Finite Group Databasebeta

← #25118467

Subgroups — #25118467

Order 11008.

914 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583178C211yesmaximal, characteristic
2#19137648C211yesmaximal, characteristic, complemented
3#19137496C211yesmaximal, characteristic
4#19135554C211yesmaximal, characteristic, complemented
5#19135355C211yesmaximal, characteristic, complemented
6#19135332C211yesmaximal, characteristic, complemented
7#19135189C211yesmaximal, characteristic, complemented
8#19135184C211yesmaximal, characteristic, complemented
9#19134855C211yesmaximal, characteristic
10#19134853C211yesmaximal, characteristic
11#19134463C211yesmaximal, characteristic, complemented
12#19134421C211yesmaximal, characteristic
13#19134419C211yesmaximal, characteristic
14#19134409C211yesmaximal, characteristic
15C43×#1943C211yesmaximal, characteristic, complemented
16C2×#13063324C2211yescharacteristic
17C2×#13063290—21no—
18C2×C4×D172C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C2×C4⋊C4×D43—21no—
22#14583178C418yescomplemented
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582803—21no—
33#14582798C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582781—21no—
36#14582780—21no—
37#14582773—21no—
38#14582770—21no—
39#14582768C2211yescharacteristic
40#14582758—21no—
41C4⋊C4×Dic43C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×Dic43⋊C4C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×Dic86—21no—
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063324—22no—
68#13063324C2×C414yescomplemented
69#13063290—44no—
70C4×D172—22no—
71C4×D172—41no—
72#13063287—22no—
73#13063287—22no—
74#13063287—41no—
75#13063287C2×C414yes—
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⋊C4—21no—
84C2×Dic43⋊C4D411yescharacteristic
85C2×Dic43⋊C4D411yescharacteristic
86C4⋊C4×D43—44no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063258C2×C414yescomplemented
96#13063256—41no—
97Dic43⋊C8C2×C414yescomplemented
98#13063247C2×C414yes—
99#13063247Q814yescomplemented
100#13063245—22no—
101#13063245C2×C414yes—
102#13063235—41no—
103C8×Dic43—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#107×C43C2×C414yescomplemented
121#106×C43—41no—
122#97×C43—41no—
123#95×C43—21no—
124#95×C43—21no—
125C23×D43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172C22×C412yes—
144C2×D172C2×Q812yes—
145C2×D172#4112yes—
146C2×C4×D43—24no—
147C2×C4×D43—42no—
148C2×C4×D43—42no—
149C2×C4×D43—42no—
150C2×C4×D43—42no—
151C2×C4×D43—42no—
152C2×C4×D43—42no—
153C2×C4×D43—81no—
154C2×C4×D43—81no—
155C2×Dic86—24no—
156C2×Dic86—42no—
157C2×Dic86—42no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43C22×C412yes—
163C2×C8×C43C2×Q812yes—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—42no—
171C4⋊C4×C43—42no—
172C4⋊C4×C43C22×C412yes—
173C4⋊C4×C43C22×C412yes—
174C42×C43—21no—
175C42×C43—21no—
176(C2×D43)⋊C4—24no—
177(C2×D43)⋊C4—42no—
178(C2×D43)⋊C4—42no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—42no—
184C4⋊Dic43C22×C412yes—
185C4⋊Dic43C2×Q812yes—
186Dic43⋊C4—24no—
187Dic43⋊C4—22no—
188Dic43⋊C4—22no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—81no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C4×Dic43—42no—
197C4×Dic43C22×C412yes—
198C4×Dic43#4112yes—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C22×C412yes—
205C23×C43C22×D411yescharacteristic
206C22×D43—22no—
207C22×D43—22no—
208C22×D43—22no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
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—41no—
231C2×C4×C43C23×C411yescharacteristic
232C2×C4×C43C22×Q811yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C2×C4×C432−1+411yescharacteristic
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—22no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—22no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43C4×D412yes—
255C2×Dic43C4×D412yes—
256C2×Dic43AGL(1,ℤ/8)12yes—
257C2×Dic43AGL(1,ℤ/8)12yes—
258D172—22no—
259D172—22no—
260D172—22no—
261D172C4×Q814yescomplemented
262C4×D43—48no—
263C4×D43—84no—
264C4×D43—84no—
265Dic86—48no—
266C8×C43—22no—
267C8×C43—22no—
268C43⋊C8—22no—
269C43⋊C8—41no—
270#22968—431nomaximal, Sylow
271C22×C43C2×C4×D411yescharacteristic
272C22×C43#54611yescharacteristic
273C22×C43D4×Q811yescharacteristic
274C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
276C22×C43#57711yescharacteristic
277C22×C43#57811yescharacteristic
278C2×D43—24no—
279C2×D43—42no—
280C2×D43—42no—
281C2×D43—42no—
282C2×D43—42no—
283C2×D43—42no—
284C2×D43—42no—
285C4×C43—41no—
286C4×C43—42no—
287C4×C43—42no—
288C4×C43—41no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43C2×C4×Q811yescharacteristic
292C4×C43#52011yescharacteristic
293C4×C43#55211yescharacteristic
294C4×C43#55411yescharacteristic
295Dic43—22no—
296Dic43—41no—
297Dic43—42no—
298Dic43—42no—
299Dic43—41no—
300Dic43—81no—
301Dic43#44214yes—
302C2×#474—431no—
303#2365—431no—
304D4×C4⋊C4—431no—
305#1990—431no—
306#1948—431no—
307#1943—431no—
308#1943D4311yescharacteristic, complemented
309#1921—431no—
310#1921—431no—
311#1864—431no—
312#1864—431no—
313#1770—431no—
314#1762—431no—
315#1762—431no—
316C4×#102—431no—
317C2×C43#236011yescharacteristic
318C2×C43C2×#44211yescharacteristic
319C2×C43#294711yescharacteristic
320C2×C43#332411yescharacteristic
321C2×C43#333011yescharacteristic
322C2×C43#338411yescharacteristic
323C2×C43#338611yescharacteristic
324D43—44no—
325C2×C4⋊Q8—431no—
326C2×C4×Q8—861no—
327C2×C4×D4—431no—
328C2×C4×D4—431no—
329C2×C4×D4—431no—
330C22×C4⋊C4—861no—
331#474—438no—
332C2×#107—431no—
333C2×#107C2×D4311yescharacteristic
334C2×#106—431no—
335C2×#106C2×D4311yescharacteristic
336C2×C4⋊C8—431no—
337C2×#102—431no—
338C2×#102—431no—
339C2×#102—431no—
340C2×#102—431no—
341C2×#97—431no—
342C2×#97C2×D4311yescharacteristic
343C2×C4×C8—431no—
344#391—861no—
345#389—431no—
346#389—431no—
347#389C2×D4311yescharacteristic
348#389C2×D4311yescharacteristic
349#387—861no—
350#387—861no—
351#385—861no—
352#385—861no—
353#384—431no—
354#380—861no—
355C4×C4⋊C4—431no—
356C4×C4⋊C4—431no—
357C4×C4⋊C4—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
367#336—431no—
368#336—431no—
369C43#2296811yescharacteristic, complemented, Sylow
370C22×Q8—861no—
371C22×D4—431no—
372C23×C4—861no—
373C23×C4—861no—
374C23×C4—861no—
375C22×C8—431no—
376C22×C8—431no—
377C22×C8C22×D4311yescharacteristic
378C22×C8C22×D4311yescharacteristic
379C4⋊Q8—434no—
380C4⋊Q8—862no—
381C4×Q8—1724no—
382C4×D4—434no—
383C4×D4—862no—
384C4×D4—862no—
385C4×D4—862no—
386C4×D4—1721no—
387C4×D4—1721no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—1724no—
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C42—431no—
409C2×C42—431no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42—861no—
413C2×C42C22×D4311yescharacteristic
414#107—434no—
415#107C4×D4314yescomplemented
416#106—41no—
417#106—1721no—
418C4⋊C8—434no—
419#102—434no—
420#102—434no—
421#102—434no—
422#102—862no—
423#97—41no—
424#97—1721no—
425C4×C8—862no—
426#95—21no—
427#95—21no—
428#95—431no—
429#95—431no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435C24—861no—
436C2×Q8—864no—
437C2×Q8—1722no—
438C2×Q8—1722no—
439C2×D4—432no—
440C2×D4—432no—
441C2×D4—432no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—864no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—3441no—
458C22×C4—3441no—
459C22×C4—1722no—
460C22×C4—1722no—
461C22×C4—1722no—
462C22×C4—1722no—
463C22×C4—1722no—
464C22×C4—1722no—
465C22×C4D4×D4311yescharacteristic
466C22×C4D4×D4311yescharacteristic
467C22×C4C23×D4311yescharacteristic
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—432no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8C2×C4×D4312yes—
479C2×C8Q8×D4312yes—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—432no—
489C4⋊C4—432no—
490C4⋊C4—862no—
491C4⋊C4—862no—
492C4⋊C4—864no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—3441no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C4⋊C4C2×C4×D4312yes—
502C4⋊C4C2×C4×D4312yes—
503C22⋊C4—864no—
504C22⋊C4—1722no—
505C22⋊C4—1722no—
506C42—21no—
507C42—21no—
508C42—432no—
509C42—432no—
510C42—861no—
511C42—861no—
512C42—1722no—
513C42—1722no—
514C42—1722no—
515C23—862no—
516C23—862no—
517C23—862no—
518C23—1721no—
519C23—1721no—
520C23—1721no—
521C23—1721no—
522C23C2×D4×D4311yescharacteristic
523Q8—1728no—
524D4—434no—
525D4—862no—
526D4—862no—
527D4—862no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—432no—
547C2×C4—432no—
548C2×C4—432no—
549C2×C4—432no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—3444no—
561C2×C4—3444no—
562C2×C4—1728no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4C22×C4×D4311yescharacteristic
571C2×C4C2×Q8×D4311yescharacteristic
572C2×C4#41×D4311yescharacteristic
573C2×C4#41×D4311yescharacteristic
574C2×C4#1306337011yescharacteristic
575C2×C4#1306337311yescharacteristic
576C8—22no—
577C8—22no—
578C8—862no—
579C8—1721no—
580C22—864no—
581C22—1722no—
582C22—1722no—
583C22—1722no—
584C22—1722no—
585C22—1722no—
586C22—1722no—
587C22C4×D4×D4311yescharacteristic
588C22#1458353811yescharacteristic
589C22#1458356411yescharacteristic
590C22AGL(1,ℤ/8)×D4311yescharacteristic
591C22AGL(1,ℤ/8)×D4311yescharacteristic
592C22#1458370811yescharacteristic
593C22#1458371511yescharacteristic
594C4—41no—
595C4—41no—
596C4—42no—
597C4—42no—
598C4—81no—
599C4—81no—
600C4—434no—
601C4—862no—
602C4—3441no—
603C4—1721no—
604C4—1721no—
605C4—1722no—
606C4—1722no—
607C4C4×Q8×D4311yescharacteristic
608C4#1458338011yescharacteristic
609C4#1458358111yescharacteristic
610C4#1458360311yescharacteristic
611C2—1724no—
612C2#1913759711yescharacteristic
613C2#442×D4311yescharacteristic
614C2#1914343711yescharacteristic
615C2#1914682111yescharacteristic
616C2#1914689511yescharacteristic
617C2#1914749111yescharacteristic
618C2#1914751311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1943C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1943D43
hypocenterC43#22968
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1943

Complements

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

NH ≅ G/Ntype
2. #19137648C2semidirect
4. #19135554C2semidirect
5. #19135355C2semidirect
6. #19135332C2semidirect
7. #19135189C2semidirect
8. #19135184C2semidirect
11. #19134463C2semidirect
15. C43×#1943C2semidirect
22. #14583178C4semidirect
68. #13063324C2×C4semidirect
95. #13063258C2×C4semidirect
97. Dic43⋊C8C2×C4semidirect
99. #13063247Q8semidirect
120. #107×C43C2×C4semidirect
261. D172C4×Q8semidirect
308. #1943D43semidirect
369. C43#22968semidirect
415. #107C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831782
#191376482
#191374962
#191355542
#191353552
#191353322
#191351892
#191351842
#191348552
#191348532
#191344632
#191344212
#191344192
#191344092
C43×#19432
#2296843