Finite Group Databasebeta

← #25096388

Subgroups — #25096388

Order 11008.

1502 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D43C211yesmaximal, characteristic
2C22×(C2×D43)⋊C8C211yesmaximal, characteristic
3#19136974C211yesmaximal, characteristic
4#19134689C212yesmaximal, complemented
5#19134688C212yesmaximal, complemented
6#19134684C212yesmaximal, complemented
7#19134680C212yesmaximal, complemented
8#19134312C211yesmaximal, characteristic, complemented
9#19134311C211yesmaximal, characteristic, complemented
10#19134311C211yesmaximal, characteristic, complemented
11C43×#1735C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C23×C43⋊C8C2211yescharacteristic
14C2×#13063284C2211yescharacteristic
15C2×#13063284C2211yescharacteristic
16C2×#13063283C2211yescharacteristic
17C2×#13063283C2211yescharacteristic
18C2×#13063282—21no—
19C2×#13063281—21no—
20#117×D43—24no—
21#117×D43C418yescomplemented
22C2×C4⋊C4×D43C2211yescharacteristic
23C2×C4⋊C4×D43C2211yescharacteristic
24C2×C22⋊C4×D43—21no—
25C2×C42×D43—21no—
26C2×(C2×D43)⋊C8—24no—
27C2×(C2×D43)⋊C8C2212yes—
28C2×(C2×D43)⋊C8C2212yes—
29#14582760—21no—
30#14582756C2212yes—
31#14582756C2212yes—
32#14582754—21no—
33C4×(C2×D43)⋊C4—21no—
34C4×(C2×D43)⋊C4—21no—
35#14582662C2212yescomplemented
36#14582662C2212yescomplemented
37#14582661C2212yescomplemented
38#14582661C2212yescomplemented
39#14582661C2212yescomplemented
40#14582661C2212yescomplemented
41C23×C8×C43C2211yescharacteristic
42C2×#117×C43C2211yescharacteristic
43C2×#117×C43C2211yescharacteristic
44C43×#340C2212yescomplemented
45C43×#340C2212yescomplemented
46C24×D43D411yescharacteristic
47C23×Dic43D411yescharacteristic
48C22×C4×D43—22no—
49C22×C4×D43—22no—
50C22×C4×D43—22no—
51C22×C4×D43—22no—
52C22×C4×D43—21no—
53C22×C4×D43—21no—
54C22×C4×D43C2×C414yes—
55C22×C4×D43D411yescharacteristic
56C22×C4×D43D411yescharacteristic
57C22×C4×D43D414yes—
58C22×C4×D43C2311yescharacteristic
59C22×C4×D43C2311yescharacteristic
60C22×C43⋊C8—22no—
61C22×C43⋊C8—22no—
62C22×C43⋊C8—22no—
63C22×C43⋊C8C2312yes—
64#13063284—22no—
65#13063284—22no—
66#13063284—22no—
67#13063284C2×C414yes—
68#13063283—22no—
69#13063283—22no—
70#13063283C2×C414yes—
71#13063283C2×C414yes—
72#13063282—28no—
73#13063281—28no—
74C2×C4⋊Dic43C2312yes—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C4⋊C4×D43—22no—
80C4⋊C4×D43—22no—
81C4⋊C4×D43C2×C414yes—
82C4⋊C4×D43C2×C414yes—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—22no—
88C2×(C2×D43)⋊C4—22no—
89C22⋊C4×D43—28no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C42×D43—28no—
95(C2×D43)⋊C8—24no—
96(C2×D43)⋊C8—24no—
97C43⋊#95—22no—
98C43⋊#95—22no—
99C23×C4×C43C2311yescharacteristic
100C22×C8×C43—22no—
101C22×C8×C43—22no—
102C22×C8×C43—22no—
103C22×C8×C43C2312yes—
104#117×C43—22no—
105#117×C43—22no—
106#117×C43—22no—
107#117×C43C2×C414yes—
108C2×C4⋊C4×C43C2312yes—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C42×C43—21no—
114C2×C42×C43—21no—
115C24×C43C2×D411yescharacteristic
116C23×D43—22no—
117C23×D43—22no—
118C23×D43—24no—
119C23×D43—42no—
120C23×D43C22⋊C414yes—
121C23×D43C2×D411yescharacteristic
122C23×D43C2×D411yescharacteristic
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43C22×C412yes—
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43#4112yes—
130C22×C4×C43#4112yes—
131C22×C4×C43#4112yes—
132C22×C4×C43#4112yes—
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—22no—
139C22×Dic43C22⋊C414yes—
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C2×C4×D43—28no—
143C2×C4×D43—28no—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—28no—
149C2×C4×D43—28no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—24no—
159C2×C4×D43—24no—
160C2×C4×D43—44no—
161C2×C4×D43—44no—
162C2×C4×D43C22⋊C414yes—
163C2×C4×D43C22⋊C414yes—
164C2×C4×D43C22×C412yes—
165C2×C4×D43C22×C412yes—
166C2×C4×D43C2×D412yes—
167C2×C4×D43C2×D412yes—
168C2×C8×C43—22no—
169C2×C8×C43—22no—
170C2×C8×C43—22no—
171C2×C8×C43—44no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43C22×C412yes—
177C4⋊C4×C43C22×C412yes—
178C22⋊C4×C43—24no—
179C22⋊C4×C43—42no—
180C42×C43—24no—
181C42×C43—42no—
182C22⋊Dic43—24no—
183C22⋊Dic43—42no—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—44no—
187(C2×D43)⋊C4—44no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—22no—
191C4⋊Dic43—22no—
192C4⋊Dic43C22×C412yes—
193C4⋊Dic43C22×C412yes—
194Dic43⋊C4—24no—
195Dic43⋊C4—24no—
196C4×Dic43—24no—
197C4×Dic43—24no—
198C4×Dic43—24no—
199C4×Dic43—42no—
200C2×C43⋊C8—22no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—44no—
204C23×C43—22no—
205C23×C43—22no—
206C23×C43C2×C22⋊C412yes—
207C23×C43#12312yes—
208C23×C43#12312yes—
209C23×C43C22×D411yescharacteristic
210C22×D43—21no—
211C22×D43—21no—
212C22×D43—22no—
213C22×D43—21no—
214C22×D43—21no—
215C22×D43—22no—
216C22×D43—22no—
217C22×D43—28no—
218C22×D43—28no—
219C22×D43—44no—
220C22×D43—48no—
221C22×D43—48no—
222C22×D43C2×C22⋊C412yes—
223C22×D43C2×C22⋊C412yes—
224C22×D43#13514yes—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43C2×C22⋊C412yes—
233C2×C4×C43#11714yes—
234C2×C4×C43#11714yes—
235C2×C4×C43#12314yes—
236C2×C4×C43#12312yes—
237C2×C4×C43#12314yes—
238C2×C4×C43#12312yes—
239C2×C4×C43C23×C411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—28no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43C2×C22⋊C412yes—
258C2×Dic43C2×C22⋊C412yes—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—22no—
267C4×D43—28no—
268C4×D43—28no—
269C4×D43—48no—
270C4×D43—48no—
271C8×C43—42no—
272C43⋊C8—42no—
273#20699—431nomaximal, Sylow
274C22×C43—24no—
275C22×C43—24no—
276C22×C43—22no—
277C22×C43—22no—
278C22×C43#38114yes—
279C22×C43C22×C22⋊C411yescharacteristic
280C22×C43C2×#12311yescharacteristic
281C22×C43C2×#12311yescharacteristic
282C22×C43C2×#13512yes—
283C22×C43#57512yes—
284C2×D43—24no—
285C2×D43—24no—
286C2×D43—22no—
287C2×D43—22no—
288C2×D43—22no—
289C2×D43—22no—
290C2×D43—22no—
291C2×D43—416no—
292C2×D43—42no—
293C2×D43—42no—
294C2×D43#41614yes—
295C4×C43—42no—
296C4×C43—42no—
297C4×C43—82no—
298C4×C43#38114yes—
299C4×C43C2×#11711yescharacteristic
300C4×C43C2×#11711yescharacteristic
301C4×C43C2×#12311yescharacteristic
302C4×C43C2×#12311yescharacteristic
303Dic43—22no—
304Dic43—22no—
305Dic43—42no—
306Dic43—42no—
307Dic43—82no—
308C22×#117—431no—
309C22×C22⋊C8—431no—
310#2280—431no—
311#1825—432no—
312#1825—432no—
313#1824—432no—
314#1823—432no—
315#1735—431no—
316#1735—431no—
317#1735—431no—
318#1735D4311yescharacteristic, complemented
319C2×C43—24no—
320C2×C43C2×#38111yescharacteristic
321C2×C43C2×#41611yescharacteristic
322C2×C43#289611yescharacteristic
323C2×C43#309112yes—
324C2×C43#309112yes—
325D43—24no—
326D43—42no—
327C24×C4—431no—
328C23×C8—431no—
329C23×C8C2×D4311yescharacteristic
330C2×#117—431no—
331C2×#117—438no—
332C2×#117—431no—
333C2×#117—431no—
334C2×#117—431no—
335C2×#117—861no—
336C2×#117—861no—
337C2×#117—864no—
338C2×#117C2×D4311yescharacteristic
339C2×#117C2×D4311yescharacteristic
340C22×C4⋊C4—431no—
341C22×C4⋊C4—431no—
342C22×C22⋊C4—861no—
343C22×C42—861no—
344C2×C22⋊C8—432no—
345C2×C22⋊C8—432no—
346C2×C22⋊C8—864no—
347#381—861no—
348#380—432no—
349#380—432no—
350#379—861no—
351C4×C22⋊C4—861no—
352C4×C22⋊C4—861no—
353#340—432no—
354#340—432no—
355#340—432no—
356#340—432no—
357#340—432no—
358#340—432no—
359#340C2×D4312yescomplemented
360#340C2×D4312yescomplemented
361C43#2069911yescharacteristic, complemented, Sylow
362C25—431no—
363C23×C4—431no—
364C23×C4—434no—
365C23×C4—434no—
366C23×C4—431no—
367C23×C4—431no—
368C23×C4—431no—
369C23×C4—431no—
370C23×C4—861no—
371C23×C4—861no—
372C23×C4—862no—
373C23×C4—862no—
374C23×C4—862no—
375C23×C4—862no—
376C23×C4C22×D4311yescharacteristic
377C22×C8—22no—
378C22×C8—22no—
379C22×C8—22no—
380C22×C8—432no—
381C22×C8—862no—
382C22×C8—862no—
383C22×C8—862no—
384C22×C8C22×D4312yes—
385#117—22no—
386#117—22no—
387#117—22no—
388#117—434no—
389#117—434no—
390#117—434no—
391#117—868no—
392#117—868no—
393#117—862no—
394#117—862no—
395#117—862no—
396#117—862no—
397#117—862no—
398#117C4×D4314yes—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—434no—
402C2×C4⋊C4—434no—
403C2×C4⋊C4—432no—
404C2×C4⋊C4—862no—
405C2×C4⋊C4—862no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4C22×D4312yes—
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—868no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—862no—
418C2×C22⋊C4—862no—
419C2×C22⋊C4—861no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—868no—
423C2×C42—861no—
424C2×C42—861no—
425C2×C42—861no—
426C2×C42—861no—
427C22⋊C8—864no—
428C22⋊C8—864no—
429#95—862no—
430#95—862no—
431C24—431no—
432C24—431no—
433C24—434no—
434C24—864no—
435C24—862no—
436C24—862no—
437C24—1722no—
438C24D4×D4311yescharacteristic
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—434no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—434no—
446C22×C4—434no—
447C22×C4—432no—
448C22×C4—432no—
449C22×C4—432no—
450C22×C4—432no—
451C22×C4—864no—
452C22×C4—864no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—868no—
456C22×C4—868no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—868no—
460C22×C4—862no—
461C22×C4—862no—
462C22×C4—868no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—862no—
474C22×C4—1724no—
475C22×C4—1724no—
476C22×C4C2×C4×D4312yes—
477C22×C4#1062189812yes—
478C22×C4#1062189812yes—
479C22×C4D4×D4312yes—
480C22×C4D4×D4311yescharacteristic
481C22×C4#1062190012yes—
482C22×C4#1062190212yes—
483C22×C4C23×D4311yescharacteristic
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—44no—
488C2×C8—862no—
489C2×C8—862no—
490C2×C8—862no—
491C2×C8—1724no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—432no—
497C4⋊C4—432no—
498C4⋊C4—864no—
499C4⋊C4—864no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4C2×C4×D4312yes—
505C4⋊C4C2×C4×D4312yes—
506C22⋊C4—24no—
507C22⋊C4—42no—
508C22⋊C4—864no—
509C22⋊C4—864no—
510C22⋊C4—864no—
511C22⋊C4—1724no—
512C22⋊C4—1724no—
513C22⋊C4—1722no—
514C42—24no—
515C42—42no—
516C42—864no—
517C42—864no—
518C42—864no—
519C42—1722no—
520C23—22no—
521C23—22no—
522C23—432no—
523C23—434no—
524C23—432no—
525C23—868no—
526C23—861no—
527C23—861no—
528C23—862no—
529C23—861no—
530C23—861no—
531C23—862no—
532C23—862no—
533C23—868no—
534C23—1724no—
535C23—1728no—
536C23—1728no—
537C23C22⋊C4×D4312yes—
538C23#1306330712yes—
539C23#1306331012yes—
540C23C2×D4×D4311yescharacteristic
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—432no—
549C2×C4—432no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—868no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—868no—
564C2×C4—868no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—1728no—
568C2×C4—1728no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4—1722no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4C22⋊C4×D4312yes—
575C2×C4#1306328214yes—
576C2×C4#1306328314yes—
577C2×C4#1306330714yes—
578C2×C4#1306330712yes—
579C2×C4#1306331014yes—
580C2×C4#1306331012yes—
581C2×C4C22×C4×D4311yescharacteristic
582C2×C4C2×D4×D4311yescharacteristic
583C2×C4C2×#1062190011yescharacteristic
584C2×C4C2×#1062189811yescharacteristic
585C2×C4C2×#1062189811yescharacteristic
586C2×C4C2×#1062190211yescharacteristic
587C8—42no—
588C8—1722no—
589C22—24no—
590C22—24no—
591C22—22no—
592C22—22no—
593C22—434no—
594C22—864no—
595C22—864no—
596C22—862no—
597C22—862no—
598C22—862no—
599C22—862no—
600C22—862no—
601C22—17216no—
602C22—1722no—
603C22—1722no—
604C22#1458276114yes—
605C22C2×C22⋊C4×D4311yescharacteristic
606C22C2×#1306330711yescharacteristic
607C22C2×#1306331011yescharacteristic
608C22#135×D4312yes—
609C22#1458369612yes—
610C4—42no—
611C4—42no—
612C4—82no—
613C4—862no—
614C4—862no—
615C4—3442no—
616C4—1722no—
617C4—1722no—
618C4#1458276114yes—
619C4C2×#1306328211yescharacteristic
620C4C2×#1306328311yescharacteristic
621C4C2×#1306330711yescharacteristic
622C4C2×#1306331011yescharacteristic
623C2—24no—
624C2—864no—
625C2—1722no—
626C2C2×#1458276111yescharacteristic
627C2#416×D4311yescharacteristic
628C2#1914311011yescharacteristic
629C2#1914450612yes—
630C2#1914451212yes—
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1735C2
socleC23×C43C22×D4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenter#1735D43
hypocenterC43#20699
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ #1735

Complements

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

NH ≅ G/Ntype
4. #19134689C2semidirect
5. #19134688C2semidirect
6. #19134684C2semidirect
7. #19134680C2semidirect
8. #19134312C2semidirect
9. #19134311C2semidirect
10. #19134311C2semidirect
11. C43×#1735C2semidirect
21. #117×D43C4semidirect
35. #14582662C22semidirect
36. #14582662C22semidirect
37. #14582661C22semidirect
38. #14582661C22semidirect
39. #14582661C22semidirect
40. #14582661C22semidirect
44. C43×#340C22semidirect
45. C43×#340C22semidirect
318. #1735D43semidirect
359. #340C2×D43semidirect
360. #340C2×D43semidirect
361. C43#20699semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D432
C22×(C2×D43)⋊C82
#191369742
#191346892
#191346882
#191346842
#191346802
#191343122
#191343112
C43×#17352
#2069943