Finite Group Databasebeta

← #25133060

Subgroups — #25133060

Order 11008.

1042 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583627C211yesmaximal, characteristic, complemented
2C2×#14583199C211yesmaximal, characteristic
3C2×C4×#10621883C211yesmaximal, characteristic
4#19135933C211yesmaximal, characteristic, complemented
5#19135928C211yesmaximal, characteristic, complemented
6#19135741C211yesmaximal, characteristic
7#19135731C211yesmaximal, characteristic
8#19135559C211yesmaximal, characteristic, complemented
9#19135532C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic
11#19134953C211yesmaximal, characteristic
12#19134862C211yesmaximal, characteristic, complemented
13#19134848C211yesmaximal, characteristic, complemented
14#19134607C211yesmaximal, characteristic, complemented
15C43×#2580C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17#14583627—24no—
18#14583627—24no—
19C2×#13063325C2211yescharacteristic
20C2×#13063323—21no—
21C2×#13063317C2211yescharacteristic
22C2×#13063317C2211yescharacteristic
23C2×#13063315—21no—
24C2×#13063315—21no—
25C2×C4×Dic86C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×C4×Dic86C2211yescharacteristic
28C2×#13063290—21no—
29#14583199—24no—
30C4×#10621883—24no—
31C2×#13063258C2211yescharacteristic
32C2×#13063256C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C4×C43⋊C8C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C43×#399—21no—
55C43×#393—21no—
56C43×#390C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#385—21no—
61C43×#385—21no—
62C43×#382C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C2×#10621883—22no—
66C2×#10621883—22no—
67C2×#10621883Q814yescomplemented
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063325—22no—
73#13063325—22no—
74#13063323—28no—
75#13063317—22no—
76#13063317—22no—
77#13063317—22no—
78#13063317D414yes—
79#13063315—28no—
80#13063315—28no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84C4×Dic86—22no—
85C4×Dic86—22no—
86C4×Dic86D414yes—
87#13063290—28no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102#13063258—22no—
103#13063256—22no—
104#13063256—22no—
105C4⋊(C43⋊C8)—22no—
106#13063248—22no—
107#13063248—22no—
108#13063248—22no—
109#13063246—22no—
110#13063246—22no—
111#13063246—22no—
112C4×C43⋊C8—22no—
113C22×Q8×C43D411yescharacteristic
114C22×D4×C43C2311yescharacteristic
115C23×C4×C43—21no—
116C4×Q8×C43—22no—
117C4×Q8×C43—22no—
118C4×D4×C43—22no—
119C4×D4×C43—22no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43D411yescharacteristic
123C2×C4⋊C4×C43D411yescharacteristic
124C2×C4⋊C4×C43D411yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139#95×C43—21no—
140C24×C43—21no—
141C2×Q8×C43—22no—
142C2×Q8×C43—22no—
143C2×Q8×C43—41no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43C2×Q812yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—42no—
154C22×C4×C43—81no—
155C22×C4×C43—81no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—24no—
171C2×Dic86—42no—
172C2×Dic86—42no—
173C2×Dic86C2×D412yes—
174C2×Dic86C2×Q812yes—
175C2×Dic86#4112yes—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—81no—
186C4⋊C4×C43—81no—
187C22⋊C4×C43—42no—
188C22⋊C4×C43—42no—
189C22⋊C4×C43—42no—
190C22⋊C4×C43—81no—
191C22⋊C4×C43—81no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—21no—
195C42×C43—21no—
196C42×C43C2×D412yes—
197C42×C43C2×D412yes—
198#10621883—28no—
199C4⋊Dic43—24no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43C2×D412yes—
204C4⋊Dic43C2×D412yes—
205C4⋊Dic43C2×D412yes—
206Dic43⋊C4—24no—
207Dic43⋊C4—24no—
208Dic43⋊C4—24no—
209Dic43⋊C4—24no—
210Dic43⋊C4—24no—
211Dic43⋊C4—24no—
212Dic43⋊C4—24no—
213C4×Dic43—24no—
214C4×Dic43—24no—
215C4×Dic43—24no—
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—
226C2×C43⋊C8—21no—
227C2×C43⋊C8C2×Q812yes—
228C23×C43—22no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43C22×D411yescharacteristic
236Q8×C43—44no—
237D4×C43—22no—
238D4×C43—22no—
239D4×C43—41no—
240D4×C43—41no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
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—21no—
251C2×C4×C43—21no—
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—84no—
266C2×C4×C43#12012yes—
267C2×C4×C43#12012yes—
268C2×C4×C43#13512yes—
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—22no—
280C2×Dic43—22no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287Dic86—22no—
288Dic86—22no—
289Dic86—22no—
290Dic86—48no—
291Dic86C22⋊Q814yes—
292C43⋊C8—22no—
293C43⋊C8—41no—
294C43⋊C8—41no—
295C43⋊C8—41no—
296#24334—431nomaximal, Sylow
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43C2×#12011yescharacteristic
305C22×C43#54811yescharacteristic
306C22×C43D4×Q811yescharacteristic
307C22×C43C2×#13511yescharacteristic
308C22×C43#57511yescharacteristic
309C22×C43#57711yescharacteristic
310C22×C43#57711yescharacteristic
311C4×C43—22no—
312C4×C43—22no—
313C4×C43—22no—
314C4×C43—41no—
315C4×C43—41no—
316C4×C43—41no—
317C4×C43—81no—
318C4×C43—81no—
319C4×C43—81no—
320C4×C43C2×C22⋊Q811yescharacteristic
321C4×C43#53611yescharacteristic
322C4×C43#54811yescharacteristic
323C4×C43D4×Q811yescharacteristic
324Dic43—24no—
325Dic43—42no—
326Dic43—42no—
327Dic43—42no—
328C2×#557—431no—
329C2×#478—431no—
330C2×C4×SD16—431no—
331#2580D4311yescharacteristic
332#2059—431no—
333#2058—431no—
334#2025—431no—
335#2023—431no—
336#1991—431no—
337#1984—431no—
338#1880—431no—
339#1880—431no—
340#1865—431no—
341#1863—431no—
342#1805—431no—
343C2×C43—82no—
344C2×C43#240911yescharacteristic
345C2×C43#300211yescharacteristic
346C2×C43#301011yescharacteristic
347C2×C43#336511yescharacteristic
348C2×C43#337111yescharacteristic
349C2×C43#338111yescharacteristic
350C2×C43#338811yescharacteristic
351C22×SD16—431no—
352#557—864no—
353#557—864no—
354C2×C4⋊Q8—431no—
355C2×C4⋊Q8—861no—
356C2×#125—431no—
357C2×#125—431no—
358C2×#125—861no—
359C2×#125—861no—
360C2×C4×Q8—431no—
361C2×C4×Q8—431no—
362C2×C4×Q8—431no—
363C2×C4×Q8—861no—
364C2×C4×Q8C2×D4311yescharacteristic
365C2×C4×D4C2×D4311yescharacteristic
366#478—864no—
367C4×SD16—864no—
368C2×#107—431no—
369C2×#106—431no—
370C2×#106—431no—
371C2×C4⋊C8—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×C4×C8—431no—
379#399—21no—
380#393—21no—
381#390C2×D4311yescharacteristic
382#390C2×D4311yescharacteristic
383#389C2×D4311yescharacteristic
384#389C2×D4311yescharacteristic
385#385—21no—
386#385—21no—
387#382C2×D4311yescharacteristic
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#336—431no—
395#336—431no—
396#336—431no—
397#336—431no—
398C43#2433411yescharacteristic, complemented, Sylow
399C22×Q8—431no—
400C22×Q8—861no—
401C22×Q8C22⋊D4311yescharacteristic
402C22×D4C22×D4311yescharacteristic
403C23×C4—21no—
404C2×SD16—434no—
405C2×SD16—862no—
406C2×SD16—862no—
407C22×C8—431no—
408C22×C8—431no—
409C22×C8—431no—
410C22×C8—431no—
411C4⋊Q8—862no—
412C4⋊Q8—862no—
413C4⋊Q8—868no—
414#125—434no—
415#125—862no—
416#125—862no—
417#125—868no—
418#125—868no—
419#125—862no—
420C4×Q8—22no—
421C4×Q8—22no—
422C4×Q8—434no—
423C4×Q8—862no—
424C4×Q8—862no—
425C4×Q8—862no—
426C4×Q8—862no—
427C4×Q8—868no—
428C4×Q8—862no—
429C4×D4—22no—
430C4×D4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
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⋊C4C22⋊D4311yescharacteristic
445C2×C4⋊C4C22⋊D4311yescharacteristic
446C2×C4⋊C4C22⋊D4311yescharacteristic
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C4⋊C4C22×D4311yescharacteristic
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C42—861no—
456C2×C42—861no—
457C2×C42—861no—
458C2×C42C22×D4311yescharacteristic
459C2×C42C22×D4311yescharacteristic
460C2×C42C22×D4311yescharacteristic
461#107—862no—
462#106—862no—
463#106—862no—
464C4⋊C8—862no—
465#103—862no—
466#103—862no—
467#103—862no—
468#102—862no—
469#102—862no—
470#102—862no—
471C4×C8—862no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476C24—21no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—41no—
480C2×Q8—432no—
481C2×Q8—432no—
482C2×Q8—432no—
483C2×Q8—864no—
484C2×Q8—861no—
485C2×Q8—861no—
486C2×Q8—861no—
487C2×Q8—1722no—
488C2×Q8—1722no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4Q8×D4312yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—42no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4C2×C22⋊D4311yescharacteristic
506C22×C4C2×C22⋊D4311yescharacteristic
507C22×C4C2×C22⋊D4311yescharacteristic
508C22×C4C2×C22⋊D4311yescharacteristic
509C22×C4C2×C22⋊D4311yescharacteristic
510C22×C4C2×C22⋊D4311yescharacteristic
511C22×C4C23×D4311yescharacteristic
512SD16—868no—
513C2×C8—432no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—81no—
535C4⋊C4—81no—
536C4⋊C4—432no—
537C4⋊C4—432no—
538C4⋊C4—432no—
539C4⋊C4—864no—
540C4⋊C4—864no—
541C4⋊C4—864no—
542C4⋊C4—864no—
543C4⋊C4—864no—
544C4⋊C4—864no—
545C4⋊C4—864no—
546C4⋊C4—864no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—81no—
554C22⋊C4—81no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—864no—
560C42—864no—
561C42—864no—
562C42D4×D4312yes—
563C42D4×D4312yes—
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23C22×C22⋊D4311yescharacteristic
572Q8—44no—
573Q8—434no—
574Q8—862no—
575Q8—862no—
576Q8—862no—
577Q8—1728no—
578D4—22no—
579D4—22no—
580D4—41no—
581D4—41no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—84no—
607C2×C4—862no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4#1306329312yes—
620C2×C4#1306329312yes—
621C2×C4#1306334512yes—
622C2×C4C2×D4×D4311yescharacteristic
623C2×C4C2×D4×D4311yescharacteristic
624C2×C4C2×Q8×D4311yescharacteristic
625C2×C4#41×D4311yescharacteristic
626C2×C4#1306337211yescharacteristic
627C2×C4#1306337311yescharacteristic
628C8—862no—
629C8—1721no—
630C8—1721no—
631C8—1721no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22C2×#1306329311yescharacteristic
640C22#1458355611yescharacteristic
641C22Q8×C22⋊D4311yescharacteristic
642C22C2×#1306334511yescharacteristic
643C22#1458369711yescharacteristic
644C22#1458371011yescharacteristic
645C22#1458371011yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—81no—
653C4—81no—
654C4—81no—
655C4—864no—
656C4—1722no—
657C4—1722no—
658C4—1722no—
659C4C22⋊Q8×D4311yescharacteristic
660C4#1458347211yescharacteristic
661C4#1458355911yescharacteristic
662C4#1458356211yescharacteristic
663C2—82no—
664C2#1913795611yescharacteristic
665C2#1914381111yescharacteristic
666C2#1914387911yescharacteristic
667C2#1914728711yescharacteristic
668C2#1914735711yescharacteristic
669C2#1914747011yescharacteristic
670C2#1914754011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2580C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2580D43
hypocenterC43#24334
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2580

Complements

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

NH ≅ G/Ntype
1. C2×#14583627C2semidirect
4. #19135933C2semidirect
5. #19135928C2semidirect
8. #19135559C2semidirect
9. #19135532C2semidirect
12. #19134862C2semidirect
13. #19134848C2semidirect
14. #19134607C2semidirect
67. C2×#10621883Q8semidirect
398. C43#24334semidirect

Maximal subgroups

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

subgroupindex
C2×#145836272
C2×#145831992
C2×C4×#106218832
#191359332
#191359282
#191357412
#191357312
#191355592
#191355322
#191349532
#191348622
#191348482
#191346072
C43×#25802
#2433443