Finite Group Databasebeta

← #25159574

Subgroups — #25159574

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×#14582979C211yesmaximal, characteristic
2#19138463C211yesmaximal, characteristic, complemented
3#19137500C211yesmaximal, characteristic, complemented
4#19136113C211yesmaximal, characteristic, complemented
5#19136080C211yesmaximal, characteristic, complemented
6#19135982C211yesmaximal, characteristic, complemented
7#19135930C211yesmaximal, characteristic, complemented
8#19135326C211yesmaximal, characteristic, complemented
9#19135149C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic
11#19134941C211yesmaximal, characteristic
12#19134854C211yesmaximal, characteristic, complemented
13#19134853C211yesmaximal, characteristic, complemented
14#19134844C211yesmaximal, characteristic, complemented
15C2×C43×#478C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20#14582979—24no—
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582834—21no—
30#14582821—21no—
31#14582801C2211yescharacteristic
32#14582800C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582795C2211yescharacteristic
37#14582772—21no—
38#14582771—21no—
39#14582770—21no—
40#14582764C2211yescharacteristic
41#14582757—21no—
42#14582756—21no—
43C4×Dic43⋊C4C2211yescharacteristic
44C2×C43⋊#95—21no—
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#125×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C43×#478—24no—
56C2×#107×C43C2211yescharacteristic
57C2×#106×C43C2211yescharacteristic
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C23×Dic43—21no—
63C23×Dic43—21no—
64C22×C4×D43—21no—
65C2×#10621882—22no—
66C2×#10621882—22no—
67C2×#10621882Q814yes—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70D4×Dic43—22no—
71D4×Dic43—22no—
72D4×Dic43—22no—
73D4×Dic43—41no—
74#13063287—22no—
75#13063287—41no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4D411yescharacteristic
84C2×Dic43⋊C4D411yescharacteristic
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×C4×Dic43C2311yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94#13063259—22no—
95#13063258—22no—
96#13063256—41no—
97#13063247—22no—
98#13063247—22no—
99#13063246—22no—
100#13063245—41no—
101C8×Dic43—22no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95D411yescharacteristic
109C43⋊#95D411yescharacteristic
110C22×D4×C43C2311yescharacteristic
111C23×C4×C43—21no—
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114#125×C43—22no—
115#125×C43—41no—
116C4×D4×C43—22no—
117C4×D4×C43—41no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124C2×C42×C43C2311yescharacteristic
125#107×C43—22no—
126#106×C43—22no—
127C4⋊C8×C43—22no—
128#102×C43—22no—
129#102×C43D414yes—
130C24×C43—21no—
131C23×D43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43C2×D412yes—
136C2×D4×C43C2×Q812yes—
137C2×D4×C43#4112yes—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—42no—
142C22×C4×C43—42no—
143C22×C4×C43—81no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—24no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43—81no—
154C22×Dic43—81no—
155C22×Dic43—81no—
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172C2×Q812yes—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×C4×D43—81no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43C2×D412yes—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—42no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43C2×D412yes—
183C22⋊C4×C43—42no—
184C42×C43—21no—
185C42×C43—21no—
186C22⋊Dic43—24no—
187C22⋊Dic43—42no—
188#10621882—28no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—81no—
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—81no—
200C4⋊Dic43#4112yes—
201Dic43⋊C4—22no—
202Dic43⋊C4—41no—
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⋊C8C2×Q812yes—
216C23×C43—22no—
217C23×C43—22no—
218C23×C43—22no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43C22×D411yescharacteristic
224C22×D43—22no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231D4×C43—22no—
232D4×C43—22no—
233D4×C43—22no—
234D4×C43C22⋊Q814yes—
235C2×C4×C43—22no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
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
257C2×Dic43—21no—
258C2×Dic43—21no—
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—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—84no—
278C2×Dic43—84no—
279C2×Dic43#13512yes—
280D172—22no—
281D172—22no—
282D172—41no—
283D172—41no—
284C4×D43—84no—
285C8×C43—22no—
286C8×C43—41no—
287C43⋊C8—22no—
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#52511yescharacteristic
298C22×C43D4211yescharacteristic
299C22×C43D4×Q811yescharacteristic
300C22×C43C2×#13511yescharacteristic
301C22×C43#57511yescharacteristic
302C22×C43#57611yescharacteristic
303C22×C43#57611yescharacteristic
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—81no—
311C4×C43—41no—
312C4×C43—42no—
313C4×C43—41no—
314C4×C43—81no—
315C4×C43—81no—
316C4×C43C2×C22⋊Q811yescharacteristic
317C4×C43#53911yescharacteristic
318C4×C43#54711yescharacteristic
319C4×C43#55411yescharacteristic
320Dic43—22no—
321Dic43—41no—
322Dic43—41no—
323Dic43—42no—
324Dic43—41no—
325Dic43—81no—
326Dic43—81no—
327C2×#478D4311yescharacteristic, complemented
328C2×C4×D8—431no—
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#244911yescharacteristic
344C2×C43#310211yescharacteristic
345C2×C43#312211yescharacteristic
346C2×C43#326811yescharacteristic
347C2×C43#328011yescharacteristic
348C2×C43#338011yescharacteristic
349C2×C43#338911yescharacteristic
350D43—82no—
351C22×D8—431no—
352C2×#125C2×D4311yescharacteristic
353C2×C4×D4—431no—
354C2×C4×D4—431no—
355C2×C4×D4—431no—
356C2×C4×D4C2×D4311yescharacteristic
357#478—24no—
358C4×D8—864no—
359C2×#107—431no—
360C2×#107—431no—
361C2×#107C2×D4311yescharacteristic
362C2×#106—431no—
363C2×#106C2×D4311yescharacteristic
364C2×C4⋊C8C2×D4311yescharacteristic
365C2×#102—431no—
366C2×#102—431no—
367C2×#102—431no—
368C2×#102—431no—
369C2×#102C2×D4311yescharacteristic
370C2×#102C2×D4311yescharacteristic
371C2×C4×C8—431no—
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×D4—431no—
398C22×D4C22×D4311yescharacteristic
399C23×C4—21no—
400C23×C4—861no—
401C23×C4—861no—
402C23×C4—861no—
403C2×D8—434no—
404C2×D8—862no—
405C2×D8—862no—
406C22×C8—431no—
407C22×C8—431no—
408C22×C8C22×D4311yescharacteristic
409C22×C8C22×D4311yescharacteristic
410#125—22no—
411#125—41no—
412C4×D4—22no—
413C4×D4—41no—
414C4×D4—862no—
415C4×D4—862no—
416C4×D4—862no—
417C4×D4—862no—
418C4×D4—1721no—
419C4×D4—1721no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—861no—
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—22no—
449#106—1721no—
450C4⋊C8—22no—
451#102—22no—
452#102—862no—
453#102—862no—
454#102—862no—
455#102—1721no—
456#102C22⋊D4314yes—
457C4×C8—862no—
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—861no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—432no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4Q8×D4312yes—
478C2×D4#1062190212yes—
479C2×D4C2×C22⋊D4312yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—81no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—864no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—3441no—
495C22×C4—3441no—
496C22×C4—3441no—
497C22×C4—3441no—
498C22×C4—1722no—
499C22×C4—1722no—
500C22×C4—1722no—
501C22×C4—1722no—
502C22×C4D4×D4311yescharacteristic
503C22×C4D4×D4311yescharacteristic
504C22×C4C23×D4311yescharacteristic
505D8—868no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—432no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8C2×C22⋊D4312yes—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—42no—
524C4⋊C4—42no—
525C4⋊C4—432no—
526C4⋊C4—862no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—3441no—
533C4⋊C4—3441no—
534C4⋊C4—3441no—
535C4⋊C4—3441no—
536C4⋊C4—1721no—
537C4⋊C4C2×C22⋊D4312yes—
538C22⋊C4—42no—
539C22⋊C4—864no—
540C22⋊C4—3441no—
541C22⋊C4—3441no—
542C22⋊C4—3441no—
543C22⋊C4—1722no—
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—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—862no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
565C23—1721no—
566C23C2×D4×D4311yescharacteristic
567D4—22no—
568D4—22no—
569D4—22no—
570D4—862no—
571D4—862no—
572D4—1721no—
573D4—1721no—
574D4#1306330114yes—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—84no—
591C2×C4—432no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—862no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—3444no—
605C2×C4—3444no—
606C2×C4—3444no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4C22×C22⋊D4311yescharacteristic
616C2×C4C2×Q8×D4311yescharacteristic
617C2×C4#41×D4311yescharacteristic
618C2×C4C2×#1062190211yescharacteristic
619C2×C4#1306337011yescharacteristic
620C2×C4#1306337211yescharacteristic
621C8—22no—
622C8—41no—
623C8—862no—
624C8—1721no—
625C22—24no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—3441no—
633C22—3441no—
634C22—3441no—
635C22—3441no—
636C22—1722no—
637C22—1722no—
638C22—1722no—
639C22#1458341211yescharacteristic
640C22D4×C22⋊D4311yescharacteristic
641C22#1458356211yescharacteristic
642C22#135×D4311yescharacteristic
643C22#1458369511yescharacteristic
644C22#1458370111yescharacteristic
645C22#1458370311yescharacteristic
646C4—41no—
647C4—42no—
648C4—41no—
649C4—81no—
650C4—81no—
651C4—862no—
652C4—3441no—
653C4—3441no—
654C4—1721no—
655C4—1722no—
656C4—1721no—
657C4—1721no—
658C4C2×#1306330111yescharacteristic
659C4#1458349811yescharacteristic
660C4#1458354811yescharacteristic
661C4#1458360311yescharacteristic
662C2—44no—
663C2—3442no—
664C2#1913840011yescharacteristic
665C2#1914461811yescharacteristic
666C2#1914484011yescharacteristic
667C2#1914612911yescharacteristic
668C2#1914627411yescharacteristic
669C2#1914745711yescharacteristic
670C2#1914755211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#478C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenterC2×#478D43
hypocenterC43#26370
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
2. #19138463C2semidirect
3. #19137500C2semidirect
4. #19136113C2semidirect
5. #19136080C2semidirect
6. #19135982C2semidirect
7. #19135930C2semidirect
8. #19135326C2semidirect
9. #19135149C2semidirect
12. #19134854C2semidirect
13. #19134853C2semidirect
14. #19134844C2semidirect
15. C2×C43×#478C2semidirect
327. C2×#478D43semidirect
396. C43#26370semidirect

Maximal subgroups

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

subgroupindex
C2×#145829792
#191384632
#191375002
#191361132
#191360802
#191359822
#191359302
#191353262
#191351492
#191349432
#191349412
#191348542
#191348532
#191348442
C2×C43×#4782
#2637043