Finite Group Databasebeta

← #25023161

Subgroups — #25023161

Order 11008.

1658 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
1C2×#14582801C211yesmaximal, characteristic
2C2×#14582788C212yesmaximal, complemented
3#19132847C212yesmaximal, complemented
4#19132843C212yesmaximal, complemented
5#19132839C212yesmaximal, complemented
6#19132835C212yesmaximal
7#19132831C212yesmaximal, complemented
8C4×C43⋊#95C211yesmaximal, characteristic, complemented
9C43×#1434C211yesmaximal, characteristic, complemented
10C23×D172C2211yescharacteristic
11C22×C4⋊Dic43C2211yescharacteristic
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#14582801C418yescomplemented
22#14582788—28no—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C22×C42×C43C2211yescharacteristic
29C2×#95×C43C2212yes—
30C2×#95×C43C2212yes—
31C2×#95×C43C2211yescharacteristic
32C2×#95×C43C2211yescharacteristic
33C24×D43C2312yes—
34C22×D172—24no—
35C22×D172—41no—
36C22×D172—41no—
37C22×D172—42no—
38C22×D172C2×C414yes—
39C23×Dic43C2312yes—
40C23×Dic43C2312yes—
41C23×Dic43C2312yes—
42C2×C4⋊Dic43—42no—
43C2×C4⋊Dic43C2×C414yes—
44C2×Dic43⋊C4—24no—
45C2×Dic43⋊C4—42no—
46C2×Dic43⋊C4—42no—
47C2×(C2×D43)⋊C4—24no—
48C2×(C2×D43)⋊C4—24no—
49C2×(C2×D43)⋊C4—24no—
50C2×(C2×D43)⋊C4—24no—
51C2×(C2×D43)⋊C4—24no—
52C2×(C2×D43)⋊C4—24no—
53C2×(C2×D43)⋊C4—42no—
54C2×(C2×D43)⋊C4—42no—
55C2×(C2×D43)⋊C4—42no—
56C2×(C2×D43)⋊C4—42no—
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)⋊C4C2×C418yes—
64C2×(C2×D43)⋊C4C2×C418yes—
65C2×C4×Dic43—22no—
66C2×C4×Dic43—41no—
67C2×C4×Dic43—41no—
68C2×C4×Dic43—41no—
69C2×C4×Dic43—41no—
70C2×C4×Dic43D414yescomplemented
71C43⋊#95—24no—
72C43⋊#95—24no—
73C43⋊#95—24no—
74C43⋊#95—42no—
75C43⋊#95—42no—
76C23×C4×C43C2312yes—
77C23×C4×C43C2312yes—
78C23×C4×C43C2311yescharacteristic
79C23×C4×C43C2311yescharacteristic
80C23×C4×C43C2311yescharacteristic
81C2×C42×C43—41no—
82C2×C42×C43—41no—
83C2×C42×C43C2×C414yes—
84#95×C43—24no—
85#95×C43—24no—
86#95×C43—41no—
87#95×C43—41no—
88C24×C43C2411yescharacteristic
89C23×D43—22no—
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×D43C22×C414yes—
104C22×C4×C43—22no—
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—21no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
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—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—21no—
128C22×C4×C43—22no—
129C22×C4×C43C22×C412yes—
130C22×C4×C43C22×C412yes—
131C22×C4×C43C22×C412yes—
132C22×C4×C43C2×D412yes—
133C22×C4×C43#4114yes—
134C22×C4×C43#4112yes—
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×Dic43C22×C414yes—
154C22×Dic43C2×D414yes—
155C22×Dic43#4114yes—
156C2×D172—28no—
157C2×D172—44no—
158C2×D172—44no—
159C2×D172—48no—
160C2×D172—48no—
161C42×C43—44no—
162(C2×D43)⋊C4—216no—
163(C2×D43)⋊C4—48no—
164(C2×D43)⋊C4—48no—
165(C2×D43)⋊C4—48no—
166(C2×D43)⋊C4—48no—
167(C2×D43)⋊C4—48no—
168C4⋊Dic43—44no—
169Dic43⋊C4—48no—
170C4×Dic43—44no—
171C4×Dic43—44no—
172C23×C43C23×C411yescharacteristic
173C23×C43C22×D411yescharacteristic
174C23×C43C2×#4112yes—
175C23×C43C2×#4112yes—
176C23×C43C2×#4111yescharacteristic
177C23×C43H(5,𝔽2)11yescharacteristic
178C23×C43H(5,𝔽2)11yescharacteristic
179C23×C43H(5,𝔽2)12yes—
180C23×C43H(5,𝔽2)12yes—
181C23×C43H(5,𝔽2)11yescharacteristic
182C23×C432−1+411yescharacteristic
183C22×D43—24no—
184C22×D43—24no—
185C22×D43—24no—
186C22×D43—24no—
187C22×D43—24no—
188C22×D43—24no—
189C22×D43—24no—
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—
216C22×D43—42no—
217C22×D43—42no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—24no—
226C2×C4×C43—24no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
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×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43#11714yes—
248C2×C4×C43C4×D414yes—
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—24no—
252C2×Dic43—24no—
253C2×Dic43—24no—
254C2×Dic43—24no—
255C2×Dic43—24no—
256C2×Dic43—24no—
257C2×Dic43—24no—
258C2×Dic43—42no—
259C2×Dic43—42no—
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—
270D172—416no—
271#14278—431nomaximal, Sylow
272C22×C43C2×#11711yescharacteristic
273C22×C43C2×C4×D411yescharacteristic
274C22×C43C4×#4111yescharacteristic
275C22×C43#51811yescharacteristic
276C22×C43#51811yescharacteristic
277C22×C43#51811yescharacteristic
278C22×C43#52011yescharacteristic
279C22×C43#52912yes—
280C22×C43#53212yes—
281C22×C43#53411yescharacteristic
282C22×C43#53512yes—
283C22×C43#53711yescharacteristic
284C22×C43#53812yes—
285C22×C43#53812yes—
286C22×C43#53812yes—
287C22×C43#53812yes—
288C22×C43#53811yescharacteristic
289C22×C43#53911yescharacteristic
290C22×C43#54012yes—
291C22×C43#54012yes—
292C22×C43#54012yes—
293C22×C43#54212yes—
294C22×C43#54212yes—
295C2×D43—44no—
296C2×D43—44no—
297C2×D43—44no—
298C2×D43—44no—
299C2×D43—44no—
300C2×D43—44no—
301C2×D43—44no—
302C2×D43—82no—
303C2×D43—82no—
304C2×D43—82no—
305C2×D43—82no—
306C2×D43—82no—
307C2×D43—82no—
308C2×D43—82no—
309C2×D43—82no—
310C4×C43—24no—
311C4×C43—24no—
312C4×C43—42no—
313C4×C43—82no—
314C4×C43—82no—
315Dic43—44no—
316Dic43—44no—
317Dic43—44no—
318C2×#390—431no—
319C2×#388—432no—
320#1441—432no—
321#1440—432no—
322#1439—432no—
323#1438—432no—
324#1437—432no—
325#1434D4311yescharacteristic, complemented
326C4×#95—431no—
327C2×C43#229311yescharacteristic
328C2×C43#231211yescharacteristic
329C2×C43#231911yescharacteristic
330C2×C43#232511yescharacteristic
331C2×C43#232811yescharacteristic
332C2×C43#233311yescharacteristic
333C2×C43#233711yescharacteristic
334C2×C43#264812yes—
335C2×C43#265112yes—
336C2×C43#266112yes—
337C2×C43#266212yes—
338D43—84no—
339C23×D4—431no—
340C22×C4⋊C4—431no—
341C22×C4⋊C4—432no—
342C22×C22⋊C4—432no—
343C22×C22⋊C4—432no—
344C22×C22⋊C4—432no—
345C22×C22⋊C4—432no—
346C22×C22⋊C4—432no—
347C22×C22⋊C4—432no—
348C22×C42—431no—
349C22×C42—431no—
350C22×C42C2×D4311yescharacteristic
351#390—438no—
352#388—868no—
353C2×#95—432no—
354C2×#95—432no—
355C2×#95—432no—
356C2×#95—432no—
357C2×#95—432no—
358C2×#95C2×D4312yes—
359C2×#95C2×D4312yes—
360C2×#95C2×D4311yescharacteristic
361C2×#95C2×D4311yescharacteristic
362C43#1427811yescharacteristic, complemented, Sylow
363C25—432no—
364C22×D4—434no—
365C22×D4—864no—
366C22×D4—1721no—
367C22×D4—1721no—
368C22×D4—1722no—
369C23×C4—432no—
370C23×C4—432no—
371C23×C4—432no—
372C23×C4C22×D4312yes—
373C23×C4C22×D4312yes—
374C23×C4C22×D4311yescharacteristic
375C23×C4C22×D4311yescharacteristic
376C23×C4C22×D4311yescharacteristic
377C2×C4⋊C4—434no—
378C2×C4⋊C4—864no—
379C2×C4⋊C4—1722no—
380C2×C4⋊C4—1722no—
381C2×C4⋊C4—1722no—
382C2×C22⋊C4—438no—
383C2×C22⋊C4—438no—
384C2×C22⋊C4—864no—
385C2×C22⋊C4—864no—
386C2×C22⋊C4—864no—
387C2×C22⋊C4—864no—
388C2×C22⋊C4—864no—
389C2×C22⋊C4—864no—
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×C22⋊C4—1722no—
398C2×C22⋊C4—1722no—
399C2×C22⋊C4—1722no—
400C2×C42—41no—
401C2×C42—41no—
402C2×C42—434no—
403C2×C42—862no—
404C2×C42—1721no—
405C2×C42—1721no—
406C2×C42—1721no—
407C2×C42—1721no—
408C2×C42C4×D4314yes—
409#95—24no—
410#95—24no—
411#95—41no—
412#95—41no—
413#95—864no—
414#95—864no—
415#95—864no—
416#95—1722no—
417#95—1722no—
418C24—434no—
419C24—862no—
420C24—862no—
421C24—862no—
422C24—862no—
423C24—862no—
424C24—862no—
425C24—862no—
426C24—862no—
427C24—862no—
428C24—862no—
429C24—862no—
430C24—862no—
431C24—862no—
432C24—862no—
433C24C23×D4311yescharacteristic
434C2×D4—868no—
435C2×D4—1724no—
436C2×D4—1724no—
437C2×D4—1728no—
438C2×D4—1728no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
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—434no—
465C22×C4—434no—
466C22×C4—434no—
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×C4—862no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4C2×C4×D4312yes—
486C22×C4C2×C4×D4312yes—
487C22×C4C2×C4×D4312yes—
488C22×C4#1062189814yes—
489C22×C4D4×D4312yes—
490C22×C4#1062190212yes—
491C4⋊C4—1724no—
492C4⋊C4—1728no—
493C22⋊C4—8616no—
494C22⋊C4—1728no—
495C22⋊C4—1728no—
496C22⋊C4—1728no—
497C22⋊C4—1728no—
498C22⋊C4—1728no—
499C42—44no—
500C42—1724no—
501C42—1724no—
502C23—864no—
503C23—864no—
504C23—864no—
505C23—864no—
506C23—864no—
507C23—864no—
508C23—864no—
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—
529C23—1722no—
530C23—1722no—
531C23—1722no—
532C23—1722no—
533C23—1722no—
534C23—1722no—
535C23—1722no—
536C23—1722no—
537C23C22×C4×D4311yescharacteristic
538C23C2×D4×D4311yescharacteristic
539C23#41×D4312yes—
540C23C2×#1062189812yes—
541C23C2×#1062190211yescharacteristic
542C23#1306337011yescharacteristic
543C23#1306337011yescharacteristic
544C23#1306337112yes—
545C23#1306337112yes—
546C23#1306337111yescharacteristic
547C23#1306337211yescharacteristic
548D4—17216no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—42no—
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—42no—
577C2×C4—42no—
578C2×C4—864no—
579C2×C4—864no—
580C2×C4—864no—
581C2×C4—864no—
582C2×C4—864no—
583C2×C4—864no—
584C2×C4—864no—
585C2×C4—864no—
586C2×C4—864no—
587C2×C4—1722no—
588C2×C4—1722no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4#1306328214yes—
600C2×C4#1306328714yes—
601C22—3442no—
602C22—3442no—
603C22—3442no—
604C22—3442no—
605C22—3442no—
606C22—3442no—
607C22—3442no—
608C22—3442no—
609C22—1724no—
610C22—1724no—
611C22—1724no—
612C22—1724no—
613C22—1724no—
614C22—1724no—
615C22—1724no—
616C22C2×#1306328211yescharacteristic
617C22C2×#1306328711yescharacteristic
618C22#1458336711yescharacteristic
619C22#1458337211yescharacteristic
620C22#1458337311yescharacteristic
621C22#1458337311yescharacteristic
622C22#1458337911yescharacteristic
623C22#1458343612yes—
624C22#1458344612yes—
625C22#1458345711yescharacteristic
626C22#1458346712yes—
627C22#1458347611yescharacteristic
628C22#1458348212yes—
629C22#1458348212yes—
630C22#1458348512yes—
631C22#1458348812yes—
632C22#1458348911yescharacteristic
633C22#1458349811yescharacteristic
634C22#1458350112yes—
635C22#1458350412yes—
636C22#1458350512yes—
637C22#1458351512yes—
638C22#1458352012yes—
639C4—24no—
640C4—24no—
641C4—42no—
642C4—82no—
643C4—82no—
644C4—1724no—
645C4—1724no—
646C4—1724no—
647C2—3444no—
648C2#1913705611yescharacteristic
649C2#1913719011yescharacteristic
650C2#1913723911yescharacteristic
651C2#1913729511yescharacteristic
652C2#1913731811yescharacteristic
653C2#1913735711yescharacteristic
654C2#1913740511yescharacteristic
655C2#1914058912yes—
656C2#1914063412yes—
657C2#1914072712yes—
658C2#1914073812yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1434C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1434D43
hypocenterC43#14278
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#14582788C2semidirect
3. #19132847C2semidirect
4. #19132843C2semidirect
5. #19132839C2semidirect
7. #19132831C2semidirect
8. C4×C43⋊#95C2semidirect
9. C43×#1434C2semidirect
21. #14582801C4semidirect
70. C2×C4×Dic43D4semidirect
325. #1434D43semidirect
362. C43#14278semidirect

Maximal subgroups

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

subgroupindex
C2×#145828012
C2×#145827882
#191328472
#191328432
#191328392
#191328352
#191328312
C4×C43⋊#952
C43×#14342
#1427843