Finite Group Databasebeta

← #25132808

Subgroups — #25132808

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×#14583529C211yesmaximal, characteristic
2C2×#14583208C211yesmaximal, characteristic, complemented
3C2×#14583192C211yesmaximal, characteristic, complemented
4#19137280C211yesmaximal, characteristic
5#19135930C211yesmaximal, characteristic, complemented
6#19135924C211yesmaximal, characteristic, complemented
7#19135736C211yesmaximal, characteristic, complemented
8#19135551C211yesmaximal, characteristic, complemented
9#19135545C211yesmaximal, characteristic, complemented
10#19134904C211yesmaximal, characteristic
11#19134899C211yesmaximal, characteristic
12#19134797C211yesmaximal, characteristic
13#19134784C211yesmaximal, characteristic
14#19134578C211yesmaximal, characteristic
15C43×#2026C211yesmaximal, characteristic, complemented
16#14583529—24no—
17#14583529—24no—
18C2×#13063325C2211yescharacteristic
19C2×#13063324—21no—
20C2×#13063324C2211yescharacteristic
21C2×#13063316C2211yescharacteristic
22C2×#13063315—21no—
23C2×#13063305—21no—
24C2×#13063303—21no—
25C2×#13063301C2211yescharacteristic
26C2×Q8×Dic43C2211yescharacteristic
27C2×#13063283C2211yescharacteristic
28C2×#13063282C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30#14583208—24no—
31#14583192—24no—
32C2×#13063259C2211yescharacteristic
33C2×#13063259C2211yescharacteristic
34C2×#13063258C2211yescharacteristic
35C2×#13063256C2211yescharacteristic
36C2×Dic43⋊C8C2211yescharacteristic
37C2×Dic43⋊C8C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582796—21no—
44#14582791—21no—
45#14582788—21no—
46#14582781—21no—
47#14582756C2211yescharacteristic
48C4⋊C4×Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582654C2211yescharacteristic
56C2×#125×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C43×#391C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86—21no—
65C22×C4×D43—21no—
66C22×C4×D43C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063325—22no—
70#13063325—22no—
71#13063324—28no—
72#13063324—22no—
73#13063324D414yes—
74#13063316—22no—
75#13063316D414yes—
76#13063315—28no—
77#13063305—28no—
78#13063303—28no—
79#13063301—22no—
80#13063301Q814yescomplemented
81Q8×Dic43—22no—
82Q8×Dic43—22no—
83#13063283—22no—
84#13063283—22no—
85#13063282—22no—
86#13063282—22no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4D411yescharacteristic
100C2×Dic43⋊C4D411yescharacteristic
101C4⋊C4×D43—22no—
102C4⋊C4×D43—22no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4D411yescharacteristic
107C2×(C2×D43)⋊C4D411yescharacteristic
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43C2311yescharacteristic
112#13063259—22no—
113#13063259—22no—
114#13063258—22no—
115#13063256—22no—
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118#13063249—22no—
119#13063249—22no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C22×Q8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128#125×C43—22no—
129#125×C43—22no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136#103×C43—22no—
137#103×C43—22no—
138#95×C43—21no—
139#95×C43—21no—
140C23×D43C2×D411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×Q812yes—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—24no—
166C2×C4×D43—81no—
167C2×C4×D43—81no—
168C2×C4×D43C2×Q812yes—
169C2×C4×D43#4112yes—
170C2×Dic86—24no—
171C2×Dic86—24no—
172C2×Dic86—81no—
173C2×Dic86—81no—
174C2×Dic86—81no—
175C2×Dic86—81no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C4⋊C4×C43—24no—
183C4⋊C4×C43—24no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43C2×D412yes—
189C4⋊C4×C43C2×D412yes—
190C42×C43—21no—
191C42×C43—21no—
192(C2×D43)⋊C4—24no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—24no—
196(C2×D43)⋊C4—81no—
197C4⋊Dic43—24no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—24no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—42no—
205C4⋊Dic43C2×D412yes—
206C4⋊Dic43C2×D412yes—
207C4⋊Dic43C2×Q812yes—
208Dic43⋊C4—24no—
209Dic43⋊C4—24no—
210Dic43⋊C4—24no—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—24no—
214Dic43⋊C4—81no—
215C4×Dic43—24no—
216C4×Dic43—42no—
217C4×Dic43—81no—
218C4×Dic43C2×D412yes—
219C4×Dic43C2×D412yes—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C23×C43C22×D411yescharacteristic
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—21no—
233C22×D43C22⋊Q812yes—
234Q8×C43—22no—
235Q8×C43—22no—
236Q8×C43—41no—
237Q8×C43—41no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
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—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×Q811yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C2×C4×C432−1+411yescharacteristic
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—22no—
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#12012yes—
281C2×Dic43#12012yes—
282C2×Dic43C22⋊Q812yes—
283C4×D43—22no—
284C4×D43—22no—
285C4×D43—22no—
286C4×D43—22no—
287C4×D43—84no—
288Dic86—84no—
289Dic86—84no—
290C8×C43—41no—
291C8×C43—41no—
292C43⋊C8—41no—
293C43⋊C8—41no—
294#24311—431nomaximal, Sylow
295C22×C43C2×#12011yescharacteristic
296C22×C43C2×C22⋊Q811yescharacteristic
297C22×C43#53611yescharacteristic
298C22×C43#57611yescharacteristic
299C22×C43#57711yescharacteristic
300C22×C43#57811yescharacteristic
301C22×C43#57811yescharacteristic
302C2×D43—22no—
303C2×D43—22no—
304C2×D43—22no—
305C2×D43—41no—
306C2×D43—41no—
307C2×D43—41no—
308C2×D43—41no—
309C4×C43—42no—
310C4×C43—41no—
311C4×C43—42no—
312C4×C43—41no—
313C4×C43—42no—
314C4×C43—81no—
315C4×C43#54811yescharacteristic
316C4×C43#54811yescharacteristic
317C4×C43D4×Q811yescharacteristic
318C4×C43D4×Q811yescharacteristic
319Dic43—22no—
320Dic43—22no—
321Dic43—22no—
322Dic43—42no—
323Dic43—42no—
324Dic43—42no—
325Dic43—81no—
326C2×#544—431no—
327C2×#479—431no—
328C2×#477—431no—
329#2323—431no—
330#2059—431no—
331#2057—431no—
332#2026D4311yescharacteristic, complemented
333#2024—431no—
334#1989—431no—
335#1988—431no—
336#1873—431no—
337#1872—431no—
338#1854—431no—
339#1852—431no—
340#1798—431no—
341C2×C43#240911yescharacteristic
342C2×C43#301111yescharacteristic
343C2×C43#301211yescharacteristic
344C2×C43#308211yescharacteristic
345C2×C43#308311yescharacteristic
346C2×C43#324211yescharacteristic
347C2×C43#324311yescharacteristic
348D43—42no—
349#544—864no—
350#544—864no—
351C2×C4⋊Q8—431no—
352C2×C4⋊Q8—431no—
353C2×C4⋊Q8—861no—
354C2×#125—431no—
355C2×#125—861no—
356C2×#125C2×D4311yescharacteristic
357C2×C22⋊Q8—431no—
358C2×C22⋊Q8—861no—
359C2×C22⋊Q8—861no—
360C2×C4×Q8—431no—
361C2×#117—431no—
362C2×#117—431no—
363C22×C4⋊C4—431no—
364#479—864no—
365#477—864no—
366C2×#107—431no—
367C2×#107—431no—
368C2×#107—431no—
369C2×#106—431no—
370C2×C4⋊C8—431no—
371C2×C4⋊C8—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103C2×D4311yescharacteristic
375C2×#103C2×D4311yescharacteristic
376C2×C22⋊C8—431no—
377C2×C22⋊C8—431no—
378#391C2×D4311yescharacteristic
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#340C2×D4311yescharacteristic
393#340C2×D4311yescharacteristic
394#336—431no—
395#336C2×D4311yescharacteristic
396C43#2431111yescharacteristic, complemented, Sylow
397C22×Q8—861no—
398C22×Q8—861no—
399C22×Q8C22×D4311yescharacteristic
400C23×C4—431no—
401C23×C4—861no—
402C22×C8—431no—
403C22×C8—431no—
404C22×C8C22×D4311yescharacteristic
405C22×C8C22×D4311yescharacteristic
406C4⋊Q8—434no—
407C4⋊Q8—862no—
408C4⋊Q8—862no—
409C4⋊Q8—862no—
410C4⋊Q8—868no—
411#125—22no—
412#125—22no—
413#125—434no—
414#125—862no—
415#125—868no—
416C22⋊Q8—434no—
417C22⋊Q8—868no—
418C22⋊Q8—868no—
419C22⋊Q8—862no—
420C4×Q8—862no—
421C4×Q8—862no—
422#117—862no—
423#117—862no—
424#117—862no—
425#117—862no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
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—862no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C22⋊C4—431no—
448C2×C22⋊C4—431no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C42—431no—
453C2×C42—861no—
454C2×C42—861no—
455C2×C42—861no—
456C2×C42C22×D4311yescharacteristic
457#107—862no—
458#107—862no—
459#107—862no—
460#106—862no—
461C4⋊C8—862no—
462C4⋊C8—862no—
463#103—22no—
464#103—22no—
465#103—862no—
466#103—862no—
467C22⋊C8—862no—
468C22⋊C8—862no—
469#95—21no—
470#95—21no—
471#95—861no—
472#95—861no—
473#95—861no—
474C24—431no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—864no—
481C2×Q8—864no—
482C2×Q8—3441no—
483C2×Q8—3441no—
484C2×Q8—3441no—
485C2×Q8—3441no—
486C2×Q8Q8×D4312yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—432no—
495C22×C4—432no—
496C22×C4—864no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—3441no—
506C22×C4—3441no—
507C22×C4D4×D4311yescharacteristic
508C22×C4D4×D4311yescharacteristic
509C22×C4C23×D4311yescharacteristic
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—432no—
529C4⋊C4—432no—
530C4⋊C4—432no—
531C4⋊C4—862no—
532C4⋊C4—862no—
533C4⋊C4—864no—
534C4⋊C4—864no—
535C4⋊C4—864no—
536C4⋊C4—864no—
537C4⋊C4—864no—
538C4⋊C4—864no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—3441no—
545C4⋊C4—1722no—
546C4⋊C4D4×D4312yes—
547C4⋊C4D4×D4312yes—
548C22⋊C4—862no—
549C22⋊C4—862no—
550C22⋊C4—864no—
551C22⋊C4—864no—
552C22⋊C4—3441no—
553C42—21no—
554C42—21no—
555C42—432no—
556C42—432no—
557C42—864no—
558C42—3441no—
559C42—1722no—
560C23—432no—
561C23—861no—
562C23—861no—
563C23—861no—
564C23—861no—
565C23—861no—
566C23—861no—
567C23C2×D4×D4311yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—3444no—
573Q8—3444no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
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—432no—
593C2×C4—432no—
594C2×C4—432no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—862no—
608C2×C4—3444no—
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×C4C2×D4×D4311yescharacteristic
619C2×C4C2×D4×D4311yescharacteristic
620C2×C4C2×Q8×D4311yescharacteristic
621C2×C4#41×D4311yescharacteristic
622C2×C4#1306337211yescharacteristic
623C2×C4#1306337211yescharacteristic
624C8—41no—
625C8—41no—
626C8—1721no—
627C8—1721no—
628C22—862no—
629C22—862no—
630C22—862no—
631C22—1721no—
632C22—1721no—
633C22—1721no—
634C22—1721no—
635C22#120×D4311yescharacteristic
636C22C22⋊Q8×D4311yescharacteristic
637C22#1458346911yescharacteristic
638C22#1458370111yescharacteristic
639C22#1458370811yescharacteristic
640C22#1458371311yescharacteristic
641C22#1458371511yescharacteristic
642C4—42no—
643C4—41no—
644C4—42no—
645C4—41no—
646C4—42no—
647C4—81no—
648C4—862no—
649C4—862no—
650C4—862no—
651C4—3441no—
652C4—1722no—
653C4—1722no—
654C4—1722no—
655C4#1458355711yescharacteristic
656C4#1458355711yescharacteristic
657C4#1458356211yescharacteristic
658C4#1458356211yescharacteristic
659C2—1722no—
660C2#1913795311yescharacteristic
661C2#1914388711yescharacteristic
662C2#1914390311yescharacteristic
663C2#1914443611yescharacteristic
664C2#1914444911yescharacteristic
665C2#1914585811yescharacteristic
666C2#1914587111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2026C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2026D43
hypocenterC43#24311
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2026

Complements

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

NH ≅ G/Ntype
2. C2×#14583208C2semidirect
3. C2×#14583192C2semidirect
5. #19135930C2semidirect
6. #19135924C2semidirect
7. #19135736C2semidirect
8. #19135551C2semidirect
9. #19135545C2semidirect
15. C43×#2026C2semidirect
80. #13063301Q8semidirect
332. #2026D43semidirect
396. C43#24311semidirect

Maximal subgroups

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

subgroupindex
C2×#145835292
C2×#145832082
C2×#145831922
#191372802
#191359302
#191359242
#191357362
#191355512
#191355452
#191349042
#191348992
#191347972
#191347842
#191345782
C43×#20262
#2431143