Finite Group Databasebeta

← #25159572

Subgroups — #25159572

Order 11008.

896 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583197C211yesmaximal, characteristic, complemented
2#19138461C211yesmaximal, characteristic, complemented
3#19137500C211yesmaximal, characteristic, complemented
4#19136114C211yesmaximal, characteristic, complemented
5#19136079C211yesmaximal, characteristic, complemented
6#19135981C211yesmaximal, characteristic, complemented
7#19135931C211yesmaximal, characteristic, complemented
8#19135328C211yesmaximal, characteristic, complemented
9#19135152C211yesmaximal, characteristic, complemented
10#19134945C211yesmaximal, characteristic
11#19134945C211yesmaximal, characteristic
12#19134856C211yesmaximal, characteristic, complemented
13#19134856C211yesmaximal, characteristic, complemented
14#19134844C211yesmaximal, characteristic, complemented
15C2×C4×D8×C43C211yesmaximal, characteristic
16C2×#13063316C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19#14583197—24no—
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29#14582835—21no—
30#14582822—21no—
31#14582802C2211yescharacteristic
32#14582802C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582795C2211yescharacteristic
37#14582772—21no—
38#14582772—21no—
39#14582771—21no—
40#14582764C2211yescharacteristic
41#14582759—21no—
42#14582757—21no—
43C4×Dic43⋊C4C2211yescharacteristic
44C2×C43⋊#95—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×D8×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C4×D8×C43—24no—
57C2×#107×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic
61C23×Dic43—21no—
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063316—22no—
66#13063316—41no—
67D4×Dic43—22no—
68D4×Dic43—22no—
69D4×Dic43—22no—
70D4×Dic43—41no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4D411yescharacteristic
82C2×Dic43⋊C4D411yescharacteristic
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063259—22no—
92#13063259—22no—
93#13063256—22no—
94#13063256—41no—
95Dic43⋊C8—22no—
96#13063246—22no—
97#13063246—22no—
98#13063246—22no—
99#13063246—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×D4×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C23×C4×C43—21no—
112C2×D8×C43—22no—
113C2×D8×C43—22no—
114C2×D8×C43Q814yes—
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C4×D4×C43—22no—
118C4×D4×C43—22no—
119C4×D4×C43—41no—
120C4×D4×C43—41no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C42×C43C2311yescharacteristic
126#107×C43—22no—
127#102×C43—22no—
128#102×C43D414yes—
129C4×C8×C43—22no—
130C24×C43—21no—
131C24×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43C2×D412yes—
141C2×D4×C43C2×Q812yes—
142C2×D4×C43C2×Q812yes—
143C2×D4×C43#4112yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—42no—
147C22×C4×C43—42no—
148C22×C4×C43—42no—
149C22×C4×C43—42no—
150C22×C4×C43—81no—
151C22×C4×C43—81no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C22×Dic43—24no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—42no—
161C22×Dic43—42no—
162C22×Dic43—81no—
163C22×Dic43—81no—
164C22×Dic43—81no—
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169D8×C43—28no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43C2×D412yes—
175C2×C8×C43C2×Q812yes—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C2×D412yes—
180C22⋊C4×C43—42no—
181C22⋊C4×C43—42no—
182C42×C43—21no—
183C42×C43—21no—
184C22⋊Dic43—24no—
185C22⋊Dic43—42no—
186C22⋊Dic43—42no—
187C22⋊Dic43—81no—
188C22⋊Dic43—81no—
189C22⋊Dic43—81no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—42no—
198C4⋊Dic43—81no—
199C4⋊Dic43#4112yes—
200Dic43⋊C4—22no—
201Dic43⋊C4—41no—
202Dic43⋊C4—42no—
203Dic43⋊C4—81no—
204Dic43⋊C4—81no—
205Dic43⋊C4—81no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C23×C43—22no—
217C23×C43—22no—
218C23×C43—22no—
219C23×C43—22no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43C22×D411yescharacteristic
231D4×C43—22no—
232D4×C43—22no—
233D4×C43—22no—
234D4×C43—22no—
235D4×C43—22no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43C22⋊Q814yes—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—22no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
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×C43—84no—
252C2×C4×C43#13512yes—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×Q811yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×C4×C432−1+411yescharacteristic
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—22no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—84no—
284C2×Dic43—84no—
285C8×C43—22no—
286C8×C43—22no—
287C43⋊C8—41no—
288C43⋊C8—41no—
289#26370—431nomaximal, Sylow
290C22×C43—24no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—42no—
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43#52511yescharacteristic
305C22×C43D4211yescharacteristic
306C22×C43D4×Q811yescharacteristic
307C22×C43C2×#13511yescharacteristic
308C22×C43#57511yescharacteristic
309C22×C43#57611yescharacteristic
310C22×C43#57611yescharacteristic
311C4×C43—22no—
312C4×C43—41no—
313C4×C43—42no—
314C4×C43—81no—
315C4×C43C2×C22⋊Q811yescharacteristic
316C4×C43#53911yescharacteristic
317C4×C43#54711yescharacteristic
318C4×C43#55411yescharacteristic
319Dic43—41no—
320Dic43—41no—
321Dic43—42no—
322Dic43—41no—
323Dic43—41no—
324Dic43—81no—
325Dic43—81no—
326Dic43—81no—
327C2×#478—431no—
328C2×C4×D8D4311yescharacteristic
329#2454—431no—
330#2349—431no—
331#2092—431no—
332#2085—431no—
333#2067—431no—
334#2059—431no—
335#1942—431no—
336#1916—431no—
337#1879—431no—
338#1879—431no—
339#1864—431no—
340#1864—431no—
341#1862—431no—
342C2×C43—44no—
343C2×C43—82no—
344C2×C43#244911yescharacteristic
345C2×C43#310211yescharacteristic
346C2×C43#312211yescharacteristic
347C2×C43#326811yescharacteristic
348C2×C43#328011yescharacteristic
349C2×C43#338011yescharacteristic
350C2×C43#338911yescharacteristic
351C22×D8C2×D4311yescharacteristic
352C2×#125—431no—
353C2×C4×D4—431no—
354C2×C4×D4—431no—
355C2×C4×D4C2×D4311yescharacteristic
356C2×C4×D4C2×D4311yescharacteristic
357#478—864no—
358C4×D8—24no—
359C2×#107—431no—
360C2×#107—431no—
361C2×#107C2×D4311yescharacteristic
362C2×#106—431no—
363C2×#106—431no—
364C2×C4⋊C8—431no—
365C2×#102—431no—
366C2×#102—431no—
367C2×#102—431no—
368C2×#102—431no—
369C2×#102C2×D4311yescharacteristic
370C2×#102C2×D4311yescharacteristic
371C2×C4×C8C2×D4311yescharacteristic
372#399—861no—
373#396—861no—
374#390—431no—
375#390—431no—
376#389—431no—
377#389—431no—
378#389—431no—
379#389—431no—
380#385—861no—
381#385—861no—
382#385—861no—
383#382—431no—
384#380—861no—
385#380—861no—
386C4×C4⋊C4—431no—
387C2×#95—861no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#336—431no—
393#336—431no—
394#336—431no—
395#336—431no—
396C43#2637011yescharacteristic, complemented, Sylow
397C22×D4C22×D4311yescharacteristic
398C22×D4C22×D4311yescharacteristic
399C23×C4—21no—
400C23×C4—21no—
401C23×C4—861no—
402C23×C4—861no—
403C2×D8—22no—
404C2×D8—22no—
405C2×D8Dic8614yes—
406C22×C8—431no—
407C22×C8—431no—
408C22×C8C22×D4311yescharacteristic
409C22×C8C22×D4311yescharacteristic
410#125—862no—
411#125—1721no—
412C4×D4—22no—
413C4×D4—22no—
414C4×D4—41no—
415C4×D4—41no—
416C4×D4—862no—
417C4×D4—862no—
418C4×D4—862no—
419C4×D4—1721no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
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—431no—
443C2×C42—431no—
444C2×C42C22×D4311yescharacteristic
445#107—22no—
446#107—862no—
447#107—862no—
448#106—862no—
449#106—1721no—
450C4⋊C8—862no—
451#102—22no—
452#102—862no—
453#102—862no—
454#102—862no—
455#102—1721no—
456#102C22⋊D4314yes—
457C4×C8—22no—
458#95—431no—
459#95—431no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466C24—21no—
467C24—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4C2×Dic8612yes—
477C2×D4C2×Dic8612yes—
478C2×D4#1062189812yes—
479C2×D4C2×C22⋊D4312yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—864no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—3441no—
498C22×C4—3441no—
499C22×C4—3441no—
500C22×C4—1722no—
501C22×C4—1722no—
502C22×C4D4×D4311yescharacteristic
503C22×C4D4×D4311yescharacteristic
504C22×C4C23×D4311yescharacteristic
505D8—28no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8C2×Dic8612yes—
517C2×C8C2×C22⋊D4312yes—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—432no—
522C4⋊C4—862no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—3441no—
531C4⋊C4—3441no—
532C4⋊C4—3441no—
533C4⋊C4—3441no—
534C4⋊C4—1721no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C4⋊C4C2×C22⋊D4312yes—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—864no—
541C22⋊C4—3441no—
542C22⋊C4—3441no—
543C22⋊C4—3441no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C42—21no—
547C42—21no—
548C42—861no—
549C42—861no—
550C42—861no—
551C42—861no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23C2×D4×D4311yescharacteristic
567D4—22no—
568D4—22no—
569D4—22no—
570D4—22no—
571D4—22no—
572D4—41no—
573D4—41no—
574D4#1306330414yes—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—84no—
587C2×C4—84no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—862no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—3444no—
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×C4—1721no—
614C2×C4#1306334412yes—
615C2×C4C22×C22⋊D4311yescharacteristic
616C2×C4C22×Dic8611yescharacteristic
617C2×C4#41×D4311yescharacteristic
618C2×C4C2×#1062189811yescharacteristic
619C2×C4#1306337011yescharacteristic
620C2×C4#1306337211yescharacteristic
621C8—22no—
622C8—22no—
623C8—1721no—
624C8—1721no—
625C22—24no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22#1458340811yescharacteristic
640C22D4×C22⋊D4311yescharacteristic
641C22D4×Dic8611yescharacteristic
642C22C2×#1306334411yescharacteristic
643C22#1458369611yescharacteristic
644C22#1458370011yescharacteristic
645C22#1458370111yescharacteristic
646C4—22no—
647C4—42no—
648C4—41no—
649C4—81no—
650C4—3441no—
651C4—3441no—
652C4—3441no—
653C4—1721no—
654C4—1721no—
655C4—1722no—
656C4—1721no—
657C4—1721no—
658C4C2×#1306330411yescharacteristic
659C4#1458349111yescharacteristic
660C4#1458354811yescharacteristic
661C4#1458360811yescharacteristic
662C2—44no—
663C2—82no—
664C2#1913839811yescharacteristic
665C2#1914460911yescharacteristic
666C2#1914483511yescharacteristic
667C2#1914613511yescharacteristic
668C2#1914628011yescharacteristic
669C2#1914746011yescharacteristic
670C2#1914755111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C4×D8×C43C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
hypercenterC2×C4×D8D43
hypocenterC43#26370
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14583197C2semidirect
2. #19138461C2semidirect
3. #19137500C2semidirect
4. #19136114C2semidirect
5. #19136079C2semidirect
6. #19135981C2semidirect
7. #19135931C2semidirect
8. #19135328C2semidirect
9. #19135152C2semidirect
12. #19134856C2semidirect
13. #19134856C2semidirect
14. #19134844C2semidirect
396. C43#26370semidirect

Maximal subgroups

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

subgroupindex
C2×#145831972
#191384612
#191375002
#191361142
#191360792
#191359812
#191359312
#191353282
#191351522
#191349452
#191348562
#191348442
C2×C4×D8×C432
#2637043