Finite Group Databasebeta

← #25159525

Subgroups — #25159525

Order 11008.

896 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583198C211yesmaximal, characteristic, complemented
2C2×#14582938C211yesmaximal, characteristic, complemented
3#19138311C211yesmaximal, characteristic, complemented
4#19137613C211yesmaximal, characteristic
5#19136129C211yesmaximal, characteristic, complemented
6#19136098C211yesmaximal, characteristic, complemented
7#19135982C211yesmaximal, characteristic, complemented
8#19135936C211yesmaximal, characteristic, complemented
9#19135166C211yesmaximal, characteristic, complemented
10#19135032C211yesmaximal, characteristic
11#19134916C211yesmaximal, characteristic
12#19134853C211yesmaximal, characteristic, complemented
13#19134786C211yesmaximal, characteristic, complemented
14#19134776C211yesmaximal, characteristic, complemented
15C43×#1948C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063300C2211yescharacteristic
19C2×C4×D172—21no—
20C2×#13063287C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14583198—24no—
24#14582938—24no—
25C2×#13063259C2211yescharacteristic
26C2×#13063258C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×Dic43⋊C8C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35#14582834—21no—
36#14582821—21no—
37#14582801C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582795C2211yescharacteristic
41#14582794—21no—
42#14582790—21no—
43#14582785—21no—
44#14582777—21no—
45#14582773—21no—
46#14582756C2211yescharacteristic
47C4×(C2×D43)⋊C4C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C43×#384C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×D172—21no—
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43C2311yescharacteristic
66C2×#10621872—22no—
67C2×#10621872—22no—
68C2×#10621872—22no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063316—22no—
72#13063316—41no—
73#13063300—22no—
74#13063300Q814yes—
75C4×D172—44no—
76#13063287—22no—
77#13063287—41no—
78#13063283—22no—
79#13063283—41no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C4⋊C4×D43—22no—
90C4⋊C4×D43—41no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4D411yescharacteristic
98C2×(C2×D43)⋊C4D411yescharacteristic
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101#13063259—22no—
102#13063258D414yescomplemented
103#13063256—22no—
104#13063256—41no—
105Dic43⋊C8—22no—
106#13063247—22no—
107#13063247—22no—
108#13063245—22no—
109#13063245—41no—
110(C2×D43)⋊C8—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C42×C43—21no—
126C2×C42×C43C2311yescharacteristic
127#106×C43—22no—
128#106×C43—22no—
129C4⋊C8×C43—22no—
130#95×C43—21no—
131C23×D43—21no—
132C23×D43C2×D411yescharacteristic
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C2×D172—21no—
147C2×D172—24no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—42no—
153C2×D172—42no—
154C2×D172C2×Q812yes—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43—81no—
164C2×C4×D43—81no—
165C2×C4×D43C2×Q812yes—
166C2×C4×D43#4112yes—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43#4112yes—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—42no—
180C4⋊C4×C43—81no—
181C4⋊C4×C43C2×D412yes—
182C4⋊C4×C43C2×Q812yes—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—42no—
186(C2×D43)⋊C4—22no—
187(C2×D43)⋊C4—24no—
188(C2×D43)⋊C4—41no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—81no—
193(C2×D43)⋊C4—81no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—42no—
200C4⋊Dic43—42no—
201C4⋊Dic43C2×D412yes—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205Dic43⋊C4—81no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—42no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8C2×D412yes—
215#10621872—28no—
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×D43C22⋊Q812yes—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
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×C43AGL(1,ℤ/8)12yes—
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×Q811yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C432−1+411yescharacteristic
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—22no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43C22⋊Q812yes—
273D172—22no—
274D172—22no—
275D172—48no—
276D172—41no—
277D172—41no—
278C4×D43—22no—
279C4×D43—22no—
280C4×D43—22no—
281C4×D43—22no—
282C4×D43—84no—
283C4×D43—84no—
284C8×C43—22no—
285C8×C43—41no—
286C43⋊C8—22no—
287C43⋊C8—41no—
288#26366—431nomaximal, Sylow
289C22×C43C2×C22⋊Q811yescharacteristic
290C22×C43D4211yescharacteristic
291C22×C43#54711yescharacteristic
292C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C43#57511yescharacteristic
294C22×C43#57711yescharacteristic
295C22×C43#57711yescharacteristic
296C2×D43—22no—
297C2×D43—22no—
298C2×D43—22no—
299C2×D43—41no—
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—41no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C4×C43—22no—
311C4×C43—42no—
312C4×C43—41no—
313C4×C43—42no—
314C4×C43—81no—
315C4×C43—81no—
316C4×C43#52511yescharacteristic
317C4×C43#53911yescharacteristic
318C4×C43D4×Q811yescharacteristic
319C4×C43#55411yescharacteristic
320Dic43—22no—
321Dic43—41no—
322Dic43—41no—
323Dic43—42no—
324Dic43—81no—
325Dic43—81no—
326C2×#478—431no—
327C2×#428—431no—
328#2441—431no—
329#2361—431no—
330#2094—431no—
331#2088—431no—
332#2067—431no—
333#2059—431no—
334#1948D4311yescharacteristic, complemented
335#1918—431no—
336#1895—431no—
337#1875—431no—
338#1864—431no—
339#1853—431no—
340#1851—431no—
341C2×C43#244911yescharacteristic
342C2×C43#307711yescharacteristic
343C2×C43#308411yescharacteristic
344C2×C43#327111yescharacteristic
345C2×C43#327211yescharacteristic
346C2×C43#334511yescharacteristic
347C2×C43#335111yescharacteristic
348D43—42no—
349D43—82no—
350C22×M16—431no—
351C2×#125—431no—
352C2×#121—431no—
353C2×C4×D4—431no—
354C2×C4×D4—861no—
355C2×#117—431no—
356C22×C4⋊C4—431no—
357#478—864no—
358#428—864no—
359C2×#107—431no—
360C2×#107—431no—
361C2×#106—431no—
362C2×#106—431no—
363C2×#106C2×D4311yescharacteristic
364C2×#106C2×D4311yescharacteristic
365C2×C4⋊C8—431no—
366C2×C4⋊C8C2×D4311yescharacteristic
367C2×#102—431no—
368C2×#102—431no—
369C2×#102—431no—
370C2×#102—431no—
371C2×C22⋊C8—431no—
372#399—861no—
373#396—861no—
374#390—431no—
375#389—431no—
376#389—431no—
377#389—431no—
378#389—861no—
379#388—861no—
380#387—861no—
381#386—861no—
382#385—861no—
383#384C2×D4311yescharacteristic
384#380—431no—
385C4×C4⋊C4C2×D4311yescharacteristic
386C4×C22⋊C4—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340C2×D4311yescharacteristic
392#340C2×D4311yescharacteristic
393#336—431no—
394#336—431no—
395C43#2636611yescharacteristic, complemented, Sylow
396C22×D4—431no—
397C22×D4—861no—
398C23×C4—431no—
399C23×C4—861no—
400C23×C4—861no—
401C2×M16—862no—
402C2×M16—862no—
403C2×M16—862no—
404C22×C8—431no—
405C22×C8—431no—
406C22×C8C22×D4311yescharacteristic
407C22×C8C22×D4311yescharacteristic
408#125—862no—
409#125—1721no—
410#121—434no—
411#121—862no—
412C4×D4—862no—
413C4×D4—1724no—
414C4×D4—1721no—
415#117—862no—
416#117—1721no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—862no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—1721no—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C22⋊C4—431no—
435C2×C22⋊C4—431no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C42—21no—
443C2×C42—431no—
444C2×C42—861no—
445C2×C42C22×D4311yescharacteristic
446#107—434no—
447#107—862no—
448#106—22no—
449#106—22no—
450#106—862no—
451#106—1721no—
452C4⋊C8—22no—
453C4⋊C8—862no—
454#102—862no—
455#102—862no—
456#102—862no—
457#102—1721no—
458C22⋊C8—862no—
459#95—21no—
460#95—431no—
461#95—431no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466C24—431no—
467C24—861no—
468C2×D4—432no—
469C2×D4—864no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—1722no—
476C2×D4—1722no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—431no—
482C22×C4—432no—
483C22×C4—432no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—3441no—
494C22×C4—3441no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4—1722no—
498C22×C4—1722no—
499C22×C4D4×D4311yescharacteristic
500C22×C4D4×D4311yescharacteristic
501C22×C4C23×D4311yescharacteristic
502M16—868no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—432no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8#1062189812yes—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—42no—
522C4⋊C4—81no—
523C4⋊C4—432no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—3441no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C4⋊C4—1722no—
534C4⋊C4—1722no—
535C4⋊C4D4×D4312yes—
536C4⋊C4Q8×D4312yes—
537C22⋊C4—864no—
538C22⋊C4—862no—
539C22⋊C4—3441no—
540C22⋊C4—3441no—
541C22⋊C4—1721no—
542C22⋊C4—1722no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C42—21no—
546C42—21no—
547C42—42no—
548C42—861no—
549C42—861no—
550C42—1722no—
551C23—432no—
552C23—861no—
553C23—861no—
554C23—861no—
555C23—861no—
556C23—861no—
557C23—861no—
558C23—862no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
565C23C2×D4×D4311yescharacteristic
566D4—862no—
567D4—862no—
568D4—1728no—
569D4—1721no—
570D4—1721no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—432no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—862no—
602C2×C4—3444no—
603C2×C4—3444no—
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#1306335212yes—
613C2×C4C2×D4×D4311yescharacteristic
614C2×C4C2×Q8×D4311yescharacteristic
615C2×C4#41×D4311yescharacteristic
616C2×C4C2×#1062189811yescharacteristic
617C2×C4#1306337111yescharacteristic
618C2×C4#1306337311yescharacteristic
619C8—22no—
620C8—41no—
621C8—862no—
622C8—1721no—
623C22—862no—
624C22—862no—
625C22—862no—
626C22—3441no—
627C22—3441no—
628C22—3441no—
629C22—3441no—
630C22—1722no—
631C22—1722no—
632C22—1722no—
633C22—1721no—
634C22—1721no—
635C22—1721no—
636C22—1721no—
637C22C22⋊Q8×D4311yescharacteristic
638C22#1458353311yescharacteristic
639C22#1458355011yescharacteristic
640C22C2×#1306335211yescharacteristic
641C22#1458369511yescharacteristic
642C22#1458370511yescharacteristic
643C22#1458370811yescharacteristic
644C4—22no—
645C4—41no—
646C4—42no—
647C4—42no—
648C4—81no—
649C4—81no—
650C4—862no—
651C4—3441no—
652C4—3441no—
653C4—1721no—
654C4—1721no—
655C4—1722no—
656C4#1458340811yescharacteristic
657C4#1458349711yescharacteristic
658C4#1458356411yescharacteristic
659C4#1458360911yescharacteristic
660C2—3442no—
661C2—1722no—
662C2#1913841111yescharacteristic
663C2#1914439311yescharacteristic
664C2#1914445411yescharacteristic
665C2#1914617511yescharacteristic
666C2#1914619811yescharacteristic
667C2#1914706111yescharacteristic
668C2#1914715111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1948C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenter#1948D43
hypocenterC43#26366
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
1. C2×#14583198C2semidirect
2. C2×#14582938C2semidirect
3. #19138311C2semidirect
5. #19136129C2semidirect
6. #19136098C2semidirect
7. #19135982C2semidirect
8. #19135936C2semidirect
9. #19135166C2semidirect
12. #19134853C2semidirect
13. #19134786C2semidirect
14. #19134776C2semidirect
15. C43×#1948C2semidirect
102. #13063258D4semidirect
334. #1948D43semidirect
395. C43#26366semidirect

Maximal subgroups

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

subgroupindex
C2×#145831982
C2×#145829382
#191383112
#191376132
#191361292
#191360982
#191359822
#191359362
#191351662
#191350322
#191349162
#191348532
#191347862
#191347762
C43×#19482
#2636643