Finite Group Databasebeta

← #25023368

Subgroups — #25023368

Order 11008.

1830 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic86C211yesmaximal, characteristic, complemented
2C2×#14582812C211yesmaximal, characteristic
3C2×#14582791C212yesmaximal
4C2×#14582790C211yesmaximal, characteristic
5#19132865C211yesmaximal, characteristic, complemented
6#19132860C211yesmaximal, characteristic, complemented
7#19132859C212yesmaximal, complemented
8#19132841C211yesmaximal, characteristic
9#19132839C212yesmaximal
10#19132819C212yesmaximal, complemented
11C43×#1434C211yesmaximal, characteristic, complemented
12C23×Dic86C2211yescharacteristic
13C2×C4×Dic86—28no—
14C2×C4×Dic86—24no—
15C22×C4⋊Dic43C2211yescharacteristic
16C22×C4⋊Dic43C2212yes—
17C22×Dic43⋊C4C2212yes—
18C22×Dic43⋊C4C2211yescharacteristic
19C22×(C2×D43)⋊C4C2211yescharacteristic
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2212yes—
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2212yes—
24C22×C4×Dic43C2212yes—
25#14582812C418yescomplemented
26#14582791—28no—
27#14582790—24no—
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C22×C42×C43C2211yescharacteristic
36C2×#95×C43C2212yes—
37C2×#95×C43C2211yescharacteristic
38C2×#95×C43C2212yes—
39C2×#95×C43C2211yescharacteristic
40C24×D43C2311yescharacteristic
41C22×Dic86—22no—
42C22×Dic86—22no—
43C22×Dic86—24no—
44C22×Dic86—24no—
45C22×Dic86C2×C414yes—
46C23×Dic43C2311yescharacteristic
47C23×Dic43C2311yescharacteristic
48C23×Dic43C2311yescharacteristic
49C23×Dic43C2312yes—
50C23×Dic43C2312yes—
51C4×Dic86—232no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—24no—
54C2×C4⋊Dic43—24no—
55C2×C4⋊Dic43—42no—
56C2×C4⋊Dic43—42no—
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—24no—
60C2×Dic43⋊C4—22no—
61C2×Dic43⋊C4—42no—
62C2×(C2×D43)⋊C4—22no—
63C2×(C2×D43)⋊C4—22no—
64C2×(C2×D43)⋊C4—24no—
65C2×(C2×D43)⋊C4—24no—
66C2×(C2×D43)⋊C4—22no—
67C2×(C2×D43)⋊C4—22no—
68C2×(C2×D43)⋊C4—24no—
69C2×(C2×D43)⋊C4—24no—
70C2×(C2×D43)⋊C4—42no—
71C2×(C2×D43)⋊C4—42no—
72C2×(C2×D43)⋊C4—42no—
73C2×(C2×D43)⋊C4C2×C414yes—
74C2×(C2×D43)⋊C4C2×C418yes—
75C2×C4×Dic43—24no—
76C2×C4×Dic43—24no—
77C2×C4×Dic43D418yes—
78C43⋊#95—22no—
79C43⋊#95—22no—
80C43⋊#95—24no—
81C43⋊#95—24no—
82C43⋊#95—42no—
83C43⋊#95—42no—
84C43⋊#95C2×C418yes—
85C23×C4×C43C2312yes—
86C23×C4×C43C2312yes—
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2311yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C2×C42×C43—24no—
91C2×C42×C43D414yes—
92#95×C43—24no—
93#95×C43—22no—
94#95×C43—42no—
95#95×C43C2×C414yes—
96C24×C43C2411yescharacteristic
97C23×D43—22no—
98C23×D43—21no—
99C23×D43—22no—
100C23×D43—21no—
101C23×D43—21no—
102C23×D43—22no—
103C23×D43—21no—
104C23×D43—21no—
105C23×D43—21no—
106C23×D43—22no—
107C23×D43C22×C412yes—
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—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—21no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43C22×C414yes—
131C22×C4×C43C22×C412yes—
132C22×C4×C43C2×D412yes—
133C22×C4×C43C2×D412yes—
134C22×C4×C43C2×D412yes—
135C22×C4×C43C2×D414yes—
136C22×C4×C43#4112yes—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—21no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—21no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—21no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43C22×C412yes—
162C22×Dic43C22×C414yes—
163C22×Dic43C2×D414yes—
164C22×Dic43C2×D414yes—
165C22×Dic43#4114yes—
166C2×Dic86—28no—
167C2×Dic86—216no—
168C2×Dic86—28no—
169C2×Dic86—28no—
170C2×Dic86—216no—
171C42×C43—28no—
172(C2×D43)⋊C4—28no—
173(C2×D43)⋊C4—216no—
174(C2×D43)⋊C4—48no—
175(C2×D43)⋊C4—44no—
176(C2×D43)⋊C4—44no—
177C4⋊Dic43—28no—
178C4⋊Dic43—48no—
179Dic43⋊C4—216no—
180Dic43⋊C4—44no—
181C4×Dic43—216no—
182C23×C43C23×C411yescharacteristic
183C23×C43C22×D412yes—
184C23×C43C22×D411yescharacteristic
185C23×C43C2×#4112yes—
186C23×C43C2×#4111yescharacteristic
187C23×C43H(5,𝔽2)11yescharacteristic
188C23×C43H(5,𝔽2)12yes—
189C23×C432−1+411yescharacteristic
190C23×C432−1+411yescharacteristic
191C23×C432−1+412yes—
192C23×C432−1+411yescharacteristic
193C22×D43—24no—
194C22×D43—22no—
195C22×D43—22no—
196C22×D43—22no—
197C22×D43—24no—
198C22×D43—41no—
199C22×D43—42no—
200C22×D43—41no—
201C22×D43—42no—
202C22×D43—41no—
203C22×D43—42no—
204C22×D43—42no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—42no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—42no—
211C22×D43—42no—
212C22×D43—41no—
213C22×D43—42no—
214C22×D43—42no—
215C22×D43—42no—
216C2×C4×C43—24no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
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—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
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×C43C4×D414yes—
244C2×C4×C43#12014yes—
245C2×Dic43—24no—
246C2×Dic43—24no—
247C2×Dic43—24no—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—22no—
252C2×Dic43—24no—
253C2×Dic43—24no—
254C2×Dic43—24no—
255C2×Dic43—24no—
256C2×Dic43—41no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—41no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—42no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—42no—
270C2×Dic43—41no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43C4×D418yes—
274Dic86—232no—
275#14301—431nomaximal, Sylow
276C22×C43C2×C4×D412yes—
277C22×C43C2×C4×D411yescharacteristic
278C22×C43#51911yescharacteristic
279C22×C43#52011yescharacteristic
280C22×C43#52012yes—
281C22×C43C2×#12011yescharacteristic
282C22×C43#52512yes—
283C22×C43#52511yescharacteristic
284C22×C43#53512yes—
285C22×C43#53511yescharacteristic
286C22×C43#53612yes—
287C22×C43#53612yes—
288C22×C43#53611yescharacteristic
289C22×C43#53611yescharacteristic
290C22×C43#53712yes—
291C22×C43#53711yescharacteristic
292C22×C43#54111yescharacteristic
293C22×C43#54112yes—
294C22×C43#54212yes—
295C22×C43#54211yescharacteristic
296C22×C43#54212yes—
297C22×C43#54212yes—
298C22×C43#54212yes—
299C2×D43—44no—
300C2×D43—42no—
301C2×D43—44no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—82no—
308C2×D43—81no—
309C2×D43—82no—
310C4×C43—24no—
311C4×C43—24no—
312C4×C43—44no—
313C4×C43—42no—
314C4×C43—82no—
315Dic43—28no—
316Dic43—42no—
317Dic43—44no—
318Dic43—81no—
319Dic43—81no—
320C22×C4×Q8—431no—
321C2×#393—431no—
322C2×#388—431no—
323C2×#388—432no—
324#1446—431no—
325#1444—432no—
326#1444—431no—
327#1439—432no—
328#1439—431no—
329#1434—432no—
330#1434D4311yescharacteristic, complemented
331C2×C43C4×#12011yescharacteristic
332C2×C43#232312yes—
333C2×C43#232311yescharacteristic
334C2×C43#232612yes—
335C2×C43#232611yescharacteristic
336C2×C43#261411yescharacteristic
337C2×C43#261511yescharacteristic
338C2×C43#263211yescharacteristic
339C2×C43#263212yes—
340C2×C43#263711yescharacteristic
341C2×C43#263712yes—
342D43—82no—
343C23×Q8—431no—
344C2×C4×Q8—868no—
345C2×C4×Q8—864no—
346C22×C4⋊C4—432no—
347C22×C4⋊C4—431no—
348C22×C4⋊C4—431no—
349C22×C4⋊C4—432no—
350C22×C22⋊C4—432no—
351C22×C22⋊C4—431no—
352C22×C22⋊C4—431no—
353C22×C22⋊C4—432no—
354C22×C22⋊C4—431no—
355C22×C42—432no—
356C22×C42C2×D4311yescharacteristic
357#393—438no—
358#388—868no—
359#388—864no—
360C2×#95—432no—
361C2×#95—431no—
362C2×#95—432no—
363C2×#95—432no—
364C2×#95—431no—
365C2×#95—432no—
366C2×#95—432no—
367C2×#95C2×D4312yes—
368C2×#95C2×D4311yescharacteristic
369C2×#95C2×D4312yes—
370C2×#95C2×D4311yescharacteristic
371C43#1430111yescharacteristic, complemented, Sylow
372C25—431no—
373C22×Q8—434no—
374C22×Q8—864no—
375C22×Q8—864no—
376C22×Q8—862no—
377C22×Q8—862no—
378C23×C4—432no—
379C23×C4—432no—
380C23×C4—431no—
381C23×C4—431no—
382C23×C4—431no—
383C23×C4C22×D4312yes—
384C23×C4C22×D4312yes—
385C23×C4C22×D4311yescharacteristic
386C23×C4C22×D4311yescharacteristic
387C23×C4C22×D4311yescharacteristic
388C4×Q8—8632no—
389C2×C4⋊C4—864no—
390C2×C4⋊C4—864no—
391C2×C4⋊C4—864no—
392C2×C4⋊C4—864no—
393C2×C4⋊C4—862no—
394C2×C4⋊C4—864no—
395C2×C4⋊C4—862no—
396C2×C4⋊C4—1722no—
397C2×C4⋊C4—1722no—
398C2×C4⋊C4—1722no—
399C2×C22⋊C4—438no—
400C2×C22⋊C4—434no—
401C2×C22⋊C4—864no—
402C2×C22⋊C4—864no—
403C2×C22⋊C4—862no—
404C2×C22⋊C4—862no—
405C2×C22⋊C4—864no—
406C2×C22⋊C4—862no—
407C2×C22⋊C4—862no—
408C2×C22⋊C4—864no—
409C2×C22⋊C4—1722no—
410C2×C22⋊C4—1722no—
411C2×C22⋊C4—1722no—
412C2×C42—24no—
413C2×C42—438no—
414C2×C42—864no—
415C2×C42—864no—
416C2×C42D17214yes—
417#95—22no—
418#95—24no—
419#95—42no—
420#95—438no—
421#95—864no—
422#95—864no—
423#95—862no—
424#95—862no—
425#95—1722no—
426#95—1722no—
427#95C4×D4314yes—
428C24—432no—
429C24—862no—
430C24—861no—
431C24—862no—
432C24—861no—
433C24—861no—
434C24—862no—
435C24—861no—
436C24—861no—
437C24—862no—
438C24—861no—
439C24C23×D4311yescharacteristic
440C2×Q8—8616no—
441C2×Q8—868no—
442C2×Q8—8616no—
443C2×Q8—868no—
444C2×Q8—868no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—434no—
468C22×C4—434no—
469C22×C4—434no—
470C22×C4—432no—
471C22×C4—434no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—861no—
478C22×C4—862no—
479C22×C4—861no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—862no—
490C22×C4—861no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4C2×C4×D4314yes—
497C22×C4C2×C4×D4312yes—
498C22×C4C2×D17212yes—
499C22×C4C2×D17212yes—
500C22×C4C2×D17212yes—
501C22×C4#1062189812yes—
502C22×C4D4×D4314yes—
503C4⋊C4—8616no—
504C4⋊C4—868no—
505C4⋊C4—1724no—
506C4⋊C4—1728no—
507C22⋊C4—8616no—
508C22⋊C4—868no—
509C22⋊C4—1724no—
510C22⋊C4—1728no—
511C22⋊C4—1724no—
512C42—28no—
513C42—8616no—
514C23—864no—
515C23—862no—
516C23—862no—
517C23—862no—
518C23—864no—
519C23—1721no—
520C23—1722no—
521C23—1721no—
522C23—1722no—
523C23—1721no—
524C23—1722no—
525C23—1722no—
526C23—1721no—
527C23—1721no—
528C23—1722no—
529C23—1721no—
530C23—1721no—
531C23—1722no—
532C23—1722no—
533C23—1721no—
534C23—1722no—
535C23—1722no—
536C23—1722no—
537C23C22×C4×D4311yescharacteristic
538C23C2×D4×D4312yes—
539C23C22×D17211yescharacteristic
540C23#41×D4312yes—
541C23C2×#1062189811yescharacteristic
542C23#1306337011yescharacteristic
543C23#1306337112yes—
544C23#1306337211yescharacteristic
545C23#1306337211yescharacteristic
546C23#1306337212yes—
547C23#1306337311yescharacteristic
548Q8—8632no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—438no—
577C2×C4—864no—
578C2×C4—864no—
579C2×C4—864no—
580C2×C4—864no—
581C2×C4—864no—
582C2×C4—864no—
583C2×C4—862no—
584C2×C4—864no—
585C2×C4—864no—
586C2×C4—864no—
587C2×C4—864no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1722no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1722no—
595C2×C4—1721no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4—1721no—
600C2×C4—1722no—
601C2×C4—1721no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4C4×D17214yes—
606C2×C4#1306329514yes—
607C22—3441no—
608C22—3442no—
609C22—3441no—
610C22—3442no—
611C22—3441no—
612C22—3441no—
613C22—1724no—
614C22—1722no—
615C22—1722no—
616C22—1724no—
617C22—1722no—
618C22C4×D4×D4312yes—
619C22C2×C4×D17211yescharacteristic
620C22#1458337511yescharacteristic
621C22#1458337811yescharacteristic
622C22#1458337912yes—
623C22C2×#1306329511yescharacteristic
624C22#1458340812yes—
625C22#1458341111yescharacteristic
626C22#1458346512yes—
627C22#1458346811yescharacteristic
628C22#1458347112yes—
629C22#1458347112yes—
630C22#1458347511yescharacteristic
631C22#1458347511yescharacteristic
632C22#1458347912yes—
633C22#1458348011yescharacteristic
634C22#1458350711yescharacteristic
635C22#1458350812yes—
636C22#1458351312yes—
637C22#1458351411yescharacteristic
638C22#1458351512yes—
639C22#1458351512yes—
640C22#1458352012yes—
641C4—24no—
642C4—24no—
643C4—44no—
644C4—42no—
645C4—82no—
646C4—868no—
647C4—3441no—
648C4—3441no—
649C4—1722no—
650C4—1724no—
651C2—3442no—
652C2C4×#1306329511yescharacteristic
653C2#1913727612yes—
654C2#1913727811yescharacteristic
655C2#1913730412yes—
656C2#1913730611yescharacteristic
657C2#1914031711yescharacteristic
658C2#1914032111yescharacteristic
659C2#1914045811yescharacteristic
660C2#1914045912yes—
661C2#1914050511yescharacteristic
662C2#1914050912yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1434C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1434D43
hypocenterC43#14301
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic86C2semidirect
5. #19132865C2semidirect
6. #19132860C2semidirect
7. #19132859C2semidirect
10. #19132819C2semidirect
11. C43×#1434C2semidirect
25. #14582812C4semidirect
330. #1434D43semidirect
371. C43#14301semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic862
C2×#145828122
C2×#145827912
C2×#145827902
#191328652
#191328602
#191328592
#191328412
#191328392
#191328192
C43×#14342
#1430143