Finite Group Databasebeta

← #25102829

Subgroups — #25102829

Order 11008.

1016 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583123C211yesmaximal, characteristic
2C2×Q16×Dic43C211yesmaximal, characteristic, complemented
3C2×#14582984C211yesmaximal, characteristic
4#19137138C211yesmaximal, characteristic
5C4×Q8×Dic43C211yesmaximal, characteristic, complemented
6#19135524C211yesmaximal, characteristic
7#19135366C211yesmaximal, characteristic, complemented
8#19135226C211yesmaximal, characteristic, complemented
9#19135216C211yesmaximal, characteristic
10#19134950C211yesmaximal, characteristic
11#19134608C211yesmaximal, characteristic, complemented
12#19134443C211yesmaximal, characteristic, complemented
13#103×Dic43C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic
15C43×#1878C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063314C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22#14583123C418yescomplemented
23Q16×Dic43—24no—
24#14582984—24no—
25C2×#13063259C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582801C2211yescharacteristic
38#14582791—21no—
39#14582791—21no—
40#14582764C2211yescharacteristic
41C4⋊C4×Dic43—21no—
42C4⋊C4×Dic43—21no—
43C4⋊C4×Dic43C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4×C4⋊Dic43—21no—
46C4×C4⋊Dic43C2211yescharacteristic
47#14582746—21no—
48#14582746—21no—
49C42×Dic43—21no—
50C42×Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582654C2211yescharacteristic
55C22×Q16×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C43×#391C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C2×#10621884—22no—
65C2×#10621884—22no—
66C2×#10621884C2×C414yes—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063314—22no—
70#13063314C2×C414yes—
71Q8×Dic43—22no—
72Q8×Dic43—22no—
73Q8×Dic43—22no—
74Q8×Dic43—22no—
75Q8×Dic43C2×C414yescomplemented
76Q8×Dic43D414yes—
77#13063287—22no—
78#13063287—22no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43D411yescharacteristic
97C2×C4×Dic43D411yescharacteristic
98C2×C4×Dic43D411yescharacteristic
99C2×C4×Dic43D411yescharacteristic
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102#13063259—22no—
103#13063256—22no—
104Dic43⋊C8—22no—
105Dic43⋊C8C2×C414yescomplemented
106#13063249—22no—
107#13063249—22no—
108#13063249C2×C414yescomplemented
109#13063247—22no—
110#13063247C2×C414yes—
111#13063245—22no—
112C8×Dic43—22no—
113C8×Dic43—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×Q8×C43C2311yescharacteristic
120C22×Q8×C43C2311yescharacteristic
121C2×Q16×C43—22no—
122C2×Q16×C43—22no—
123C2×Q16×C43C2×C414yescomplemented
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C4×Q8×C43—22no—
127C4×Q8×C43—22no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133#103×C43—22no—
134#103×C43—22no—
135#95×C43—21no—
136#95×C43—21no—
137C23×D43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C22×C412yes—
147C2×Q8×C43C22×C412yes—
148C2×Q8×C43C2×D412yes—
149C2×Q8×C43#4112yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172C22×C412yes—
170C2×C4×D43—42no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173Q16×C43—28no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C22×C412yes—
180C4⋊C4×C43—24no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43#4112yes—
185C42×C43—24no—
186C42×C43—21no—
187C42×C43—21no—
188#10621884—28no—
189(C2×D43)⋊C4—24no—
190(C2×D43)⋊C4—24no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—24no—
197C4⋊Dic43—24no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—42no—
201C4⋊Dic43C22×C412yes—
202C4⋊Dic43C2×D412yes—
203C4×Dic43—22no—
204C4×Dic43—24no—
205C4×Dic43—24no—
206C4×Dic43—22no—
207C4×Dic43—22no—
208C4×Dic43—41no—
209C4×Dic43—42no—
210C4×Dic43—42no—
211C4×Dic43—42no—
212C4×Dic43—42no—
213C4×Dic43C22×C412yes—
214C4×Dic43C2×D412yes—
215C4×Dic43#4112yes—
216C4×Dic43#4112yes—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8C22×C412yes—
223C23×C43C22×D411yescharacteristic
224C22×D43—22no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231Q8×C43—22no—
232Q8×C43—22no—
233Q8×C43—22no—
234Q8×C43—22no—
235Q8×C43—22no—
236Q8×C43—41no—
237Q8×C43—41no—
238Q8×C43C4×D414yes—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—21no—
246C2×C4×C43—22no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43#13512yes—
257C2×C4×C43C23×C411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43C4×D412yes—
279C2×Dic43C4×D412yes—
280C2×Dic43#12112yes—
281C2×Dic43#12112yes—
282C2×Dic43#13512yes—
283C2×Dic43#13712yes—
284D172—22no—
285D172—22no—
286D172—41no—
287D172—41no—
288C4×D43—84no—
289C8×C43—22no—
290C8×C43—41no—
291C43⋊C8—22no—
292C43⋊C8—41no—
293C4×#464—431nomaximal, Sylow
294C22×C43C2×C4×D411yescharacteristic
295C22×C43C2×#12111yescharacteristic
296C22×C43#52511yescharacteristic
297C22×C43C2×#13511yescharacteristic
298C22×C43C2×#13511yescharacteristic
299C22×C43C2×#13711yescharacteristic
300C22×C43#57511yescharacteristic
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—81no—
308C4×C43—22no—
309C4×C43—24no—
310C4×C43—41no—
311C4×C43—42no—
312C4×C43—42no—
313C4×C43—81no—
314C4×C43C2×C4×D411yescharacteristic
315C4×C43C4×#4111yescharacteristic
316C4×C43#52911yescharacteristic
317C4×C43#53211yescharacteristic
318Dic43—22no—
319Dic43—22no—
320Dic43—22no—
321Dic43—42no—
322Dic43—42no—
323Dic43—81no—
324Dic43#46414yescomplemented
325C2×#464—431no—
326C2×C4×Q16—431no—
327C2×C4×SD16—431no—
328C4×#124—431no—
329C42×Q8—431no—
330#1983—431no—
331#1949—431no—
332#1927—431no—
333#1925—431no—
334#1880—431no—
335#1878D4311yescharacteristic, complemented
336#1805—431no—
337C4×C4⋊C8—431no—
338C4×#103—431no—
339C4×#102—431no—
340C2×C43C4×#12111yescharacteristic
341C2×C43C4×#13511yescharacteristic
342C2×C43C4×#13711yescharacteristic
343C2×C43C2×#46411yescharacteristic
344C2×C43#303511yescharacteristic
345C2×C43#310211yescharacteristic
346C2×C43#310811yescharacteristic
347D43—82no—
348C22×Q16C2×D4311yescharacteristic
349C22×SD16—431no—
350C2×#124—431no—
351C2×C4×Q8—431no—
352C2×C4×Q8—431no—
353C2×C4×Q8—431no—
354C2×C4×Q8C2×D4311yescharacteristic
355C2×C4×D4—431no—
356#464—438no—
357C4×Q16—864no—
358C4×SD16—864no—
359C2×#107—431no—
360C2×#106—431no—
361C2×C4⋊C8—431no—
362C2×C4⋊C8—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#103—431no—
366C2×#103C2×D4311yescharacteristic
367C2×#103C2×D4311yescharacteristic
368C2×#102—431no—
369C2×#102—431no—
370C2×#102—431no—
371C2×C4×C8—431no—
372C2×C4×C8—431no—
373#391C2×D4311yescharacteristic
374#390—431no—
375#388—861no—
376#388—861no—
377#382—431no—
378C4×C4⋊C4—431no—
379C4×C4⋊C4—431no—
380C4×C4⋊C4—431no—
381C4×C4⋊C4—861no—
382C4×C4⋊C4—861no—
383C4×C4⋊C4—861no—
384C4×C22⋊C4—861no—
385C4×C22⋊C4—861no—
386C43—431no—
387C43—861no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340C2×D4311yescharacteristic
392#336—431no—
393#336C2×D4311yescharacteristic
394C43C4×#46411yescharacteristic, complemented, Sylow
395C22×Q8C22×D4311yescharacteristic
396C22×Q8C22×D4311yescharacteristic
397C22×D4—431no—
398C23×C4—861no—
399C2×Q16—22no—
400C2×Q16—22no—
401C2×Q16C4×D4314yescomplemented
402C2×SD16—434no—
403C2×SD16—862no—
404C2×SD16—862no—
405C22×C8—431no—
406C22×C8—431no—
407C22×C8C22×D4311yescharacteristic
408C22×C8C22×D4311yescharacteristic
409#124—434no—
410#124—862no—
411C4×Q8—22no—
412C4×Q8—22no—
413C4×Q8—434no—
414C4×Q8—434no—
415C4×Q8—862no—
416C4×Q8—862no—
417C4×Q8—862no—
418C4×Q8—862no—
419C4×D4—862no—
420C4×D4—862no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C42—21no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—861no—
443C2×C42—861no—
444C2×C42—861no—
445C2×C42—861no—
446C2×C42—861no—
447C2×C42—861no—
448C2×C42C22×D4311yescharacteristic
449#107—862no—
450#106—862no—
451C4⋊C8—434no—
452C4⋊C8—862no—
453#103—22no—
454#103—22no—
455#103—434no—
456#103—862no—
457#103—862no—
458#102—434no—
459#102—862no—
460#102—862no—
461C4×C8—862no—
462C4×C8—862no—
463#95—21no—
464#95—21no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470C24—861no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8C2×C4×D4312yes—
480C2×Q8C2×C4×D4312yes—
481C2×Q8D4×D4312yes—
482C2×Q8#1062190012yes—
483C2×D4—432no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—861no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—1722no—
501C22×C4—1722no—
502C22×C4—1722no—
503C22×C4D4×D4311yescharacteristic
504C22×C4D4×D4311yescharacteristic
505C22×C4C23×D4311yescharacteristic
506Q16—28no—
507SD16—868no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—432no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8C2×C4×D4312yes—
520C4⋊C4—24no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—432no—
525C4⋊C4—432no—
526C4⋊C4—864no—
527C4⋊C4—864no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—1722no—
533C4⋊C4#1062190012yes—
534C22⋊C4—864no—
535C22⋊C4—864no—
536C22⋊C4—1722no—
537C22⋊C4—1722no—
538C22⋊C4—1722no—
539C42—24no—
540C42—21no—
541C42—21no—
542C42—432no—
543C42—432no—
544C42—432no—
545C42—432no—
546C42—862no—
547C42—862no—
548C42—864no—
549C42—864no—
550C42—862no—
551C42—1721no—
552C42—1722no—
553C42—1722no—
554C42—1722no—
555C42—1722no—
556C23—862no—
557C23—1721no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23C2×D4×D4311yescharacteristic
564Q8—22no—
565Q8—22no—
566Q8—22no—
567Q8—22no—
568Q8—22no—
569Q8—41no—
570Q8—41no—
571Q8(C22⋊D43)⋊C414yes—
572D4—862no—
573D4—862no—
574D4—1721no—
575D4—1721no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—432no—
594C2×C4—432no—
595C2×C4—432no—
596C2×C4—432no—
597C2×C4—432no—
598C2×C4—432no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—3444no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4#1306334812yes—
616C2×C4C22×C4×D4311yescharacteristic
617C2×C4C2×D4×D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4#41×D4311yescharacteristic
620C2×C4C2×#1062190011yescharacteristic
621C2×C4C2×#1062190011yescharacteristic
622C8—22no—
623C8—41no—
624C8—862no—
625C8—1721no—
626C22—3441no—
627C22—3441no—
628C22—3441no—
629C22—3441no—
630C22—1722no—
631C22—1722no—
632C22—1722no—
633C22C4×D4×D4311yescharacteristic
634C22#121×D4311yescharacteristic
635C22#1458340511yescharacteristic
636C22#135×D4311yescharacteristic
637C22C2×#1306334811yescharacteristic
638C22#137×D4311yescharacteristic
639C22#1458369811yescharacteristic
640C4—24no—
641C4—22no—
642C4—42no—
643C4—41no—
644C4—42no—
645C4—81no—
646C4—434no—
647C4—862no—
648C4—862no—
649C4—862no—
650C4—3441no—
651C4—1722no—
652C4—1722no—
653C4C2×(C22⋊D43)⋊C411yescharacteristic
654C4C4×#1062190011yescharacteristic
655C4#1458342611yescharacteristic
656C4#1458344411yescharacteristic
657C2—3442no—
658C2#1913710511yescharacteristic
659C2C4×#1306334811yescharacteristic
660C2#1914341111yescharacteristic
661C2#464×D4311yescharacteristic
662C2#1914405311yescharacteristic
663C2#1914461411yescharacteristic
664C2#1914467611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1878C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1878D43
hypocenterC43C4×#464
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
2. C2×Q16×Dic43C2semidirect
5. C4×Q8×Dic43C2semidirect
7. #19135366C2semidirect
8. #19135226C2semidirect
11. #19134608C2semidirect
12. #19134443C2semidirect
13. #103×Dic43C2semidirect
15. C43×#1878C2semidirect
22. #14583123C4semidirect
75. Q8×Dic43C2×C4semidirect
105. Dic43⋊C8C2×C4semidirect
108. #13063249C2×C4semidirect
123. C2×Q16×C43C2×C4semidirect
324. Dic43#464semidirect
335. #1878D43semidirect
394. C43C4×#464semidirect
401. C2×Q16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831232
C2×Q16×Dic432
C2×#145829842
#191371382
C4×Q8×Dic432
#191355242
#191353662
#191352262
#191352162
#191349502
#191346082
#191344432
#103×Dic432
#191344092
C43×#18782
C4×#46443