Finite Group Databasebeta

← #25096633

Subgroups — #25096633

Order 11008.

1402 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621902C211yesmaximal, characteristic
2C2×#14582951C211yesmaximal, characteristic, complemented
3#19137000C211yesmaximal, characteristic, complemented
4#19134689C212yesmaximal, complemented
5#19134600C211yesmaximal, characteristic, complemented
6#19134596C211yesmaximal, characteristic, complemented
7#19134592C211yesmaximal, characteristic, complemented
8#19134534C212yesmaximal
9#103×Dic43C212yesmaximal, complemented
10#19134409C212yesmaximal, complemented
11C43×#1803C211yesmaximal, characteristic, complemented
12C22×#10621902C2211yescharacteristic
13C4×#10621902—24no—
14C4×#10621902C418yescomplemented
15C2×Q8×Dic43C2211yescharacteristic
16C2×C4×D172—21no—
17C2×C4×D172C2211yescharacteristic
18C2×#13063287—21no—
19C2×#13063287C2211yescharacteristic
20C2×#13063283—21no—
21C2×#13063283—21no—
22C2×#13063283C2211yescharacteristic
23C2×C42×D43—21no—
24C2×C42×D43C2211yescharacteristic
25#14582951—24no—
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063249C2212yes—
28C2×#13063247C2212yes—
29C2×#13063245C2212yes—
30C2×(C2×D43)⋊C8C2212yes—
31C2×C8×Dic43C2212yes—
32#14582769C2211yescharacteristic
33#14582764—21no—
34#14582756—21no—
35#14582756C2212yes—
36C4⋊C4×Dic43—21no—
37C4⋊C4×Dic43C2212yes—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C2×C4×Q8×C43C2211yescharacteristic
42C2×C4⋊C8×C43C2211yescharacteristic
43C2×#103×C43C2212yes—
44C43×#384C2211yescharacteristic
45C43×#340C2212yes—
46C2×#10621902—22no—
47C2×#10621902—22no—
48C2×#10621902—22no—
49C2×#10621902—22no—
50C2×#10621902—22no—
51C2×#10621902C2×C414yes—
52C22×D172—21no—
53C22×D172C2311yescharacteristic
54C22×C4×D43—21no—
55C22×C4×D43—21no—
56C22×C4×D43—21no—
57C22×C4×D43D411yescharacteristic
58C22×C4×D43D411yescharacteristic
59C22×C4×D43C2311yescharacteristic
60C22×C43⋊C8C2312yes—
61Q8×Dic43—22no—
62Q8×Dic43C2×C414yes—
63C4×D172—28no—
64C4×D172—22no—
65C4×D172C2×C414yes—
66#13063287—28no—
67#13063287—22no—
68#13063287C2×C414yes—
69#13063283—22no—
70#13063283—28no—
71#13063283—44no—
72#13063283C2×C414yes—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2312yes—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—22no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—22no—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88C42×D43—28no—
89C42×D43C2×C414yes—
90C42×D43D414yes—
91C4⋊(C43⋊C8)—22no—
92#13063249—24no—
93#13063247—24no—
94#13063245—24no—
95(C2×D43)⋊C8—24no—
96C8×Dic43—24no—
97C43⋊#95—22no—
98C43⋊#95—22no—
99C22×Q8×C43C2311yescharacteristic
100C22×C8×C43C2312yes—
101C4×Q8×C43—22no—
102C4×Q8×C43C2×C414yes—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2312yes—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C42×C43—21no—
109C2×C42×C43C2311yescharacteristic
110C4⋊C8×C43—22no—
111#103×C43—24no—
112C23×D43—21no—
113C23×D43C2×D411yescharacteristic
114C2×Q8×C43—21no—
115C2×Q8×C43—21no—
116C2×Q8×C43—21no—
117C2×Q8×C43C22×C412yes—
118C2×Q8×C43#4112yes—
119C2×Q8×C43#4112yes—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2411yescharacteristic
126C22×Dic43—21no—
127C22×Dic43—22no—
128C22×Dic43C2×D411yescharacteristic
129C22×Dic43C2×D411yescharacteristic
130C22×Dic43C2×D411yescharacteristic
131#10621902—28no—
132#10621902—28no—
133#10621902—28no—
134#10621902—28no—
135C2×D172—24no—
136C2×D172—24no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—24no—
141C2×D172C22×C412yes—
142C2×D172#4112yes—
143C2×D172#4112yes—
144C2×C4×D43—24no—
145C2×C4×D43—24no—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—24no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—24no—
156C2×C4×D43—24no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43C22⋊C414yes—
162C2×C4×D43C22⋊C414yes—
163C2×C4×D43C22×C412yes—
164C2×C4×D43C2×D412yes—
165C2×C8×C43—22no—
166C2×C8×C43—22no—
167C2×C8×C43—22no—
168C4⋊C4×C43—24no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—42no—
173C4⋊C4×C43—42no—
174C4⋊C4×C43C22×C412yes—
175C42×C43—24no—
176C42×C43C22×C412yes—
177C42×C43C2×D412yes—
178(C2×D43)⋊C4—24no—
179(C2×D43)⋊C4—24no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—44no—
182C4⋊Dic43—21no—
183C4⋊Dic43—24no—
184C4⋊Dic43—22no—
185C4⋊Dic43—22no—
186C4⋊Dic43—42no—
187C4⋊Dic43—42no—
188C4⋊Dic43C22×C412yes—
189C4×Dic43—24no—
190C4×Dic43—24no—
191C4×Dic43—44no—
192C4×Dic43C22⋊C414yes—
193C4×Dic43C22⋊C414yes—
194C4×Dic43C22×C412yes—
195C4×Dic43C2×D412yes—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—22no—
199C23×C43C22×D411yescharacteristic
200C22×D43—22no—
201C22×D43—21no—
202C22×D43—21no—
203C22×D43—22no—
204C22×D43—22no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43C2×C22⋊C412yes—
214Q8×C43—22no—
215Q8×C43—22no—
216Q8×C43—22no—
217Q8×C43#11714yescomplemented
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—22no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43C2×C22⋊C412yes—
230C2×C4×C43C2×C22⋊C412yes—
231C2×C4×C43#13512yes—
232C2×C4×C43#13512yes—
233C2×C4×C43C23×C411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—22no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43C2×C22⋊C412yes—
250C2×Dic43C2×C22⋊C412yes—
251C2×Dic43C2×C22⋊C412yes—
252C2×Dic43AGL(1,ℤ/8)12yes—
253C2×Dic43#13712yes—
254D172—216no—
255D172—22no—
256D172—22no—
257D172—22no—
258D172#11714yescomplemented
259C4×D43—216no—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—28no—
265C4×D43—28no—
266C4×D43—48no—
267C4×D43—48no—
268C8×C43—42no—
269C43⋊C8—42no—
270#20737—431nomaximal, Sylow
271C22×C43C22×C22⋊C411yescharacteristic
272C22×C43#52511yescharacteristic
273C22×C43#52511yescharacteristic
274C22×C43C2×#13511yescharacteristic
275C22×C43C2×#13511yescharacteristic
276C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C43C2×#13711yescharacteristic
278C2×D43—22no—
279C2×D43—22no—
280C2×D43—24no—
281C2×D43—22no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—42no—
285C2×D43—42no—
286C2×D43—41no—
287C2×D43—41no—
288C2×D43—42no—
289C2×D43—42no—
290C2×D43—42no—
291C2×D43—42no—
292C4×C43—22no—
293C4×C43—24no—
294C4×C43—42no—
295C4×C43—82no—
296C4×C43#41614yes—
297C4×C43C2×#11711yescharacteristic
298C4×C43C2×#11711yescharacteristic
299C4×C43#52511yescharacteristic
300C4×C43#52511yescharacteristic
301Dic43—22no—
302Dic43—22no—
303Dic43—42no—
304Dic43—82no—
305Dic43#41714yes—
306C2×C4×#41—431no—
307C2×#431—431no—
308#2285—431no—
309#1825—432no—
310#1803—431no—
311#1803D4311yescharacteristic, complemented
312#1802—431no—
313#1802—431no—
314#1788—432no—
315C4×#103—432no—
316C4×#102—432no—
317C2×C43#228011yescharacteristic
318C2×C43C2×#41611yescharacteristic
319C2×C43C2×#41711yescharacteristic
320C2×C43#310611yescharacteristic
321C2×C43#310611yescharacteristic
322C2×C43#310711yescharacteristic
323C2×C43#310711yescharacteristic
324D43—42no—
325D43—44no—
326C22×#41—431no—
327C4×#41—438no—
328C4×#41—864no—
329C2×C4×Q8—431no—
330C2×C4×Q8C2×D4311yescharacteristic
331C2×C4×D4—431no—
332C2×C4×D4—431no—
333C2×C4×D4—861no—
334C2×C4×D4—861no—
335C2×#117—431no—
336C2×#117—861no—
337C2×#117—861no—
338C22×C42—431no—
339C22×C42—861no—
340#431—864no—
341C2×C4⋊C8—431no—
342C2×C4⋊C8C2×D4311yescharacteristic
343C2×#103—432no—
344C2×#103C2×D4312yes—
345C2×#102—432no—
346C2×#102—432no—
347C2×C22⋊C8—432no—
348C2×C4×C8—432no—
349#384—431no—
350#384C2×D4311yescharacteristic
351#382—861no—
352#380—432no—
353#380—861no—
354C4×C4⋊C4—432no—
355C4×C4⋊C4—861no—
356#340—432no—
357#340—432no—
358#340—432no—
359#340C2×D4312yes—
360C43#2073711yescharacteristic, complemented, Sylow
361C2×#41—434no—
362C2×#41—862no—
363C2×#41—862no—
364C2×#41—862no—
365C2×#41—862no—
366C2×#41—862no—
367C22×Q8C22×D4311yescharacteristic
368C22×D4—431no—
369C22×D4—861no—
370C23×C4—431no—
371C23×C4—431no—
372C23×C4—431no—
373C23×C4—861no—
374C23×C4—861no—
375C23×C4—861no—
376C22×C8—432no—
377C22×C8C22×D4312yes—
378C4×Q8—22no—
379C4×Q8—434no—
380C4×Q8—862no—
381C4×Q8C4×D4314yes—
382C4×D4—434no—
383C4×D4—434no—
384C4×D4—868no—
385C4×D4—862no—
386C4×D4—868no—
387C4×D4—862no—
388#117—434no—
389#117—868no—
390#117—862no—
391#117—1724no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—432no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4C22×D4312yes—
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—862no—
406C2×C42—21no—
407C2×C42—431no—
408C2×C42—431no—
409C2×C42—431no—
410C2×C42—434no—
411C2×C42—434no—
412C2×C42—868no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42—862no—
416C2×C42C22×D4311yescharacteristic
417C4⋊C8—22no—
418C4⋊C8—862no—
419#103—24no—
420#103—864no—
421#102—864no—
422#102—864no—
423C22⋊C8—864no—
424C4×C8—864no—
425#95—862no—
426#95—862no—
427C24—431no—
428C24—861no—
429#41—868no—
430#41—868no—
431#41—868no—
432#41—868no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8C2×C4×D4312yes—
437C2×Q8#1062190012yes—
438C2×Q8#1062190212yes—
439C2×D4—432no—
440C2×D4—432no—
441C2×D4—432no—
442C2×D4—864no—
443C2×D4—864no—
444C2×D4—864no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—434no—
455C22×C4—434no—
456C22×C4—432no—
457C22×C4—432no—
458C22×C4—864no—
459C22×C4—862no—
460C22×C4—862no—
461C22×C4—864no—
462C22×C4—864no—
463C22×C4—864no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—864no—
472C22×C4—862no—
473C22×C4—1722no—
474C22×C4—1722no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4D4×D4311yescharacteristic
478C22×C4D4×D4311yescharacteristic
479C22×C4C23×D4311yescharacteristic
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—862no—
484C2×C8—862no—
485C2×C8—862no—
486C4⋊C4—24no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—432no—
493C4⋊C4—864no—
494C4⋊C4—861no—
495C4⋊C4—862no—
496C4⋊C4—862no—
497C4⋊C4—1722no—
498C4⋊C4—1722no—
499C4⋊C4C2×C4×D4312yes—
500C22⋊C4—864no—
501C22⋊C4—864no—
502C22⋊C4—864no—
503C22⋊C4—1724no—
504C42—24no—
505C42—434no—
506C42—434no—
507C42—432no—
508C42—432no—
509C42—864no—
510C42—864no—
511C42—1724no—
512C42C2×C4×D4312yes—
513C42D4×D4312yes—
514C23—432no—
515C23—862no—
516C23—862no—
517C23—861no—
518C23—862no—
519C23—861no—
520C23—861no—
521C23—861no—
522C23—861no—
523C23—861no—
524C23—1721no—
525C23—1721no—
526C23—1721no—
527C23—1721no—
528C23C2×D4×D4311yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—22no—
532Q8#1306328314yescomplemented
533D4—434no—
534D4—8616no—
535D4—862no—
536D4—862no—
537D4—862no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—432no—
550C2×C4—432no—
551C2×C4—432no—
552C2×C4—432no—
553C2×C4—432no—
554C2×C4—868no—
555C2×C4—8616no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—868no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—1728no—
567C2×C4—1722no—
568C2×C4—1722no—
569C2×C4—1722no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1728no—
573C2×C4C22⋊C4×D4312yes—
574C2×C4C22⋊C4×D4312yes—
575C2×C4#1306334612yes—
576C2×C4#1306334812yes—
577C2×C4C22×C4×D4311yescharacteristic
578C2×C4C2×D4×D4311yescharacteristic
579C2×C4#41×D4311yescharacteristic
580C2×C4#41×D4311yescharacteristic
581C2×C4C2×#1062190011yescharacteristic
582C2×C4C2×#1062190211yescharacteristic
583C8—42no—
584C8—1722no—
585C22—862no—
586C22—862no—
587C22—864no—
588C22—862no—
589C22—1722no—
590C22—1722no—
591C22—1721no—
592C22—1722no—
593C22—1721no—
594C22—1722no—
595C22—1721no—
596C22—1722no—
597C22—1721no—
598C22—1722no—
599C22C2×C22⋊C4×D4311yescharacteristic
600C22#1458340911yescharacteristic
601C22#1458341211yescharacteristic
602C22C2×#1306334611yescharacteristic
603C22C2×#1306334811yescharacteristic
604C22AGL(1,ℤ/8)×D4311yescharacteristic
605C22#137×D4311yescharacteristic
606C4—22no—
607C4—24no—
608C4—42no—
609C4—82no—
610C4—434no—
611C4—862no—
612C4—862no—
613C4—3442no—
614C4—1722no—
615C4#1458289414yes—
616C4#117×D4311yescharacteristic
617C4C2×#1306328311yescharacteristic
618C4#1458340911yescharacteristic
619C4#1458341211yescharacteristic
620C2—1722no—
621C2—1724no—
622C2#1913697711yescharacteristic
623C2C2×#1458289411yescharacteristic
624C2#417×D4311yescharacteristic
625C2#1914465411yescharacteristic
626C2#1914465811yescharacteristic
627C2#1914466511yescharacteristic
628C2#1914466911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1803C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
cosocleC22×C4×C43C24
hypercenter#1803D43
hypocenterC43#20737
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. C2×#14582951C2semidirect
3. #19137000C2semidirect
4. #19134689C2semidirect
5. #19134600C2semidirect
6. #19134596C2semidirect
7. #19134592C2semidirect
9. #103×Dic43C2semidirect
10. #19134409C2semidirect
11. C43×#1803C2semidirect
14. C4×#10621902C4semidirect
217. Q8×C43#117semidirect
258. D172#117semidirect
311. #1803D43semidirect
360. C43#20737semidirect
532. Q8#13063283semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106219022
C2×#145829512
#191370002
#191346892
#191346002
#191345962
#191345922
#191345342
#103×Dic432
#191344092
C43×#18032
#2073743