Finite Group Databasebeta

← #25138160

Subgroups — #25138160

Order 11008.

946 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583123C211yesmaximal, characteristic
2C2×#14583121C211yesmaximal, characteristic
3C2×#14583107C211yesmaximal, characteristic, complemented
4C2×#14582984C211yesmaximal, characteristic
5#19139592C211yesmaximal, characteristic
6Q8×Dic43⋊C4C211yesmaximal, characteristic, complemented
7#19135977C211yesmaximal, characteristic, complemented
8#19135976C211yesmaximal, characteristic, complemented
9#19135837C211yesmaximal, characteristic
10#19135832C211yesmaximal, characteristic
11#19135395C211yesmaximal, characteristic, complemented
12#19135312C211yesmaximal, characteristic, complemented
13#19134934C211yesmaximal, characteristic, complemented
14#19134594C211yesmaximal, characteristic
15C43×#1878C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063323C2211yescharacteristic
19C2×#13063314C2211yescharacteristic
20C2×#13063313C2211yescharacteristic
21C2×Q8×Dic43C2211yescharacteristic
22C2×Q8×Dic43C2211yescharacteristic
23C2×#13063287C2211yescharacteristic
24#14583123—24no—
25#14583121—24no—
26#14583107—24no—
27#14582984—24no—
28C2×#13063256C2211yescharacteristic
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×Dic43⋊C8C2211yescharacteristic
31C2×Dic43⋊C8C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×C8×Dic43C2211yescharacteristic
41#14582828—21no—
42#14582828—21no—
43#14582804C2211yescharacteristic
44#14582797—21no—
45#14582797C2211yescharacteristic
46#14582795—21no—
47#14582795C2211yescharacteristic
48#14582768—21no—
49#14582768C2211yescharacteristic
50#14582758—21no—
51#14582758—21no—
52C4×Dic43⋊C4—21no—
53C4×Dic43⋊C4C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×Q16×C43C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C43×#391C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C4×D43—21no—
66C2×#10621885—22no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C2×#10621884D414yes—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063323—22no—
75#13063323—22no—
76#13063314—22no—
77#13063314—41no—
78#13063313—22no—
79#13063313—41no—
80Q8×Dic43—22no—
81Q8×Dic43—22no—
82Q8×Dic43—41no—
83Q8×Dic43D414yes—
84#13063287—22no—
85#13063287—22no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4D411yescharacteristic
97C2×Dic43⋊C4D411yescharacteristic
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2311yescharacteristic
106C2×C4×Dic43C2311yescharacteristic
107#13063256—22no—
108C4⋊(C43⋊C8)—22no—
109Dic43⋊C8—22no—
110Dic43⋊C8—22no—
111#13063250—22no—
112#13063250—41no—
113#13063249—22no—
114#13063249—22no—
115#13063248—22no—
116#13063247—22no—
117#13063247—22no—
118#13063245—22no—
119C8×Dic43—22no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95D411yescharacteristic
125C43⋊#95D411yescharacteristic
126C22×Q8×C43C2311yescharacteristic
127C22×Q8×C43C2311yescharacteristic
128C2×Q16×C43—22no—
129C2×Q16×C43—22no—
130C2×Q16×C43—22no—
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C4×Q8×C43—22no—
134C4×Q8×C43—41no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C42×C43—21no—
139C2×C42×C43C2311yescharacteristic
140#103×C43—22no—
141#103×C43—41no—
142#95×C43—21no—
143#95×C43—21no—
144C23×D43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43C2×D412yes—
155C2×Q8×C43C2×D412yes—
156C2×Q8×C43#4112yes—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172C2×D412yes—
177C2×C4×D43—42no—
178C2×C4×D43—42no—
179C2×C4×D43—42no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186Q16×C43—44no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—42no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—42no—
201#10621885—44no—
202#10621884—28no—
203(C2×D43)⋊C4—42no—
204(C2×D43)⋊C4—42no—
205(C2×D43)⋊C4—42no—
206(C2×D43)⋊C4—42no—
207(C2×D43)⋊C4—42no—
208C4⋊Dic43—21no—
209C4⋊Dic43—24no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—42no—
213C4⋊Dic43C2×D412yes—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—42no—
217Dic43⋊C4—42no—
218Dic43⋊C4—42no—
219Dic43⋊C4—81no—
220Dic43⋊C4—81no—
221Dic43⋊C4—81no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—24no—
225C4×Dic43—42no—
226C4×Dic43C2×D412yes—
227C4×Dic43#4112yes—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8C2×D412yes—
234C23×C43C22×D411yescharacteristic
235C22×D43—22no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—41no—
240C22×D43—41no—
241C22×D43—41no—
242Q8×C43—22no—
243Q8×C43—22no—
244Q8×C43—22no—
245Q8×C43—41no—
246Q8×C43—41no—
247Q8×C43—41no—
248Q8×C43—41no—
249Q8×C43#12114yes—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
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—41no—
267C2×C4×C43—41no—
268C2×C4×C43C22×D411yescharacteristic
269C2×C4×C43C22×D411yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C43H(5,𝔽2)11yescharacteristic
273C2×C4×C432−1+411yescharacteristic
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—22no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43#12112yes—
292C2×Dic43#12112yes—
293C2×Dic43#13512yes—
294C2×Dic43#13712yes—
295D172—22no—
296D172—22no—
297D172—41no—
298D172—41no—
299C4×D43—84no—
300Dic86—41no—
301Dic86—41no—
302Dic86—41no—
303Dic86—41no—
304C8×C43—41no—
305C8×C43—41no—
306C43⋊C8—22no—
307C43⋊C8—41no—
308#24729—431nomaximal, Sylow
309C22×C43C2×#12111yescharacteristic
310C22×C43D4211yescharacteristic
311C22×C43#54811yescharacteristic
312C22×C43C2×#13511yescharacteristic
313C22×C43C2×#13711yescharacteristic
314C22×C43#57711yescharacteristic
315C22×C43#57811yescharacteristic
316C2×D43—42no—
317C2×D43—42no—
318C2×D43—42no—
319C2×D43—81no—
320C2×D43—81no—
321C2×D43—81no—
322C2×D43—81no—
323C4×C43—24no—
324C4×C43—41no—
325C4×C43—41no—
326C4×C43—81no—
327C4×C43—81no—
328C4×C43—81no—
329C4×C43C2×#12111yescharacteristic
330C4×C43#53711yescharacteristic
331C4×C43#54711yescharacteristic
332C4×C43#55311yescharacteristic
333Dic43—22no—
334Dic43—41no—
335Dic43—41no—
336Dic43—42no—
337Dic43—81no—
338Dic43—81no—
339Dic43#46414yescomplemented
340C2×#464—431no—
341C2×#464—431no—
342C2×#462—431no—
343C2×C4×SD16—431no—
344#2547—431no—
345Q8×C4⋊C4—431no—
346#2066—431no—
347#2066—431no—
348#2042—431no—
349#2042—431no—
350#1956—431no—
351#1939—431no—
352#1878—431no—
353#1878D4311yescharacteristic, complemented
354#1802—431no—
355C2×C43#241611yescharacteristic
356C2×C43C2×#46411yescharacteristic
357C2×C43#304611yescharacteristic
358C2×C43#327611yescharacteristic
359C2×C43#328411yescharacteristic
360C2×C43#336411yescharacteristic
361C2×C43#336911yescharacteristic
362D43—82no—
363C22×Q16—431no—
364C22×Q16C2×D4311yescharacteristic
365C22×SD16—431no—
366C2×C4⋊Q8—431no—
367C2×#124—431no—
368C2×#124—431no—
369C2×C4×Q8—431no—
370C2×C4×Q8—431no—
371C2×C4×Q8C2×D4311yescharacteristic
372C2×C4×D4—431no—
373#464—864no—
374#464—864no—
375#462—864no—
376C4×SD16—864no—
377C2×#106—431no—
378C2×C4⋊C8—431no—
379C2×C4⋊C8—431no—
380C2×C4⋊C8—431no—
381C2×#103—431no—
382C2×#103—431no—
383C2×#103—431no—
384C2×#103—431no—
385C2×#103—431no—
386C2×#103C2×D4311yescharacteristic
387C2×#103C2×D4311yescharacteristic
388C2×#102—431no—
389C2×#102—431no—
390C2×#102—431no—
391C2×C4×C8—431no—
392#397—861no—
393#397—861no—
394#391—431no—
395#391C2×D4311yescharacteristic
396#389—431no—
397#389—431no—
398#389—861no—
399#389—861no—
400#384—431no—
401#384—861no—
402#380—861no—
403#380—861no—
404C4×C4⋊C4—431no—
405C4×C4⋊C4—861no—
406#340—431no—
407#340C2×D4311yescharacteristic
408#336—431no—
409#336C2×D4311yescharacteristic
410C43#2472911yescharacteristic, complemented, Sylow
411C22×Q8—431no—
412C22×Q8C22×D4311yescharacteristic
413C22×Q8C22×D4311yescharacteristic
414C22×D4—431no—
415C23×C4—861no—
416C2×Q16—22no—
417C2×Q16—22no—
418C2×Q16—22no—
419C2×Q16—862no—
420C2×Q16—862no—
421C2×Q16—862no—
422C2×SD16—434no—
423C2×SD16—862no—
424C2×SD16—862no—
425C22×C8—431no—
426C22×C8—431no—
427C22×C8C22×D4311yescharacteristic
428C22×C8C22×D4311yescharacteristic
429C4⋊Q8—862no—
430C4⋊Q8—862no—
431#124—862no—
432#124—862no—
433#124—1721no—
434#124—1721no—
435C4×Q8—22no—
436C4×Q8—41no—
437C4×Q8—434no—
438C4×Q8—862no—
439C4×Q8—862no—
440C4×Q8—1721no—
441C4×D4—862no—
442C4×D4—862no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—431no—
447C2×C4⋊C4—431no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4—861no—
453C2×C4⋊C4—861no—
454C2×C4⋊C4—861no—
455C2×C4⋊C4—861no—
456C2×C4⋊C4C22×D4311yescharacteristic
457C2×C4⋊C4C22×D4311yescharacteristic
458C2×C22⋊C4—861no—
459C2×C22⋊C4—861no—
460C2×C22⋊C4—861no—
461C2×C22⋊C4—861no—
462C2×C22⋊C4—861no—
463C2×C42—21no—
464C2×C42—431no—
465C2×C42—431no—
466C2×C42—861no—
467C2×C42—861no—
468C2×C42C22×D4311yescharacteristic
469#106—862no—
470C4⋊C8—862no—
471C4⋊C8—862no—
472C4⋊C8—862no—
473#103—22no—
474#103—41no—
475#103—862no—
476#103—862no—
477#103—862no—
478#103—862no—
479#103—1721no—
480#102—862no—
481#102—862no—
482#102—862no—
483C4×C8—862no—
484#95—21no—
485#95—21no—
486#95—431no—
487#95—431no—
488#95—861no—
489#95—861no—
490#95—861no—
491#95—861no—
492C24—861no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—861no—
503C2×Q8—861no—
504C2×Q8—861no—
505C2×Q8—861no—
506C2×Q8—861no—
507C2×Q8—861no—
508C2×Q8#1062189812yes—
509C2×Q8D4×D4312yes—
510C2×Q8D4×D4312yes—
511C2×D4—432no—
512C2×D4—861no—
513C2×D4—861no—
514C2×D4—861no—
515C2×D4—861no—
516C2×D4—861no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—431no—
524C22×C4—431no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—1722no—
529C22×C4—1722no—
530C22×C4—1722no—
531C22×C4D4×D4311yescharacteristic
532C22×C4D4×D4311yescharacteristic
533C22×C4C23×D4311yescharacteristic
534Q16—44no—
535Q16—1724no—
536SD16—868no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—432no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—42no—
554C4⋊C4—432no—
555C4⋊C4—862no—
556C4⋊C4—862no—
557C4⋊C4—864no—
558C4⋊C4—861no—
559C4⋊C4—861no—
560C4⋊C4—861no—
561C4⋊C4—3441no—
562C4⋊C4—3441no—
563C4⋊C4—3441no—
564C4⋊C4—1722no—
565C4⋊C4—1722no—
566C4⋊C4—1722no—
567C4⋊C4—1722no—
568C22⋊C4—1722no—
569C22⋊C4—1722no—
570C22⋊C4—1722no—
571C22⋊C4—1722no—
572C22⋊C4—1722no—
573C42—21no—
574C42—21no—
575C42—42no—
576C42—432no—
577C42—432no—
578C42—864no—
579C42—861no—
580C42—861no—
581C42—1722no—
582C23—862no—
583C23—1721no—
584C23—1721no—
585C23—1721no—
586C23—1721no—
587C23—1721no—
588C23—1721no—
589C23C2×D4×D4311yescharacteristic
590Q8—22no—
591Q8—22no—
592Q8—22no—
593Q8—41no—
594Q8—41no—
595Q8—41no—
596Q8—41no—
597Q8—1721no—
598Q8—1721no—
599Q8—1721no—
600Q8—1721no—
601Q8#1306329814yes—
602D4—862no—
603D4—862no—
604D4—1721no—
605D4—1721no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—432no—
625C2×C4—432no—
626C2×C4—432no—
627C2×C4—432no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—862no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—861no—
634C2×C4—861no—
635C2×C4—861no—
636C2×C4—861no—
637C2×C4—3444no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4C2×D4×D4311yescharacteristic
647C2×C4C2×D4×D4311yescharacteristic
648C2×C4#41×D4311yescharacteristic
649C2×C4C2×#1062189811yescharacteristic
650C2×C4#1306337011yescharacteristic
651C2×C4#1306337211yescharacteristic
652C8—41no—
653C8—41no—
654C8—862no—
655C8—1721no—
656C22—3441no—
657C22—3441no—
658C22—3441no—
659C22—3441no—
660C22—1722no—
661C22—1722no—
662C22—1722no—
663C22#121×D4311yescharacteristic
664C22#1458353111yescharacteristic
665C22#1458355811yescharacteristic
666C22#135×D4311yescharacteristic
667C22#137×D4311yescharacteristic
668C22#1458370811yescharacteristic
669C22#1458371211yescharacteristic
670C4—24no—
671C4—41no—
672C4—41no—
673C4—81no—
674C4—81no—
675C4—81no—
676C4—434no—
677C4—862no—
678C4—3441no—
679C4—3441no—
680C4—1721no—
681C4—1722no—
682C4—1721no—
683C4C2×#1306329811yescharacteristic
684C4#1458347611yescharacteristic
685C4#1458354711yescharacteristic
686C4#1458359811yescharacteristic
687C2—3442no—
688C2#1913803411yescharacteristic
689C2#464×D4311yescharacteristic
690C2#1914414211yescharacteristic
691C2#1914623411yescharacteristic
692C2#1914631811yescharacteristic
693C2#1914728111yescharacteristic
694C2#1914733611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1878C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1878D43
hypocenterC43#24729
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
3. C2×#14583107C2semidirect
6. Q8×Dic43⋊C4C2semidirect
7. #19135977C2semidirect
8. #19135976C2semidirect
11. #19135395C2semidirect
12. #19135312C2semidirect
13. #19134934C2semidirect
15. C43×#1878C2semidirect
339. Dic43#464semidirect
353. #1878D43semidirect
410. C43#24729semidirect

Maximal subgroups

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

subgroupindex
C2×#145831232
C2×#145831212
C2×#145831072
C2×#145829842
#191395922
Q8×Dic43⋊C42
#191359772
#191359762
#191358372
#191358322
#191353952
#191353122
#191349342
#191345942
C43×#18782
#2472943