Finite Group Databasebeta

← #25159517

Subgroups — #25159517

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×#14583199C211yesmaximal, characteristic, complemented
2C2×#14582938C211yesmaximal, characteristic, complemented
3#19138310C211yesmaximal, characteristic, complemented
4#19137607C211yesmaximal, characteristic
5#19136126C211yesmaximal, characteristic, complemented
6#19136096C211yesmaximal, characteristic, complemented
7#19135981C211yesmaximal, characteristic, complemented
8#19135934C211yesmaximal, characteristic, complemented
9#19135355C211yesmaximal, characteristic, complemented
10#19135164C211yesmaximal, characteristic, complemented
11#19135030C211yesmaximal, characteristic
12#19134914C211yesmaximal, characteristic
13#19134789C211yesmaximal, characteristic, complemented
14#19134779C211yesmaximal, characteristic, complemented
15C43×#1864C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19C2×C4×C22⋊D43—21no—
20C2×#13063283C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22#14583199—24no—
23#14582938—24no—
24C2×#13063259C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×Dic43⋊C8C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34#14582834—21no—
35#14582823—21no—
36#14582802C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582794—21no—
40#14582793—21no—
41#14582781—21no—
42#14582775—21no—
43#14582772—21no—
44#14582768C2211yescharacteristic
45#14582756C2211yescharacteristic
46C4⋊C4×Dic43C2211yescharacteristic
47C4×(C2×D43)⋊C4C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×C22⋊D43—21no—
62C22×C4×D43—21no—
63C22×C4×D43C2311yescharacteristic
64C2×#10621872—22no—
65C2×#10621872—22no—
66C2×#10621872—22no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063317—22no—
70#13063317—41no—
71#13063296—22no—
72#13063296Q814yes—
73C4×C22⋊D43—44no—
74#13063283—22no—
75#13063283—41no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
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⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C4⋊C4×D43—22no—
88C4⋊C4×D43—41no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4D411yescharacteristic
95C2×(C2×D43)⋊C4D411yescharacteristic
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99#13063259—22no—
100#13063258D414yescomplemented
101#13063257—41no—
102#13063256—22no—
103#13063256—22no—
104C4⋊(C43⋊C8)—22no—
105Dic43⋊C8—22no—
106#13063246—22no—
107#13063246—22no—
108(C2×D43)⋊C8—22no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95D411yescharacteristic
114C43⋊#95D411yescharacteristic
115C22×D4×C43C2311yescharacteristic
116C23×C4×C43—21no—
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C4×D4×C43—22no—
120C4×D4×C43—41no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C42×C43C2311yescharacteristic
127#106×C43—22no—
128#102×C43—22no—
129#102×C43—41no—
130#95×C43—21no—
131C24×C43—21no—
132C23×D43C2×D411yescharacteristic
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43C2×Q812yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—42no—
143C22×C4×C43—42no—
144C22×C4×C43—81no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C2×C22⋊D43—24no—
149C2×C22⋊D43—42no—
150C2×C22⋊D43—42no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
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—81no—
179C4⋊C4×C43C2×D412yes—
180C22⋊C4×C43—42no—
181C42×C43—21no—
182C42×C43—21no—
183C22⋊Dic43—24no—
184C22⋊Dic43—42no—
185C22⋊Dic43—81no—
186(C2×D43)⋊C4—22no—
187(C2×D43)⋊C4—41no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—81no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43C2×D412yes—
197C4⋊Dic43C2×Q812yes—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200Dic43⋊C4—42no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204Dic43⋊C4—81no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—42no—
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×C43—22no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43C22×D411yescharacteristic
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43C22⋊Q812yes—
231D4×C43—22no—
232D4×C43—22no—
233D4×C43—41no—
234D4×C43—41no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
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×C43—41no—
250C2×C4×C43—84no—
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C22×Q811yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C2×C4×C432−1+411yescharacteristic
257C22⋊D43—48no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43C22⋊Q812yes—
278C2×Dic43AGL(1,ℤ/8)12yes—
279C4×D43—22no—
280C4×D43—22no—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—84no—
284C8×C43—22no—
285C8×C43—41no—
286C43⋊C8—22no—
287C43⋊C8—41no—
288#26366—431nomaximal, Sylow
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43C2×C22⋊Q811yescharacteristic
297C22×C43D4211yescharacteristic
298C22×C43#54711yescharacteristic
299C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C43#57511yescharacteristic
301C22×C43#57711yescharacteristic
302C22×C43#57711yescharacteristic
303C2×D43—22no—
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—41no—
307C2×D43—41no—
308C2×D43—41no—
309C2×D43—41no—
310C4×C43—41no—
311C4×C43—42no—
312C4×C43—41no—
313C4×C43—81no—
314C4×C43—81no—
315C4×C43#52511yescharacteristic
316C4×C43#53911yescharacteristic
317C4×C43D4×Q811yescharacteristic
318C4×C43#55411yescharacteristic
319Dic43—22no—
320Dic43—22no—
321Dic43—42no—
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#1948—431no—
335#1918—431no—
336#1895—431no—
337#1875—431no—
338#1864D4311yescharacteristic, complemented
339#1853—431no—
340#1851—431no—
341C2×C43—82no—
342C2×C43#244911yescharacteristic
343C2×C43#307711yescharacteristic
344C2×C43#308411yescharacteristic
345C2×C43#327111yescharacteristic
346C2×C43#327211yescharacteristic
347C2×C43#334511yescharacteristic
348C2×C43#335111yescharacteristic
349D43—42no—
350C22×M16—431no—
351C2×#125—431no—
352C2×#121—431no—
353C2×C4×D4—861no—
354C2×C4×D4C2×D4311yescharacteristic
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×#106—431no—
364C2×#106C2×D4311yescharacteristic
365C2×C4⋊C8—431no—
366C2×C4⋊C8—431no—
367C2×#102—431no—
368C2×#102—431no—
369C2×#102C2×D4311yescharacteristic
370C2×#102C2×D4311yescharacteristic
371C2×C22⋊C8—431no—
372#399—861no—
373#396—861no—
374#390—431no—
375#389—431no—
376#389—431no—
377#389—861no—
378#389C2×D4311yescharacteristic
379#388—861no—
380#387—861no—
381#386—861no—
382#385—861no—
383#384—431no—
384#380—431no—
385C4×C4⋊C4—431no—
386C4×C22⋊C4—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340C2×D4311yescharacteristic
393#336—431no—
394#336C2×D4311yescharacteristic
395C43#2636611yescharacteristic, complemented, Sylow
396C22×D4—861no—
397C22×D4C22×D4311yescharacteristic
398C23×C4—21no—
399C23×C4—431no—
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—22no—
413C4×D4—41no—
414C4×D4—1724no—
415#117—862no—
416#117—1721no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—431no—
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—861no—
430C2×C4⋊C4—1721no—
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—431no—
436C2×C22⋊C4—431no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C42—431no—
443C2×C42—861no—
444C2×C42—861no—
445C2×C42C22×D4311yescharacteristic
446#107—434no—
447#107—862no—
448#106—22no—
449#106—862no—
450#106—862no—
451#106—1721no—
452C4⋊C8—862no—
453C4⋊C8—862no—
454#102—22no—
455#102—41no—
456#102—862no—
457#102—862no—
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—21no—
467C24—431no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—864no—
474C2×D4—1722no—
475C2×D4—1722no—
476C2×D4Q8×D4312yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—81no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—432no—
486C22×C4—432no—
487C22×C4—431no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—3441no—
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—81no—
521C4⋊C4—432no—
522C4⋊C4—432no—
523C4⋊C4—861no—
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⋊C4—1722no—
536C4⋊C4D4×D4312yes—
537C22⋊C4—42no—
538C22⋊C4—862no—
539C22⋊C4—864no—
540C22⋊C4—3441no—
541C22⋊C4—3441no—
542C22⋊C4—1721no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C42—21no—
546C42—21no—
547C42—861no—
548C42—861no—
549C42—1722no—
550C42—1722no—
551C23—22no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—432no—
559C23—861no—
560C23—861no—
561C23—861no—
562C23—861no—
563C23—861no—
564C23—861no—
565C23C2×D4×D4311yescharacteristic
566D4—22no—
567D4—22no—
568D4—41no—
569D4—41no—
570D4—1728no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
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—84no—
587C2×C4—432no—
588C2×C4—432no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—861no—
598C2×C4—862no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—862no—
602C2×C4—3444no—
603C2×C4—1721no—
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×C4C2×D4×D4311yescharacteristic
614C2×C4C2×Q8×D4311yescharacteristic
615C2×C4#41×D4311yescharacteristic
616C2×C4C2×#1062189811yescharacteristic
617C2×C4#1306337011yescharacteristic
618C2×C4#1306337211yescharacteristic
619C8—22no—
620C8—41no—
621C8—862no—
622C8—1721no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—862no—
631C22—862no—
632C22—862no—
633C22—1721no—
634C22—1721no—
635C22—1721no—
636C22—1721no—
637C22C22⋊Q8×D4311yescharacteristic
638C22#1458353111yescharacteristic
639C22#1458355411yescharacteristic
640C22AGL(1,ℤ/8)×D4311yescharacteristic
641C22#1458369611yescharacteristic
642C22#1458370511yescharacteristic
643C22#1458370911yescharacteristic
644C4—41no—
645C4—41no—
646C4—42no—
647C4—81no—
648C4—81no—
649C4—862no—
650C4—862no—
651C4—3441no—
652C4—3441no—
653C4—1721no—
654C4—1722no—
655C4—1722no—
656C4#1458340811yescharacteristic
657C4#1458349211yescharacteristic
658C4#1458356211yescharacteristic
659C4#1458360411yescharacteristic
660C2—82no—
661C2—1722no—
662C2#1913840311yescharacteristic
663C2#1914439011yescharacteristic
664C2#1914445211yescharacteristic
665C2#1914617311yescharacteristic
666C2#1914619311yescharacteristic
667C2#1914707011yescharacteristic
668C2#1914716011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1864C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#1864D43
hypocenterC43#26366
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
1. C2×#14583199C2semidirect
2. C2×#14582938C2semidirect
3. #19138310C2semidirect
5. #19136126C2semidirect
6. #19136096C2semidirect
7. #19135981C2semidirect
8. #19135934C2semidirect
9. #19135355C2semidirect
10. #19135164C2semidirect
13. #19134789C2semidirect
14. #19134779C2semidirect
15. C43×#1864C2semidirect
100. #13063258D4semidirect
338. #1864D43semidirect
395. C43#26366semidirect

Maximal subgroups

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

subgroupindex
C2×#145831992
C2×#145829382
#191383102
#191376072
#191361262
#191360962
#191359812
#191359342
#191353552
#191351642
#191350302
#191349142
#191347892
#191347792
C43×#18642
#2636643