Finite Group Databasebeta

← #19137966

Subgroups — #19137966

Order 5504.

1246 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D43C211yesmaximal, characteristic, complemented
2C2×#13063297C211yesmaximal, characteristic, complemented
3C2×#13063293C211yesmaximal, characteristic, complemented
4C2×#13063293C211yesmaximal, characteristic, complemented
5C22×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
6#14582816C211yesmaximal, characteristic, complemented
7#14582814C211yesmaximal, characteristic, complemented
8#14582808C211yesmaximal, characteristic, complemented
9#14582807C211yesmaximal, characteristic, complemented
10#14582779C211yesmaximal, characteristic, complemented
11#14582778C211yesmaximal, characteristic, complemented
12#14582775C211yesmaximal, characteristic, complemented
13#14582770C211yesmaximal, characteristic, complemented
14#14582754C211yesmaximal, characteristic, complemented
15C2×#121×C43C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C24×D43C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C22×C22⋊D43C2211yescharacteristic
22C22×C22⋊D43C2211yescharacteristic, complemented
23C22×C22⋊D43C2211yescharacteristic, complemented
24C2×D4×D43—24no—
25C2×D4×D43—24no—
26C2×D4×D43—24no—
27C23×Dic43C2211yescharacteristic, complemented
28C22×C4×D43C2211yescharacteristic
29#13063297—24no—
30#13063293—24no—
31#13063293—24no—
32C2×Dic43⋊C4C2211yescharacteristic, complemented
33C2×C22⋊Dic43C2211yescharacteristic, complemented
34C2×C22⋊Dic43C2211yescharacteristic, complemented
35C2×C22⋊Dic43C2211yescharacteristic, complemented
36C2×C22⋊Dic43C2211yescharacteristic, complemented
37C2×(C2×D43)⋊C4—24no—
38C2×(C2×D43)⋊C4C2211yescharacteristic
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C2×(C2×D43)⋊C4C2211yescharacteristic
41C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
46C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
47C43⋊#95C2211yescharacteristic, complemented
48C43⋊#95C2211yescharacteristic, complemented
49C43⋊#95C2211yescharacteristic, complemented
50C43⋊#95C2211yescharacteristic, complemented
51C22×D4×C43C2211yescharacteristic
52C22×D4×C43C2211yescharacteristic, complemented
53C22×D4×C43C2211yescharacteristic, complemented
54C23×C4×C43C2211yescharacteristic, complemented
55#121×C43—24no—
56C2×C4⋊C4×C43C2211yescharacteristic, complemented
57C2×C22⋊C4×C43C2211yescharacteristic, complemented
58C2×C22⋊C4×C43C2211yescharacteristic, complemented
59C24×C43C2311yescharacteristic
60C24×C43C2311yescharacteristic
61C24×C43C2311yescharacteristic
62C23×D43—22no—
63C23×D43—22no—
64C23×D43—22no—
65C23×D43—22no—
66C23×D43—22no—
67C23×D43—22no—
68C23×D43—22no—
69C23×D43—22no—
70C23×D43—22no—
71C23×D43—41no—
72C23×D43—41no—
73C23×D43—41no—
74C23×D43—41no—
75C23×D43D414yescomplemented
76C23×D43C2311yescharacteristic
77C23×D43C2311yescharacteristic
78C23×D43C2311yescharacteristic
79C2×D4×C43—22no—
80C2×D4×C43—22no—
81C2×D4×C43—22no—
82C2×D4×C43—22no—
83C2×D4×C43—22no—
84C2×D4×C43—22no—
85C2×D4×C43—22no—
86C2×D4×C43—41no—
87C2×D4×C43D414yescomplemented
88C22×C4×C43—22no—
89C22×C4×C43—22no—
90C22×C4×C43—41no—
91C22×C4×C43C2311yescharacteristic
92C22×C4×C43C2311yescharacteristic
93C22×C4×C43C2311yescharacteristic
94C22×C4×C43C2311yescharacteristic
95C2×C22⋊D43—22no—
96C2×C22⋊D43—22no—
97C2×C22⋊D43—22no—
98C2×C22⋊D43—22no—
99C2×C22⋊D43—22no—
100C2×C22⋊D43—22no—
101C2×C22⋊D43—22no—
102C2×C22⋊D43—22no—
103C2×C22⋊D43—22no—
104C2×C22⋊D43—22no—
105C2×C22⋊D43—22no—
106C2×C22⋊D43—41no—
107C2×C22⋊D43—41no—
108C2×C22⋊D43—41no—
109C2×C22⋊D43D414yescomplemented
110C22×Dic43—22no—
111C22×Dic43—22no—
112C22×Dic43—41no—
113C22×Dic43C2311yescharacteristic
114C22×Dic43C2311yescharacteristic
115C22×Dic43C2311yescharacteristic
116C22×Dic43C2311yescharacteristic
117C22×Dic43C2311yescharacteristic
118D4×D43—232no—
119C2×D172—22no—
120C2×D172—22no—
121C2×D172—22no—
122C2×C4×D43—22no—
123C2×C4×D43—22no—
124C2×C4×D43—22no—
125C4⋊C4×C43—22no—
126C22⋊C4×C43—22no—
127C22⋊C4×C43—22no—
128C22⋊Dic43—22no—
129C22⋊Dic43—22no—
130C22⋊Dic43—22no—
131C22⋊Dic43—41no—
132(C2×D43)⋊C4—22no—
133(C2×D43)⋊C4—22no—
134(C2×D43)⋊C4—22no—
135(C2×D43)⋊C4—22no—
136(C2×D43)⋊C4—22no—
137(C2×D43)⋊C4—22no—
138(C2×D43)⋊C4—22no—
139(C2×D43)⋊C4—41no—
140(C2×D43)⋊C4D414yescomplemented
141Dic43⋊C4—22no—
142C23×C43—21no—
143C23×C43—21no—
144C23×C43—21no—
145C23×C43—21no—
146C23×C43—21no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—21no—
150C23×C43—21no—
151C23×C43—21no—
152C23×C43—21no—
153C23×C43—21no—
154C23×C43—21no—
155C23×C43—21no—
156C23×C43—21no—
157C23×C43—21no—
158C23×C43—21no—
159C23×C43C2×D412yes—
160C23×C43C2×D412yes—
161C23×C43C2×D412yes—
162C23×C43C2×D412yes—
163C23×C43C2411yescharacteristic
164C22×D43—21no—
165C22×D43—21no—
166C22×D43—21no—
167C22×D43—21no—
168C22×D43—28no—
169C22×D43—28no—
170C22×D43—21no—
171C22×D43—21no—
172C22×D43—21no—
173C22×D43—21no—
174C22×D43—21no—
175C22×D43—21no—
176C22×D43—21no—
177C22×D43—21no—
178C22×D43—21no—
179C22×D43—21no—
180C22×D43—21no—
181C22×D43—21no—
182C22×D43—28no—
183C22×D43—44no—
184C22×D43—44no—
185C22×D43—44no—
186C22×D43—44no—
187C22×D43—44no—
188C22×D43—44no—
189C22×D43—44no—
190C22×D43—44no—
191C22×D43—44no—
192C22×D43—44no—
193C22×D43—44no—
194C22×D43C2×D412yes—
195C22×D43C2×D412yes—
196C22×D43C2×D412yes—
197C22×D43C2×D412yes—
198C22×D43#4112yes—
199D4×C43—28no—
200D4×C43—44no—
201D4×C43—44no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—44no—
213C2×C4×C43C2×D412yes—
214C2×C4×C43C2×D412yescomplemented
215C22⋊D43—28no—
216C22⋊D43—28no—
217C22⋊D43—44no—
218C22⋊D43—44no—
219C22⋊D43—44no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—44no—
234C2×Dic43C2×D412yes—
235C2×Dic43C2×D412yescomplemented
236D172—28no—
237C4×D43—28no—
238C22×C43—22no—
239C22×C43—22no—
240C22×C43—22no—
241C22×C43—22no—
242C22×C43—22no—
243C22×C43—22no—
244C22×C43—22no—
245C22×C43—22no—
246C22×C43—22no—
247C22×C43—41no—
248C22×C43—41no—
249C22×C43—41no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43#12014yescomplemented
259C22×C43C22×D411yescharacteristic
260C22×C43C22×D411yescharacteristic
261C22×C43C22×D411yescharacteristic
262C22×C43C22×D411yescharacteristic
263C22×C43C2×#4111yescharacteristic
264C22×C43H(5,𝔽2)11yescharacteristic
265C22×C43H(5,𝔽2)11yescharacteristic
266C2×D43—22no—
267C2×D43—22no—
268C2×D43—22no—
269C2×D43—22no—
270C2×D43—22no—
271C2×D43—22no—
272C2×D43—22no—
273C2×D43—22no—
274C2×D43—22no—
275C2×D43—22no—
276C2×D43—22no—
277C2×D43—22no—
278C2×D43—416no—
279C2×D43—416no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C2×D43#12114yescomplemented
289C4×C43—22no—
290C4×C43—22no—
291C4×C43—41no—
292C4×C43—41no—
293Dic43—22no—
294Dic43—22no—
295Dic43—41no—
296Dic43—41no—
297Dic43—41no—
298#2410—431nomaximal, Sylow
299C2×C43—24no—
300C2×C43—42no—
301C2×C43—81no—
302C2×C43C2×#12011yescharacteristic
303C2×C43C2×#12111yescharacteristic
304C2×C43#53411yescharacteristic
305C2×C43D4211yescharacteristic
306C2×C43D4211yescharacteristic
307C2×C43#54611yescharacteristic
308C2×C43#54611yescharacteristic
309D43—24no—
310D43—42no—
311D43—42no—
312C23×D4—431no—
313C2×#121—431no—
314C2×#121D4311yescharacteristic, complemented
315C2×#120—431no—
316C2×#120—431no—
317C22×C22⋊C4—431no—
318#394—431no—
319#394—431no—
320#392—431no—
321#392—431no—
322#386—431no—
323#386—431no—
324#386—431no—
325#385—431no—
326#379—431no—
327C43#241011yescharacteristic, complemented, Sylow
328C25—431no—
329C25—431no—
330C22×D4—431no—
331C22×D4—431no—
332C22×D4—431no—
333C22×D4—431no—
334C22×D4—431no—
335C22×D4—431no—
336C22×D4—864no—
337C22×D4—864no—
338C22×D4—864no—
339C22×D4C2×D4311yescharacteristic
340C22×D4C2×D4311yescharacteristic, complemented
341C22×D4C2×D4311yescharacteristic, complemented
342C23×C4—431no—
343C23×C4—431no—
344C23×C4C2×D4311yescharacteristic, complemented
345#121—24no—
346#121—864no—
347#120—864no—
348#120—864no—
349C2×C4⋊C4—431no—
350C2×C4⋊C4C2×D4311yescharacteristic, complemented
351C2×C22⋊C4—431no—
352C2×C22⋊C4—431no—
353C2×C22⋊C4—431no—
354C2×C22⋊C4—431no—
355C2×C22⋊C4—431no—
356C2×C22⋊C4—431no—
357C2×C22⋊C4—431no—
358C2×C22⋊C4—431no—
359C2×C22⋊C4—431no—
360C2×C22⋊C4—431no—
361C2×C22⋊C4—431no—
362C2×C22⋊C4—431no—
363C2×C22⋊C4—431no—
364C2×C22⋊C4—864no—
365C2×C22⋊C4C2×D4311yescharacteristic, complemented
366C2×C22⋊C4C2×D4311yescharacteristic, complemented
367#95—431no—
368#95—431no—
369#95—431no—
370#95—431no—
371C24—431no—
372C24—431no—
373C24—431no—
374C24—434no—
375C24—862no—
376C24—862no—
377C24—862no—
378C24—862no—
379C24—862no—
380C24—862no—
381C24—862no—
382C24—862no—
383C24—862no—
384C24—1721no—
385C24—1721no—
386C24—1721no—
387C24—1721no—
388C24C22×D4311yescharacteristic
389C24C22×D4311yescharacteristic
390C24C22×D4311yescharacteristic
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—41no—
399C2×D4—434no—
400C2×D4—862no—
401C2×D4—862no—
402C2×D4—862no—
403C2×D4—862no—
404C2×D4—8632no—
405C2×D4—862no—
406C2×D4—862no—
407C2×D4—862no—
408C2×D4—862no—
409C2×D4—862no—
410C2×D4—862no—
411C2×D4—862no—
412C2×D4—862no—
413C2×D4—862no—
414C2×D4—862no—
415C2×D4—1721no—
416C2×D4—1721no—
417C2×D4—1721no—
418C2×D4C22⋊D4314yescomplemented
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—41no—
422C22×C4—431no—
423C22×C4—431no—
424C22×C4—431no—
425C22×C4—431no—
426C22×C4—431no—
427C22×C4—862no—
428C22×C4—862no—
429C22×C4—862no—
430C22×C4—862no—
431C22×C4—862no—
432C22×C4—1721no—
433C22×C4C22×D4311yescharacteristic
434C22×C4C22×D4311yescharacteristic
435C22×C4C22×D4311yescharacteristic
436C22×C4C22×D4311yescharacteristic
437C4⋊C4—22no—
438C4⋊C4—862no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—434no—
442C22⋊C4—862no—
443C22⋊C4—862no—
444C22⋊C4—862no—
445C22⋊C4—862no—
446C22⋊C4—862no—
447C22⋊C4—862no—
448C22⋊C4—862no—
449C22⋊C4—862no—
450C22⋊C4—862no—
451C22⋊C4—862no—
452C22⋊C4—1721no—
453C22⋊C4—1721no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—432no—
472C23—432no—
473C23—432no—
474C23—432no—
475C23—432no—
476C23—868no—
477C23—868no—
478C23—861no—
479C23—861no—
480C23—861no—
481C23—861no—
482C23—868no—
483C23—861no—
484C23—861no—
485C23—861no—
486C23—861no—
487C23—861no—
488C23—861no—
489C23—861no—
490C23—861no—
491C23—861no—
492C23—861no—
493C23—861no—
494C23—861no—
495C23—1724no—
496C23—1724no—
497C23—1724no—
498C23—1724no—
499C23—1724no—
500C23—1724no—
501C23—1724no—
502C23—1724no—
503C23—1724no—
504C23—1724no—
505C23—1724no—
506C23D4×D4312yes—
507C23D4×D4312yes—
508C23C2×C22⋊D4312yes—
509C23C2×C22⋊D4312yes—
510C23C23×D4311yescharacteristic
511D4—28no—
512D4—44no—
513D4—44no—
514D4—868no—
515D4—868no—
516D4—868no—
517D4—1724no—
518D4—1724no—
519D4—1724no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—44no—
531C2×C4—432no—
532C2×C4—432no—
533C2×C4—868no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—1724no—
548C2×C4D4×D4312yescomplemented
549C2×C4C2×C22⋊D4312yes—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—434no—
571C22—862no—
572C22—862no—
573C22—862no—
574C22—862no—
575C22—862no—
576C22—862no—
577C22—862no—
578C22—862no—
579C22—862no—
580C22—862no—
581C22—862no—
582C22—862no—
583C22—17216no—
584C22—17216no—
585C22—1721no—
586C22—1721no—
587C22—1721no—
588C22—1721no—
589C22—1721no—
590C22—1721no—
591C22—1721no—
592C22—1721no—
593C22#1306329314yescomplemented
594C22C2×D4×D4311yescharacteristic
595C22C2×D4×D4311yescharacteristic
596C22C2×D4×D4311yescharacteristic
597C22C22×C22⋊D4311yescharacteristic
598C22#41×D4311yescharacteristic
599C22#1306337011yescharacteristic
600C22#1306337111yescharacteristic
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—862no—
606C4—862no—
607C4—1721no—
608C4—1721no—
609C4—1721no—
610C2—24no—
611C2—42no—
612C2—81no—
613C2—864no—
614C2—1722no—
615C2—1722no—
616C2C2×#1306329311yescharacteristic
617C2#121×D4311yescharacteristic
618C2#1458345711yescharacteristic
619C2D4×C22⋊D4311yescharacteristic
620C2#1458353311yescharacteristic
621C2#1458353711yescharacteristic
622C2#1458353811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#121×C43C2
hypercenterC2×#121D43
hypocenterC43#2410
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×D4×D43C2semidirect
2. C2×#13063297C2semidirect
3. C2×#13063293C2semidirect
4. C2×#13063293C2semidirect
5. C22×(C2×D43)⋊C4C2semidirect
6. #14582816C2semidirect
7. #14582814C2semidirect
8. #14582808C2semidirect
9. #14582807C2semidirect
10. #14582779C2semidirect
11. #14582778C2semidirect
12. #14582775C2semidirect
13. #14582770C2semidirect
14. #14582754C2semidirect
15. C2×#121×C43C2semidirect
22. C22×C22⋊D43C22semidirect
23. C22×C22⋊D43C22semidirect
27. C23×Dic43C22semidirect
32. C2×Dic43⋊C4C22semidirect
33. C2×C22⋊Dic43C22semidirect
34. C2×C22⋊Dic43C22semidirect
35. C2×C22⋊Dic43C22semidirect
36. C2×C22⋊Dic43C22semidirect
41. C2×(C2×D43)⋊C4C22semidirect
42. C2×(C2×D43)⋊C4C22semidirect
43. C2×(C2×D43)⋊C4C22semidirect
44. C2×(C2×D43)⋊C4C22semidirect
45. C2×(C2×D43)⋊C4C22semidirect
46. C2×(C2×D43)⋊C4C22semidirect
47. C43⋊#95C22semidirect
48. C43⋊#95C22semidirect
49. C43⋊#95C22semidirect
50. C43⋊#95C22semidirect
52. C22×D4×C43C22semidirect
53. C22×D4×C43C22semidirect
54. C23×C4×C43C22semidirect
56. C2×C4⋊C4×C43C22semidirect
57. C2×C22⋊C4×C43C22semidirect
58. C2×C22⋊C4×C43C22semidirect
75. C23×D43D4semidirect
87. C2×D4×C43D4semidirect
109. C2×C22⋊D43D4semidirect
140. (C2×D43)⋊C4D4semidirect
214. C2×C4×C43C2×D4semidirect
235. C2×Dic43C2×D4semidirect
258. C22×C43#120semidirect
288. C2×D43#121semidirect
314. C2×#121D43semidirect
327. C43#2410semidirect
340. C22×D4C2×D43semidirect
341. C22×D4C2×D43semidirect
344. C23×C4C2×D43semidirect
350. C2×C4⋊C4C2×D43semidirect
365. C2×C22⋊C4C2×D43semidirect
366. C2×C22⋊C4C2×D43semidirect
418. C2×D4C22⋊D43semidirect
548. C2×C4D4×D43semidirect
593. C22#13063293semidirect