Finite Group Databasebeta

← #25126524

Subgroups — #25126524

Order 11008.

814 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137076C211yesmaximal, characteristic
2#382×D43C211yesmaximal, characteristic
3#19136168C211yesmaximal, characteristic, complemented
4#19136167C211yesmaximal, characteristic, complemented
5#19136166C211yesmaximal, characteristic, complemented
6#19136165C211yesmaximal, characteristic, complemented
7#19136164C211yesmaximal, characteristic, complemented
8#19136163C211yesmaximal, characteristic, complemented
9#19136162C211yesmaximal, characteristic, complemented
10#19134313C211yesmaximal, characteristic
11#19134313C211yesmaximal, characteristic
12#19134313C211yesmaximal, characteristic
13#19134313C211yesmaximal, characteristic
14#19134287C211yesmaximal, characteristic
15C43×#2101C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×#13063283C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×C4⋊C4×D43C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C42×D43C2211yescharacteristic
23#14582798C2211yescharacteristic
24#14582797C2211yescharacteristic
25#14582795C2211yescharacteristic
26#14582773—21no—
27#14582770—21no—
28#14582765C2211yescharacteristic
29#14582764C2211yescharacteristic
30#14582764C2211yescharacteristic
31#14582763—21no—
32#14582763—21no—
33C4⋊C4×Dic43—21no—
34#14582750—21no—
35#95×D43—21no—
36#95×D43—21no—
37#14582662C2211yescharacteristic
38#14582662C2211yescharacteristic
39#14582662C2211yescharacteristic
40#14582662C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#382C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C4×D43—21no—
60C22×C4×D43—21no—
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C2×#10621872—22no—
65C2×#10621872—22no—
66C2×#10621872—22no—
67C2×#10621872—22no—
68C2×#10621872—22no—
69C2×#10621872—22no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063283—22no—
73#13063283—22no—
74#13063283—22no—
75#13063283Q814yes—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
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—
85C4⋊C4×D43—22no—
86C4⋊C4×D43—22no—
87C4⋊C4×D43—22no—
88C4⋊C4×D43—22no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43D411yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96C42×D43—22no—
97C42×D43—22no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118C23×D43C2×D411yescharacteristic
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2411yescharacteristic
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43C2×D411yescharacteristic
131C22×Dic43C2×D411yescharacteristic
132C22×Dic43C2×D411yescharacteristic
133C2×C4×D43—22no—
134C2×C4×D43—22no—
135C2×C4×D43—41no—
136C2×C4×D43—41no—
137C2×C4×D43—41no—
138C2×C4×D43—41no—
139C2×C4×D43—42no—
140C2×C4×D43—42no—
141C2×C4×D43—42no—
142C2×C4×D43—42no—
143C2×C4×D43—42no—
144C2×C4×D43—42no—
145C2×C4×D43C2×Q812yes—
146C2×C4×D43#4112yes—
147C2×C4×D43#4112yes—
148C2×C4×D43#4112yes—
149C2×C4×D43#4112yes—
150C2×C4×D43#4112yes—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—42no—
165C4⋊C4×C43C2×Q812yes—
166C42×C43—21no—
167C42×C43—21no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—42no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—42no—
178C4⋊Dic43C2×Q812yes—
179Dic43⋊C4—42no—
180Dic43⋊C4—42no—
181Dic43⋊C4—42no—
182Dic43⋊C4—42no—
183C4×Dic43—21no—
184C4×Dic43—21no—
185C4×Dic43—24no—
186C4×Dic43—22no—
187C4×Dic43—22no—
188C4×Dic43—42no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195#10621872—44no—
196#10621872—44no—
197C23×C43C22×D411yescharacteristic
198C22×D43—21no—
199C22×D43—21no—
200C22×D43—21no—
201C22×D43—21no—
202C22×D43C22⋊Q812yes—
203C22×D43#12312yes—
204C22×D43#12412yes—
205C2×C4×C43—22no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43C22×Q811yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×Dic43—22no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43C22⋊Q812yes—
248C2×Dic43#12312yes—
249C2×Dic43#12412yes—
250C4×D43—44no—
251C4×D43—44no—
252C4×D43—84no—
253C4×D43—84no—
254C4×D43#12514yes—
255C4×D43#12514yes—
256C4×D43#12614yes—
257C4×D43#12614yes—
258C8×C43—41no—
259C8×C43—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262#23746—431nomaximal, Sylow
263C22×C43C2×C22⋊Q811yescharacteristic
264C22×C43C2×#12311yescharacteristic
265C22×C43C2×#12411yescharacteristic
266C22×C43#57511yescharacteristic
267C22×C43#57511yescharacteristic
268C22×C43#57511yescharacteristic
269C22×C43#57511yescharacteristic
270C2×D43—22no—
271C2×D43—22no—
272C2×D43—22no—
273C2×D43—22no—
274C2×D43—22no—
275C2×D43—22no—
276C2×D43#40014yes—
277C4×C43—42no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43C2×#12511yescharacteristic
284C4×C43C2×#12511yescharacteristic
285C4×C43C2×#12611yescharacteristic
286C4×C43C2×#12611yescharacteristic
287Dic43—42no—
288Dic43—41no—
289Dic43—41no—
290Dic43—81no—
291Dic43—81no—
292Dic43—81no—
293Dic43#40014yes—
294#2296—431no—
295C2×#382—431no—
296#2101—431no—
297#2101—431no—
298#2101—431no—
299#2101—431no—
300#2101—431no—
301#2101—431no—
302#2101—431no—
303#2101D4311yescharacteristic, complemented
304#1736—431no—
305#1736—431no—
306#1736—431no—
307#1736—431no—
308#1728—431no—
309C2×C43C2×#40011yescharacteristic
310C2×C43#308011yescharacteristic
311C2×C43#308011yescharacteristic
312C2×C43#309311yescharacteristic
313C2×C43#309311yescharacteristic
314C2×C43#314011yescharacteristic
315C2×C43#314011yescharacteristic
316D43—24no—
317C22×M16—431no—
318C22×M16—431no—
319C2×#117—431no—
320C2×#117—431no—
321C22×C4⋊C4—431no—
322C22×C4⋊C4—431no—
323C22×C42—431no—
324#389—431no—
325#389—431no—
326#389—431no—
327#389C2×D4311yescharacteristic
328#385—861no—
329#385—861no—
330#382—431no—
331#382—431no—
332#382—431no—
333#382—861no—
334#382—861no—
335#382C2×D4311yescharacteristic
336C4×C4⋊C4—861no—
337C4×C4⋊C4—861no—
338C2×#95—861no—
339C2×#95—861no—
340#340—431no—
341#340—431no—
342#340—431no—
343#340—431no—
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340C2×D4311yescharacteristic
353#340C2×D4311yescharacteristic
354#340C2×D4311yescharacteristic
355#340C2×D4311yescharacteristic
356#336—431no—
357#336—431no—
358#336—431no—
359#336C2×D4311yescharacteristic
360C43#2374611yescharacteristic, complemented, Sylow
361C23×C4—431no—
362C23×C4—431no—
363C23×C4—431no—
364C23×C4—861no—
365C23×C4—861no—
366C2×M16—862no—
367C2×M16—862no—
368C2×M16—862no—
369C2×M16—862no—
370C2×M16—862no—
371C2×M16—862no—
372C22×C8—431no—
373C22×C8—431no—
374C22×C8C22×D4311yescharacteristic
375C22×C8C22×D4311yescharacteristic
376#117—434no—
377#117—862no—
378#117—862no—
379#117—862no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—862no—
386C2×C4⋊C4—862no—
387C2×C4⋊C4—862no—
388C2×C4⋊C4—862no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4C22×D4311yescharacteristic
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C42—431no—
401C2×C42—431no—
402C2×C42—431no—
403C2×C42—862no—
404C2×C42—862no—
405C2×C42—861no—
406C2×C42—861no—
407C2×C42C22×D4311yescharacteristic
408#95—21no—
409#95—21no—
410#95—21no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420C24—431no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—431no—
426C22×C4—432no—
427C22×C4—432no—
428C22×C4—432no—
429C22×C4—432no—
430C22×C4—432no—
431C22×C4—432no—
432C22×C4—431no—
433C22×C4—431no—
434C22×C4—862no—
435C22×C4—862no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—1721no—
441C22×C4—1721no—
442C22×C4—1721no—
443C22×C4—1721no—
444C22×C4—1722no—
445C22×C4—1722no—
446C22×C4—1722no—
447C22×C4—1722no—
448C22×C4—1722no—
449C22×C4—1722no—
450C22×C4D4×D4311yescharacteristic
451C22×C4D4×D4311yescharacteristic
452C22×C4C23×D4311yescharacteristic
453M16—1724no—
454M16—1724no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—42no—
475C4⋊C4—432no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—1722no—
484C4⋊C4—1722no—
485C4⋊C4—1722no—
486C4⋊C4—1722no—
487C4⋊C4—1722no—
488C4⋊C4Q8×D4312yes—
489C22⋊C4—864no—
490C22⋊C4—1722no—
491C42—21no—
492C42—21no—
493C42—862no—
494C42—862no—
495C42—864no—
496C42—861no—
497C42—861no—
498C42—1722no—
499C23—432no—
500C23—432no—
501C23—432no—
502C23—861no—
503C23—861no—
504C23—861no—
505C23—861no—
506C23C2×D4×D4311yescharacteristic
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—432no—
526C2×C4—432no—
527C2×C4—432no—
528C2×C4—434no—
529C2×C4—434no—
530C2×C4—434no—
531C2×C4—434no—
532C2×C4—862no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—3444no—
540C2×C4—3444no—
541C2×C4—1724no—
542C2×C4—1724no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4C2×Q8×D4311yescharacteristic
555C2×C4#41×D4311yescharacteristic
556C2×C4#41×D4311yescharacteristic
557C2×C4#41×D4311yescharacteristic
558C2×C4#41×D4311yescharacteristic
559C2×C4#41×D4311yescharacteristic
560C8—41no—
561C8—41no—
562C8—1721no—
563C8—1721no—
564C22—434no—
565C22—862no—
566C22—862no—
567C22—862no—
568C22—862no—
569C22—862no—
570C22—862no—
571C22C22⋊Q8×D4311yescharacteristic
572C22#123×D4311yescharacteristic
573C22#124×D4311yescharacteristic
574C22#1458369511yescharacteristic
575C22#1458369611yescharacteristic
576C22#1458369611yescharacteristic
577C22#1458369811yescharacteristic
578C4—41no—
579C4—41no—
580C4—42no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—434no—
585C4—3441no—
586C4—3441no—
587C4—3441no—
588C4—1721no—
589C4—1721no—
590C4—1722no—
591C4#125×D4311yescharacteristic
592C4#125×D4311yescharacteristic
593C4#126×D4311yescharacteristic
594C4#126×D4311yescharacteristic
595C2—864no—
596C2#400×D4311yescharacteristic
597C2#1914441211yescharacteristic
598C2#1914441411yescharacteristic
599C2#1914452311yescharacteristic
600C2#1914452711yescharacteristic
601C2#1914497811yescharacteristic
602C2#1914498011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2101C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2101D43
hypocenterC43#23746
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2101

Complements

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

NH ≅ G/Ntype
3. #19136168C2semidirect
4. #19136167C2semidirect
5. #19136166C2semidirect
6. #19136165C2semidirect
7. #19136164C2semidirect
8. #19136163C2semidirect
9. #19136162C2semidirect
15. C43×#2101C2semidirect
303. #2101D43semidirect
360. C43#23746semidirect

Maximal subgroups

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

subgroupindex
#191370762
#382×D432
#191361682
#191361672
#191361662
#191361652
#191361642
#191361632
#191361622
#191343132
#191342872
C43×#21012
#2374643