Finite Group Databasebeta

← #25033321

Subgroups — #25033321

Order 11008.

1566 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582833C212yesmaximal
2C2×#14582832C212yesmaximal
3C2×#14582796C211yesmaximal, characteristic
4C2×#14582768C212yesmaximal
5C2×#14582768C211yesmaximal, characteristic
6#19132860C211yesmaximal, characteristic
7#19132859C211yesmaximal, characteristic
8#19132858C211yesmaximal, characteristic
9Dic43⋊#95C212yesmaximal
10#95×Dic43C211yesmaximal, characteristic
11C43×#1444C211yesmaximal, characteristic
12C22×C4⋊Dic43C2211yescharacteristic
13C22×C4⋊Dic43C2212yes—
14C22×C4⋊Dic43C2211yescharacteristic
15C22×Dic43⋊C4C2211yescharacteristic
16C22×Dic43⋊C4C2211yescharacteristic
17C22×Dic43⋊C4C2212yes—
18C22×Dic43⋊C4C2212yes—
19C22×Dic43⋊C4C2212yes—
20C22×Dic43⋊C4C2212yes—
21C22×Dic43⋊C4C2211yescharacteristic
22C22×C4×Dic43C2211yescharacteristic
23C22×C4×Dic43C2212yes—
24#14582833—28no—
25#14582832—28no—
26#14582796—24no—
27#14582768—28no—
28#14582768—24no—
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2211yescharacteristic
35C22×C4⋊C4×C43C2212yes—
36C22×C4⋊C4×C43C2211yescharacteristic
37C2×#95×C43C2211yescharacteristic
38C2×#95×C43C2212yes—
39C2×#95×C43C2211yescharacteristic
40C23×Dic43C2312yes—
41C23×Dic43C2311yescharacteristic
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2311yescharacteristic
44C23×Dic43C2312yes—
45C23×Dic43C2311yescharacteristic
46C2×C4⋊Dic43—24no—
47C2×C4⋊Dic43—22no—
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43—24no—
50C2×C4⋊Dic43—24no—
51C2×C4⋊Dic43—42no—
52C2×C4⋊Dic43—42no—
53C2×Dic43⋊C4—22no—
54C2×Dic43⋊C4—22no—
55C2×Dic43⋊C4—24no—
56C2×Dic43⋊C4—22no—
57C2×Dic43⋊C4—22no—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—24no—
60C2×Dic43⋊C4—24no—
61C2×Dic43⋊C4—24no—
62C2×Dic43⋊C4—24no—
63C2×Dic43⋊C4—24no—
64C2×Dic43⋊C4—24no—
65C2×Dic43⋊C4—24no—
66C2×Dic43⋊C4—24no—
67C2×Dic43⋊C4—24no—
68C2×Dic43⋊C4—24no—
69C2×Dic43⋊C4—42no—
70C2×Dic43⋊C4—42no—
71C2×Dic43⋊C4D414yes—
72C2×C4×Dic43—24no—
73C2×C4×Dic43—24no—
74C2×C4×Dic43—24no—
75C2×C4×Dic43D414yes—
76C2×C4×Dic43Q818yes—
77C43⋊#95—22no—
78C43⋊#95—24no—
79C43⋊#95—24no—
80C43⋊#95—24no—
81C43⋊#95D418yes—
82C43⋊#95Q814yes—
83C23×C4×C43C2312yes—
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C23×C4×C43C2312yes—
87C23×C4×C43C2311yescharacteristic
88C2×C4⋊C4×C43—24no—
89C2×C4⋊C4×C43—24no—
90C2×C4⋊C4×C43—22no—
91C2×C4⋊C4×C43—42no—
92C2×C4⋊C4×C43—42no—
93#95×C43—22no—
94#95×C43—24no—
95#95×C43Q814yes—
96C24×C43C2411yescharacteristic
97C22×C4×C43—22no—
98C22×C4×C43—21no—
99C22×C4×C43—22no—
100C22×C4×C43—22no—
101C22×C4×C43—21no—
102C22×C4×C43—22no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—21no—
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—21no—
118C22×C4×C43—21no—
119C22×C4×C43C2×D412yes—
120C22×C4×C43C2×D414yes—
121C22×C4×C43C2×D412yes—
122C22×C4×C43C2×Q814yes—
123C22×C4×C43C2×Q812yes—
124C22×C4×C43C2×Q812yes—
125C22×C4×C43C2×Q814yes—
126C22×Dic43—22no—
127C22×Dic43—21no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—21no—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—21no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—22no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D412yes—
150C22×Dic43C2×D414yes—
151C22×Dic43C2×D412yes—
152C22×Dic43C2×D414yes—
153C22×Dic43C2×D412yes—
154C22×Dic43C2×D412yes—
155C22×Dic43C2×Q814yes—
156C22×Dic43C2×Q814yes—
157C22×Dic43C2×Q814yes—
158C22×Dic43#4112yes—
159C22×Dic43#4114yes—
160C4⋊C4×C43—48no—
161C4⋊C4×C43—44no—
162C4⋊Dic43—48no—
163C4⋊Dic43—44no—
164C4⋊Dic43—44no—
165Dic43⋊C4—28no—
166Dic43⋊C4—48no—
167Dic43⋊C4—48no—
168Dic43⋊C4—48no—
169Dic43⋊C4—44no—
170Dic43⋊C4—44no—
171Dic43⋊C4—48no—
172C4×Dic43—216no—
173C4×Dic43—28no—
174C23×C43C22×D411yescharacteristic
175C23×C43C22×D411yescharacteristic
176C23×C43C22×D412yes—
177C23×C43C22×Q812yes—
178C23×C43C22×Q811yescharacteristic
179C23×C43C22×Q811yescharacteristic
180C23×C43C2×#4111yescharacteristic
181C23×C43C2×#4112yes—
182C23×C43H(5,𝔽2)12yes—
183C23×C432−1+411yescharacteristic
184C23×C432−1+411yescharacteristic
185C2×C4×C43—24no—
186C2×C4×C43—22no—
187C2×C4×C43—22no—
188C2×C4×C43—24no—
189C2×C4×C43—24no—
190C2×C4×C43—24no—
191C2×C4×C43—24no—
192C2×C4×C43—24no—
193C2×C4×C43—24no—
194C2×C4×C43—24no—
195C2×C4×C43—22no—
196C2×C4×C43—24no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—42no—
204C2×C4×C43—42no—
205C2×C4×C43—41no—
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×C43C4⋊Q818yes—
213C2×C4×C43C4⋊Q814yes—
214C2×Dic43—24no—
215C2×Dic43—22no—
216C2×Dic43—22no—
217C2×Dic43—24no—
218C2×Dic43—24no—
219C2×Dic43—24no—
220C2×Dic43—24no—
221C2×Dic43—24no—
222C2×Dic43—24no—
223C2×Dic43—24no—
224C2×Dic43—22no—
225C2×Dic43—24no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—42no—
229C2×Dic43—42no—
230C2×Dic43—41no—
231C2×Dic43—42no—
232C2×Dic43—41no—
233C2×Dic43—42no—
234C2×Dic43—41no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43#12114yes—
242C2×Dic43C22⋊Q818yes—
243C2×Dic43#12314yes—
244C2×Dic43#12518yes—
245C2×Dic43#12714yes—
246C2×Dic43C4⋊Q818yes—
247C2×Dic43C4⋊Q814yes—
248#15145—431nomaximal, Sylow
249C22×C43C2×#12111yescharacteristic
250C22×C43C2×C22⋊Q812yes—
251C22×C43C2×#12311yescharacteristic
252C22×C43C2×#12512yes—
253C22×C43C2×#12711yescharacteristic
254C22×C43C2×C4⋊Q811yescharacteristic
255C22×C43C2×C4⋊Q812yes—
256C22×C43C2×C4⋊Q812yes—
257C22×C43C2×C4⋊Q811yescharacteristic
258C22×C43#53511yescharacteristic
259C22×C43#53611yescharacteristic
260C22×C43#54412yes—
261C22×C43#54412yes—
262C22×C43D4212yes—
263C22×C43#54712yes—
264C22×C43#54712yes—
265C22×C43D4×Q811yescharacteristic
266C22×C43D4×Q811yescharacteristic
267C22×C43#55012yes—
268C22×C43#55412yes—
269C22×C43#55412yes—
270C22×C43#55711yescharacteristic
271C22×C43#55711yescharacteristic
272C4×C43—28no—
273C4×C43—24no—
274C4×C43—42no—
275C4×C43—81no—
276C4×C43—82no—
277Dic43—28no—
278Dic43—24no—
279Dic43—42no—
280Dic43—81no—
281Dic43—82no—
282Dic43#39818yescomplemented
283C2×#398—432no—
284C2×#398—432no—
285C2×#389—431no—
286C2×#384—432no—
287C2×#384—431no—
288#1444—431no—
289#1444—431no—
290#1444—431no—
291#1444D4311yescharacteristic
292C4⋊#95—432no—
293C4×#95—431no—
294C2×C43C2×#39811yescharacteristic
295C2×C43#244012yes—
296C2×C43#244012yes—
297C2×C43#250111yescharacteristic
298C2×C43#250211yescharacteristic
299C2×C43#254111yescharacteristic
300C2×C43#254611yescharacteristic
301C2×C43#255212yes—
302C2×C43#255212yes—
303C2×C43#266011yescharacteristic
304C2×C43#286811yescharacteristic
305C22×C4⋊C4—431no—
306C22×C4⋊C4—432no—
307C22×C4⋊C4—431no—
308C22×C4⋊C4—431no—
309C22×C4⋊C4—432no—
310C22×C4⋊C4—431no—
311C22×C4⋊C4—432no—
312C22×C4⋊C4—432no—
313C22×C4⋊C4—432no—
314C22×C4⋊C4—431no—
315C22×C4⋊C4C2×D4312yes—
316C22×C4⋊C4C2×D4311yescharacteristic
317C22×C42—432no—
318C22×C42—431no—
319#398—868no—
320#398—868no—
321#389—864no—
322#384—864no—
323#384—868no—
324C2×#95—432no—
325C2×#95—431no—
326C2×#95—432no—
327C2×#95—432no—
328C2×#95—432no—
329C2×#95—431no—
330C2×#95C2×D4312yes—
331C2×#95C2×D4311yescharacteristic
332C2×#95C2×D4311yescharacteristic
333C43#1514511yescharacteristic, complemented, Sylow
334C23×C4—431no—
335C23×C4—431no—
336C23×C4—432no—
337C23×C4—431no—
338C23×C4—432no—
339C23×C4—431no—
340C23×C4C22×D4312yes—
341C23×C4C22×D4311yescharacteristic
342C23×C4C22×D4311yescharacteristic
343C23×C4C22×D4312yes—
344C23×C4C22×D4311yescharacteristic
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—434no—
351C2×C4⋊C4—862no—
352C2×C4⋊C4—862no—
353C2×C4⋊C4—864no—
354C2×C4⋊C4—864no—
355C2×C4⋊C4—864no—
356C2×C4⋊C4—864no—
357C2×C4⋊C4—864no—
358C2×C4⋊C4—864no—
359C2×C4⋊C4—862no—
360C2×C4⋊C4—862no—
361C2×C4⋊C4—864no—
362C2×C4⋊C4—864no—
363C2×C4⋊C4—864no—
364C2×C4⋊C4—864no—
365C2×C4⋊C4—864no—
366C2×C4⋊C4—864no—
367C2×C4⋊C4—862no—
368C2×C4⋊C4—864no—
369C2×C4⋊C4—864no—
370C2×C4⋊C4—862no—
371C2×C4⋊C4—864no—
372C2×C4⋊C4—1722no—
373C2×C4⋊C4—1722no—
374C2×C4⋊C4—1722no—
375C2×C4⋊C4—1722no—
376C2×C42—434no—
377C2×C42—438no—
378C2×C42—864no—
379C2×C42—864no—
380C2×C42—864no—
381#95—22no—
382#95—24no—
383#95—438no—
384#95—434no—
385#95—864no—
386#95—864no—
387#95—862no—
388#95—864no—
389#95Dic8614yes—
390C24C23×D4311yescharacteristic
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—432no—
414C22×C4—432no—
415C22×C4—434no—
416C22×C4—434no—
417C22×C4—432no—
418C22×C4—434no—
419C22×C4—434no—
420C22×C4—432no—
421C22×C4—434no—
422C22×C4—434no—
423C22×C4—432no—
424C22×C4—862no—
425C22×C4—862no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—861no—
429C22×C4—862no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—862no—
433C22×C4—861no—
434C22×C4—862no—
435C22×C4—862no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—861no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4C2×Dic8614yes—
448C22×C4C2×Dic8612yes—
449C22×C4D4×D4312yes—
450C22×C4D4×D4314yes—
451C22×C4D4×D4312yes—
452C22×C4Q8×D4312yes—
453C22×C4Q8×D4314yes—
454C4⋊C4—48no—
455C4⋊C4—44no—
456C4⋊C4—868no—
457C4⋊C4—1728no—
458C4⋊C4—1728no—
459C4⋊C4—1724no—
460C4⋊C4—1728no—
461C4⋊C4—1724no—
462C4⋊C4—1728no—
463C4⋊C4—1724no—
464C4⋊C4—1724no—
465C4⋊C4—1728no—
466C42—8616no—
467C42—868no—
468C23C2×D4×D4311yescharacteristic
469C23C2×D4×D4312yes—
470C23C2×D4×D4311yescharacteristic
471C23C2×Q8×D4311yescharacteristic
472C23C2×Q8×D4312yes—
473C23C22×Dic8611yescharacteristic
474C23#41×D4311yescharacteristic
475C23#41×D4312yes—
476C23#1306337012yes—
477C23#1306337211yescharacteristic
478C23#1306337311yescharacteristic
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—434no—
507C2×C4—438no—
508C2×C4—434no—
509C2×C4—438no—
510C2×C4—434no—
511C2×C4—434no—
512C2×C4—438no—
513C2×C4—864no—
514C2×C4—864no—
515C2×C4—864no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—864no—
519C2×C4—864no—
520C2×C4—864no—
521C2×C4—864no—
522C2×C4—864no—
523C2×C4—862no—
524C2×C4—864no—
525C2×C4—1722no—
526C2×C4—1722no—
527C2×C4—1722no—
528C2×C4—1721no—
529C2×C4—1722no—
530C2×C4—1721no—
531C2×C4—1722no—
532C2×C4—1721no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4#1306332418yes—
541C2×C4#1306332414yes—
542C22#121×D4311yescharacteristic
543C22C22⋊Q8×D4312yes—
544C22#123×D4311yescharacteristic
545C22#125×D4312yes—
546C22#127×D4311yescharacteristic
547C22C4⋊Q8×D4311yescharacteristic
548C22C4⋊Q8×D4312yes—
549C22C2×#1306332412yes—
550C22C2×#1306332411yescharacteristic
551C22#1458346411yescharacteristic
552C22#1458347211yescharacteristic
553C22#1458352612yes—
554C22#1458352812yes—
555C22#1458353112yes—
556C22#1458354712yes—
557C22#1458355112yes—
558C22#1458356411yescharacteristic
559C22D4×Dic8611yescharacteristic
560C22#1458356712yes—
561C22#1458360312yes—
562C22#1458360812yes—
563C22#1458362511yescharacteristic
564C22#1458362611yescharacteristic
565C4—28no—
566C4—24no—
567C4—42no—
568C4—82no—
569C4—81no—
570C4—438no—
571C4—868no—
572C4—864no—
573C4—3442no—
574C4—3441no—
575C4—1722no—
576C2#398×D4311yescharacteristic
577C2#1913829012yes—
578C2#1913829612yes—
579C2#1913906111yescharacteristic
580C2#1913907111yescharacteristic
581C2#1913953611yescharacteristic
582C2#1913958211yescharacteristic
583C2#1913962512yes—
584C2#1913963212yes—
585C2#1914071311yescharacteristic
586C2#1914299211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, prime radical, cosocleC24×C43C24
FittingC43×#1444C2
hypercenter#1444D43
hypocenterC43#15145
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
282. Dic43#398semidirect
333. C43#15145semidirect

Maximal subgroups

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

subgroupindex
C2×#145828332
C2×#145828322
C2×#145827962
C2×#145827682
#191328602
#191328592
#191328582
Dic43⋊#952
#95×Dic432
C43×#14442
#1514543