Finite Group Databasebeta

← #25169760

Subgroups — #25169760

Order 11008.

848 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137659C211yesmaximal, characteristic
2#19136129C211yesmaximal, characteristic, complemented
3#19135910C211yesmaximal, characteristic, complemented
4#19135829C211yesmaximal, characteristic
5#19135682C211yesmaximal, characteristic
6#19135452C211yesmaximal, characteristic, complemented
7#19135226C211yesmaximal, characteristic, complemented
8#19135222C211yesmaximal, characteristic, complemented
9#19135177C211yesmaximal, characteristic, complemented
10#19135154C211yesmaximal, characteristic, complemented
11#19134932C211yesmaximal, characteristic, complemented
12#19134932C211yesmaximal, characteristic, complemented
13#19134592C211yesmaximal, characteristic, complemented
14C4×#13063245C211yesmaximal, characteristic, complemented
15C43×#2511C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063322C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063287—21no—
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582800—21no—
37#14582777—21no—
38#14582777—21no—
39C4×C4⋊Dic43C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C43×#400—21no—
49C43×#400—21no—
50C43×#391C2211yescharacteristic
51C43×#391C2211yescharacteristic
52C43×#391C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#387—21no—
55C43×#387—21no—
56C43×#384C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C22×D172—21no—
60C22×D172—21no—
61C22×D172C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621884—41no—
69C2×#10621884—41no—
70C2×#10621884—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063322—22no—
76#13063322—22no—
77C4×D172—22no—
78C4×D172—22no—
79C4×D172—41no—
80C4×D172—41no—
81#13063287—44no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
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—
89C2×(C2×D43)⋊C4—21no—
90C2×C4×Dic43—21no—
91#13063256—22no—
92#13063256—41no—
93C4⋊(C43⋊C8)—41no—
94#13063249—22no—
95#13063249—41no—
96#13063245—22no—
97#13063245—22no—
98#13063245—22no—
99#13063245—41no—
100#13063245—41no—
101#13063245—41no—
102C4×C43⋊C8—41no—
103C43⋊#95—21no—
104C22×Q8×C43C2311yescharacteristic
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43D411yescharacteristic
109C2×C4⋊C4×C43D411yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C42×C43—21no—
114C2×C42×C43C2311yescharacteristic
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43D411yescharacteristic
126#95×C43D411yescharacteristic
127C23×D43—21no—
128C23×D43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C2×D172—24no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—24no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—42no—
161C2×D172—42no—
162C2×D172—81no—
163C2×D172—81no—
164C2×D172#4112yes—
165C2×D172#4112yes—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170C2×C4×D43—81no—
171C2×C4×D43—81no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43—42no—
180C4⋊C4×C43—81no—
181C4⋊C4×C43—81no—
182C4⋊C4×C43SD1614yescomplemented
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—81no—
190#10621884—44no—
191#10621884—44no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—81no—
197(C2×D43)⋊C4—81no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43#4112yes—
202C4×Dic43—42no—
203C2×C43⋊C8—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—
215C23×C43C22×D411yescharacteristic
216C22×D43—22no—
217C22×D43—22no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230Q8×C43—41no—
231Q8×C43—41no—
232Q8×C43—41no—
233Q8×C43—41no—
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—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—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43C2×SD1612yes—
262C2×C4×C43C2×SD1612yes—
263C2×C4×C43C2×SD1612yes—
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43H(5,𝔽2)11yescharacteristic
269C2×C4×C43H(5,𝔽2)11yescharacteristic
270C2×Dic43—22no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276D172—22no—
277D172—22no—
278D172—22no—
279D172—22no—
280D172—48no—
281D172—41no—
282D172—41no—
283D172—41no—
284D172—41no—
285D172—84no—
286C4×D43—84no—
287C4×D43—84no—
288C43⋊C8—22no—
289C43⋊C8—41no—
290C43⋊C8—41no—
291C43⋊C8—41no—
292#27064—431nomaximal, Sylow
293C22×C43#52511yescharacteristic
294C22×C43#54611yescharacteristic
295C22×C43#55011yescharacteristic
296C22×C43C22×SD1611yescharacteristic
297C22×C43#57511yescharacteristic
298C22×C43#57611yescharacteristic
299C22×C43#57711yescharacteristic
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C4×C43—22no—
315C4×C43—22no—
316C4×C43—22no—
317C4×C43—41no—
318C4×C43—41no—
319C4×C43—41no—
320C4×C43—81no—
321C4×C43—81no—
322C4×C43—81no—
323C4×C43—81no—
324C4×C43#52911yescharacteristic
325C4×C43#53811yescharacteristic
326C4×C43#55111yescharacteristic
327C4×C43#55311yescharacteristic
328Dic43—42no—
329Dic43—81no—
330#2511D4311yescharacteristic, complemented
331#2366—431no—
332#2094—431no—
333#2055—431no—
334#2041—431no—
335#2014—431no—
336#1968—431no—
337#1927—431no—
338#1926—431no—
339#1920—431no—
340#1916—431no—
341#1877—431no—
342#1877—431no—
343#1802—431no—
344C4×#102—431no—
345C2×C43#246711yescharacteristic
346C2×C43#310111yescharacteristic
347C2×C43#311811yescharacteristic
348C2×C43#329511yescharacteristic
349C2×C43#331711yescharacteristic
350C2×C43#339211yescharacteristic
351C2×C43#340311yescharacteristic
352D43—82no—
353D43—82no—
354C22×SD16—431no—
355C22×SD16—431no—
356C2×#127—431no—
357C2×C4×D4—431no—
358C2×C4×D4—431no—
359C2×C4×D4—861no—
360C2×#106—431no—
361C2×#106—431no—
362C2×C4⋊C8—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#102—431no—
366C2×#102—431no—
367C2×#102—431no—
368C2×#102—431no—
369C2×#102—431no—
370C2×#102—431no—
371C2×C4×C8—431no—
372#400—21no—
373#400—21no—
374#391C2×D4311yescharacteristic
375#391C2×D4311yescharacteristic
376#391C2×D4311yescharacteristic
377#390—431no—
378#390—431no—
379#390—861no—
380#389C2×D4311yescharacteristic
381#387—21no—
382#387—21no—
383#386—861no—
384#386—861no—
385#384C2×D4311yescharacteristic
386C4×C4⋊C4—431no—
387C4×C4⋊C4C2×D4311yescharacteristic
388C4×C4⋊C4C2×D4311yescharacteristic
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#336—431no—
394#336—431no—
395#336—431no—
396#336—431no—
397C43#2706411yescharacteristic, complemented, Sylow
398C22×Q8C22×D4311yescharacteristic
399C22×D4—431no—
400C22×D4—431no—
401C22×D4—861no—
402C22×D4—861no—
403C23×C4—861no—
404C23×C4—861no—
405C2×SD16—862no—
406C2×SD16—862no—
407C2×SD16—862no—
408C2×SD16—1721no—
409C2×SD16—1721no—
410C2×SD16—1721no—
411C22×C8—431no—
412C22×C8—431no—
413C22×C8—431no—
414C22×C8—431no—
415#127—862no—
416#127—862no—
417C4×D4—862no—
418C4×D4—862no—
419C4×D4—1721no—
420C4×D4—1721no—
421C4×D4—1724no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4C22⋊D4311yescharacteristic
428C2×C4⋊C4C22⋊D4311yescharacteristic
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C42—21no—
439C2×C42—861no—
440C2×C42C22×D4311yescharacteristic
441C2×C42C22×D4311yescharacteristic
442C2×C42C22×D4311yescharacteristic
443#106—862no—
444#106—1721no—
445C4⋊C8—1721no—
446#103—862no—
447#103—1721no—
448#102—862no—
449#102—862no—
450#102—862no—
451#102—1721no—
452#102—1721no—
453#102—1721no—
454C4×C8—1721no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—861no—
464#95C22⋊D4311yescharacteristic
465#95C22⋊D4311yescharacteristic
466C24—861no—
467C24—861no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×D4—432no—
475C2×D4—432no—
476C2×D4—864no—
477C2×D4—864no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—3441no—
489C2×D4—3441no—
490C2×D4—1722no—
491C2×D4—1722no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—3441no—
499C22×C4—3441no—
500C22×C4—1722no—
501C22×C4—1722no—
502C22×C4—1722no—
503C22×C4—1722no—
504C22×C4C2×C22⋊D4311yescharacteristic
505C22×C4C2×C22⋊D4311yescharacteristic
506C22×C4C2×C22⋊D4311yescharacteristic
507C22×C4C2×C22⋊D4311yescharacteristic
508C22×C4C2×C22⋊D4311yescharacteristic
509C22×C4C2×C22⋊D4311yescharacteristic
510C22×C4C23×D4311yescharacteristic
511SD16—1724no—
512SD16—1724no—
513C2×C8—432no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—41no—
532C4⋊C4—42no—
533C4⋊C4—81no—
534C4⋊C4—81no—
535C4⋊C4—432no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4#1062188414yescomplemented
540C22⋊C4—3441no—
541C22⋊C4—3441no—
542C22⋊C4—1722no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—81no—
553C42—1722no—
554C23—862no—
555C23—862no—
556C23—1721no—
557C23—1721no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23C22×C22⋊D4311yescharacteristic
569Q8—41no—
570Q8—41no—
571Q8—41no—
572Q8—41no—
573D4—862no—
574D4—862no—
575D4—862no—
576D4—862no—
577D4—3444no—
578D4—1728no—
579D4—1721no—
580D4—1721no—
581D4—1721no—
582D4—1721no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—862no—
611C2×C4—3444no—
612C2×C4—3444no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4C2×#1062188412yes—
619C2×C4C2×#1062188412yes—
620C2×C4C2×#1062188412yes—
621C2×C4#41×D4311yescharacteristic
622C2×C4#41×D4311yescharacteristic
623C2×C4#41×D4311yescharacteristic
624C2×C4#41×D4311yescharacteristic
625C2×C4#1306337111yescharacteristic
626C2×C4#1306337111yescharacteristic
627C8—862no—
628C8—1721no—
629C8—1721no—
630C8—1721no—
631C22—3441no—
632C22—3441no—
633C22—3441no—
634C22—3441no—
635C22—3441no—
636C22—3441no—
637C22—3441no—
638C22—3441no—
639C22—1722no—
640C22—1722no—
641C22—1722no—
642C22—1722no—
643C22—1722no—
644C22—1722no—
645C22#1458340611yescharacteristic
646C22#1458353711yescharacteristic
647C22#1458356811yescharacteristic
648C22C22×#1062188411yescharacteristic
649C22#1458369711yescharacteristic
650C22#1458370211yescharacteristic
651C22#1458370711yescharacteristic
652C4—22no—
653C4—22no—
654C4—22no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4—3441no—
663C4—1722no—
664C4#1458343211yescharacteristic
665C4#1458348811yescharacteristic
666C4#1458357411yescharacteristic
667C4#1458360011yescharacteristic
668C2—3442no—
669C2—3442no—
670C2#1913864211yescharacteristic
671C2#1914459911yescharacteristic
672C2#1914477311yescharacteristic
673C2#1914641311yescharacteristic
674C2#1914671511yescharacteristic
675C2#1914757211yescharacteristic
676C2#1914767911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2511C2
socleC23×C43C22×D4
prime radicalC2×#13063322C22
hypercenter#2511D43
hypocenterC43#27064
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2511

Complements

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

NH ≅ G/Ntype
2. #19136129C2semidirect
3. #19135910C2semidirect
6. #19135452C2semidirect
7. #19135226C2semidirect
8. #19135222C2semidirect
9. #19135177C2semidirect
10. #19135154C2semidirect
11. #19134932C2semidirect
12. #19134932C2semidirect
13. #19134592C2semidirect
14. C4×#13063245C2semidirect
15. C43×#2511C2semidirect
182. C4⋊C4×C43SD16semidirect
330. #2511D43semidirect
397. C43#27064semidirect
539. C4⋊C4#10621884semidirect

Maximal subgroups

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

subgroupindex
#191376592
#191361292
#191359102
#191358292
#191356822
#191354522
#191352262
#191352222
#191351772
#191351542
#191349322
#191345922
C4×#130632452
C43×#25112
#2706443