Finite Group Databasebeta

← #25033353

Subgroups — #25033353

Order 11008.

1410 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582830C211yesmaximal, characteristic
2C2×#14582794C212yesmaximal
3C2×#14582794C211yesmaximal, characteristic
4C2×C4⋊C4×Dic43C211yesmaximal, characteristic
5#19132854C212yesmaximal
6#19132853C212yesmaximal
7#19132849C211yesmaximal, characteristic
8#19132848C211yesmaximal, characteristic
9Dic43⋊#95C212yesmaximal
10Dic43⋊#95C211yesmaximal, characteristic
11C2×C43×#398C211yesmaximal, characteristic
12C22×C4⋊Dic43C2211yescharacteristic
13C22×Dic43⋊C4C2211yescharacteristic
14C22×Dic43⋊C4C2211yescharacteristic
15C22×Dic43⋊C4C2212yes—
16C22×Dic43⋊C4C2211yescharacteristic
17C22×Dic43⋊C4C2212yes—
18C22×C4×Dic43C2212yes—
19C22×C4×Dic43C2211yescharacteristic
20#14582830—24no—
21#14582794—28no—
22#14582794—24no—
23C4⋊C4×Dic43—24no—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2211yescharacteristic
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C22×C4⋊C4×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2212yes—
36C22×C4⋊C4×C43C2211yescharacteristic
37C43×#398—24no—
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2212yes—
40C23×Dic43C2311yescharacteristic
41C23×Dic43C2311yescharacteristic
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2312yes—
44C23×Dic43C2312yes—
45C23×Dic43C2311yescharacteristic
46C2×C4⋊Dic43—22no—
47C2×C4⋊Dic43—24no—
48C2×Dic43⋊C4—22no—
49C2×Dic43⋊C4—24no—
50C2×Dic43⋊C4—22no—
51C2×Dic43⋊C4—24no—
52C2×Dic43⋊C4—22no—
53C2×Dic43⋊C4—24no—
54C2×Dic43⋊C4—22no—
55C2×Dic43⋊C4—22no—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—22no—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—42no—
60C2×Dic43⋊C4D414yes—
61C2×Dic43⋊C4Q818yes—
62C2×C4×Dic43—24no—
63C2×C4×Dic43—24no—
64C2×C4×Dic43—24no—
65C2×C4×Dic43—24no—
66C2×C4×Dic43D414yes—
67C43⋊#95—24no—
68C43⋊#95—22no—
69C43⋊#95—24no—
70C43⋊#95—24no—
71C43⋊#95—22no—
72C43⋊#95—22no—
73C43⋊#95—24no—
74C43⋊#95—24no—
75C43⋊#95—24no—
76C43⋊#95—42no—
77C23×C4×C43C2311yescharacteristic
78C23×C4×C43C2311yescharacteristic
79C23×C4×C43C2312yes—
80C23×C4×C43C2312yes—
81C23×C4×C43C2311yescharacteristic
82C2×C4⋊C4×C43—22no—
83C2×C4⋊C4×C43—22no—
84C2×C4⋊C4×C43—24no—
85C2×C4⋊C4×C43—22no—
86C2×C4⋊C4×C43—24no—
87C2×C4⋊C4×C43—22no—
88C2×C4⋊C4×C43—22no—
89C2×C4⋊C4×C43—42no—
90C2×C4⋊C4×C43D414yes—
91#95×C43—22no—
92#95×C43—24no—
93C24×C43C2411yescharacteristic
94C22×C4×C43—22no—
95C22×C4×C43—21no—
96C22×C4×C43—22no—
97C22×C4×C43—21no—
98C22×C4×C43—22no—
99C22×C4×C43—22no—
100C22×C4×C43—21no—
101C22×C4×C43—21no—
102C22×C4×C43—22no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—21no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—21no—
109C22×C4×C43—22no—
110C22×C4×C43—21no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—21no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43C2×D412yes—
120C22×C4×C43C2×D412yes—
121C22×C4×C43C2×D414yes—
122C22×C4×C43C2×D412yes—
123C22×C4×C43C2×Q814yes—
124C22×C4×C43#4112yes—
125C22×Dic43—22no—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—21no—
129C22×Dic43—22no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—21no—
137C22×Dic43—22no—
138C22×Dic43—21no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—22no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43C2×D412yes—
153C22×Dic43C2×D412yes—
154C22×Dic43C2×D412yes—
155C22×Dic43C2×D412yes—
156C22×Dic43C2×Q814yes—
157C22×Dic43C2×Q814yes—
158C22×Dic43#4114yes—
159C22×Dic43#4112yes—
160C22×Dic43#4114yes—
161C4⋊C4×C43—28no—
162C4⋊C4×C43—48no—
163C4⋊C4×C43—44no—
164C4⋊Dic43—28no—
165Dic43⋊C4—28no—
166Dic43⋊C4—216no—
167Dic43⋊C4—48no—
168Dic43⋊C4—44no—
169Dic43⋊C4—44no—
170C4×Dic43—28no—
171C4×Dic43—48no—
172C23×C43C22×D411yescharacteristic
173C23×C43C22×D411yescharacteristic
174C23×C43C22×D411yescharacteristic
175C23×C43C22×Q812yes—
176C23×C43C2×#4111yescharacteristic
177C23×C43C2×#4112yes—
178C23×C43C2×#4112yes—
179C23×C43C2×#4111yescharacteristic
180C23×C43H(5,𝔽2)11yescharacteristic
181C23×C432−1+411yescharacteristic
182C23×C432−1+412yes—
183C2×C4×C43—22no—
184C2×C4×C43—22no—
185C2×C4×C43—24no—
186C2×C4×C43—24no—
187C2×C4×C43—22no—
188C2×C4×C43—24no—
189C2×C4×C43—24no—
190C2×C4×C43—24no—
191C2×C4×C43—22no—
192C2×C4×C43—24no—
193C2×C4×C43—22no—
194C2×C4×C43—24no—
195C2×C4×C43—24no—
196C2×C4×C43—42no—
197C2×C4×C43—41no—
198C2×C4×C43—42no—
199C2×C4×C43—42no—
200C2×C4×C43—41no—
201C2×C4×C43—42no—
202C2×C4×C43—42no—
203C2×C4×C43—41no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43#12114yes—
214C2×Dic43—22no—
215C2×Dic43—24no—
216C2×Dic43—22no—
217C2×Dic43—24no—
218C2×Dic43—22no—
219C2×Dic43—22no—
220C2×Dic43—22no—
221C2×Dic43—22no—
222C2×Dic43—24no—
223C2×Dic43—24no—
224C2×Dic43—24no—
225C2×Dic43—24no—
226C2×Dic43—42no—
227C2×Dic43—41no—
228C2×Dic43—42no—
229C2×Dic43—42no—
230C2×Dic43—41no—
231C2×Dic43—42no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235C2×Dic43—41no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43#12114yes—
246C2×Dic43C22⋊Q818yes—
247C2×Dic43#12314yes—
248C2×Dic43#12518yes—
249C2×Dic43C4⋊Q814yes—
250#15149—431nomaximal, Sylow
251C22×C43C2×#12111yescharacteristic
252C22×C43C2×#12111yescharacteristic
253C22×C43C2×C22⋊Q812yes—
254C22×C43C2×#12311yescharacteristic
255C22×C43#52511yescharacteristic
256C22×C43C2×#12512yes—
257C22×C43#52912yes—
258C22×C43C2×C4⋊Q811yescharacteristic
259C22×C43#53212yes—
260C22×C43#53611yescharacteristic
261C22×C43#53711yescharacteristic
262C22×C43#54112yes—
263C22×C43#54212yes—
264C22×C43D4211yescharacteristic
265C22×C43#54711yescharacteristic
266C22×C43#54711yescharacteristic
267C22×C43#54812yes—
268C22×C43D4×Q812yes—
269C22×C43#55212yes—
270C22×C43#55412yes—
271C22×C43#55511yescharacteristic
272C22×C43#55712yes—
273C22×C43#55712yes—
274C4×C43—24no—
275C4×C43—44no—
276C4×C43—42no—
277C4×C43—44no—
278C4×C43—81no—
279Dic43—42no—
280Dic43—44no—
281Dic43—44no—
282Dic43—42no—
283Dic43—81no—
284Dic43#39818yescomplemented
285C2×#398—431no—
286C2×#398D4311yescharacteristic
287C2×#389—432no—
288C2×#389—431no—
289C2×C4×C4⋊C4—431no—
290#1442—432no—
291#1442—432no—
292#1441—431no—
293#1441—431no—
294C4⋊#95—431no—
295C4⋊#95—432no—
296C2×C43C2×#39811yescharacteristic
297C2×C43#245212yes—
298C2×C43#245312yes—
299C2×C43#250612yes—
300C2×C43#250812yes—
301C2×C43#253611yescharacteristic
302C2×C43#253711yescharacteristic
303C2×C43#254611yescharacteristic
304C2×C43#258411yescharacteristic
305C2×C43#262511yescharacteristic
306C2×C43#285411yescharacteristic
307C22×C4⋊C4—432no—
308C22×C4⋊C4—431no—
309C22×C4⋊C4—431no—
310C22×C4⋊C4—431no—
311C22×C4⋊C4—431no—
312C22×C4⋊C4—432no—
313C22×C4⋊C4C2×D4311yescharacteristic
314C22×C4⋊C4C2×D4312yes—
315C22×C4⋊C4C2×D4311yescharacteristic
316C22×C42—431no—
317C22×C42—432no—
318#398—24no—
319#398—864no—
320#389—864no—
321#389—868no—
322C4×C4⋊C4—864no—
323C2×#95—431no—
324C2×#95—432no—
325C2×#95—432no—
326C2×#95—432no—
327C2×#95—432no—
328C2×#95—432no—
329C2×#95—432no—
330C2×#95—431no—
331C2×#95—431no—
332C2×#95—432no—
333C2×#95C2×D4311yescharacteristic
334C2×#95C2×D4312yes—
335C43#1514911yescharacteristic, complemented, Sylow
336C23×C4—431no—
337C23×C4—431no—
338C23×C4—432no—
339C23×C4—432no—
340C23×C4—431no—
341C23×C4—431no—
342C23×C4C22×D4311yescharacteristic
343C23×C4C22×D4311yescharacteristic
344C23×C4C22×D4312yes—
345C23×C4C22×D4312yes—
346C23×C4C22×D4311yescharacteristic
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—434no—
356C2×C4⋊C4—438no—
357C2×C4⋊C4—862no—
358C2×C4⋊C4—864no—
359C2×C4⋊C4—862no—
360C2×C4⋊C4—864no—
361C2×C4⋊C4—864no—
362C2×C4⋊C4—862no—
363C2×C4⋊C4—864no—
364C2×C4⋊C4—864no—
365C2×C4⋊C4—862no—
366C2×C4⋊C4—862no—
367C2×C4⋊C4—862no—
368C2×C4⋊C4—864no—
369C2×C4⋊C4—862no—
370C2×C4⋊C4—1722no—
371C2×C4⋊C4C22⋊D4314yes—
372C2×C42—434no—
373C2×C42—864no—
374C2×C42—864no—
375C2×C42—864no—
376C2×C42—864no—
377#95—22no—
378#95—24no—
379#95—864no—
380#95—864no—
381#95—864no—
382#95—862no—
383#95—864no—
384#95—862no—
385#95—864no—
386#95—862no—
387#95—864no—
388#95—1722no—
389C24C23×D4311yescharacteristic
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—432no—
416C22×C4—432no—
417C22×C4—434no—
418C22×C4—432no—
419C22×C4—434no—
420C22×C4—432no—
421C22×C4—432no—
422C22×C4—434no—
423C22×C4—434no—
424C22×C4—862no—
425C22×C4—862no—
426C22×C4—861no—
427C22×C4—862no—
428C22×C4—862no—
429C22×C4—861no—
430C22×C4—862no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4—861no—
434C22×C4—862no—
435C22×C4—862no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—862no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—861no—
451C22×C4D4×D4312yes—
452C22×C4D4×D4312yes—
453C22×C4#1062190012yes—
454C22×C4Q8×D4314yes—
455C22×C4C2×C22⋊D4314yes—
456C22×C4C2×C22⋊D4312yes—
457C4⋊C4—28no—
458C4⋊C4—48no—
459C4⋊C4—44no—
460C4⋊C4—868no—
461C4⋊C4—8616no—
462C4⋊C4—868no—
463C4⋊C4—1728no—
464C4⋊C4—1724no—
465C4⋊C4—1724no—
466C42—868no—
467C42—1728no—
468C23C2×D4×D4311yescharacteristic
469C23C2×D4×D4311yescharacteristic
470C23C22×C22⋊D4311yescharacteristic
471C23C2×Q8×D4312yes—
472C23#41×D4312yes—
473C23#41×D4311yescharacteristic
474C23#41×D4312yes—
475C23C2×#1062190011yescharacteristic
476C23#1306337011yescharacteristic
477C23#1306337211yescharacteristic
478C23#1306337312yes—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—434no—
510C2×C4—438no—
511C2×C4—434no—
512C2×C4—438no—
513C2×C4—434no—
514C2×C4—864no—
515C2×C4—864no—
516C2×C4—864no—
517C2×C4—864no—
518C2×C4—862no—
519C2×C4—864no—
520C2×C4—862no—
521C2×C4—864no—
522C2×C4—862no—
523C2×C4—862no—
524C2×C4—862no—
525C2×C4—862no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1722no—
530C2×C4—1722no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1721no—
535C2×C4—1722no—
536C2×C4—1721no—
537C2×C4—1722no—
538C2×C4—1722no—
539C2×C4—1721no—
540C2×C4—1722no—
541C2×C4—1722no—
542C2×C4—1722no—
543C2×C4—1722no—
544C2×C4—1721no—
545C2×C4#1306329714yes—
546C22#121×D4311yescharacteristic
547C22C2×#1306329711yescharacteristic
548C22C22⋊Q8×D4312yes—
549C22#123×D4311yescharacteristic
550C22#1458340711yescharacteristic
551C22#125×D4312yes—
552C22#1458342612yes—
553C22C4⋊Q8×D4311yescharacteristic
554C22#1458344512yes—
555C22#1458347411yescharacteristic
556C22#1458347811yescharacteristic
557C22#1458350812yes—
558C22#1458351912yes—
559C22D4×C22⋊D4311yescharacteristic
560C22#1458354811yescharacteristic
561C22#1458354911yescharacteristic
562C22#1458355912yes—
563C22Q8×C22⋊D4312yes—
564C22#1458358112yes—
565C22#1458360312yes—
566C22#1458361311yescharacteristic
567C22#1458362412yes—
568C22#1458362612yes—
569C4—24no—
570C4—44no—
571C4—42no—
572C4—44no—
573C4—81no—
574C4—438no—
575C4—3441no—
576C4—1722no—
577C4—1724no—
578C4—1724no—
579C4—1722no—
580C2#398×D4311yescharacteristic
581C2#1913844412yes—
582C2#1913845112yes—
583C2#1913911012yes—
584C2#1913912812yes—
585C2#1913950111yescharacteristic
586C2#1913950911yescharacteristic
587C2#1913958111yescharacteristic
588C2#1913997911yescharacteristic
589C2#1914039811yescharacteristic
590C2#1914292411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, prime radical, cosocleC24×C43C24
FittingC2×C43×#398C2
hypercenterC2×#398D43
hypocenterC43#15149
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
284. Dic43#398semidirect
335. C43#15149semidirect

Maximal subgroups

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

subgroupindex
C2×#145828302
C2×#145827942
C2×C4⋊C4×Dic432
#191328542
#191328532
#191328492
#191328482
Dic43⋊#952
C2×C43×#3982
#1514943