Finite Group Databasebeta

← #25133137

Subgroups — #25133137

Order 11008.

1036 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583625C211yesmaximal, characteristic, complemented
2C2×#14583188C211yesmaximal, characteristic
3C2×#14583002C211yesmaximal, characteristic
4#19139955C211yesmaximal, characteristic
5#19135935C211yesmaximal, characteristic, complemented
6#19135933C211yesmaximal, characteristic, complemented
7#19135742C211yesmaximal, characteristic
8#19135740C211yesmaximal, characteristic
9#19135566C211yesmaximal, characteristic, complemented
10#19135533C211yesmaximal, characteristic, complemented
11#19134950C211yesmaximal, characteristic
12#19134948C211yesmaximal, characteristic
13#19134861C211yesmaximal, characteristic, complemented
14#19134608C211yesmaximal, characteristic, complemented
15C43×#1865C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17#14583625—24no—
18#14583625—24no—
19C2×#13063324—21no—
20C2×#13063324C2211yescharacteristic
21C2×#13063317—21no—
22C2×#13063317C2211yescharacteristic
23C2×#13063316—21no—
24C2×#13063316C2211yescharacteristic
25C2×Q8×Dic43C2211yescharacteristic
26C2×Q8×Dic43C2211yescharacteristic
27C2×C4×Dic86—21no—
28C2×C4×Dic86C2211yescharacteristic
29C2×#13063287C2211yescharacteristic
30#14583188—24no—
31#14583002—24no—
32C2×#13063258C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×Dic43⋊C8C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063235C2211yescharacteristic
40#14582834—21no—
41#14582812—21no—
42#14582801C2211yescharacteristic
43#14582800C2211yescharacteristic
44#14582795C2211yescharacteristic
45#14582773—21no—
46#14582770—21no—
47#14582764C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C2×#106×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C43×#389C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86D411yescharacteristic
65C22×D172C2311yescharacteristic
66C22×C4×D43—21no—
67C2×#10621884—22no—
68C2×#10621884—22no—
69C2×#10621884Q814yescomplemented
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063324—28no—
73#13063324—22no—
74#13063324D414yes—
75#13063317—28no—
76#13063317—22no—
77#13063317—22no—
78#13063316—28no—
79#13063316—22no—
80#13063316—22no—
81Q8×Dic43—22no—
82Q8×Dic43—22no—
83Q8×Dic43—22no—
84Q8×Dic43D414yes—
85C4×Dic86—28no—
86C4×Dic86—22no—
87C4×Dic86—22no—
88#13063287—22no—
89#13063287—22no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43D411yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4D411yescharacteristic
103C2×Dic43⋊C4D411yescharacteristic
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43C2311yescharacteristic
112C2×C4×Dic43C2311yescharacteristic
113#13063258—22no—
114#13063256—22no—
115Dic43⋊C8—22no—
116#13063249—22no—
117#13063247—22no—
118#13063247—22no—
119#13063245—22no—
120#13063235—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C22×Q8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C4×Q8×C43—22no—
128C4×Q8×C43—22no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136#106×C43—22no—
137#103×C43—22no—
138#103×C43—22no—
139#95×C43—21no—
140C23×D43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43C2×D412yes—
145C2×Q8×C43C2×Q812yes—
146C2×Q8×C43#4112yes—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172C2×Q812yes—
167C2×C4×D43—42no—
168C2×C4×D43—81no—
169C2×C4×D43—81no—
170C2×Dic86—22no—
171C2×Dic86—24no—
172C2×Dic86—41no—
173C2×Dic86—41no—
174C2×Dic86—42no—
175C2×Dic86—42no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C4⋊C4×C43—24no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—81no—
189C4⋊C4×C43C2×D412yes—
190C42×C43—24no—
191C42×C43—21no—
192C42×C43—21no—
193#10621884—28no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—81no—
198(C2×D43)⋊C4—81no—
199C4⋊Dic43—24no—
200C4⋊Dic43—24no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—24no—
204C4⋊Dic43—22no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43C2×D412yes—
208C4⋊Dic43C2×D412yes—
209Dic43⋊C4—24no—
210Dic43⋊C4—24no—
211Dic43⋊C4—24no—
212Dic43⋊C4—24no—
213Dic43⋊C4—22no—
214Dic43⋊C4—22no—
215Dic43⋊C4—81no—
216C4×Dic43—24no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—24no—
220C4×Dic43C2×D412yes—
221C4×Dic43C2×D412yes—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8C2×Q812yes—
228C23×C43C22×D411yescharacteristic
229C22×D43—22no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236Q8×C43—22no—
237Q8×C43—22no—
238Q8×C43—22no—
239Q8×C43C22⋊Q814yes—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C22×Q811yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C432−1+411yescharacteristic
263C2×C4×C432−1+411yescharacteristic
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—22no—
270C2×Dic43—21no—
271C2×Dic43—22no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43#12012yes—
284C2×Dic43#12012yes—
285D172—22no—
286D172—22no—
287D172—41no—
288D172—41no—
289C4×D43—84no—
290Dic86—44no—
291Dic86—48no—
292C8×C43—41no—
293C8×C43—41no—
294C43⋊C8—22no—
295C43⋊C8—41no—
296#24340—431nomaximal, Sylow
297C22×C43C2×#12011yescharacteristic
298C22×C43#54811yescharacteristic
299C22×C43D4×Q811yescharacteristic
300C22×C43#57511yescharacteristic
301C22×C43#57511yescharacteristic
302C22×C43#57711yescharacteristic
303C22×C43#57711yescharacteristic
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—81no—
311C4×C43—24no—
312C4×C43—41no—
313C4×C43—42no—
314C4×C43—41no—
315C4×C43—81no—
316C4×C43—81no—
317C4×C43C2×C22⋊Q811yescharacteristic
318C4×C43#53611yescharacteristic
319C4×C43#54811yescharacteristic
320C4×C43D4×Q811yescharacteristic
321Dic43—22no—
322Dic43—22no—
323Dic43—41no—
324Dic43—42no—
325Dic43—41no—
326Dic43—42no—
327Dic43—81no—
328C2×#557—431no—
329C2×#476—431no—
330C2×#440—431no—
331#2580—431no—
332#2059—431no—
333#2059—431no—
334#2025—431no—
335#2025—431no—
336#1993—431no—
337#1985—431no—
338#1880—431no—
339#1880—431no—
340#1865—431no—
341#1865D4311yescharacteristic, complemented
342#1805—431no—
343C2×C43#240911yescharacteristic
344C2×C43#300511yescharacteristic
345C2×C43#301011yescharacteristic
346C2×C43#337111yescharacteristic
347C2×C43#337111yescharacteristic
348C2×C43#338811yescharacteristic
349C2×C43#338811yescharacteristic
350D43—82no—
351C22×SD16—431no—
352#557—864no—
353#557—864no—
354C2×C4⋊Q8—431no—
355C2×C4⋊Q8—861no—
356C2×#125—431no—
357C2×#125—431no—
358C2×#125—861no—
359C2×#125—861no—
360C2×C4×Q8—431no—
361C2×C4×Q8—431no—
362C2×C4×Q8—431no—
363C2×C4×Q8—861no—
364C2×C4×Q8C2×D4311yescharacteristic
365C2×C4×D4—431no—
366#476—864no—
367#440—864no—
368C2×#107—431no—
369C2×#106—431no—
370C2×#106C2×D4311yescharacteristic
371C2×C4⋊C8—431no—
372C2×#103—431no—
373C2×#103C2×D4311yescharacteristic
374C2×#103C2×D4311yescharacteristic
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×#97—431no—
379#399—861no—
380#393—861no—
381#390—431no—
382#390—431no—
383#389—431no—
384#389C2×D4311yescharacteristic
385#385—861no—
386#385—861no—
387#382—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340C2×D4311yescharacteristic
394#336—431no—
395#336—431no—
396#336—431no—
397#336C2×D4311yescharacteristic
398C43#2434011yescharacteristic, complemented, Sylow
399C22×Q8—431no—
400C22×Q8—861no—
401C22×Q8C22×D4311yescharacteristic
402C22×D4—431no—
403C23×C4—861no—
404C2×SD16—434no—
405C2×SD16—862no—
406C2×SD16—862no—
407C22×C8—431no—
408C22×C8—431no—
409C22×C8C22×D4311yescharacteristic
410C22×C8C22×D4311yescharacteristic
411C4⋊Q8—434no—
412C4⋊Q8—862no—
413C4⋊Q8—868no—
414#125—862no—
415#125—862no—
416#125—868no—
417#125—862no—
418#125—868no—
419#125—862no—
420C4×Q8—22no—
421C4×Q8—22no—
422C4×Q8—434no—
423C4×Q8—862no—
424C4×Q8—862no—
425C4×Q8—868no—
426C4×Q8—862no—
427C4×Q8—862no—
428C4×Q8—862no—
429C4×D4—862no—
430C4×D4—862no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C4⋊C4C22×D4311yescharacteristic
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C42—21no—
456C2×C42—431no—
457C2×C42—431no—
458C2×C42—861no—
459C2×C42—861no—
460C2×C42C22×D4311yescharacteristic
461#107—862no—
462#106—22no—
463#106—862no—
464C4⋊C8—862no—
465#103—22no—
466#103—22no—
467#103—862no—
468#102—862no—
469#102—862no—
470#102—862no—
471#97—862no—
472#95—21no—
473#95—861no—
474#95—861no—
475#95—861no—
476C24—861no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—864no—
481C2×Q8—862no—
482C2×Q8—1721no—
483C2×Q8—1721no—
484C2×Q8—1722no—
485C2×Q8—1722no—
486C2×Q8#1062189812yes—
487C2×Q8D4×D4312yes—
488C2×Q8Q8×D4312yes—
489C2×D4—432no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—3441no—
507C22×C4—3441no—
508C22×C4—1722no—
509C22×C4D4×D4311yescharacteristic
510C22×C4D4×D4311yescharacteristic
511C22×C4C23×D4311yescharacteristic
512SD16—868no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—432no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C4⋊C4—24no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—81no—
532C4⋊C4—432no—
533C4⋊C4—432no—
534C4⋊C4—862no—
535C4⋊C4—862no—
536C4⋊C4—862no—
537C4⋊C4—864no—
538C4⋊C4—864no—
539C4⋊C4—864no—
540C4⋊C4—864no—
541C4⋊C4—864no—
542C4⋊C4—864no—
543C4⋊C4—864no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—3441no—
549C4⋊C4D4×D4312yes—
550C22⋊C4—3441no—
551C22⋊C4—3441no—
552C22⋊C4—1722no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C42—24no—
556C42—21no—
557C42—21no—
558C42—432no—
559C42—432no—
560C42—864no—
561C42—864no—
562C42—861no—
563C42—861no—
564C23—862no—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23—1721no—
571C23C2×D4×D4311yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—22no—
575Q8—1724no—
576Q8—1728no—
577Q8#1306330314yes—
578D4—862no—
579D4—862no—
580D4—1721no—
581D4—1721no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—432no—
601C2×C4—432no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—862no—
608C2×C4—862no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—3444no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4C2×D4×D4311yescharacteristic
623C2×C4C2×D4×D4311yescharacteristic
624C2×C4C2×Q8×D4311yescharacteristic
625C2×C4C2×#1062189811yescharacteristic
626C2×C4#1306337211yescharacteristic
627C2×C4#1306337211yescharacteristic
628C8—41no—
629C8—41no—
630C8—862no—
631C8—1721no—
632C22—3441no—
633C22—3441no—
634C22—3441no—
635C22—3441no—
636C22—1722no—
637C22—1722no—
638C22—1722no—
639C22#120×D4311yescharacteristic
640C22#1458355811yescharacteristic
641C22#1458356211yescharacteristic
642C22#1458369611yescharacteristic
643C22#1458369811yescharacteristic
644C22#1458370511yescharacteristic
645C22#1458370811yescharacteristic
646C4—24no—
647C4—41no—
648C4—42no—
649C4—41no—
650C4—81no—
651C4—81no—
652C4—862no—
653C4—862no—
654C4—3441no—
655C4—1721no—
656C4—1722no—
657C4—1721no—
658C4—1722no—
659C4C2×#1306330311yescharacteristic
660C4#1458347111yescharacteristic
661C4#1458355811yescharacteristic
662C4#1458356211yescharacteristic
663C2—3442no—
664C2#1913795911yescharacteristic
665C2#1914383811yescharacteristic
666C2#1914387611yescharacteristic
667C2#1914735911yescharacteristic
668C2#1914736411yescharacteristic
669C2#1914753811yescharacteristic
670C2#1914754711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1865C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1865D43
hypocenterC43#24340
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
1. C2×#14583625C2semidirect
5. #19135935C2semidirect
6. #19135933C2semidirect
9. #19135566C2semidirect
10. #19135533C2semidirect
13. #19134861C2semidirect
14. #19134608C2semidirect
15. C43×#1865C2semidirect
69. C2×#10621884Q8semidirect
341. #1865D43semidirect
398. C43#24340semidirect

Maximal subgroups

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

subgroupindex
C2×#145836252
C2×#145831882
C2×#145830022
#191399552
#191359352
#191359332
#191357422
#191357402
#191355662
#191355332
#191349502
#191349482
#191348612
#191346082
C43×#18652
#2434043