Finite Group Databasebeta

← #25017846

Subgroups — #25017846

Order 11008.

2102 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063283C211yesmaximal, characteristic
2C2×#14582758C212yesmaximal
3C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
4C2×#14582750C211yesmaximal, characteristic, complemented
5#19132833C211yesmaximal, characteristic
6#19132831C211yesmaximal, characteristic
7#19132831C212yesmaximal
8#19132829C212yesmaximal, complemented
9#19132827C211yesmaximal, characteristic, complemented
10Dic43⋊#95C212yesmaximal, complemented
11C43×#1436C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C2×#13063283—24no—
14C2×#13063283—24no—
15C2×#13063283C418yescomplemented
16C22×C4⋊Dic43C2211yescharacteristic
17C22×Dic43⋊C4C2212yes—
18C22×Dic43⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2211yescharacteristic
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2212yes—
22C22×(C2×D43)⋊C4C2212yes—
23C22×C4×Dic43C2211yescharacteristic
24C22×C4×Dic43C2211yescharacteristic
25C22×C4×Dic43C2212yes—
26C22×C4×Dic43C2211yescharacteristic
27#14582758C4116yescomplemented
28C4×Dic43⋊C4—24no—
29#14582750—24no—
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2212yes—
36C22×C4⋊C4×C43C2211yescharacteristic
37C22×C42×C43C2211yescharacteristic
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2212yes—
40C2×#95×C43C2212yes—
41C24×D43C2311yescharacteristic
42C23×Dic43C2312yes—
43C23×Dic43C2312yes—
44C23×Dic43C2311yescharacteristic
45C23×Dic43C2311yescharacteristic
46C23×Dic43C2311yescharacteristic
47C22×C4×D43—22no—
48C22×C4×D43—22no—
49C22×C4×D43—24no—
50C22×C4×D43C2×C414yes—
51C22×C4×D43C2×C418yes—
52#13063283—232no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43C2×C414yes—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—24no—
60C2×Dic43⋊C4C2×C418yes—
61C2×Dic43⋊C4C2×C418yes—
62C2×(C2×D43)⋊C4—22no—
63C2×(C2×D43)⋊C4—22no—
64C2×(C2×D43)⋊C4—22no—
65C2×(C2×D43)⋊C4—22no—
66C2×(C2×D43)⋊C4—42no—
67C2×(C2×D43)⋊C4—42no—
68C2×(C2×D43)⋊C4—42no—
69C2×(C2×D43)⋊C4—42no—
70C2×(C2×D43)⋊C4C2×C414yes—
71C2×(C2×D43)⋊C4C2×C414yes—
72C2×(C2×D43)⋊C4C2×C418yes—
73C2×(C2×D43)⋊C4C2×C418yes—
74C2×C4×Dic43—22no—
75C2×C4×Dic43—22no—
76C2×C4×Dic43—22no—
77C2×C4×Dic43—24no—
78C2×C4×Dic43—42no—
79C2×C4×Dic43—42no—
80C2×C4×Dic43—42no—
81C2×C4×Dic43C2×C414yes—
82C2×C4×Dic43C2×C414yes—
83C2×C4×Dic43D414yes—
84C2×C4×Dic43D414yes—
85C43⋊#95—22no—
86C43⋊#95—24no—
87C43⋊#95—42no—
88C43⋊#95—42no—
89C43⋊#95—42no—
90C43⋊#95C2×C418yes—
91C23×C4×C43C2312yes—
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2312yes—
94C23×C4×C43C2311yescharacteristic
95C23×C4×C43C2311yescharacteristic
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43C2×C414yes—
99C2×C42×C43—22no—
100C2×C42×C43—42no—
101#95×C43—22no—
102#95×C43—42no—
103#95×C43C2×C418yes—
104C24×C43C2411yescharacteristic
105C23×D43—21no—
106C23×D43—21no—
107C23×D43—22no—
108C23×D43—22no—
109C23×D43—22no—
110C23×D43—22no—
111C23×D43—22no—
112C23×D43C22×C412yes—
113C23×D43C22×C414yes—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43C22×C414yes—
136C22×C4×C43C22×C414yes—
137C22×C4×C43C22×C412yes—
138C22×C4×C43C22×C414yes—
139C22×C4×C43C22×C412yes—
140C22×C4×C43C22×C412yes—
141C22×C4×C43C2×D412yes—
142C22×C4×C43C2×D412yes—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43C22×C414yes—
162C22×Dic43C22×C414yes—
163C22×Dic43C22×C412yes—
164C22×Dic43C22×C412yes—
165C22×Dic43C22×C412yes—
166C22×Dic43C22×C414yes—
167C22×Dic43C2×D412yes—
168C22×Dic43C2×D412yes—
169C22×Dic43C2×D412yes—
170C22×Dic43C2×D412yes—
171C22×Dic43#4114yes—
172C2×C4×D43—28no—
173C2×C4×D43—28no—
174C2×C4×D43—216no—
175C2×C4×D43—216no—
176C2×C4×D43C42116yescomplemented
177C4⋊C4×C43—28no—
178C42×C43—44no—
179(C2×D43)⋊C4—28no—
180(C2×D43)⋊C4—28no—
181(C2×D43)⋊C4—48no—
182(C2×D43)⋊C4—48no—
183C4⋊Dic43—28no—
184Dic43⋊C4—216no—
185Dic43⋊C4—216no—
186C4×Dic43—28no—
187C4×Dic43—48no—
188C4×Dic43—44no—
189C4×Dic43C22⋊C4116yescomplemented
190C23×C43C23×C411yescharacteristic
191C23×C43C23×C412yes—
192C23×C43C22×D411yescharacteristic
193C23×C43C22×D411yescharacteristic
194C23×C43C2×#4112yes—
195C23×C43H(5,𝔽2)12yes—
196C23×C43H(5,𝔽2)12yes—
197C23×C432−1+412yes—
198C23×C432−1+412yes—
199C22×D43—22no—
200C22×D43—22no—
201C22×D43—24no—
202C22×D43—24no—
203C22×D43—24no—
204C22×D43—24no—
205C22×D43—24no—
206C22×D43—24no—
207C22×D43—24no—
208C22×D43—24no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—42no—
214C22×D43—42no—
215C22×D43—42no—
216C22×D43—42no—
217C22×D43—42no—
218C22×D43—42no—
219C22×D43C2×C4214yes—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—24no—
223C2×C4×C43—24no—
224C2×C4×C43—24no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—24no—
228C2×C4×C43—22no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—24no—
233C2×C4×C43—24no—
234C2×C4×C43—24no—
235C2×C4×C43—24no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43C2×C4214yes—
248C2×C4×C43C2×C22⋊C414yes—
249C2×Dic43—24no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—24no—
253C2×Dic43—22no—
254C2×Dic43—24no—
255C2×Dic43—24no—
256C2×Dic43—24no—
257C2×Dic43—24no—
258C2×Dic43—24no—
259C2×Dic43—24no—
260C2×Dic43—24no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43C2×C4214yes—
273C2×Dic43C2×C22⋊C414yes—
274C2×Dic43C2×C22⋊C414yes—
275C2×Dic43#11714yes—
276C2×Dic43C4×D418yes—
277C2×Dic43C4×D418yes—
278C4×D43—232no—
279#13777—431nomaximal, Sylow
280C22×C43C22×C4211yescharacteristic
281C22×C43C22×C22⋊C411yescharacteristic
282C22×C43C2×#11711yescharacteristic
283C22×C43C2×C4×D412yes—
284C22×C43C2×C4×D412yes—
285C22×C43#51812yes—
286C22×C43#51912yes—
287C22×C43#52012yes—
288C22×C43#52012yes—
289C22×C43#52012yes—
290C22×C43#52012yes—
291C22×C43#53511yescharacteristic
292C22×C43#53511yescharacteristic
293C22×C43#53611yescharacteristic
294C22×C43#53611yescharacteristic
295C22×C43#53712yes—
296C22×C43#53712yes—
297C22×C43#54012yes—
298C22×C43#54112yes—
299C22×C43#54212yes—
300C22×C43#54212yes—
301C2×D43—24no—
302C2×D43—28no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—44no—
306C2×D43—44no—
307C2×D43—44no—
308C2×D43—44no—
309C2×D43—44no—
310C4×C43—24no—
311C4×C43—24no—
312C4×C43—42no—
313C4×C43—44no—
314C4×C43—44no—
315Dic43—24no—
316Dic43—42no—
317Dic43—44no—
318Dic43—44no—
319Dic43C4×C22⋊C418yes—
320C22×#117—431no—
321C2×#380—432no—
322C2×C4×C4⋊C4—431no—
323C2×C4×C4⋊C4—431no—
324#1437—431no—
325#1437—432no—
326#1437—431no—
327#1436—432no—
328#1436—431no—
329#1436D4311yescharacteristic, complemented
330C4⋊#95—432no—
331C2×C43C2×C4×C22⋊C411yescharacteristic
332C2×C43#227412yes—
333C2×C43#231111yescharacteristic
334C2×C43#231111yescharacteristic
335C2×C43#231412yes—
336C2×C43#232312yes—
337C2×C43#232312yes—
338C2×C43#232412yes—
339C2×C43#232412yes—
340D43—44no—
341C24×C4—431no—
342C2×#117—438no—
343C2×#117—864no—
344C2×#117—864no—
345C22×C4⋊C4—432no—
346C22×C4⋊C4—432no—
347C22×C4⋊C4—431no—
348C22×C4⋊C4C2×D4311yescharacteristic
349C22×C22⋊C4—431no—
350C22×C22⋊C4—431no—
351C22×C22⋊C4—432no—
352C22×C22⋊C4—432no—
353C22×C42—431no—
354C22×C42—431no—
355C22×C42—432no—
356C22×C42—431no—
357C22×C42C2×D4311yescharacteristic
358#380—4316no—
359C4×C4⋊C4—864no—
360C4×C4⋊C4—864no—
361C2×#95—432no—
362C2×#95—432no—
363C2×#95—431no—
364C2×#95—432no—
365C2×#95—432no—
366C2×#95—432no—
367C2×#95C2×D4311yescharacteristic
368C2×#95C2×D4312yes—
369C2×#95C2×D4312yes—
370C43#1377711yescharacteristic, complemented, Sylow
371C25—431no—
372C23×C4—431no—
373C23×C4—431no—
374C23×C4—434no—
375C23×C4—438no—
376C23×C4—432no—
377C23×C4—432no—
378C23×C4—431no—
379C23×C4—862no—
380C23×C4—862no—
381C23×C4—864no—
382C23×C4C22×D4312yes—
383C23×C4C22×D4312yes—
384C23×C4C22×D4311yescharacteristic
385C23×C4C22×D4311yescharacteristic
386C23×C4C22×D4311yescharacteristic
387#117—8632no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—434no—
391C2×C4⋊C4—438no—
392C2×C4⋊C4—438no—
393C2×C4⋊C4—862no—
394C2×C4⋊C4—862no—
395C2×C4⋊C4—864no—
396C2×C4⋊C4—864no—
397C2×C4⋊C4—864no—
398C2×C4⋊C4—864no—
399C2×C4⋊C4C4×D4314yes—
400C2×C22⋊C4—434no—
401C2×C22⋊C4—434no—
402C2×C22⋊C4—438no—
403C2×C22⋊C4—438no—
404C2×C22⋊C4—862no—
405C2×C22⋊C4—862no—
406C2×C22⋊C4—862no—
407C2×C22⋊C4—862no—
408C2×C22⋊C4—1722no—
409C2×C22⋊C4—1722no—
410C2×C22⋊C4—1722no—
411C2×C22⋊C4—1722no—
412C2×C42—22no—
413C2×C42—42no—
414C2×C42—434no—
415C2×C42—434no—
416C2×C42—434no—
417C2×C42—434no—
418C2×C42—862no—
419C2×C42—862no—
420C2×C42—864no—
421C2×C42—862no—
422C2×C42—1722no—
423C2×C42—1722no—
424C2×C42—1722no—
425#95—22no—
426#95—42no—
427#95—438no—
428#95—864no—
429#95—862no—
430#95—1722no—
431#95—1722no—
432#95—1722no—
433#95C4×D4318yes—
434C24—432no—
435C24—434no—
436C24—861no—
437C24—861no—
438C24—862no—
439C24—862no—
440C24—862no—
441C24—862no—
442C24—862no—
443C24C23×D4311yescharacteristic
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—432no—
466C22×C4—434no—
467C22×C4—432no—
468C22×C4—432no—
469C22×C4—434no—
470C22×C4—432no—
471C22×C4—432no—
472C22×C4—432no—
473C22×C4—4316no—
474C22×C4—434no—
475C22×C4—434no—
476C22×C4—432no—
477C22×C4—868no—
478C22×C4—868no—
479C22×C4—8616no—
480C22×C4—8616no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4C2×C4×D4314yes—
500C22×C4C2×C4×D4314yes—
501C22×C4C2×C4×D4312yes—
502C22×C4C2×C4×D4314yes—
503C22×C4C2×C4×D4312yes—
504C22×C4C2×C4×D4312yes—
505C22×C4D4×D4312yes—
506C22×C4D4×D4312yes—
507C4⋊C4—28no—
508C4⋊C4—868no—
509C4⋊C4—8616no—
510C4⋊C4—8616no—
511C22⋊C4—868no—
512C22⋊C4—868no—
513C22⋊C4—1728no—
514C22⋊C4—1728no—
515C42—44no—
516C42—4316no—
517C42—868no—
518C42—1724no—
519C42—1728no—
520C23—434no—
521C23—862no—
522C23—862no—
523C23—864no—
524C23—864no—
525C23—864no—
526C23—864no—
527C23—864no—
528C23—864no—
529C23—864no—
530C23—864no—
531C23—1721no—
532C23—1721no—
533C23—1721no—
534C23—1721no—
535C23—1722no—
536C23—1722no—
537C23—1722no—
538C23—1722no—
539C23—1722no—
540C23—1722no—
541C23C22×C4×D4311yescharacteristic
542C23C22×C4×D4312yes—
543C23C2×D4×D4311yescharacteristic
544C23C2×D4×D4311yescharacteristic
545C23#41×D4312yes—
546C23#1306337012yes—
547C23#1306337112yes—
548C23#1306337212yes—
549C23#1306337312yes—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—434no—
578C2×C4—434no—
579C2×C4—434no—
580C2×C4—438no—
581C2×C4—438no—
582C2×C4—434no—
583C2×C4—8632no—
584C2×C4—864no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—864no—
588C2×C4—862no—
589C2×C4—864no—
590C2×C4—864no—
591C2×C4—864no—
592C2×C4—864no—
593C2×C4—864no—
594C2×C4—864no—
595C2×C4—864no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4C42×D4314yes—
608C2×C4C22⋊C4×D4314yes—
609C22—864no—
610C22—868no—
611C22—1724no—
612C22—1724no—
613C22—1722no—
614C22—1722no—
615C22—1724no—
616C22—1724no—
617C22—1724no—
618C22C2×C42×D4311yescharacteristic
619C22C2×C22⋊C4×D4311yescharacteristic
620C22#117×D4311yescharacteristic
621C22C4×D4×D4312yes—
622C22C4×D4×D4312yes—
623C22#1458337112yes—
624C22#1458337512yes—
625C22#1458337812yes—
626C22#1458337912yes—
627C22#1458338012yes—
628C22#1458338112yes—
629C22#1458346411yescharacteristic
630C22#1458346711yescharacteristic
631C22#1458347111yescharacteristic
632C22#1458347411yescharacteristic
633C22#1458347612yes—
634C22#1458347912yes—
635C22#1458350112yes—
636C22#1458350812yes—
637C22#1458351512yes—
638C22#1458351912yes—
639C4—24no—
640C4—24no—
641C4—44no—
642C4—44no—
643C4—42no—
644C4—438no—
645C4—864no—
646C4—1724no—
647C4—1724no—
648C4—1722no—
649C2—1724no—
650C2C4×C22⋊C4×D4311yescharacteristic
651C2#1913694912yes—
652C2#1913718211yescharacteristic
653C2#1913718611yescharacteristic
654C2#1913720112yes—
655C2#1913727212yes—
656C2#1913727612yes—
657C2#1913728312yes—
658C2#1913728712yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1436D43
hypocenterC43#13777
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic43⋊C4C2semidirect
4. C2×#14582750C2semidirect
8. #19132829C2semidirect
9. #19132827C2semidirect
10. Dic43⋊#95C2semidirect
11. C43×#1436C2semidirect
15. C2×#13063283C4semidirect
27. #14582758C4semidirect
176. C2×C4×D43C42semidirect
189. C4×Dic43C22⋊C4semidirect
329. #1436D43semidirect
370. C43#13777semidirect

Maximal subgroups

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

subgroupindex
C22×#130632832
C2×#145827582
C2×C4×Dic43⋊C42
C2×#145827502
#191328332
#191328312
#191328292
#191328272
Dic43⋊#952
C43×#14362
#1377743