Finite Group Databasebeta

← #25125245

Subgroups — #25125245

Order 11008.

1054 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582934C211yesmaximal, characteristic
2C2×#14582924C211yesmaximal, characteristic
3C2×#14582906C211yesmaximal, characteristic
4C2×#103×D43C211yesmaximal, characteristic
5#19137217C211yesmaximal, characteristic
6#19137178C211yesmaximal, characteristic
7#19135991C211yesmaximal, characteristic, complemented
8#19135990C211yesmaximal, characteristic, complemented
9#19135987C211yesmaximal, characteristic, complemented
10#19135986C211yesmaximal, characteristic, complemented
11#19135975C211yesmaximal, characteristic, complemented
12#19135974C211yesmaximal, characteristic, complemented
13#19135971C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic
15C43×#2066C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×#13063282C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14582934—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27#14582924—24no—
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×Dic43⋊C8C2211yescharacteristic
30C2×Dic43⋊C8C2211yescharacteristic
31#14582906—24no—
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38#103×D43—24no—
39#14582806C2211yescharacteristic
40#14582805C2211yescharacteristic
41#14582804C2211yescharacteristic
42#14582803—21no—
43#14582803—21no—
44#14582798C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582795C2211yescharacteristic
47#14582773—21no—
48#14582770—21no—
49#14582768—21no—
50#14582763—21no—
51#14582761—21no—
52#14582761—21no—
53#14582662C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C43×#391C2211yescharacteristic
61C43×#389C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C2×Q8×D43—22no—
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43Q814yes—
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C22×C4×D43C2311yescharacteristic
74C2×#10621872—22no—
75C2×#10621872—22no—
76C2×#10621872—22no—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C2×C8×D43—22no—
80C2×C8×D43—22no—
81C2×C8×D43D414yes—
82#13063283—22no—
83#13063283—22no—
84#13063283—22no—
85#13063283D414yes—
86#13063282—22no—
87#13063282—22no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4D411yescharacteristic
96C2×Dic43⋊C4D411yescharacteristic
97C4⋊C4×D43—22no—
98C4⋊C4×D43—22no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4D411yescharacteristic
102C2×(C2×D43)⋊C4D411yescharacteristic
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2311yescharacteristic
106#13063258—22no—
107#13063258—22no—
108#13063257—22no—
109C4⋊(C43⋊C8)—22no—
110Dic43⋊C8—22no—
111Dic43⋊C8—22no—
112#13063250—22no—
113#13063250—22no—
114#13063249—22no—
115#13063249—22no—
116#13063248—22no—
117#13063248—22no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C22×Q8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C42×C43C2311yescharacteristic
135#106×C43—22no—
136C4⋊C8×C43—22no—
137#103×C43—22no—
138#103×C43—22no—
139#95×C43—21no—
140#95×C43—21no—
141#95×C43—21no—
142C23×D43C2×D411yescharacteristic
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×Q812yes—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163Q8×D43—28no—
164Q8×D43—28no—
165Q8×D43—44no—
166Q8×D43—44no—
167C2×C4×D43—24no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170C2×C4×D43—42no—
171C2×C4×D43—81no—
172C2×C4×D43—81no—
173C2×C4×D43C2×D412yes—
174C2×C4×D43C2×D412yes—
175C2×C4×D43C2×Q812yes—
176C2×C4×D43#4112yes—
177C2×C4×D43#4112yes—
178C2×C4×D43#4112yes—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—24no—
185C2×Dic86—42no—
186C2×Dic86—42no—
187C2×Dic86C2×Q812yes—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43C2×D412yes—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—81no—
200C4⋊C4×C43C2×D412yes—
201C42×C43—21no—
202C42×C43—21no—
203(C2×D43)⋊C4—24no—
204(C2×D43)⋊C4—22no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—42no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—81no—
213C4⋊Dic43C2×D412yes—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—42no—
217Dic43⋊C4—81no—
218Dic43⋊C4—81no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—24no—
222C4×Dic43—42no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8C2×D412yes—
229#10621872—44no—
230C8×D43—28no—
231C23×C43C22×D411yescharacteristic
232C22×D43—21no—
233C22×D43—21no—
234C22×D43—21no—
235C22×D43—21no—
236C22×D43#12112yes—
237C22×D43#12112yes—
238C22×D43C22⋊Q812yes—
239Q8×C43—22no—
240Q8×C43—22no—
241Q8×C43—41no—
242Q8×C43—41no—
243C2×C4×C43—22no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—22no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
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×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C22×Q811yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43#12112yes—
286C2×Dic43#12112yes—
287C2×Dic43C22⋊Q812yes—
288C4×D43—48no—
289C4×D43—84no—
290C4×D43#12114yes—
291C4×D43C22⋊Q814yes—
292C4×D43C22⋊Q814yes—
293C4×D43#12614yes—
294Dic86—22no—
295Dic86—22no—
296Dic86—41no—
297Dic86—41no—
298Dic86—48no—
299C8×C43—22no—
300C8×C43—41no—
301C43⋊C8—22no—
302C43⋊C8—41no—
303#23613—431nomaximal, Sylow
304C22×C43C2×#12111yescharacteristic
305C22×C43C2×#12111yescharacteristic
306C22×C43C2×C22⋊Q811yescharacteristic
307C22×C43#57711yescharacteristic
308C22×C43#57711yescharacteristic
309C22×C43#57811yescharacteristic
310C22×C43#57811yescharacteristic
311C2×D43—22no—
312C2×D43—22no—
313C2×D43—22no—
314C2×D43—22no—
315C2×D43—22no—
316C2×D43—22no—
317C2×D43#39614yes—
318C4×C43—42no—
319C4×C43—42no—
320C4×C43—41no—
321C4×C43—41no—
322C4×C43—81no—
323C4×C43—81no—
324C4×C43C2×#12111yescharacteristic
325C4×C43C2×C22⋊Q811yescharacteristic
326C4×C43C2×C22⋊Q811yescharacteristic
327C4×C43C2×#12611yescharacteristic
328Dic43—42no—
329Dic43—42no—
330Dic43—41no—
331Dic43—41no—
332Dic43—81no—
333Dic43—81no—
334Dic43#39614yes—
335C2×#427—431no—
336C2×#424—431no—
337C2×#419—431no—
338C22×#103—431no—
339#2317—431no—
340#2310—431no—
341#2068—431no—
342#2068—431no—
343#2068—431no—
344#2068—431no—
345#2066—431no—
346#2066—431no—
347#2066—431no—
348#2066D4311yescharacteristic, complemented
349#1736—431no—
350C2×C43C2×#39611yescharacteristic
351C2×C43#304611yescharacteristic
352C2×C43#304611yescharacteristic
353C2×C43#305711yescharacteristic
354C2×C43#305911yescharacteristic
355C2×C43#308211yescharacteristic
356C2×C43#308211yescharacteristic
357D43—24no—
358C23×Q8—431no—
359C22×M16—431no—
360C23×C8—431no—
361C2×#117—431no—
362C2×#117—431no—
363C2×#117—431no—
364C22×C4⋊C4—431no—
365#427—864no—
366C2×#107—431no—
367C2×#107—431no—
368C2×#106—431no—
369C2×#106C2×D4311yescharacteristic
370#424—864no—
371C2×C4⋊C8—431no—
372C2×C4⋊C8—431no—
373C2×C4⋊C8—431no—
374C2×C4⋊C8C2×D4311yescharacteristic
375#419—864no—
376C2×#103—431no—
377C2×#103—431no—
378C2×#103—431no—
379C2×#103—431no—
380C2×#103—431no—
381C2×#103—431no—
382C2×#103—864no—
383C2×#103C2×D4311yescharacteristic
384C2×#103C2×D4311yescharacteristic
385#391—431no—
386#391—431no—
387#391—431no—
388#391—861no—
389#391—861no—
390#391C2×D4311yescharacteristic
391#389—431no—
392#389—431no—
393#389—431no—
394#389C2×D4311yescharacteristic
395#385—861no—
396#385—861no—
397#384—861no—
398#382—861no—
399#381—861no—
400#381—861no—
401#340—431no—
402#340—431no—
403#340—431no—
404#340C2×D4311yescharacteristic
405C43#2361311yescharacteristic, complemented, Sylow
406C22×Q8—434no—
407C22×Q8—431no—
408C22×Q8—861no—
409C22×Q8—862no—
410C22×Q8—862no—
411C22×Q8—862no—
412C22×Q8—862no—
413C22×Q8—862no—
414C22×Q8C22×D4311yescharacteristic
415C23×C4—431no—
416C23×C4—861no—
417C23×C4—861no—
418C2×M16—862no—
419C2×M16—862no—
420C2×M16—862no—
421C22×C8—431no—
422C22×C8—434no—
423C22×C8—431no—
424C22×C8—862no—
425C22×C8—862no—
426C22×C8C22×D4311yescharacteristic
427C22×C8C22×D4311yescharacteristic
428#117—434no—
429#117—862no—
430#117—862no—
431#117—862no—
432#117—862no—
433#117—862no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—862no—
441C2×C4⋊C4—862no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C4⋊C4C22×D4311yescharacteristic
449C2×C22⋊C4—431no—
450C2×C22⋊C4—431no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C42—431no—
454C2×C42—861no—
455C2×C42—861no—
456C2×C42C22×D4311yescharacteristic
457#107—862no—
458#107—862no—
459#106—22no—
460#106—862no—
461C4⋊C8—22no—
462C4⋊C8—862no—
463C4⋊C8—862no—
464C4⋊C8—862no—
465#103—22no—
466#103—22no—
467#103—862no—
468#103—862no—
469#103—862no—
470#103—862no—
471#103—862no—
472#103—862no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—861no—
477#95—861no—
478#95—861no—
479#95—861no—
480#95—861no—
481#95—861no—
482#95—861no—
483#95—861no—
484#95—861no—
485C24—431no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—432no—
492C2×Q8—864no—
493C2×Q8—868no—
494C2×Q8—868no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8—861no—
500C2×Q8—1722no—
501C2×Q8—1722no—
502C2×Q8—1724no—
503C2×Q8—1724no—
504C2×Q8Q8×D4312yes—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—431no—
510C22×C4—432no—
511C22×C4—432no—
512C22×C4—432no—
513C22×C4—432no—
514C22×C4—432no—
515C22×C4—432no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—864no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—3441no—
524C22×C4—3441no—
525C22×C4—1722no—
526C22×C4—1722no—
527C22×C4—1722no—
528C22×C4D4×D4311yescharacteristic
529C22×C4D4×D4311yescharacteristic
530C22×C4C23×D4311yescharacteristic
531M16—1724no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—432no—
538C2×C8—868no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8D4×D4312yes—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—81no—
551C4⋊C4—432no—
552C4⋊C4—862no—
553C4⋊C4—862no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—3441no—
560C4⋊C4—3441no—
561C4⋊C4—3441no—
562C4⋊C4—1722no—
563C4⋊C4D4×D4312yes—
564C22⋊C4—862no—
565C22⋊C4—862no—
566C22⋊C4—864no—
567C22⋊C4—1722no—
568C42—21no—
569C42—21no—
570C42—864no—
571C42—861no—
572C42—861no—
573C42—1722no—
574C23—432no—
575C23—432no—
576C23—432no—
577C23—861no—
578C23—861no—
579C23—861no—
580C23—861no—
581C23C2×D4×D4311yescharacteristic
582Q8—22no—
583Q8—22no—
584Q8—41no—
585Q8—41no—
586Q8—862no—
587Q8—862no—
588Q8—1728no—
589Q8—1721no—
590Q8—1721no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—432no—
610C2×C4—432no—
611C2×C4—432no—
612C2×C4—434no—
613C2×C4—434no—
614C2×C4—434no—
615C2×C4—434no—
616C2×C4—862no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—862no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—3444no—
625C2×C4—1728no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4C2×D4×D4311yescharacteristic
637C2×C4C2×D4×D4311yescharacteristic
638C2×C4C2×Q8×D4311yescharacteristic
639C2×C4#41×D4311yescharacteristic
640C2×C4#41×D4311yescharacteristic
641C2×C4#41×D4311yescharacteristic
642C8—22no—
643C8—41no—
644C8—862no—
645C8—1721no—
646C22—434no—
647C22—862no—
648C22—862no—
649C22—862no—
650C22—862no—
651C22—862no—
652C22—862no—
653C22#121×D4311yescharacteristic
654C22#121×D4311yescharacteristic
655C22C22⋊Q8×D4311yescharacteristic
656C22#1458370511yescharacteristic
657C22#1458370611yescharacteristic
658C22#1458371511yescharacteristic
659C22#1458371511yescharacteristic
660C4—42no—
661C4—41no—
662C4—41no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—434no—
667C4—3441no—
668C4—3441no—
669C4—1722no—
670C4—1721no—
671C4—1721no—
672C4—1722no—
673C4#121×D4311yescharacteristic
674C4C22⋊Q8×D4311yescharacteristic
675C4C22⋊Q8×D4311yescharacteristic
676C4#126×D4311yescharacteristic
677C2—864no—
678C2#396×D4311yescharacteristic
679C2#1914414011yescharacteristic
680C2#1914414811yescharacteristic
681C2#1914422911yescharacteristic
682C2#1914424811yescharacteristic
683C2#1914443011yescharacteristic
684C2#1914443411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2066C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2066D43
hypocenterC43#23613
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2066

Complements

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

NH ≅ G/Ntype
7. #19135991C2semidirect
8. #19135990C2semidirect
9. #19135987C2semidirect
10. #19135986C2semidirect
11. #19135975C2semidirect
12. #19135974C2semidirect
13. #19135971C2semidirect
15. C43×#2066C2semidirect
348. #2066D43semidirect
405. C43#23613semidirect

Maximal subgroups

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

subgroupindex
C2×#145829342
C2×#145829242
C2×#145829062
C2×#103×D432
#191372172
#191371782
#191359912
#191359902
#191359872
#191359862
#191359752
#191359742
#191359712
#191343132
C43×#20662
#2361343