Finite Group Databasebeta

← #25025059

Subgroups — #25025059

Order 11008.

1758 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582800C211yesmaximal, characteristic
2C2×#14582790C212yesmaximal, complemented
3C2×#14582788C212yesmaximal, complemented
4#19132839C212yesmaximal, complemented
5#19132839C212yesmaximal, complemented
6#19132835C212yesmaximal
7#19132827C211yesmaximal, characteristic, complemented
8Dic43⋊#95C212yesmaximal, complemented
9C43×#1436C211yesmaximal, characteristic, complemented
10C23×D172C2211yescharacteristic
11C22×Dic43⋊C4C2212yes—
12C22×Dic43⋊C4C2212yes—
13C22×(C2×D43)⋊C4C2212yes—
14C22×(C2×D43)⋊C4C2212yes—
15C22×(C2×D43)⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2212yes—
18C22×(C2×D43)⋊C4C2212yes—
19C22×C4×Dic43C2211yescharacteristic
20C22×C4×Dic43C2211yescharacteristic
21#14582800C418yescomplemented
22#14582790—28no—
23#14582788—28no—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2211yescharacteristic
29C22×C4⋊C4×C43C2211yescharacteristic
30C22×C42×C43C2211yescharacteristic
31C2×#95×C43C2212yes—
32C2×#95×C43C2212yes—
33C2×#95×C43C2211yescharacteristic
34C24×D43C2312yes—
35C22×D172—24no—
36C22×D172—41no—
37C22×D172—41no—
38C22×D172—42no—
39C22×D172C2×C414yes—
40C23×Dic43C2312yes—
41C23×Dic43C2312yes—
42C23×Dic43C2312yes—
43C2×Dic43⋊C4—24no—
44C2×Dic43⋊C4—42no—
45C2×Dic43⋊C4—42no—
46C2×Dic43⋊C4—42no—
47C2×Dic43⋊C4—42no—
48C2×Dic43⋊C4D418yescomplemented
49C2×(C2×D43)⋊C4—24no—
50C2×(C2×D43)⋊C4—24no—
51C2×(C2×D43)⋊C4—24no—
52C2×(C2×D43)⋊C4—24no—
53C2×(C2×D43)⋊C4—24no—
54C2×(C2×D43)⋊C4—24no—
55C2×(C2×D43)⋊C4—24no—
56C2×(C2×D43)⋊C4—24no—
57C2×(C2×D43)⋊C4—42no—
58C2×(C2×D43)⋊C4—42no—
59C2×(C2×D43)⋊C4—42no—
60C2×(C2×D43)⋊C4—42no—
61C2×(C2×D43)⋊C4—42no—
62C2×(C2×D43)⋊C4—42no—
63C2×(C2×D43)⋊C4—42no—
64C2×(C2×D43)⋊C4—42no—
65C2×(C2×D43)⋊C4C2×C418yes—
66C2×(C2×D43)⋊C4C2×C418yes—
67C2×C4×Dic43—24no—
68C2×C4×Dic43—42no—
69C2×C4×Dic43—41no—
70C2×C4×Dic43C2×C414yes—
71C43⋊#95—24no—
72C43⋊#95—24no—
73C43⋊#95—24no—
74C43⋊#95—24no—
75C43⋊#95—41no—
76C23×C4×C43C2312yes—
77C23×C4×C43C2311yescharacteristic
78C23×C4×C43C2311yescharacteristic
79C23×C4×C43C2312yes—
80C23×C4×C43C2311yescharacteristic
81C2×C4⋊C4×C43—41no—
82C2×C4⋊C4×C43—41no—
83C2×C4⋊C4×C43C2×C414yes—
84C2×C42×C43—24no—
85C2×C42×C43—41no—
86#95×C43—24no—
87#95×C43—24no—
88#95×C43—41no—
89C24×C43C2411yescharacteristic
90C23×D43—22no—
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×D43—22no—
104C23×D43C22×C414yes—
105C22×C4×C43—22no—
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—21no—
115C22×C4×C43—21no—
116C22×C4×C43—22no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—22no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
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×C43C22×C412yes—
130C22×C4×C43C22×C412yes—
131C22×C4×C43C22×C412yes—
132C22×C4×C43C2×D414yes—
133C22×C4×C43#4114yes—
134C22×Dic43—22no—
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×Dic43C22×C414yes—
152C22×Dic43C2×D414yes—
153C22×Dic43C2×D414yes—
154C22×Dic43#4114yes—
155C2×D172—28no—
156C2×D172—44no—
157C2×D172—44no—
158C2×D172—48no—
159C2×D172—48no—
160C4⋊C4×C43—44no—
161C42×C43—44no—
162(C2×D43)⋊C4—216no—
163(C2×D43)⋊C4—216no—
164(C2×D43)⋊C4—48no—
165(C2×D43)⋊C4—48no—
166(C2×D43)⋊C4—48no—
167(C2×D43)⋊C4—48no—
168Dic43⋊C4—48no—
169Dic43⋊C4—48no—
170C4×Dic43—44no—
171C4×Dic43—44no—
172C23×C43C23×C411yescharacteristic
173C23×C43C22×D412yes—
174C23×C43C2×#4112yes—
175C23×C43C2×#4112yes—
176C23×C43H(5,𝔽2)11yescharacteristic
177C23×C43H(5,𝔽2)11yescharacteristic
178C23×C43H(5,𝔽2)12yes—
179C23×C43H(5,𝔽2)12yes—
180C23×C432−1+412yes—
181C22×D43—24no—
182C22×D43—24no—
183C22×D43—24no—
184C22×D43—24no—
185C22×D43—24no—
186C22×D43—24no—
187C22×D43—24no—
188C22×D43—42no—
189C22×D43—42no—
190C22×D43—42no—
191C22×D43—42no—
192C22×D43—42no—
193C22×D43—42no—
194C22×D43—42no—
195C22×D43—42no—
196C22×D43—42no—
197C22×D43—42no—
198C22×D43—42no—
199C22×D43—42no—
200C22×D43—42no—
201C22×D43—42no—
202C22×D43—42no—
203C22×D43—42no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43—42no—
212C22×D43—42no—
213C22×D43—42no—
214C22×D43—42no—
215C22×D43—42no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—24no—
219C2×C4×C43—24no—
220C2×C4×C43—24no—
221C2×C4×C43—24no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—24no—
225C2×C4×C43—24no—
226C2×C4×C43—24no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
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#11714yes—
245C2×Dic43—24no—
246C2×Dic43—24no—
247C2×Dic43—24no—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—24no—
252C2×Dic43—24no—
253C2×Dic43—24no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43C4×D418yes—
266D172—416no—
267#14445—431nomaximal, Sylow
268C22×C43C2×#11711yescharacteristic
269C22×C43C2×C4×D412yes—
270C22×C43#51811yescharacteristic
271C22×C43#51811yescharacteristic
272C22×C43#52012yes—
273C22×C43#53412yes—
274C22×C43#53712yes—
275C22×C43#53812yes—
276C22×C43#53812yes—
277C22×C43#53812yes—
278C22×C43#53912yes—
279C22×C43D4211yescharacteristic
280C22×C43#54712yes—
281C22×C43#55012yes—
282C22×C43#55012yes—
283C22×C43#55512yes—
284C22×C43#55612yes—
285C22×C43#55911yescharacteristic
286C22×C43H(3,𝔽4)11yescharacteristic
287C22×C43#56212yes—
288C22×C43#56311yescharacteristic
289C2×D43—44no—
290C2×D43—44no—
291C2×D43—44no—
292C2×D43—44no—
293C2×D43—44no—
294C2×D43—44no—
295C2×D43—44no—
296C2×D43—82no—
297C2×D43—82no—
298C2×D43—82no—
299C2×D43—82no—
300C2×D43—82no—
301C2×D43—82no—
302C2×D43—82no—
303C2×D43—82no—
304C4×C43—24no—
305C4×C43—42no—
306C4×C43—42no—
307C4×C43—44no—
308C4×C43—82no—
309Dic43—28no—
310Dic43—44no—
311Dic43—82no—
312C2×#390—431no—
313C2×#388—432no—
314C2×#388—432no—
315#1439—432no—
316#1439—432no—
317#1438—432no—
318#1436—431no—
319#1436D4311yescharacteristic, complemented
320C4⋊#95—432no—
321C2×C43#231211yescharacteristic
322C2×C43#232512yes—
323C2×C43#235412yes—
324C2×C43#236611yescharacteristic
325C2×C43#237911yescharacteristic
326C2×C43#268212yes—
327C2×C43#272712yes—
328C2×C43#273312yes—
329C2×C43#280812yes—
330D43—84no—
331C23×D4—431no—
332C22×C4⋊C4—432no—
333C22×C4⋊C4—432no—
334C22×C4⋊C4C2×D4311yescharacteristic
335C22×C22⋊C4—432no—
336C22×C22⋊C4—432no—
337C22×C22⋊C4—432no—
338C22×C22⋊C4—432no—
339C22×C22⋊C4—432no—
340C22×C22⋊C4—432no—
341C22×C42—431no—
342C22×C42—431no—
343C22×C42C2×D4311yescharacteristic
344#390—438no—
345#388—868no—
346#388—868no—
347C2×#95—432no—
348C2×#95—432no—
349C2×#95—432no—
350C2×#95—432no—
351C2×#95—431no—
352C2×#95C2×D4312yes—
353C2×#95C2×D4312yes—
354C2×#95C2×D4311yescharacteristic
355C43#1444511yescharacteristic, complemented, Sylow
356C25—432no—
357C22×D4—434no—
358C22×D4—864no—
359C22×D4—1721no—
360C22×D4—1721no—
361C22×D4—1722no—
362C23×C4—432no—
363C23×C4—432no—
364C23×C4—432no—
365C23×C4C22×D4312yes—
366C23×C4C22×D4311yescharacteristic
367C23×C4C22×D4311yescharacteristic
368C23×C4C22×D4312yes—
369C23×C4C22×D4311yescharacteristic
370C2×C4⋊C4—41no—
371C2×C4⋊C4—41no—
372C2×C4⋊C4—438no—
373C2×C4⋊C4—864no—
374C2×C4⋊C4—1722no—
375C2×C4⋊C4—1722no—
376C2×C4⋊C4—1722no—
377C2×C4⋊C4—1722no—
378C2×C4⋊C4C4×D4314yes—
379C2×C22⋊C4—438no—
380C2×C22⋊C4—438no—
381C2×C22⋊C4—864no—
382C2×C22⋊C4—864no—
383C2×C22⋊C4—864no—
384C2×C22⋊C4—864no—
385C2×C22⋊C4—864no—
386C2×C22⋊C4—864no—
387C2×C22⋊C4—864no—
388C2×C22⋊C4—864no—
389C2×C22⋊C4—1722no—
390C2×C22⋊C4—1722no—
391C2×C22⋊C4—1722no—
392C2×C22⋊C4—1722no—
393C2×C22⋊C4—1722no—
394C2×C22⋊C4—1722no—
395C2×C22⋊C4—1722no—
396C2×C22⋊C4—1722no—
397C2×C42—24no—
398C2×C42—41no—
399C2×C42—434no—
400C2×C42—864no—
401C2×C42—1722no—
402C2×C42—1721no—
403#95—24no—
404#95—24no—
405#95—41no—
406#95—864no—
407#95—864no—
408#95—864no—
409#95—864no—
410#95—1721no—
411C24—434no—
412C24—862no—
413C24—862no—
414C24—862no—
415C24—862no—
416C24—862no—
417C24—862no—
418C24—862no—
419C24—862no—
420C24—862no—
421C24—862no—
422C24—862no—
423C24—862no—
424C24—862no—
425C24—862no—
426C24C23×D4311yescharacteristic
427C2×D4—868no—
428C2×D4—1724no—
429C2×D4—1724no—
430C2×D4—1728no—
431C2×D4—1728no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—434no—
457C22×C4—434no—
458C22×C4—434no—
459C22×C4—434no—
460C22×C4—862no—
461C22×C4—862no—
462C22×C4—862no—
463C22×C4—862no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4C2×C4×D4312yes—
478C22×C4C2×C4×D4312yes—
479C22×C4C2×C4×D4312yes—
480C22×C4#1062189814yes—
481C22×C4D4×D4314yes—
482C4⋊C4—44no—
483C4⋊C4—1728no—
484C4⋊C4—1728no—
485C22⋊C4—8616no—
486C22⋊C4—8616no—
487C22⋊C4—1728no—
488C22⋊C4—1728no—
489C22⋊C4—1728no—
490C22⋊C4—1728no—
491C42—44no—
492C42—1724no—
493C42—1724no—
494C23—864no—
495C23—864no—
496C23—864no—
497C23—864no—
498C23—864no—
499C23—864no—
500C23—864no—
501C23—1722no—
502C23—1722no—
503C23—1722no—
504C23—1722no—
505C23—1722no—
506C23—1722no—
507C23—1722no—
508C23—1722no—
509C23—1722no—
510C23—1722no—
511C23—1722no—
512C23—1722no—
513C23—1722no—
514C23—1722no—
515C23—1722no—
516C23—1722no—
517C23—1722no—
518C23—1722no—
519C23—1722no—
520C23—1722no—
521C23—1722no—
522C23—1722no—
523C23—1722no—
524C23—1722no—
525C23—1722no—
526C23—1722no—
527C23—1722no—
528C23—1722no—
529C23C22×C4×D4311yescharacteristic
530C23C2×D4×D4312yes—
531C23#41×D4312yes—
532C23C2×#1062189812yes—
533C23#1306337011yescharacteristic
534C23#1306337011yescharacteristic
535C23#1306337112yes—
536C23#1306337112yes—
537C23#1306337312yes—
538D4—17216no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—438no—
568C2×C4—864no—
569C2×C4—864no—
570C2×C4—864no—
571C2×C4—864no—
572C2×C4—864no—
573C2×C4—864no—
574C2×C4—864no—
575C2×C4—864no—
576C2×C4—864no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4—1722no—
584C2×C4—1722no—
585C2×C4—1722no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4#1306328214yes—
589C22—3442no—
590C22—3442no—
591C22—3442no—
592C22—3442no—
593C22—3442no—
594C22—3442no—
595C22—3442no—
596C22—3442no—
597C22—1724no—
598C22—1724no—
599C22—1724no—
600C22—1724no—
601C22—1724no—
602C22—1724no—
603C22—1724no—
604C22C2×#1306328211yescharacteristic
605C22C4×D4×D4312yes—
606C22#1458337211yescharacteristic
607C22#1458337311yescharacteristic
608C22#1458338112yes—
609C22#1458346012yes—
610C22#1458347912yes—
611C22#1458348212yes—
612C22#1458348212yes—
613C22#1458348812yes—
614C22#1458349712yes—
615C22#1458353111yescharacteristic
616C22#1458355012yes—
617C22#1458356712yes—
618C22#1458357012yes—
619C22#1458361212yes—
620C22#1458362112yes—
621C22#1458363311yescharacteristic
622C22#1458364111yescharacteristic
623C22#1458364512yes—
624C22#1458364811yescharacteristic
625C4—24no—
626C4—44no—
627C4—42no—
628C4—42no—
629C4—82no—
630C4—868no—
631C4—3442no—
632C4—1724no—
633C2—3444no—
634C2#1913719011yescharacteristic
635C2#1913729412yes—
636C2#1913754012yes—
637C2#1913765811yescharacteristic
638C2#1913776711yescharacteristic
639C2#1914096112yes—
640C2#1914155712yes—
641C2#1914162212yes—
642C2#1914257112yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1436D43
hypocenterC43#14445
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#14582790C2semidirect
3. C2×#14582788C2semidirect
4. #19132839C2semidirect
5. #19132839C2semidirect
7. #19132827C2semidirect
8. Dic43⋊#95C2semidirect
9. C43×#1436C2semidirect
21. #14582800C4semidirect
48. C2×Dic43⋊C4D4semidirect
319. #1436D43semidirect
355. C43#14445semidirect

Maximal subgroups

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

subgroupindex
C2×#145828002
C2×#145827902
C2×#145827882
#191328392
#191328352
#191328272
Dic43⋊#952
C43×#14362
#1444543