Finite Group Databasebeta

← #25027646

Subgroups — #25027646

Order 11008.

1334 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063315C211yesmaximal, characteristic
2C2×#14582764C211yesmaximal, characteristic
3C2×#14582763C211yesmaximal, characteristic
4#19132861C212yesmaximal
5#19132861C212yesmaximal
6#19132849C211yesmaximal, characteristic
7#19132848C211yesmaximal, characteristic
8#19132847C212yesmaximal
9#19132846C212yesmaximal
10#19132845C211yesmaximal, characteristic
11C43×#1441C211yesmaximal, characteristic
12C2×#13063315—24no—
13C2×#13063315—24no—
14C2×#13063315C418yescomplemented
15C22×C4⋊Dic43C2211yescharacteristic
16C22×C4⋊Dic43C2211yescharacteristic
17C22×Dic43⋊C4C2211yescharacteristic
18C22×Dic43⋊C4C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2212yes—
22C22×C4×Dic43C2211yescharacteristic
23#14582764—24no—
24#14582763—24no—
25C2×C43⋊#95C2211yescharacteristic
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C4⋊C4×C43C2211yescharacteristic
37C2×#95×C43C2211yescharacteristic
38C2×#95×C43C2212yes—
39C2×#95×C43C2212yes—
40C23×Dic43C2312yes—
41C23×Dic43C2312yes—
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2311yescharacteristic
44C23×Dic43C2311yescharacteristic
45C23×Dic43C2311yescharacteristic
46#13063315—232no—
47C2×C4⋊Dic43—22no—
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43—22no—
50C2×C4⋊Dic43—42no—
51C2×C4⋊Dic43C2×C414yes—
52C2×Dic43⋊C4—22no—
53C2×Dic43⋊C4—22no—
54C2×Dic43⋊C4—22no—
55C2×Dic43⋊C4—22no—
56C2×Dic43⋊C4—22no—
57C2×Dic43⋊C4—22no—
58C2×Dic43⋊C4—22no—
59C2×Dic43⋊C4—22no—
60C2×Dic43⋊C4—24no—
61C2×Dic43⋊C4—42no—
62C2×Dic43⋊C4—42no—
63C2×Dic43⋊C4C2×C414yes—
64C2×Dic43⋊C4C2×C414yes—
65C2×Dic43⋊C4C2×C414yes—
66C2×Dic43⋊C4C2×C414yes—
67C2×C4×Dic43C2×C414yes—
68C2×C4×Dic43D414yes—
69C2×C4×Dic43D414yes—
70C43⋊#95—22no—
71C43⋊#95—24no—
72C43⋊#95—24no—
73C43⋊#95—24no—
74C43⋊#95—42no—
75C43⋊#95—42no—
76C43⋊#95—42no—
77C43⋊#95—42no—
78C43⋊#95—42no—
79C43⋊#95—42no—
80C23×C4×C43C2312yes—
81C23×C4×C43C2312yes—
82C23×C4×C43C2311yescharacteristic
83C23×C4×C43C2311yescharacteristic
84C23×C4×C43C2311yescharacteristic
85C2×C4⋊C4×C43—22no—
86C2×C4⋊C4×C43—22no—
87C2×C4⋊C4×C43—22no—
88C2×C4⋊C4×C43—42no—
89C2×C4⋊C4×C43C2×C414yes—
90#95×C43—22no—
91#95×C43—42no—
92#95×C43—42no—
93C24×C43C2411yescharacteristic
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43—22no—
99C22×C4×C43—22no—
100C22×C4×C43—22no—
101C22×C4×C43—21no—
102C22×C4×C43—22no—
103C22×C4×C43—21no—
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—22no—
113C22×C4×C43—21no—
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×C43C22×C412yes—
121C22×C4×C43C22×C412yes—
122C22×C4×C43C22×C412yes—
123C22×C4×C43C2×D412yes—
124C22×C4×C43C2×D412yes—
125C22×Dic43—21no—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—22no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—21no—
144C22×Dic43—22no—
145C22×Dic43—21no—
146C22×Dic43—22no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43C22×C412yes—
156C22×Dic43C22×C412yes—
157C22×Dic43C22×C412yes—
158C22×Dic43C22×C412yes—
159C22×Dic43C2×D412yes—
160C22×Dic43C2×D412yes—
161C22×Dic43C2×D412yes—
162C22×Dic43C2×D412yes—
163C4⋊C4×C43—28no—
164C4⋊C4×C43—44no—
165C4⋊Dic43—28no—
166C4⋊Dic43—44no—
167Dic43⋊C4—28no—
168Dic43⋊C4—28no—
169Dic43⋊C4—28no—
170Dic43⋊C4—28no—
171Dic43⋊C4—48no—
172C4×Dic43C22⋊C4116yes—
173C23×C43C23×C411yescharacteristic
174C23×C43C22×D411yescharacteristic
175C23×C43C22×D411yescharacteristic
176C23×C43H(5,𝔽2)12yes—
177C23×C43H(5,𝔽2)11yescharacteristic
178C23×C43H(5,𝔽2)11yescharacteristic
179C23×C432−1+412yes—
180C23×C432−1+412yes—
181C23×C432−1+411yescharacteristic
182C23×C432−1+412yes—
183C23×C432−1+411yescharacteristic
184C2×C4×C43—24no—
185C2×C4×C43—22no—
186C2×C4×C43—22no—
187C2×C4×C43—24no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—24no—
191C2×C4×C43—22no—
192C2×C4×C43—22no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—42no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—42no—
201C2×C4×C43—42no—
202C2×C4×C43—42no—
203C2×C4×C43—42no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43C2×C22⋊C414yes—
215C2×Dic43—24no—
216C2×Dic43—22no—
217C2×Dic43—22no—
218C2×Dic43—22no—
219C2×Dic43—22no—
220C2×Dic43—24no—
221C2×Dic43—22no—
222C2×Dic43—22no—
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—22no—
227C2×Dic43—24no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—42no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—42no—
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×Dic43C2×C22⋊C414yes—
252C2×Dic43C2×C22⋊C414yes—
253#14664—431nomaximal, Sylow
254C22×C43C22×C22⋊C411yescharacteristic
255C22×C43#51912yes—
256C22×C43#52012yes—
257C22×C43#52011yescharacteristic
258C22×C43#52011yescharacteristic
259C22×C43#53511yescharacteristic
260C22×C43#53511yescharacteristic
261C22×C43#53611yescharacteristic
262C22×C43#53611yescharacteristic
263C22×C43#53612yes—
264C22×C43#53611yescharacteristic
265C22×C43#53611yescharacteristic
266C22×C43#53712yes—
267C22×C43#53711yescharacteristic
268C22×C43#53711yescharacteristic
269C22×C43#56212yes—
270C22×C43#56212yes—
271C22×C43#56312yes—
272C22×C43#56312yes—
273C22×C43#56312yes—
274C22×C43#56312yes—
275C22×C43#56412yes—
276C22×C43#56412yes—
277C4×C43—24no—
278C4×C43—42no—
279C4×C43—42no—
280C4×C43—82no—
281C4×C43—82no—
282Dic43—24no—
283Dic43—24no—
284Dic43—42no—
285Dic43—42no—
286Dic43—82no—
287Dic43—82no—
288C22×#125—431no—
289C2×#382—431no—
290C2×#382—431no—
291#1445—432no—
292#1445—432no—
293#1441—432no—
294#1441—432no—
295#1441—431no—
296#1441—431no—
297#1441—431no—
298#1441D4311yescharacteristic
299C2×C43#231011yescharacteristic
300C2×C43#231111yescharacteristic
301C2×C43#231111yescharacteristic
302C2×C43#238212yes—
303C2×C43#238212yes—
304C2×C43#282012yes—
305C2×C43#282011yescharacteristic
306C2×C43#282011yescharacteristic
307C2×C43#282212yes—
308C2×C43#282211yescharacteristic
309C2×C43#282211yescharacteristic
310C2×#125—438no—
311C2×#125—864no—
312C2×#125—864no—
313C22×C4⋊C4—431no—
314C22×C4⋊C4—431no—
315C22×C4⋊C4—431no—
316C22×C4⋊C4—431no—
317C22×C4⋊C4—431no—
318C22×C4⋊C4—432no—
319C22×C4⋊C4—431no—
320C22×C4⋊C4C2×D4311yescharacteristic
321C22×C4⋊C4C2×D4311yescharacteristic
322C22×C42—431no—
323#382—864no—
324#382—864no—
325C2×#95—432no—
326C2×#95—431no—
327C2×#95—432no—
328C2×#95—432no—
329C2×#95—432no—
330C2×#95—432no—
331C2×#95—432no—
332C2×#95—432no—
333C2×#95—432no—
334C2×#95—432no—
335C2×#95C2×D4311yescharacteristic
336C2×#95C2×D4312yes—
337C2×#95C2×D4312yes—
338C43#1466411yescharacteristic, complemented, Sylow
339C23×C4—431no—
340C23×C4—431no—
341C23×C4—431no—
342C23×C4—431no—
343C23×C4—432no—
344C23×C4—432no—
345C23×C4C22×D4312yes—
346C23×C4C22×D4312yes—
347C23×C4C22×D4311yescharacteristic
348C23×C4C22×D4311yescharacteristic
349C23×C4C22×D4311yescharacteristic
350#125—8632no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—434no—
356C2×C4⋊C4—434no—
357C2×C4⋊C4—434no—
358C2×C4⋊C4—434no—
359C2×C4⋊C4—434no—
360C2×C4⋊C4—862no—
361C2×C4⋊C4—862no—
362C2×C4⋊C4—862no—
363C2×C4⋊C4—862no—
364C2×C4⋊C4—862no—
365C2×C4⋊C4—862no—
366C2×C4⋊C4—862no—
367C2×C4⋊C4—862no—
368C2×C4⋊C4—862no—
369C2×C4⋊C4—862no—
370C2×C4⋊C4—864no—
371C2×C4⋊C4—862no—
372C2×C4⋊C4—1722no—
373C2×C4⋊C4—1722no—
374C2×C4⋊C4—1722no—
375C2×C4⋊C4C4×D4314yes—
376C2×C42—434no—
377C2×C42—434no—
378C2×C42—434no—
379#95—22no—
380#95—42no—
381#95—42no—
382#95—864no—
383#95—864no—
384#95—864no—
385#95—862no—
386#95—1722no—
387#95—1722no—
388#95—1722no—
389#95—1722no—
390#95—1722no—
391#95—1722no—
392C24C23×D4311yescharacteristic
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—432no—
420C22×C4—432no—
421C22×C4—432no—
422C22×C4—432no—
423C22×C4—432no—
424C22×C4—432no—
425C22×C4—432no—
426C22×C4—432no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—862no—
430C22×C4—861no—
431C22×C4—862no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—862no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—862no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—862no—
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×C4C2×C4×D4312yes—
458C22×C4C2×C4×D4312yes—
459C22×C4C2×C4×D4312yes—
460C22×C4D4×D4312yes—
461C22×C4D4×D4312yes—
462C4⋊C4—28no—
463C4⋊C4—44no—
464C4⋊C4—868no—
465C4⋊C4—868no—
466C4⋊C4—868no—
467C4⋊C4—868no—
468C4⋊C4—868no—
469C4⋊C4—1724no—
470C4⋊C4—1728no—
471C42—4316no—
472C23C22×C4×D4311yescharacteristic
473C23C2×D4×D4311yescharacteristic
474C23C2×D4×D4311yescharacteristic
475C23#1306337012yes—
476C23#1306337011yescharacteristic
477C23#1306337111yescharacteristic
478C23#1306337212yes—
479C23#1306337212yes—
480C23#1306337211yescharacteristic
481C23#1306337312yes—
482C23#1306337311yescharacteristic
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—434no—
514C2×C4—434no—
515C2×C4—864no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—862no—
519C2×C4—862no—
520C2×C4—864no—
521C2×C4—862no—
522C2×C4—862no—
523C2×C4—862no—
524C2×C4—862no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—864no—
528C2×C4—862no—
529C2×C4—862no—
530C2×C4—1722no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1722no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4—1722no—
542C2×C4—1722no—
543C2×C4—1722no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1722no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4C22⋊C4×D4314yes—
552C22C2×C22⋊C4×D4311yescharacteristic
553C22#1458337512yes—
554C22#1458337812yes—
555C22#1458337911yescharacteristic
556C22#1458338011yescharacteristic
557C22#1458346411yescharacteristic
558C22#1458346511yescharacteristic
559C22#1458346911yescharacteristic
560C22#1458347111yescharacteristic
561C22#1458347211yescharacteristic
562C22#1458347212yes—
563C22#1458347411yescharacteristic
564C22#1458347612yes—
565C22#1458347811yescharacteristic
566C22#1458347911yescharacteristic
567C22#1458364412yes—
568C22#1458364512yes—
569C22#1458364812yes—
570C22#1458365012yes—
571C22#1458365112yes—
572C22#1458365212yes—
573C22C43⋊#56412yes—
574C22C43⋊#56412yes—
575C4—24no—
576C4—42no—
577C4—42no—
578C4—82no—
579C4—82no—
580C4—864no—
581C4—864no—
582C4—3442no—
583C4—3442no—
584C4—1722no—
585C4—1722no—
586C2#1913717811yescharacteristic
587C2#1913718211yescharacteristic
588C2#1913718411yescharacteristic
589C2#1913777712yes—
590C2#1913777912yes—
591C2#1914264412yes—
592C2#1914264811yescharacteristic
593C2#1914265011yescharacteristic
594C2#1914266112yes—
595C2#1914266411yescharacteristic
596C2#1914266511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1441C2
socle, prime radical, cosocleC24×C43C24
hypercenter#1441D43
hypocenterC43#14664
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
14. C2×#13063315C4semidirect
338. C43#14664semidirect

Maximal subgroups

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

subgroupindex
C22×#130633152
C2×#145827642
C2×#145827632
#191328612
#191328492
#191328482
#191328472
#191328462
#191328452
C43×#14412
#1466443