Finite Group Databasebeta

← #25159544

Subgroups — #25159544

Order 11008.

968 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582979C211yesmaximal, characteristic
2#19138441C211yesmaximal, characteristic, complemented
3D4×Dic43⋊C4C211yesmaximal, characteristic, complemented
4#19136120C211yesmaximal, characteristic, complemented
5#19136069C211yesmaximal, characteristic, complemented
6#19135982C211yesmaximal, characteristic, complemented
7#19135920C211yesmaximal, characteristic, complemented
8#19135326C211yesmaximal, characteristic, complemented
9#19135149C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic
11#19134941C211yesmaximal, characteristic
12#19134844C211yesmaximal, characteristic, complemented
13#19134840C211yesmaximal, characteristic, complemented
14#19134839C211yesmaximal, characteristic, complemented
15C2×C43×#474C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×#13063301—21no—
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C22×Dic43⋊C4—21no—
22#14582979—24no—
23C2×#13063259C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582821—21no—
32#14582810—21no—
33#14582801C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582795C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582772—21no—
40#14582771—21no—
41#14582770—21no—
42#14582768C2211yescharacteristic
43#14582757—21no—
44C4×Dic43⋊C4C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×C4⋊Q8×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C43×#474—24no—
56C2×#107×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C23×Dic43—21no—
63C23×Dic43—21no—
64C22×C4×D43—21no—
65C2×#10621882—22no—
66C2×#10621882—22no—
67C2×#10621882Q814yescomplemented
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063301—44no—
71D4×Dic43—22no—
72D4×Dic43—22no—
73D4×Dic43—22no—
74D4×Dic43—41no—
75#13063287—22no—
76#13063287—41no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—44no—
87C2×Dic43⋊C4D411yescharacteristic
88C2×Dic43⋊C4D411yescharacteristic
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×C4×Dic43C2311yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98#13063259—22no—
99#13063258—22no—
100#13063258—41no—
101#13063247—22no—
102#13063247—22no—
103#13063246—22no—
104#13063245—41no—
105C8×Dic43—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C22×Q8×C43—21no—
113C22×D4×C43C2311yescharacteristic
114C23×C4×C43—21no—
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C4⋊Q8×C43—22no—
118C4⋊Q8×C43—41no—
119C4×D4×C43—22no—
120C4×D4×C43—41no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C42×C43C2311yescharacteristic
127#107×C43—22no—
128#107×C43—22no—
129C4⋊C8×C43—22no—
130#102×C43—22no—
131#102×C43D414yes—
132C24×C43—21no—
133C23×D43—21no—
134C2×Q8×C43—42no—
135C2×Q8×C43—42no—
136C2×Q8×C43—81no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43C2×D412yes—
141C2×D4×C43C2×Q812yes—
142C2×D4×C43#4112yes—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—42no—
147C22×C4×C43—42no—
148C22×C4×C43—81no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—24no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—42no—
157C22×Dic43—42no—
158C22×Dic43—42no—
159C22×Dic43—42no—
160C22×Dic43—81no—
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172C2×Q812yes—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×C4×D43—81no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C2×D412yes—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—42no—
186C4⋊C4×C43C2×D412yes—
187C22⋊C4×C43—42no—
188C42×C43—21no—
189C42×C43—21no—
190C22⋊Dic43—24no—
191C22⋊Dic43—42no—
192#10621882—28no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—81no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—42no—
204C4⋊Dic43#4112yes—
205Dic43⋊C4—41no—
206Dic43⋊C4—42no—
207Dic43⋊C4—42no—
208Dic43⋊C4—42no—
209Dic43⋊C4—42no—
210Dic43⋊C4—81no—
211Dic43⋊C4D814yescomplemented
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8C2×Q812yes—
222C23×C43—22no—
223C23×C43—22no—
224C23×C43—22no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43C22×D411yescharacteristic
230C22×D43—22no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237Q8×C43—84no—
238D4×C43—22no—
239D4×C43—22no—
240D4×C43—22no—
241D4×C43C22⋊Q814yescomplemented
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
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×C43—84no—
257C2×C4×C43C2×D812yes—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×Q811yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C2×C4×C432−1+411yescharacteristic
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—21no—
275C2×Dic43—48no—
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—84no—
285C2×Dic43C2×D812yes—
286C2×Dic43C2×D812yes—
287D172—22no—
288D172—22no—
289D172—41no—
290D172—41no—
291C4×D43—84no—
292C8×C43—22no—
293C8×C43—41no—
294C43⋊C8—22no—
295C43⋊C8—41no—
296#26368—431nomaximal, Sylow
297C22×C43—24no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43#52511yescharacteristic
305C22×C43D4211yescharacteristic
306C22×C43D4×Q811yescharacteristic
307C22×C43C22×D811yescharacteristic
308C22×C43#57511yescharacteristic
309C22×C43#57611yescharacteristic
310C22×C43#57811yescharacteristic
311C2×D43—42no—
312C2×D43—42no—
313C2×D43—42no—
314C2×D43—81no—
315C2×D43—81no—
316C2×D43—81no—
317C2×D43—81no—
318C4×C43—22no—
319C4×C43—41no—
320C4×C43—42no—
321C4×C43—81no—
322C4×C43—81no—
323C4×C43C2×C22⋊Q811yescharacteristic
324C4×C43#53911yescharacteristic
325C4×C43#54711yescharacteristic
326C4×C43#55411yescharacteristic
327Dic43—22no—
328Dic43—22no—
329Dic43—42no—
330Dic43—41no—
331Dic43—41no—
332Dic43—81no—
333Dic43—81no—
334C2×#474D4311yescharacteristic, complemented
335C2×C4×D8—431no—
336#2452—431no—
337D4×C4⋊C4—431no—
338#2093—431no—
339#2083—431no—
340#2067—431no—
341#2057—431no—
342#1942—431no—
343#1916—431no—
344#1879—431no—
345#1879—431no—
346#1862—431no—
347#1862—431no—
348#1862—431no—
349C2×C43—44no—
350C2×C43#244911yescharacteristic
351C2×C43#310011yescharacteristic
352C2×C43#312411yescharacteristic
353C2×C43#326911yescharacteristic
354C2×C43D4×D811yescharacteristic
355C2×C43Q8×D811yescharacteristic
356C2×C43#338911yescharacteristic
357D43—82no—
358C22×D8—431no—
359C2×C4⋊Q8C2×D4311yescharacteristic
360C2×C22⋊Q8—861no—
361C2×C4×D4—431no—
362C2×C4×D4—431no—
363C2×C4×D4—431no—
364C2×C4×D4C2×D4311yescharacteristic
365C22×C4⋊C4—861no—
366#474—24no—
367C4×D8—864no—
368C2×#107—431no—
369C2×#107—431no—
370C2×#107—431no—
371C2×#107C2×D4311yescharacteristic
372C2×#107C2×D4311yescharacteristic
373C2×C4⋊C8C2×D4311yescharacteristic
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×#102C2×D4311yescharacteristic
379C2×#102C2×D4311yescharacteristic
380C2×C4×C8—431no—
381#396—861no—
382#393—861no—
383#390—431no—
384#390—431no—
385#389—431no—
386#389—431no—
387#389—431no—
388#389—431no—
389#385—861no—
390#385—861no—
391#385—861no—
392#384—431no—
393#380—861no—
394C4×C4⋊C4—431no—
395#340—431no—
396#340—431no—
397#340—431no—
398#340—431no—
399#336—431no—
400#336—431no—
401#336—431no—
402#336—431no—
403C43#2636811yescharacteristic, complemented, Sylow
404C22×Q8—21no—
405C22×D4—431no—
406C22×D4C22×D4311yescharacteristic
407C23×C4—21no—
408C23×C4—861no—
409C23×C4—861no—
410C23×C4—861no—
411C2×D8—434no—
412C2×D8—862no—
413C2×D8—862no—
414C22×C8—431no—
415C22×C8—431no—
416C22×C8C22×D4311yescharacteristic
417C22×C8C22×D4311yescharacteristic
418C4⋊Q8—22no—
419C4⋊Q8—41no—
420C22⋊Q8—1724no—
421C4×D4—22no—
422C4×D4—41no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—1721no—
428C4×D4—1721no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
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—1724no—
442C2×C4⋊C4C22×D4311yescharacteristic
443C2×C4⋊C4C22×D4311yescharacteristic
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C42—431no—
454C2×C42—431no—
455C2×C42C22×D4311yescharacteristic
456#107—22no—
457#107—22no—
458#107—862no—
459#107—862no—
460#107—1721no—
461C4⋊C8—22no—
462#102—22no—
463#102—862no—
464#102—862no—
465#102—862no—
466#102—1721no—
467#102C22⋊D4314yes—
468C4×C8—862no—
469#95—431no—
470#95—431no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475C24—21no—
476C24—861no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—81no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—432no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—861no—
489C2×D4Q8×D4312yes—
490C2×D4#1062190212yes—
491C2×D4C2×C22⋊D4312yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—81no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—864no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—3441no—
507C22×C4—3441no—
508C22×C4—1722no—
509C22×C4—1722no—
510C22×C4—1722no—
511C22×C4—1722no—
512C22×C4—1722no—
513C22×C4—1722no—
514C22×C4D4×D4311yescharacteristic
515C22×C4D4×D4311yescharacteristic
516C22×C4C23×D4311yescharacteristic
517D8—868no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—432no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8C2×C22⋊D4312yes—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—42no—
536C4⋊C4—434no—
537C4⋊C4—432no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—3441no—
544C4⋊C4—1721no—
545C4⋊C4—1722no—
546C4⋊C4—1722no—
547C4⋊C4—1722no—
548C4⋊C4—1722no—
549C4⋊C4—1722no—
550C4⋊C4C2×C22⋊D4312yes—
551C22⋊C4—42no—
552C22⋊C4—864no—
553C22⋊C4—3441no—
554C22⋊C4—1722no—
555C22⋊C4—1722no—
556C22⋊C4—1722no—
557C22⋊C4—1722no—
558C22⋊C4—1722no—
559C42—21no—
560C42—21no—
561C42—861no—
562C42—861no—
563C42—861no—
564C42—861no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—862no—
573C23—1721no—
574C23—1721no—
575C23—1721no—
576C23—1721no—
577C23—1721no—
578C23—1721no—
579C23C2×D4×D4311yescharacteristic
580Q8—84no—
581D4—22no—
582D4—22no—
583D4—22no—
584D4—862no—
585D4—862no—
586D4—1721no—
587D4—1721no—
588D4#1306330114yescomplemented
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—84no—
604C2×C4—432no—
605C2×C4—432no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—862no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—3444no—
618C2×C4—3444no—
619C2×C4—1728no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4D8×D4312yes—
629C2×C4C22×C22⋊D4311yescharacteristic
630C2×C4C2×Q8×D4311yescharacteristic
631C2×C4#41×D4311yescharacteristic
632C2×C4C2×#1062190211yescharacteristic
633C2×C4#1306337011yescharacteristic
634C2×C4#1306337211yescharacteristic
635C8—22no—
636C8—41no—
637C8—862no—
638C8—1721no—
639C22—24no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—3441no—
647C22—3441no—
648C22—3441no—
649C22—3441no—
650C22—1722no—
651C22—1722no—
652C22—1722no—
653C22#1458341211yescharacteristic
654C22D4×C22⋊D4311yescharacteristic
655C22#1458356211yescharacteristic
656C22C2×D8×D4311yescharacteristic
657C22#1458369811yescharacteristic
658C22#1458370011yescharacteristic
659C22#1458371511yescharacteristic
660C4—22no—
661C4—42no—
662C4—41no—
663C4—81no—
664C4—81no—
665C4—862no—
666C4—862no—
667C4—3441no—
668C4—3441no—
669C4—1722no—
670C4—1721no—
671C4—1721no—
672C4C2×#1306330111yescharacteristic
673C4#1458349811yescharacteristic
674C4#1458354811yescharacteristic
675C4#1458360311yescharacteristic
676C2—44no—
677C2—3442no—
678C2#1913840011yescharacteristic
679C2#1914459711yescharacteristic
680C2#1914486211yescharacteristic
681C2#1914614411yescharacteristic
682C2D8×C22⋊D4311yescharacteristic
683C2#1914744511yescharacteristic
684C2#1914754811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#474C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenterC2×#474D43
hypocenterC43#26368
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
2. #19138441C2semidirect
3. D4×Dic43⋊C4C2semidirect
4. #19136120C2semidirect
5. #19136069C2semidirect
6. #19135982C2semidirect
7. #19135920C2semidirect
8. #19135326C2semidirect
9. #19135149C2semidirect
12. #19134844C2semidirect
13. #19134840C2semidirect
14. #19134839C2semidirect
15. C2×C43×#474C2semidirect
67. C2×#10621882Q8semidirect
211. Dic43⋊C4D8semidirect
241. D4×C43C22⋊Q8semidirect
334. C2×#474D43semidirect
403. C43#26368semidirect
588. D4#13063301semidirect

Maximal subgroups

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

subgroupindex
C2×#145829792
#191384412
D4×Dic43⋊C42
#191361202
#191360692
#191359822
#191359202
#191353262
#191351492
#191349432
#191349412
#191348442
#191348402
#191348392
C2×C43×#4742
#2636843