Finite Group Databasebeta

← #25133102

Subgroups — #25133102

Order 11008.

1070 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583610C211yesmaximal, characteristic
2C2×#14583208C211yesmaximal, characteristic, complemented
3C2×#14582984C211yesmaximal, characteristic
4#19139959C211yesmaximal, characteristic, complemented
5#19135936C211yesmaximal, characteristic, complemented
6#19135925C211yesmaximal, characteristic, complemented
7#19135744C211yesmaximal, characteristic, complemented
8#19135558C211yesmaximal, characteristic, complemented
9#19135529C211yesmaximal, characteristic, complemented
10#19134932C211yesmaximal, characteristic
11#19134926C211yesmaximal, characteristic
12#19134857C211yesmaximal, characteristic
13#19134845C211yesmaximal, characteristic
14#19134604C211yesmaximal, characteristic
15C43×#2024C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17#14583610—24no—
18#14583610—24no—
19C2×#13063316C2211yescharacteristic
20C2×#13063316C2211yescharacteristic
21C2×#13063305—21no—
22C2×#13063301—21no—
23C2×#13063301—21no—
24C2×Q8×Dic43C2211yescharacteristic
25C2×C4×Dic86C2211yescharacteristic
26C2×C4×D172C2211yescharacteristic
27C2×#13063287C2211yescharacteristic
28C2×#13063287C2211yescharacteristic
29C2×C4⋊C4×D43—21no—
30#14583208—24no—
31#14582984—24no—
32C2×#13063259C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×#13063256C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×C8×Dic43C2211yescharacteristic
41#14582841—21no—
42#14582820—21no—
43#14582806C2211yescharacteristic
44#14582798C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582786—21no—
47#14582782—21no—
48#14582764C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C4⋊Q8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C43×#391C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86D411yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C22×C4×D43—21no—
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884Q814yescomplemented
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063316—22no—
74#13063316—22no—
75#13063316—22no—
76#13063316D414yes—
77#13063305—28no—
78#13063301—28no—
79#13063301—28no—
80Q8×Dic43—22no—
81Q8×Dic43—22no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84C4×D172—22no—
85C4×D172—22no—
86#13063287—22no—
87#13063287—22no—
88#13063287—22no—
89#13063287D414yes—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43D411yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4D411yescharacteristic
102C2×Dic43⋊C4D411yescharacteristic
103C4⋊C4×D43—28no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43C2311yescharacteristic
109C2×C4×Dic43C2311yescharacteristic
110#13063259—22no—
111#13063256—22no—
112#13063256—22no—
113Dic43⋊C8—22no—
114#13063249—22no—
115#13063247—22no—
116#13063247—22no—
117#13063245—22no—
118C8×Dic43—22no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C22×Q8×C43—21no—
126C22×Q8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C4⋊Q8×C43—22no—
130C4⋊Q8×C43—22no—
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×D43—21no—
141C2×Q8×C43—24no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—81no—
148C2×Q8×C43—81no—
149C2×Q8×C43C2×Q812yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172C2×D412yes—
168C2×D172C2×Q812yes—
169C2×D172#4112yes—
170C2×C4×D43—24no—
171C2×C4×D43—24no—
172C2×C4×D43—24no—
173C2×C4×D43—42no—
174C2×C4×D43—42no—
175C2×C4×D43—81no—
176C2×C4×D43—81no—
177C2×C4×D43—81no—
178C2×C4×D43—81no—
179C2×Dic86—22no—
180C2×Dic86—22no—
181C2×Dic86—41no—
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—24no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43C2×D412yes—
194C4⋊C4×C43C2×D412yes—
195C42×C43—21no—
196C42×C43—21no—
197#10621884—28no—
198(C2×D43)⋊C4—24no—
199(C2×D43)⋊C4—24no—
200(C2×D43)⋊C4—24no—
201C4⋊Dic43—24no—
202C4⋊Dic43—21no—
203C4⋊Dic43—22no—
204C4⋊Dic43—24no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—42no—
210C4⋊Dic43—42no—
211C4⋊Dic43C2×D412yes—
212Dic43⋊C4—24no—
213Dic43⋊C4—24no—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—42no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—42no—
220C4×Dic43C2×D412yes—
221C4×Dic43C2×D412yes—
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×C43C22×D411yescharacteristic
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—22no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236Q8×C43—22no—
237Q8×C43—22no—
238Q8×C43—41no—
239Q8×C43—41no—
240Q8×C43—84no—
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—21no—
248C2×C4×C43—21no—
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×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43#13512yes—
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C22×Q811yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C432−1+411yescharacteristic
264C2×C4×C432−1+411yescharacteristic
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—22no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43#12012yes—
285C2×Dic43#12012yes—
286D172—22no—
287D172—22no—
288D172—22no—
289D172C22⋊Q814yes—
290C4×D43—48no—
291C4×D43—84no—
292C4×D43—84no—
293Dic86—44no—
294C8×C43—41no—
295C8×C43—41no—
296C43⋊C8—22no—
297C43⋊C8—41no—
298#24337—431nomaximal, Sylow
299C22×C43C2×#12011yescharacteristic
300C22×C43#54811yescharacteristic
301C22×C43D4×Q811yescharacteristic
302C22×C43C2×#13511yescharacteristic
303C22×C43#57511yescharacteristic
304C22×C43#57711yescharacteristic
305C22×C43#57711yescharacteristic
306C2×D43—24no—
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—42no—
311C2×D43—42no—
312C2×D43—42no—
313C4×C43—22no—
314C4×C43—42no—
315C4×C43—42no—
316C4×C43—42no—
317C4×C43—41no—
318C4×C43—81no—
319C4×C43C2×C22⋊Q811yescharacteristic
320C4×C43#53611yescharacteristic
321C4×C43#54811yescharacteristic
322C4×C43D4×Q811yescharacteristic
323Dic43—22no—
324Dic43—22no—
325Dic43—41no—
326Dic43—42no—
327Dic43—41no—
328Dic43—81no—
329Dic43—81no—
330C2×#554—431no—
331C2×#479—431no—
332C2×C4×SD16—431no—
333#2581—431no—
334#2059—431no—
335#2058—431no—
336#2026—431no—
337#2024D4311yescharacteristic, complemented
338#1991—431no—
339#1984—431no—
340#1877—431no—
341#1877—431no—
342#1864—431no—
343#1862—431no—
344#1804—431no—
345C2×C43#240911yescharacteristic
346C2×C43#300211yescharacteristic
347C2×C43#300911yescharacteristic
348C2×C43#336011yescharacteristic
349C2×C43#337611yescharacteristic
350C2×C43#338111yescharacteristic
351C2×C43#338811yescharacteristic
352D43—44no—
353C22×SD16—431no—
354#554—864no—
355#554—864no—
356C2×C4⋊Q8C2×D4311yescharacteristic
357C2×#125—431no—
358C2×#125—431no—
359C2×C22⋊Q8—861no—
360C2×C22⋊Q8—861no—
361C2×C22⋊Q8—861no—
362C2×C4×Q8—431no—
363C2×C4×Q8—431no—
364C2×C4×D4—431no—
365C2×C4×D4—431no—
366C2×C4×D4—431no—
367C22×C4⋊C4—861no—
368#479—864no—
369C4×SD16—864no—
370C2×#107—431no—
371C2×#106—431no—
372C2×#106—431no—
373C2×C4⋊C8—431no—
374C2×#103—431no—
375C2×#103C2×D4311yescharacteristic
376C2×#103C2×D4311yescharacteristic
377C2×#102—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×C4×C8—431no—
381#400—861no—
382#395—861no—
383#391—431no—
384#391C2×D4311yescharacteristic
385#389—431no—
386#389—431no—
387#387—861no—
388#387—861no—
389#382—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340C2×D4311yescharacteristic
395#340C2×D4311yescharacteristic
396#336—431no—
397#336—431no—
398#336—431no—
399#336C2×D4311yescharacteristic
400C43#2433711yescharacteristic, complemented, Sylow
401C22×Q8—21no—
402C22×Q8—431no—
403C22×Q8C22×D4311yescharacteristic
404C22×D4—431no—
405C23×C4—861no—
406C23×C4—861no—
407C23×C4—861no—
408C2×SD16—434no—
409C2×SD16—862no—
410C2×SD16—862no—
411C22×C8—431no—
412C22×C8—431no—
413C22×C8C22×D4311yescharacteristic
414C22×C8C22×D4311yescharacteristic
415C4⋊Q8—22no—
416C4⋊Q8—22no—
417#125—434no—
418#125—862no—
419#125—862no—
420#125—862no—
421C22⋊Q8—868no—
422C22⋊Q8—868no—
423C22⋊Q8—868no—
424C4×Q8—862no—
425C4×Q8—862no—
426C4×Q8—862no—
427C4×Q8—862no—
428C4×D4—434no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4—862no—
432C4×D4—862no—
433C4×D4—862no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—868no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C4⋊C4C22×D4311yescharacteristic
451C2×C4⋊C4C22×D4311yescharacteristic
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C42—431no—
456C2×C42—431no—
457C2×C42—861no—
458C2×C42C22×D4311yescharacteristic
459#107—862no—
460#106—862no—
461#106—862no—
462C4⋊C8—862no—
463#103—22no—
464#103—22no—
465#103—862no—
466#102—862no—
467#102—862no—
468#102—862no—
469C4×C8—862no—
470#95—21no—
471#95—21no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478C24—861no—
479C2×Q8—24no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—81no—
486C2×Q8—81no—
487C2×Q8—862no—
488C2×Q8—862no—
489C2×Q8—1721no—
490C2×Q8Q8×D4312yes—
491C2×D4—432no—
492C2×D4—432no—
493C2×D4—432no—
494C2×D4—861no—
495C2×D4—861no—
496C2×D4—861no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—864no—
506C22×C4—864no—
507C22×C4—864no—
508C22×C4—861no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—3441no—
512C22×C4—3441no—
513C22×C4—3441no—
514C22×C4—3441no—
515C22×C4—1722no—
516C22×C4—1722no—
517C22×C4D4×D4311yescharacteristic
518C22×C4D4×D4311yescharacteristic
519C22×C4C23×D4311yescharacteristic
520SD16—868no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—432no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C4⋊C4—24no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—432no—
539C4⋊C4—862no—
540C4⋊C4—862no—
541C4⋊C4—862no—
542C4⋊C4—864no—
543C4⋊C4—864no—
544C4⋊C4—864no—
545C4⋊C4—864no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—1722no—
552C4⋊C4—1722no—
553C4⋊C4—1722no—
554C4⋊C4D4×D4312yes—
555C4⋊C4D4×D4312yes—
556C22⋊C4—864no—
557C22⋊C4—864no—
558C22⋊C4—864no—
559C42—21no—
560C42—21no—
561C42—432no—
562C42—432no—
563C42—861no—
564C42—861no—
565C42—1722no—
566C23—862no—
567C23—862no—
568C23—862no—
569C23—1721no—
570C23—1721no—
571C23—1721no—
572C23—1721no—
573C23C2×D4×D4311yescharacteristic
574Q8—22no—
575Q8—22no—
576Q8—41no—
577Q8—41no—
578Q8—84no—
579Q8—1724no—
580D4—434no—
581D4—862no—
582D4—862no—
583D4—862no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—22no—
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—432no—
602C2×C4—432no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—862no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—3444no—
615C2×C4—3444no—
616C2×C4—1728no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4#1306334812yes—
626C2×C4C2×D4×D4311yescharacteristic
627C2×C4C2×D4×D4311yescharacteristic
628C2×C4C2×Q8×D4311yescharacteristic
629C2×C4#41×D4311yescharacteristic
630C2×C4#1306337211yescharacteristic
631C2×C4#1306337211yescharacteristic
632C8—41no—
633C8—41no—
634C8—862no—
635C8—1721no—
636C22—864no—
637C22—1722no—
638C22—1722no—
639C22—1722no—
640C22—1722no—
641C22—1722no—
642C22—1722no—
643C22#120×D4311yescharacteristic
644C22#1458355711yescharacteristic
645C22#1458356211yescharacteristic
646C22C2×#1306334811yescharacteristic
647C22#1458369811yescharacteristic
648C22#1458370511yescharacteristic
649C22#1458370911yescharacteristic
650C4—22no—
651C4—42no—
652C4—41no—
653C4—42no—
654C4—42no—
655C4—81no—
656C4—862no—
657C4—862no—
658C4—3441no—
659C4—3441no—
660C4—1721no—
661C4—1722no—
662C4—1721no—
663C4C22⋊Q8×D4311yescharacteristic
664C4#1458346911yescharacteristic
665C4#1458355711yescharacteristic
666C4#1458356211yescharacteristic
667C2—1724no—
668C2#1913795311yescharacteristic
669C2#1914381811yescharacteristic
670C2#1914386711yescharacteristic
671C2#1914724911yescharacteristic
672C2#1914742111yescharacteristic
673C2#1914746911yescharacteristic
674C2#1914754711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2024C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2024D43
hypocenterC43#24337
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
2. C2×#14583208C2semidirect
4. #19139959C2semidirect
5. #19135936C2semidirect
6. #19135925C2semidirect
7. #19135744C2semidirect
8. #19135558C2semidirect
9. #19135529C2semidirect
15. C43×#2024C2semidirect
70. C2×#10621884Q8semidirect
337. #2024D43semidirect
400. C43#24337semidirect

Maximal subgroups

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

subgroupindex
C2×#145836102
C2×#145832082
C2×#145829842
#191399592
#191359362
#191359252
#191357442
#191355582
#191355292
#191349322
#191349262
#191348572
#191348452
#191346042
C43×#20242
#2433743