Finite Group Databasebeta

← #25023009

Subgroups — #25023009

Order 11008.

3390 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
1C23×(C2×D43)⋊C4C211yesmaximal, characteristic
2C2×#14582771C211yesmaximal, characteristic, complemented
3C2×#14582754C211yesmaximal, characteristic
4C2×#14582754C211yesmaximal, characteristic
5#19132839C214yesmaximal, complemented
6#19132837C214yesmaximal, complemented
7#19132818C211yesmaximal, characteristic, complemented
8#19132817C211yesmaximal, characteristic, complemented
9C2×C43×#385C211yesmaximal, characteristic, complemented
10C25×D43C2211yescharacteristic
11C24×Dic43C2211yescharacteristic
12C22×Dic43⋊C4C2212yescomplemented
13C22×C22⋊Dic43C2211yescharacteristic
14C22×C22⋊Dic43C2211yescharacteristic
15C22×(C2×D43)⋊C4—24no—
16C22×(C2×D43)⋊C4—24no—
17C22×(C2×D43)⋊C4—24no—
18C22×(C2×D43)⋊C4C2214yes—
19C22×(C2×D43)⋊C4C2212yes—
20C22×(C2×D43)⋊C4C2212yes—
21C22×(C2×D43)⋊C4C2214yes—
22#14582771—24no—
23#14582754—24no—
24#14582754C418yescomplemented
25C2×C43⋊#95C2212yescomplemented
26C2×C43⋊#95C2214yescomplemented
27C2×C43⋊#95C2214yescomplemented
28C24×C4×C43C2211yescharacteristic
29C22×C4⋊C4×C43C2212yescomplemented
30C22×C22⋊C4×C43C2211yescharacteristic
31C22×C22⋊C4×C43C2211yescharacteristic
32C43×#385—24no—
33C2×#95×C43C2212yescomplemented
34C24×D43—22no—
35C24×D43—22no—
36C24×D43—22no—
37C24×D43—22no—
38C24×D43—44no—
39C24×D43—44no—
40C24×D43C2×C414yes—
41C24×D43D414yes—
42C24×D43Q814yes—
43C24×D43C2312yes—
44C23×Dic43—22no—
45C23×Dic43—22no—
46C23×Dic43—44no—
47C23×Dic43D414yes—
48C23×Dic43C2312yes—
49C23×Dic43C2312yes—
50C23×Dic43C2312yes—
51C2×Dic43⋊C4—24no—
52C2×Dic43⋊C4—44no—
53C2×C22⋊Dic43—22no—
54C2×C22⋊Dic43—22no—
55C2×C22⋊Dic43—22no—
56C2×C22⋊Dic43—22no—
57C2×C22⋊Dic43—22no—
58C2×C22⋊Dic43C2×C414yes—
59C2×(C2×D43)⋊C4—232no—
60C2×(C2×D43)⋊C4—28no—
61C2×(C2×D43)⋊C4—28no—
62C2×(C2×D43)⋊C4—28no—
63C2×(C2×D43)⋊C4—24no—
64C2×(C2×D43)⋊C4—24no—
65C2×(C2×D43)⋊C4—44no—
66C2×(C2×D43)⋊C4—44no—
67C2×(C2×D43)⋊C4—44no—
68C2×(C2×D43)⋊C4—44no—
69C2×(C2×D43)⋊C4C2×C4116yescomplemented
70C43⋊#95—24no—
71C43⋊#95—44no—
72C43⋊#95—44no—
73C25×C43C2311yescharacteristic
74C23×C4×C43—22no—
75C23×C4×C43—22no—
76C23×C4×C43—44no—
77C23×C4×C43D414yes—
78C23×C4×C43C2311yescharacteristic
79C23×C4×C43C2311yescharacteristic
80C23×C4×C43C2312yes—
81C23×C4×C43C2312yes—
82C2×C4⋊C4×C43—24no—
83C2×C4⋊C4×C43—44no—
84C2×C22⋊C4×C43—22no—
85C2×C22⋊C4×C43—22no—
86C2×C22⋊C4×C43—22no—
87C2×C22⋊C4×C43—22no—
88C2×C22⋊C4×C43—22no—
89C2×C22⋊C4×C43C2×C414yes—
90#95×C43—24no—
91C24×C43—24no—
92C24×C43—24no—
93C24×C43C22×C412yes—
94C24×C43C2×D412yes—
95C24×C43C2×D412yes—
96C24×C43C2×D412yes—
97C24×C43C2×Q812yes—
98C24×C43#4112yes—
99C24×C43#4112yes—
100C24×C43C2411yescharacteristic
101C23×D43—28no—
102C23×D43—28no—
103C23×D43—28no—
104C23×D43—28no—
105C23×D43—28no—
106C23×D43—28no—
107C23×D43—22no—
108C23×D43—22no—
109C23×D43—22no—
110C23×D43—22no—
111C23×D43—24no—
112C23×D43—24no—
113C23×D43—24no—
114C23×D43—24no—
115C23×D43—416no—
116C23×D43—48no—
117C23×D43—48no—
118C23×D43—416no—
119C23×D43—48no—
120C23×D43—48no—
121C23×D43—48no—
122C23×D43—48no—
123C23×D43—416no—
124C23×D43—416no—
125C23×D43C4⋊C4116yescomplemented
126C23×D43C22×C414yes—
127C23×D43C2×D414yes—
128C23×D43C2×Q814yes—
129C22×C4×C43—28no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—22no—
140C22×C4×C43—24no—
141C22×C4×C43—24no—
142C22×C4×C43—24no—
143C22×C4×C43—24no—
144C22×C4×C43—24no—
145C22×C4×C43—24no—
146C22×C4×C43—48no—
147C22×C4×C43—48no—
148C22×C4×C43—48no—
149C22×C4×C43C22×C414yes—
150C22×C4×C43C2×D414yes—
151C22×Dic43—28no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—24no—
160C22×Dic43—24no—
161C22×Dic43—24no—
162C22×Dic43—24no—
163C22×Dic43—24no—
164C22×Dic43—24no—
165C22×Dic43—48no—
166C22×Dic43—48no—
167C22×Dic43—48no—
168C22×Dic43C22×C414yes—
169C22×Dic43C2×D414yes—
170C4⋊C4×C43—48no—
171C22⋊C4×C43—28no—
172C22⋊C4×C43—44no—
173C22⋊Dic43—28no—
174C22⋊Dic43—44no—
175(C2×D43)⋊C4—232no—
176(C2×D43)⋊C4—416no—
177(C2×D43)⋊C4—48no—
178(C2×D43)⋊C4—48no—
179Dic43⋊C4—48no—
180C23×C43—28no—
181C23×C43—24no—
182C23×C43—24no—
183C23×C43—24no—
184C23×C43—24no—
185C23×C43—24no—
186C23×C43—24no—
187C23×C43—28no—
188C23×C43—28no—
189C23×C43—28no—
190C23×C43C2×C4⋊C414yes—
191C23×C43C4×D414yes—
192C23×C43C4×D414yes—
193C23×C43#12014yes—
194C23×C43C22⋊Q814yes—
195C23×C43C22⋊Q814yes—
196C23×C43#12314yes—
197C23×C43C23×C411yescharacteristic
198C23×C43C22×D411yescharacteristic
199C23×C43C22×D411yescharacteristic
200C23×C43C22×D411yescharacteristic
201C23×C43C22×Q811yescharacteristic
202C23×C43C2×#4111yescharacteristic
203C23×C43C2×#4111yescharacteristic
204C23×C43H(5,𝔽2)14yes—
205C23×C43H(5,𝔽2)14yes—
206C22×D43—24no—
207C22×D43—24no—
208C22×D43—28no—
209C22×D43—28no—
210C22×D43—24no—
211C22×D43—24no—
212C22×D43—24no—
213C22×D43—24no—
214C22×D43—24no—
215C22×D43—24no—
216C22×D43—24no—
217C22×D43—24no—
218C22×D43—28no—
219C22×D43—28no—
220C22×D43—232no—
221C22×D43—432no—
222C22×D43—432no—
223C22×D43—432no—
224C22×D43—416no—
225C22×D43—416no—
226C22×D43—432no—
227C22×D43—432no—
228C22×D43—432no—
229C22×D43—44no—
230C22×D43—44no—
231C22×D43—44no—
232C22×D43—44no—
233C22×D43—44no—
234C22×D43—44no—
235C22×D43—44no—
236C22×D43—44no—
237C22×D43C2×C4⋊C418yes—
238C2×C4×C43—24no—
239C2×C4×C43—28no—
240C2×C4×C43—24no—
241C2×C4×C43—24no—
242C2×C4×C43—24no—
243C2×C4×C43—416no—
244C2×C4×C43—42no—
245C2×C4×C43—44no—
246C2×C4×C43—42no—
247C2×C4×C43—44no—
248C2×C4×C43—44no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×Dic43—24no—
258C2×Dic43—28no—
259C2×Dic43—24no—
260C2×Dic43—24no—
261C2×Dic43—24no—
262C2×Dic43—416no—
263C2×Dic43—42no—
264C2×Dic43—44no—
265C2×Dic43—42no—
266C2×Dic43—44no—
267C2×Dic43—44no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—44no—
272C2×Dic43—44no—
273#14262—431nomaximal, Sylow
274C22×C43—28no—
275C22×C43—28no—
276C22×C43—28no—
277C22×C43—24no—
278C22×C43—24no—
279C22×C43—28no—
280C22×C43—28no—
281C22×C43—28no—
282C22×C43#38518yes—
283C22×C43C22×C4⋊C411yescharacteristic
284C22×C43C2×C4×D411yescharacteristic
285C22×C43C2×C4×D411yescharacteristic
286C22×C43#51814yes—
287C22×C43C2×#12011yescharacteristic
288C22×C43C2×C22⋊Q811yescharacteristic
289C22×C43C2×C22⋊Q811yescharacteristic
290C22×C43C2×#12311yescharacteristic
291C22×C43#53412yes—
292C22×C43#53412yes—
293C22×C43#53412yes—
294C22×C43#53412yes—
295C22×C43#53512yes—
296C22×C43#53512yes—
297C22×C43#53814yes—
298C22×C43#53814yes—
299C22×C43#54314yes—
300C2×D43—28no—
301C2×D43—28no—
302C2×D43—28no—
303C2×D43—464no—
304C2×D43—48no—
305C2×D43—48no—
306C2×D43—44no—
307C2×D43—44no—
308C2×D43—44no—
309C2×D43—44no—
310C2×D43—48no—
311C2×D43—48no—
312C4×C43—44no—
313C4×C43—44no—
314C4×C43—81no—
315C4×C43—81no—
316Dic43—44no—
317Dic43—44no—
318Dic43—82no—
319C23×C22⋊C4—431no—
320C2×#385—431no—
321C2×#385D4311yescharacteristic, complemented
322C2×#379—431no—
323C2×#379—431no—
324#1439—434no—
325#1439—434no—
326C22⋊#95—431no—
327C22⋊#95—431no—
328C2×C43—28no—
329C2×C43C2×#38511yescharacteristic
330C2×C43#231512yes—
331C2×C43#232112yes—
332C2×C43#232112yes—
333C2×C43#261311yescharacteristic
334C2×C43#261311yescharacteristic
335C2×C43#262212yes—
336C2×C43#262612yes—
337C2×C43#262612yes—
338D43—48no—
339C26—431no—
340C24×C4—431no—
341C24×C4C2×D4311yescharacteristic
342C22×C4⋊C4—432no—
343C22×C4⋊C4C2×D4312yescomplemented
344C22×C22⋊C4—431no—
345C22×C22⋊C4—434no—
346C22×C22⋊C4—431no—
347C22×C22⋊C4—434no—
348C22×C22⋊C4—432no—
349C22×C22⋊C4—432no—
350C22×C22⋊C4—864no—
351C22×C22⋊C4—864no—
352C22×C22⋊C4—864no—
353C22×C22⋊C4C2×D4311yescharacteristic
354C22×C22⋊C4C2×D4311yescharacteristic
355#385—24no—
356#385—864no—
357#379—438no—
358#379—864no—
359C2×#95—432no—
360C2×#95—434no—
361C2×#95—434no—
362C2×#95C2×D4312yescomplemented
363C43#1426211yescharacteristic, complemented, Sylow
364C25—432no—
365C25—434no—
366C25—434no—
367C25—434no—
368C25—862no—
369C25—862no—
370C25—862no—
371C25—862no—
372C25—1724no—
373C25—1724no—
374C25C22×D4311yescharacteristic
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—44no—
378C23×C4—432no—
379C23×C4—432no—
380C23×C4—434no—
381C23×C4—432no—
382C23×C4—862no—
383C23×C4—862no—
384C23×C4—1724no—
385C23×C4C22⋊D4314yes—
386C23×C4C22×D4311yescharacteristic
387C23×C4C22×D4311yescharacteristic
388C23×C4C22×D4312yes—
389C23×C4C22×D4312yes—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—864no—
393C2×C4⋊C4—1724no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—434no—
400C2×C22⋊C4—4316no—
401C2×C22⋊C4—868no—
402C2×C22⋊C4—868no—
403C2×C22⋊C4—8632no—
404C2×C22⋊C4—862no—
405C2×C22⋊C4—862no—
406C2×C22⋊C4—868no—
407C2×C22⋊C4—864no—
408C2×C22⋊C4—864no—
409C2×C22⋊C4—862no—
410C2×C22⋊C4—862no—
411C2×C22⋊C4—862no—
412C2×C22⋊C4—1724no—
413C2×C22⋊C4—1724no—
414C2×C22⋊C4—1724no—
415C2×C22⋊C4—1724no—
416C2×C22⋊C4C4×D4314yes—
417#95—24no—
418#95—864no—
419#95—1724no—
420#95—1724no—
421C24—24no—
422C24—24no—
423C24—434no—
424C24—434no—
425C24—434no—
426C24—4316no—
427C24—868no—
428C24—868no—
429C24—868no—
430C24—868no—
431C24—868no—
432C24—868no—
433C24—862no—
434C24—862no—
435C24—862no—
436C24—862no—
437C24—864no—
438C24—864no—
439C24—864no—
440C24—864no—
441C24—17216no—
442C24—1728no—
443C24—1728no—
444C24—17216no—
445C24—1728no—
446C24—1728no—
447C24—1728no—
448C24—1728no—
449C24—17216no—
450C24—17216no—
451C24C2×C4×D4312yes—
452C24#1062189812yes—
453C24D4×D4312yes—
454C24D4×D4312yes—
455C24Q8×D4312yes—
456C24#1062190212yes—
457C24C2×C22⋊D4312yes—
458C24C23×D4311yescharacteristic
459C22×C4—28no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—48no—
477C22×C4—48no—
478C22×C4—48no—
479C22×C4—434no—
480C22×C4—434no—
481C22×C4—868no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—864no—
487C22×C4—864no—
488C22×C4—864no—
489C22×C4—864no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—864no—
494C22×C4—864no—
495C22×C4—1728no—
496C22×C4—1728no—
497C22×C4—1728no—
498C22×C4C2×C4×D4314yes—
499C22×C4C2×C22⋊D4314yes—
500C4⋊C4—48no—
501C4⋊C4—1728no—
502C22⋊C4—28no—
503C22⋊C4—44no—
504C22⋊C4—8632no—
505C22⋊C4—868no—
506C22⋊C4—17216no—
507C22⋊C4—1728no—
508C22⋊C4—1728no—
509C22⋊C4—1724no—
510C23—28no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—28no—
518C23—28no—
519C23—28no—
520C23—438no—
521C23—864no—
522C23—864no—
523C23—868no—
524C23—868no—
525C23—864no—
526C23—864no—
527C23—864no—
528C23—864no—
529C23—864no—
530C23—864no—
531C23—864no—
532C23—864no—
533C23—868no—
534C23—868no—
535C23—8632no—
536C23—17232no—
537C23—17232no—
538C23—17232no—
539C23—17232no—
540C23—17216no—
541C23—17216no—
542C23—17232no—
543C23—17232no—
544C23—1724no—
545C23—1724no—
546C23—1724no—
547C23—1724no—
548C23—1724no—
549C23—1724no—
550C23—1724no—
551C23—1724no—
552C23C4⋊C4×D4314yes—
553C23C4×C22⋊D4314yes—
554C23#1306328714yes—
555C23#1306329314yes—
556C23#1306330114yes—
557C23#1306330314yes—
558C23#1306331014yes—
559C23C22×C4×D4311yescharacteristic
560C23C2×D4×D4311yescharacteristic
561C23C2×D4×D4311yescharacteristic
562C23C22×C22⋊D4311yescharacteristic
563C23C2×Q8×D4311yescharacteristic
564C23C2×#1062189811yescharacteristic
565C23C2×#1062190211yescharacteristic
566C23#1306337014yes—
567C23#1306337114yes—
568C2×C4—24no—
569C2×C4—28no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—416no—
574C2×C4—42no—
575C2×C4—44no—
576C2×C4—42no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—864no—
588C2×C4—868no—
589C2×C4—864no—
590C2×C4—864no—
591C2×C4—864no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1724no—
596C2×C4—1724no—
597C2×C4—17216no—
598C2×C4—1722no—
599C2×C4—1724no—
600C2×C4—1724no—
601C2×C4—1722no—
602C2×C4—1724no—
603C22—28no—
604C22—28no—
605C22—28no—
606C22—28no—
607C22—24no—
608C22—24no—
609C22—28no—
610C22—28no—
611C22—868no—
612C22—868no—
613C22—868no—
614C22—17264no—
615C22—1724no—
616C22—1724no—
617C22—1728no—
618C22—1728no—
619C22—1724no—
620C22—1724no—
621C22—1728no—
622C22—1728no—
623C22#1458277018yes—
624C22C2×C4⋊C4×D4311yescharacteristic
625C22C2×C4×C22⋊D4311yescharacteristic
626C22C2×#1306328711yescharacteristic
627C22#1458337114yes—
628C22C2×#1306329311yescharacteristic
629C22C2×#1306330111yescharacteristic
630C22C2×#1306330311yescharacteristic
631C22C2×#1306331011yescharacteristic
632C22#1458345812yes—
633C22#1458345912yes—
634C22#1458346012yes—
635C22#1458346012yes—
636C22#1458346312yes—
637C22#1458346412yes—
638C22#1458348214yes—
639C22#1458348914yes—
640C22#1458352414yes—
641C4—44no—
642C4—44no—
643C4—81no—
644C4—81no—
645C4—3442no—
646C4—1724no—
647C4—1724no—
648C2—28no—
649C2—1728no—
650C2C2×#1458277011yescharacteristic
651C2#1913720612yes—
652C2#1913724912yes—
653C2#1913725212yes—
654C2#1914030911yescharacteristic
655C2#1914031111yescharacteristic
656C2#1914037312yes—
657C2#1914040212yes—
658C2#1914040612yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#385C2
socle, cosocleC24×C43C24
prime radicalC25×D43C22
hypercenterC2×#385D43
hypocenterC43#14262
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#14582771C2semidirect
5. #19132839C2semidirect
6. #19132837C2semidirect
7. #19132818C2semidirect
8. #19132817C2semidirect
9. C2×C43×#385C2semidirect
12. C22×Dic43⋊C4C22semidirect
24. #14582754C4semidirect
25. C2×C43⋊#95C22semidirect
26. C2×C43⋊#95C22semidirect
27. C2×C43⋊#95C22semidirect
29. C22×C4⋊C4×C43C22semidirect
33. C2×#95×C43C22semidirect
69. C2×(C2×D43)⋊C4C2×C4semidirect
125. C23×D43C4⋊C4semidirect
321. C2×#385D43semidirect
343. C22×C4⋊C4C2×D43semidirect
362. C2×#95C2×D43semidirect
363. C43#14262semidirect

Maximal subgroups

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

subgroupindex
C23×(C2×D43)⋊C42
C2×#145827712
C2×#145827542
#191328392
#191328372
#191328182
#191328172
C2×C43×#3852
#1426243