Finite Group Databasebeta

← #25023320

Subgroups — #25023320

Order 11008.

1566 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582761C211yesmaximal, characteristic
2C2×#14582756C211yesmaximal, characteristic
3C2×#14582746C211yesmaximal, characteristic
4#19132860C211yesmaximal, characteristic, complemented
5#19132858C211yesmaximal, characteristic, complemented
6#19132851C211yesmaximal, characteristic, complemented
7#19132841C212yesmaximal
8#19132839C212yesmaximal
9#19132829C212yesmaximal, complemented
10#19132826C212yesmaximal, complemented
11C43×#1442C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×C4⋊Dic43C2212yes—
14C22×C4⋊Dic43C2211yescharacteristic
15C22×Dic43⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2211yescharacteristic
17C22×(C2×D43)⋊C4C2211yescharacteristic
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2212yes—
20C22×C4×Dic43C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22#14582761C418yescomplemented
23#14582756—24no—
24#14582746—24no—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C2×#95×C43C2211yescharacteristic
35C2×#95×C43C2212yes—
36C2×#95×C43C2212yes—
37C2×#95×C43C2211yescharacteristic
38C24×D43C2311yescharacteristic
39C23×Dic43C2312yes—
40C23×Dic43C2312yes—
41C23×Dic43C2311yescharacteristic
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2311yescharacteristic
44C22×C4×D43—42no—
45C22×C4×D43—42no—
46C22×C4×D43C2×C414yes—
47C22×C4×D43D414yes—
48C22×C4×D43Q814yes—
49C2×C4⋊Dic43—22no—
50C2×C4⋊Dic43—24no—
51C2×C4⋊Dic43—42no—
52C2×C4⋊Dic43—42no—
53C2×C4⋊Dic43—42no—
54C2×Dic43⋊C4—24no—
55C2×Dic43⋊C4—42no—
56C2×Dic43⋊C4—42no—
57C2×(C2×D43)⋊C4—22no—
58C2×(C2×D43)⋊C4—22no—
59C2×(C2×D43)⋊C4—22no—
60C2×(C2×D43)⋊C4—22no—
61C2×(C2×D43)⋊C4—22no—
62C2×(C2×D43)⋊C4—22no—
63C2×(C2×D43)⋊C4—24no—
64C2×(C2×D43)⋊C4—42no—
65C2×(C2×D43)⋊C4—42no—
66C2×(C2×D43)⋊C4—42no—
67C2×(C2×D43)⋊C4—42no—
68C2×(C2×D43)⋊C4C2×C418yes—
69C2×C4×Dic43—22no—
70C2×C4×Dic43—22no—
71C2×C4×Dic43—42no—
72C2×C4×Dic43—42no—
73C43⋊#95—22no—
74C43⋊#95—24no—
75C43⋊#95—24no—
76C43⋊#95—42no—
77C43⋊#95—42no—
78C43⋊#95—42no—
79C43⋊#95C2×C414yes—
80C43⋊#95C2×C418yes—
81C23×C4×C43C2312yes—
82C23×C4×C43C2312yes—
83C23×C4×C43C2311yescharacteristic
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43—22no—
87C2×C4⋊C4×C43—42no—
88#95×C43—22no—
89#95×C43—24no—
90#95×C43—42no—
91#95×C43C2×C414yes—
92C24×C43C2411yescharacteristic
93C23×D43—21no—
94C23×D43—21no—
95C23×D43—21no—
96C23×D43—21no—
97C23×D43—22no—
98C23×D43—22no—
99C23×D43—22no—
100C23×D43—22no—
101C23×D43C22×C412yes—
102C23×D43C2×D412yes—
103C23×D43C2×Q812yes—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
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—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
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×C43C22×C414yes—
128C22×C4×C43C22×C412yes—
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×Q812yes—
131C22×C4×C43#4112yes—
132C22×C4×C43#4112yes—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—21no—
138C22×Dic43—21no—
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×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43C22×C414yes—
157C22×Dic43C22×C412yes—
158C22×Dic43C2×D412yes—
159C22×Dic43C2×Q812yes—
160C22×Dic43#4112yes—
161C22×Dic43#4112yes—
162C2×C4×D43—48no—
163C2×C4×D43—44no—
164C2×C4×D43—44no—
165C2×C4×D43—48no—
166C2×C4×D43C4⋊C4116yescomplemented
167C4⋊C4×C43—44no—
168(C2×D43)⋊C4—28no—
169(C2×D43)⋊C4—28no—
170(C2×D43)⋊C4—48no—
171(C2×D43)⋊C4—48no—
172C4⋊Dic43—48no—
173C4⋊Dic43—44no—
174Dic43⋊C4—48no—
175C4×Dic43—44no—
176C4×Dic43—44no—
177C23×C43C23×C411yescharacteristic
178C23×C43C22×D411yescharacteristic
179C23×C43C22×Q811yescharacteristic
180C23×C43C2×#4111yescharacteristic
181C23×C43C2×#4111yescharacteristic
182C23×C43C2×#4111yescharacteristic
183C23×C43C2×#4111yescharacteristic
184C23×C43H(5,𝔽2)12yes—
185C23×C43H(5,𝔽2)12yes—
186C23×C43H(5,𝔽2)12yes—
187C23×C432−1+412yes—
188C22×D43—22no—
189C22×D43—22no—
190C22×D43—24no—
191C22×D43—24no—
192C22×D43—22no—
193C22×D43—22no—
194C22×D43—22no—
195C22×D43—22no—
196C22×D43—22no—
197C22×D43—22no—
198C22×D43—22no—
199C22×D43—22no—
200C22×D43—24no—
201C22×D43—24no—
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×D43C2×C4⋊C414yes—
211C2×C4×C43—24no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—24no—
215C2×C4×C43—24no—
216C2×C4×C43—24no—
217C2×C4×C43—24no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—24no—
221C2×C4×C43—24no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
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×C43C2×C4⋊C414yes—
240C2×Dic43—24no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—24no—
244C2×Dic43—24no—
245C2×Dic43—24no—
246C2×Dic43—24no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
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×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43C2×C4⋊C414yes—
269C4×D43—416no—
270#14295—431nomaximal, Sylow
271C22×C43C22×C4⋊C411yescharacteristic
272C22×C43C4×#4111yescharacteristic
273C22×C43C4×#4111yescharacteristic
274C22×C43#51812yes—
275C22×C43#52012yes—
276C22×C43#52511yescharacteristic
277C22×C43#52511yescharacteristic
278C22×C43#53311yescharacteristic
279C22×C43#53311yescharacteristic
280C22×C43#53411yescharacteristic
281C22×C43#53411yescharacteristic
282C22×C43#53511yescharacteristic
283C22×C43#53611yescharacteristic
284C22×C43#53812yes—
285C22×C43#53812yes—
286C22×C43#53912yes—
287C22×C43#53912yes—
288C22×C43#54012yes—
289C22×C43#54012yes—
290C22×C43#54212yes—
291C22×C43#54212yes—
292C22×C43#54312yes—
293C22×C43#54412yes—
294C2×D43—24no—
295C2×D43—24no—
296C2×D43—24no—
297C2×D43—44no—
298C2×D43—44no—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—44no—
304C2×D43—44no—
305C4×C43—24no—
306C4×C43—44no—
307C4×C43—42no—
308C4×C43—42no—
309C4×C43—82no—
310Dic43—24no—
311Dic43—44no—
312Dic43—42no—
313Dic43—42no—
314Dic43—82no—
315C2×#381—431no—
316C2×#380—431no—
317C2×C4×C22⋊C4—431no—
318#1444—431no—
319#1444—431no—
320#1442—431no—
321#1442D4311yescharacteristic, complemented
322#1439—432no—
323#1439—432no—
324#1436—432no—
325#1436—432no—
326C2×C43#229611yescharacteristic
327C2×C43#231511yescharacteristic
328C2×C43#231711yescharacteristic
329C2×C43#233512yes—
330C2×C43#233512yes—
331C2×C43#263511yescharacteristic
332C2×C43#263511yescharacteristic
333C2×C43#263811yescharacteristic
334C2×C43#263811yescharacteristic
335C2×C43#266512yes—
336C2×C43#266712yes—
337D43—44no—
338C24×C4—431no—
339C22×C4⋊C4—432no—
340C22×C4⋊C4—432no—
341C22×C4⋊C4—431no—
342C22×C4⋊C4C2×D4311yescharacteristic
343C22×C22⋊C4—432no—
344C22×C22⋊C4—431no—
345C22×C22⋊C4—431no—
346C22×C22⋊C4—432no—
347C22×C42—431no—
348C22×C42—431no—
349#381—438no—
350#380—864no—
351C4×C22⋊C4—864no—
352C2×#95—432no—
353C2×#95—431no—
354C2×#95—432no—
355C2×#95—432no—
356C2×#95—431no—
357C2×#95—432no—
358C2×#95—432no—
359C2×#95—432no—
360C2×#95C2×D4312yes—
361C2×#95C2×D4311yescharacteristic
362C2×#95C2×D4312yes—
363C2×#95C2×D4311yescharacteristic
364C43#1429511yescharacteristic, complemented, Sylow
365C25—431no—
366C23×C4—431no—
367C23×C4—434no—
368C23×C4—434no—
369C23×C4—434no—
370C23×C4—431no—
371C23×C4—431no—
372C23×C4—432no—
373C23×C4—432no—
374C23×C4—1722no—
375C23×C4—1722no—
376C23×C4C22×D4312yes—
377C23×C4C22×D4312yes—
378C23×C4C22×D4311yescharacteristic
379C23×C4C22×D4311yescharacteristic
380C23×C4C22×D4311yescharacteristic
381C2×C4⋊C4—22no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—864no—
384C2×C4⋊C4—864no—
385C2×C4⋊C4—862no—
386C2×C4⋊C4—1722no—
387C2×C4⋊C4—1722no—
388C2×C4⋊C4—1722no—
389C2×C4⋊C4—1722no—
390C2×C4⋊C4—1722no—
391C2×C22⋊C4—438no—
392C2×C22⋊C4—862no—
393C2×C22⋊C4—862no—
394C2×C22⋊C4—862no—
395C2×C22⋊C4—862no—
396C2×C22⋊C4—862no—
397C2×C22⋊C4—862no—
398C2×C22⋊C4—864no—
399C2×C22⋊C4—1722no—
400C2×C22⋊C4—1722no—
401C2×C22⋊C4—1722no—
402C2×C22⋊C4—1722no—
403C2×C42—862no—
404C2×C42—862no—
405C2×C42—1722no—
406C2×C42—1722no—
407#95—22no—
408#95—24no—
409#95—42no—
410#95—438no—
411#95—434no—
412#95—864no—
413#95—862no—
414#95—864no—
415#95—1722no—
416#95—1722no—
417#95—1722no—
418#95C4×D4314yes—
419C24—432no—
420C24—432no—
421C24—432no—
422C24—861no—
423C24—861no—
424C24—861no—
425C24—861no—
426C24—862no—
427C24—862no—
428C24—862no—
429C24—862no—
430C24C23×D4311yescharacteristic
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
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—432no—
455C22×C4—432no—
456C22×C4—432no—
457C22×C4—4316no—
458C22×C4—434no—
459C22×C4—432no—
460C22×C4—432no—
461C22×C4—862no—
462C22×C4—862no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—862no—
466C22×C4—861no—
467C22×C4—862no—
468C22×C4—861no—
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—1728no—
485C22×C4—1724no—
486C22×C4—1724no—
487C22×C4—1728no—
488C22×C4C2×C4×D4314yes—
489C22×C4C2×C4×D4312yes—
490C22×C4D4×D4312yes—
491C22×C4#1062190012yes—
492C22×C4Q8×D4312yes—
493C22×C4#1062190212yes—
494C4⋊C4—44no—
495C4⋊C4—1724no—
496C4⋊C4—1728no—
497C4⋊C4—1728no—
498C22⋊C4—868no—
499C22⋊C4—868no—
500C22⋊C4—1728no—
501C22⋊C4—1728no—
502C42—1724no—
503C42—1724no—
504C23—434no—
505C23—862no—
506C23—862no—
507C23—864no—
508C23—864no—
509C23—862no—
510C23—862no—
511C23—862no—
512C23—862no—
513C23—862no—
514C23—862no—
515C23—862no—
516C23—862no—
517C23—864no—
518C23—864no—
519C23—1722no—
520C23—1722no—
521C23—1722no—
522C23—1722no—
523C23—1722no—
524C23—1722no—
525C23—1722no—
526C23—1722no—
527C23C22×C4×D4311yescharacteristic
528C23C2×D4×D4311yescharacteristic
529C23C2×Q8×D4311yescharacteristic
530C23#41×D4311yescharacteristic
531C23#41×D4311yescharacteristic
532C23C2×#1062190011yescharacteristic
533C23C2×#1062190211yescharacteristic
534C23#1306337012yes—
535C23#1306337112yes—
536C23#1306337112yes—
537C23#1306337212yes—
538C2×C4—24no—
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—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—434no—
567C2×C4—864no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—864no—
571C2×C4—864no—
572C2×C4—864no—
573C2×C4—864no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—864no—
577C2×C4—864no—
578C2×C4—17216no—
579C2×C4—1722no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4—1722no—
584C2×C4—1722no—
585C2×C4—1722no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4C4⋊C4×D4314yes—
597C22—864no—
598C22—864no—
599C22—864no—
600C22—1724no—
601C22—1724no—
602C22—1722no—
603C22—1722no—
604C22—1724no—
605C22—1722no—
606C22—1722no—
607C22—1724no—
608C22C2×C4⋊C4×D4311yescharacteristic
609C22C4×#1062190011yescharacteristic
610C22C4×#1062190211yescharacteristic
611C22#1458337112yes—
612C22#1458337912yes—
613C22#1458340911yescharacteristic
614C22#1458341211yescharacteristic
615C22#1458345411yescharacteristic
616C22#1458345511yescharacteristic
617C22#1458345911yescharacteristic
618C22#1458346011yescharacteristic
619C22#1458346711yescharacteristic
620C22#1458346911yescharacteristic
621C22#1458348512yes—
622C22#1458348812yes—
623C22#1458349312yes—
624C22#1458349812yes—
625C22#1458350212yes—
626C22#1458350512yes—
627C22#1458351312yes—
628C22#1458351512yes—
629C22#1458352412yes—
630C22#1458352912yes—
631C4—24no—
632C4—44no—
633C4—42no—
634C4—42no—
635C4—82no—
636C4—864no—
637C4—3442no—
638C4—1724no—
639C4—1722no—
640C4—1722no—
641C2—1724no—
642C2#1913707611yescharacteristic
643C2#1913720611yescharacteristic
644C2#1913722011yescharacteristic
645C2#1913738412yes—
646C2#1913739212yes—
647C2#1914048711yescharacteristic
648C2#1914048811yescharacteristic
649C2#1914051711yescharacteristic
650C2#1914051811yescharacteristic
651C2#1914077212yes—
652C2#1914079412yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1442C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1442D43
hypocenterC43#14295
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
4. #19132860C2semidirect
5. #19132858C2semidirect
6. #19132851C2semidirect
9. #19132829C2semidirect
10. #19132826C2semidirect
11. C43×#1442C2semidirect
22. #14582761C4semidirect
166. C2×C4×D43C4⋊C4semidirect
321. #1442D43semidirect
364. C43#14295semidirect

Maximal subgroups

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

subgroupindex
C2×#145827612
C2×#145827562
C2×#145827462
#191328602
#191328582
#191328512
#191328412
#191328392
#191328292
#191328262
C43×#14422
#1429543