Finite Group Databasebeta

← #25025054

Subgroups — #25025054

Order 11008.

1658 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×#14582792C212yesmaximal, complemented
2#19132844C212yesmaximal, complemented
3#19132840C212yesmaximal, complemented
4#19132836C212yesmaximal
5#19132832C212yesmaximal, complemented
6#19132827C212yesmaximal, complemented
7#19132825C211yesmaximal, characteristic, complemented
8#19132822C211yesmaximal, characteristic, complemented
9C2×C43×#390C211yesmaximal, characteristic
10C22×C4⋊Dic43C2212yes—
11C22×C22⋊Dic43C2212yes—
12C22×C22⋊Dic43C2212yes—
13C22×C22⋊Dic43C2212yes—
14C22×C22⋊Dic43C2212yes—
15C22×C4×Dic43C2212yes—
16#14582792—28no—
17C2×C43⋊#95C2212yes—
18C2×C43⋊#95C2212yes—
19C2×C43⋊#95C2211yescharacteristic
20C2×C43⋊#95C2212yes—
21C2×C43⋊#95C2212yes—
22C2×C43⋊#95C2211yescharacteristic
23C2×C43⋊#95C2211yescharacteristic
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2211yescharacteristic
27C23×D4×C43C2211yescharacteristic
28C22×C4⋊C4×C43C2211yescharacteristic
29C22×C22⋊C4×C43C2212yes—
30C22×C22⋊C4×C43C2212yes—
31C22×C42×C43C2211yescharacteristic
32C43×#390C418yescomplemented
33C23×Dic43C2312yes—
34C23×Dic43C2312yes—
35C23×Dic43C2312yes—
36C23×Dic43C2312yes—
37C2×C4⋊Dic43—24no—
38C2×C4⋊Dic43—24no—
39C2×C4⋊Dic43—42no—
40C2×C22⋊Dic43—24no—
41C2×C22⋊Dic43—24no—
42C2×C22⋊Dic43—24no—
43C2×C22⋊Dic43—24no—
44C2×C22⋊Dic43—42no—
45C2×C22⋊Dic43—42no—
46C2×C22⋊Dic43—42no—
47C2×C22⋊Dic43—42no—
48C2×C22⋊Dic43—42no—
49C2×C22⋊Dic43—42no—
50C2×C22⋊Dic43—42no—
51C2×C22⋊Dic43—42no—
52C2×C4×Dic43—24no—
53C2×C4×Dic43—42no—
54C2×C4×Dic43—42no—
55C43⋊#95—24no—
56C43⋊#95—24no—
57C43⋊#95—22no—
58C43⋊#95—24no—
59C43⋊#95—42no—
60C43⋊#95—41no—
61C43⋊#95—42no—
62C43⋊#95—42no—
63C43⋊#95—41no—
64C43⋊#95D414yescomplemented
65C25×C43C2312yes—
66C22×D4×C43—22no—
67C22×D4×C43—22no—
68C22×D4×C43—42no—
69C22×D4×C43—42no—
70C22×D4×C43C2×C414yes—
71C23×C4×C43C2311yescharacteristic
72C23×C4×C43C2312yes—
73C23×C4×C43C2311yescharacteristic
74C23×C4×C43C2311yescharacteristic
75C2×C4⋊C4×C43—42no—
76C2×C4⋊C4×C43C2×C414yes—
77C2×C22⋊C4×C43—24no—
78C2×C22⋊C4×C43—24no—
79C2×C22⋊C4×C43—42no—
80C2×C22⋊C4×C43—42no—
81C2×C22⋊C4×C43C2×C418yes—
82C2×C22⋊C4×C43C2×C418yes—
83C2×C42×C43—42no—
84C2×C42×C43C2×C414yes—
85C24×C43—22no—
86C24×C43—22no—
87C24×C43—22no—
88C24×C43—22no—
89C24×C43—22no—
90C24×C43—22no—
91C24×C43—22no—
92C24×C43—22no—
93C24×C43—22no—
94C24×C43—22no—
95C24×C43—22no—
96C24×C43—22no—
97C24×C43—22no—
98C24×C43—22no—
99C24×C43C22×C414yes—
100C24×C43C2411yescharacteristic
101C2×D4×C43—28no—
102C2×D4×C43—44no—
103C2×D4×C43—44no—
104C2×D4×C43—48no—
105C2×D4×C43—48no—
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—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43C22×C412yes—
121C22×C4×C43C22×C414yes—
122C22×C4×C43C22×C412yes—
123C22×C4×C43C22×C412yes—
124C22×C4×C43C2×D412yes—
125C22×C4×C43#4112yes—
126C22×C4×C43#4112yes—
127C22×C4×C43#4112yes—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—22no—
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×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43C2×D414yes—
155C22×Dic43#4114yes—
156C4⋊C4×C43—44no—
157C22⋊C4×C43—216no—
158C22⋊C4×C43—48no—
159C42×C43—44no—
160C22⋊Dic43—48no—
161C22⋊Dic43—48no—
162C22⋊Dic43—48no—
163C22⋊Dic43—48no—
164C4⋊Dic43—48no—
165C4×Dic43—48no—
166C23×C43—24no—
167C23×C43—24no—
168C23×C43—24no—
169C23×C43—24no—
170C23×C43—24no—
171C23×C43—24no—
172C23×C43—24no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—42no—
176C23×C43—42no—
177C23×C43—42no—
178C23×C43—42no—
179C23×C43—42no—
180C23×C43—42no—
181C23×C43—42no—
182C23×C43—42no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—42no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43—42no—
189C23×C43—42no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43—42no—
196C23×C43—42no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43—42no—
201C23×C43C23×C411yescharacteristic
202C23×C43C22×D411yescharacteristic
203C23×C43C2×#4112yes—
204C23×C43C2×#4111yescharacteristic
205C23×C43C2×#4111yescharacteristic
206C23×C43C2×#4111yescharacteristic
207C23×C43H(5,𝔽2)12yes—
208C23×C43H(5,𝔽2)12yes—
209C23×C43H(5,𝔽2)12yes—
210C23×C43H(5,𝔽2)11yescharacteristic
211C23×C432−1+411yescharacteristic
212D4×C43—416no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—24no—
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—22no—
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#11714yes—
234C2×C4×C43C4×D414yes—
235C2×Dic43—24no—
236C2×Dic43—24no—
237C2×Dic43—24no—
238C2×Dic43—24no—
239C2×Dic43—24no—
240C2×Dic43—24no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43—42no—
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—
263#14444—431nomaximal, Sylow
264C22×C43—44no—
265C22×C43—44no—
266C22×C43—44no—
267C22×C43—44no—
268C22×C43—44no—
269C22×C43—44no—
270C22×C43—44no—
271C22×C43—82no—
272C22×C43—82no—
273C22×C43—82no—
274C22×C43—82no—
275C22×C43—82no—
276C22×C43—82no—
277C22×C43—82no—
278C22×C43—82no—
279C22×C43C2×#11711yescharacteristic
280C22×C43C2×C4×D411yescharacteristic
281C22×C43C4×#4111yescharacteristic
282C22×C43#51811yescharacteristic
283C22×C43#51811yescharacteristic
284C22×C43#51811yescharacteristic
285C22×C43#52011yescharacteristic
286C22×C43#53512yes—
287C22×C43#53812yes—
288C22×C43#53812yes—
289C22×C43#53812yes—
290C22×C43#54012yes—
291C22×C43#54212yes—
292C22×C43#54612yes—
293C22×C43#54711yescharacteristic
294C22×C43#55011yescharacteristic
295C22×C43#55312yes—
296C22×C43#55312yes—
297C22×C43#55511yescharacteristic
298C22×C43#55611yescharacteristic
299C22×C43#55912yes—
300C22×C43#56012yes—
301C22×C43#56212yes—
302C4×C43—24no—
303C4×C43—24no—
304C4×C43—44no—
305C4×C43—42no—
306Dic43—44no—
307Dic43—44no—
308Dic43—82no—
309Dic43—82no—
310C2×#390D4311yescharacteristic
311C2×#388—432no—
312#1440—432no—
313#1439—432no—
314#1438—432no—
315#1437—432no—
316#1436—432no—
317C4⋊#95—431no—
318#1434—431no—
319C2×C43—84no—
320C2×C43#231211yescharacteristic
321C2×C43#232811yescharacteristic
322C2×C43#233711yescharacteristic
323C2×C43#235411yescharacteristic
324C2×C43#235711yescharacteristic
325C2×C43#236411yescharacteristic
326C2×C43#237711yescharacteristic
327C2×C43#271012yes—
328C2×C43#271412yes—
329C2×C43#280012yes—
330C2×C43#280312yes—
331C23×D4C2×D4311yescharacteristic
332C22×C4⋊C4—432no—
333C22×C4⋊C4C2×D4311yescharacteristic
334C22×C22⋊C4—432no—
335C22×C22⋊C4—432no—
336C22×C22⋊C4—432no—
337C22×C22⋊C4—432no—
338C22×C22⋊C4C2×D4312yes—
339C22×C22⋊C4C2×D4312yes—
340C22×C42—432no—
341C22×C42C2×D4311yescharacteristic
342#390Dic4318yescomplemented
343#388—868no—
344C2×#95—431no—
345C2×#95—432no—
346C2×#95—431no—
347C2×#95—432no—
348C2×#95—432no—
349C2×#95—432no—
350C2×#95—431no—
351C2×#95—431no—
352C2×#95—432no—
353C2×#95—432no—
354C43#1444411yescharacteristic, complemented, Sylow
355C25C22×D4312yes—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4C2×Dic4314yes—
361C23×C4—432no—
362C23×C4—432no—
363C23×C4—432no—
364C23×C4—432no—
365C23×C4C22×D4312yes—
366C23×C4C22×D4311yescharacteristic
367C23×C4C22×D4311yescharacteristic
368C23×C4C22×D4311yescharacteristic
369C2×C4⋊C4—42no—
370C2×C4⋊C4—864no—
371C2×C4⋊C4—864no—
372C2×C4⋊C4—1722no—
373C2×C4⋊C4C2×Dic4314yes—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—864no—
379C2×C22⋊C4—864no—
380C2×C22⋊C4—864no—
381C2×C22⋊C4—864no—
382C2×C22⋊C4—1722no—
383C2×C22⋊C4—1722no—
384C2×C22⋊C4—1722no—
385C2×C22⋊C4—1722no—
386C2×C22⋊C4—1722no—
387C2×C22⋊C4—1722no—
388C2×C22⋊C4—1722no—
389C2×C22⋊C4—1722no—
390C2×C22⋊C4C2×Dic4318yes—
391C2×C22⋊C4C2×Dic4318yes—
392C2×C42—42no—
393C2×C42—864no—
394C2×C42—1722no—
395C2×C42—1722no—
396C2×C42C2×Dic4314yes—
397#95—434no—
398#95—864no—
399#95—864no—
400#95—864no—
401#95—862no—
402#95—1722no—
403#95—1722no—
404#95—1722no—
405#95—1721no—
406#95—1721no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24C22×Dic4314yes—
422C24C23×D4311yescharacteristic
423C2×D4—28no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—48no—
427C2×D4—48no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—434no—
443C22×C4—434no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—862no—
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#1062189812yes—
471C22×C4#1062189812yes—
472C22×C4D4×D4312yes—
473C22×C4#1062190012yes—
474C22×C4C22×Dic4312yes—
475C22×C4C22×Dic4314yes—
476C22×C4C22×Dic4312yes—
477C22×C4C22×Dic4312yes—
478C4⋊C4—44no—
479C4⋊C4—1728no—
480C22⋊C4—216no—
481C22⋊C4—48no—
482C22⋊C4—1728no—
483C22⋊C4—1728no—
484C22⋊C4—1728no—
485C22⋊C4—1728no—
486C42—44no—
487C42—1728no—
488C23—24no—
489C23—24no—
490C23—24no—
491C23—24no—
492C23—24no—
493C23—24no—
494C23—24no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23C23×Dic4311yescharacteristic
524C23C2×D4×D4311yescharacteristic
525C23#41×D4312yes—
526C23C2×#1062190011yescharacteristic
527C23C2×#1062189811yescharacteristic
528C23C2×#1062189811yescharacteristic
529C23#1306337012yes—
530C23#1306337012yes—
531C23#1306337012yes—
532C23#1306337111yescharacteristic
533C23#1306337211yescharacteristic
534D4—416no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—864no—
556C2×C4—864no—
557C2×C4—864no—
558C2×C4—864no—
559C2×C4—864no—
560C2×C4—864no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1722no—
566C2×C4—1722no—
567C2×C4—1722no—
568C2×C4—1722no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4—1722no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4—1722no—
576C2×C4—1722no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4#1306328414yes—
584C2×C4D4×Dic4314yes—
585C22—44no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—82no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—82no—
597C22—82no—
598C22—82no—
599C22—82no—
600C22C2×#1306328411yescharacteristic
601C22C2×D4×Dic4311yescharacteristic
602C22#41×Dic4311yescharacteristic
603C22#1458337411yescharacteristic
604C22#1458337411yescharacteristic
605C22#1458337411yescharacteristic
606C22#1458338211yescharacteristic
607C22#1458346212yes—
608C22#1458348312yes—
609C22#1458348712yes—
610C22#1458348712yes—
611C22#1458350312yes—
612C22#1458351312yes—
613C22#1458353812yes—
614C22#1458355411yescharacteristic
615C22#1458357011yescharacteristic
616C22#1458359212yes—
617C22#1458359912yes—
618C22#1458361411yescharacteristic
619C22#1458361911yescharacteristic
620C22#1458363212yes—
621C22#1458363712yes—
622C22#1458364412yes—
623C4—24no—
624C4—24no—
625C4—44no—
626C4—42no—
627C4—3442no—
628C4—3442no—
629C4—1724no—
630C4—1724no—
631C2—84no—
632C2#1913719311yescharacteristic
633C2#1913732111yescharacteristic
634C2#1913741011yescharacteristic
635C2#1913754411yescharacteristic
636C2#1913756811yescharacteristic
637C2#1913764711yescharacteristic
638C2#1913775211yescharacteristic
639C2#1914133412yes—
640C2#1914138812yes—
641C2#1914249212yes—
642C2#1914252912yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#390C2
socle, cosocleC24×C43C24
prime radicalC23×D4×C43C22
hypercenterC2×#390D43
hypocenterC43#14444
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×#14582792C2semidirect
2. #19132844C2semidirect
3. #19132840C2semidirect
5. #19132832C2semidirect
6. #19132827C2semidirect
7. #19132825C2semidirect
8. #19132822C2semidirect
32. C43×#390C4semidirect
64. C43⋊#95D4semidirect
342. #390Dic43semidirect
354. C43#14444semidirect

Maximal subgroups

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

subgroupindex
C2×#145827922
#191328442
#191328402
#191328362
#191328322
#191328272
#191328252
#191328222
C2×C43×#3902
#1444443