Finite Group Databasebeta

← #25115018

Subgroups — #25115018

Order 11008.

986 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621873C211yesmaximal, characteristic
2C2×#14582986C211yesmaximal, characteristic
3C2×#14582986C211yesmaximal, characteristic
4#19137514C211yesmaximal, characteristic, complemented
5#19137504C211yesmaximal, characteristic
6#19135324C211yesmaximal, characteristic, complemented
7#19134850C211yesmaximal, characteristic, complemented
8#19134848C211yesmaximal, characteristic, complemented
9#19134843C211yesmaximal, characteristic
10#19134841C211yesmaximal, characteristic
11#19134756C211yesmaximal, characteristic, complemented
12#19134609C211yesmaximal, characteristic, complemented
13#19134604C211yesmaximal, characteristic
14C8×Dic43⋊C4C211yesmaximal, characteristic, complemented
15C43×#1941C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23C4×#10621873—24no—
24#14582986—24no—
25#14582986C418yescomplemented
26C2×#13063258C2211yescharacteristic
27C2×#13063258C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×Dic43⋊C8C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582796—21no—
41#14582794—21no—
42#14582773—21no—
43#14582770—21no—
44#14582764C2211yescharacteristic
45#14582764C2211yescharacteristic
46#14582763—21no—
47#14582756—21no—
48C4⋊C4×Dic43—21no—
49C4×Dic43⋊C4C2211yescharacteristic
50#95×D43—21no—
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C2×#10621873C2×C414yes—
68C2×#10621873D414yes—
69C2×#10621873Q814yes—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C4×Dic86—22no—
73C4×Dic86—41no—
74#13063290—22no—
75#13063290—22no—
76#13063290—41no—
77#13063290C2×C414yescomplemented
78C4×D172—22no—
79C4×D172—41no—
80#13063287—22no—
81#13063287—22no—
82#13063287—41no—
83#13063287C2×C414yes—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4D411yescharacteristic
92C2×Dic43⋊C4D411yescharacteristic
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43C2311yescharacteristic
100C2×C4×Dic43C2311yescharacteristic
101#13063258—41no—
102#13063258—41no—
103#13063257—22no—
104Dic43⋊C8—22no—
105#13063250—22no—
106#13063248—22no—
107#13063248C2×C414yescomplemented
108#13063247—22no—
109#13063245—22no—
110#13063245C2×C414yes—
111C8×Dic43—22no—
112C8×Dic43C2×C414yescomplemented
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95D411yescharacteristic
120C43⋊#95D411yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C42×C43C2311yescharacteristic
130#106×C43—22no—
131#106×C43C2×C414yescomplemented
132C4×C8×C43—22no—
133#95×C43—21no—
134#95×C43—21no—
135C23×D43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2411yescharacteristic
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172C22×C412yes—
154C2×D172C2×D412yes—
155C2×D172C2×Q812yes—
156C2×C4×D43—24no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×C4×D43—81no—
164C2×C4×D43—81no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86C22×C412yes—
169C2×Dic86C2×D412yes—
170C2×Dic86C2×Q812yes—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43C22×C412yes—
175C2×C8×C43C2×D412yes—
176C2×C8×C43C2×Q812yes—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—42no—
184C4⋊C4×C43—81no—
185C4⋊C4×C43C22×C412yes—
186C4⋊C4×C43C22×C412yes—
187C42×C43—21no—
188C42×C43—21no—
189(C2×D43)⋊C4—24no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—42no—
197C4⋊Dic43—81no—
198Dic43⋊C4—22no—
199Dic43⋊C4—24no—
200Dic43⋊C4—22no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—24no—
206C4×Dic43—42no—
207C4×Dic43—42no—
208C4×Dic43C22×C412yes—
209C4×Dic43#4112yes—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8C22×C412yes—
216#10621873C4⋊C4116yescomplemented
217C23×C43C22×D411yescharacteristic
218C22×D43—22no—
219C22×D43—22no—
220C22×D43—22no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
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#13512yes—
243C2×C4×C43C23×C411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×Q811yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C2×Dic43—22no—
250C2×Dic43—21no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43C4×D412yes—
268C2×Dic43C4×D412yes—
269C2×Dic43#13512yes—
270D172—22no—
271D172—22no—
272D172—22no—
273D172C2×C4⋊C414yes—
274C4×D43—84no—
275C4×D43—84no—
276C4×D43—84no—
277Dic86—22no—
278Dic86—22no—
279Dic86—22no—
280Dic86C2×C4⋊C414yes—
281C8×C43—41no—
282C8×C43C2×C4⋊C414yes—
283C43⋊C8—22no—
284C43⋊C8—41no—
285#22683—431nomaximal, Sylow
286C22×C43C2×C4×D411yescharacteristic
287C22×C43D4211yescharacteristic
288C22×C43D4×Q811yescharacteristic
289C22×C43C2×#13511yescharacteristic
290C22×C43C2×#13511yescharacteristic
291C22×C43#57711yescharacteristic
292C22×C43#57711yescharacteristic
293C2×D43—24no—
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C4×C43—22no—
301C4×C43—42no—
302C4×C43—42no—
303C4×C43—41no—
304C4×C43—81no—
305C4×C43—81no—
306C4×C43C22×C4⋊C411yescharacteristic
307C4×C43#52011yescharacteristic
308C4×C43#54711yescharacteristic
309C4×C43#55411yescharacteristic
310Dic43—24no—
311Dic43—22no—
312Dic43—22no—
313Dic43—22no—
314Dic43—41no—
315Dic43—81no—
316Dic43—81no—
317C2×C4×SD16—431no—
318C2×C4×SD16—431no—
319C2×C4×SD16—431no—
320#2351—431no—
321#2349—431no—
322#1941—431no—
323#1941D4311yescharacteristic, complemented
324#1863—431no—
325#1863—431no—
326#1862—431no—
327#1862—431no—
328#1846—431no—
329#1805—431no—
330#1804—431no—
331C8×C4⋊C4—431no—
332C2×C43D4×C4⋊C411yescharacteristic
333C2×C43C4×#13511yescharacteristic
334C2×C43#294911yescharacteristic
335C2×C43#328211yescharacteristic
336C2×C43#328211yescharacteristic
337C2×C43#338111yescharacteristic
338C2×C43#338111yescharacteristic
339D43—44no—
340C22×SD16—431no—
341C2×C4×Q8—431no—
342C2×C4×Q8—431no—
343C2×C4×Q8—431no—
344C2×C4×D4—431no—
345C2×C4×D4—431no—
346C2×C4×D4—431no—
347C4×SD16—438no—
348C4×SD16—864no—
349C4×SD16—864no—
350C2×#107—431no—
351C2×#107—431no—
352C2×#106—431no—
353C2×#106C2×D4311yescharacteristic
354C2×#106C2×D4311yescharacteristic
355C2×C4⋊C8—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#103—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×#102—431no—
362C2×C4×C8—431no—
363C2×C4×C8—431no—
364C2×C4×C8C2×D4311yescharacteristic
365#389—431no—
366#389—431no—
367#389—861no—
368#389—861no—
369#389C2×D4311yescharacteristic
370#389C2×D4311yescharacteristic
371#385—861no—
372#385—861no—
373#382—431no—
374#382—431no—
375#382—861no—
376#380—861no—
377C4×C4⋊C4—431no—
378C4×C4⋊C4—861no—
379C2×#95—861no—
380#340—431no—
381#340—431no—
382#340C2×D4311yescharacteristic
383#340C2×D4311yescharacteristic
384#336—431no—
385#336—431no—
386C43#2268311yescharacteristic, complemented, Sylow
387C22×Q8—431no—
388C22×D4—431no—
389C23×C4—861no—
390C23×C4—861no—
391C23×C4—861no—
392C2×SD16—434no—
393C2×SD16—434no—
394C2×SD16—434no—
395C22×C8—431no—
396C22×C8—431no—
397C22×C8C22×D4311yescharacteristic
398C22×C8C22×D4311yescharacteristic
399C4×Q8—434no—
400C4×Q8—862no—
401C4×Q8—862no—
402C4×Q8—862no—
403C4×Q8—1721no—
404C4×Q8—1721no—
405C4×D4—434no—
406C4×D4—862no—
407C4×D4—862no—
408C4×D4—862no—
409C4×D4—1721no—
410C4×D4—1721no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C42—431no—
430C2×C42—431no—
431C2×C42—861no—
432C2×C42—861no—
433C2×C42—861no—
434C2×C42C22×D4311yescharacteristic
435#107—1721no—
436#107—1721no—
437#106—22no—
438#106—862no—
439#106C4×D4314yescomplemented
440C4⋊C8—862no—
441#103—434no—
442#103—862no—
443#103—862no—
444#102—434no—
445#102—862no—
446#102—862no—
447C4×C8—22no—
448C4×C8—434no—
449C4×C8—862no—
450#95—21no—
451#95—21no—
452#95—431no—
453#95—431no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460C24—861no—
461C2×Q8—432no—
462C2×Q8—432no—
463C2×Q8—432no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×D4—432no—
468C2×D4—432no—
469C2×D4—432no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—864no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—3441no—
486C22×C4—3441no—
487C22×C4—3441no—
488C22×C4—3441no—
489C22×C4—1722no—
490C22×C4—1722no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4D4×D4311yescharacteristic
494C22×C4D4×D4311yescharacteristic
495C22×C4C23×D4311yescharacteristic
496SD16—4316no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—432no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8C2×C4×D4312yes—
507C2×C8D4×D4312yes—
508C2×C8Q8×D4312yes—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—42no—
516C4⋊C4—81no—
517C4⋊C4—862no—
518C4⋊C4—864no—
519C4⋊C4—862no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—3441no—
525C4⋊C4—1722no—
526C4⋊C4—1722no—
527C4⋊C4—1722no—
528C4⋊C4C2×C4×D4312yes—
529C4⋊C4C2×C4×D4312yes—
530C22⋊C4—864no—
531C22⋊C4—1722no—
532C22⋊C4—1722no—
533C42—21no—
534C42—21no—
535C42—432no—
536C42—432no—
537C42—864no—
538C42—861no—
539C42—861no—
540C42—1722no—
541C42—1722no—
542C23—862no—
543C23—862no—
544C23—862no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23—1721no—
549C23C2×D4×D4311yescharacteristic
550Q8—434no—
551Q8—862no—
552Q8—862no—
553Q8—862no—
554D4—434no—
555D4—862no—
556D4—862no—
557D4—862no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
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—432no—
576C2×C4—432no—
577C2×C4—432no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—862no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—3444no—
591C2×C4—3444no—
592C2×C4—3444no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4#1306334612yes—
600C2×C4C22×C4×D4311yescharacteristic
601C2×C4C2×D4×D4311yescharacteristic
602C2×C4C2×Q8×D4311yescharacteristic
603C2×C4#41×D4311yescharacteristic
604C2×C4#1306337111yescharacteristic
605C2×C4#1306337311yescharacteristic
606C8—41no—
607C8—862no—
608C8—1721no—
609C8C4⋊C4×D4314yes—
610C22—864no—
611C22—1722no—
612C22—1722no—
613C22—1722no—
614C22—1722no—
615C22—1722no—
616C22—1722no—
617C22C4×D4×D4311yescharacteristic
618C22#1458353311yescharacteristic
619C22#1458356411yescharacteristic
620C22#135×D4311yescharacteristic
621C22C2×#1306334611yescharacteristic
622C22#1458370511yescharacteristic
623C22#1458370611yescharacteristic
624C4—22no—
625C4—42no—
626C4—41no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—862no—
631C4—862no—
632C4—862no—
633C4—864no—
634C4—3441no—
635C4—3441no—
636C4—1721no—
637C4C2×C4⋊C4×D4311yescharacteristic
638C4#1458338111yescharacteristic
639C4#1458355111yescharacteristic
640C4#1458360511yescharacteristic
641C2—1724no—
642C2#1913749611yescharacteristic
643C2C4×#1306334611yescharacteristic
644C2#1914344911yescharacteristic
645C2#1914629911yescharacteristic
646C2#1914630911yescharacteristic
647C2#1914746711yescharacteristic
648C2#1914747511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1941C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1941D43
hypocenterC43#22683
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1941

Complements

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

NH ≅ G/Ntype
4. #19137514C2semidirect
6. #19135324C2semidirect
7. #19134850C2semidirect
8. #19134848C2semidirect
11. #19134756C2semidirect
12. #19134609C2semidirect
14. C8×Dic43⋊C4C2semidirect
15. C43×#1941C2semidirect
25. #14582986C4semidirect
77. #13063290C2×C4semidirect
107. #13063248C2×C4semidirect
112. C8×Dic43C2×C4semidirect
131. #106×C43C2×C4semidirect
216. #10621873C4⋊C4semidirect
323. #1941D43semidirect
386. C43#22683semidirect
439. #106C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106218732
C2×#145829862
#191375142
#191375042
#191353242
#191348502
#191348482
#191348432
#191348412
#191347562
#191346092
#191346042
C8×Dic43⋊C42
C43×#19412
#2268343