Finite Group Databasebeta

← #25102952

Subgroups — #25102952

Order 11008.

980 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583006C211yesmaximal, characteristic, complemented
2C2×SD16×Dic43C211yesmaximal, characteristic
3#19137308C211yesmaximal, characteristic
4#19136960C211yesmaximal, characteristic, complemented
5#19135528C211yesmaximal, characteristic
6#19135359C211yesmaximal, characteristic, complemented
7#19135231C211yesmaximal, characteristic, complemented
8#19135224C211yesmaximal, characteristic
9#19134952C211yesmaximal, characteristic
10#19134938C211yesmaximal, characteristic, complemented
11#19134600C211yesmaximal, characteristic, complemented
12#19134454C211yesmaximal, characteristic, complemented
13#19134422C211yesmaximal, characteristic
14#103×Dic43C211yesmaximal, characteristic, complemented
15C2×C43×#464C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20#14583006—24no—
21SD16×Dic43—24no—
22C2×#13063257C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582792—21no—
36#14582792—21no—
37#14582774—21no—
38#14582774—21no—
39#14582769C2211yescharacteristic
40C4⋊C4×Dic43—21no—
41C4⋊C4×Dic43—21no—
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×C4⋊Dic43—21no—
45C4×C4⋊Dic43C2211yescharacteristic
46#14582745—21no—
47#14582745C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×Q16×C43C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C2×#124×C43C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C43×#464C418yescomplemented
59C2×C4⋊C8×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65Q8×Dic43—22no—
66Q8×Dic43—22no—
67Q8×Dic43—22no—
68Q8×Dic43—22no—
69Q8×Dic43—22no—
70Q8×Dic43D414yes—
71D4×Dic43—22no—
72D4×Dic43—22no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063257—22no—
94#13063257—22no—
95C4⋊(C43⋊C8)—22no—
96#13063249—22no—
97#13063249—22no—
98#13063249—22no—
99#13063249—22no—
100#13063246—22no—
101#13063246—22no—
102#13063235—22no—
103C8×Dic43—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C43⋊#95D411yescharacteristic
113C22×Q8×C43C2311yescharacteristic
114C22×Q8×C43C2311yescharacteristic
115C22×D4×C43C2311yescharacteristic
116C2×Q16×C43—22no—
117C2×Q16×C43—22no—
118C2×Q16×C43C2×C414yescomplemented
119C2×SD16×C43—22no—
120C2×SD16×C43—22no—
121C2×SD16×C43C2×C414yes—
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124#124×C43—22no—
125#124×C43C2×C414yes—
126C4×Q8×C43—22no—
127C4×Q8×C43C2×C414yescomplemented
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43C2×C414yescomplemented
135#103×C43C2×C414yescomplemented
136#102×C43C2×C414yes—
137C24×C43—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—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43C22×C412yes—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—42no—
167C22×Dic43—81no—
168C22×Dic43—81no—
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173Q16×C43—28no—
174SD16×C43—28no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C22×C412yes—
180C2×C8×C43C22×C412yes—
181C4⋊C4×C43—24no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43C22×C412yes—
184C22⋊C4×C43—24no—
185C22⋊C4×C43—24no—
186C42×C43—24no—
187C42×C43C22×C412yes—
188C42×C43#4112yes—
189C22⋊Dic43—42no—
190C22⋊Dic43—81no—
191C22⋊Dic43—81no—
192C4⋊Dic43—24no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—24no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—42no—
201C4⋊Dic43—81no—
202C4⋊Dic43—81no—
203C4⋊Dic43C2×D412yes—
204C4⋊Dic43#4112yes—
205C4×Dic43—24no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—24no—
209C4×Dic43—42no—
210C4×Dic43—81no—
211C4×Dic43—81no—
212C4×Dic43—81no—
213C4×Dic43C2×D412yes—
214C4×Dic43#4112yes—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C23×C43—22no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43C22×D411yescharacteristic
229Q8×C43—22no—
230Q8×C43—22no—
231Q8×C43—22no—
232Q8×C43—22no—
233Q8×C43—22no—
234Q8×C43—41no—
235Q8×C43—41no—
236Q8×C43C4×D414yes—
237D4×C43—22no—
238D4×C43—22no—
239D4×C43—41no—
240D4×C43—41no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43C4×D412yes—
255C2×C4×C43C4×D412yes—
256C2×C4×C43C23×C411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—22no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—22no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—84no—
285C2×Dic43#12112yes—
286C2×Dic43#12112yes—
287C8×C43—22no—
288C8×C43—22no—
289C43⋊C8—41no—
290C43⋊C8—41no—
291#21511—431nomaximal, Sylow
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43C2×C4×D411yescharacteristic
300C22×C43C2×#12111yescharacteristic
301C22×C43#52511yescharacteristic
302C22×C43#57711yescharacteristic
303C22×C43#57711yescharacteristic
304C22×C43#57711yescharacteristic
305C22×C43#57811yescharacteristic
306C4×C43—22no—
307C4×C43—22no—
308C4×C43—24no—
309C4×C43—42no—
310C4×C43—42no—
311C4×C43C2×C4×D411yescharacteristic
312C4×C43C4×#4111yescharacteristic
313C4×C43#52911yescharacteristic
314C4×C43#53211yescharacteristic
315Dic43—22no—
316Dic43—22no—
317Dic43—41no—
318Dic43—41no—
319Dic43—42no—
320Dic43—42no—
321Dic43—81no—
322Dic43—81no—
323C2×#464D4311yescharacteristic
324C2×#441—431no—
325C2×C4×SD16—431no—
326#2326—431no—
327#2276—431no—
328#1983—431no—
329#1948—431no—
330#1927—431no—
331#1926—431no—
332#1880—431no—
333#1878—431no—
334#1803—431no—
335#1768—431no—
336#1762—431no—
337C4×#103—431no—
338C2×C43—82no—
339C2×C43C4×#12111yescharacteristic
340C2×C43#294711yescharacteristic
341C2×C43#295211yescharacteristic
342C2×C43#304311yescharacteristic
343C2×C43#304611yescharacteristic
344C2×C43#312111yescharacteristic
345C2×C43#312511yescharacteristic
346C22×Q16C2×D4311yescharacteristic
347C22×SD16C2×D4311yescharacteristic
348C2×#124C2×D4311yescharacteristic
349C2×C4×Q8—431no—
350C2×C4×Q8—431no—
351C2×C4×Q8—431no—
352C2×C4×Q8C2×D4311yescharacteristic
353C2×C4×D4—431no—
354#464Dic4318yescomplemented
355#441—864no—
356C4×SD16—864no—
357C2×#106—431no—
358C2×#106—431no—
359C2×C4⋊C8—431no—
360C2×C4⋊C8C2×D4311yescharacteristic
361C2×#103—431no—
362C2×#103—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#103C2×D4311yescharacteristic
366C2×#102—431no—
367C2×#102—431no—
368C2×#102C2×D4311yescharacteristic
369C2×#97—431no—
370C2×C4×C8—431no—
371#391—431no—
372#390—431no—
373#388—861no—
374#388—861no—
375#385—861no—
376#385—861no—
377#384—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—
384#376—431no—
385#376—861no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#336—431no—
391#336—431no—
392C43#2151111yescharacteristic, complemented, Sylow
393C22×Q8C22×D4311yescharacteristic
394C22×Q8C22×D4311yescharacteristic
395C22×D4C22×D4311yescharacteristic
396C23×C4—861no—
397C2×Q16—22no—
398C2×Q16—22no—
399C2×Q16C2×Dic4314yescomplemented
400C2×SD16—22no—
401C2×SD16—22no—
402C2×SD16C2×Dic4314yes—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8C22×D4311yescharacteristic
406C22×C8C22×D4311yescharacteristic
407#124—22no—
408#124C2×Dic4314yes—
409C4×Q8—22no—
410C4×Q8—434no—
411C4×Q8—862no—
412C4×Q8—862no—
413C4×Q8—862no—
414C4×Q8—862no—
415C4×Q8—862no—
416C4×Q8C2×Dic4314yescomplemented
417C4×D4—862no—
418C4×D4—862no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C42—21no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—861no—
439C2×C42—861no—
440C2×C42—861no—
441C2×C42—861no—
442C2×C42—861no—
443C2×C42—861no—
444C2×C42C22×D4311yescharacteristic
445#106—862no—
446#106—862no—
447C4⋊C8—862no—
448C4⋊C8C2×Dic4314yescomplemented
449#103—862no—
450#103—862no—
451#103—862no—
452#103—862no—
453#103C2×Dic4314yescomplemented
454#102—862no—
455#102—862no—
456#102C2×Dic4314yes—
457#97—862no—
458C4×C8—862no—
459#95—431no—
460#95—431no—
461#95—431no—
462#95—431no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468C24—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8D4×D4312yes—
478C2×Q8#1062190012yes—
479C2×Q8C22×Dic4312yes—
480C2×Q8C22×Dic4312yes—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4C22×Dic4312yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—3441no—
499C22×C4—3441no—
500C22×C4—1722no—
501C22×C4D4×D4311yescharacteristic
502C22×C4D4×D4311yescharacteristic
503C22×C4C23×D4311yescharacteristic
504Q16—28no—
505SD16—28no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8C22×Dic4312yes—
517C2×C8C22×Dic4312yes—
518C4⋊C4—24no—
519C4⋊C4—21no—
520C4⋊C4—432no—
521C4⋊C4—432no—
522C4⋊C4—864no—
523C4⋊C4—864no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—3441no—
531C4⋊C4—3441no—
532C4⋊C4—1722no—
533C4⋊C4C22×Dic4312yes—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—3441no—
537C22⋊C4—3441no—
538C22⋊C4—1722no—
539C42—24no—
540C42—432no—
541C42—432no—
542C42—864no—
543C42—864no—
544C42—861no—
545C42—861no—
546C42—3441no—
547C42—3441no—
548C42—3441no—
549C42—1722no—
550C42#1062190012yes—
551C42C22×Dic4312yes—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23C2×D4×D4311yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—22no—
563Q8—22no—
564Q8—22no—
565Q8—41no—
566Q8—41no—
567Q8D4×Dic4314yes—
568D4—22no—
569D4—22no—
570D4—41no—
571D4—41no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—432no—
586C2×C4—432no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—862no—
592C2×C4—861no—
593C2×C4—862no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—3444no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4D4×Dic4312yes—
611C2×C4D4×Dic4312yes—
612C2×C4C23×Dic4311yescharacteristic
613C2×C4C2×D4×D4311yescharacteristic
614C2×C4#41×D4311yescharacteristic
615C2×C4#41×D4311yescharacteristic
616C2×C4C2×#1062190011yescharacteristic
617C2×C4C2×#1062190011yescharacteristic
618C8—22no—
619C8—22no—
620C8—1721no—
621C8—1721no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22C2×D4×Dic4311yescharacteristic
630C22#121×D4311yescharacteristic
631C22#1458340911yescharacteristic
632C22#1458370611yescharacteristic
633C22#1458370611yescharacteristic
634C22#1458370811yescharacteristic
635C22#1458371511yescharacteristic
636C4—22no—
637C4—22no—
638C4—24no—
639C4—42no—
640C4—42no—
641C4—862no—
642C4—862no—
643C4—3441no—
644C4—3441no—
645C4—1721no—
646C4—1721no—
647C4—1722no—
648C4—1722no—
649C4C2×D4×Dic4311yescharacteristic
650C4#41×Dic4311yescharacteristic
651C4#1458343011yescharacteristic
652C4#1458344411yescharacteristic
653C2—82no—
654C2#121×Dic4311yescharacteristic
655C2#1914343911yescharacteristic
656C2#1914347911yescharacteristic
657C2#1914411411yescharacteristic
658C2#1914414811yescharacteristic
659C2#1914482111yescharacteristic
660C2#1914487111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenterC2×#464D43
hypocenterC43#21511
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#14583006C2semidirect
4. #19136960C2semidirect
6. #19135359C2semidirect
7. #19135231C2semidirect
10. #19134938C2semidirect
11. #19134600C2semidirect
12. #19134454C2semidirect
14. #103×Dic43C2semidirect
58. C43×#464C4semidirect
118. C2×Q16×C43C2×C4semidirect
127. C4×Q8×C43C2×C4semidirect
134. C4⋊C8×C43C2×C4semidirect
135. #103×C43C2×C4semidirect
354. #464Dic43semidirect
392. C43#21511semidirect
399. C2×Q16C2×Dic43semidirect
416. C4×Q8C2×Dic43semidirect
448. C4⋊C8C2×Dic43semidirect
453. #103C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830062
C2×SD16×Dic432
#191373082
#191369602
#191355282
#191353592
#191352312
#191352242
#191349522
#191349382
#191346002
#191344542
#191344222
#103×Dic432
C2×C43×#4642
#2151143