Finite Group Databasebeta

← #25125308

Subgroups — #25125308

Order 11008.

1102 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582940C211yesmaximal, characteristic
2C2×#14582921C211yesmaximal, characteristic
3C2×#14582906C211yesmaximal, characteristic
4C2×#14582906C211yesmaximal, characteristic
5#19137076C211yesmaximal, characteristic
6#391×D43C211yesmaximal, characteristic
7#19135987C211yesmaximal, characteristic, complemented
8#19135986C211yesmaximal, characteristic, complemented
9#19135985C211yesmaximal, characteristic, complemented
10#19135977C211yesmaximal, characteristic, complemented
11#19135976C211yesmaximal, characteristic, complemented
12#19135975C211yesmaximal, characteristic, complemented
13#19135974C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic
15C43×#2068C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C42×D43C2211yescharacteristic
23#14582940—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063257C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27#14582921—24no—
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×Dic43⋊C8C2211yescharacteristic
30C2×Dic43⋊C8C2211yescharacteristic
31#14582906—24no—
32#14582906—24no—
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39#14582806C2211yescharacteristic
40#14582805C2211yescharacteristic
41#14582804C2211yescharacteristic
42#14582803—21no—
43#14582803—21no—
44#14582798C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582795C2211yescharacteristic
47#14582773—21no—
48#14582770—21no—
49C4⋊C4×Dic43—21no—
50#14582750—21no—
51#95×D43—21no—
52#95×D43—21no—
53#14582662C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C2×#107×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×D43D411yescharacteristic
74C22×C4×D43D411yescharacteristic
75C22×C4×D43C2311yescharacteristic
76C2×#10621872—22no—
77C2×#10621872—22no—
78C2×#10621872—22no—
79C2×#10621872—22no—
80C2×#10621872—22no—
81C2×#10621872D414yes—
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84#13063283—22no—
85#13063283—22no—
86#13063283—22no—
87#13063283D414yes—
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—
95C4⋊C4×D43—22no—
96C4⋊C4×D43—22no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43D411yescharacteristic
102C2×C4×Dic43D411yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104C42×D43—22no—
105C42×D43—22no—
106#13063258—22no—
107#13063257—22no—
108#13063256—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#107×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—22no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—24no—
172C2×C4×D43—41no—
173C2×C4×D43—41no—
174C2×C4×D43—42no—
175C2×C4×D43—42no—
176C2×C4×D43—42no—
177C2×C4×D43—42no—
178C2×C4×D43—42no—
179C2×C4×D43C2×D412yes—
180C2×C4×D43C2×D412yes—
181C2×C4×D43C2×Q812yes—
182C2×C4×D43#4112yes—
183C2×C4×D43#4112yes—
184C2×C4×D43#4112yes—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—24no—
191C2×Dic86—42no—
192C2×Dic86—42no—
193C2×Dic86C2×Q812yes—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43C2×D412yes—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—42no—
206C4⋊C4×C43C2×D412yes—
207C42×C43—21no—
208C42×C43—21no—
209(C2×D43)⋊C4—24no—
210(C2×D43)⋊C4—42no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—42no—
217C4⋊Dic43C2×D412yes—
218Dic43⋊C4—42no—
219Dic43⋊C4—42no—
220Dic43⋊C4—42no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—22no—
224C4×Dic43—22no—
225C4×Dic43—24no—
226C4×Dic43—42no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8C2×D412yes—
233#10621872—28no—
234#10621872—44no—
235C23×C43C22×D411yescharacteristic
236C22×D43—21no—
237C22×D43—21no—
238C22×D43—21no—
239C22×D43—21no—
240C22×D43#12112yes—
241C22×D43#12112yes—
242C22×D43C22⋊Q812yes—
243Q8×C43—22no—
244Q8×C43—22no—
245Q8×C43—41no—
246Q8×C43—41no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—22no—
250C2×C4×C43—21no—
251C2×C4×C43—22no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
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×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43#13712yes—
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C22×Q811yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43#12112yes—
289C2×Dic43#12112yes—
290C2×Dic43C22⋊Q812yes—
291C2×Dic43#13712yes—
292C4×D43—44no—
293C4×D43—44no—
294C4×D43—48no—
295C4×D43—84no—
296C4×D43#12114yes—
297C4×D43C22⋊Q814yes—
298C4×D43C22⋊Q814yes—
299C4×D43#12614yes—
300Dic86—22no—
301Dic86—22no—
302Dic86—41no—
303Dic86—41no—
304Dic86—48no—
305C8×C43—22no—
306C8×C43—41no—
307C43⋊C8—22no—
308C43⋊C8—41no—
309#23619—431nomaximal, Sylow
310C22×C43C2×#12111yescharacteristic
311C22×C43C2×#12111yescharacteristic
312C22×C43C2×C22⋊Q811yescharacteristic
313C22×C43C2×#13711yescharacteristic
314C22×C43C2×#13711yescharacteristic
315C22×C43#57511yescharacteristic
316C22×C43#57511yescharacteristic
317C2×D43—22no—
318C2×D43—22no—
319C2×D43—22no—
320C2×D43—22no—
321C2×D43—22no—
322C2×D43—22no—
323C2×D43#39614yes—
324C4×C43—22no—
325C4×C43—42no—
326C4×C43—42no—
327C4×C43—41no—
328C4×C43—81no—
329C4×C43—81no—
330C4×C43C2×#12111yescharacteristic
331C4×C43C2×C22⋊Q811yescharacteristic
332C4×C43C2×C22⋊Q811yescharacteristic
333C4×C43C2×#12611yescharacteristic
334Dic43—22no—
335Dic43—42no—
336Dic43—42no—
337Dic43—41no—
338Dic43—81no—
339Dic43—81no—
340Dic43#39614yes—
341C2×#428—431no—
342C2×#423—431no—
343C2×#419—431no—
344C2×#419—431no—
345#2296—431no—
346C2×#391—431no—
347#2068—431no—
348#2068—431no—
349#2068—431no—
350#2068D4311yescharacteristic, complemented
351#2066—431no—
352#2066—431no—
353#2066—431no—
354#2066—431no—
355#1736—431no—
356C2×C43C2×#39611yescharacteristic
357C2×C43#303911yescharacteristic
358C2×C43#304011yescharacteristic
359C2×C43#305611yescharacteristic
360C2×C43#305611yescharacteristic
361C2×C43#307811yescharacteristic
362C2×C43#307811yescharacteristic
363D43—24no—
364C23×Q8—431no—
365C22×M16—431no—
366C22×M16—431no—
367C2×#117—431no—
368C2×#117—431no—
369C22×C4⋊C4—431no—
370C22×C42—431no—
371#428—864no—
372C2×#107—431no—
373C2×#107C2×D4311yescharacteristic
374C2×#106—431no—
375C2×#106—431no—
376#423—864no—
377C2×C4⋊C8—431no—
378C2×C4⋊C8—431no—
379C2×C4⋊C8—431no—
380C2×C4⋊C8C2×D4311yescharacteristic
381#419—864no—
382#419—864no—
383C2×#103—431no—
384C2×#103—431no—
385C2×#103—431no—
386C2×#103—431no—
387C2×#103—431no—
388C2×#103—431no—
389C2×#103C2×D4311yescharacteristic
390C2×#103C2×D4311yescharacteristic
391#391—431no—
392#391—431no—
393#391—431no—
394#391—861no—
395#391—861no—
396#391C2×D4311yescharacteristic
397#389—431no—
398#389—431no—
399#389—431no—
400#389C2×D4311yescharacteristic
401#385—861no—
402#385—861no—
403C4×C4⋊C4—861no—
404C4×C4⋊C4—861no—
405C2×#95—861no—
406C2×#95—861no—
407#340—431no—
408#340—431no—
409#340—431no—
410#340C2×D4311yescharacteristic
411C43#2361911yescharacteristic, complemented, Sylow
412C22×Q8—434no—
413C22×Q8—431no—
414C22×Q8—861no—
415C22×Q8—862no—
416C22×Q8—862no—
417C22×Q8—862no—
418C22×Q8—862no—
419C22×Q8—862no—
420C22×Q8C22×D4311yescharacteristic
421C23×C4—431no—
422C23×C4—431no—
423C23×C4—431no—
424C23×C4—861no—
425C23×C4—861no—
426C2×M16—434no—
427C2×M16—862no—
428C2×M16—862no—
429C2×M16—862no—
430C2×M16—862no—
431C2×M16—862no—
432C22×C8—431no—
433C22×C8—431no—
434C22×C8C22×D4311yescharacteristic
435C22×C8C22×D4311yescharacteristic
436#117—434no—
437#117—862no—
438#117—862no—
439#117—862no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—862no—
445C2×C4⋊C4—862no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4C22×D4311yescharacteristic
451C2×C4⋊C4C22×D4311yescharacteristic
452C2×C4⋊C4C22×D4311yescharacteristic
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C42—431no—
456C2×C42—431no—
457C2×C42—431no—
458C2×C42—862no—
459C2×C42—862no—
460C2×C42—861no—
461C2×C42—861no—
462C2×C42C22×D4311yescharacteristic
463#107—22no—
464#107—862no—
465#106—862no—
466#106—862no—
467C4⋊C8—22no—
468C4⋊C8—862no—
469C4⋊C8—862no—
470C4⋊C8—862no—
471#103—22no—
472#103—22no—
473#103—862no—
474#103—862no—
475#103—862no—
476#103—862no—
477#103—862no—
478#103—862no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—861no—
483#95—861no—
484#95—861no—
485#95—861no—
486#95—861no—
487#95—861no—
488#95—861no—
489#95—861no—
490#95—861no—
491C24—431no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—432no—
498C2×Q8—864no—
499C2×Q8—868no—
500C2×Q8—868no—
501C2×Q8—861no—
502C2×Q8—861no—
503C2×Q8—861no—
504C2×Q8—861no—
505C2×Q8—861no—
506C2×Q8—1722no—
507C2×Q8—1722no—
508C2×Q8—1724no—
509C2×Q8—1724no—
510C2×Q8Q8×D4312yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—431no—
516C22×C4—432no—
517C22×C4—432no—
518C22×C4—432no—
519C22×C4—432no—
520C22×C4—432no—
521C22×C4—432no—
522C22×C4—431no—
523C22×C4—431no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—862no—
527C22×C4—864no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—862no—
531C22×C4—861no—
532C22×C4—861no—
533C22×C4—1721no—
534C22×C4—1721no—
535C22×C4—1722no—
536C22×C4—1722no—
537C22×C4—1722no—
538C22×C4—1722no—
539C22×C4—1722no—
540C22×C4D4×D4311yescharacteristic
541C22×C4D4×D4311yescharacteristic
542C22×C4C23×D4311yescharacteristic
543M16—868no—
544M16—1724no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—432no—
551C2×C8—861no—
552C2×C8—861no—
553C2×C8—861no—
554C2×C8—861no—
555C2×C8—861no—
556C2×C8D4×D4312yes—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—42no—
563C4⋊C4—432no—
564C4⋊C4—861no—
565C4⋊C4—861no—
566C4⋊C4—861no—
567C4⋊C4—861no—
568C4⋊C4—861no—
569C4⋊C4—1722no—
570C4⋊C4—1722no—
571C4⋊C4—1722no—
572C4⋊C4—1722no—
573C4⋊C4D4×D4312yes—
574C22⋊C4—864no—
575C22⋊C4—1722no—
576C42—21no—
577C42—21no—
578C42—862no—
579C42—862no—
580C42—864no—
581C42—861no—
582C42—861no—
583C42—1722no—
584C23—432no—
585C23—432no—
586C23—432no—
587C23—861no—
588C23—861no—
589C23—861no—
590C23—861no—
591C23C2×D4×D4311yescharacteristic
592Q8—22no—
593Q8—22no—
594Q8—41no—
595Q8—41no—
596Q8—862no—
597Q8—862no—
598Q8—1728no—
599Q8—1721no—
600Q8—1721no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—432no—
619C2×C4—432no—
620C2×C4—432no—
621C2×C4—434no—
622C2×C4—434no—
623C2×C4—434no—
624C2×C4—434no—
625C2×C4—432no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—3444no—
634C2×C4—1724no—
635C2×C4—1724no—
636C2×C4—1728no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1721no—
647C2×C4#1306335712yes—
648C2×C4C2×D4×D4311yescharacteristic
649C2×C4C2×D4×D4311yescharacteristic
650C2×C4C2×Q8×D4311yescharacteristic
651C2×C4#41×D4311yescharacteristic
652C2×C4#41×D4311yescharacteristic
653C2×C4#41×D4311yescharacteristic
654C8—22no—
655C8—41no—
656C8—862no—
657C8—1721no—
658C22—434no—
659C22—862no—
660C22—862no—
661C22—862no—
662C22—862no—
663C22—862no—
664C22—862no—
665C22#121×D4311yescharacteristic
666C22#121×D4311yescharacteristic
667C22C22⋊Q8×D4311yescharacteristic
668C22#137×D4311yescharacteristic
669C22C2×#1306335711yescharacteristic
670C22#1458369511yescharacteristic
671C22#1458369611yescharacteristic
672C4—22no—
673C4—42no—
674C4—41no—
675C4—42no—
676C4—81no—
677C4—81no—
678C4—434no—
679C4—862no—
680C4—3441no—
681C4—3441no—
682C4—1722no—
683C4—1721no—
684C4—1722no—
685C4#121×D4311yescharacteristic
686C4C22⋊Q8×D4311yescharacteristic
687C4C22⋊Q8×D4311yescharacteristic
688C4#126×D4311yescharacteristic
689C2—864no—
690C2#396×D4311yescharacteristic
691C2#1914407911yescharacteristic
692C2#1914408411yescharacteristic
693C2#1914422011yescharacteristic
694C2#1914422211yescharacteristic
695C2#1914439811yescharacteristic
696C2#1914440111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2068C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2068D43
hypocenterC43#23619
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2068

Complements

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

NH ≅ G/Ntype
7. #19135987C2semidirect
8. #19135986C2semidirect
9. #19135985C2semidirect
10. #19135977C2semidirect
11. #19135976C2semidirect
12. #19135975C2semidirect
13. #19135974C2semidirect
15. C43×#2068C2semidirect
350. #2068D43semidirect
411. C43#23619semidirect

Maximal subgroups

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

subgroupindex
C2×#145829402
C2×#145829212
C2×#145829062
#191370762
#391×D432
#191359872
#191359862
#191359852
#191359772
#191359762
#191359752
#191359742
#191343132
C43×#20682
#2361943