Finite Group Databasebeta

← #25200741

Subgroups — #25200741

Order 11008.

822 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137320C211yesmaximal, characteristic, complemented
2#19136076C211yesmaximal, characteristic, complemented
3#19136008C211yesmaximal, characteristic, complemented
4#19135829C211yesmaximal, characteristic, complemented
5#19135665C211yesmaximal, characteristic
6#19135470C211yesmaximal, characteristic, complemented
7#19135460C211yesmaximal, characteristic, complemented
8#19135291C211yesmaximal, characteristic, complemented
9#19135277C211yesmaximal, characteristic, complemented
10#19134946C211yesmaximal, characteristic, complemented
11#19134946C211yesmaximal, characteristic, complemented
12#19134855C211yesmaximal, characteristic, complemented
13#19134841C211yesmaximal, characteristic, complemented
14#19134347C211yesmaximal, characteristic, complemented
15C43×#2644C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063322C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063236C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33#14582801C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582777—21no—
36#14582777—21no—
37#14582777—21no—
38#14582777—21no—
39#14582765C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C43×#397—21no—
49C43×#397—21no—
50C43×#397—21no—
51C43×#396—21no—
52C43×#390C2211yescharacteristic
53C43×#390C2211yescharacteristic
54C43×#390C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#376C2211yescharacteristic
59C22×D172—21no—
60C22×D172—21no—
61C22×D172C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C2×#10621882—22no—
66C2×#10621882—22no—
67C2×#10621882—22no—
68C2×#10621882—22no—
69C2×#10621882—41no—
70C2×#10621882—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063322—22no—
76#13063322—22no—
77C4×D172—41no—
78C4×D172—41no—
79C4×D172—41no—
80C4×D172—41no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
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×(C2×D43)⋊C4—21no—
89#13063258—41no—
90#13063256—41no—
91#13063246—41no—
92#13063246—41no—
93#13063245—22no—
94#13063245—22no—
95#13063245—22no—
96#13063245—22no—
97#13063245—41no—
98#13063245—41no—
99#13063236—22no—
100C4×C43⋊C8—22no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C22×D4×C43C2311yescharacteristic
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C22⋊C4×C43—21no—
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×C42×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119#95×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124#95×C43D411yescharacteristic
125#95×C43D411yescharacteristic
126C24×C43—21no—
127C23×D43—21no—
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—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—24no—
150C2×D172—24no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—81no—
160C2×D172—81no—
161C2×D172—81no—
162C2×D172—81no—
163C2×D172#4112yes—
164C2×D172#4112yes—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×C4×D43—81no—
168C2×C4×D43—81no—
169C2×C4×D43—81no—
170C2×C4×D43—81no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—81no—
178C4⋊C4×C43—81no—
179C4⋊C4×C43—81no—
180C22⋊C4×C43—81no—
181C22⋊C4×C43—81no—
182C22⋊C4×C43—81no—
183C22⋊C4×C43—81no—
184C22⋊C4×C43—81no—
185C22⋊C4×C43—81no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192#10621882—44no—
193#10621882—44no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—81no—
197(C2×D43)⋊C4—81no—
198(C2×D43)⋊C4—81no—
199(C2×D43)⋊C4—81no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
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#4112yes—
215C2×C43⋊C8#4112yes—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43C22×D411yescharacteristic
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
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—
242C2×C4×C43—21no—
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—21no—
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—21no—
259C2×C4×C43—21no—
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×C43C2×#4111yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43H(5,𝔽2)11yescharacteristic
274C2×C4×C43H(5,𝔽2)11yescharacteristic
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281D172—22no—
282D172—22no—
283D172—22no—
284D172—22no—
285D172—41no—
286D172—41no—
287D172—41no—
288D172—41no—
289D172—84no—
290D172—84no—
291C4×D43—84no—
292C4×D43—84no—
293C43⋊C8—22no—
294C43⋊C8—22no—
295C43⋊C8—41no—
296C43⋊C8—41no—
297#29505—431nomaximal, Sylow
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43#52511yescharacteristic
306C22×C43#53211yescharacteristic
307C22×C43#53511yescharacteristic
308C22×C43#57611yescharacteristic
309C22×C43#57611yescharacteristic
310C22×C43#57611yescharacteristic
311C22×C43#57711yescharacteristic
312C2×D43—42no—
313C2×D43—42no—
314C2×D43—42no—
315C2×D43—42no—
316C2×D43—42no—
317C2×D43—42no—
318C2×D43—81no—
319C2×D43—81no—
320C2×D43—81no—
321C2×D43—81no—
322C2×D43—81no—
323C2×D43—81no—
324C2×D43—81no—
325C2×D43—81no—
326C4×C43—41no—
327C4×C43—41no—
328C4×C43—41no—
329C4×C43—41no—
330C4×C43—41no—
331C4×C43—41no—
332C4×C43—81no—
333C4×C43—81no—
334C4×C43—81no—
335C4×C43#55111yescharacteristic
336C4×C43#55111yescharacteristic
337C4×C43#55311yescharacteristic
338C4×C43#55311yescharacteristic
339Dic43—81no—
340Dic43—81no—
341#2644D4311yescharacteristic, complemented
342#2328—431no—
343#2085—431no—
344#2073—431no—
345#2041—431no—
346#2011—431no—
347#1972—431no—
348#1970—431no—
349#1936—431no—
350#1934—431no—
351#1879—431no—
352#1879—431no—
353#1864—431no—
354#1862—431no—
355#1746—431no—
356C2×C43—161no—
357C2×C43#260311yescharacteristic
358C2×C43#311811yescharacteristic
359C2×C43#312211yescharacteristic
360C2×C43#317611yescharacteristic
361C2×C43#317911yescharacteristic
362C2×C43#322011yescharacteristic
363C2×C43#322411yescharacteristic
364D43—82no—
365D43—82no—
366C22×D8—431no—
367C22×D8—431no—
368C2×#127—431no—
369C2×C4×D4—431no—
370C2×C4×D4—431no—
371C2×#107—431no—
372C2×#106—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×#97—431no—
382C2×C4×C8—431no—
383#397—21no—
384#397—21no—
385#397—21no—
386#396—21no—
387#390—431no—
388#390—431no—
389#390C2×D4311yescharacteristic
390#390C2×D4311yescharacteristic
391#390C2×D4311yescharacteristic
392#389C2×D4311yescharacteristic
393#389C2×D4311yescharacteristic
394#389C2×D4311yescharacteristic
395#386—861no—
396#386—861no—
397#386—861no—
398#386—861no—
399#382—431no—
400#376C2×D4311yescharacteristic
401#340—431no—
402#340—431no—
403#340—431no—
404#340—431no—
405#336—431no—
406#336—431no—
407#336—431no—
408#336—431no—
409C43#2950511yescharacteristic, complemented, Sylow
410C22×D4—431no—
411C22×D4—431no—
412C22×D4—861no—
413C22×D4—861no—
414C22×D4C22×D4311yescharacteristic
415C23×C4—861no—
416C23×C4—861no—
417C2×D8—862no—
418C2×D8—862no—
419C2×D8—862no—
420C2×D8—862no—
421C2×D8—1721no—
422C2×D8—1721no—
423C22×C8—431no—
424C22×C8—431no—
425C22×C8—431no—
426C22×C8—431no—
427#127—862no—
428#127—862no—
429C4×D4—1721no—
430C4×D4—1721no—
431C4×D4—1721no—
432C4×D4—1721no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
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⋊C4—861no—
453C2×C42C22×D4311yescharacteristic
454C2×C42C22×D4311yescharacteristic
455C2×C42C22×D4311yescharacteristic
456#107—1721no—
457#106—1721no—
458#102—862no—
459#102—862no—
460#102—862no—
461#102—862no—
462#102—1721no—
463#102—1721no—
464#102—1721no—
465#102—1721no—
466#97—862no—
467C4×C8—862no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—861no—
472#95—861no—
473#95C22⋊D4311yescharacteristic
474#95C22⋊D4311yescharacteristic
475#95C22⋊D4311yescharacteristic
476#95C22⋊D4311yescharacteristic
477C24—21no—
478C24—861no—
479C24—861no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—432no—
487C2×D4—432no—
488C2×D4—864no—
489C2×D4—864no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C2×D4—861no—
496C2×D4—861no—
497C2×D4—861no—
498C2×D4—861no—
499C2×D4—861no—
500C2×D4—3441no—
501C2×D4—3441no—
502C2×D4—3441no—
503C2×D4—3441no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—3441no—
510C22×C4—3441no—
511C22×C4—3441no—
512C22×C4—3441no—
513C22×C4—1722no—
514C22×C4—1722no—
515C22×C4C2×C22⋊D4311yescharacteristic
516C22×C4C2×C22⋊D4311yescharacteristic
517C22×C4C2×C22⋊D4311yescharacteristic
518C22×C4C2×C22⋊D4311yescharacteristic
519C22×C4C2×C22⋊D4311yescharacteristic
520C22×C4C2×C22⋊D4311yescharacteristic
521C22×C4C23×D4311yescharacteristic
522D8—1724no—
523D8—1724no—
524C2×C8—432no—
525C2×C8—432no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8—861no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—81no—
543C4⋊C4—81no—
544C4⋊C4—81no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C22⋊C4—81no—
550C22⋊C4—81no—
551C22⋊C4—81no—
552C22⋊C4—81no—
553C22⋊C4—81no—
554C22⋊C4—81no—
555C22⋊C4—3441no—
556C22⋊C4—3441no—
557C22⋊C4—3441no—
558C22⋊C4—3441no—
559C22⋊C4—1722no—
560C22⋊C4—1722no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—862no—
575C23—862no—
576C23—1721no—
577C23—1721no—
578C23—1721no—
579C23—1721no—
580C23—1721no—
581C23—1721no—
582C23—1721no—
583C23—1721no—
584C23—1721no—
585C23—1721no—
586C23—1721no—
587C23—1721no—
588C23C22×C22⋊D4311yescharacteristic
589D4—41no—
590D4—41no—
591D4—41no—
592D4—41no—
593D4—862no—
594D4—862no—
595D4—862no—
596D4—862no—
597D4—3444no—
598D4—3444no—
599D4—1721no—
600D4—1721no—
601D4—1721no—
602D4—1721no—
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—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—3444no—
631C2×C4—3444no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4#41×D4311yescharacteristic
639C2×C4#41×D4311yescharacteristic
640C2×C4#41×D4311yescharacteristic
641C2×C4#41×D4311yescharacteristic
642C2×C4#1306337111yescharacteristic
643C2×C4#1306337111yescharacteristic
644C8—862no—
645C8—862no—
646C8—1721no—
647C8—1721no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—3441no—
656C22—3441no—
657C22—3441no—
658C22—3441no—
659C22—3441no—
660C22—3441no—
661C22—3441no—
662C22—3441no—
663C22—1722no—
664C22—1722no—
665C22—1722no—
666C22—1722no—
667C22—1722no—
668C22—1722no—
669C22#1458340611yescharacteristic
670C22#1458344511yescharacteristic
671C22#1458346311yescharacteristic
672C22#1458370211yescharacteristic
673C22#1458370211yescharacteristic
674C22#1458370211yescharacteristic
675C22#1458370711yescharacteristic
676C4—41no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—41no—
682C4—81no—
683C4—81no—
684C4—81no—
685C4—3441no—
686C4—3441no—
687C4#1458357411yescharacteristic
688C4#1458357411yescharacteristic
689C4#1458360011yescharacteristic
690C4#1458360011yescharacteristic
691C2—161no—
692C2—3442no—
693C2—3442no—
694C2#1914022411yescharacteristic
695C2#1914477311yescharacteristic
696C2#1914483311yescharacteristic
697C2#1914523911yescharacteristic
698C2#1914527211yescharacteristic
699C2#1914563911yescharacteristic
700C2#1914568311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2644C2
socleC23×C43C22×D4
prime radical#19135665C2
hypercenter#2644D43
hypocenterC43#29505
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #2644

Complements

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

NH ≅ G/Ntype
1. #19137320C2semidirect
2. #19136076C2semidirect
3. #19136008C2semidirect
4. #19135829C2semidirect
6. #19135470C2semidirect
7. #19135460C2semidirect
8. #19135291C2semidirect
9. #19135277C2semidirect
10. #19134946C2semidirect
11. #19134946C2semidirect
12. #19134855C2semidirect
13. #19134841C2semidirect
14. #19134347C2semidirect
15. C43×#2644C2semidirect
341. #2644D43semidirect
409. C43#29505semidirect

Maximal subgroups

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

subgroupindex
#191373202
#191360762
#191360082
#191358292
#191356652
#191354702
#191354602
#191352912
#191352772
#191349462
#191348552
#191348412
#191343472
C43×#26442
#2950543