Finite Group Databasebeta

← #25116036

Subgroups — #25116036

Order 11008.

866 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582998C211yesmaximal, characteristic
2#19137540C211yesmaximal, characteristic
3#19137514C211yesmaximal, characteristic, complemented
4#19135291C211yesmaximal, characteristic
5#19135279C211yesmaximal, characteristic
6#19135168C211yesmaximal, characteristic, complemented
7#19134951C211yesmaximal, characteristic
8#19134949C211yesmaximal, characteristic
9#19134727C211yesmaximal, characteristic, complemented
10#19134604C211yesmaximal, characteristic
11#19134599C211yesmaximal, characteristic, complemented
12#19134468C211yesmaximal, characteristic, complemented
13#19134428C211yesmaximal, characteristic, complemented
14#19134414C211yesmaximal, characteristic, complemented
15C43×#1921C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C2×#13063282—21no—
22#14582998C418yescomplemented
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582801C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582796—21no—
37#14582794—21no—
38#14582790—21no—
39#14582788—21no—
40#14582768C2211yescharacteristic
41#14582764C2211yescharacteristic
42#14582763—21no—
43#14582758—21no—
44C4⋊C4×Dic43—21no—
45C4⋊C4×Dic43C2211yescharacteristic
46C4×Dic43⋊C4C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C43×#389C2211yescharacteristic
55C4×C4⋊C4×C43C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C2×#10621873—22no—
64C2×#10621873—22no—
65C2×#10621873C2×C414yes—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C4×Dic86—22no—
69C4×Dic86—41no—
70#13063290—22no—
71#13063290—22no—
72#13063290—41no—
73#13063290C2×C414yes—
74#13063287—22no—
75#13063287C2×C414yes—
76#13063282—44no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4D411yescharacteristic
86C2×Dic43⋊C4D411yescharacteristic
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98Dic43⋊C8—22no—
99#13063250—22no—
100#13063248—22no—
101#13063248C2×C414yes—
102#13063247—41no—
103#13063245—41no—
104#13063245C2×C414yes—
105#13063236—41no—
106#13063235C2×C414yes—
107C8×Dic43—41no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95D411yescharacteristic
113C43⋊#95D411yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#107×C43C2×C414yes—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172C22×C412yes—
147C2×C4×D43—24no—
148C2×C4×D43—42no—
149C2×C4×D43—42no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86C22×C412yes—
154C2×Dic86#4112yes—
155C2×Dic86#4112yes—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43C22×C412yes—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—42no—
169C4⋊C4×C43C22×C412yes—
170C4⋊C4×C43C22×C412yes—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—42no—
174(C2×D43)⋊C4—24no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—81no—
178(C2×D43)⋊C4—81no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—42no—
184Dic43⋊C4—24no—
185Dic43⋊C4—22no—
186Dic43⋊C4—41no—
187Dic43⋊C4—42no—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190Dic43⋊C4—81no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—24no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C4×Dic43—42no—
197C4×Dic43C22×C412yes—
198C4×Dic43#4112yes—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C22×C412yes—
205#10621873—28no—
206C23×C43C22×D411yescharacteristic
207C22×D43—22no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—41no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
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—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×C43C23×C411yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43H(5,𝔽2)11yescharacteristic
237C2×C4×C432−1+411yescharacteristic
238C2×Dic43—22no—
239C2×Dic43—21no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43C4×D412yes—
257C2×Dic43C4×D412yes—
258C2×Dic43AGL(1,ℤ/8)12yes—
259D172—22no—
260D172—22no—
261D172—41no—
262D172—41no—
263C4×D43—48no—
264Dic86—22no—
265Dic86—22no—
266Dic86—22no—
267Dic86#11714yescomplemented
268C8×C43—22no—
269C8×C43—41no—
270C43⋊C8—22no—
271C43⋊C8—41no—
272#22781—431nomaximal, Sylow
273C22×C43C2×C4×D411yescharacteristic
274C22×C43#54611yescharacteristic
275C22×C43#54811yescharacteristic
276C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C43#57511yescharacteristic
278C22×C43#57711yescharacteristic
279C22×C43#57811yescharacteristic
280C2×D43—42no—
281C2×D43—42no—
282C2×D43—42no—
283C2×D43—81no—
284C2×D43—81no—
285C2×D43—81no—
286C2×D43—81no—
287C4×C43—42no—
288C4×C43—42no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43C2×#11711yescharacteristic
294C4×C43#52011yescharacteristic
295C4×C43#55211yescharacteristic
296C4×C43#55311yescharacteristic
297Dic43—24no—
298Dic43—22no—
299Dic43—22no—
300Dic43—22no—
301Dic43—41no—
302Dic43—81no—
303Dic43—81no—
304C2×#440—431no—
305#2354—431no—
306#2351—431no—
307#1936—431no—
308#1934—431no—
309#1921D4311yescharacteristic, complemented
310#1918—431no—
311#1880—431no—
312#1880—431no—
313#1836—431no—
314#1804—431no—
315#1803—431no—
316#1771—431no—
317#1763—431no—
318C4×#103—431no—
319C2×C43#235211yescharacteristic
320C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
321C2×C43#294711yescharacteristic
322C2×C43#330811yescharacteristic
323C2×C43#332111yescharacteristic
324C2×C43#336811yescharacteristic
325C2×C43#337711yescharacteristic
326D43—82no—
327C22×SD16—431no—
328C2×C4×Q8—431no—
329C2×C4×Q8—431no—
330C2×C4×Q8—431no—
331C2×C4×D4—431no—
332C2×#117—861no—
333#440—438no—
334C2×#107C2×D4311yescharacteristic
335C2×C4⋊C8—431no—
336C2×#103—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#102—431no—
340C2×#102—431no—
341C2×#102—431no—
342C2×#97—431no—
343C2×#97—431no—
344C2×C4×C8—431no—
345#390—431no—
346#390—431no—
347#389—431no—
348#389—861no—
349#389—861no—
350#389C2×D4311yescharacteristic
351#388—861no—
352#388—861no—
353#384—431no—
354#382—431no—
355#382—861no—
356#380—861no—
357C4×C4⋊C4—431no—
358C4×C4⋊C4—431no—
359C4×C4⋊C4—861no—
360C4×C4⋊C4C2×D4311yescharacteristic
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340C2×D4311yescharacteristic
367#340C2×D4311yescharacteristic
368#340C2×D4311yescharacteristic
369#336—431no—
370#336C2×D4311yescharacteristic
371C43#2278111yescharacteristic, complemented, Sylow
372C22×Q8—431no—
373C22×D4—431no—
374C23×C4—861no—
375C2×SD16—434no—
376C2×SD16—862no—
377C2×SD16—862no—
378C22×C8—431no—
379C22×C8—431no—
380C22×C8C22×D4311yescharacteristic
381C22×C8C22×D4311yescharacteristic
382C4×Q8—434no—
383C4×Q8—862no—
384C4×Q8—862no—
385C4×Q8—862no—
386C4×Q8—1721no—
387C4×Q8—1721no—
388C4×D4—434no—
389C4×D4—862no—
390#117—1724no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C42—21no—
412C2×C42—431no—
413C2×C42—431no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42—861no—
417C2×C42—861no—
418C2×C42C22×D4311yescharacteristic
419#107C4×D4314yes—
420C4⋊C8—862no—
421#103—434no—
422#103—862no—
423#103—862no—
424#102—434no—
425#102—1721no—
426#102—1721no—
427#97—434no—
428#97—1721no—
429C4×C8—1721no—
430#95—21no—
431#95—21no—
432#95—431no—
433#95—431no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438C24—861no—
439C2×Q8—432no—
440C2×Q8—432no—
441C2×Q8—432no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×Q8—861no—
445C2×D4—432no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—861no—
449C2×D4—861no—
450C2×D4—861no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—864no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—1722no—
464C22×C4—1722no—
465C22×C4D4×D4311yescharacteristic
466C22×C4D4×D4311yescharacteristic
467C22×C4C23×D4311yescharacteristic
468SD16—868no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—432no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8C2×C4×D4312yes—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—42no—
488C4⋊C4—862no—
489C4⋊C4—864no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—3441no—
495C4⋊C4—1721no—
496C4⋊C4—1722no—
497C4⋊C4—1722no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4C2×C4×D4312yes—
501C4⋊C4C2×C4×D4312yes—
502C22⋊C4—864no—
503C22⋊C4—3441no—
504C22⋊C4—3441no—
505C22⋊C4—1722no—
506C22⋊C4—1722no—
507C42—21no—
508C42—21no—
509C42—42no—
510C42—432no—
511C42—432no—
512C42—864no—
513C42—861no—
514C42—861no—
515C42—1722no—
516C42—1722no—
517C42—1722no—
518C23—862no—
519C23—1721no—
520C23—1721no—
521C23—1721no—
522C23—1721no—
523C23—1721no—
524C23—1721no—
525C23C2×D4×D4311yescharacteristic
526Q8—434no—
527Q8—862no—
528Q8—862no—
529Q8—862no—
530D4—862no—
531D4—862no—
532D4—1721no—
533D4—1721no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
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—432no—
553C2×C4—432no—
554C2×C4—432no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—862no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—1728no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4C22×C4×D4311yescharacteristic
575C2×C4#41×D4311yescharacteristic
576C2×C4#41×D4311yescharacteristic
577C2×C4#41×D4311yescharacteristic
578C2×C4#1306337111yescharacteristic
579C2×C4#1306337311yescharacteristic
580C8—22no—
581C8—41no—
582C8—862no—
583C8—1721no—
584C22—3441no—
585C22—3441no—
586C22—3441no—
587C22—3441no—
588C22—1722no—
589C22—1722no—
590C22—1722no—
591C22C4×D4×D4311yescharacteristic
592C22#1458354111yescharacteristic
593C22#1458355911yescharacteristic
594C22AGL(1,ℤ/8)×D4311yescharacteristic
595C22#1458369511yescharacteristic
596C22#1458370611yescharacteristic
597C22#1458371211yescharacteristic
598C4—41no—
599C4—41no—
600C4—42no—
601C4—42no—
602C4—81no—
603C4—81no—
604C4—862no—
605C4—862no—
606C4—862no—
607C4—864no—
608C4—3441no—
609C4—3441no—
610C4—1721no—
611C4#117×D4311yescharacteristic
612C4#1458338111yescharacteristic
613C4#1458358111yescharacteristic
614C4#1458360011yescharacteristic
615C2—3442no—
616C2#1913751911yescharacteristic
617C2#1914340611yescharacteristic
618C2#1914343311yescharacteristic
619C2#1914658911yescharacteristic
620C2#1914678411yescharacteristic
621C2#1914732711yescharacteristic
622C2#1914744411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1921C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1921D43
hypocenterC43#22781
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
3. #19137514C2semidirect
6. #19135168C2semidirect
9. #19134727C2semidirect
11. #19134599C2semidirect
12. #19134468C2semidirect
13. #19134428C2semidirect
14. #19134414C2semidirect
15. C43×#1921C2semidirect
22. #14582998C4semidirect
267. Dic86#117semidirect
309. #1921D43semidirect
371. C43#22781semidirect

Maximal subgroups

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

subgroupindex
C2×#145829982
#191375402
#191375142
#191352912
#191352792
#191351682
#191349512
#191349492
#191347272
#191346042
#191345992
#191344682
#191344282
#191344142
C43×#19212
#2278143