Finite Group Databasebeta

← #25103002

Subgroups — #25103002

Order 11008.

1008 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583103C211yesmaximal, characteristic
2C2×#14582997C211yesmaximal, characteristic
3C2×C4×#10621873C211yesmaximal, characteristic
4#19137311C211yesmaximal, characteristic, complemented
5#19136955C211yesmaximal, characteristic
6#19135516C211yesmaximal, characteristic, complemented
7#19135362C211yesmaximal, characteristic, complemented
8#19135234C211yesmaximal, characteristic, complemented
9#19135231C211yesmaximal, characteristic, complemented
10#19134930C211yesmaximal, characteristic
11#19134926C211yesmaximal, characteristic
12#19134604C211yesmaximal, characteristic
13#19134453C211yesmaximal, characteristic, complemented
14#19134428C211yesmaximal, characteristic, complemented
15C4×#103×C43C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063323C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23#14583103C418yescomplemented
24#14582997—24no—
25C4×#10621873—24no—
26C2×#13063258C2211yescharacteristic
27C2×#13063257C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×Dic43⋊C8C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37#14582806C2211yescharacteristic
38#14582804C2211yescharacteristic
39#14582783—21no—
40#14582783—21no—
41#14582780—21no—
42#14582780—21no—
43#14582764C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4×(C2×D43)⋊C4—21no—
47C4×(C2×D43)⋊C4—21no—
48#14582746—21no—
49#14582745C2211yescharacteristic
50#95×D43—21no—
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C2×#10621873—22no—
68C2×#10621873—22no—
69C2×#10621873C2×C414yes—
70C2×#10621884—22no—
71C2×#10621884—22no—
72C2×#10621884C2×C414yes—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063323—22no—
76#13063323C2×C414yescomplemented
77C4×Dic86—22no—
78C4×Dic86—22no—
79C4×D172—22no—
80C4×D172D414yes—
81#13063287—22no—
82#13063287—22no—
83#13063287—22no—
84#13063287C2×C414yes—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98#13063258—22no—
99#13063257—22no—
100Dic43⋊C8—22no—
101Dic43⋊C8C2×C414yescomplemented
102#13063250—22no—
103#13063249—22no—
104#13063248—22no—
105#13063248C2×C414yescomplemented
106#13063247—22no—
107#13063245—22no—
108#13063236—22no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95D411yescharacteristic
118C43⋊#95D411yescharacteristic
119C43⋊#95D411yescharacteristic
120C43⋊#95D411yescharacteristic
121C22×Q8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C4×Q8×C43—22no—
125C4×Q8×C43—22no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C42×C43—21no—
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133#103×C43—22no—
134#103×C43C2×C414yescomplemented
135C4×C8×C43—22no—
136#95×C43—21no—
137C23×D43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172C22×C412yes—
162C2×D172C2×D412yes—
163C2×D172#4112yes—
164C2×C4×D43—24no—
165C2×C4×D43—24no—
166C2×C4×D43—24no—
167C2×C4×D43—81no—
168C2×C4×D43—81no—
169C2×C4×D43—81no—
170C2×C4×D43—81no—
171C2×C4×D43—81no—
172C2×C4×D43—81no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86C22×C412yes—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43C22×C412yes—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—42no—
190C4⋊C4×C43C22×C412yes—
191C4⋊C4×C43#4112yes—
192C42×C43—42no—
193C42×C43—81no—
194C42×C43C2×D412yes—
195C42×C43#4112yes—
196#10621884—28no—
197(C2×D43)⋊C4—24no—
198(C2×D43)⋊C4—24no—
199(C2×D43)⋊C4—24no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43C2×D412yes—
204Dic43⋊C4—24no—
205Dic43⋊C4—24no—
206Dic43⋊C4—42no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—42no—
210C4×Dic43—81no—
211C4×Dic43—81no—
212C4×Dic43C22×C412yes—
213C4×Dic43#4112yes—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8C22×C412yes—
220#10621873—28no—
221C23×C43C22×D411yescharacteristic
222C22×D43—22no—
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229Q8×C43—22no—
230Q8×C43—22no—
231Q8×C43—41no—
232Q8×C43—41no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43#12112yes—
250C2×C4×C43#12112yes—
251C2×C4×C43C23×C411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43C4×D412yes—
277C2×Dic43C4×D412yes—
278D172—22no—
279D172—22no—
280D172—22no—
281D172C4×D414yes—
282C4×D43—84no—
283C4×D43—84no—
284C4×D43—84no—
285Dic86—22no—
286Dic86—22no—
287Dic86—41no—
288Dic86—41no—
289C8×C43—22no—
290C8×C43—41no—
291C43⋊C8—22no—
292C43⋊C8—41no—
293#21514—431nomaximal, Sylow
294C22×C43C2×C4×D411yescharacteristic
295C22×C43C2×#12111yescharacteristic
296C22×C43#52511yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57711yescharacteristic
299C22×C43#57711yescharacteristic
300C22×C43#57811yescharacteristic
301C2×D43—24no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C4×C43—22no—
309C4×C43—22no—
310C4×C43—42no—
311C4×C43—42no—
312C4×C43—42no—
313C4×C43—81no—
314C4×C43C2×C4×D411yescharacteristic
315C4×C43C4×#4111yescharacteristic
316C4×C43#52911yescharacteristic
317C4×C43#53211yescharacteristic
318Dic43—22no—
319Dic43—22no—
320Dic43—41no—
321Dic43—41no—
322Dic43—42no—
323Dic43—42no—
324Dic43—81no—
325C2×#461—431no—
326C2×#440—431no—
327C2×C4×SD16—431no—
328#2327—431no—
329#2275—431no—
330#1981—431no—
331#1949—431no—
332#1928—431no—
333#1927—431no—
334#1877—431no—
335#1877—431no—
336#1804—431no—
337#1768—431no—
338#1763—431no—
339C4×#103D4311yescharacteristic, complemented
340C2×C43C4×#12111yescharacteristic
341C2×C43#294711yescharacteristic
342C2×C43#294911yescharacteristic
343C2×C43#304211yescharacteristic
344C2×C43#304611yescharacteristic
345C2×C43#312011yescharacteristic
346C2×C43#312311yescharacteristic
347D43—44no—
348C22×SD16—431no—
349C22×SD16—431no—
350C2×C4⋊Q8—431no—
351C2×C4×Q8—431no—
352C2×C4×Q8C2×D4311yescharacteristic
353C2×C4×D4—431no—
354C2×C4×D4—431no—
355C2×C4×D4—431no—
356#461—438no—
357#440—864no—
358C4×SD16—864no—
359C2×#107—431no—
360C2×#106—431no—
361C2×C4⋊C8—431no—
362C2×C4⋊C8—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#103—431no—
366C2×#103—431no—
367C2×#103C2×D4311yescharacteristic
368C2×#103C2×D4311yescharacteristic
369C2×#102—431no—
370C2×#102—431no—
371C2×#97—431no—
372C2×C4×C8C2×D4311yescharacteristic
373#391—431no—
374#391—431no—
375#387—861no—
376#387—861no—
377#387—861no—
378#387—861no—
379#382—431no—
380C4×C4⋊C4—431no—
381C4×C4⋊C4—431no—
382C4×C4⋊C4C2×D4311yescharacteristic
383C4×C22⋊C4—861no—
384C4×C22⋊C4—861no—
385C4×C22⋊C4—861no—
386#376—431no—
387C2×#95—861no—
388#340—431no—
389#340—431no—
390#340C2×D4311yescharacteristic
391#340C2×D4311yescharacteristic
392#336—431no—
393#336—431no—
394C43#2151411yescharacteristic, complemented, Sylow
395C22×Q8—431no—
396C22×Q8C22×D4311yescharacteristic
397C22×D4—431no—
398C23×C4—861no—
399C23×C4—861no—
400C23×C4—861no—
401C2×SD16—434no—
402C2×SD16—434no—
403C2×SD16—862no—
404C2×SD16—862no—
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—22no—
414C4×Q8—22no—
415C4×Q8—862no—
416C4×Q8—862no—
417C4×D4—434no—
418C4×D4—434no—
419C4×D4—862no—
420C4×D4—862no—
421C4×D4—862no—
422C4×D4—862no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—861no—
440C2×C42—861no—
441C2×C42—861no—
442C2×C42C22×D4311yescharacteristic
443#107—862no—
444#106—862no—
445C4⋊C8—434no—
446C4⋊C8—862no—
447#103—22no—
448#103—434no—
449#103—862no—
450#103—862no—
451#103—862no—
452#103C4×D4314yescomplemented
453#102—862no—
454#102—862no—
455#97—862no—
456C4×C8—22no—
457#95—21no—
458#95—431no—
459#95—431no—
460#95—431no—
461#95—431no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470C24—861no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—432no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8C2×C4×D4312yes—
483C2×D4—432no—
484C2×D4—432no—
485C2×D4—432no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—861no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—864no—
498C22×C4—864no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—864no—
502C22×C4—861no—
503C22×C4—3441no—
504C22×C4—3441no—
505C22×C4—3441no—
506C22×C4—3441no—
507C22×C4—3441no—
508C22×C4—3441no—
509C22×C4D4×D4311yescharacteristic
510C22×C4D4×D4311yescharacteristic
511C22×C4C23×D4311yescharacteristic
512SD16—868no—
513SD16—868no—
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—
525C2×C8C2×C4×D4312yes—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—432no—
532C4⋊C4—864no—
533C4⋊C4—864no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—1722no—
538C4⋊C4C2×C4×D4312yes—
539C4⋊C4#1062189812yes—
540C22⋊C4—864no—
541C22⋊C4—864no—
542C22⋊C4—864no—
543C42—42no—
544C42—81no—
545C42—432no—
546C42—432no—
547C42—861no—
548C42—861no—
549C42—3441no—
550C42—3441no—
551C42—1722no—
552C42#1062189812yes—
553C42D4×D4312yes—
554C23—862no—
555C23—862no—
556C23—862no—
557C23—1721no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23C2×D4×D4311yescharacteristic
562Q8—22no—
563Q8—22no—
564Q8—41no—
565Q8—41no—
566Q8—862no—
567Q8—862no—
568Q8—1721no—
569Q8—1721no—
570D4—434no—
571D4—862no—
572D4—862no—
573D4—862no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—432no—
591C2×C4—432no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—3444no—
605C2×C4—3444no—
606C2×C4—3444no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4#1306329812yes—
615C2×C4#1306329812yes—
616C2×C4C22×C4×D4311yescharacteristic
617C2×C4C2×D4×D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4#41×D4311yescharacteristic
620C2×C4C2×#1062189811yescharacteristic
621C2×C4C2×#1062189811yescharacteristic
622C8—22no—
623C8—41no—
624C8—862no—
625C8—1721no—
626C22—864no—
627C22—1722no—
628C22—1722no—
629C22—1722no—
630C22—1722no—
631C22—1722no—
632C22—1722no—
633C22C4×D4×D4311yescharacteristic
634C22C2×#1306329811yescharacteristic
635C22#1458340811yescharacteristic
636C22#1458370511yescharacteristic
637C22#1458370611yescharacteristic
638C22#1458370611yescharacteristic
639C22#1458371211yescharacteristic
640C4—22no—
641C4—22no—
642C4—42no—
643C4—42no—
644C4—42no—
645C4—81no—
646C4—862no—
647C4—862no—
648C4—3441no—
649C4—1722no—
650C4—1721no—
651C4—1721no—
652C4—1722no—
653C4C4×D4×D4311yescharacteristic
654C4C4×#1062189811yescharacteristic
655C4#1458342711yescharacteristic
656C4#1458344611yescharacteristic
657C2—1724no—
658C2C4×#1306329811yescharacteristic
659C2#1914343311yescharacteristic
660C2#1914344911yescharacteristic
661C2#1914411011yescharacteristic
662C2#1914415011yescharacteristic
663C2#1914481511yescharacteristic
664C2#1914484411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#103×C43C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenterC4×#103D43
hypocenterC43#21514
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
4. #19137311C2semidirect
6. #19135516C2semidirect
7. #19135362C2semidirect
8. #19135234C2semidirect
9. #19135231C2semidirect
13. #19134453C2semidirect
14. #19134428C2semidirect
15. C4×#103×C43C2semidirect
23. #14583103C4semidirect
76. #13063323C2×C4semidirect
101. Dic43⋊C8C2×C4semidirect
105. #13063248C2×C4semidirect
134. #103×C43C2×C4semidirect
339. C4×#103D43semidirect
394. C43#21514semidirect
452. #103C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831032
C2×#145829972
C2×C4×#106218732
#191373112
#191369552
#191355162
#191353622
#191352342
#191352312
#191349302
#191349262
#191346042
#191344532
#191344282
C4×#103×C432
#2151443