Finite Group Databasebeta

← #25133133

Subgroups — #25133133

Order 11008.

1036 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×#14583626C211yesmaximal, characteristic, complemented
2C2×#14583188C211yesmaximal, characteristic
3C2×#14582998C211yesmaximal, characteristic
4#19139955C211yesmaximal, characteristic
5#19135931C211yesmaximal, characteristic, complemented
6#19135740C211yesmaximal, characteristic
7#19135738C211yesmaximal, characteristic
8#19135566C211yesmaximal, characteristic, complemented
9#19135533C211yesmaximal, characteristic, complemented
10#19134951C211yesmaximal, characteristic
11#19134949C211yesmaximal, characteristic
12#19134862C211yesmaximal, characteristic, complemented
13#19134860C211yesmaximal, characteristic, complemented
14#19134609C211yesmaximal, characteristic, complemented
15C43×#2059C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17#14583626—24no—
18#14583626—24no—
19C2×#13063324—21no—
20C2×#13063324C2211yescharacteristic
21C2×#13063316C2211yescharacteristic
22C2×#13063315—21no—
23C2×#13063315—21no—
24C2×C4×Dic86C2211yescharacteristic
25C2×C4×Dic86C2211yescharacteristic
26C2×#13063290—21no—
27C2×#13063290C2211yescharacteristic
28C2×#13063290C2211yescharacteristic
29C2×#13063287C2211yescharacteristic
30#14583188—24no—
31#14582998—24no—
32C2×#13063256C2211yescharacteristic
33C2×Dic43⋊C8C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063235C2211yescharacteristic
41#14582834—21no—
42#14582812—21no—
43#14582801C2211yescharacteristic
44#14582800C2211yescharacteristic
45#14582795C2211yescharacteristic
46#14582773—21no—
47#14582770—21no—
48#14582764C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×#125×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×#106×C43C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86D411yescharacteristic
65C22×Dic86C2311yescharacteristic
66C22×D172C2311yescharacteristic
67C22×C4×D43—21no—
68C2×#10621873—22no—
69C2×#10621873—22no—
70C2×#10621873Q814yescomplemented
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063324—28no—
74#13063324—22no—
75#13063324D414yes—
76#13063316—22no—
77#13063316—22no—
78#13063315—28no—
79#13063315—28no—
80C4×Dic86—22no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84#13063290—28no—
85#13063290—22no—
86#13063290—22no—
87#13063290—22no—
88#13063290D414yes—
89#13063287—22no—
90#13063287—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43D411yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4D411yescharacteristic
102C2×Dic43⋊C4D411yescharacteristic
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43C2311yescharacteristic
112C2×C4×Dic43C2311yescharacteristic
113#13063256—22no—
114Dic43⋊C8—22no—
115#13063250—22no—
116#13063248—22no—
117#13063248—22no—
118#13063247—22no—
119#13063245—22no—
120#13063245—22no—
121#13063235—22no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127#125×C43—22no—
128#125×C43—22no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C42×C43C2311yescharacteristic
137#107×C43—22no—
138#106×C43—22no—
139#95×C43—21no—
140C23×D43—21no—
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×C43C2411yescharacteristic
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172C2×Q812yes—
161C2×C4×D43—42no—
162C2×C4×D43—81no—
163C2×C4×D43—81no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—24no—
168C2×Dic86—22no—
169C2×Dic86—41no—
170C2×Dic86—41no—
171C2×Dic86—42no—
172C2×Dic86—42no—
173C2×Dic86C2×D412yes—
174C2×Dic86C2×Q812yes—
175C2×Dic86#4112yes—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43C2×Q812yes—
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×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—81no—
191C4⋊C4×C43C2×D412yes—
192C4⋊C4×C43C2×D412yes—
193C42×C43—21no—
194C42×C43—21no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—42no—
198(C2×D43)⋊C4—81no—
199(C2×D43)⋊C4—81no—
200C4⋊Dic43—24no—
201C4⋊Dic43—21no—
202C4⋊Dic43—22no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43C2×D412yes—
206Dic43⋊C4—24no—
207Dic43⋊C4—24no—
208Dic43⋊C4—24no—
209Dic43⋊C4—24no—
210Dic43⋊C4—24no—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—81no—
214C4×Dic43—24no—
215C4×Dic43—24no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—24no—
219C4×Dic43C2×D412yes—
220C4×Dic43C2×D412yes—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227#10621873—28no—
228C23×C43C22×D411yescharacteristic
229C22×D43—22no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×Q811yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C432−1+411yescharacteristic
259C2×C4×C432−1+411yescharacteristic
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—22no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43#12012yes—
280C2×Dic43#12012yes—
281D172—22no—
282D172—22no—
283D172—41no—
284D172—41no—
285C4×D43—84no—
286Dic86—22no—
287Dic86—22no—
288Dic86—22no—
289Dic86—44no—
290Dic86—48no—
291Dic86C22⋊Q814yes—
292C8×C43—22no—
293C8×C43—41no—
294C43⋊C8—41no—
295C43⋊C8—41no—
296#24340—431nomaximal, Sylow
297C22×C43C2×#12011yescharacteristic
298C22×C43#54811yescharacteristic
299C22×C43D4×Q811yescharacteristic
300C22×C43#57511yescharacteristic
301C22×C43#57511yescharacteristic
302C22×C43#57711yescharacteristic
303C22×C43#57711yescharacteristic
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—81no—
311C4×C43—41no—
312C4×C43—42no—
313C4×C43—41no—
314C4×C43—42no—
315C4×C43—81no—
316C4×C43—81no—
317C4×C43C2×C22⋊Q811yescharacteristic
318C4×C43#53611yescharacteristic
319C4×C43#54811yescharacteristic
320C4×C43D4×Q811yescharacteristic
321Dic43—24no—
322Dic43—22no—
323Dic43—22no—
324Dic43—41no—
325Dic43—42no—
326Dic43—41no—
327Dic43—81no—
328C2×#557—431no—
329C2×#476—431no—
330C2×#440—431no—
331#2580—431no—
332#2059—431no—
333#2059D4311yescharacteristic, complemented
334#2025—431no—
335#2025—431no—
336#1993—431no—
337#1985—431no—
338#1880—431no—
339#1880—431no—
340#1865—431no—
341#1865—431no—
342#1805—431no—
343C2×C43#240911yescharacteristic
344C2×C43#300511yescharacteristic
345C2×C43#301011yescharacteristic
346C2×C43#337111yescharacteristic
347C2×C43#337111yescharacteristic
348C2×C43#338811yescharacteristic
349C2×C43#338811yescharacteristic
350D43—82no—
351C22×SD16—431no—
352#557—864no—
353#557—864no—
354C2×C4⋊Q8—431no—
355C2×C4⋊Q8—861no—
356C2×#125—431no—
357C2×#125—861no—
358C2×#125—861no—
359C2×#125C2×D4311yescharacteristic
360C2×C4×Q8—431no—
361C2×C4×Q8—431no—
362C2×C4×Q8—431no—
363C2×C4×Q8—431no—
364C2×C4×Q8—861no—
365C2×C4×D4—431no—
366#476—864no—
367#440—864no—
368C2×#107C2×D4311yescharacteristic
369C2×#106—431no—
370C2×#106C2×D4311yescharacteristic
371C2×C4⋊C8—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×#97—431no—
379#399—861no—
380#393—861no—
381#390—431no—
382#390—431no—
383#389—431no—
384#389C2×D4311yescharacteristic
385#385—861no—
386#385—861no—
387#382—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340C2×D4311yescharacteristic
393#340C2×D4311yescharacteristic
394#336—431no—
395#336—431no—
396#336—431no—
397#336C2×D4311yescharacteristic
398C43#2434011yescharacteristic, complemented, Sylow
399C22×Q8—431no—
400C22×Q8—431no—
401C22×Q8—861no—
402C22×D4—431no—
403C23×C4—861no—
404C2×SD16—434no—
405C2×SD16—862no—
406C2×SD16—862no—
407C22×C8—431no—
408C22×C8—431no—
409C22×C8C22×D4311yescharacteristic
410C22×C8C22×D4311yescharacteristic
411C4⋊Q8—434no—
412C4⋊Q8—862no—
413C4⋊Q8—868no—
414#125—22no—
415#125—22no—
416#125—862no—
417#125—868no—
418#125—868no—
419#125—862no—
420C4×Q8—434no—
421C4×Q8—862no—
422C4×Q8—862no—
423C4×Q8—862no—
424C4×Q8—862no—
425C4×Q8—862no—
426C4×Q8—862no—
427C4×Q8—868no—
428C4×Q8—862no—
429C4×D4—862no—
430C4×D4—862no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
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⋊C4—861no—
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C4⋊C4C22×D4311yescharacteristic
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C42—431no—
456C2×C42—431no—
457C2×C42—861no—
458C2×C42—861no—
459C2×C42—861no—
460C2×C42C22×D4311yescharacteristic
461#107—22no—
462#106—22no—
463#106—862no—
464C4⋊C8—862no—
465#103—862no—
466#103—862no—
467#103—862no—
468#102—862no—
469#102—862no—
470#102—862no—
471#97—862no—
472#95—21no—
473#95—861no—
474#95—861no—
475#95—861no—
476C24—861no—
477C2×Q8—432no—
478C2×Q8—432no—
479C2×Q8—432no—
480C2×Q8—864no—
481C2×Q8—862no—
482C2×Q8—861no—
483C2×Q8—861no—
484C2×Q8—861no—
485C2×Q8—1721no—
486C2×Q8—1721no—
487C2×Q8—1722no—
488C2×Q8—1722no—
489C2×D4—432no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—3441no—
507C22×C4—3441no—
508C22×C4—1722no—
509C22×C4D4×D4311yescharacteristic
510C22×C4D4×D4311yescharacteristic
511C22×C4C23×D4311yescharacteristic
512SD16—868no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8Q8×D4312yes—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—81no—
534C4⋊C4—432no—
535C4⋊C4—862no—
536C4⋊C4—862no—
537C4⋊C4—862no—
538C4⋊C4—864no—
539C4⋊C4—864no—
540C4⋊C4—864no—
541C4⋊C4—864no—
542C4⋊C4—864no—
543C4⋊C4—864no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—3441no—
548C4⋊C4D4×D4312yes—
549C4⋊C4D4×D4312yes—
550C22⋊C4—3441no—
551C22⋊C4—3441no—
552C22⋊C4—1722no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C42—21no—
556C42—21no—
557C42—432no—
558C42—432no—
559C42—864no—
560C42—864no—
561C42—864no—
562C42—861no—
563C42—861no—
564C23—862no—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23—1721no—
571C23C2×D4×D4311yescharacteristic
572Q8—434no—
573Q8—862no—
574Q8—862no—
575Q8—862no—
576Q8—1724no—
577Q8—1728no—
578D4—862no—
579D4—862no—
580D4—1721no—
581D4—1721no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
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—432no—
601C2×C4—432no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—862no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—3444no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4C2×D4×D4311yescharacteristic
623C2×C4C2×D4×D4311yescharacteristic
624C2×C4C2×Q8×D4311yescharacteristic
625C2×C4#41×D4311yescharacteristic
626C2×C4#1306337311yescharacteristic
627C2×C4#1306337311yescharacteristic
628C8—22no—
629C8—41no—
630C8—1721no—
631C8—1721no—
632C22—3441no—
633C22—3441no—
634C22—3441no—
635C22—3441no—
636C22—1722no—
637C22—1722no—
638C22—1722no—
639C22#120×D4311yescharacteristic
640C22#1458355911yescharacteristic
641C22#1458356411yescharacteristic
642C22#1458369611yescharacteristic
643C22#1458369811yescharacteristic
644C22#1458370611yescharacteristic
645C22#1458370911yescharacteristic
646C4—41no—
647C4—42no—
648C4—41no—
649C4—42no—
650C4—81no—
651C4—81no—
652C4—862no—
653C4—864no—
654C4—862no—
655C4—3441no—
656C4—1721no—
657C4—1722no—
658C4—1721no—
659C4C22⋊Q8×D4311yescharacteristic
660C4#1458347411yescharacteristic
661C4#1458355911yescharacteristic
662C4#1458356411yescharacteristic
663C2—3442no—
664C2#1913795511yescharacteristic
665C2#1914383811yescharacteristic
666C2#1914387811yescharacteristic
667C2#1914736111yescharacteristic
668C2#1914736611yescharacteristic
669C2#1914753911yescharacteristic
670C2#1914754611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2059C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2059D43
hypocenterC43#24340
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2059

Complements

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

NH ≅ G/Ntype
1. C2×#14583626C2semidirect
5. #19135931C2semidirect
8. #19135566C2semidirect
9. #19135533C2semidirect
12. #19134862C2semidirect
13. #19134860C2semidirect
14. #19134609C2semidirect
15. C43×#2059C2semidirect
70. C2×#10621873Q8semidirect
333. #2059D43semidirect
398. C43#24340semidirect

Maximal subgroups

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

subgroupindex
C2×#145836262
C2×#145831882
C2×#145829982
#191399552
#191359312
#191357402
#191357382
#191355662
#191355332
#191349512
#191349492
#191348622
#191348602
#191346092
C43×#20592
#2434043