Finite Group Databasebeta

← #25114273

Subgroups — #25114273

Order 11008.

838 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#106×D43C211yesmaximal, characteristic
2#19137471C211yesmaximal, characteristic
3#19137463C211yesmaximal, characteristic
4#19135339C211yesmaximal, characteristic, complemented
5#19135183C211yesmaximal, characteristic, complemented
6#19135177C211yesmaximal, characteristic, complemented
7#19135176C211yesmaximal, characteristic, complemented
8#19135170C211yesmaximal, characteristic, complemented
9#19134684C211yesmaximal, characteristic
10#19134680C211yesmaximal, characteristic
11#19134621C211yesmaximal, characteristic
12#19134494C211yesmaximal, characteristic, complemented
13#19134492C211yesmaximal, characteristic, complemented
14#19134372C211yesmaximal, characteristic
15C43×#1944C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17C2×#13063283—21no—
18C2×C4⋊C4×D43C2211yescharacteristic
19C2×C4⋊C4×D43C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24#106×D43C418yescomplemented
25C2×(C2×D43)⋊C8C2211yescharacteristic
26C2×#13063235C2211yescharacteristic
27#14582798C2211yescharacteristic
28#14582798C2211yescharacteristic
29#14582786—21no—
30#14582786—21no—
31#14582780—21no—
32#14582780—21no—
33#14582761—21no—
34#14582756—21no—
35#14582756C2211yescharacteristic
36#14582756C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41C4×(C2×D43)⋊C4C2211yescharacteristic
42#14582746—21no—
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
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×C4×D43—21no—
61C22×C4×D43—21no—
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C2×C8×D43—22no—
66C2×C8×D43—22no—
67C2×C8×D43C2×C414yes—
68#13063283—44no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C4⋊C4×D43—22no—
78C4⋊C4×D43—22no—
79C4⋊C4×D43C2×C414yes—
80C4⋊C4×D43C2×C414yes—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4D411yescharacteristic
84C2×(C2×D43)⋊C4D411yescharacteristic
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90#13063259—22no—
91#13063257C2×C414yes—
92#13063256C2×C414yes—
93#13063256C2×C414yes—
94(C2×D43)⋊C8—22no—
95#13063235—22no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115#107×C43—22no—
116#106×C43C2×C414yes—
117#97×C43—22no—
118#95×C43—21no—
119#95×C43—21no—
120C23×D43C2×D411yescharacteristic
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—21no—
138C2×C4×D43—21no—
139C2×C4×D43—24no—
140C2×C4×D43—24no—
141C2×C4×D43—42no—
142C2×C4×D43—42no—
143C2×C4×D43—81no—
144C2×C4×D43—81no—
145C2×C4×D43C22×C412yes—
146C2×C4×D43#4112yes—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43C22×C412yes—
151C2×C8×C43#4112yes—
152C2×C8×C43#4112yes—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—42no—
160C4⋊C4×C43—81no—
161C4⋊C4×C43C22×C412yes—
162C4⋊C4×C43C22×C412yes—
163C42×C43—21no—
164C42×C43—21no—
165(C2×D43)⋊C4—22no—
166(C2×D43)⋊C4—22no—
167(C2×D43)⋊C4—42no—
168(C2×D43)⋊C4—42no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—42no—
176C4⋊Dic43—81no—
177C4⋊Dic43C22×C412yes—
178C4⋊Dic43C22×C412yes—
179Dic43⋊C4—24no—
180Dic43⋊C4—24no—
181C4×Dic43—21no—
182C4×Dic43—21no—
183C4×Dic43—42no—
184C4×Dic43—42no—
185C4×Dic43—81no—
186C4×Dic43—81no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8C22×C412yes—
193C8×D43—28no—
194C23×C43C22×D411yescharacteristic
195C22×D43—21no—
196C22×D43—21no—
197C22×D43—21no—
198C22×D43—21no—
199C22×D43C4×D412yes—
200C22×D43AGL(1,ℤ/8)12yes—
201C22×D43#13712yes—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43C23×C411yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C432−1+411yescharacteristic
225C2×C4×C432−1+411yescharacteristic
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43C4×D412yes—
247C4×D43—22no—
248C4×D43—22no—
249C4×D43—22no—
250C4×D43—22no—
251C4×D43—48no—
252C4×D43—84no—
253C8×C43—41no—
254C8×C43#11714yescomplemented
255C43⋊C8—22no—
256C43⋊C8—41no—
257#22615—431nomaximal, Sylow
258C22×C43C2×C4×D411yescharacteristic
259C22×C43#54711yescharacteristic
260C22×C43#54711yescharacteristic
261C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
262C22×C43C2×#13711yescharacteristic
263C22×C43#57711yescharacteristic
264C22×C43#57711yescharacteristic
265C2×D43—22no—
266C2×D43—22no—
267C2×D43—22no—
268C2×D43—22no—
269C2×D43—22no—
270C2×D43—22no—
271C2×D43#44014yes—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—42no—
275C4×C43—42no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43C2×#11711yescharacteristic
279C4×C43#51911yescharacteristic
280C4×C43#55211yescharacteristic
281C4×C43#55211yescharacteristic
282Dic43—22no—
283Dic43—41no—
284Dic43—41no—
285Dic43—42no—
286Dic43—42no—
287Dic43—81no—
288Dic43—81no—
289C22×#106—431no—
290#2345—431no—
291#2344—431no—
292#1944—431no—
293#1944D4311yescharacteristic, complemented
294#1920—431no—
295#1920—431no—
296#1919—431no—
297#1919—431no—
298#1824—431no—
299#1823—431no—
300#1808—431no—
301#1776—431no—
302#1776—431no—
303#1752—431no—
304C2×C43#234411yescharacteristic
305C2×C43C2×#44011yescharacteristic
306C2×C43#294911yescharacteristic
307C2×C43#334411yescharacteristic
308C2×C43#334411yescharacteristic
309C2×C43#334511yescharacteristic
310C2×C43#334511yescharacteristic
311D43—24no—
312C23×C8—431no—
313C2×#117—861no—
314C22×C4⋊C4—431no—
315C22×C4⋊C4—431no—
316C2×#107—431no—
317C2×#107C2×D4311yescharacteristic
318C2×#106—431no—
319C2×#106—431no—
320C2×#106—431no—
321C2×#106—438no—
322C2×#106C2×D4311yescharacteristic
323C2×C22⋊C8—431no—
324C2×#97—431no—
325C2×#97C2×D4311yescharacteristic
326#389—431no—
327#389—431no—
328#389C2×D4311yescharacteristic
329#389C2×D4311yescharacteristic
330#387—861no—
331#387—861no—
332#387—861no—
333#387—861no—
334#381—861no—
335#380—431no—
336#380—431no—
337#380—861no—
338C4×C4⋊C4—431no—
339C4×C4⋊C4—431no—
340C4×C4⋊C4—431no—
341C4×C4⋊C4—431no—
342C4×C22⋊C4—431no—
343C4×C22⋊C4—861no—
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340C2×D4311yescharacteristic
353#340C2×D4311yescharacteristic
354#336—431no—
355#336—431no—
356C43#2261511yescharacteristic, complemented, Sylow
357C23×C4—431no—
358C23×C4—861no—
359C23×C4—861no—
360C22×C8—431no—
361C22×C8—434no—
362C22×C8—431no—
363C22×C8—862no—
364C22×C8—862no—
365C22×C8C22×D4311yescharacteristic
366C22×C8C22×D4311yescharacteristic
367#117—1724no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—434no—
373C2×C4⋊C4—434no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—862no—
377C2×C4⋊C4—862no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4C22×D4311yescharacteristic
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C22⋊C4—431no—
387C2×C22⋊C4—431no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C42—431no—
391C2×C42—861no—
392C2×C42—861no—
393C2×C42—861no—
394C2×C42—861no—
395C2×C42C22×D4311yescharacteristic
396#107—22no—
397#107—862no—
398#106—434no—
399#106—434no—
400#106—434no—
401#106C4×D4314yes—
402C22⋊C8—862no—
403#97—22no—
404#97—862no—
405#95—21no—
406#95—21no—
407#95—431no—
408#95—431no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417C24—431no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—431no—
423C22×C4—432no—
424C22×C4—432no—
425C22×C4—431no—
426C22×C4—431no—
427C22×C4—864no—
428C22×C4—864no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—3441no—
438C22×C4—3441no—
439C22×C4—1722no—
440C22×C4—1722no—
441C22×C4D4×D4311yescharacteristic
442C22×C4D4×D4311yescharacteristic
443C22×C4C23×D4311yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—432no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—868no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8C2×C4×D4312yes—
455C2×C8#1062190012yes—
456C2×C8#1062190212yes—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—42no—
464C4⋊C4—81no—
465C4⋊C4—432no—
466C4⋊C4—432no—
467C4⋊C4—864no—
468C4⋊C4—864no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—3441no—
476C4⋊C4—1722no—
477C4⋊C4C2×C4×D4312yes—
478C4⋊C4C2×C4×D4312yes—
479C22⋊C4—862no—
480C22⋊C4—862no—
481C22⋊C4—1722no—
482C22⋊C4—1722no—
483C42—21no—
484C42—21no—
485C42—861no—
486C42—861no—
487C42—3441no—
488C42—3441no—
489C42—1722no—
490C42—1722no—
491C23—432no—
492C23—432no—
493C23—432no—
494C23—861no—
495C23—861no—
496C23—861no—
497C23—861no—
498C23C2×D4×D4311yescharacteristic
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—432no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—862no—
521C2×C4—862no—
522C2×C4—862no—
523C2×C4—862no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—862no—
527C2×C4—862no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—3444no—
533C2×C4—1728no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4C22×C4×D4311yescharacteristic
545C2×C4#41×D4311yescharacteristic
546C2×C4C2×#1062190011yescharacteristic
547C2×C4C2×#1062190211yescharacteristic
548C2×C4#1306337211yescharacteristic
549C2×C4#1306337311yescharacteristic
550C8—41no—
551C8—862no—
552C8—1721no—
553C8#1306328314yescomplemented
554C22—434no—
555C22—862no—
556C22—862no—
557C22—862no—
558C22—862no—
559C22—862no—
560C22—862no—
561C22C4×D4×D4311yescharacteristic
562C22#1458354911yescharacteristic
563C22#1458355211yescharacteristic
564C22AGL(1,ℤ/8)×D4311yescharacteristic
565C22#137×D4311yescharacteristic
566C22#1458370811yescharacteristic
567C22#1458370911yescharacteristic
568C4—42no—
569C4—41no—
570C4—41no—
571C4—42no—
572C4—81no—
573C4—81no—
574C4—862no—
575C4—3441no—
576C4—3441no—
577C4—1722no—
578C4—1721no—
579C4—1721no—
580C4—1722no—
581C4C2×#1306328311yescharacteristic
582C4#1458337511yescharacteristic
583C4#1458358311yescharacteristic
584C4#1458358711yescharacteristic
585C2—864no—
586C2#1913746311yescharacteristic
587C2#440×D4311yescharacteristic
588C2#1914345111yescharacteristic
589C2#1914704511yescharacteristic
590C2#1914704911yescharacteristic
591C2#1914706011yescharacteristic
592C2#1914706411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1944C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1944D43
hypocenterC43#22615
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
4. #19135339C2semidirect
5. #19135183C2semidirect
6. #19135177C2semidirect
7. #19135176C2semidirect
8. #19135170C2semidirect
12. #19134494C2semidirect
13. #19134492C2semidirect
15. C43×#1944C2semidirect
24. #106×D43C4semidirect
254. C8×C43#117semidirect
293. #1944D43semidirect
356. C43#22615semidirect
553. C8#13063283semidirect

Maximal subgroups

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

subgroupindex
C2×#106×D432
#191374712
#191374632
#191353392
#191351832
#191351772
#191351762
#191351702
#191346842
#191346802
#191346212
#191344942
#191344922
#191343722
C43×#19442
#2261543