Finite Group Databasebeta

← #25114203

Subgroups — #25114203

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143255C211yesmaximal, characteristic
2#19143253C211yesmaximal, characteristic
3#19143184C211yesmaximal, characteristic
4#19135347C211yesmaximal, characteristic, complemented
5#19135342C211yesmaximal, characteristic, complemented
6#19135197C211yesmaximal, characteristic, complemented
7#19135197C211yesmaximal, characteristic, complemented
8#19135192C211yesmaximal, characteristic, complemented
9#19135192C211yesmaximal, characteristic, complemented
10#19134695C211yesmaximal, characteristic
11#19134635C211yesmaximal, characteristic
12#19134478C211yesmaximal, characteristic, complemented
13#19134473C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic
15C43×#1826C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18#14582960—21no—
19#14582960—21no—
20#14582957—21no—
21#14582957—21no—
22#14582956—21no—
23#14582953—21no—
24#14582952—21no—
25#14582949—21no—
26C2×#13063260C2211yescharacteristic
27C2×#13063260C2211yescharacteristic
28#14582942C411yescharacteristic, complemented
29#14582942C411yescharacteristic, complemented
30#14582942C411yescharacteristic, complemented
31#14582942C411yescharacteristic, complemented
32#14582939C411yescharacteristic, complemented
33#14582939C411yescharacteristic, complemented
34#14582939C411yescharacteristic, complemented
35#14582939C411yescharacteristic, complemented
36#14582935C2211yescharacteristic
37#14582935C2211yescharacteristic
38#14582935C2211yescharacteristic
39#14582935C2211yescharacteristic
40#14582927C2211yescharacteristic
41#14582927C2211yescharacteristic
42#14582926C2211yescharacteristic
43#14582926C2211yescharacteristic
44#14582863C2211yescharacteristic
45C2×C22⋊(C43⋊C8)C2211yescharacteristic
46#14582857C2211yescharacteristic
47#14582857C2211yescharacteristic
48#14582855C2211yescharacteristic
49#14582855C2211yescharacteristic
50C2×#13063236C2211yescharacteristic
51C2×C4×C43⋊C8C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582663C2211yescharacteristic
54#14582659C2211yescharacteristic
55#14582659C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582659C2211yescharacteristic
58#14582654C2211yescharacteristic
59#14582654C2211yescharacteristic
60C2×#117×C43C2211yescharacteristic
61C43×#407C2211yescharacteristic
62C4×C22⋊C4×C43C2211yescharacteristic
63C43×#339C2211yescharacteristic
64C43×#339C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#339C2211yescharacteristic
67C2×#10621877—22no—
68C2×#10621877—22no—
69C2×#10621877C2×C411yescharacteristic
70C2×#10621877C2×C411yescharacteristic
71C2×#10621877C2×C411yescharacteristic
72C2×#10621877C2×C411yescharacteristic
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063284—21no—
80#13063284—21no—
81#13063284C2×C411yescharacteristic
82#13063284C2×C411yescharacteristic
83#13063284C2311yescharacteristic
84#13063284C2311yescharacteristic
85C2×C4⋊Dic43C2×C411yescharacteristic
86C2×C4⋊Dic43C2×C411yescharacteristic
87C2×C22⋊Dic43—21no—
88C2×C4×Dic43—21no—
89#13063260—22no—
90#13063260—22no—
91#13063258C2×C411yescharacteristic
92#13063258C2×C411yescharacteristic
93#13063258C2×C411yescharacteristic
94#13063258C2×C411yescharacteristic
95#13063258C2×C411yescharacteristic
96#13063258C2×C411yescharacteristic
97#13063258C2×C411yescharacteristic
98#13063258C2×C411yescharacteristic
99#13063256C2×C411yescharacteristic
100#13063256C2×C411yescharacteristic
101#13063256C2×C411yescharacteristic
102#13063256C2×C411yescharacteristic
103#13063256C2×C411yescharacteristic
104#13063256C2×C411yescharacteristic
105#13063256C2×C411yescharacteristic
106#13063256C2×C411yescharacteristic
107C4⋊(C43⋊C8)—21no—
108C4⋊(C43⋊C8)—21no—
109C4⋊(C43⋊C8)—21no—
110C4⋊(C43⋊C8)—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115C22⋊(C43⋊C8)—21no—
116C22⋊(C43⋊C8)—21no—
117C22⋊(C43⋊C8)D411yescharacteristic
118C22⋊(C43⋊C8)D411yescharacteristic
119C22⋊(C43⋊C8)D411yescharacteristic
120C22⋊(C43⋊C8)D411yescharacteristic
121#13063236—21no—
122#13063236—21no—
123#13063236—22no—
124#13063235—21no—
125#13063235—21no—
126C4×C43⋊C8—21no—
127C4×C43⋊C8—21no—
128C4×C43⋊C8—22no—
129C8×Dic43—21no—
130C8×Dic43—21no—
131C23×C4×C43C2311yescharacteristic
132C2×M16×C43C2311yescharacteristic
133C2×M16×C43C2311yescharacteristic
134#117×C43—21no—
135#117×C43—21no—
136#117×C43C2×C411yescharacteristic
137#117×C43C2×C411yescharacteristic
138#117×C43C2311yescharacteristic
139#117×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2×C411yescharacteristic
141C2×C4⋊C4×C43C2×C411yescharacteristic
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C42×C43—21no—
145C2×C42×C43C2311yescharacteristic
146C2×C42×C43C2311yescharacteristic
147C22⋊C8×C43—21no—
148C22⋊C8×C43—21no—
149#95×C43—21no—
150C24×C43#4111yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43C22×C411yescharacteristic
160C22×C4×C43C22×C411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43#4111yescharacteristic
164C22×C4×C43C2411yescharacteristic
165C22×Dic43—21no—
166C22×Dic43—21no—
167M16×C43—21no—
168M16×C43—21no—
169M16×C43—21no—
170M16×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43C22×C411yescharacteristic
176C4⋊C4×C43C22×C411yescharacteristic
177C4⋊C4×C43C22×C411yescharacteristic
178C4⋊C4×C43C22×C411yescharacteristic
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—42no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C22⋊Dic43—21no—
193C22⋊Dic43—21no—
194C22⋊Dic43—21no—
195C22⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43C22×C411yescharacteristic
199C4⋊Dic43C22×C411yescharacteristic
200C4⋊Dic43C22×C411yescharacteristic
201C4⋊Dic43C22×C411yescharacteristic
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206#10621877—22no—
207#10621877—22no—
208#10621877—22no—
209#10621877—22no—
210#10621877—21no—
211#10621877—21no—
212#10621877—21no—
213#10621877—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8C22×C411yescharacteristic
223C2×C43⋊C8C22×C411yescharacteristic
224C2×C43⋊C8C22×C411yescharacteristic
225C2×C43⋊C8C22×C411yescharacteristic
226C2×C43⋊C8C2×D411yescharacteristic
227C2×C43⋊C8C2×D411yescharacteristic
228C2×C43⋊C8C2×D411yescharacteristic
229C2×C43⋊C8C2×D411yescharacteristic
230C2×C43⋊C8#4112yes—
231C2×C43⋊C8#4112yes—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43C4×D411yescharacteristic
237C23×C43C4×D411yescharacteristic
238C23×C43C2×#4111yescharacteristic
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—22no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—41no—
255C2×C4×C43—42no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—81no—
261C2×C4×C43C4×D411yescharacteristic
262C2×C4×C43C4×D411yescharacteristic
263C2×C4×C43C23×C411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C432−1+411yescharacteristic
268C2×C4×C432−1+411yescharacteristic
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—42no—
274C2×Dic43—81no—
275C8×C43—41no—
276C8×C43—41no—
277C43⋊C8—21no—
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—21no—
281C43⋊C8—21no—
282C43⋊C8—21no—
283C43⋊C8—41no—
284C43⋊C8—41no—
285C43⋊C8#11712yes—
286C43⋊C8#11712yes—
287#22608—431nomaximal, Sylow
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—21no—
291C22×C43—21no—
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—21no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43C2×C4×D411yescharacteristic
299C22×C43#55211yescharacteristic
300C22×C43#55211yescharacteristic
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—42no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43—81no—
309C4×C43C2×#11711yescharacteristic
310C4×C43#51911yescharacteristic
311C4×C43#54711yescharacteristic
312C4×C43#54711yescharacteristic
313Dic43—41no—
314Dic43—41no—
315Dic43—41no—
316Dic43—41no—
317#2924—431no—
318#2924—431no—
319#2911—431no—
320#1946—431no—
321#1945—431no—
322#1922—431no—
323#1922—431no—
324#1922—431no—
325#1922—431no—
326#1826—431no—
327#1826D4311yescharacteristic
328#1811—431no—
329#1773—431no—
330#1772—431no—
331#1753—431no—
332C2×C43—21no—
333C2×C43—21no—
334C2×C43—41no—
335C2×C43—41no—
336C2×C43#234411yescharacteristic
337C2×C43#295511yescharacteristic
338C2×C43#295611yescharacteristic
339C22×M16—431no—
340C2×#117—431no—
341C2×#117C2×D4311yescharacteristic
342#433—861no—
343#433—861no—
344#433—861no—
345#433—861no—
346#432—861no—
347#432—861no—
348#431—861no—
349#431—861no—
350C2×#108—431no—
351C2×#108—431no—
352#428—431no—
353#428—431no—
354#428—431no—
355#428—431no—
356#428—431no—
357#428—431no—
358#428—431no—
359#428—431no—
360#427—431no—
361#427—431no—
362#427—431no—
363#427—431no—
364#424—431no—
365#424—431no—
366#424—431no—
367#424—431no—
368#407—431no—
369#407C2×D4311yescharacteristic
370C2×C22⋊C8—431no—
371#405—431no—
372#405—431no—
373#405—431no—
374#405—431no—
375C2×#97—431no—
376C2×C4×C8—431no—
377C4×C22⋊C4C2×D4311yescharacteristic
378#341—431no—
379#341—431no—
380#339—431no—
381#339—431no—
382#339—431no—
383#339—431no—
384#339C2×D4311yescharacteristic
385#339C2×D4311yescharacteristic
386#339C2×D4311yescharacteristic
387#339C2×D4311yescharacteristic
388#336—431no—
389#336—431no—
390C43#2260811yescharacteristic, complemented, Sylow
391C23×C4C22×D4311yescharacteristic
392C2×M16—431no—
393C2×M16—431no—
394C2×M16—431no—
395C2×M16—431no—
396C2×M16—431no—
397C2×M16—431no—
398C2×M16—862no—
399C2×M16—862no—
400C2×M16C22×D4311yescharacteristic
401C2×M16C22×D4311yescharacteristic
402C22×C8—431no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8—431no—
406#117—21no—
407#117—21no—
408#117—431no—
409#117—431no—
410#117—431no—
411#117—431no—
412#117—861no—
413#117—861no—
414#117C4×D4311yescharacteristic
415#117C4×D4311yescharacteristic
416#117C22×D4311yescharacteristic
417#117C22×D4311yescharacteristic
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4C4×D4311yescharacteristic
421C2×C4⋊C4C4×D4311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—861no—
425C2×C42—21no—
426C2×C42—861no—
427C2×C42C22×D4311yescharacteristic
428C2×C42C22×D4311yescharacteristic
429#108—862no—
430#108—862no—
431#107—431no—
432#107—431no—
433#107—431no—
434#107—431no—
435#107—431no—
436#107—431no—
437#107—431no—
438#107—431no—
439#106—431no—
440#106—431no—
441#106—431no—
442#106—431no—
443#106—431no—
444#106—431no—
445#106—431no—
446#106—431no—
447C4⋊C8—861no—
448C4⋊C8—861no—
449C4⋊C8—861no—
450C4⋊C8—861no—
451C4⋊C8—861no—
452C4⋊C8—861no—
453C4⋊C8—861no—
454C4⋊C8—861no—
455C22⋊C8—21no—
456C22⋊C8—21no—
457C22⋊C8—431no—
458C22⋊C8—431no—
459C22⋊C8—431no—
460C22⋊C8—431no—
461C22⋊C8—861no—
462C22⋊C8—861no—
463#97—862no—
464#97—861no—
465#97—861no—
466#97—861no—
467#97—861no—
468C4×C8—862no—
469C4×C8—861no—
470C4×C8—861no—
471C4×C8—861no—
472C4×C8—861no—
473#95—21no—
474C24#1062190011yescharacteristic
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4C2×C4×D4311yescharacteristic
486C22×C4C2×C4×D4311yescharacteristic
487C22×C4D4×D4311yescharacteristic
488C22×C4D4×D4311yescharacteristic
489C22×C4#1062190011yescharacteristic
490C22×C4C23×D4311yescharacteristic
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—862no—
496M16—862no—
497M16—862no—
498M16—862no—
499M16—861no—
500M16—861no—
501M16—861no—
502M16—861no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—431no—
506C2×C8—431no—
507C2×C8—432no—
508C2×C8—432no—
509C2×C8—431no—
510C2×C8—431no—
511C2×C8—431no—
512C2×C8—431no—
513C2×C8—431no—
514C2×C8—431no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—431no—
526C4⋊C4—431no—
527C4⋊C4—431no—
528C4⋊C4—431no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4C2×C4×D4311yescharacteristic
532C4⋊C4C2×C4×D4311yescharacteristic
533C4⋊C4C2×C4×D4311yescharacteristic
534C4⋊C4C2×C4×D4311yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—42no—
540C22⋊C4—861no—
541C22⋊C4—861no—
542C22⋊C4—861no—
543C22⋊C4—861no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—861no—
553C42—861no—
554C42—861no—
555C42—861no—
556C23—21no—
557C23—21no—
558C23—41no—
559C23—41no—
560C23(C22⋊D43)⋊C411yescharacteristic
561C23(C22⋊D43)⋊C411yescharacteristic
562C23C2×#1062190011yescharacteristic
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—81no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—3441no—
590C2×C4—1722no—
591C2×C4(C22⋊D43)⋊C411yescharacteristic
592C2×C4(C22⋊D43)⋊C411yescharacteristic
593C2×C4C22×C4×D4311yescharacteristic
594C2×C4C2×D4×D4311yescharacteristic
595C2×C4#41×D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4#1306337211yescharacteristic
598C2×C4#1306337211yescharacteristic
599C8—41no—
600C8—41no—
601C8—432no—
602C8—432no—
603C8—861no—
604C8—861no—
605C8—861no—
606C8—861no—
607C8—861no—
608C8—861no—
609C8—1721no—
610C8—1721no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—81no—
620C22—81no—
621C22C2×(C22⋊D43)⋊C411yescharacteristic
622C22#1458358611yescharacteristic
623C22#1458358611yescharacteristic
624C4—21no—
625C4—21no—
626C4—42no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—81no—
632C4—1721no—
633C4—1721no—
634C4—1721no—
635C4—1721no—
636C4#117×D4311yescharacteristic
637C4#1458337611yescharacteristic
638C4#1458354711yescharacteristic
639C4#1458354711yescharacteristic
640C2—21no—
641C2—21no—
642C2—41no—
643C2—41no—
644C2#1913745911yescharacteristic
645C2#1914349411yescharacteristic
646C2#1914350111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1826C2
socleC22×C43C2×C4×D4
prime radicalC24×C43#41
cosocleC22×C4×C43C24
hypercenter#1826D43
hypocenterC43#22608
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
4. #19135347C2semidirect
5. #19135342C2semidirect
6. #19135197C2semidirect
7. #19135197C2semidirect
8. #19135192C2semidirect
9. #19135192C2semidirect
12. #19134478C2semidirect
13. #19134473C2semidirect
28. #14582942C4semidirect
29. #14582942C4semidirect
30. #14582942C4semidirect
31. #14582942C4semidirect
32. #14582939C4semidirect
33. #14582939C4semidirect
34. #14582939C4semidirect
35. #14582939C4semidirect
390. C43#22608semidirect

Maximal subgroups

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

subgroupindex
#191432552
#191432532
#191431842
#191353472
#191353422
#191351972
#191351922
#191346952
#191346352
#191344782
#191344732
#191343792
C43×#18262
#2260843