Finite Group Databasebeta

← #25199570

Subgroups — #25199570

Order 11008.

780 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137288C211yesmaximal, characteristic
2#19137277C211yesmaximal, characteristic, complemented
3#19136028C211yesmaximal, characteristic, complemented
4#19135792C211yesmaximal, characteristic, complemented
5#19135785C211yesmaximal, characteristic
6#19135600C211yesmaximal, characteristic
7#19135230C211yesmaximal, characteristic, complemented
8#19135223C211yesmaximal, characteristic, complemented
9#19135181C211yesmaximal, characteristic, complemented
10#19135174C211yesmaximal, characteristic, complemented
11#19134949C211yesmaximal, characteristic, complemented
12#19134928C211yesmaximal, characteristic, complemented
13#19134866C211yesmaximal, characteristic, complemented
14#19134859C211yesmaximal, characteristic, complemented
15C43×#1818C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30#14582805C2211yescharacteristic
31#14582801C2211yescharacteristic
32#14582799—21no—
33#14582797C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582794—21no—
36#14582793—21no—
37#14582789—21no—
38#14582787—21no—
39#14582780—21no—
40#14582775—21no—
41#14582770—21no—
42#14582759C2211yescharacteristic
43#14582759C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×#117×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C4×D43—21no—
63C2×#10621873—22no—
64C2×#10621873—22no—
65C2×#10621873—41no—
66#13063304—22no—
67#13063304—22no—
68#13063299—22no—
69#13063299—22no—
70C4×Dic86—41no—
71C4×Dic86—41no—
72C4×D172—41no—
73C4×D172—41no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94#13063257—22no—
95#13063257—22no—
96#13063257—41no—
97#13063250—22no—
98#13063250—22no—
99#13063250—41no—
100#13063247—22no—
101#13063247—22no—
102#13063247—41no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C23×C4×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116#117×C43—41no—
117#117×C43—41no—
118C2×C4⋊C4×C43D411yescharacteristic
119C2×C4⋊C4×C43D411yescharacteristic
120C2×C22⋊C4×C43D411yescharacteristic
121C2×C22⋊C4×C43D411yescharacteristic
122C2×C42×C43C2311yescharacteristic
123C2×C42×C43C2311yescharacteristic
124C22⋊C8×C43—41no—
125C22⋊C8×C43—41no—
126C24×C43C2×D411yescharacteristic
127C23×D43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C2×C22⋊D43—24no—
141C2×C22⋊D43—81no—
142C2×C22⋊D43—81no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172#4112yes—
156C2×C4×D43—42no—
157C2×C4×D43—81no—
158C2×C4×D43—81no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86#4112yes—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C22⋊C4×C43—41no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C22⋊Dic43—24no—
186C22⋊Dic43—81no—
187C22⋊Dic43—81no—
188(C2×D43)⋊C4—24no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—81no—
191(C2×D43)⋊C4—81no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43#4112yes—
203C4⋊Dic43#4112yes—
204Dic43⋊C4—24no—
205Dic43⋊C4—42no—
206Dic43⋊C4—81no—
207Dic43⋊C4—81no—
208C4×Dic43—42no—
209C4×Dic43—81no—
210C4×Dic43—81no—
211#10621873—44no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43C22×D411yescharacteristic
220C22×D43—22no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C2×C4×C43H(5,𝔽2)11yescharacteristic
252C22⋊D43—84no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274D172—22no—
275D172—22no—
276D172—41no—
277D172—41no—
278C4×D43—84no—
279Dic86—22no—
280Dic86—22no—
281Dic86—41no—
282Dic86—41no—
283C8×C43—41no—
284C8×C43—41no—
285C8×C43—41no—
286C8×C43—41no—
287#29424—431nomaximal, Sylow
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43#52511yescharacteristic
296C22×C43#52511yescharacteristic
297C22×C43#53411yescharacteristic
298C22×C43#57711yescharacteristic
299C22×C43#57711yescharacteristic
300C22×C43#57711yescharacteristic
301C22×C43#57711yescharacteristic
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43—41no—
313C4×C43—41no—
314C4×C43#55111yescharacteristic
315C4×C43#55311yescharacteristic
316C4×C43#55311yescharacteristic
317C4×C43#55911yescharacteristic
318Dic43—42no—
319Dic43—42no—
320Dic43—42no—
321Dic43—81no—
322Dic43—81no—
323Dic43—81no—
324Dic43—81no—
325#2324—431no—
326#2323—431no—
327#2077—431no—
328#2035—431no—
329#2034—431no—
330#2000—431no—
331#1927—431no—
332#1926—431no—
333#1920—431no—
334#1919—431no—
335#1880—431no—
336#1877—431no—
337#1865—431no—
338#1864—431no—
339#1818D4311yescharacteristic, complemented
340C2×C43—81no—
341C2×C43#260011yescharacteristic
342C2×C43#312311yescharacteristic
343C2×C43#312511yescharacteristic
344C2×C43#312511yescharacteristic
345C2×C43#312611yescharacteristic
346C2×C43#320011yescharacteristic
347C2×C43#320411yescharacteristic
348D43—82no—
349C22×SD16—431no—
350C2×C22⋊Q8—431no—
351C2×#121—431no—
352C2×C4×Q8—431no—
353C2×C4×D4—431no—
354C2×#117C2×D4311yescharacteristic
355C2×#106—431no—
356C2×#106—431no—
357C2×#106—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#103—431no—
361C2×#102—431no—
362C2×#102—431no—
363C2×#102—431no—
364C2×C22⋊C8C2×D4311yescharacteristic
365C2×C22⋊C8C2×D4311yescharacteristic
366#391—431no—
367#390—431no—
368#390—861no—
369#389—431no—
370#389—431no—
371#389—861no—
372#388—861no—
373#388—861no—
374#388—861no—
375#387—861no—
376#386—861no—
377#385—861no—
378#380—431no—
379#380—431no—
380C4×C4⋊C4—431no—
381C4×C4⋊C4—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#336C2×D4311yescharacteristic
389#336C2×D4311yescharacteristic
390#336C2×D4311yescharacteristic
391#336C2×D4311yescharacteristic
392C43#2942411yescharacteristic, complemented, Sylow
393C22×Q8—431no—
394C22×D4—431no—
395C22×D4—861no—
396C23×C4—861no—
397C23×C4C22×D4311yescharacteristic
398C2×SD16—862no—
399C2×SD16—862no—
400C2×SD16—1721no—
401C22×C8C22×D4311yescharacteristic
402C22×C8C22×D4311yescharacteristic
403C22×C8C22×D4311yescharacteristic
404C22×C8C22×D4311yescharacteristic
405C22⋊Q8—862no—
406C22⋊Q8—862no—
407#121—862no—
408#121—862no—
409C4×Q8—1721no—
410C4×Q8—1721no—
411C4×D4—1721no—
412C4×D4—1721no—
413#117—41no—
414#117—41no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4D17211yescharacteristic
426C2×C4⋊C4D17211yescharacteristic
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4D17211yescharacteristic
435C2×C22⋊C4D17211yescharacteristic
436C2×C42—861no—
437C2×C42—861no—
438C2×C42—861no—
439C2×C42C22×D4311yescharacteristic
440C2×C42C22×D4311yescharacteristic
441#106—862no—
442#106—862no—
443#106—1721no—
444#103—862no—
445#103—862no—
446#103—1721no—
447#102—862no—
448#102—862no—
449#102—1721no—
450C22⋊C8—41no—
451C22⋊C8—41no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460C24—861no—
461C24C2×D17211yescharacteristic
462C2×Q8—432no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×D4—432no—
469C2×D4—864no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—3441no—
476C2×D4—3441no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—3441no—
491C22×C4—3441no—
492C22×C4—1722no—
493C22×C4C2×D17211yescharacteristic
494C22×C4C2×D17211yescharacteristic
495C22×C4C2×D17211yescharacteristic
496C22×C4C2×D17211yescharacteristic
497C22×C4C2×D17211yescharacteristic
498C22×C4C23×D4311yescharacteristic
499SD16—1724no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—432no—
515C4⋊C4—432no—
516C4⋊C4—864no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—3441no—
528C4⋊C4—3441no—
529C4⋊C4—1722no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—864no—
533C22⋊C4—864no—
534C22⋊C4—3441no—
535C22⋊C4—3441no—
536C22⋊C4—3441no—
537C22⋊C4—3441no—
538C22⋊C4—1722no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—3441no—
544C42—3441no—
545C42—1722no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—862no—
554C23—1721no—
555C23—1721no—
556C23—1721no—
557C23—1721no—
558C23—1721no—
559C23—1721no—
560C23C22×D17211yescharacteristic
561Q8—862no—
562Q8—862no—
563Q8—1721no—
564Q8—1721no—
565D4—862no—
566D4—862no—
567D4—3444no—
568D4—1721no—
569D4—1721no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—3444no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4#41×D4311yescharacteristic
612C2×C4#41×D4311yescharacteristic
613C2×C4#41×D4311yescharacteristic
614C2×C4#41×D4311yescharacteristic
615C2×C4#1306337011yescharacteristic
616C2×C4#1306337011yescharacteristic
617C8—41no—
618C8—41no—
619C8—41no—
620C8—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—3441no—
629C22—3441no—
630C22—3441no—
631C22—3441no—
632C22—1722no—
633C22—1722no—
634C22—1722no—
635C22#1458341111yescharacteristic
636C22#1458341111yescharacteristic
637C22#1458346111yescharacteristic
638C22#1458371111yescharacteristic
639C22#1458371111yescharacteristic
640C22#1458371111yescharacteristic
641C22#1458371111yescharacteristic
642C4—41no—
643C4—41no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—3441no—
648C4—3441no—
649C4—3441no—
650C4—3441no—
651C4—1722no—
652C4—1722no—
653C4—1722no—
654C4#1458357711yescharacteristic
655C4#1458359411yescharacteristic
656C4#1458359411yescharacteristic
657C4#1458363311yescharacteristic
658C2—81no—
659C2—3442no—
660C2#1914018211yescharacteristic
661C2#1914484811yescharacteristic
662C2#1914487411yescharacteristic
663C2#1914487411yescharacteristic
664C2#1914488711yescharacteristic
665C2#1914546811yescharacteristic
666C2#1914550711yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1818C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#1818D43
hypocenterC43#29424
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1818

Complements

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

NH ≅ G/Ntype
2. #19137277C2semidirect
3. #19136028C2semidirect
4. #19135792C2semidirect
7. #19135230C2semidirect
8. #19135223C2semidirect
9. #19135181C2semidirect
10. #19135174C2semidirect
11. #19134949C2semidirect
12. #19134928C2semidirect
13. #19134866C2semidirect
14. #19134859C2semidirect
15. C43×#1818C2semidirect
339. #1818D43semidirect
392. C43#29424semidirect

Maximal subgroups

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

subgroupindex
#191372882
#191372772
#191360282
#191357922
#191357852
#191356002
#191352302
#191352232
#191351812
#191351742
#191349492
#191349282
#191348662
#191348592
C43×#18182
#2942443