Finite Group Databasebeta

← #25196678

Subgroups — #25196678

Order 11008.

804 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142946C211yesmaximal, characteristic
2C4×#13063305C211yesmaximal, characteristic
3#19136156C211yesmaximal, characteristic, complemented
4#19136135C211yesmaximal, characteristic, complemented
5#19135922C211yesmaximal, characteristic, complemented
6#19135735C211yesmaximal, characteristic, complemented
7#19135180C211yesmaximal, characteristic, complemented
8#19135027C211yesmaximal, characteristic
9#19135027C211yesmaximal, characteristic
10#19134852C211yesmaximal, characteristic, complemented
11#19134848C211yesmaximal, characteristic, complemented
12#19134627C211yesmaximal, characteristic
13#19134625C211yesmaximal, characteristic
14#19134287C211yesmaximal, characteristic
15C43×#1920C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×#13063324C2211yescharacteristic
19C2×#13063305C2211yescharacteristic
20C2×#13063303—21no—
21C2×C4×Dic86C2211yescharacteristic
22C2×C42×D43C2211yescharacteristic
23C2×#13063259C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30#14582804C2211yescharacteristic
31#14582803—21no—
32#14582798C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582794—21no—
35#14582784—21no—
36#14582773—21no—
37#14582768C2211yescharacteristic
38#14582758—21no—
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42C4×C4⋊Dic43—21no—
43C4×(C2×D43)⋊C4—21no—
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C22×Dic86C2311yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C2×#10621872—22no—
65C2×#10621872—22no—
66C2×#10621872—22no—
67C2×#10621872—22no—
68C2×#10621872—41no—
69C2×#10621872—41no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063324—41no—
73#13063324—41no—
74#13063305—22no—
75#13063305Q814yescomplemented
76#13063303—44no—
77C4×Dic86—41no—
78C4×Dic86—41no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43D411yescharacteristic
95C2×C4×Dic43D411yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97C42×D43—41no—
98C42×D43—41no—
99#13063259—41no—
100#13063258—41no—
101#13063256—22no—
102#13063250—22no—
103#13063250—41no—
104#13063248—22no—
105#13063248—41no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C42×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#106×C43—22no—
123#95×C43—21no—
124#95×C43—21no—
125C23×D43C2×D411yescharacteristic
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43—21no—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—41no—
148C2×C4×D43—41no—
149C2×C4×D43—41no—
150C2×C4×D43C2×Q812yes—
151C2×C4×D43#4112yes—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—42no—
158C2×Dic86—42no—
159C2×Dic86—42no—
160C2×Dic86C2×Q812yes—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43#4112yes—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—42no—
175C4⋊C4×C43C2×Q812yes—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—42no—
179(C2×D43)⋊C4—24no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—42no—
182(C2×D43)⋊C4—42no—
183C4⋊Dic43—24no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—41no—
199C4×Dic43—41no—
200C4×Dic43—42no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8#4112yes—
207#10621872—44no—
208#10621872—44no—
209C23×C43C22×D411yescharacteristic
210C22×D43—21no—
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43—21no—
215C22×D43—21no—
216C22×D43C22⋊Q812yes—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—22no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
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×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43#13712yes—
235C2×C4×C43C22×Q811yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43H(5,𝔽2)11yescharacteristic
240C2×C4×C43H(5,𝔽2)11yescharacteristic
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—22no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43C22⋊Q812yes—
260C2×Dic43AGL(1,ℤ/8)12yes—
261C2×Dic43#13712yes—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—44no—
267C4×D43—44no—
268Dic86—22no—
269Dic86—22no—
270Dic86—41no—
271Dic86—41no—
272Dic86—84no—
273C8×C43—22no—
274C8×C43—41no—
275C43⋊C8—22no—
276C43⋊C8—41no—
277#29165—431nomaximal, Sylow
278C22×C43C2×C22⋊Q811yescharacteristic
279C22×C43#53211yescharacteristic
280C22×C43#53411yescharacteristic
281C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C43C2×#13711yescharacteristic
283C22×C43C2×#13711yescharacteristic
284C22×C43#57511yescharacteristic
285C2×D43—22no—
286C2×D43—22no—
287C2×D43—22no—
288C2×D43—41no—
289C2×D43—41no—
290C2×D43—41no—
291C2×D43—41no—
292C4×C43—22no—
293C4×C43—42no—
294C4×C43—41no—
295C4×C43—81no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43#55111yescharacteristic
299C4×C43#55111yescharacteristic
300C4×C43#55411yescharacteristic
301C4×C43#55411yescharacteristic
302Dic43—22no—
303Dic43—22no—
304Dic43—22no—
305Dic43—42no—
306Dic43—81no—
307Dic43—81no—
308Dic43—81no—
309#2857—431no—
310C4×C22⋊Q8—431no—
311#2099—431no—
312#2096—431no—
313#2057—431no—
314#2024—431no—
315#1920—431no—
316#1920D4311yescharacteristic, complemented
317#1894—431no—
318#1894—431no—
319#1863—431no—
320#1863—431no—
321#1809—431no—
322#1809—431no—
323#1728—431no—
324C2×C43#256411yescharacteristic
325C2×C43#307811yescharacteristic
326C2×C43#307911yescharacteristic
327C2×C43#317211yescharacteristic
328C2×C43#318211yescharacteristic
329C2×C43#319411yescharacteristic
330C2×C43#319511yescharacteristic
331D43—42no—
332C22×M16—431no—
333C22×M16—431no—
334C2×C4⋊Q8—431no—
335C2×C22⋊Q8—431no—
336C2×C22⋊Q8—861no—
337C2×C4×Q8—431no—
338C22×C42—431no—
339C2×#107—431no—
340C2×#107—431no—
341C2×#106—431no—
342C2×#106C2×D4311yescharacteristic
343C2×#103—431no—
344C2×#103—431no—
345C2×#103—431no—
346C2×#103—431no—
347#391—431no—
348#391—861no—
349#389—431no—
350#389—431no—
351#389—861no—
352#389C2×D4311yescharacteristic
353#387—861no—
354#385—861no—
355#384—431no—
356#380—431no—
357#380—431no—
358#380—431no—
359#380—861no—
360C4×C4⋊C4—861no—
361C4×C4⋊C4C2×D4311yescharacteristic
362C4×C22⋊C4—861no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340C2×D4311yescharacteristic
369#340C2×D4311yescharacteristic
370#340C2×D4311yescharacteristic
371#336—431no—
372#336—431no—
373#336—431no—
374#336C2×D4311yescharacteristic
375C43#2916511yescharacteristic, complemented, Sylow
376C22×Q8—431no—
377C22×Q8—861no—
378C23×C4—431no—
379C23×C4—431no—
380C23×C4—431no—
381C2×M16—862no—
382C2×M16—862no—
383C2×M16—862no—
384C2×M16—862no—
385C2×M16—1721no—
386C2×M16—1721no—
387C22×C8—431no—
388C22×C8—431no—
389C22×C8C22×D4311yescharacteristic
390C22×C8C22×D4311yescharacteristic
391C4⋊Q8—1721no—
392C4⋊Q8—1721no—
393C22⋊Q8—434no—
394C22⋊Q8—862no—
395C22⋊Q8—1724no—
396C4×Q8—1721no—
397C4×Q8—1721no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C4⋊C4C22×D4311yescharacteristic
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C42—21no—
418C2×C42—431no—
419C2×C42—431no—
420C2×C42—431no—
421C2×C42—861no—
422C2×C42—1721no—
423C2×C42—1721no—
424C2×C42C22×D4311yescharacteristic
425#107—1721no—
426#107—1721no—
427#106—22no—
428#106—862no—
429#103—862no—
430#103—862no—
431#103—1721no—
432#103—1721no—
433#95—21no—
434#95—21no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442C24—431no—
443C2×Q8—432no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—1722no—
450C2×Q8—1722no—
451C2×Q8—1722no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—432no—
460C22×C4—432no—
461C22×C4—862no—
462C22×C4—862no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—862no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—1721no—
473C22×C4—1721no—
474C22×C4—1721no—
475C22×C4D4×D4311yescharacteristic
476C22×C4D4×D4311yescharacteristic
477C22×C4C23×D4311yescharacteristic
478M16—1724no—
479M16—1724no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—432no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8#1062189812yes—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—42no—
500C4⋊C4—864no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—1722no—
508C4⋊C4—1722no—
509C4⋊C4—1722no—
510C4⋊C4—1722no—
511C4⋊C4—1722no—
512C4⋊C4—1722no—
513C4⋊C4Q8×D4312yes—
514C22⋊C4—864no—
515C22⋊C4—1722no—
516C22⋊C4—1722no—
517C22⋊C4—1722no—
518C42—21no—
519C42—21no—
520C42—42no—
521C42—861no—
522C42—861no—
523C42—1721no—
524C42—1721no—
525C42—1722no—
526C23—432no—
527C23—861no—
528C23—861no—
529C23—861no—
530C23—861no—
531C23—861no—
532C23—861no—
533C23C2×D4×D4311yescharacteristic
534Q8—862no—
535Q8—862no—
536Q8—3444no—
537Q8—1721no—
538Q8—1721no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—432no—
557C2×C4—432no—
558C2×C4—432no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—1724no—
571C2×C4—1724no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4#1306335412yes—
584C2×C4C2×Q8×D4311yescharacteristic
585C2×C4#41×D4311yescharacteristic
586C2×C4#41×D4311yescharacteristic
587C2×C4C2×#1062189811yescharacteristic
588C2×C4#1306337111yescharacteristic
589C2×C4#1306337111yescharacteristic
590C8—22no—
591C8—41no—
592C8—862no—
593C8—1721no—
594C22—862no—
595C22—862no—
596C22—862no—
597C22—1721no—
598C22—1721no—
599C22—1721no—
600C22—1721no—
601C22C22⋊Q8×D4311yescharacteristic
602C22#1458344611yescharacteristic
603C22#1458346011yescharacteristic
604C22AGL(1,ℤ/8)×D4311yescharacteristic
605C22#137×D4311yescharacteristic
606C22C2×#1306335411yescharacteristic
607C22#1458369611yescharacteristic
608C4—22no—
609C4—41no—
610C4—42no—
611C4—81no—
612C4—81no—
613C4—81no—
614C4—862no—
615C4—862no—
616C4—862no—
617C4—3441no—
618C4—3441no—
619C4—3441no—
620C4—1722no—
621C4#1458357311yescharacteristic
622C4#1458357411yescharacteristic
623C4#1458360511yescharacteristic
624C4#1458360911yescharacteristic
625C2—1722no—
626C2#1913977411yescharacteristic
627C2#1914439811yescharacteristic
628C2#1914440711yescharacteristic
629C2#1914519711yescharacteristic
630C2#1914531011yescharacteristic
631C2#1914541311yescharacteristic
632C2#1914541811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1920C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1920D43
hypocenterC43#29165
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
3. #19136156C2semidirect
4. #19136135C2semidirect
5. #19135922C2semidirect
6. #19135735C2semidirect
7. #19135180C2semidirect
10. #19134852C2semidirect
11. #19134848C2semidirect
15. C43×#1920C2semidirect
75. #13063305Q8semidirect
316. #1920D43semidirect
375. C43#29165semidirect

Maximal subgroups

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

subgroupindex
#191429462
C4×#130633052
#191361562
#191361352
#191359222
#191357352
#191351802
#191350272
#191348522
#191348482
#191346272
#191346252
#191342872
C43×#19202
#2916543