311yescharacteristic, complemented
318#1921—431no—
319#1919—431no—
320#1864—431no—
321#1854—431no—
322#1825—431no—
323C4×#102—431no—
324C2×C43—81no—
325C2×C43#246611yescharacteristic
326C2×C43#310711yescharacteristic
327C2×C43#312211yescharacteristic
328C2×C43#330511yescharacteristic
329C2×C43#331411yescharacteristic
330C2×C43#333911yescharacteristic
331C2×C43#335711yescharacteristic
332D43—82no—
333C2×#121—431no—
334C2×C4×D4—431no—
335C2×#117—431no—
336C2×#107—431no—
337C2×#107—431no—
338C2×#107—431no—
339C2×#106—431no—
340C2×C4⋊C8C2×D4311yescharacteristic
341C2×#102—431no—
342C2×#102—431no—
343C2×#102—431no—
344C2×#102—431no—
345C2×C22⋊C8C2×D4311yescharacteristic
346C2×C22⋊C8C2×D4311yescharacteristic
347C2×C4×C8C2×D4311yescharacteristic
348#400—861no—
349#396—861no—
350#390—431no—
351#390—861no—
352#389—431no—
353#389—431no—
354#389—431no—
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⋊C4—431no—
364C4×C22⋊C4—861no—
365C4×C22⋊C4C2×D4311yescharacteristic
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#336C2×D4311yescharacteristic
375#336C2×D4311yescharacteristic
376C43#2704111yescharacteristic, complemented, Sylow
377C22×D4—431no—
378C22×D4—861no—
379C23×C4—861no—
380C23×C4C22×D4311yescharacteristic
381C22×C8C22×D4311yescharacteristic
382C22×C8C22×D4311yescharacteristic
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—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4D17211yescharacteristic
411C2×C22⋊C4D17211yescharacteristic
412C2×C42—861no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42C22×D4311yescharacteristic
416C2×C42C22×D4311yescharacteristic
417#107—862no—
418#107—862no—
419#107—1721no—
420#106—862no—
421C4⋊C8—22no—
422#102—862no—
423#102—862no—
424#102—862no—
425#102—1721no—
426C22⋊C8—22no—
427C22⋊C8—41no—
428C4×C8—41no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95D17211yescharacteristic
437#95D17211yescharacteristic
438C24—861no—
439C24C2×D17211yescharacteristic
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—21no—
454C22×C4—21no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—3441no—
463C22×C4—1722no—
464C22×C4—1722no—
465C22×C4C2×D17211yescharacteristic
466C22×C4C2×D17211yescharacteristic
467C22×C4C2×D17211yescharacteristic
468C22×C4C2×D17211yescharacteristic
469C22×C4C2×D17211yescharacteristic
470C22×C4C23×D4311yescharacteristic
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8#1062190012yes—
483C4⋊C4—432no—
484C4⋊C4—432no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
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—3441no—
501C4⋊C4—1722no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—864no—
505C22⋊C4—3441no—
506C22⋊C4—3441no—
507C22⋊C4—3441no—
508C22⋊C4—1722no—
509C22⋊C4—1722no—
510C22⋊C4—1722no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—3441no—
516C42—3441no—
517C42—1722no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—862no—
526C23—1721no—
527C23—1721no—
528C23—1721no—
529C23—1721no—
530C23—1721no—
531C23—1721no—
532C23C22×D17211yescharacteristic
533D4—862no—
534D4—862no—
535D4—3444no—
536D4—1721no—
537D4—1721no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—862no—
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—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#1306334712yes—
578C2×C4#1306335812yes—
579C2×C4#41×D4311yescharacteristic
580C2×C4#41×D4311yescharacteristic
581C2×C4#41×D4311yescharacteristic
582C2×C4C2×#1062190011yescharacteristic
583C2×C4#1306337011yescharacteristic
584C2×C4#1306337211yescharacteristic
585C8—22no—
586C8—41no—
587C8—41no—
588C8—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—3441no—
597C22—3441no—
598C22—3441no—
599C22—3441no—
600C22—1722no—
601C22—1722no—
602C22—1722no—
603C22#1458341111yescharacteristic
604C22#1458354411yescharacteristic
605C22#1458355311yescharacteristic
606C22C2×#1306334711yescharacteristic
607C22C2×#1306335811yescharacteristic
608C22#1458370411yescharacteristic
609C22#1458370411yescharacteristic
610C4—22no—
611C4—22no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—3441no—
616C4—3441no—
617C4—3441no—
618C4—3441no—
619C4—3441no—
620C4—1722no—
621C4—1722no—
622C4#1458342811yescharacteristic
623C4#1458349211yescharacteristic
624C4#1458359211yescharacteristic
625C4#1458361611yescharacteristic
626C2—81no—
627C2—3442no—
628C2#1913862911yescharacteristic
629C2#1914466711yescharacteristic
630C2#1914483911yescharacteristic
631C2#1914654611yescharacteristic
632C2#1914667811yescharacteristic
633C2#1914699811yescharacteristic
634C2#1914722211yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1923C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#1923D43
hypocenterC43#27041
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
1. #19139028C2semidirect
3. #19136000C2semidirect
4. #19135982C2semidirect
7. #19135354C2semidirect
8. #19135328C2semidirect
9. #19135188C2semidirect
10. #19135174C2semidirect
11. #19134859C2semidirect
12. #19134796C2semidirect
13. #19134691C2semidirect
14. C4×#13063247C2semidirect
15. C43×#1923C2semidirect
317. #1923D43semidirect
376. C43#27041semidirect

Maximal subgroups

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

subgroupindex
#191390282
#191376312
#191360002
#191359822
#191357782
#191353542
#191353282
#191351882
#191351742
#191348592
#191347962
#191346912
C4×#130632472
C43×#19232
#2704143