Finite Group Databasebeta

← #25154126

Subgroups — #25154126

Order 11008.

920 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583205C211yesmaximal, characteristic, complemented
2C2×#14582909C211yesmaximal, characteristic
3#19138309C211yesmaximal, characteristic
4#19137427C211yesmaximal, characteristic
5#19136130C211yesmaximal, characteristic, complemented
6#19135977C211yesmaximal, characteristic, complemented
7#19135971C211yesmaximal, characteristic, complemented
8#19135745C211yesmaximal, characteristic, complemented
9#19134860C211yesmaximal, characteristic, complemented
10#19134850C211yesmaximal, characteristic, complemented
11#19134792C211yesmaximal, characteristic
12#19134778C211yesmaximal, characteristic
13#19134599C211yesmaximal, characteristic, complemented
14#19134529C211yesmaximal, characteristic
15C43×#1809C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21#14583205—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26#14582909—24no—
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36#14582835—21no—
37#14582822—21no—
38#14582804C2211yescharacteristic
39#14582804C2211yescharacteristic
40#14582803—21no—
41#14582803—21no—
42#14582798C2211yescharacteristic
43#14582796—21no—
44#14582795C2211yescharacteristic
45#14582786—21no—
46#14582768C2211yescharacteristic
47#14582757—21no—
48C22⋊C4×Dic43—21no—
49C4×C22⋊Dic43C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×M16×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—22no—
62C22×Dic86—22no—
63C22×Dic86—21no—
64C22×Dic86—22no—
65C22×Dic86—41no—
66C22×Dic86—41no—
67C22×Dic86Q814yes—
68C22×Dic86C2311yescharacteristic
69C22×Dic86C2311yescharacteristic
70C23×Dic43—21no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063316—22no—
74#13063316—41no—
75#13063290—22no—
76#13063290—22no—
77#13063290—41no—
78#13063290—41no—
79#13063284—22no—
80#13063284—41no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43D411yescharacteristic
93C2×C22⋊Dic43D411yescharacteristic
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98C2×C4×Dic43C2311yescharacteristic
99#13063258—41no—
100#13063256—22no—
101Dic43⋊C8—22no—
102Dic43⋊C8—41no—
103#13063250—22no—
104#13063250—22no—
105#13063250—22no—
106#13063250D414yes—
107#13063248—22no—
108#13063248—22no—
109#13063248—41no—
110#13063248—41no—
111C22⋊(C43⋊C8)—22no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95D411yescharacteristic
119C43⋊#95D411yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C2×M16×C43—22no—
122C2×M16×C43—22no—
123C2×M16×C43—41no—
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132#107×C43—22no—
133#106×C43—41no—
134#95×C43—21no—
135#95×C43—21no—
136C24×C43C2×D411yescharacteristic
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×Q812yes—
147C22×C4×C43#4112yes—
148C22×C4×C43C2411yescharacteristic
149C22×Dic43—24no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—42no—
155C22×Dic43—42no—
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—28no—
168C2×Dic86—24no—
169C2×Dic86—21no—
170C2×Dic86—44no—
171C2×Dic86—44no—
172C2×Dic86—44no—
173C2×Dic86—42no—
174C2×Dic86—42no—
175C2×Dic86C2×D412yes—
176C2×Dic86C2×Q812yes—
177C2×Dic86C2×Q812yes—
178C2×Dic86#4112yes—
179M16×C43—44no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43C2×D412yes—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C22⋊C4×C43—42no—
195C22⋊C4×C43—81no—
196C22⋊Dic43—22no—
197C22⋊Dic43—41no—
198C22⋊Dic43—42no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—42no—
203C4⋊Dic43—81no—
204C4⋊Dic43C2×D412yes—
205Dic43⋊C4—42no—
206Dic43⋊C4—42no—
207Dic43⋊C4—42no—
208Dic43⋊C4—42no—
209Dic43⋊C4—42no—
210Dic43⋊C4—81no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—42no—
216C4×Dic43—42no—
217C4×Dic43—42no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43C22⋊Q812yes—
231C23×C43C22×D411yescharacteristic
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
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—41no—
250C2×C4×C43C22⋊Q812yes—
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C22×Q811yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—21no—
260C2×Dic43—22no—
261C2×Dic43—21no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—22no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—48no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43#13712yes—
282Dic86—22no—
283Dic86—22no—
284Dic86—22no—
285Dic86—22no—
286Dic86—22no—
287Dic86—48no—
288Dic86—41no—
289Dic86—41no—
290Dic86C22⋊Q814yes—
291C8×C43—22no—
292C8×C43—41no—
293C43⋊C8—41no—
294C43⋊C8—41no—
295#25981—431nomaximal, Sylow
296C22×C43—22no—
297C22×C43—22no—
298C22×C43—22no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43—41no—
303C22×C43C2×C22⋊Q811yescharacteristic
304C22×C43D4211yescharacteristic
305C22×C43#54611yescharacteristic
306C22×C43C2×#13711yescharacteristic
307C22×C43#57511yescharacteristic
308C22×C43#57711yescharacteristic
309C22×C43#57811yescharacteristic
310C4×C43—22no—
311C4×C43—81no—
312C4×C43—81no—
313C4×C43—81no—
314C4×C43—81no—
315C4×C43C2×C22⋊Q811yescharacteristic
316C4×C43#54311yescharacteristic
317C4×C43#54611yescharacteristic
318C4×C43#55111yescharacteristic
319Dic43—24no—
320Dic43—22no—
321Dic43—42no—
322Dic43—41no—
323Dic43—41no—
324Dic43—42no—
325Dic43—41no—
326Dic43—81no—
327C2×#479—431no—
328C2×#419—431no—
329#2441—431no—
330Q8×C22⋊C4—431no—
331#2095—431no—
332#2066—431no—
333#2066—431no—
334#2026—431no—
335#1865—431no—
336#1863—431no—
337#1854—431no—
338#1851—431no—
339#1809D4311yescharacteristic
340#1803—431no—
341#1787—431no—
342C2×C43—42no—
343C2×C43#243711yescharacteristic
344C2×C43#307811yescharacteristic
345C2×C43#308211yescharacteristic
346C2×C43#327111yescharacteristic
347C2×C43#327611yescharacteristic
348C2×C43#332011yescharacteristic
349C2×C43#332711yescharacteristic
350C23×Q8—431no—
351C22×M16C2×D4311yescharacteristic
352C2×#125—431no—
353C2×C4×Q8—431no—
354C2×C4×Q8—431no—
355C2×#117—431no—
356#479—864no—
357C2×#107—431no—
358C2×#107C2×D4311yescharacteristic
359C2×#106—431no—
360C2×#106C2×D4311yescharacteristic
361C2×C4⋊C8—431no—
362C2×C4⋊C8—431no—
363#419—864no—
364C2×#103—431no—
365C2×#103—431no—
366C2×#103—431no—
367C2×#103—431no—
368C2×#103—431no—
369C2×#103—431no—
370C2×#103—431no—
371C2×#103—431no—
372C2×C22⋊C8—431no—
373#399—861no—
374#396—861no—
375#391—431no—
376#391—431no—
377#391—861no—
378#391—861no—
379#389—431no—
380#389—431no—
381#389—861no—
382#387—861no—
383#384—431no—
384#380—861no—
385#380C2×D4311yescharacteristic
386#380C2×D4311yescharacteristic
387C4×C22⋊C4—431no—
388C4×C22⋊C4—861no—
389#340—431no—
390#340—431no—
391#340C2×D4311yescharacteristic
392#340C2×D4311yescharacteristic
393#336—431no—
394#336—431no—
395C43#2598111yescharacteristic, complemented, Sylow
396C22×Q8—434no—
397C22×Q8—431no—
398C22×Q8—431no—
399C22×Q8—862no—
400C22×Q8—862no—
401C22×Q8—862no—
402C22×Q8—861no—
403C22×Q8—1721no—
404C22×Q8—1721no—
405C23×C4—861no—
406C23×C4C22×D4311yescharacteristic
407C2×M16—22no—
408C2×M16—22no—
409C2×M16—41no—
410C22×C8—431no—
411C22×C8—431no—
412C22×C8C22×D4311yescharacteristic
413C22×C8C22×D4311yescharacteristic
414#125—862no—
415#125—1721no—
416C4×Q8—862no—
417C4×Q8—862no—
418C4×Q8—1721no—
419C4×Q8—1721no—
420#117—862no—
421#117—1721no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C4⋊C4C22×D4311yescharacteristic
435C2×C4⋊C4C22×D4311yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—431no—
439C2×C22⋊C4—431no—
440C2×C22⋊C4—861no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—861no—
444C2×C42—861no—
445C2×C42—861no—
446#107—22no—
447#107—1721no—
448#106—41no—
449#106—862no—
450C4⋊C8—862no—
451C4⋊C8—1721no—
452#103—434no—
453#103—862no—
454#103—862no—
455#103—862no—
456#103—862no—
457#103—862no—
458#103—1721no—
459#103—1721no—
460C22⋊C8—862no—
461#95—21no—
462#95—21no—
463#95—431no—
464#95—431no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471C24D4×D4311yescharacteristic
472C2×Q8—432no—
473C2×Q8—432no—
474C2×Q8—432no—
475C2×Q8—432no—
476C2×Q8—868no—
477C2×Q8—864no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8—861no—
483C2×Q8—861no—
484C2×Q8—861no—
485C2×Q8—861no—
486C2×Q8—1722no—
487C2×Q8—1722no—
488C2×Q8—1724no—
489C2×Q8—1724no—
490C2×Q8—1724no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
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—864no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—1722no—
509C22×C4—1722no—
510C22×C4#1062189812yes—
511C22×C4D4×D4311yescharacteristic
512C22×C4Q8×D4312yes—
513C22×C4C23×D4311yescharacteristic
514M16—44no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8D4×D4312yes—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—432no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—3441no—
540C4⋊C4—3441no—
541C4⋊C4—1722no—
542C4⋊C4—1722no—
543C4⋊C4—1722no—
544C4⋊C4—1722no—
545C4⋊C4—1722no—
546C4⋊C4—1722no—
547C22⋊C4—42no—
548C22⋊C4—81no—
549C22⋊C4—862no—
550C22⋊C4—1721no—
551C22⋊C4—1722no—
552C42—861no—
553C42—861no—
554C42—861no—
555C42—861no—
556C42—1722no—
557C42—1722no—
558C42—1722no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23#1306330312yes—
566C23C2×D4×D4311yescharacteristic
567Q8—434no—
568Q8—862no—
569Q8—862no—
570Q8—862no—
571Q8—862no—
572Q8—862no—
573Q8—1728no—
574Q8—1721no—
575Q8—1721no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
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—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—432no—
595C2×C4—862no—
596C2×C4—861no—
597C2×C4—862no—
598C2×C4—861no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—862no—
610C2×C4—861no—
611C2×C4—1728no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4#1306330312yes—
620C2×C4C2×D4×D4311yescharacteristic
621C2×C4C2×Q8×D4311yescharacteristic
622C2×C4#41×D4311yescharacteristic
623C2×C4C2×#1062189811yescharacteristic
624C2×C4#1306337011yescharacteristic
625C2×C4#1306337111yescharacteristic
626C8—22no—
627C8—41no—
628C8—1721no—
629C8—1721no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22C2×#1306330311yescharacteristic
638C22#1458353311yescharacteristic
639C22#1458353811yescharacteristic
640C22#137×D4311yescharacteristic
641C22#1458369511yescharacteristic
642C22#1458370911yescharacteristic
643C22#1458371511yescharacteristic
644C4—22no—
645C4—81no—
646C4—81no—
647C4—81no—
648C4—81no—
649C4—862no—
650C4—864no—
651C4—3441no—
652C4—1721no—
653C4—1721no—
654C4—1722no—
655C4—1721no—
656C4—1722no—
657C4C22⋊Q8×D4311yescharacteristic
658C4#1458352411yescharacteristic
659C4#1458353911yescharacteristic
660C4#1458357311yescharacteristic
661C2—42no—
662C2#1913826311yescharacteristic
663C2#1914439911yescharacteristic
664C2#1914443511yescharacteristic
665C2#1914618711yescharacteristic
666C2#1914623811yescharacteristic
667C2#1914676111yescharacteristic
668C2#1914686911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1809C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1809D43
hypocenterC43#25981
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
1. C2×#14583205C2semidirect
5. #19136130C2semidirect
6. #19135977C2semidirect
7. #19135971C2semidirect
8. #19135745C2semidirect
9. #19134860C2semidirect
10. #19134850C2semidirect
13. #19134599C2semidirect
395. C43#25981semidirect

Maximal subgroups

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

subgroupindex
C2×#145832052
C2×#145829092
#191383092
#191374272
#191361302
#191359772
#191359712
#191357452
#191348602
#191348502
#191347922
#191347782
#191345992
#191345292
C43×#18092
#2598143