Finite Group Databasebeta

← #25096593

Subgroups — #25096593

Order 11008.

1802 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D43C211yesmaximal, characteristic
2C2×#14582950C211yesmaximal, characteristic, complemented
3#19136999C211yesmaximal, characteristic, complemented
4#19134680C212yesmaximal, complemented
5#19134594C212yesmaximal, complemented
6#19134593C212yesmaximal, complemented
7#19134524C212yesmaximal
8C4×#13063245C211yesmaximal, characteristic, complemented
9C4×#13063247C211yesmaximal, characteristic, complemented
10C4×#13063246C211yesmaximal, characteristic, complemented
11C4×#102×C43C211yesmaximal, characteristic, complemented
12C22×D4×D43C2211yescharacteristic
13C23×C4×D43—21no—
14C2×C4×D172C2211yescharacteristic
15C2×D4×Dic43C2211yescharacteristic
16C2×#13063287C2211yescharacteristic
17C2×C4×C22⋊D43—21no—
18C2×(C22⋊D43)⋊C4—21no—
19C4×D4×D43—24no—
20C4×D4×D43C418yescomplemented
21C2×#13063282—21no—
22C2×C4⋊C4×D43C2211yescharacteristic
23C2×C22⋊C4×D43—21no—
24C2×C42×D43C2211yescharacteristic
25#14582950—24no—
26C2×Dic43⋊C8C2212yescomplemented
27C2×#13063247C2212yes—
28C2×#13063246C2212yes—
29C2×#13063245C2212yes—
30C2×(C2×D43)⋊C8C2212yes—
31C2×C4×C43⋊C8C2211yescharacteristic, complemented
32#14582768C2212yescomplemented
33#14582763—21no—
34#14582758—21no—
35#14582756C2212yes—
36C4×Dic43⋊C4—21no—
37C4×C4⋊Dic43C2211yescharacteristic, complemented
38#14582662C2212yescomplemented
39#14582661C2212yescomplemented
40#14582661C2212yescomplemented
41C2×C4×D4×C43C2211yescharacteristic
42C2×#102×C43C2212yes—
43C2×C4×C8×C43C2211yescharacteristic, complemented
44C4×C4⋊C4×C43C2211yescharacteristic, complemented
45C43×#340C2212yescomplemented
46C24×D43—21no—
47C22×D172C2311yescharacteristic
48C22×C22⋊D43—21no—
49C2×D4×D43—24no—
50C2×D4×D43—24no—
51C2×D4×D43—22no—
52C2×D4×D43C2×C414yes—
53C23×Dic43—21no—
54C22×C4×D43—21no—
55C22×C4×D43—21no—
56C22×C4×D43—21no—
57C22×C4×D43—28no—
58C22×C4×D43—44no—
59C22×C4×D43—44no—
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2312yes—
64C4×D172—22no—
65C4×D172C2×C414yes—
66D4×Dic43—22no—
67D4×Dic43C2×C414yes—
68#13063287—22no—
69#13063287C2×C414yes—
70C4×C22⋊D43—28no—
71(C22⋊D43)⋊C4—28no—
72#13063282—44no—
73C2×C4⋊Dic43C2312yes—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—22no—
77C2×Dic43⋊C4—22no—
78C4⋊C4×D43—22no—
79C4⋊C4×D43C2×C414yes—
80C2×C22⋊Dic43—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—22no—
84C22⋊C4×D43—28no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89C42×D43C2×C414yes—
90C42×D43D414yes—
91Dic43⋊C8—24no—
92#13063247—24no—
93#13063246—24no—
94#13063245—24no—
95(C2×D43)⋊C8—24no—
96C4×C43⋊C8—22no—
97C43⋊#95—21no—
98C43⋊#95—22no—
99C22×D4×C43C2311yescharacteristic
100C23×C4×C43—21no—
101C22×C8×C43C2312yes—
102C4×D4×C43—22no—
103C4×D4×C43C2×C414yes—
104C2×C4⋊C4×C43C2312yes—
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C22⋊C4×C43—21no—
107C2×C42×C43—21no—
108C2×C42×C43C2311yescharacteristic
109#102×C43—24no—
110C4×C8×C43—22no—
111#95×C43—21no—
112C24×C43—21no—
113C23×D43—28no—
114C23×D43—21no—
115C23×D43—24no—
116C23×D43—44no—
117C23×D43—42no—
118C23×D43—42no—
119C23×D43C2×D411yescharacteristic
120C2×D4×C43—21no—
121C2×D4×C43—22no—
122C2×D4×C43C22×C412yes—
123C2×D4×C43#4114yes—
124C22×C4×C43—24no—
125C22×C4×C43—21no—
126C22×C4×C43—22no—
127C22×C4×C43—42no—
128C22×C4×C43—42no—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2411yescharacteristic
132C2×C22⋊D43—28no—
133C2×C22⋊D43—24no—
134C22×Dic43—24no—
135C22×Dic43—21no—
136C22×Dic43—22no—
137C22×Dic43—42no—
138C22×Dic43—42no—
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142D4×D43—216no—
143D4×D43—28no—
144D4×D43—28no—
145C2×D172—21no—
146C2×D172—22no—
147C2×D172C22×C412yes—
148C2×D172#4114yes—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43—24no—
152C2×C4×D43—24no—
153C2×C4×D43—24no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—432no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43C22⋊C414yes—
163C2×C4×D43C22⋊C414yes—
164C2×C4×D43D814yes—
165C2×C4×D43SD1614yes—
166C2×C4×D43C22×C412yes—
167C2×C4×D43C2×D412yes—
168C2×C8×C43—22no—
169C2×C8×C43—22no—
170C2×C8×C43—22no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43C22×C412yes—
175C22⋊C4×C43—24no—
176C42×C43—42no—
177C42×C43C22×C412yes—
178C42×C43C2×D412yes—
179C22⋊Dic43—24no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—44no—
183C4⋊Dic43—21no—
184C4⋊Dic43—22no—
185C4⋊Dic43—22no—
186C4⋊Dic43C22×C412yes—
187Dic43⋊C4—24no—
188Dic43⋊C4—44no—
189Dic43⋊C4—44no—
190C4×Dic43—42no—
191C4×Dic43C22⋊C414yes—
192C4×Dic43C22⋊C414yes—
193C4×Dic43C22×C412yes—
194C4×Dic43C2×D412yes—
195C2×C43⋊C8—22no—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—22no—
198C23×C43—22no—
199C23×C43—24no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—42no—
203C23×C43C22×D411yescharacteristic
204C22×D43—22no—
205C22×D43—22no—
206C22×D43—216no—
207C22×D43—22no—
208C22×D43—24no—
209C22×D43—416no—
210C22×D43—416no—
211C22×D43—48no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—42no—
215C22×D43—48no—
216C22×D43C2×C22⋊C412yes—
217C22×D43C2×D812yes—
218C22×D43C2×SD1612yes—
219D4×C43—22no—
220D4×C43—24no—
221D4×C43#11714yescomplemented
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—48no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43C2×C22⋊C412yes—
231C2×C4×C43C2×C22⋊C412yes—
232C2×C4×C43C2×D812yes—
233C2×C4×C43C2×SD1612yes—
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C2×#4112yes—
237C2×C4×C43C2×#4112yes—
238C22⋊D43—216no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—48no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43C2×C22⋊C412yes—
249C2×Dic43C2×C22⋊C412yes—
250C2×Dic43C2×C22⋊C412yes—
251C2×Dic43C2×D812yes—
252C2×Dic43C2×SD1612yes—
253D172—22no—
254D172—24no—
255D172#11714yescomplemented
256C4×D43—22no—
257C4×D43—22no—
258C4×D43—24no—
259C4×D43—44no—
260C4×D43—48no—
261C4×D43—48no—
262C4×D43—48no—
263C4×D43#102116yescomplemented
264C8×C43—42no—
265C43⋊C8—42no—
266#20732—431nomaximal, Sylow
267C22×C43—24no—
268C22×C43—44no—
269C22×C43—44no—
270C22×C43—42no—
271C22×C43—42no—
272C22×C43C22×C22⋊C411yescharacteristic
273C22×C43#52512yes—
274C22×C43C22×D811yescharacteristic
275C22×C43C22×SD1611yescharacteristic
276C22×C43#57512yes—
277C2×D43—24no—
278C2×D43—24no—
279C2×D43—22no—
280C2×D43—22no—
281C2×D43—24no—
282C2×D43—432no—
283C2×D43—44no—
284C2×D43—44no—
285C2×D43—42no—
286C2×D43—42no—
287C2×D43C2×#10214yes—
288C4×C43—22no—
289C4×C43—42no—
290C4×C43—82no—
291C4×C43C2×#10214yes—
292C4×C43C2×#11711yescharacteristic
293C4×C43C2×#11711yescharacteristic
294C4×C43#52512yes—
295Dic43—22no—
296Dic43—22no—
297Dic43—42no—
298Dic43—82no—
299Dic43C2×#10214yes—
300C22×C4×D4—431no—
301C2×#431—431no—
302#2285—431no—
303#1823—432no—
304#1802—432no—
305#1802—432no—
306#1786—432no—
307C4×#102—431no—
308C4×#102—431no—
309C4×#102—431no—
310C4×#102D4311yescharacteristic, complemented
311C2×C43—44no—
312C2×C43#228011yescharacteristic
313C2×C43C22×#10211yescharacteristic
314C2×C43#289611yescharacteristic
315C2×C43#310012yes—
316C2×C43#310112yes—
317D43—24no—
318D43—44no—
319C23×D4—431no—
320C24×C4—861no—
321C2×C4×D4—431no—
322C2×C4×D4—438no—
323C2×C4×D4—431no—
324C2×C4×D4—431no—
325C2×C4×D4—861no—
326C2×C4×D4—864no—
327C2×C4×D4—861no—
328C2×C4×D4C2×D4311yescharacteristic
329C2×#117—861no—
330C22×C4⋊C4—431no—
331C22×C22⋊C4—861no—
332C22×C42—431no—
333#431—864no—
334C2×C4⋊C8—432no—
335C2×#102—432no—
336C2×#102—432no—
337C2×#102—432no—
338C2×#102C2×D4312yes—
339C2×C22⋊C8—432no—
340C2×C4×C8—431no—
341C2×C4×C8C2×D4311yescharacteristic, complemented
342#384—432no—
343#382—861no—
344#380—432no—
345#380—861no—
346C4×C4⋊C4—431no—
347C4×C4⋊C4—861no—
348C4×C4⋊C4C2×D4311yescharacteristic, complemented
349#340—432no—
350#340—432no—
351#340—432no—
352#340C2×D4312yescomplemented
353C43#2073211yescharacteristic, complemented, Sylow
354C25—861no—
355C22×D4—434no—
356C22×D4—431no—
357C22×D4—862no—
358C22×D4—861no—
359C22×D4—864no—
360C22×D4—864no—
361C22×D4C22×D4311yescharacteristic
362C23×C4—21no—
363C23×C4—431no—
364C23×C4—431no—
365C23×C4—431no—
366C23×C4—861no—
367C23×C4—868no—
368C23×C4—861no—
369C23×C4—861no—
370C23×C4—861no—
371C23×C4—1724no—
372C23×C4—1724no—
373C22×C8—432no—
374C22×C8C22×D4312yes—
375C4×D4—22no—
376C4×D4—434no—
377C4×D4—434no—
378C4×D4—434no—
379C4×D4—868no—
380C4×D4—862no—
381C4×D4—868no—
382C4×D4—862no—
383C4×D4—862no—
384C4×D4C4×D4314yes—
385#117—1724no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—434no—
388C2×C4⋊C4—432no—
389C2×C4⋊C4—862no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—862no—
392C2×C4⋊C4—862no—
393C2×C4⋊C4C22×D4312yes—
394C2×C4⋊C4C22×D4311yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—868no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—862no—
401C2×C42—21no—
402C2×C42—431no—
403C2×C42—431no—
404C2×C42—431no—
405C2×C42—434no—
406C2×C42—434no—
407C2×C42—861no—
408C2×C42C22×D4311yescharacteristic
409C4⋊C8—864no—
410#102—24no—
411#102—864no—
412#102—864no—
413#102—864no—
414C22⋊C8—864no—
415C4×C8—22no—
416C4×C8—862no—
417#95—21no—
418#95—862no—
419#95—861no—
420C24—21no—
421C24—431no—
422C24—864no—
423C24—868no—
424C24—861no—
425C24—1722no—
426C24—1722no—
427C24—1724no—
428C2×D4—21no—
429C2×D4—22no—
430C2×D4—432no—
431C2×D4—434no—
432C2×D4—864no—
433C2×D4—868no—
434C2×D4—8616no—
435C2×D4—868no—
436C2×D4—868no—
437C2×D4—861no—
438C2×D4—862no—
439C2×D4C2×C4×D4312yes—
440C2×D4#1062189814yes—
441C22×C4—21no—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—431no—
447C22×C4—434no—
448C22×C4—434no—
449C22×C4—434no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—432no—
453C22×C4—432no—
454C22×C4—434no—
455C22×C4—864no—
456C22×C4—864no—
457C22×C4—864no—
458C22×C4—862no—
459C22×C4—862no—
460C22×C4—861no—
461C22×C4—864no—
462C22×C4—862no—
463C22×C4—1722no—
464C22×C4—1722no—
465C22×C4—1722no—
466C22×C4—17232no—
467C22×C4—1722no—
468C22×C4—1722no—
469C22×C4—1722no—
470C22×C4—1722no—
471C22×C4—1722no—
472C22×C4—1722no—
473C22×C4D4×D4311yescharacteristic
474C22×C4D4×D4311yescharacteristic
475C22×C4C23×D4311yescharacteristic
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—862no—
480C2×C8—862no—
481C2×C8—862no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—432no—
486C4⋊C4—864no—
487C4⋊C4—861no—
488C4⋊C4—862no—
489C4⋊C4—862no—
490C4⋊C4—1724no—
491C4⋊C4—1724no—
492C4⋊C4C2×C4×D4312yes—
493C22⋊C4—24no—
494C22⋊C4—864no—
495C22⋊C4—864no—
496C22⋊C4—864no—
497C22⋊C4—1724no—
498C42—42no—
499C42—434no—
500C42—434no—
501C42—432no—
502C42—432no—
503C42—1722no—
504C42C2×C4×D4312yes—
505C42D4×D4312yes—
506C23—22no—
507C23—24no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—432no—
512C23—432no—
513C23—432no—
514C23—8616no—
515C23—862no—
516C23—862no—
517C23—862no—
518C23—864no—
519C23—1728no—
520C23—17216no—
521C23—17216no—
522C23—1728no—
523C23—1721no—
524C23—1721no—
525C23—1722no—
526C23C2×D4×D4311yescharacteristic
527D4—22no—
528D4—24no—
529D4—434no—
530D4—8616no—
531D4—862no—
532D4—864no—
533D4#1306328214yescomplemented
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—48no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—432no—
543C2×C4—432no—
544C2×C4—432no—
545C2×C4—4316no—
546C2×C4—432no—
547C2×C4—432no—
548C2×C4—862no—
549C2×C4—862no—
550C2×C4—862no—
551C2×C4—862no—
552C2×C4—864no—
553C2×C4—862no—
554C2×C4—1724no—
555C2×C4—1728no—
556C2×C4—1728no—
557C2×C4—1728no—
558C2×C4—1722no—
559C2×C4—1722no—
560C2×C4—1722no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1728no—
564C2×C4C22⋊C4×D4312yes—
565C2×C4C22⋊C4×D4312yes—
566C2×C4D8×D4312yes—
567C2×C4SD16×D4312yes—
568C2×C4C22×C4×D4311yescharacteristic
569C2×C4C2×D4×D4311yescharacteristic
570C2×C4#41×D4312yes—
571C2×C4C2×#1062189812yes—
572C8—42no—
573C8—1722no—
574C22—24no—
575C22—44no—
576C22—44no—
577C22—42no—
578C22—42no—
579C22—434no—
580C22—864no—
581C22—864no—
582C22—862no—
583C22—862no—
584C22—864no—
585C22—17232no—
586C22—1724no—
587C22—1724no—
588C22—1722no—
589C22—1722no—
590C22C2×C22⋊C4×D4311yescharacteristic
591C22#1458340812yes—
592C22C2×D8×D4311yescharacteristic
593C22C2×SD16×D4311yescharacteristic
594C22#1458369612yes—
595C4—22no—
596C4—42no—
597C4—82no—
598C4—434no—
599C4—862no—
600C4—862no—
601C4—3442no—
602C4—1722no—
603C4#102×D4314yes—
604C4#117×D4311yescharacteristic
605C4C2×#1306328211yescharacteristic
606C4#1458340812yes—
607C2—44no—
608C2—864no—
609C2—1724no—
610C2#1913697611yescharacteristic
611C2C2×#102×D4311yescharacteristic
612C2#1914311011yescharacteristic
613C2#1914459312yes—
614C2#1914460112yes—
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenterC4×#102D43
hypocenterC43#20732
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×#14582950C2semidirect
3. #19136999C2semidirect
4. #19134680C2semidirect
5. #19134594C2semidirect
6. #19134593C2semidirect
8. C4×#13063245C2semidirect
9. C4×#13063247C2semidirect
10. C4×#13063246C2semidirect
11. C4×#102×C43C2semidirect
20. C4×D4×D43C4semidirect
26. C2×Dic43⋊C8C22semidirect
31. C2×C4×C43⋊C8C22semidirect
32. #14582768C22semidirect
37. C4×C4⋊Dic43C22semidirect
38. #14582662C22semidirect
39. #14582661C22semidirect
40. #14582661C22semidirect
43. C2×C4×C8×C43C22semidirect
44. C4×C4⋊C4×C43C22semidirect
45. C43×#340C22semidirect
221. D4×C43#117semidirect
255. D172#117semidirect
263. C4×D43#102semidirect
310. C4×#102D43semidirect
341. C2×C4×C8C2×D43semidirect
348. C4×C4⋊C4C2×D43semidirect
352. #340C2×D43semidirect
353. C43#20732semidirect
533. D4#13063282semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D432
C2×#145829502
#191369992
#191346802
#191345942
#191345932
#191345242
C4×#130632452
C4×#130632472
C4×#130632462
C4×#102×C432
#2073243