Finite Group Databasebeta

← #25132807

Subgroups — #25132807

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×#14583206C211yesmaximal, characteristic, complemented
3C2×#14583194C211yesmaximal, characteristic, complemented
4#19135933C211yesmaximal, characteristic, complemented
5#19135923C211yesmaximal, characteristic, complemented
6#19135746C211yesmaximal, characteristic, complemented
7#19135736C211yesmaximal, characteristic, complemented
8#19135552C211yesmaximal, characteristic, complemented
9#19135547C211yesmaximal, characteristic, complemented
10#19134908C211yesmaximal, characteristic
11#19134903C211yesmaximal, characteristic
12#19134792C211yesmaximal, characteristic
13#19134782C211yesmaximal, characteristic
14#19134579C211yesmaximal, characteristic
15C43×#2323C211yesmaximal, characteristic
16#14583527—24no—
17#14583527—24no—
18C2×#13063325C2211yescharacteristic
19C2×#13063325C2211yescharacteristic
20C2×#13063324—21no—
21C2×#13063317C2211yescharacteristic
22C2×#13063317C2211yescharacteristic
23C2×#13063316—21no—
24C2×#13063302—21no—
25C2×#13063302—21no—
26C2×#13063284C2211yescharacteristic
27C22×C4⋊Dic43C2211yescharacteristic
28#14583206—24no—
29#14583194—24no—
30C2×#13063258C2211yescharacteristic
31C2×#13063258C2211yescharacteristic
32C2×#13063258C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C2×C4⋊(C43⋊C8)C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×C22⋊Q8×C43C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C43×#389—21no—
57C43×#389C2211yescharacteristic
58C43×#388—21no—
59C43×#388—21no—
60C43×#387—21no—
61C43×#380C2211yescharacteristic
62C4×C4⋊C4×C43C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86—21no—
65C23×Dic43—21no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063325—22no—
71#13063325—22no—
72#13063325—22no—
73#13063325D414yes—
74#13063324—28no—
75#13063317—22no—
76#13063317—22no—
77#13063317—22no—
78#13063317D414yes—
79#13063316—28no—
80#13063302—28no—
81#13063302—28no—
82#13063284—22no—
83#13063284—22no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×C22⋊Dic43—21no—
98C2×C4×Dic43—21no—
99#13063258—22no—
100#13063258—22no—
101#13063258—22no—
102#13063256—22no—
103C4⋊(C43⋊C8)—22no—
104C4⋊(C43⋊C8)—22no—
105#13063249—22no—
106#13063249—22no—
107#13063249—22no—
108#13063249—22no—
109C22⋊(C43⋊C8)—22no—
110C22⋊(C43⋊C8)—22no—
111C22×Q8×C43C2311yescharacteristic
112C23×C4×C43C2311yescharacteristic
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43Q814yescomplemented
115C4×Q8×C43—22no—
116C4×Q8×C43—22no—
117#117×C43—22no—
118#117×C43—22no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43D411yescharacteristic
123C2×C4⋊C4×C43D411yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C42×C43—21no—
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C2×C42×C43C2311yescharacteristic
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139#95×C43—21no—
140C24×C43C2×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×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×Q812yes—
161C22×C4×C43#4112yes—
162C22×C4×C43C2411yescharacteristic
163C22×Dic43—24no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—81no—
169C22×Dic43—81no—
170C2×Dic86—24no—
171C2×Dic86—24no—
172C2×Dic86—81no—
173C2×Dic86—81no—
174C2×Dic86—81no—
175C2×Dic86—81no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—24no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—42no—
185C4⋊C4×C43—81no—
186C4⋊C4×C43C2×Q812yes—
187C22⋊C4×C43—22no—
188C22⋊C4×C43—22no—
189C22⋊C4×C43—24no—
190C22⋊C4×C43—81no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—42no—
194C42×C43—81no—
195C42×C43C2×D412yes—
196C42×C43C2×D412yes—
197C22⋊Dic43—24no—
198C4⋊Dic43—24no—
199C4⋊Dic43—24no—
200C4⋊Dic43—24no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43C2×D412yes—
206C4⋊Dic43C2×D412yes—
207C4⋊Dic43C2×D412yes—
208C4⋊Dic43C2×D412yes—
209Dic43⋊C4—24no—
210Dic43⋊C4—24no—
211Dic43⋊C4—24no—
212Dic43⋊C4—24no—
213C4×Dic43—24no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
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×C43—21no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43C22⋊Q812yes—
233C23×C43C22×D411yescharacteristic
234Q8×C43—22no—
235Q8×C43—22no—
236Q8×C43—41no—
237Q8×C43—41no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
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—41no—
265C2×C4×C43—41no—
266C2×C4×C43#12012yes—
267C2×C4×C43#12012yes—
268C2×C4×C43C22⋊Q812yes—
269C2×C4×C43C22×D411yescharacteristic
270C2×C4×C43C22×D411yescharacteristic
271C2×C4×C43C22×Q811yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C432−1+411yescharacteristic
274C2×C4×C432−1+411yescharacteristic
275C2×Dic43—22no—
276C2×Dic43—22no—
277C2×Dic43—22no—
278C2×Dic43—22no—
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—84no—
288Dic86—84no—
289Dic86—84no—
290C43⋊C8—41no—
291C43⋊C8—41no—
292C43⋊C8—41no—
293C43⋊C8—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—42no—
313C4×C43—42no—
314C4×C43—41no—
315C4×C43—41no—
316C4×C43—81no—
317C4×C43—81no—
318C4×C43#54811yescharacteristic
319C4×C43#54811yescharacteristic
320C4×C43D4×Q811yescharacteristic
321C4×C43D4×Q811yescharacteristic
322Dic43—42no—
323Dic43—42no—
324Dic43—42no—
325Dic43—42no—
326C2×#544—431no—
327C2×#479—431no—
328C2×#477—431no—
329#2323D4311yescharacteristic
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#1798—431no—
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—861no—
358C2×C22⋊Q8—861no—
359C2×C22⋊Q8C2×D4311yescharacteristic
360C2×C4×Q8C2×D4311yescharacteristic
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⋊C8—431no—
371C2×C4⋊C8—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×C22⋊C8—431no—
377C2×C22⋊C8—431no—
378#391C2×D4311yescharacteristic
379#389—21no—
380#389C2×D4311yescharacteristic
381#388—21no—
382#388—21no—
383#387—21no—
384#380C2×D4311yescharacteristic
385C4×C4⋊C4C2×D4311yescharacteristic
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#336—431no—
395#336—431no—
396C43#2431111yescharacteristic, complemented, Sylow
397C22×Q8—861no—
398C22×Q8—861no—
399C22×Q8C22×D4311yescharacteristic
400C23×C4—861no—
401C23×C4C22×D4311yescharacteristic
402C22×C8—431no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8—431no—
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—22no—
417C22⋊Q8—868no—
418C22⋊Q8—868no—
419C22⋊Q8Dic8614yescomplemented
420C4×Q8—22no—
421C4×Q8—22no—
422#117—22no—
423#117—22no—
424#117—862no—
425#117—862no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
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⋊C4C22⋊D4311yescharacteristic
443C2×C4⋊C4C22⋊D4311yescharacteristic
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4C22⋊D4311yescharacteristic
451C2×C22⋊C4C22⋊D4311yescharacteristic
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—861no—
455C2×C42C22×D4311yescharacteristic
456C2×C42C22×D4311yescharacteristic
457#107—862no—
458#107—862no—
459#107—862no—
460#106—862no—
461C4⋊C8—862no—
462C4⋊C8—862no—
463#103—862no—
464#103—862no—
465#103—862no—
466#103—862no—
467C22⋊C8—862no—
468C22⋊C8—862no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474C24C2×C22⋊D4311yescharacteristic
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×Q8C2×Dic8612yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—864no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—3441no—
501C22×C4—3441no—
502C22×C4C2×Dic8612yes—
503C22×C4#1062189812yes—
504C22×C4C2×C22⋊D4311yescharacteristic
505C22×C4C2×C22⋊D4311yescharacteristic
506C22×C4C2×C22⋊D4311yescharacteristic
507C22×C4C2×C22⋊D4311yescharacteristic
508C22×C4C2×C22⋊D4311yescharacteristic
509C22×C4C23×D4311yescharacteristic
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—24no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—81no—
532C4⋊C4—432no—
533C4⋊C4—432no—
534C4⋊C4—432no—
535C4⋊C4—432no—
536C4⋊C4—864no—
537C4⋊C4—864no—
538C4⋊C4—864no—
539C4⋊C4—864no—
540C4⋊C4—864no—
541C4⋊C4—864no—
542C4⋊C4—864no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4C2×Dic8612yes—
548C22⋊C4—24no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—81no—
552C22⋊C4—864no—
553C42—21no—
554C42—21no—
555C42—42no—
556C42—81no—
557C42—864no—
558C42D4×D4312yes—
559C42D4×D4312yes—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23#1306330412yes—
567C23C22×C22⋊D4311yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—3444no—
573Q8—3444no—
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—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—3444no—
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#1306329312yes—
616C2×C4#1306329312yes—
617C2×C4#1306330412yes—
618C2×C4C2×D4×D4311yescharacteristic
619C2×C4C2×D4×D4311yescharacteristic
620C2×C4C22×Dic8611yescharacteristic
621C2×C4C2×#1062189811yescharacteristic
622C2×C4#1306337211yescharacteristic
623C2×C4#1306337211yescharacteristic
624C8—1721no—
625C8—1721no—
626C8—1721no—
627C8—1721no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#1306329311yescharacteristic
636C22C2×#1306330411yescharacteristic
637C22#1458347011yescharacteristic
638C22#1458370211yescharacteristic
639C22#1458370711yescharacteristic
640C22#1458371411yescharacteristic
641C22#1458371411yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—42no—
646C4—41no—
647C4—41no—
648C4—42no—
649C4—81no—
650C4—81no—
651C4—1722no—
652C4—1722no—
653C4—1722no—
654C4—1722no—
655C4#1458355811yescharacteristic
656C4#1458355811yescharacteristic
657C4D4×Dic8611yescharacteristic
658C4D4×Dic8611yescharacteristic
659C2—42no—
660C2#1913796011yescharacteristic
661C2#1914388811yescharacteristic
662C2#1914389611yescharacteristic
663C2#1914443711yescharacteristic
664C2#1914444611yescharacteristic
665C2#1914585711yescharacteristic
666C2#1914587211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2323C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2323D43
hypocenterC43#24311
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C2×#14583206C2semidirect
3. C2×#14583194C2semidirect
4. #19135933C2semidirect
5. #19135923C2semidirect
6. #19135746C2semidirect
7. #19135736C2semidirect
8. #19135552C2semidirect
9. #19135547C2semidirect
114. C22⋊Q8×C43Q8semidirect
396. C43#24311semidirect
419. C22⋊Q8Dic86semidirect

Maximal subgroups

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

subgroupindex
C2×#145835272
C2×#145832062
C2×#145831942
#191359332
#191359232
#191357462
#191357362
#191355522
#191355472
#191349082
#191349032
#191347922
#191347822
#191345792
C43×#23232
#2431143