Finite Group Databasebeta

← #25154117

Subgroups — #25154117

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×#14583208C211yesmaximal, characteristic, complemented
2C2×#14582906C211yesmaximal, characteristic
3#19138306C211yesmaximal, characteristic
4Q8×(C2×D43)⋊C4C211yesmaximal, characteristic
5#19136132C211yesmaximal, characteristic, complemented
6#19135973C211yesmaximal, characteristic, complemented
7#19135971C211yesmaximal, characteristic, complemented
8#19135745C211yesmaximal, characteristic, complemented
9#19134851C211yesmaximal, characteristic, complemented
10#19134797C211yesmaximal, characteristic
11#19134779C211yesmaximal, characteristic
12#19134625C211yesmaximal, characteristic
13#19134600C211yesmaximal, characteristic, complemented
14#19134528C211yesmaximal, characteristic
15C43×#1865C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×#13063316C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21#14583208—24no—
22C2×#13063259C2211yescharacteristic
23C2×#13063259C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27#14582906—24no—
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35#14582836—21no—
36#14582821—21no—
37#14582805—21no—
38#14582805C2211yescharacteristic
39#14582804—21no—
40#14582804C2211yescharacteristic
41#14582798—21no—
42#14582798C2211yescharacteristic
43#14582784—21no—
44#14582769C2211yescharacteristic
45#14582756—21no—
46#14582756C2211yescharacteristic
47#14582756C2211yescharacteristic
48C4×(C2×D43)⋊C4—21no—
49C4×(C2×D43)⋊C4C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C2×Q8×D43—22no—
64C2×Q8×D43—22no—
65C2×Q8×D43—22no—
66C2×Q8×D43—41no—
67C2×Q8×D43—41no—
68C2×Q8×D43Q814yes—
69C22×C4×D43—21no—
70C22×C4×D43C2311yescharacteristic
71C2×#10621872—22no—
72C2×#10621872—22no—
73C2×#10621872—41no—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063316—22no—
77#13063316—41no—
78Q8×Dic43—22no—
79Q8×Dic43—41no—
80#13063283—22no—
81#13063283—41no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4D411yescharacteristic
95C2×(C2×D43)⋊C4D411yescharacteristic
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99#13063259—22no—
100#13063259—41no—
101#13063256—22no—
102C4⋊(C43⋊C8)—41no—
103Dic43⋊C8—22no—
104#13063250—22no—
105#13063250—41no—
106#13063249—22no—
107#13063249—22no—
108#13063248—22no—
109#13063248—41no—
110(C2×D43)⋊C8—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95D411yescharacteristic
119C43⋊#95D411yescharacteristic
120C22×Q8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C4×Q8×C43—22no—
124C4×Q8×C43—41no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C42×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#106×C43—41no—
133#103×C43—22no—
134#103×C43D414yes—
135#95×C43—21no—
136C23×D43C2×D411yescharacteristic
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43C2×D412yes—
141C2×Q8×C43C2×Q812yes—
142C2×Q8×C43#4112yes—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157Q8×D43—28no—
158Q8×D43—44no—
159Q8×D43—44no—
160Q8×D43—44no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—24no—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×C4×D43C2×Q812yes—
169C2×C4×D43#4112yes—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—24no—
176C2×Dic86—42no—
177C2×Dic86—42no—
178C2×Dic86C2×Q812yes—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43C2×D412yes—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—42no—
191C4⋊C4×C43—42no—
192C4⋊C4×C43C2×D412yes—
193C42×C43—21no—
194C42×C43—21no—
195C42×C43—42no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—41no—
198(C2×D43)⋊C4—42no—
199(C2×D43)⋊C4—42no—
200(C2×D43)⋊C4—81no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—42no—
208C4⋊Dic43—42no—
209C4⋊Dic43—42no—
210C4⋊Dic43—81no—
211C4⋊Dic43—81no—
212Dic43⋊C4—42no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—42no—
216C4×Dic43—42no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223#10621872—44no—
224C23×C43C22×D411yescharacteristic
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43C22⋊Q812yes—
232Q8×C43—22no—
233Q8×C43—22no—
234Q8×C43—22no—
235Q8×C43C22⋊Q814yes—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—21no—
239C2×C4×C43—22no—
240C2×C4×C43—21no—
241C2×C4×C43—22no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43#13712yes—
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C22×Q811yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×Dic43—21no—
261C2×Dic43—21no—
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×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43C22⋊Q812yes—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—22no—
284C4×D43—22no—
285C4×D43—48no—
286Dic86—22no—
287Dic86—22no—
288Dic86—48no—
289Dic86—41no—
290Dic86—41no—
291C8×C43—22no—
292C8×C43—41no—
293C43⋊C8—41no—
294C43⋊C8—41no—
295#25981—431nomaximal, Sylow
296C22×C43C2×C22⋊Q811yescharacteristic
297C22×C43D4211yescharacteristic
298C22×C43#54611yescharacteristic
299C22×C43C2×#13711yescharacteristic
300C22×C43#57511yescharacteristic
301C22×C43#57711yescharacteristic
302C22×C43#57811yescharacteristic
303C2×D43—22no—
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—41no—
307C2×D43—41no—
308C2×D43—41no—
309C2×D43—41no—
310C4×C43—24no—
311C4×C43—22no—
312C4×C43—42no—
313C4×C43—41no—
314C4×C43—81no—
315C4×C43—81no—
316C4×C43C2×C22⋊Q811yescharacteristic
317C4×C43#54311yescharacteristic
318C4×C43#54611yescharacteristic
319C4×C43#55111yescharacteristic
320Dic43—22no—
321Dic43—42no—
322Dic43—41no—
323Dic43—41no—
324Dic43—81no—
325Dic43—81no—
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#1865D4311yescharacteristic, complemented
336#1863—431no—
337#1854—431no—
338#1851—431no—
339#1809—431no—
340#1803—431no—
341#1787—431no—
342C2×C43#243711yescharacteristic
343C2×C43#307811yescharacteristic
344C2×C43#308211yescharacteristic
345C2×C43#327111yescharacteristic
346C2×C43#327611yescharacteristic
347C2×C43#332011yescharacteristic
348C2×C43#332711yescharacteristic
349D43—42no—
350C23×Q8—431no—
351C22×M16—431no—
352C2×#125—431no—
353C2×C4×Q8—431no—
354C2×C4×Q8C2×D4311yescharacteristic
355C2×#117—431no—
356#479—864no—
357C2×#107—431no—
358C2×#107—431no—
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×#103C2×D4311yescharacteristic
371C2×#103C2×D4311yescharacteristic
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—861no—
381#389C2×D4311yescharacteristic
382#387—861no—
383#384—431no—
384#380—431no—
385#380—431no—
386#380—861no—
387C4×C22⋊C4—431no—
388C4×C22⋊C4—861no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340C2×D4311yescharacteristic
393#336—431no—
394#336C2×D4311yescharacteristic
395C43#2598111yescharacteristic, complemented, Sylow
396C22×Q8—434no—
397C22×Q8—431no—
398C22×Q8—861no—
399C22×Q8—862no—
400C22×Q8—862no—
401C22×Q8—862no—
402C22×Q8—1721no—
403C22×Q8—1721no—
404C22×Q8C22×D4311yescharacteristic
405C23×C4—431no—
406C23×C4—861no—
407C2×M16—862no—
408C2×M16—862no—
409C2×M16—1721no—
410C22×C8—431no—
411C22×C8—431no—
412C22×C8C22×D4311yescharacteristic
413C22×C8C22×D4311yescharacteristic
414#125—862no—
415#125—1721no—
416C4×Q8—22no—
417C4×Q8—41no—
418C4×Q8—862no—
419C4×Q8—1721no—
420#117—862no—
421#117—1721no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C4⋊C4C22×D4311yescharacteristic
435C2×C4⋊C4C22×D4311yescharacteristic
436C2×C22⋊C4—431no—
437C2×C22⋊C4—431no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C42—21no—
442C2×C42—431no—
443C2×C42—861no—
444C2×C42—861no—
445C2×C42C22×D4311yescharacteristic
446#107—862no—
447#107—1721no—
448#106—41no—
449#106—862no—
450C4⋊C8—862no—
451C4⋊C8—1721no—
452#103—22no—
453#103—862no—
454#103—862no—
455#103—862no—
456#103—862no—
457#103—1721no—
458#103—1721no—
459#103D17214yes—
460C22⋊C8—862no—
461#95—21no—
462#95—431no—
463#95—431no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471C24—431no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—432no—
476C2×Q8—864no—
477C2×Q8—861no—
478C2×Q8—868no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8—861no—
483C2×Q8—1722no—
484C2×Q8—1722no—
485C2×Q8—1724no—
486C2×Q8—1724no—
487C2×Q8—1724no—
488C2×Q8C2×D17212yes—
489C2×Q8#1062190012yes—
490C2×Q8Q8×D4312yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—431no—
496C22×C4—432no—
497C22×C4—432no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—864no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—1722no—
510C22×C4—1722no—
511C22×C4D4×D4311yescharacteristic
512C22×C4D4×D4311yescharacteristic
513C22×C4C23×D4311yescharacteristic
514M16—1724no—
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×C8C2×D17212yes—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—3441no—
541C4⋊C4—3441no—
542C4⋊C4—1722no—
543C4⋊C4—1722no—
544C4⋊C4—1722no—
545C4⋊C4—1722no—
546C4⋊C4C2×D17212yes—
547C22⋊C4—862no—
548C22⋊C4—3441no—
549C22⋊C4—1721no—
550C22⋊C4—1722no—
551C22⋊C4—1722no—
552C42—21no—
553C42—21no—
554C42—42no—
555C42—861no—
556C42—861no—
557C42—1722no—
558C42—1722no—
559C23—432no—
560C23—861no—
561C23—861no—
562C23—861no—
563C23—861no—
564C23—861no—
565C23—861no—
566C23C2×D4×D4311yescharacteristic
567Q8—22no—
568Q8—22no—
569Q8—22no—
570Q8—862no—
571Q8—862no—
572Q8—1728no—
573Q8—1721no—
574Q8—1721no—
575Q8#1306330514yes—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
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—432no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
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—1728no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4#1306335412yes—
620C2×C4C22×D17211yescharacteristic
621C2×C4C2×Q8×D4311yescharacteristic
622C2×C4#41×D4311yescharacteristic
623C2×C4C2×#1062190011yescharacteristic
624C2×C4#1306337011yescharacteristic
625C2×C4#1306337111yescharacteristic
626C8—22no—
627C8—41no—
628C8—1721no—
629C8—1721no—
630C22—862no—
631C22—862no—
632C22—862no—
633C22—1721no—
634C22—1721no—
635C22—1721no—
636C22—1721no—
637C22C22⋊Q8×D4311yescharacteristic
638C22D4×D17211yescharacteristic
639C22#1458353611yescharacteristic
640C22C2×#1306335411yescharacteristic
641C22#1458369811yescharacteristic
642C22#1458370811yescharacteristic
643C22#1458371311yescharacteristic
644C4—22no—
645C4—24no—
646C4—42no—
647C4—41no—
648C4—81no—
649C4—81no—
650C4—862no—
651C4—3441no—
652C4—3441no—
653C4—3441no—
654C4—1721no—
655C4—1721no—
656C4—1722no—
657C4C2×#1306330511yescharacteristic
658C4#1458352411yescharacteristic
659C4#1458354411yescharacteristic
660C4#1458357211yescharacteristic
661C2—1722no—
662C2#1913825911yescharacteristic
663C2#1914439511yescharacteristic
664C2#1914443611yescharacteristic
665C2#1914618211yescharacteristic
666C2#1914624211yescharacteristic
667C2#1914677011yescharacteristic
668C2#1914685611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1865C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1865D43
hypocenterC43#25981
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
1. C2×#14583208C2semidirect
5. #19136132C2semidirect
6. #19135973C2semidirect
7. #19135971C2semidirect
8. #19135745C2semidirect
9. #19134851C2semidirect
13. #19134600C2semidirect
15. C43×#1865C2semidirect
335. #1865D43semidirect
395. C43#25981semidirect

Maximal subgroups

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

subgroupindex
C2×#145832082
C2×#145829062
#191383062
Q8×(C2×D43)⋊C42
#191361322
#191359732
#191359712
#191357452
#191348512
#191347972
#191347792
#191346252
#191346002
#191345282
C43×#18652
#2598143