Finite Group Databasebeta

← #25025381

Subgroups — #25025381

Order 11008.

2134 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063313C211yesmaximal, characteristic
2C2×#14582777C212yesmaximal
3#19132865C212yesmaximal, complemented
4#19132843C212yesmaximal, complemented
5#19132843C212yesmaximal, complemented
6#19132822C211yesmaximal, characteristic, complemented
7(C2×D43)⋊#95C212yesmaximal, complemented
8(C2×D43)⋊#95C212yesmaximal, complemented
9C43×#1434C211yesmaximal, characteristic, complemented
10C23×Dic86C2211yescharacteristic
11C23×D172C2211yescharacteristic
12C23×C4×D43C2212yes—
13C2×#13063313—28no—
14C2×#13063313C418yescomplemented
15C22×(C2×D43)⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2212yes—
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2212yes—
20#14582777—28no—
21C2×C43⋊#95C2212yes—
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2211yescharacteristic
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2212yes—
29C22×C42×C43C2211yescharacteristic
30C2×#95×C43C2212yes—
31C2×#95×C43C2212yes—
32C2×#95×C43C2211yescharacteristic
33C2×#95×C43C2211yescharacteristic
34C24×D43C2312yes—
35C22×Dic86—24no—
36C22×Dic86—42no—
37C22×Dic86—41no—
38C22×Dic86—41no—
39C22×Dic86C2×C414yescomplemented
40C22×D172—41no—
41C22×D172—42no—
42C22×D172—41no—
43C22×D172C2×C414yes—
44C22×D172D418yes—
45C23×Dic43C2312yes—
46C23×Dic43C2312yes—
47C23×Dic43C2312yes—
48C22×C4×D43—24no—
49C22×C4×D43—24no—
50C22×C4×D43—24no—
51C22×C4×D43—42no—
52C22×C4×D43—42no—
53C22×C4×D43—42no—
54C22×C4×D43—42no—
55#13063313—232no—
56C2×(C2×D43)⋊C4—24no—
57C2×(C2×D43)⋊C4—24no—
58C2×(C2×D43)⋊C4—24no—
59C2×(C2×D43)⋊C4—24no—
60C2×(C2×D43)⋊C4—24no—
61C2×(C2×D43)⋊C4—24no—
62C2×(C2×D43)⋊C4—24no—
63C2×(C2×D43)⋊C4—24no—
64C2×(C2×D43)⋊C4—24no—
65C2×(C2×D43)⋊C4—42no—
66C2×(C2×D43)⋊C4—42no—
67C2×(C2×D43)⋊C4—42no—
68C2×(C2×D43)⋊C4—42no—
69C2×(C2×D43)⋊C4C2×C418yescomplemented
70C2×(C2×D43)⋊C4C2×C418yescomplemented
71C43⋊#95—24no—
72C43⋊#95—24no—
73C43⋊#95—41no—
74C43⋊#95—42no—
75C43⋊#95—42no—
76C43⋊#95—42no—
77C43⋊#95—42no—
78C43⋊#95—41no—
79C23×C4×C43C2312yes—
80C23×C4×C43C2311yescharacteristic
81C23×C4×C43C2311yescharacteristic
82C23×C4×C43C2312yes—
83C23×C4×C43C2311yescharacteristic
84C2×C42×C43—24no—
85C2×C42×C43C2×C414yescomplemented
86#95×C43—24no—
87#95×C43—24no—
88#95×C43—41no—
89#95×C43—41no—
90C24×C43C2411yescharacteristic
91C23×D43—22no—
92C23×D43—22no—
93C23×D43—22no—
94C23×D43—22no—
95C23×D43—22no—
96C23×D43—22no—
97C23×D43—22no—
98C23×D43—22no—
99C23×D43—22no—
100C23×D43—22no—
101C23×D43—22no—
102C23×D43—22no—
103C23×D43C22×C414yes—
104C23×D43C2×D414yes—
105C23×D43C2×D414yes—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—22no—
120C22×C4×C43—21no—
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—21no—
128C22×C4×C43—21no—
129C22×C4×C43—22no—
130C22×C4×C43C22×C412yes—
131C22×C4×C43C22×C412yes—
132C22×C4×C43C22×C412yes—
133C22×C4×C43C2×D414yes—
134C22×C4×C43#4114yes—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43C22×C414yes—
155C22×Dic43#4114yes—
156C2×D172—44no—
157C2×D172—44no—
158C2×D172—48no—
159C2×D172—48no—
160C2×D172C22⋊C4116yes—
161C2×C4×D43—48no—
162C2×C4×D43—48no—
163C2×C4×D43—48no—
164C2×C4×D43—48no—
165C2×C4×D43—48no—
166C2×C4×D43—48no—
167C2×C4×D43—48no—
168C2×Dic86—28no—
169C2×Dic86—44no—
170C2×Dic86—44no—
171C2×Dic86—48no—
172C2×Dic86—48no—
173C42×C43—28no—
174(C2×D43)⋊C4—216no—
175(C2×D43)⋊C4—216no—
176(C2×D43)⋊C4—48no—
177(C2×D43)⋊C4—48no—
178(C2×D43)⋊C4—48no—
179C23×C43C23×C411yescharacteristic
180C23×C43C22×D412yes—
181C23×C43C2×#4112yes—
182C23×C43C2×#4112yes—
183C23×C43H(5,𝔽2)11yescharacteristic
184C23×C43H(5,𝔽2)12yes—
185C23×C43H(5,𝔽2)11yescharacteristic
186C23×C43H(5,𝔽2)11yescharacteristic
187C23×C43H(5,𝔽2)11yescharacteristic
188C23×C432−1+411yescharacteristic
189C23×C432−1+411yescharacteristic
190C22×D43—24no—
191C22×D43—24no—
192C22×D43—24no—
193C22×D43—24no—
194C22×D43—24no—
195C22×D43—24no—
196C22×D43—24no—
197C22×D43—24no—
198C22×D43—24no—
199C22×D43—24no—
200C22×D43—24no—
201C22×D43—24no—
202C22×D43—24no—
203C22×D43—24no—
204C22×D43—24no—
205C22×D43—24no—
206C22×D43—24no—
207C22×D43—24no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43—42no—
212C22×D43—42no—
213C22×D43—42no—
214C22×D43—42no—
215C22×D43—42no—
216C22×D43—42no—
217C22×D43—42no—
218C22×D43—42no—
219C22×D43—42no—
220C22×D43—42no—
221C22×D43—42no—
222C22×D43—42no—
223C22×D43—42no—
224C22×D43C2×C22⋊C418yes—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—24no—
228C2×C4×C43—24no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—24no—
236C2×C4×C43—24no—
237C2×C4×C43—24no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
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×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43C2×C22⋊C414yes—
254C2×Dic43—24no—
255C2×Dic43—24no—
256C2×Dic43—24no—
257C2×Dic43—24no—
258C2×Dic43—24no—
259C2×Dic43—24no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43—42no—
274C2×Dic43—42no—
275D172—416no—
276C4×D43—432no—
277Dic86—416no—
278#14473—431nomaximal, Sylow
279C22×C43C22×C22⋊C411yescharacteristic
280C22×C43C4×#4111yescharacteristic
281C22×C43C4×#4111yescharacteristic
282C22×C43#51811yescharacteristic
283C22×C43#51811yescharacteristic
284C22×C43#52011yescharacteristic
285C22×C43#52011yescharacteristic
286C22×C43#53412yes—
287C22×C43#53412yes—
288C22×C43#53812yes—
289C22×C43#53812yes—
290C22×C43#54212yes—
291C22×C43#54212yes—
292C22×C43#54612yes—
293C22×C43#54612yes—
294C22×C43#54712yes—
295C22×C43#54712yes—
296C22×C43#55112yes—
297C22×C43#55512yes—
298C22×C43H(3,𝔽4)11yescharacteristic
299C22×C43#56211yescharacteristic
300C22×C43#56211yescharacteristic
301C22×C43#56311yescharacteristic
302C2×D43—28no—
303C2×D43—28no—
304C2×D43—28no—
305C2×D43—44no—
306C2×D43—44no—
307C2×D43—44no—
308C2×D43—44no—
309C2×D43—44no—
310C2×D43—44no—
311C2×D43—44no—
312C2×D43—44no—
313C2×D43—44no—
314C2×D43—44no—
315C2×D43—44no—
316C2×D43—44no—
317C4×C43—24no—
318C4×C43—42no—
319C4×C43—42no—
320C4×C43—44no—
321C4×C43—82no—
322Dic43—44no—
323Dic43—44no—
324Dic43—82no—
325C22×#124—431no—
326C2×#386—432no—
327#1446—432no—
328#1440—432no—
329#1440—432no—
330#1434—431no—
331#1434D4311yescharacteristic, complemented
332C22⋊#95—432no—
333C22⋊#95—432no—
334C2×C43#230811yescharacteristic
335C2×C43#233711yescharacteristic
336C2×C43#233711yescharacteristic
337C2×C43#233911yescharacteristic
338C2×C43#233911yescharacteristic
339C2×C43#237211yescharacteristic
340C2×C43#237911yescharacteristic
341C2×C43#268412yes—
342C2×C43#268612yes—
343C2×C43#268612yes—
344C2×C43#271712yes—
345D43—48no—
346C23×Q8—431no—
347C23×D4—431no—
348C24×C4—432no—
349C2×#124—438no—
350C2×#124—868no—
351C22×C22⋊C4—432no—
352C22×C22⋊C4—432no—
353C22×C22⋊C4—432no—
354C22×C22⋊C4—432no—
355C22×C22⋊C4—432no—
356C22×C42C2×D4311yescharacteristic
357#386—868no—
358C2×#95—432no—
359C2×#95—432no—
360C2×#95—431no—
361C2×#95—432no—
362C2×#95—432no—
363C2×#95—432no—
364C2×#95—431no—
365C2×#95—432no—
366C2×#95C2×D4312yes—
367C2×#95C2×D4312yes—
368C2×#95C2×D4311yescharacteristic
369C2×#95C2×D4311yescharacteristic
370C43#1447311yescharacteristic, complemented, Sylow
371C25—432no—
372C22×Q8—434no—
373C22×Q8—864no—
374C22×Q8—1721no—
375C22×Q8—1721no—
376C22×Q8—1722no—
377C22×D4—434no—
378C22×D4—438no—
379C22×D4—1721no—
380C22×D4—1722no—
381C22×D4—1721no—
382C23×C4—432no—
383C23×C4—432no—
384C23×C4—432no—
385C23×C4—864no—
386C23×C4—864no—
387C23×C4—864no—
388C23×C4—1722no—
389C23×C4—1722no—
390C23×C4—1722no—
391C23×C4—1722no—
392C23×C4C22×D4312yes—
393C23×C4C22×D4311yescharacteristic
394C23×C4C22×D4311yescharacteristic
395C23×C4C22×D4312yes—
396C23×C4C22×D4311yescharacteristic
397#124—8632no—
398C2×C22⋊C4—438no—
399C2×C22⋊C4—438no—
400C2×C22⋊C4—864no—
401C2×C22⋊C4—864no—
402C2×C22⋊C4—864no—
403C2×C22⋊C4—864no—
404C2×C22⋊C4—864no—
405C2×C22⋊C4—864no—
406C2×C22⋊C4—864no—
407C2×C22⋊C4—864no—
408C2×C22⋊C4—864no—
409C2×C22⋊C4—1722no—
410C2×C22⋊C4—1722no—
411C2×C22⋊C4—1722no—
412C2×C22⋊C4—1722no—
413C2×C42—24no—
414C2×C42C4×D4314yescomplemented
415#95—24no—
416#95—24no—
417#95—41no—
418#95—41no—
419#95—864no—
420#95—864no—
421#95—1721no—
422#95—1721no—
423#95—1722no—
424#95—1722no—
425#95—1722no—
426#95—1722no—
427C24—434no—
428C24—434no—
429C24—434no—
430C24—862no—
431C24—862no—
432C24—862no—
433C24—862no—
434C24—862no—
435C24—862no—
436C24—862no—
437C24—862no—
438C24—862no—
439C24—862no—
440C24—862no—
441C24—862no—
442C24C23×D4311yescharacteristic
443C2×Q8—868no—
444C2×Q8—1724no—
445C2×Q8—1724no—
446C2×Q8—1728no—
447C2×Q8—1728no—
448C2×D4—4316no—
449C2×D4—1724no—
450C2×D4—1724no—
451C2×D4—1728no—
452C2×D4—1728no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—434no—
478C22×C4—434no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
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—1728no—
499C22×C4—1728no—
500C22×C4—1728no—
501C22×C4—1728no—
502C22×C4—1728no—
503C22×C4—1728no—
504C22×C4—1728no—
505C22×C4C2×C4×D4312yes—
506C22×C4C2×C4×D4312yes—
507C22×C4C2×C4×D4312yes—
508C22×C4#1062189814yes—
509C22×C4D4×D4314yes—
510C22⋊C4—8616no—
511C22⋊C4—8616no—
512C22⋊C4—1728no—
513C22⋊C4—1728no—
514C22⋊C4—1728no—
515C42—28no—
516C23—438no—
517C23—864no—
518C23—864no—
519C23—864no—
520C23—864no—
521C23—864no—
522C23—864no—
523C23—864no—
524C23—864no—
525C23—864no—
526C23—864no—
527C23—864no—
528C23—864no—
529C23—864no—
530C23—864no—
531C23—864no—
532C23—864no—
533C23—864no—
534C23—864no—
535C23—1722no—
536C23—1722no—
537C23—1722no—
538C23—1722no—
539C23—1722no—
540C23—1722no—
541C23—1722no—
542C23—1722no—
543C23—1722no—
544C23—1722no—
545C23—1722no—
546C23—1722no—
547C23—1722no—
548C23—1722no—
549C23—1722no—
550C23—1722no—
551C23C22×C4×D4311yescharacteristic
552C23C2×D4×D4312yes—
553C23#41×D4312yes—
554C23C2×#1062189812yes—
555C23#1306337011yescharacteristic
556C23#1306337111yescharacteristic
557C23#1306337111yescharacteristic
558C23#1306337112yes—
559C23#1306337111yescharacteristic
560C23#1306337211yescharacteristic
561C23#1306337311yescharacteristic
562Q8—17216no—
563D4—17216no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—864no—
593C2×C4—864no—
594C2×C4—864no—
595C2×C4—864no—
596C2×C4—864no—
597C2×C4—864no—
598C2×C4—17232no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4—1722no—
612C2×C4—1722no—
613C2×C4—1722no—
614C2×C4C22⋊C4×D4314yes—
615C22—868no—
616C22—868no—
617C22—868no—
618C22—1724no—
619C22—1724no—
620C22—1724no—
621C22—1724no—
622C22—1724no—
623C22—1724no—
624C22—1724no—
625C22—1724no—
626C22—1724no—
627C22—1724no—
628C22—1724no—
629C22—1724no—
630C22C2×C22⋊C4×D4311yescharacteristic
631C22#1458336711yescharacteristic
632C22C4×#1062189811yescharacteristic
633C22#1458337311yescharacteristic
634C22#1458337311yescharacteristic
635C22#1458337911yescharacteristic
636C22#1458338011yescharacteristic
637C22#1458346012yes—
638C22#1458346012yes—
639C22#1458348212yes—
640C22#1458348812yes—
641C22#1458351512yes—
642C22#1458352112yes—
643C22#1458354512yes—
644C22#1458354612yes—
645C22#1458355112yes—
646C22#1458355412yes—
647C22#1458357312yes—
648C22#1458361212yes—
649C22#1458364111yescharacteristic
650C22#1458364311yescharacteristic
651C22#1458364711yescharacteristic
652C22#1458365311yescharacteristic
653C4—24no—
654C4—44no—
655C4—42no—
656C4—42no—
657C4—82no—
658C4—3442no—
659C4—1724no—
660C4—1724no—
661C2—1728no—
662C2#1913717211yescharacteristic
663C2#1913740511yescharacteristic
664C2#1913740811yescharacteristic
665C2#1913742311yescharacteristic
666C2#1913742611yescharacteristic
667C2#1913770511yescharacteristic
668C2#1913776611yescharacteristic
669C2#1914097612yes—
670C2#1914100212yes—
671C2#1914100412yes—
672C2#1914143512yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1434C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1434D43
hypocenterC43#14473
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. #19132865C2semidirect
4. #19132843C2semidirect
5. #19132843C2semidirect
6. #19132822C2semidirect
7. (C2×D43)⋊#95C2semidirect
8. (C2×D43)⋊#95C2semidirect
9. C43×#1434C2semidirect
14. C2×#13063313C4semidirect
39. C22×Dic86C2×C4semidirect
69. C2×(C2×D43)⋊C4C2×C4semidirect
70. C2×(C2×D43)⋊C4C2×C4semidirect
85. C2×C42×C43C2×C4semidirect
331. #1434D43semidirect
370. C43#14473semidirect
414. C2×C42C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633132
C2×#145827772
#191328652
#191328432
#191328222
(C2×D43)⋊#952
C43×#14342
#1447343