Finite Group Databasebeta

← #25140937

Subgroups — #25140937

Order 11008.

854 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138897C211yesmaximal, characteristic
2C4⋊C4×C22⋊D43C211yesmaximal, characteristic
3#19136155C211yesmaximal, characteristic, complemented
4#19136070C211yesmaximal, characteristic, complemented
5#19136022C211yesmaximal, characteristic, complemented
6#19136020C211yesmaximal, characteristic, complemented
7#19135165C211yesmaximal, characteristic, complemented
8#19135164C211yesmaximal, characteristic, complemented
9#19134887C211yesmaximal, characteristic
10#19134784C211yesmaximal, characteristic, complemented
11#19134783C211yesmaximal, characteristic, complemented
12#19134681C211yesmaximal, characteristic, complemented
13#19134680C211yesmaximal, characteristic, complemented
14#19134624C211yesmaximal, characteristic, complemented
15C2×C43×#340C211yesmaximal, characteristic, complemented
16C2×#13063308—21no—
17C2×C4×C22⋊D43—21no—
18C2×C4×C22⋊D43C2211yescharacteristic
19C2×C4⋊C4×D43C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25C2×(C2×D43)⋊C8C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27#14582830—21no—
28#14582825—21no—
29#14582795C2211yescharacteristic
30#14582795C2211yescharacteristic
31#14582794—21no—
32#14582772—21no—
33#14582770—21no—
34#14582768C2211yescharacteristic
35#14582762—21no—
36#14582759C2211yescharacteristic
37#14582759C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C23×C8×C43C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C22×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×C22⋊D43D411yescharacteristic
60C22×C4×D43—21no—
61C22×C4×D43C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063308—44no—
65C4×C22⋊D43—22no—
66C4×C22⋊D43—22no—
67C4×C22⋊D43—44no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4D411yescharacteristic
78C4⋊C4×D43—22no—
79C4⋊C4×D43—41no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43D411yescharacteristic
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4D411yescharacteristic
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89#13063259—22no—
90#13063259—41no—
91#13063258—22no—
92#13063258—41no—
93C22⋊(C43⋊C8)—22no—
94(C2×D43)⋊C8—22no—
95(C2×D43)⋊C8—41no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C23×C4×C43—21no—
105C23×C4×C43—21no—
106C23×C4×C43C2311yescharacteristic
107C22×C8×C43—22no—
108C22×C8×C43—22no—
109C22×C8×C43—41no—
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C2×C4⋊C4×C43—22no—
113C2×C4⋊C4×C43—22no—
114C2×C4⋊C4×C43—22no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—41no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C24×C43C2×D411yescharacteristic
123C23×D43C2×D411yescharacteristic
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—42no—
133C22×C4×C43—42no—
134C22×C4×C43—42no—
135C22×C4×C43—42no—
136C22×C4×C43—42no—
137C22×C4×C43—81no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43#4112yes—
140C22×C4×C43#4112yes—
141C22×C4×C43C2411yescharacteristic
142C2×C22⋊D43—22no—
143C2×C22⋊D43—22no—
144C2×C22⋊D43D814yes—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—81no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—44no—
167C2×C8×C43#4112yes—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—42no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43#4112yes—
178C22⋊Dic43—22no—
179C22⋊Dic43—42no—
180C22⋊Dic43—42no—
181(C2×D43)⋊C4—22no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—42no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193Dic43⋊C4—22no—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198Dic43⋊C4—81no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—42no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43#12312yes—
213C23×C43C2×D812yes—
214C23×C43#13712yes—
215C23×C43C22×D411yescharacteristic
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43C2×D812yes—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—84no—
242C2×C4×C43—84no—
243C2×C4×C43#12312yes—
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C22⋊D43—28no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43C2×D812yes—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—41no—
275C4×D43—41no—
276C4×D43—84no—
277C8×C43—22no—
278C8×C43—41no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281#24933—431nomaximal, Sylow
282C22×C43—22no—
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43#48014yes—
289C22×C43C2×#12311yescharacteristic
290C22×C43#54611yescharacteristic
291C22×C43#54711yescharacteristic
292C22×C43C22×D811yescharacteristic
293C22×C43C2×#13711yescharacteristic
294C22×C43#57711yescharacteristic
295C22×C43#57811yescharacteristic
296C2×D43—22no—
297C2×D43—22no—
298C2×D43—22no—
299C2×D43—41no—
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—41no—
303C4×C43—22no—
304C4×C43—42no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43#52911yescharacteristic
309C4×C43#53911yescharacteristic
310C4×C43#55111yescharacteristic
311C4×C43#55211yescharacteristic
312Dic43—22no—
313Dic43—41no—
314Dic43—41no—
315Dic43—81no—
316Dic43—81no—
317Dic43—81no—
318Dic43—81no—
319#2486—431no—
320D4×C4⋊C4—431no—
321#2099—431no—
322#2083—431no—
323#2075—431no—
324#2075—431no—
325#1918—431no—
326#1918—431no—
327#1869—431no—
328#1852—431no—
329#1852—431no—
330#1823—431no—
331#1823—431no—
332#1808—431no—
333C2×#340D4311yescharacteristic, complemented
334C2×C43—24no—
335C2×C43#241911yescharacteristic
336C2×C43C2×#48011yescharacteristic
337C2×C43#309711yescharacteristic
338C2×C43#329411yescharacteristic
339C2×C43#331211yescharacteristic
340C2×C43#333411yescharacteristic
341C2×C43#334411yescharacteristic
342D43—42no—
343C23×C8C2×D4311yescharacteristic
344C2×#123—861no—
345C2×C4×D4—431no—
346C2×C4×D4—861no—
347C22×C4⋊C4—431no—
348C22×C4⋊C4C2×D4311yescharacteristic
349C22×C4⋊C4C2×D4311yescharacteristic
350C2×#107—431no—
351C2×#107—431no—
352C2×#107—431no—
353C2×#107—431no—
354C2×C22⋊C8—431no—
355C2×C22⋊C8—431no—
356C2×C22⋊C8—431no—
357#398—861no—
358#397—861no—
359#389—431no—
360#389—431no—
361#389—861no—
362#385—861no—
363#385—861no—
364#384—431no—
365#381—861no—
366#380—431no—
367#380—431no—
368#380—431no—
369#380—431no—
370#380—431no—
371C4×C4⋊C4—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340C2×D4311yescharacteristic
381#340C2×D4311yescharacteristic
382#340C2×D4311yescharacteristic
383#340C2×D4311yescharacteristic
384#336—431no—
385#336—431no—
386C43#2493311yescharacteristic, complemented, Sylow
387C22×D4—431no—
388C23×C4—21no—
389C23×C4—21no—
390C23×C4—431no—
391C23×C4—861no—
392C23×C4C22×D4311yescharacteristic
393C22×C8—22no—
394C22×C8—22no—
395C22×C8—41no—
396C22×C8—431no—
397C22×C8—431no—
398C22×C8C22×D4311yescharacteristic
399C22×C8C22×D4311yescharacteristic
400#123—1724no—
401C4×D4—862no—
402C4×D4—862no—
403C4×D4—1724no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—41no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—862no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—1721no—
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C22⋊C4—431no—
427C2×C22⋊C4—431no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C42—431no—
434C2×C42—861no—
435#107—862no—
436#107—862no—
437#107—1721no—
438#107—1721no—
439C22⋊C8—862no—
440C22⋊C8—862no—
441C22⋊C8—1721no—
442#95—861no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450C24—431no—
451C24D4×D4311yescharacteristic
452C2×D4—434no—
453C2×D4—862no—
454C2×D4—862no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—81no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—3441no—
483C22×C4—1722no—
484C22×C4—1722no—
485C22×C4#1062189812yes—
486C22×C4D4×D4311yescharacteristic
487C22×C4#1062190012yes—
488C22×C4C23×D4311yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—44no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8#1062189812yes—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—862no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—3441no—
521C4⋊C4—1722no—
522C4⋊C4—1722no—
523C4⋊C4—1722no—
524C4⋊C4—1722no—
525C4⋊C4#1062189812yes—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—1722no—
529C22⋊C4—1722no—
530C22⋊C4—1722no—
531C22⋊C4—1722no—
532C22⋊C4—1722no—
533C42—861no—
534C42—861no—
535C42—1722no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—432no—
541C23—861no—
542C23—861no—
543C23—861no—
544C23—861no—
545C23—861no—
546C23—861no—
547C23#1306330712yes—
548C23D8×D4312yes—
549C23#1306335412yes—
550C23C2×D4×D4311yescharacteristic
551D4—868no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—84no—
571C2×C4—84no—
572C2×C4—432no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—3444no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4#1306330712yes—
599C2×C4C2×#1062190011yescharacteristic
600C2×C4C2×#1062189811yescharacteristic
601C2×C4C2×#1062189811yescharacteristic
602C2×C4C2×#1062189811yescharacteristic
603C2×C4#1306337011yescharacteristic
604C2×C4#1306337311yescharacteristic
605C8—22no—
606C8—41no—
607C8—1721no—
608C8—1721no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—862no—
616C22—862no—
617C22—862no—
618C22—1721no—
619C22—1721no—
620C22—1721no—
621C22—1721no—
622C22#1458321114yes—
623C22C2×#1306330711yescharacteristic
624C22#1458353911yescharacteristic
625C22#1458355011yescharacteristic
626C22C2×D8×D4311yescharacteristic
627C22C2×#1306335411yescharacteristic
628C22#1458370511yescharacteristic
629C22#1458371211yescharacteristic
630C4—22no—
631C4—42no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—862no—
636C4—3441no—
637C4—3441no—
638C4—3441no—
639C4—3441no—
640C4—1721no—
641C4—1721no—
642C4#1458343311yescharacteristic
643C4#1458349611yescharacteristic
644C4#1458357511yescharacteristic
645C4#1458358411yescharacteristic
646C2—24no—
647C2—1722no—
648C2#1913807211yescharacteristic
649C2C2×#1458321111yescharacteristic
650C2#1914456011yescharacteristic
651C2#1914640411yescharacteristic
652C2#1914664211yescharacteristic
653C2#1914694011yescharacteristic
654C2#1914704611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#340C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC2×#340D43
hypocenterC43#24933
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
3. #19136155C2semidirect
4. #19136070C2semidirect
5. #19136022C2semidirect
6. #19136020C2semidirect
7. #19135165C2semidirect
8. #19135164C2semidirect
10. #19134784C2semidirect
11. #19134783C2semidirect
12. #19134681C2semidirect
13. #19134680C2semidirect
14. #19134624C2semidirect
15. C2×C43×#340C2semidirect
333. C2×#340D43semidirect
386. C43#24933semidirect

Maximal subgroups

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

subgroupindex
#191388972
C4⋊C4×C22⋊D432
#191361552
#191360702
#191360222
#191360202
#191351652
#191351642
#191348872
#191347842
#191347832
#191346812
#191346802
#191346242
C2×C43×#3402
#2493343