Finite Group Databasebeta

← #19137968

Subgroups — #19137968

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×#13063299C211yesmaximal, characteristic, complemented
3C2×#13063297C211yesmaximal, characteristic, complemented
4C2×#13063295C211yesmaximal, characteristic, complemented
5C2×#13063295C211yesmaximal, characteristic, complemented
6C22×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
7#14582817C211yesmaximal, characteristic, complemented
8#14582815C211yesmaximal, characteristic, complemented
9#14582809C211yesmaximal, characteristic, complemented
10#14582808C211yesmaximal, characteristic, complemented
11#14582777C211yesmaximal, characteristic, complemented
12#14582776C211yesmaximal, characteristic, complemented
13#14582773C211yesmaximal, characteristic, complemented
14#14582754C211yesmaximal, characteristic, complemented
15C43×#386C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C24×D43C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×D172C2211yescharacteristic
20C22×D172C2211yescharacteristic, complemented
21C22×D172C2211yescharacteristic, complemented
22C22×C22⋊D43C2211yescharacteristic
23C22×C22⋊D43C2211yescharacteristic
24C22×C22⋊D43C2211yescharacteristic, complemented
25C22×C22⋊D43C2211yescharacteristic, complemented
26C2×D4×D43—24no—
27C2×D4×D43—24no—
28C2×D4×D43—24no—
29C23×Dic43C2211yescharacteristic, complemented
30C22×C4×D43C2211yescharacteristic
31#13063299—24no—
32#13063297—24no—
33#13063295—24no—
34#13063295—24no—
35C2×C4⋊Dic43C2211yescharacteristic, complemented
36C2×Dic43⋊C4C2211yescharacteristic, complemented
37C2×C22⋊Dic43C2211yescharacteristic, complemented
38C2×(C2×D43)⋊C4—24no—
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C2×(C2×D43)⋊C4C2211yescharacteristic
41C2×(C2×D43)⋊C4C2211yescharacteristic
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
47C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
48C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
49C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
50C43⋊#95C2211yescharacteristic, complemented
51C43⋊#95C2211yescharacteristic, complemented
52C22×D4×C43C2211yescharacteristic
53C23×C4×C43C2211yescharacteristic, complemented
54C2×C22⋊C4×C43C2211yescharacteristic, complemented
55C2×C22⋊C4×C43C2211yescharacteristic, complemented
56C2×C22⋊C4×C43C2211yescharacteristic, complemented
57#95×C43C2211yescharacteristic, complemented
58#95×C43C2211yescharacteristic, complemented
59C24×C43C2311yescharacteristic
60C24×C43C2311yescharacteristic
61C23×D43—22no—
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—41no—
71C23×D43—41no—
72C23×D43—41no—
73C23×D43—41no—
74C23×D43D414yescomplemented
75C23×D43C2311yescharacteristic
76C23×D43C2311yescharacteristic
77C23×D43C2311yescharacteristic
78C23×D43C2311yescharacteristic
79C2×D4×C43—22no—
80C2×D4×C43—22no—
81C2×D4×C43D414yescomplemented
82C22×C4×C43—22no—
83C22×C4×C43—22no—
84C22×C4×C43—41no—
85C22×C4×C43C2311yescharacteristic
86C22×C4×C43C2311yescharacteristic
87C22×C4×C43C2311yescharacteristic
88C22×C4×C43C2311yescharacteristic
89C22×C4×C43C2311yescharacteristic
90C2×C22⋊D43—22no—
91C2×C22⋊D43—22no—
92C2×C22⋊D43—22no—
93C2×C22⋊D43—22no—
94C2×C22⋊D43—22no—
95C2×C22⋊D43—22no—
96C2×C22⋊D43—22no—
97C2×C22⋊D43—22no—
98C2×C22⋊D43—22no—
99C2×C22⋊D43—22no—
100C2×C22⋊D43—41no—
101C2×C22⋊D43D414yescomplemented
102C22×Dic43—22no—
103C22×Dic43—22no—
104C22×Dic43—41no—
105C22×Dic43C2311yescharacteristic
106C22×Dic43C2311yescharacteristic
107C22×Dic43C2311yescharacteristic
108C22×Dic43C2311yescharacteristic
109D4×D43—232no—
110C2×D172—22no—
111C2×D172—22no—
112C2×D172—22no—
113C2×D172—22no—
114C2×D172—22no—
115C2×D172—22no—
116C2×D172—22no—
117C2×D172—22no—
118C2×D172—22no—
119C2×D172—41no—
120C2×D172—41no—
121C2×D172—41no—
122C2×C4×D43—22no—
123C2×C4×D43—22no—
124C2×C4×D43—22no—
125C22⋊C4×C43—22no—
126C22⋊C4×C43—22no—
127C22⋊C4×C43—41no—
128C22⋊Dic43—22no—
129(C2×D43)⋊C4—22no—
130(C2×D43)⋊C4—22no—
131(C2×D43)⋊C4—22no—
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—41no—
139(C2×D43)⋊C4D414yescomplemented
140C4⋊Dic43—22no—
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×C43C2×D412yes—
153C23×C43C2×D412yes—
154C23×C43C2×D412yes—
155C23×C43C2×D412yes—
156C23×C43C2411yescharacteristic
157C22×D43—21no—
158C22×D43—21no—
159C22×D43—21no—
160C22×D43—21no—
161C22×D43—28no—
162C22×D43—28no—
163C22×D43—21no—
164C22×D43—21no—
165C22×D43—21no—
166C22×D43—21no—
167C22×D43—21no—
168C22×D43—21no—
169C22×D43—21no—
170C22×D43—21no—
171C22×D43—21no—
172C22×D43—21no—
173C22×D43—21no—
174C22×D43—21no—
175C22×D43—28no—
176C22×D43—21no—
177C22×D43—21no—
178C22×D43—21no—
179C22×D43—21no—
180C22×D43—21no—
181C22×D43—21no—
182C22×D43—21no—
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—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
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—21no—
213C2×C4×C43—44no—
214C2×C4×C43C2×D412yes—
215C2×C4×C43C2×D412yescomplemented
216C22⋊D43—28no—
217C22⋊D43—28no—
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—44no—
231C2×Dic43C2×D412yes—
232C2×Dic43C2×D412yescomplemented
233D172—28no—
234D172—44no—
235D172—44no—
236D172—44no—
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#12014yescomplemented
252C22×C43C22×D411yescharacteristic
253C22×C43C22×D411yescharacteristic
254C22×C43C22×D411yescharacteristic
255C22×C43C22×D411yescharacteristic
256C22×C43C2×#4111yescharacteristic
257C22×C43H(5,𝔽2)11yescharacteristic
258C22×C43H(5,𝔽2)11yescharacteristic
259C2×D43—22no—
260C2×D43—22no—
261C2×D43—22no—
262C2×D43—22no—
263C2×D43—22no—
264C2×D43—22no—
265C2×D43—22no—
266C2×D43—22no—
267C2×D43—22no—
268C2×D43—22no—
269C2×D43—22no—
270C2×D43—22no—
271C2×D43—416no—
272C2×D43—416no—
273C2×D43—41no—
274C2×D43—41no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—41no—
278C2×D43—41no—
279C2×D43—41no—
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—
293C4×C43—41no—
294Dic43—22no—
295Dic43—22no—
296Dic43—41no—
297Dic43—41no—
298#2410—431nomaximal, Sylow
299C2×C43—24no—
300C2×C43—42no—
301C2×C43C2×#12011yescharacteristic
302C2×C43C2×#12111yescharacteristic
303C2×C43#53411yescharacteristic
304C2×C43D4211yescharacteristic
305C2×C43D4211yescharacteristic
306C2×C43#54611yescharacteristic
307C2×C43#54611yescharacteristic
308D43—24no—
309D43—42no—
310D43—42no—
311D43—81no—
312C23×D4—431no—
313C2×#121—431no—
314C2×#121—431no—
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#386D4311yescharacteristic, complemented
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—431no—
337C22×D4—431no—
338C22×D4—864no—
339C22×D4—864no—
340C22×D4—864no—
341C22×D4C2×D4311yescharacteristic
342C23×C4—431no—
343C23×C4—431no—
344C23×C4C2×D4311yescharacteristic, complemented
345#121—864no—
346#121—864no—
347#120—864no—
348#120—864no—
349C2×C4⋊C4—431no—
350C2×C4⋊C4—431no—
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—864no—
364C2×C22⋊C4C2×D4311yescharacteristic, complemented
365C2×C22⋊C4C2×D4311yescharacteristic, complemented
366C2×C22⋊C4C2×D4311yescharacteristic, complemented
367#95—431no—
368#95—431no—
369#95C2×D4311yescharacteristic, complemented
370#95C2×D4311yescharacteristic, complemented
371C24—431no—
372C24—431no—
373C24—431no—
374C24—434no—
375C24—431no—
376C24—862no—
377C24—862no—
378C24—862no—
379C24—862no—
380C24—862no—
381C24—862no—
382C24—862no—
383C24—862no—
384C24—862no—
385C24—1721no—
386C24—1721no—
387C24—1721no—
388C24—1721no—
389C24C22×D4311yescharacteristic
390C24C22×D4311yescharacteristic
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—434no—
394C2×D4—862no—
395C2×D4—862no—
396C2×D4—862no—
397C2×D4—862no—
398C2×D4—862no—
399C2×D4—862no—
400C2×D4—862no—
401C2×D4—862no—
402C2×D4—862no—
403C2×D4—8632no—
404C2×D4—862no—
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—1721no—
415C2×D4—1721no—
416C2×D4—1721no—
417C2×D4—1721no—
418C2×D4D17214yescomplemented
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—41no—
422C22×C4—431no—
423C22×C4—431no—
424C22×C4—431no—
425C22×C4—431no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—862no—
429C22×C4—862no—
430C22×C4—862no—
431C22×C4—1721no—
432C22×C4C22×D4311yescharacteristic
433C22×C4C22×D4311yescharacteristic
434C22×C4C22×D4311yescharacteristic
435C22×C4C22×D4311yescharacteristic
436C22×C4C22×D4311yescharacteristic
437C4⋊C4—862no—
438C4⋊C4—862no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—41no—
442C22⋊C4—434no—
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—862no—
453C22⋊C4—1721no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—432no—
465C23—432no—
466C23—432no—
467C23—432no—
468C23—432no—
469C23—868no—
470C23—868no—
471C23—861no—
472C23—861no—
473C23—861no—
474C23—861no—
475C23—868no—
476C23—861no—
477C23—861no—
478C23—861no—
479C23—861no—
480C23—861no—
481C23—861no—
482C23—861no—
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—
506C23C2×D17212yes—
507C23C2×D17212yes—
508C23D4×D4312yes—
509C23D4×D4312yes—
510C23C23×D4311yescharacteristic
511D4—28no—
512D4—868no—
513D4—868no—
514D4—868no—
515D4—1724no—
516D4—1724no—
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—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—44no—
534C2×C4—432no—
535C2×C4—432no—
536C2×C4—868no—
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×C4C2×D17212yes—
549C2×C4D4×D4312yescomplemented
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—434no—
564C22—862no—
565C22—862no—
566C22—862no—
567C22—862no—
568C22—862no—
569C22—862no—
570C22—862no—
571C22—862no—
572C22—862no—
573C22—862no—
574C22—862no—
575C22—862no—
576C22—17216no—
577C22—17216no—
578C22—1721no—
579C22—1721no—
580C22—1721no—
581C22—1721no—
582C22—1721no—
583C22—1721no—
584C22—1721no—
585C22—1721no—
586C22—1721no—
587C22—1721no—
588C22—1721no—
589C22—1721no—
590C22—1721no—
591C22—1721no—
592C22—1721no—
593C22#1306329514yescomplemented
594C22C2×D4×D4311yescharacteristic
595C22C2×D4×D4311yescharacteristic
596C22C2×D4×D4311yescharacteristic
597C22C22×D17211yescharacteristic
598C22#41×D4311yescharacteristic
599C22#1306337011yescharacteristic
600C22#1306337111yescharacteristic
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—862no—
607C4—862no—
608C4—1721no—
609C4—1721no—
610C2—24no—
611C2—42no—
612C2—864no—
613C2—3441no—
614C2—1722no—
615C2—1722no—
616C2C2×#1306329511yescharacteristic
617C2#121×D4311yescharacteristic
618C2#1458345711yescharacteristic
619C2#1458353111yescharacteristic
620C2D4×D17211yescharacteristic
621C2#1458354111yescharacteristic
622C2#1458354411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#386C2
hypercenter#386D43
hypocenterC43#2410
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C22×D4×D43C2semidirect
2. C2×#13063299C2semidirect
3. C2×#13063297C2semidirect
4. C2×#13063295C2semidirect
5. C2×#13063295C2semidirect
6. C22×(C2×D43)⋊C4C2semidirect
7. #14582817C2semidirect
8. #14582815C2semidirect
9. #14582809C2semidirect
10. #14582808C2semidirect
11. #14582777C2semidirect
12. #14582776C2semidirect
13. #14582773C2semidirect
14. #14582754C2semidirect
15. C43×#386C2semidirect
20. C22×D172C22semidirect
21. C22×D172C22semidirect
24. C22×C22⋊D43C22semidirect
25. C22×C22⋊D43C22semidirect
29. C23×Dic43C22semidirect
35. C2×C4⋊Dic43C22semidirect
36. C2×Dic43⋊C4C22semidirect
37. C2×C22⋊Dic43C22semidirect
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. C2×(C2×D43)⋊C4C22semidirect
48. C2×(C2×D43)⋊C4C22semidirect
49. C2×(C2×D43)⋊C4C22semidirect
50. C43⋊#95C22semidirect
51. C43⋊#95C22semidirect
53. C23×C4×C43C22semidirect
54. C2×C22⋊C4×C43C22semidirect
55. C2×C22⋊C4×C43C22semidirect
56. C2×C22⋊C4×C43C22semidirect
57. #95×C43C22semidirect
58. #95×C43C22semidirect
74. C23×D43D4semidirect
81. C2×D4×C43D4semidirect
101. C2×C22⋊D43D4semidirect
139. (C2×D43)⋊C4D4semidirect
215. C2×C4×C43C2×D4semidirect
232. C2×Dic43C2×D4semidirect
251. C22×C43#120semidirect
288. C2×D43#121semidirect
324. #386D43semidirect
327. C43#2410semidirect
344. C23×C4C2×D43semidirect
364. C2×C22⋊C4C2×D43semidirect
365. C2×C22⋊C4C2×D43semidirect
366. C2×C22⋊C4C2×D43semidirect
369. #95C2×D43semidirect
370. #95C2×D43semidirect
418. C2×D4D172semidirect
549. C2×C4D4×D43semidirect
593. C22#13063295semidirect