Finite Group Databasebeta

← #25150771

Subgroups — #25150771

Order 11008.

1028 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583623C211yesmaximal, characteristic
2C2×#14583260C211yesmaximal, characteristic
3C2×#14583182C211yesmaximal, characteristic, complemented
4#19139802C211yesmaximal, characteristic, complemented
5#19135838C211yesmaximal, characteristic, complemented
6#19135833C211yesmaximal, characteristic
7#19135832C211yesmaximal, characteristic
8#19135533C211yesmaximal, characteristic, complemented
9#19135524C211yesmaximal, characteristic
10#19134865C211yesmaximal, characteristic, complemented
11#19134861C211yesmaximal, characteristic, complemented
12#19134859C211yesmaximal, characteristic
13#19134855C211yesmaximal, characteristic
14#19134427C211yesmaximal, characteristic, complemented
15C43×#2043C211yesmaximal, characteristic, complemented
16#14583623—24no—
17#14583623—24no—
18C2×#13063324C2211yescharacteristic
19C2×#13063320—21no—
20C2×#13063320—21no—
21C2×#13063314C2211yescharacteristic
22C2×#13063314C2211yescharacteristic
23C2×#13063305—21no—
24C2×Q8×Dic43C2211yescharacteristic
25C2×Q8×Dic43C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28C2×#13063283—21no—
29#14583260—24no—
30#14583182—24no—
31C2×#13063257C2211yescharacteristic
32C2×#13063256C2211yescharacteristic
33C2×Dic43⋊C8C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063235C2211yescharacteristic
43#14582820—21no—
44#14582819—21no—
45#14582803—21no—
46#14582798C2211yescharacteristic
47#14582797C2211yescharacteristic
48#14582795C2211yescharacteristic
49#14582768—21no—
50C4⋊C4×Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C4⋊Q8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C43×#389C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86D411yescharacteristic
65C22×D172C2311yescharacteristic
66C22×C4×D43—21no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063324—22no—
70#13063324—22no—
71#13063320—28no—
72#13063320—28no—
73#13063314—22no—
74#13063314—22no—
75#13063314—22no—
76#13063314D414yes—
77#13063305—28no—
78Q8×Dic43—22no—
79Q8×Dic43—22no—
80Q8×Dic43—22no—
81Q8×Dic43D414yes—
82C4×Dic86—22no—
83C4×Dic86—22no—
84C4×D172—22no—
85C4×D172—22no—
86#13063283—28no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43D411yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4D411yescharacteristic
98C2×Dic43⋊C4D411yescharacteristic
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43C2311yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109#13063257—22no—
110#13063256—22no—
111Dic43⋊C8—22no—
112#13063249—22no—
113#13063249—22no—
114#13063249—22no—
115#13063249—22no—
116#13063247—22no—
117#13063247—22no—
118#13063245—22no—
119#13063245—22no—
120#13063235—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C22×Q8×C43C2311yescharacteristic
126C22×Q8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C4⋊Q8×C43—22no—
130C4⋊Q8×C43—22no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C42×C43C2311yescharacteristic
137#103×C43—22no—
138#103×C43—22no—
139#103×C43—22no—
140#103×C43—22no—
141#95×C43—21no—
142C23×D43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43C2×D412yes—
154C2×Q8×C43C2×D412yes—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172C2×D412yes—
175C2×C4×D43—24no—
176C2×C4×D43—42no—
177C2×C4×D43—42no—
178C2×Dic86—22no—
179C2×Dic86—22no—
180C2×Dic86—41no—
181C2×Dic86—42no—
182C2×Dic86—81no—
183C2×Dic86—81no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C4⋊C4×C43—24no—
191C4⋊C4×C43—24no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—81no—
196C4⋊C4×C43#4112yes—
197C42×C43—21no—
198C42×C43—21no—
199(C2×D43)⋊C4—24no—
200(C2×D43)⋊C4—24no—
201(C2×D43)⋊C4—24no—
202(C2×D43)⋊C4—24no—
203(C2×D43)⋊C4—24no—
204C4⋊Dic43—24no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—24no—
208C4⋊Dic43—22no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—81no—
212C4⋊Dic43C2×D412yes—
213C4⋊Dic43#4112yes—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—42no—
217Dic43⋊C4—81no—
218Dic43⋊C4—81no—
219C4×Dic43—24no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—24no—
223C4×Dic43—42no—
224C4×Dic43C2×D412yes—
225C4×Dic43C2×D412yes—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C23×C43C22×D411yescharacteristic
233C22×D43—22no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—41no—
240Q8×C43—22no—
241Q8×C43—22no—
242Q8×C43—22no—
243Q8×C43—22no—
244Q8×C43—41no—
245Q8×C43—41no—
246Q8×C43—41no—
247Q8×C43—41no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—21no—
253C2×C4×C43—22no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43#13712yes—
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C432−1+411yescharacteristic
271C2×C4×C432−1+411yescharacteristic
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—22no—
278C2×Dic43—21no—
279C2×Dic43—22no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43#12012yes—
292C2×Dic43#12012yes—
293D172—22no—
294D172—22no—
295D172—41no—
296D172—41no—
297C4×D43—48no—
298Dic86—44no—
299Dic86—84no—
300C8×C43—41no—
301C8×C43—41no—
302C43⋊C8—41no—
303C43⋊C8—41no—
304#25662—431nomaximal, Sylow
305C22×C43C2×#12011yescharacteristic
306C22×C43#54811yescharacteristic
307C22×C43#54811yescharacteristic
308C22×C43C2×#13711yescharacteristic
309C22×C43#57511yescharacteristic
310C22×C43#57711yescharacteristic
311C22×C43#57711yescharacteristic
312C2×D43—42no—
313C2×D43—42no—
314C2×D43—42no—
315C2×D43—81no—
316C2×D43—81no—
317C2×D43—81no—
318C2×D43—81no—
319C4×C43—22no—
320C4×C43—42no—
321C4×C43—42no—
322C4×C43—42no—
323C4×C43—41no—
324C4×C43—81no—
325C4×C43#53211yescharacteristic
326C4×C43#53611yescharacteristic
327C4×C43#54711yescharacteristic
328C4×C43#54711yescharacteristic
329Dic43—22no—
330Dic43—22no—
331Dic43—42no—
332Dic43—41no—
333Dic43—42no—
334Dic43—41no—
335Dic43—81no—
336C2×#556—431no—
337C2×#489—431no—
338C2×#475—431no—
339#2567—431no—
340#2043—431no—
341#2043D4311yescharacteristic, complemented
342#2042—431no—
343#2042—431no—
344#1985—431no—
345#1983—431no—
346#1865—431no—
347#1865—431no—
348#1864—431no—
349#1864—431no—
350#1763—431no—
351C2×C43#243211yescharacteristic
352C2×C43#300711yescharacteristic
353C2×C43#301011yescharacteristic
354C2×C43#336911yescharacteristic
355C2×C43#336911yescharacteristic
356C2×C43#337611yescharacteristic
357C2×C43#337611yescharacteristic
358D43—82no—
359#556—864no—
360#556—864no—
361C2×C4⋊Q8—431no—
362C2×C4⋊Q8C2×D4311yescharacteristic
363C2×#126—861no—
364C2×#126—861no—
365C2×#124—431no—
366C2×#124—431no—
367C2×C22⋊Q8—861no—
368C2×C4×Q8—431no—
369C2×C4×Q8—431no—
370C2×C4×Q8—431no—
371C2×C4×D4—431no—
372C2×#117—861no—
373#489—864no—
374#475—864no—
375C2×#106—431no—
376C2×#106—431no—
377C2×C4⋊C8—431no—
378C2×#103—431no—
379C2×#103—431no—
380C2×#103—431no—
381C2×#103—431no—
382C2×#103C2×D4311yescharacteristic
383C2×#103C2×D4311yescharacteristic
384C2×#103C2×D4311yescharacteristic
385C2×#103C2×D4311yescharacteristic
386C2×#102—431no—
387C2×#102—431no—
388C2×#102—431no—
389C2×#102—431no—
390C2×#97—431no—
391#395—861no—
392#395—861no—
393#391—861no—
394#389—431no—
395#389—431no—
396#389—431no—
397#389C2×D4311yescharacteristic
398#384—861no—
399C4×C4⋊C4—431no—
400#340—431no—
401#340—431no—
402#336—431no—
403#336—431no—
404#336—431no—
405#336C2×D4311yescharacteristic
406C43#2566211yescharacteristic, complemented, Sylow
407C22×Q8—431no—
408C22×Q8—861no—
409C22×Q8C22×D4311yescharacteristic
410C22×Q8C22×D4311yescharacteristic
411C22×D4—431no—
412C23×C4—861no—
413C22×C8—431no—
414C22×C8—431no—
415C22×C8C22×D4311yescharacteristic
416C22×C8C22×D4311yescharacteristic
417C4⋊Q8—22no—
418C4⋊Q8—22no—
419C4⋊Q8—862no—
420C4⋊Q8—862no—
421#126—868no—
422#126—868no—
423#124—434no—
424#124—862no—
425#124—862no—
426#124—862no—
427C22⋊Q8—868no—
428C4×Q8—434no—
429C4×Q8—862no—
430C4×Q8—862no—
431C4×Q8—862no—
432C4×Q8—862no—
433C4×Q8—862no—
434C4×D4—862no—
435C4×D4—862no—
436#117—868no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4C22×D4311yescharacteristic
453C2×C4⋊C4C22×D4311yescharacteristic
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—861no—
462C2×C42—861no—
463C2×C42—861no—
464C2×C42C22×D4311yescharacteristic
465#106—862no—
466#106—862no—
467C4⋊C8—862no—
468#103—22no—
469#103—22no—
470#103—22no—
471#103—22no—
472#103—862no—
473#103—862no—
474#103—862no—
475#103—862no—
476#102—862no—
477#102—862no—
478#102—862no—
479#102—862no—
480#97—862no—
481#95—21no—
482#95—861no—
483#95—861no—
484#95—861no—
485#95—861no—
486C24—861no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—862no—
498C2×Q8—862no—
499C2×Q8—3441no—
500C2×Q8—3441no—
501C2×Q8—1721no—
502C2×Q8—1722no—
503C2×Q8D4×D4312yes—
504C2×Q8D4×D4312yes—
505C2×D4—432no—
506C2×D4—861no—
507C2×D4—861no—
508C2×D4—861no—
509C2×D4—861no—
510C2×D4—861no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—431no—
519C22×C4—864no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—1722no—
524C22×C4—1722no—
525C22×C4D4×D4311yescharacteristic
526C22×C4D4×D4311yescharacteristic
527C22×C4C23×D4311yescharacteristic
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—861no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C4⋊C4—24no—
541C4⋊C4—24no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—81no—
546C4⋊C4—432no—
547C4⋊C4—432no—
548C4⋊C4—862no—
549C4⋊C4—862no—
550C4⋊C4—862no—
551C4⋊C4—864no—
552C4⋊C4—864no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—3441no—
558C4⋊C4—3441no—
559C4⋊C4—3441no—
560C4⋊C4—1722no—
561C4⋊C4#1062190012yes—
562C22⋊C4—864no—
563C22⋊C4—864no—
564C22⋊C4—864no—
565C22⋊C4—864no—
566C22⋊C4—864no—
567C42—21no—
568C42—21no—
569C42—432no—
570C42—432no—
571C42—864no—
572C42—864no—
573C42—861no—
574C42—861no—
575C42—1722no—
576C23—862no—
577C23—1721no—
578C23—1721no—
579C23—1721no—
580C23—1721no—
581C23—1721no—
582C23—1721no—
583C23C2×D4×D4311yescharacteristic
584Q8—22no—
585Q8—22no—
586Q8—22no—
587Q8—22no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591Q8—41no—
592Q8—3444no—
593Q8—1724no—
594D4—862no—
595D4—862no—
596D4—1721no—
597D4—1721no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—432no—
616C2×C4—432no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—862no—
622C2×C4—861no—
623C2×C4—862no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—1728no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4#1306335712yes—
638C2×C4C2×D4×D4311yescharacteristic
639C2×C4C2×D4×D4311yescharacteristic
640C2×C4#41×D4311yescharacteristic
641C2×C4C2×#1062190011yescharacteristic
642C2×C4#1306337211yescharacteristic
643C2×C4#1306337211yescharacteristic
644C8—41no—
645C8—41no—
646C8—1721no—
647C8—1721no—
648C22—3441no—
649C22—3441no—
650C22—3441no—
651C22—3441no—
652C22—1722no—
653C22—1722no—
654C22—1722no—
655C22#120×D4311yescharacteristic
656C22#1458355511yescharacteristic
657C22#1458355711yescharacteristic
658C22C2×#1306335711yescharacteristic
659C22#1458369811yescharacteristic
660C22#1458370511yescharacteristic
661C22#1458370811yescharacteristic
662C4—22no—
663C4—42no—
664C4—42no—
665C4—42no—
666C4—41no—
667C4—81no—
668C4—862no—
669C4—862no—
670C4—3441no—
671C4—1722no—
672C4—1721no—
673C4—1722no—
674C4—1721no—
675C4#1458344411yescharacteristic
676C4#1458347111yescharacteristic
677C4#1458354711yescharacteristic
678C4#1458354911yescharacteristic
679C2—3442no—
680C2#1913821811yescharacteristic
681C2#1914385411yescharacteristic
682C2#1914387611yescharacteristic
683C2#1914733911yescharacteristic
684C2#1914734011yescharacteristic
685C2#1914741511yescharacteristic
686C2#1914741711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2043C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2043D43
hypocenterC43#25662
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
3. C2×#14583182C2semidirect
4. #19139802C2semidirect
5. #19135838C2semidirect
8. #19135533C2semidirect
10. #19134865C2semidirect
11. #19134861C2semidirect
14. #19134427C2semidirect
15. C43×#2043C2semidirect
341. #2043D43semidirect
406. C43#25662semidirect

Maximal subgroups

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

subgroupindex
C2×#145836232
C2×#145832602
C2×#145831822
#191398022
#191358382
#191358332
#191358322
#191355332
#191355242
#191348652
#191348612
#191348592
#191348552
#191344272
C43×#20432
#2566243