Finite Group Databasebeta

← #25137951

Subgroups — #25137951

Order 11008.

794 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583196C211yesmaximal, characteristic, complemented
2C2×#14582960C211yesmaximal, characteristic, complemented
3#19137288C211yesmaximal, characteristic
4#19136032C211yesmaximal, characteristic, complemented
5#19136026C211yesmaximal, characteristic, complemented
6#19135777C211yesmaximal, characteristic
7#19135777C211yesmaximal, characteristic
8#19135553C211yesmaximal, characteristic, complemented
9#19135351C211yesmaximal, characteristic, complemented
10#19135330C211yesmaximal, characteristic, complemented
11#19135325C211yesmaximal, characteristic, complemented
12#19135291C211yesmaximal, characteristic, complemented
13#19135277C211yesmaximal, characteristic, complemented
14#19134592C211yesmaximal, characteristic, complemented
15C43×#2629C211yesmaximal, characteristic, complemented
16C2×#13063299C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18#14583196—24no—
19#14582960—24no—
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063236C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582799—21no—
36#14582797C2211yescharacteristic
37#14582789—21no—
38#14582775—21no—
39#14582770—21no—
40#14582759C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50C2×#125×C43C2211yescharacteristic
51C2×#117×C43C2211yescharacteristic
52C43×#398—21no—
53C43×#398—21no—
54C43×#396—21no—
55C43×#396—21no—
56C43×#389C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#384C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C22×C4×D43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063299—22no—
69#13063299—22no—
70C4×D172—22no—
71C4×D172—22no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×C22⋊Dic43—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×C4×Dic43—21no—
82#13063258—22no—
83#13063258—22no—
84#13063258—22no—
85#13063256—22no—
86C4⋊(C43⋊C8)—22no—
87C4⋊(C43⋊C8)D414yescomplemented
88#13063245—22no—
89#13063245—22no—
90#13063245—22no—
91#13063245—22no—
92C22⋊(C43⋊C8)—22no—
93C22⋊(C43⋊C8)—22no—
94#13063236—22no—
95C4×C43⋊C8—22no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C23×C4×C43C2311yescharacteristic
100#125×C43—22no—
101#125×C43—22no—
102#117×C43—22no—
103#117×C43—22no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43D411yescharacteristic
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43D411yescharacteristic
119C2×C22⋊C4×C43D411yescharacteristic
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C24×C43C2×D411yescharacteristic
127C23×D43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C2×C22⋊D43—24no—
145C2×C22⋊D43—81no—
146C2×C22⋊D43—81no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172#4112yes—
156C2×C4×D43—42no—
157C2×C4×D43—81no—
158C2×C4×D43—81no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—42no—
170C4⋊C4×C43—42no—
171C4⋊C4×C43—81no—
172C4⋊C4×C43—81no—
173C4⋊C4×C43—81no—
174C4⋊C4×C43—81no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—81no—
178C22⋊C4×C43—81no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43C2×D412yes—
182C42×C43#4112yes—
183C22⋊Dic43—81no—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—81no—
187(C2×D43)⋊C4—81no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43#4112yes—
194Dic43⋊C4—81no—
195C4×Dic43—81no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8C2×D412yes—
207C2×C43⋊C8C2×D412yes—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43C22×D411yescharacteristic
216C22×D43—22no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
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—41no—
251C2×C4×C43—41no—
252C2×C4×C43#12112yes—
253C2×C4×C43#12112yes—
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C432−1+411yescharacteristic
259C2×C4×C432−1+411yescharacteristic
260C22⋊D43—84no—
261C2×Dic43—22no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270D172—22no—
271D172—22no—
272D172—41no—
273D172—41no—
274C4×D43—84no—
275C43⋊C8—22no—
276C43⋊C8—22no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#24713—431nomaximal, Sylow
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43C2×#12111yescharacteristic
288C22×C43#52511yescharacteristic
289C22×C43#53611yescharacteristic
290C22×C43#57611yescharacteristic
291C22×C43#57611yescharacteristic
292C22×C43#57711yescharacteristic
293C22×C43#57811yescharacteristic
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C4×C43—22no—
302C4×C43—22no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43—81no—
310C4×C43#54711yescharacteristic
311C4×C43#54811yescharacteristic
312C4×C43#55211yescharacteristic
313C4×C43#55611yescharacteristic
314Dic43—42no—
315Dic43—81no—
316Dic43—81no—
317C2×#478—431no—
318C2×#433—431no—
319#2629D4311yescharacteristic, complemented
320#2324—431no—
321#2077—431no—
322#2076—431no—
323#2033—431no—
324#2033—431no—
325#1989—431no—
326#1947—431no—
327#1943—431no—
328#1942—431no—
329#1936—431no—
330#1934—431no—
331#1802—431no—
332C2×C43—81no—
333C2×C43#241511yescharacteristic
334C2×C43#306111yescharacteristic
335C2×C43#306211yescharacteristic
336C2×C43#312011yescharacteristic
337C2×C43#312211yescharacteristic
338C2×C43#324111yescharacteristic
339C2×C43#324311yescharacteristic
340D43—82no—
341C2×#125C2×D4311yescharacteristic
342C2×#121—431no—
343C2×C4×D4—431no—
344C2×#117C2×D4311yescharacteristic
345#478—864no—
346#433—864no—
347C2×#107—431no—
348C2×#107—431no—
349C2×#107—431no—
350C2×#106—431no—
351C2×C4⋊C8—431no—
352C2×C4⋊C8—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×C22⋊C8—431no—
358C2×C22⋊C8—431no—
359C2×#97—431no—
360C2×C4×C8—431no—
361#398—21no—
362#398—21no—
363#396—21no—
364#396—21no—
365#390—431no—
366#390—861no—
367#389—431no—
368#389C2×D4311yescharacteristic
369#389C2×D4311yescharacteristic
370#388—861no—
371#386—861no—
372#385—861no—
373#384C2×D4311yescharacteristic
374#380—431no—
375#380C2×D4311yescharacteristic
376#380C2×D4311yescharacteristic
377C4×C4⋊C4—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386C43#2471311yescharacteristic, complemented, Sylow
387C22×D4—431no—
388C22×D4—861no—
389C23×C4—861no—
390C23×C4C22×D4311yescharacteristic
391C22×C8—431no—
392C22×C8—431no—
393C22×C8—431no—
394C22×C8—431no—
395#125—22no—
396#125—22no—
397#121—862no—
398#121—862no—
399C4×D4—862no—
400C4×D4—862no—
401#117—22no—
402#117—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4C22⋊D4311yescharacteristic
414C2×C4⋊C4C22⋊D4311yescharacteristic
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4C22⋊D4311yescharacteristic
427C2×C22⋊C4C22⋊D4311yescharacteristic
428C2×C42—861no—
429C2×C42C22×D4311yescharacteristic
430C2×C42C22×D4311yescharacteristic
431#107—862no—
432#107—862no—
433#107—862no—
434#106—862no—
435C4⋊C8—434no—
436C4⋊C8—862no—
437#102—862no—
438#102—862no—
439#102—862no—
440#102—862no—
441C22⋊C8—862no—
442C22⋊C8—862no—
443#97—862no—
444C4×C8—862no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—861no—
450#95—861no—
451#95—861no—
452C24—861no—
453C24C2×C22⋊D4311yescharacteristic
454C2×D4—432no—
455C2×D4—864no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—3441no—
462C2×D4—3441no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—3441no—
477C22×C4—3441no—
478C22×C4—1722no—
479C22×C4C2×C22⋊D4311yescharacteristic
480C22×C4C2×C22⋊D4311yescharacteristic
481C22×C4C2×C22⋊D4311yescharacteristic
482C22×C4C2×C22⋊D4311yescharacteristic
483C22×C4C2×C22⋊D4311yescharacteristic
484C22×C4C23×D4311yescharacteristic
485C2×C8—432no—
486C2×C8—432no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—81no—
510C4⋊C4—81no—
511C4⋊C4—81no—
512C4⋊C4—81no—
513C4⋊C4—432no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—3441no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—81no—
523C22⋊C4—81no—
524C22⋊C4—864no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C22⋊C4—1722no—
529C42—21no—
530C42—21no—
531C42—3441no—
532C42D4×D4312yes—
533C42#1062190012yes—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—862no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23C22×C22⋊D4311yescharacteristic
549D4—862no—
550D4—862no—
551D4—3444no—
552D4—1721no—
553D4—1721no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—862no—
584C2×C4—3444no—
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#1306329712yes—
594C2×C4#1306329712yes—
595C2×C4C2×D4×D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4#41×D4311yescharacteristic
598C2×C4C2×#1062190011yescharacteristic
599C2×C4#1306337311yescharacteristic
600C2×C4#1306337311yescharacteristic
601C8—862no—
602C8—862no—
603C8—1721no—
604C8—1721no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22—3441no—
616C22—1722no—
617C22—1722no—
618C22—1722no—
619C22C2×#1306329711yescharacteristic
620C22#1458340611yescharacteristic
621C22#1458347311yescharacteristic
622C22#1458370211yescharacteristic
623C22#1458370211yescharacteristic
624C22#1458370711yescharacteristic
625C22#1458371411yescharacteristic
626C4—22no—
627C4—22no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—3441no—
636C4—3441no—
637C4—1722no—
638C4#1458355111yescharacteristic
639C4#1458355911yescharacteristic
640C4#1458358311yescharacteristic
641C4#1458362011yescharacteristic
642C2—81no—
643C2—3442no—
644C2#1913802511yescharacteristic
645C2#1914426211yescharacteristic
646C2#1914427711yescharacteristic
647C2#1914480311yescharacteristic
648C2#1914483311yescharacteristic
649C2#1914584811yescharacteristic
650C2#1914587811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2629C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#2629D43
hypocenterC43#24713
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2629

Complements

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

NH ≅ G/Ntype
1. C2×#14583196C2semidirect
2. C2×#14582960C2semidirect
4. #19136032C2semidirect
5. #19136026C2semidirect
8. #19135553C2semidirect
9. #19135351C2semidirect
10. #19135330C2semidirect
11. #19135325C2semidirect
12. #19135291C2semidirect
13. #19135277C2semidirect
14. #19134592C2semidirect
15. C43×#2629C2semidirect
87. C4⋊(C43⋊C8)D4semidirect
319. #2629D43semidirect
386. C43#24713semidirect

Maximal subgroups

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

subgroupindex
C2×#145831962
C2×#145829602
#191372882
#191360322
#191360262
#191357772
#191355532
#191353512
#191353302
#191353252
#191352912
#191352772
#191345922
C43×#26292
#2471343