Finite Group Databasebeta

← #25096553

Subgroups — #25096553

Order 11008.

1694 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D43C211yesmaximal, characteristic
2#19143226C212yesmaximal, complemented
3#19134674C212yesmaximal, complemented
4#19134586C212yesmaximal, complemented
5#19134585C212yesmaximal, complemented
6#19134514C212yesmaximal
7C4×#13063241C212yesmaximal, complemented
8C4×#13063242C211yesmaximal, characteristic, complemented
9C4×#100×C43C211yesmaximal, characteristic, complemented
10C22×D4×D43C2211yescharacteristic
11C23×C4×D43C412yes—
12C2×C4×D172C2211yescharacteristic
13C2×D4×Dic43C2211yescharacteristic
14C2×#13063287C2211yescharacteristic
15C2×C4×C22⋊D43C412yes—
16C2×(C22⋊D43)⋊C4C412yes—
17C4×D4×D43—22no—
18C4×D4×D43—22no—
19C4×D4×D43—22no—
20C4×D4×D43—22no—
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C22⋊C4×D43C412yes—
23C2×C42×D43C2211yescharacteristic
24#14582954—22no—
25#14582954—22no—
26#14582950—22no—
27#14582950—22no—
28#14582922C2214yescomplemented
29C2×#13063242C2212yes—
30C2×#13063241C2214yes—
31#14582862C2214yes—
32C4×#10621877C2212yescomplemented
33#14582668C2212yescomplemented
34#14582667C2214yescomplemented
35C2×C4×D4×C43C2211yescharacteristic
36C2×#100×C43C2212yes—
37C4×M16×C43C2212yescomplemented
38C43×#343C2212yescomplemented
39C24×D43C2×C412yes—
40C22×D172C2311yescharacteristic
41C22×C22⋊D43C2×C412yes—
42C2×D4×D43—24no—
43C2×D4×D43—24no—
44C2×D4×D43—22no—
45C2×D4×D43—22no—
46C23×Dic43C2×C412yes—
47C22×C4×D43—22no—
48C22×C4×D43—22no—
49C22×C4×D43—22no—
50C22×C4×D43—22no—
51C22×C4×D43—48no—
52C22×C4×D43C2×C411yescharacteristic
53C22×C4×D43C2×C412yes—
54C22×C4×D43C2×C412yes—
55C22×C4×D43C2×C412yes—
56C22×C4×D43C2×C411yescharacteristic
57C22×C4×D43C2311yescharacteristic
58C2×#10621877C2314yes—
59C4×D172—22no—
60C4×D172—22no—
61D4×Dic43—22no—
62D4×Dic43—22no—
63#13063287—22no—
64#13063287—22no—
65C4×C22⋊D43—24no—
66C4×C22⋊D43—24no—
67(C22⋊D43)⋊C4—24no—
68(C22⋊D43)⋊C4—24no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×Dic43⋊C4C2×C412yes—
71C4⋊C4×D43—22no—
72C4⋊C4×D43—22no—
73C2×C22⋊Dic43C2×C412yes—
74C2×(C2×D43)⋊C4C2×C412yes—
75C2×(C2×D43)⋊C4C2×C412yes—
76C22⋊C4×D43—24no—
77C22⋊C4×D43—24no—
78C2×C4×Dic43C2×C411yescharacteristic
79C2×C4×Dic43C2×C411yescharacteristic
80C2×C4×Dic43C2311yescharacteristic
81C42×D43D412yes—
82C42×D43D412yes—
83C42×D43D412yes—
84C42×D43D412yes—
85Dic43⋊C8—24no—
86Dic43⋊C8—24no—
87#13063242—24no—
88#13063241—28no—
89(C2×D43)⋊C8—24no—
90(C2×D43)⋊C8—24no—
91#13063236—22no—
92C4×C43⋊C8—22no—
93C22×D4×C43C2311yescharacteristic
94C23×C4×C43C2×C412yes—
95C2×M16×C43C2314yes—
96C4×D4×C43—22no—
97C4×D4×C43—22no—
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C22⋊C4×C43C2×C412yes—
100C2×C42×C43C2311yescharacteristic
101#100×C43—24no—
102#97×C43—22no—
103C4×C8×C43—22no—
104C24×C43C22×C412yes—
105C23×D43—24no—
106C23×D43—22no—
107C23×D43—22no—
108C23×D43—24no—
109C23×D43—44no—
110C23×D43—44no—
111C23×D43C22×C411yescharacteristic
112C23×D43C22×C412yes—
113C2×D4×C43—22no—
114C2×D4×C43—22no—
115C2×D4×C43#4114yes—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—44no—
119C22×C4×C43C22×C411yescharacteristic
120C22×C4×C43C22×C412yes—
121C22×C4×C43C22×C411yescharacteristic
122C22×C4×C43C2411yescharacteristic
123C2×C22⋊D43—24no—
124C2×C22⋊D43—24no—
125C2×C22⋊D43—24no—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—44no—
129C22×Dic43C22×C411yescharacteristic
130C22×Dic43C22×C411yescharacteristic
131C22×Dic43C22×C412yes—
132C22×Dic43C22×C411yescharacteristic
133D4×D43—216no—
134D4×D43—216no—
135C2×D172—22no—
136C2×D172—22no—
137C2×D172#4114yes—
138C2×C4×D43—22no—
139C2×C4×D43—22no—
140C2×C4×D43—24no—
141C2×C4×D43—22no—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—42no—
148C2×C4×D43—44no—
149C2×C4×D43—48no—
150C2×C4×D43—48no—
151C2×C4×D43—48no—
152C2×C4×D43—48no—
153C2×C4×D43—44no—
154C2×C4×D43—44no—
155C2×C4×D43C22⋊C412yes—
156C2×C4×D43C22⋊C411yescharacteristic
157C2×C4×D43C22⋊C411yescharacteristic
158C2×C4×D43C22⋊C411yescharacteristic
159C2×C4×D43C22⋊C412yes—
160C2×C4×D43C22⋊C411yescharacteristic
161C2×C4×D43C2×D412yes—
162C2×C4×D43C2×D412yes—
163M16×C43—24no—
164M16×C43—24no—
165C2×C8×C43—24no—
166C4⋊C4×C43—22no—
167C22⋊C4×C43—24no—
168C42×C43C2×D412yes—
169C42×C43C2×D412yes—
170C22⋊Dic43—24no—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—24no—
173C4⋊Dic43—22no—
174Dic43⋊C4—24no—
175C4×Dic43C22⋊C412yes—
176C4×Dic43C22⋊C412yes—
177C4×Dic43C22⋊C412yes—
178C4×Dic43C22⋊C412yes—
179C4×Dic43C2×D412yes—
180C4×Dic43C2×D412yes—
181#10621877—24no—
182#10621877—24no—
183C2×C43⋊C8—24no—
184C23×C43—22no—
185C23×C43—22no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43#11714yes—
189C23×C43C23×C411yescharacteristic
190C22×D43—21no—
191C22×D43—21no—
192C22×D43—22no—
193C22×D43—22no—
194C22×D43—28no—
195C22×D43—28no—
196C22×D43—22no—
197C22×D43—22no—
198C22×D43—44no—
199C22×D43—416no—
200C22×D43—416no—
201C22×D43—44no—
202C22×D43—44no—
203C22×D43—44no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43C2×C22⋊C411yescharacteristic
207C22×D43C2×C22⋊C411yescharacteristic
208C22×D43#11714yes—
209D4×C43—28no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—41no—
213C2×C4×C43—44no—
214C2×C4×C43—44no—
215C2×C4×C43—42no—
216C2×C4×C43C2×C22⋊C412yes—
217C2×C4×C43C2×C22⋊C411yescharacteristic
218C2×C4×C43C2×C22⋊C411yescharacteristic
219C2×C4×C43C22×D412yes—
220C2×C4×C43C2×#4112yes—
221C2×C4×C43C2×#4112yes—
222C22⋊D43—216no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—22no—
226C2×Dic43—22no—
227C2×Dic43—41no—
228C2×Dic43—44no—
229C2×Dic43—44no—
230C2×Dic43—42no—
231C2×Dic43C2×C22⋊C412yes—
232C2×Dic43C2×C22⋊C412yes—
233C2×Dic43C2×C22⋊C411yescharacteristic
234C2×Dic43C2×C22⋊C411yescharacteristic
235D172—28no—
236C4×D43—22no—
237C4×D43—24no—
238C4×D43—24no—
239C4×D43—24no—
240C4×D43—22no—
241C4×D43—22no—
242C4×D43—42no—
243C4×D43—44no—
244C4×D43—44no—
245C4×D43—44no—
246C4×D43—44no—
247C4×D43—44no—
248C4×D43—44no—
249C4×D43#10014yescomplemented
250C8×C43—44no—
251C43⋊C8—44no—
252#20726—431nomaximal, Sylow
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—24no—
256C22×C43—44no—
257C22×C43—44no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43C22×C22⋊C411yescharacteristic
261C22×C43C2×#11711yescharacteristic
262C22×C43C2×#11711yescharacteristic
263C2×D43—24no—
264C2×D43—24no—
265C2×D43—21no—
266C2×D43—21no—
267C2×D43—21no—
268C2×D43—21no—
269C2×D43—24no—
270C2×D43—416no—
271C2×D43—416no—
272C2×D43—44no—
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—44no—
276C2×D43C2×#10012yes—
277C2×D43#41312yes—
278C4×C43—21no—
279C4×C43—22no—
280C4×C43—42no—
281C4×C43C2×#10012yes—
282C4×C43#52514yes—
283Dic43—21no—
284Dic43—22no—
285Dic43—22no—
286Dic43—42no—
287Dic43C2×#10012yes—
288C22×C4×D4—431no—
289#2920—432no—
290#1821—432no—
291#1800—432no—
292#1800—432no—
293#1783—432no—
294C4×#100—432no—
295C4×#100—431no—
296C4×#100D4311yescharacteristic, complemented
297C2×C43—21no—
298C2×C43—21no—
299C2×C43—44no—
300C2×C43#228011yescharacteristic
301C2×C43C22×#10011yescharacteristic
302C2×C43C2×#41311yescharacteristic
303D43—22no—
304D43—22no—
305D43—44no—
306C23×D4—431no—
307C24×C4—432no—
308C2×C4×D4—431no—
309C2×C4×D4—432no—
310C2×C4×D4—431no—
311C2×C4×D4—432no—
312C2×C4×D4—431no—
313C2×C4×D4—862no—
314C2×C4×D4—862no—
315C2×C4×D4—862no—
316C2×C4×D4—862no—
317C2×C4×D4C2×D4311yescharacteristic
318C22×C4⋊C4—431no—
319C22×C22⋊C4—432no—
320C22×C42—431no—
321#432—862no—
322#432—862no—
323#431—862no—
324#431—862no—
325#423—434no—
326C2×#100—432no—
327C2×#100—434no—
328C2×#100C2×D4312yes—
329#407—434no—
330C4×M16—432no—
331C4×M16C2×D4312yescomplemented
332#343—434no—
333#343—432no—
334#343C2×D4312yescomplemented
335C43#2072611yescharacteristic, complemented, Sylow
336C25—432no—
337C22×D4—432no—
338C22×D4—431no—
339C22×D4—862no—
340C22×D4—862no—
341C22×D4—864no—
342C22×D4—864no—
343C22×D4C22×D4311yescharacteristic
344C23×C4—431no—
345C23×C4—431no—
346C23×C4—431no—
347C23×C4—432no—
348C23×C4—432no—
349C23×C4—432no—
350C23×C4—432no—
351C23×C4—862no—
352C23×C4—862no—
353C23×C4—862no—
354C23×C4—862no—
355C23×C4—1728no—
356C23×C4C4×D4312yes—
357C2×M16—434no—
358C2×M16C22×D4314yes—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—864no—
362C4×D4—864no—
363C4×D4—862no—
364C4×D4—862no—
365C4×D4—864no—
366C4×D4—864no—
367C4×D4—862no—
368C4×D4—862no—
369C4×D4—862no—
370C4×D4—862no—
371C2×C4⋊C4—432no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—862no—
374C2×C4⋊C4—862no—
375C2×C4⋊C4C22×D4311yescharacteristic
376C2×C22⋊C4—432no—
377C2×C22⋊C4—432no—
378C2×C22⋊C4—432no—
379C2×C22⋊C4—864no—
380C2×C22⋊C4—864no—
381C2×C22⋊C4C4×D4312yes—
382C2×C42—431no—
383C2×C42—431no—
384C2×C42—431no—
385C2×C42—432no—
386C2×C42—432no—
387C2×C42—432no—
388C2×C42—432no—
389C2×C42C22×D4311yescharacteristic
390C4⋊C8—864no—
391C4⋊C8—864no—
392#100—24no—
393#100—868no—
394#100—864no—
395C22⋊C8—864no—
396C22⋊C8—864no—
397#97—22no—
398#97—862no—
399C4×C8—22no—
400C4×C8—862no—
401C24—431no—
402C24—432no—
403C24—862no—
404C24—862no—
405C24—864no—
406C24—864no—
407C24—1724no—
408C24—1724no—
409C24C2×C4×D4312yes—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—434no—
413C2×D4—864no—
414C2×D4—8616no—
415C2×D4—8616no—
416C2×D4—864no—
417C2×D4—864no—
418C2×D4—862no—
419C2×D4—862no—
420C2×D4#1062189814yes—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—44no—
424C22×C4—431no—
425C22×C4—431no—
426C22×C4—431no—
427C22×C4—431no—
428C22×C4—432no—
429C22×C4—431no—
430C22×C4—431no—
431C22×C4—431no—
432C22×C4—432no—
433C22×C4—432no—
434C22×C4—432no—
435C22×C4—432no—
436C22×C4—864no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—1724no—
448C22×C4—1728no—
449C22×C4—1722no—
450C22×C4—1728no—
451C22×C4—1728no—
452C22×C4—1728no—
453C22×C4—1724no—
454C22×C4—1724no—
455C22×C4—1724no—
456C22×C4C2×C4×D4311yescharacteristic
457C22×C4C2×C4×D4312yes—
458C22×C4C2×C4×D4311yescharacteristic
459C22×C4C23×D4311yescharacteristic
460M16—24no—
461M16—24no—
462M16—864no—
463M16—864no—
464C2×C8—24no—
465C2×C8—864no—
466C4⋊C4—22no—
467C4⋊C4—864no—
468C4⋊C4—862no—
469C22⋊C4—24no—
470C22⋊C4—864no—
471C22⋊C4—864no—
472C22⋊C4—864no—
473C42—432no—
474C42—432no—
475C42—432no—
476C42—432no—
477C42—432no—
478C42—432no—
479C42D4×D4312yes—
480C42D4×D4312yes—
481C23—22no—
482C23—22no—
483C23—42no—
484C23—42no—
485C23—431no—
486C23—431no—
487C23—434no—
488C23—862no—
489C23—862no—
490C23—868no—
491C23—868no—
492C23—861no—
493C23—861no—
494C23—862no—
495C23—862no—
496C23—1722no—
497C23—1722no—
498C23—1724no—
499C23—1724no—
500C23—1724no—
501C23—17216no—
502C23—17216no—
503C23—1724no—
504C23#1306328214yes—
505C23C22×C4×D4311yescharacteristic
506D4—28no—
507D4—8616no—
508D4—868no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—431no—
516C2×C4—434no—
517C2×C4—432no—
518C2×C4—432no—
519C2×C4—431no—
520C2×C4—862no—
521C2×C4—862no—
522C2×C4—864no—
523C2×C4—862no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—862no—
527C2×C4—864no—
528C2×C4—864no—
529C2×C4—862no—
530C2×C4—1722no—
531C2×C4—1724no—
532C2×C4—1724no—
533C2×C4—1724no—
534C2×C4—1724no—
535C2×C4—1724no—
536C2×C4—1724no—
537C2×C4—1721no—
538C2×C4—1724no—
539C2×C4—1724no—
540C2×C4—1722no—
541C2×C4C22⋊C4×D4312yes—
542C2×C4C22⋊C4×D4311yescharacteristic
543C2×C4C22⋊C4×D4311yescharacteristic
544C2×C4C2×D4×D4312yes—
545C2×C4#41×D4312yes—
546C2×C4C2×#1062189812yes—
547C8—44no—
548C8—1724no—
549C22—21no—
550C22—21no—
551C22—24no—
552C22—44no—
553C22—44no—
554C22—42no—
555C22—42no—
556C22—432no—
557C22—432no—
558C22—864no—
559C22—864no—
560C22—861no—
561C22—861no—
562C22—861no—
563C22—861no—
564C22—864no—
565C22—1724no—
566C22—1724no—
567C22—17216no—
568C22—17216no—
569C22—1722no—
570C22—1722no—
571C22C2×C22⋊C4×D4311yescharacteristic
572C22#117×D4311yescharacteristic
573C22C2×#1306328211yescharacteristic
574C4—21no—
575C4—22no—
576C4—42no—
577C4—432no—
578C4—861no—
579C4—862no—
580C4—862no—
581C4—1722no—
582C4#100×D4312yes—
583C4#1458340814yes—
584C2—21no—
585C2—21no—
586C2—44no—
587C2—862no—
588C2—862no—
589C2—1724no—
590C2#1913697611yescharacteristic
591C2C2×#100×D4311yescharacteristic
592C2#413×D4311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#100×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenterC4×#100D43
hypocenterC43#20726
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
2. #19143226C2semidirect
3. #19134674C2semidirect
4. #19134586C2semidirect
5. #19134585C2semidirect
7. C4×#13063241C2semidirect
8. C4×#13063242C2semidirect
9. C4×#100×C43C2semidirect
28. #14582922C22semidirect
32. C4×#10621877C22semidirect
33. #14582668C22semidirect
34. #14582667C22semidirect
37. C4×M16×C43C22semidirect
38. C43×#343C22semidirect
249. C4×D43#100semidirect
296. C4×#100D43semidirect
331. C4×M16C2×D43semidirect
334. #343C2×D43semidirect
335. C43#20726semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D432
#191432262
#191346742
#191345862
#191345852
#191345142
C4×#130632412
C4×#130632422
C4×#100×C432
#2072643