Finite Group Databasebeta

← #25132809

Subgroups — #25132809

Order 11008.

1012 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583527C211yesmaximal, characteristic
2C2×#14583207C211yesmaximal, characteristic, complemented
3C2×#14583195C211yesmaximal, characteristic, complemented
4#19137277C211yesmaximal, characteristic
5#19135934C211yesmaximal, characteristic, complemented
6#19135924C211yesmaximal, characteristic, complemented
7#19135747C211yesmaximal, characteristic, complemented
8#19135737C211yesmaximal, characteristic, complemented
9#19135550C211yesmaximal, characteristic, complemented
10#19135546C211yesmaximal, characteristic, complemented
11#19134905C211yesmaximal, characteristic
12#19134900C211yesmaximal, characteristic
13#19134796C211yesmaximal, characteristic
14#19134785C211yesmaximal, characteristic
15C43×#1798C211yesmaximal, characteristic
16#14583527—24no—
17#14583527—24no—
18C2×#13063325C2211yescharacteristic
19C2×#13063325C2211yescharacteristic
20C2×#13063324—21no—
21C2×#13063317C2211yescharacteristic
22C2×#13063317C2211yescharacteristic
23C2×#13063316—21no—
24C2×#13063304C2211yescharacteristic
25C2×#13063302—21no—
26C2×#13063302—21no—
27C2×C4×Dic86C2211yescharacteristic
28C2×#13063284C2211yescharacteristic
29C22×C4⋊Dic43C2211yescharacteristic
30#14583207—24no—
31#14583195—24no—
32C2×#13063259C2211yescharacteristic
33C2×#13063259C2211yescharacteristic
34C2×#13063259C2211yescharacteristic
35C2×#13063257C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063250C2211yescharacteristic
40#14582805C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582794—21no—
43#14582793—21no—
44#14582787—21no—
45#14582780—21no—
46#14582759C2211yescharacteristic
47C4×C4⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582662C2211yescharacteristic
56C2×#117×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86—21no—
65C22×Dic86C2311yescharacteristic
66C23×Dic43—21no—
67#13063325—22no—
68#13063325—22no—
69#13063325—22no—
70#13063325D414yes—
71#13063324—28no—
72#13063317—22no—
73#13063317—22no—
74#13063317—22no—
75#13063317D414yes—
76#13063316—28no—
77#13063304—22no—
78#13063304Q814yescomplemented
79#13063302—28no—
80#13063302—28no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83#13063284—22no—
84#13063284—22no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43—22no—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110#13063259—22no—
111#13063259—22no—
112#13063259—22no—
113#13063257—22no—
114#13063250—22no—
115#13063250—22no—
116#13063250—22no—
117#13063250—22no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C23×C4×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128#117×C43—22no—
129#117×C43—22no—
130C2×C4⋊C4×C43D411yescharacteristic
131C2×C4⋊C4×C43D411yescharacteristic
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C22⋊C4×C43D411yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—22no—
137C4⋊C8×C43—22no—
138C22⋊C8×C43—22no—
139C22⋊C8×C43—22no—
140C24×C43C2×D411yescharacteristic
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×Q812yes—
151C22×C4×C43#4112yes—
152C22×C4×C43C2411yescharacteristic
153C22×Dic43—24no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—81no—
163C22×Dic43—81no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—24no—
170C2×Dic86—24no—
171C2×Dic86—81no—
172C2×Dic86—81no—
173C2×Dic86—81no—
174C2×Dic86—81no—
175C2×Dic86C2×Q812yes—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—22no—
190C22⋊C4×C43—22no—
191C22⋊C4×C43—22no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43C2×D412yes—
195C42×C43C2×D412yes—
196C22⋊Dic43—24no—
197C22⋊Dic43—24no—
198C22⋊Dic43—81no—
199C4⋊Dic43—24no—
200C4⋊Dic43—24no—
201C4⋊Dic43—24no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43C2×D412yes—
212C4⋊Dic43C2×D412yes—
213C4⋊Dic43C2×D412yes—
214C4⋊Dic43C2×D412yes—
215C4⋊Dic43C2×Q812yes—
216Dic43⋊C4—24no—
217Dic43⋊C4—24no—
218Dic43⋊C4—24no—
219Dic43⋊C4—24no—
220Dic43⋊C4—24no—
221Dic43⋊C4—42no—
222Dic43⋊C4—81no—
223C4×Dic43—24no—
224C4×Dic43—42no—
225C4×Dic43—81no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43C22⋊Q812yes—
233C23×C43C22×D411yescharacteristic
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43#12012yes—
251C2×C4×C43#12012yes—
252C2×C4×C43C22⋊Q812yes—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C22×Q811yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C432−1+411yescharacteristic
258C2×C4×C432−1+411yescharacteristic
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
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×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—84no—
284Dic86—22no—
285Dic86—22no—
286Dic86—41no—
287Dic86—41no—
288Dic86—84no—
289Dic86—84no—
290C8×C43—41no—
291C8×C43—41no—
292C8×C43—41no—
293C8×C43—41no—
294#24311—431nomaximal, Sylow
295C22×C43—22no—
296C22×C43—22no—
297C22×C43—22no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43C2×#12011yescharacteristic
303C22×C43C2×C22⋊Q811yescharacteristic
304C22×C43#53611yescharacteristic
305C22×C43#57611yescharacteristic
306C22×C43#57711yescharacteristic
307C22×C43#57811yescharacteristic
308C22×C43#57811yescharacteristic
309C4×C43—22no—
310C4×C43—22no—
311C4×C43—22no—
312C4×C43—41no—
313C4×C43—41no—
314C4×C43#54811yescharacteristic
315C4×C43#54811yescharacteristic
316C4×C43D4×Q811yescharacteristic
317C4×C43D4×Q811yescharacteristic
318Dic43—42no—
319Dic43—42no—
320Dic43—42no—
321Dic43—42no—
322Dic43—42no—
323Dic43—42no—
324Dic43—81no—
325Dic43—81no—
326C2×#544—431no—
327C2×#479—431no—
328C2×#477—431no—
329#2323—431no—
330#2059—431no—
331#2057—431no—
332#2026—431no—
333#2024—431no—
334#1989—431no—
335#1988—431no—
336#1873—431no—
337#1872—431no—
338#1854—431no—
339#1852—431no—
340#1798D4311yescharacteristic
341C2×C43—42no—
342C2×C43#240911yescharacteristic
343C2×C43#301111yescharacteristic
344C2×C43#301211yescharacteristic
345C2×C43#308211yescharacteristic
346C2×C43#308311yescharacteristic
347C2×C43#324211yescharacteristic
348C2×C43#324311yescharacteristic
349#544—864no—
350#544—864no—
351C2×C4⋊Q8—431no—
352C2×C4⋊Q8—431no—
353C2×C4⋊Q8—861no—
354C2×#125—431no—
355C2×#125—431no—
356C2×#125—861no—
357C2×C22⋊Q8—431no—
358C2×C22⋊Q8—861no—
359C2×C22⋊Q8—861no—
360C2×C4×Q8—431no—
361C2×#117—431no—
362C2×#117C2×D4311yescharacteristic
363C22×C4⋊C4—431no—
364#479—864no—
365#477—864no—
366C2×#107—431no—
367C2×#107—431no—
368C2×#107—431no—
369C2×#106—431no—
370C2×C4⋊C8C2×D4311yescharacteristic
371C2×C4⋊C8C2×D4311yescharacteristic
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×C22⋊C8C2×D4311yescharacteristic
377C2×C22⋊C8C2×D4311yescharacteristic
378#391—431no—
379#389—431no—
380#389—861no—
381#388—861no—
382#388—861no—
383#387—861no—
384#380—431no—
385C4×C4⋊C4—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#336C2×D4311yescharacteristic
395#336C2×D4311yescharacteristic
396C43#2431111yescharacteristic, complemented, Sylow
397C22×Q8—431no—
398C22×Q8—861no—
399C22×Q8—861no—
400C23×C4—861no—
401C23×C4C22×D4311yescharacteristic
402C22×C8C22×D4311yescharacteristic
403C22×C8C22×D4311yescharacteristic
404C22×C8C22×D4311yescharacteristic
405C22×C8C22×D4311yescharacteristic
406C4⋊Q8—434no—
407C4⋊Q8—862no—
408C4⋊Q8—862no—
409C4⋊Q8—868no—
410C4⋊Q8—862no—
411#125—434no—
412#125—862no—
413#125—862no—
414#125—868no—
415#125—862no—
416C22⋊Q8—434no—
417C22⋊Q8—868no—
418C22⋊Q8—868no—
419C22⋊Q8—862no—
420C4×Q8—862no—
421C4×Q8—862no—
422#117—22no—
423#117—22no—
424#117—862no—
425#117—862no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—862no—
434C2×C4⋊C4—862no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4D17211yescharacteristic
446C2×C4⋊C4D17211yescharacteristic
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4D17211yescharacteristic
451C2×C22⋊C4D17211yescharacteristic
452C2×C42—861no—
453C2×C42—861no—
454C2×C42—861no—
455C2×C42C22×D4311yescharacteristic
456C2×C42C22×D4311yescharacteristic
457#107—862no—
458#107—862no—
459#107—862no—
460#106—862no—
461C4⋊C8—22no—
462C4⋊C8—22no—
463#103—862no—
464#103—862no—
465#103—862no—
466#103—862no—
467C22⋊C8—22no—
468C22⋊C8—22no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474C24C2×D17211yescharacteristic
475C2×Q8—432no—
476C2×Q8—864no—
477C2×Q8—864no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8—861no—
483C2×Q8—3441no—
484C2×Q8—3441no—
485C2×Q8—3441no—
486C2×Q8—3441no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—864no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—3441no—
501C22×C4—3441no—
502C22×C4C2×D17211yescharacteristic
503C22×C4C2×D17211yescharacteristic
504C22×C4C2×D17211yescharacteristic
505C22×C4C2×D17211yescharacteristic
506C22×C4C2×D17211yescharacteristic
507C22×C4#1062190012yes—
508C22×C4Q8×D4312yes—
509C22×C4C23×D4311yescharacteristic
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—432no—
525C4⋊C4—432no—
526C4⋊C4—432no—
527C4⋊C4—432no—
528C4⋊C4—432no—
529C4⋊C4—864no—
530C4⋊C4—864no—
531C4⋊C4—864no—
532C4⋊C4—864no—
533C4⋊C4—864no—
534C4⋊C4—864no—
535C4⋊C4—864no—
536C4⋊C4—864no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—3441no—
547C4⋊C4—1722no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—864no—
551C22⋊C4—864no—
552C22⋊C4—3441no—
553C42—21no—
554C42—21no—
555C42—864no—
556C42—3441no—
557C42—1722no—
558C42D4×D4312yes—
559C42D4×D4312yes—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23#1306330512yes—
567C23C22×D17211yescharacteristic
568Q8—862no—
569Q8—862no—
570Q8—3444no—
571Q8—3444no—
572Q8—1721no—
573Q8—1721no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—3444no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4#1306329512yes—
616C2×C4#1306329512yes—
617C2×C4#1306330512yes—
618C2×C4C2×D4×D4311yescharacteristic
619C2×C4C2×D4×D4311yescharacteristic
620C2×C4C2×Q8×D4311yescharacteristic
621C2×C4C2×#1062190011yescharacteristic
622C2×C4#1306337211yescharacteristic
623C2×C4#1306337211yescharacteristic
624C8—41no—
625C8—41no—
626C8—41no—
627C8—41no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#1306329511yescharacteristic
636C22C2×#1306330511yescharacteristic
637C22#1458347511yescharacteristic
638C22#1458370411yescharacteristic
639C22#1458371111yescharacteristic
640C22#1458371611yescharacteristic
641C22#1458371611yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—41no—
646C4—41no—
647C4—3441no—
648C4—3441no—
649C4—1722no—
650C4—1722no—
651C4—1722no—
652C4—1722no—
653C4—1722no—
654C4—1722no—
655C4#1458355511yescharacteristic
656C4#1458355511yescharacteristic
657C4#1458356211yescharacteristic
658C4#1458356211yescharacteristic
659C2—42no—
660C2#1913796111yescharacteristic
661C2#1914389211yescharacteristic
662C2#1914390211yescharacteristic
663C2#1914443811yescharacteristic
664C2#1914444811yescharacteristic
665C2#1914586511yescharacteristic
666C2#1914588011yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1798C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1798D43
hypocenterC43#24311
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. C2×#14583207C2semidirect
3. C2×#14583195C2semidirect
5. #19135934C2semidirect
6. #19135924C2semidirect
7. #19135747C2semidirect
8. #19135737C2semidirect
9. #19135550C2semidirect
10. #19135546C2semidirect
78. #13063304Q8semidirect
396. C43#24311semidirect

Maximal subgroups

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

subgroupindex
C2×#145835272
C2×#145832072
C2×#145831952
#191372772
#191359342
#191359242
#191357472
#191357372
#191355502
#191355462
#191349052
#191349002
#191347962
#191347852
C43×#17982
#2431143