Finite Group Databasebeta

← #25137983

Subgroups — #25137983

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583206C211yesmaximal, characteristic, complemented
2C2×#14582959C211yesmaximal, characteristic
3#19140428C211yesmaximal, characteristic
4#19137271C211yesmaximal, characteristic
5#19136034C211yesmaximal, characteristic
6#19136022C211yesmaximal, characteristic
7#19135796C211yesmaximal, characteristic
8#19135796C211yesmaximal, characteristic
9#19135550C211yesmaximal, characteristic, complemented
10#19135351C211yesmaximal, characteristic, complemented
11#19135332C211yesmaximal, characteristic, complemented
12#19135327C211yesmaximal, characteristic, complemented
13#19135287C211yesmaximal, characteristic, complemented
14#19135273C211yesmaximal, characteristic, complemented
15C43×#1803C211yesmaximal, characteristic, complemented
16C2×#13063317C2211yescharacteristic
17C2×#13063301C2211yescharacteristic
18C2×#13063282C2211yescharacteristic
19#14583206—24no—
20#14582959—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582829—21no—
33#14582829—21no—
34#14582821—21no—
35#14582821—21no—
36#14582806C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582794—21no—
41#14582790—21no—
42#14582789—21no—
43#14582783—21no—
44#14582756C2211yescharacteristic
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47C4×C4⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C43×#384C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×C4×D43C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063317—22no—
65#13063317—22no—
66#13063301—22no—
67#13063301—22no—
68#13063282—22no—
69#13063282—22no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4D411yescharacteristic
81C2×Dic43⋊C4D411yescharacteristic
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4D411yescharacteristic
87C2×(C2×D43)⋊C4D411yescharacteristic
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90#13063258—22no—
91#13063258—22no—
92#13063258—22no—
93#13063256—22no—
94C4⋊(C43⋊C8)D414yes—
95#13063249—22no—
96#13063249—22no—
97(C2×D43)⋊C8—22no—
98(C2×D43)⋊C8—22no—
99#13063235—22no—
100C8×Dic43—22no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C22×Q8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C4×Q8×C43—22no—
114C4×Q8×C43—22no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123C4⋊C8×C43—22no—
124#103×C43—22no—
125#103×C43—22no—
126C23×D43C2×D411yescharacteristic
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43#4112yes—
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×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—42no—
166C4⋊C4×C43—81no—
167C4⋊C4×C43—81no—
168C42×C43—42no—
169C42×C43C2×D412yes—
170C42×C43#4112yes—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—22no—
173(C2×D43)⋊C4—22no—
174(C2×D43)⋊C4—81no—
175(C2×D43)⋊C4—81no—
176(C2×D43)⋊C4—81no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—81no—
185C4⋊Dic43—81no—
186C4⋊Dic43#4112yes—
187Dic43⋊C4—24no—
188Dic43⋊C4—22no—
189Dic43⋊C4—22no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—81no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—81no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8C2×D412yes—
201C2×C43⋊C8C2×D412yes—
202C23×C43C22×D411yescharacteristic
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210Q8×C43—22no—
211Q8×C43—22no—
212Q8×C43—41no—
213Q8×C43—41no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43#12112yes—
231C2×C4×C43#12112yes—
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C432−1+411yescharacteristic
237C2×C4×C432−1+411yescharacteristic
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—22no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C4×D43—41no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—41no—
263C8×C43—41no—
264C8×C43—41no—
265C43⋊C8—22no—
266C43⋊C8—22no—
267#24715—431nomaximal, Sylow
268C22×C43C2×#12111yescharacteristic
269C22×C43#52511yescharacteristic
270C22×C43#53611yescharacteristic
271C22×C43#57611yescharacteristic
272C22×C43#57711yescharacteristic
273C22×C43#57811yescharacteristic
274C22×C43#57811yescharacteristic
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—41no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C4×C43—22no—
283C4×C43—22no—
284C4×C43—42no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43#54711yescharacteristic
289C4×C43#54811yescharacteristic
290C4×C43#55211yescharacteristic
291C4×C43#55611yescharacteristic
292Dic43—42no—
293Dic43—41no—
294Dic43—41no—
295Dic43—41no—
296Dic43—81no—
297Dic43—81no—
298Dic43—81no—
299C2×#479—431no—
300C2×#433—431no—
301#2629—431no—
302#2323—431no—
303#2077—431no—
304#2075—431no—
305#2036—431no—
306#2036—431no—
307#1989—431no—
308#1947—431no—
309#1943—431no—
310#1942—431no—
311#1935—431no—
312#1933—431no—
313#1803D4311yescharacteristic, complemented
314C2×C43#241511yescharacteristic
315C2×C43#306111yescharacteristic
316C2×C43#306311yescharacteristic
317C2×C43#311911yescharacteristic
318C2×C43#312711yescharacteristic
319C2×C43#324211yescharacteristic
320C2×C43#324311yescharacteristic
321D43—81no—
322C2×#125—431no—
323C2×C22⋊Q8—431no—
324C2×C4×Q8C2×D4311yescharacteristic
325C2×#117—431no—
326#479—864no—
327#433—864no—
328C2×#107—431no—
329C2×#107—431no—
330C2×#107—431no—
331C2×#106—431no—
332C2×C4⋊C8—431no—
333C2×C4⋊C8C2×D4311yescharacteristic
334C2×#103—431no—
335C2×#103—431no—
336C2×#103C2×D4311yescharacteristic
337C2×#103C2×D4311yescharacteristic
338C2×C22⋊C8—431no—
339C2×C22⋊C8—431no—
340C2×#97—431no—
341C2×C4×C8—431no—
342#398—861no—
343#398—861no—
344#396—861no—
345#396—861no—
346#391—431no—
347#389—431no—
348#389—431no—
349#389—431no—
350#389—861no—
351#388—861no—
352#388—861no—
353#387—861no—
354#384C2×D4311yescharacteristic
355#380—431no—
356#380—431no—
357#380—431no—
358C4×C4⋊C4—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340C2×D4311yescharacteristic
366#340C2×D4311yescharacteristic
367C43#2471511yescharacteristic, complemented, Sylow
368C22×Q8C22×D4311yescharacteristic
369C23×C4—431no—
370C22×C8—431no—
371C22×C8—431no—
372C22×C8C22×D4311yescharacteristic
373C22×C8C22×D4311yescharacteristic
374#125—862no—
375#125—862no—
376C22⋊Q8—862no—
377C22⋊Q8—862no—
378C4×Q8—22no—
379C4×Q8—22no—
380#117—862no—
381#117—862no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C22⋊C4—431no—
401C2×C22⋊C4—431no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C42—21no—
407C2×C42—431no—
408C2×C42—861no—
409C2×C42C22×D4311yescharacteristic
410#107—862no—
411#107—862no—
412#107—862no—
413#106—862no—
414C4⋊C8—22no—
415C4⋊C8—434no—
416#103—22no—
417#103—22no—
418#103—862no—
419#103—862no—
420C22⋊C8—862no—
421C22⋊C8—862no—
422#97—862no—
423C4×C8—862no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433C24—431no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8#1062190012yes—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4D4×D4311yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4C23×D4311yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—432no—
467C2×C8—432no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—42no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4—432no—
482C4⋊C4—864no—
483C4⋊C4—862no—
484C4⋊C4—862no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—3441no—
493C4⋊C4—3441no—
494C4⋊C4—3441no—
495C4⋊C4—1722no—
496C4⋊C4—1722no—
497C22⋊C4—864no—
498C22⋊C4—862no—
499C22⋊C4—862no—
500C22⋊C4—3441no—
501C22⋊C4—3441no—
502C22⋊C4—3441no—
503C42—42no—
504C42—861no—
505C42—861no—
506C42—3441no—
507C42#1062189812yes—
508C42D4×D4312yes—
509C23—861no—
510C23—861no—
511C23—861no—
512C23—861no—
513C23—861no—
514C23—861no—
515C23—861no—
516C23C2×D4×D4311yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—41no—
520Q8—41no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—862no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4#1306329812yes—
563C2×C4#1306329812yes—
564C2×C4C2×D4×D4311yescharacteristic
565C2×C4#41×D4311yescharacteristic
566C2×C4C2×#1062190011yescharacteristic
567C2×C4C2×#1062189811yescharacteristic
568C2×C4#1306337211yescharacteristic
569C2×C4#1306337311yescharacteristic
570C8—41no—
571C8—41no—
572C8—862no—
573C8—862no—
574C22—1721no—
575C22—1721no—
576C22—1721no—
577C22—1721no—
578C22—1721no—
579C22—1721no—
580C22—1721no—
581C22C2×#1306329811yescharacteristic
582C22#1458340911yescharacteristic
583C22#1458347211yescharacteristic
584C22#1458370311yescharacteristic
585C22#1458370511yescharacteristic
586C22#1458371211yescharacteristic
587C22#1458371511yescharacteristic
588C4—22no—
589C4—22no—
590C4—42no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—3441no—
595C4—3441no—
596C4—3441no—
597C4—1721no—
598C4—1722no—
599C4—1721no—
600C4—1721no—
601C4#1458355111yescharacteristic
602C4#1458355511yescharacteristic
603C4#1458358411yescharacteristic
604C4#1458361711yescharacteristic
605C2—3441no—
606C2#1913802611yescharacteristic
607C2#1914426411yescharacteristic
608C2#1914428411yescharacteristic
609C2#1914479311yescharacteristic
610C2#1914489311yescharacteristic
611C2#1914587011yescharacteristic
612C2#1914588311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1803C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1803D43
hypocenterC43#24715
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
1. C2×#14583206C2semidirect
9. #19135550C2semidirect
10. #19135351C2semidirect
11. #19135332C2semidirect
12. #19135327C2semidirect
13. #19135287C2semidirect
14. #19135273C2semidirect
15. C43×#1803C2semidirect
313. #1803D43semidirect
367. C43#24715semidirect

Maximal subgroups

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

subgroupindex
C2×#145832062
C2×#145829592
#191404282
#191372712
#191360342
#191360222
#191357962
#191355502
#191353512
#191353322
#191353272
#191352872
#191352732
C43×#18032
#2471543