Finite Group Databasebeta

← #25137900

Subgroups — #25137900

Order 11008.

912 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583178C211yesmaximal, characteristic, complemented
2C2×#14582954C211yesmaximal, characteristic, complemented
3#19142946C211yesmaximal, characteristic, complemented
4#19137103C211yesmaximal, characteristic
5#19136027C211yesmaximal, characteristic, complemented
6#19136024C211yesmaximal, characteristic, complemented
7#19135787C211yesmaximal, characteristic
8#19135786C211yesmaximal, characteristic
9#19135545C211yesmaximal, characteristic, complemented
10#19135355C211yesmaximal, characteristic, complemented
11#19135335C211yesmaximal, characteristic, complemented
12#19135292C211yesmaximal, characteristic, complemented
13#19135291C211yesmaximal, characteristic, complemented
14#19134594C211yesmaximal, characteristic, complemented
15C43×#1944C211yesmaximal, characteristic, complemented
16C2×#13063324C2211yescharacteristic
17C2×#13063303—21no—
18C2×#13063300C2211yescharacteristic
19C2×#13063287—21no—
20C2×#13063287C2211yescharacteristic
21C2×C42×D43C2211yescharacteristic
22#14583178—24no—
23#14582954—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×#13063236C2211yescharacteristic
35#14582803—21no—
36#14582801C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582794—21no—
39#14582789—21no—
40#14582777—21no—
41#14582768C2211yescharacteristic
42#14582758—21no—
43#14582756C2211yescharacteristic
44#14582756C2211yescharacteristic
45#14582756C2211yescharacteristic
46C4⋊C4×Dic43C2211yescharacteristic
47#14582746—21no—
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×D172—21no—
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C22×C4×D43D411yescharacteristic
66C22×C4×D43D411yescharacteristic
67C22×C4×D43C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063324—22no—
71#13063324—22no—
72#13063303—44no—
73#13063300—22no—
74#13063300—22no—
75#13063287—22no—
76#13063287—22no—
77#13063287—44no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊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×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43D411yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96C42×D43—22no—
97C42×D43—22no—
98#13063258—22no—
99#13063256—22no—
100Dic43⋊C8—22no—
101Dic43⋊C8D414yescomplemented
102#13063247—22no—
103#13063247—22no—
104#13063245—22no—
105#13063245—22no—
106(C2×D43)⋊C8—22no—
107(C2×D43)⋊C8—22no—
108#13063236—22no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123#107×C43—22no—
124#106×C43—22no—
125#97×C43—22no—
126#95×C43—21no—
127#95×C43—21no—
128C23×D43—21no—
129C23×D43C2×D411yescharacteristic
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×C43C2411yescharacteristic
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C2×D172—24no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—42no—
150C2×D172—42no—
151C2×D172#4112yes—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—22no—
159C2×C4×D43—22no—
160C2×C4×D43—22no—
161C2×C4×D43—22no—
162C2×C4×D43—22no—
163C2×C4×D43—41no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×Dic86—42no—
168C2×Dic86—42no—
169C2×Dic86—42no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43C2×D412yes—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—42no—
184C4⋊C4×C43—42no—
185C4⋊C4×C43#4112yes—
186C42×C43—21no—
187C42×C43—21no—
188(C2×D43)⋊C4—24no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—42no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205C4×Dic43—22no—
206C4×Dic43—22no—
207C4×Dic43—42no—
208C4×Dic43C2×D412yes—
209C4×Dic43#4112yes—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8C2×D412yes—
216C23×C43C22×D411yescharacteristic
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—22no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43#13712yes—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C432−1+411yescharacteristic
254C2×C4×C432−1+411yescharacteristic
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
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#12112yes—
270C2×Dic43#12112yes—
271C2×Dic43AGL(1,ℤ/8)12yes—
272C2×Dic43AGL(1,ℤ/8)12yes—
273D172—22no—
274D172—22no—
275D172—48no—
276D172—41no—
277D172—41no—
278C4×D43—44no—
279C4×D43—41no—
280C4×D43—41no—
281C4×D43—41no—
282C4×D43—41no—
283C4×D43—44no—
284C4×D43—84no—
285Dic86—84no—
286C8×C43—22no—
287C8×C43—41no—
288C43⋊C8—22no—
289C43⋊C8—41no—
290#24709—431nomaximal, Sylow
291C22×C43C2×#12111yescharacteristic
292C22×C43#52511yescharacteristic
293C22×C43#53611yescharacteristic
294C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
295C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C43C2×#13711yescharacteristic
297C22×C43#57511yescharacteristic
298C2×D43—22no—
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—41no—
302C2×D43—41no—
303C2×D43—41no—
304C2×D43—41no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—81no—
311C2×D43—81no—
312C4×C43—42no—
313C4×C43—41no—
314C4×C43—41no—
315C4×C43—81no—
316C4×C43—81no—
317C4×C43—81no—
318C4×C43#54711yescharacteristic
319C4×C43#54811yescharacteristic
320C4×C43#55211yescharacteristic
321C4×C43#55611yescharacteristic
322Dic43—22no—
323Dic43—41no—
324Dic43—81no—
325Dic43—81no—
326Dic43—81no—
327Dic43#46914yes—
328C2×#474—431no—
329C2×#432—431no—
330#2857—431no—
331C4×#121—431no—
332#2076—431no—
333#2076—431no—
334#2034—431no—
335#2034—431no—
336#1988—431no—
337#1948—431no—
338#1944—431no—
339#1944D4311yescharacteristic, complemented
340#1936—431no—
341#1936—431no—
342#1802—431no—
343C2×C43#241511yescharacteristic
344C2×C43C2×#46911yescharacteristic
345C2×C43#305611yescharacteristic
346C2×C43#311011yescharacteristic
347C2×C43#311511yescharacteristic
348C2×C43#323511yescharacteristic
349C2×C43#323911yescharacteristic
350D43—42no—
351D43—82no—
352C2×C4⋊Q8—431no—
353C2×C22⋊Q8—861no—
354C2×#121—431no—
355C2×C4×D4—431no—
356C2×C4×D4—861no—
357C22×C42—431no—
358#474—864no—
359#432—864no—
360C2×#107—431no—
361C2×#107C2×D4311yescharacteristic
362C2×#106—431no—
363C2×#106C2×D4311yescharacteristic
364C2×C4⋊C8—431no—
365C2×C4⋊C8—431no—
366C2×#102—431no—
367C2×#102—431no—
368C2×#102—431no—
369C2×#102—431no—
370C2×C22⋊C8—431no—
371C2×C22⋊C8—431no—
372C2×#97—431no—
373C2×#97C2×D4311yescharacteristic
374#391—861no—
375#390—431no—
376#389—431no—
377#389—861no—
378#389C2×D4311yescharacteristic
379#389C2×D4311yescharacteristic
380#388—861no—
381#386—861no—
382#384—431no—
383#380—431no—
384#380—431no—
385#380—431no—
386#380—861no—
387C4×C4⋊C4—431no—
388C4×C22⋊C4—861no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340—431no—
395#340C2×D4311yescharacteristic
396#340C2×D4311yescharacteristic
397C43#2470911yescharacteristic, complemented, Sylow
398C22×Q8—861no—
399C22×D4—431no—
400C22×D4—861no—
401C23×C4—431no—
402C23×C4—431no—
403C23×C4—431no—
404C23×C4—861no—
405C22×C8—431no—
406C22×C8—431no—
407C22×C8C22×D4311yescharacteristic
408C22×C8C22×D4311yescharacteristic
409C4⋊Q8—862no—
410C4⋊Q8—862no—
411C22⋊Q8—1724no—
412#121—862no—
413#121—862no—
414C4×D4—862no—
415C4×D4—862no—
416C4×D4—1724no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—862no—
441C2×C42—862no—
442C2×C42—861no—
443C2×C42C22×D4311yescharacteristic
444#107—22no—
445#107—862no—
446#106—22no—
447#106—862no—
448C4⋊C8—434no—
449C4⋊C8—862no—
450#102—862no—
451#102—862no—
452#102—862no—
453#102—862no—
454C22⋊C8—862no—
455C22⋊C8—862no—
456#97—22no—
457#97—862no—
458#95—21no—
459#95—21no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465C24—431no—
466C24—861no—
467C2×Q8—1722no—
468C2×Q8—1722no—
469C2×Q8—1722no—
470C2×D4—432no—
471C2×D4—864no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—1722no—
478C2×D4—1722no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—1721no—
501C22×C4—1722no—
502C22×C4—1722no—
503C22×C4—1722no—
504C22×C4D4×D4311yescharacteristic
505C22×C4D4×D4311yescharacteristic
506C22×C4C23×D4311yescharacteristic
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—432no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8D4×D4312yes—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4#1062189812yes—
539C22⋊C4—864no—
540C22⋊C4—1722no—
541C22⋊C4—1722no—
542C22⋊C4—1722no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C42—21no—
547C42—21no—
548C42—432no—
549C42—432no—
550C42—862no—
551C42—862no—
552C42—1722no—
553C23—432no—
554C23—861no—
555C23—861no—
556C23—861no—
557C23—861no—
558C23—861no—
559C23—861no—
560C23—862no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
565C23—1721no—
566C23—1721no—
567C23C2×D4×D4311yescharacteristic
568Q8—3444no—
569D4—862no—
570D4—862no—
571D4—1728no—
572D4—1721no—
573D4—1721no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—432no—
593C2×C4—432no—
594C2×C4—432no—
595C2×C4—432no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—3444no—
602C2×C4—1724no—
603C2×C4—1724no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4C2×D4×D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4#41×D4311yescharacteristic
620C2×C4C2×#1062189811yescharacteristic
621C2×C4#1306337311yescharacteristic
622C2×C4#1306337311yescharacteristic
623C8—22no—
624C8—41no—
625C8—862no—
626C8—1721no—
627C22—862no—
628C22—862no—
629C22—862no—
630C22—3441no—
631C22—3441no—
632C22—3441no—
633C22—3441no—
634C22—1722no—
635C22—1722no—
636C22—1722no—
637C22—1721no—
638C22—1721no—
639C22—1721no—
640C22—1721no—
641C22#121×D4311yescharacteristic
642C22#1458340811yescharacteristic
643C22#1458347411yescharacteristic
644C22AGL(1,ℤ/8)×D4311yescharacteristic
645C22AGL(1,ℤ/8)×D4311yescharacteristic
646C22#137×D4311yescharacteristic
647C22#1458369811yescharacteristic
648C4—41no—
649C4—42no—
650C4—41no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4—434no—
655C4—862no—
656C4—3441no—
657C4—3441no—
658C4—3441no—
659C4—1721no—
660C4#1458355011yescharacteristic
661C4#1458355911yescharacteristic
662C4#1458358111yescharacteristic
663C4#1458362111yescharacteristic
664C2—3442no—
665C2—1722no—
666C2#1913802311yescharacteristic
667C2#469×D4311yescharacteristic
668C2#1914422411yescharacteristic
669C2#1914469211yescharacteristic
670C2#1914474411yescharacteristic
671C2#1914579411yescharacteristic
672C2#1914582611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1944C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenter#1944D43
hypocenterC43#24709
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
1. C2×#14583178C2semidirect
2. C2×#14582954C2semidirect
3. #19142946C2semidirect
5. #19136027C2semidirect
6. #19136024C2semidirect
9. #19135545C2semidirect
10. #19135355C2semidirect
11. #19135335C2semidirect
12. #19135292C2semidirect
13. #19135291C2semidirect
14. #19134594C2semidirect
15. C43×#1944C2semidirect
101. Dic43⋊C8D4semidirect
339. #1944D43semidirect
397. C43#24709semidirect

Maximal subgroups

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

subgroupindex
C2×#145831782
C2×#145829542
#191429462
#191371032
#191360272
#191360242
#191357872
#191357862
#191355452
#191353552
#191353352
#191352922
#191352912
#191345942
C43×#19442
#2470943