Finite Group Databasebeta

← #25102835

Subgroups — #25102835

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×#14583118C211yesmaximal, characteristic
2C2×#14582991C211yesmaximal, characteristic, complemented
3C2×#14582990C211yesmaximal, characteristic
4#124×Dic43C211yesmaximal, characteristic
5C4×#13063290C211yesmaximal, characteristic, complemented
6#19135363C211yesmaximal, characteristic, complemented
7#19135232C211yesmaximal, characteristic, complemented
8#19135218C211yesmaximal, characteristic
9#19134947C211yesmaximal, characteristic
10#19134933C211yesmaximal, characteristic, complemented
11#19134611C211yesmaximal, characteristic, complemented
12C4⋊C8×Dic43C211yesmaximal, characteristic, complemented
13#103×Dic43C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic
15C43×#1983C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×D4×Dic43C2211yescharacteristic
23#14583118C418yescomplemented
24#14582991—24no—
25#14582990—24no—
26C2×#13063258C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35#14582806C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582792—21no—
38#14582792—21no—
39#14582765C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×Dic43⋊C4—21no—
43#14582750—21no—
44#14582750—21no—
45C22⋊C4×Dic43—21no—
46C22⋊C4×Dic43—21no—
47C42×Dic43—21no—
48C42×Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×#124×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C2×#10621885—22no—
65C2×#10621885—22no—
66C2×#10621885C2×C414yescomplemented
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883C2×C414yes—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72Q8×Dic43—22no—
73Q8×Dic43—22no—
74C4×Dic86—22no—
75C4×Dic86C2×C414yescomplemented
76#13063290—22no—
77#13063290—22no—
78#13063290—22no—
79#13063290D414yes—
80D4×Dic43—22no—
81D4×Dic43—22no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43D411yescharacteristic
99C2×C4×Dic43D411yescharacteristic
100C2×C4×Dic43D411yescharacteristic
101C2×C4×Dic43D411yescharacteristic
102C2×C4×Dic43C2311yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104#13063258—22no—
105#13063256—22no—
106C4⋊(C43⋊C8)C2×C414yescomplemented
107#13063250—22no—
108#13063250—22no—
109#13063249C2×C414yescomplemented
110#13063246C2×C414yes—
111C8×Dic43—22no—
112C8×Dic43—22no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×Q8×C43C2311yescharacteristic
120C22×D4×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123#124×C43—22no—
124#124×C43C2×C414yes—
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—22no—
132#103×C43—22no—
133#103×C43—22no—
134#102×C43—22no—
135#102×C43—22no—
136#95×C43—21no—
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×C43C22×C412yes—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43C22×C412yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—42no—
161C22×Dic43—42no—
162C22×Dic43—42no—
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86C22×C412yes—
171C2×Dic86C2×D412yes—
172C2×Dic86#4112yes—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C2×D412yes—
182C4⋊C4×C43#4112yes—
183C22⋊C4×C43—24no—
184C22⋊C4×C43—24no—
185C42×C43—42no—
186C42×C43C22×C412yes—
187C42×C43#4112yes—
188C22⋊Dic43—42no—
189C22⋊Dic43—42no—
190C22⋊Dic43—42no—
191#10621885—28no—
192#10621883—28no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—42no—
199C4⋊Dic43C22×C412yes—
200Dic43⋊C4—24no—
201Dic43⋊C4—24no—
202Dic43⋊C4—24no—
203C4×Dic43—24no—
204C4×Dic43—24no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—24no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43—41no—
212C4×Dic43—42no—
213C4×Dic43—42no—
214C4×Dic43—42no—
215C4×Dic43C2×D412yes—
216C4×Dic43#4112yes—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8C22×C412yes—
222C2×C43⋊C8C22×C412yes—
223C23×C43—22no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43C22×D411yescharacteristic
231Q8×C43—22no—
232Q8×C43—22no—
233Q8×C43—41no—
234Q8×C43—41no—
235D4×C43—22no—
236D4×C43—22no—
237D4×C43—41no—
238D4×C43—41no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43C4×D412yes—
253C2×C4×C43C4×D412yes—
254C2×C4×C43C23×C411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—84no—
280C2×Dic43#12112yes—
281C2×Dic43#12112yes—
282C2×Dic43#13512yes—
283C2×Dic43#13512yes—
284C2×Dic43#13712yes—
285Dic86—22no—
286Dic86—22no—
287Dic86—22no—
288Dic86C4×D414yes—
289C8×C43—41no—
290C8×C43—41no—
291C43⋊C8—22no—
292C43⋊C8—22no—
293C4×#464—431nomaximal, Sylow
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—42no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43C2×C4×D411yescharacteristic
302C22×C43C2×#12111yescharacteristic
303C22×C43#52511yescharacteristic
304C22×C43C2×#13511yescharacteristic
305C22×C43C2×#13511yescharacteristic
306C22×C43C2×#13711yescharacteristic
307C22×C43#57511yescharacteristic
308C4×C43—22no—
309C4×C43—22no—
310C4×C43—42no—
311C4×C43—42no—
312C4×C43—42no—
313C4×C43C2×C4×D411yescharacteristic
314C4×C43C4×#4111yescharacteristic
315C4×C43#52911yescharacteristic
316C4×C43#53211yescharacteristic
317Dic43—22no—
318Dic43—22no—
319Dic43—24no—
320Dic43—41no—
321Dic43—42no—
322Dic43—81no—
323Dic43—81no—
324Dic43#46414yescomplemented
325C2×#464—431no—
326C2×C4×Q16—431no—
327C2×C4×SD16—431no—
328C4×#124—431no—
329C42×Q8—431no—
330#1983D4311yescharacteristic
331#1949—431no—
332#1927—431no—
333#1925—431no—
334#1880—431no—
335#1878—431no—
336#1805—431no—
337C4×C4⋊C8—431no—
338C4×#103—431no—
339C4×#102—431no—
340C2×C43—82no—
341C2×C43C4×#12111yescharacteristic
342C2×C43C4×#13511yescharacteristic
343C2×C43C4×#13711yescharacteristic
344C2×C43C2×#46411yescharacteristic
345C2×C43#303511yescharacteristic
346C2×C43#310211yescharacteristic
347C2×C43#310811yescharacteristic
348C22×Q16—431no—
349C22×SD16—431no—
350C2×#124C2×D4311yescharacteristic
351C2×C4×Q8—431no—
352C2×C4×Q8—431no—
353C2×C4×Q8—431no—
354C2×C4×Q8—431no—
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⋊C8C2×D4311yescharacteristic
363C2×#103—431no—
364C2×#103—431no—
365C2×#103—431no—
366C2×#103C2×D4311yescharacteristic
367C2×#103C2×D4311yescharacteristic
368C2×#102—431no—
369C2×#102C2×D4311yescharacteristic
370C2×#102C2×D4311yescharacteristic
371C2×C4×C8—431no—
372C2×C4×C8—431no—
373#391—431no—
374#390—431no—
375#388—861no—
376#388—861no—
377#382—431no—
378C4×C4⋊C4—431no—
379C4×C4⋊C4—431no—
380C4×C4⋊C4—861no—
381C4×C4⋊C4—861no—
382C4×C4⋊C4—861no—
383C4×C4⋊C4C2×D4311yescharacteristic
384C4×C22⋊C4—861no—
385C4×C22⋊C4—861no—
386C43—431no—
387C43—861no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#336—431no—
393#336—431no—
394C43C4×#46411yescharacteristic, complemented, Sylow
395C22×Q8—431no—
396C22×Q8C22×D4311yescharacteristic
397C22×D4C22×D4311yescharacteristic
398C23×C4—861no—
399C2×Q16—434no—
400C2×Q16—862no—
401C2×Q16—862no—
402C2×SD16—434no—
403C2×SD16—862no—
404C2×SD16—862no—
405C22×C8—431no—
406C22×C8—431no—
407C22×C8C22×D4311yescharacteristic
408C22×C8C22×D4311yescharacteristic
409#124—22no—
410#124C4×D4314yes—
411C4×Q8—434no—
412C4×Q8—434no—
413C4×Q8—862no—
414C4×Q8—862no—
415C4×Q8—862no—
416C4×Q8—862no—
417C4×Q8—862no—
418C4×Q8—862no—
419C4×D4—862no—
420C4×D4—862no—
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⋊C4C22×D4311yescharacteristic
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—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—22no—
452C4⋊C8—434no—
453#103—22no—
454#103—22no—
455#103—434no—
456#103—862no—
457#103—862no—
458#102—22no—
459#102—22no—
460#102—434no—
461C4×C8—862no—
462C4×C8—862no—
463#95—21no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470C24—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—432no—
477C2×Q8—432no—
478C2×Q8—432no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8C2×C4×D4312yes—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4C2×C4×D4312yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—861no—
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—868no—
507SD16—868no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—432no—
515C2×C8—432no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—432no—
523C4⋊C4—864no—
524C4⋊C4—864no—
525C4⋊C4—864no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—1722no—
532C4⋊C4D4×D4312yes—
533C4⋊C4#1062190012yes—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—1722no—
537C22⋊C4—1722no—
538C22⋊C4—1722no—
539C42—42no—
540C42—432no—
541C42—432no—
542C42—862no—
543C42—862no—
544C42—862no—
545C42—864no—
546C42—864no—
547C42—864no—
548C42—861no—
549C42—861no—
550C42—1721no—
551C42—1722no—
552C42—1722no—
553C42—1722no—
554C42C2×C4×D4312yes—
555C42#1062190012yes—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23C2×D4×D4311yescharacteristic
564Q8—22no—
565Q8—22no—
566Q8—41no—
567Q8—41no—
568Q8—434no—
569Q8—862no—
570Q8—862no—
571Q8—862no—
572D4—22no—
573D4—22no—
574D4—41no—
575D4—41no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—432no—
590C2×C4—432no—
591C2×C4—432no—
592C2×C4—432no—
593C2×C4—432no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—861no—
597C2×C4—862no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—862no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—3444no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4(C22⋊D43)⋊C412yes—
615C2×C4(C22⋊D43)⋊C412yes—
616C2×C4C22×C4×D4311yescharacteristic
617C2×C4C2×D4×D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4#41×D4311yescharacteristic
620C2×C4C2×#1062190011yescharacteristic
621C2×C4C2×#1062190011yescharacteristic
622C8—41no—
623C8—41no—
624C8—862no—
625C8—862no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22C2×(C22⋊D43)⋊C411yescharacteristic
634C22#121×D4311yescharacteristic
635C22#1458340911yescharacteristic
636C22#135×D4311yescharacteristic
637C22#135×D4311yescharacteristic
638C22#137×D4311yescharacteristic
639C22#1458369511yescharacteristic
640C4—22no—
641C4—22no—
642C4—42no—
643C4—42no—
644C4—42no—
645C4—434no—
646C4—864no—
647C4—862no—
648C4—862no—
649C4—3441no—
650C4—3441no—
651C4—1721no—
652C4—1722no—
653C4C4×D4×D4311yescharacteristic
654C4C4×#1062190011yescharacteristic
655C4#1458342811yescharacteristic
656C4#1458344711yescharacteristic
657C2—82no—
658C2#1913711111yescharacteristic
659C2#1914336311yescharacteristic
660C2#1914341911yescharacteristic
661C2#464×D4311yescharacteristic
662C2#1914404711yescharacteristic
663C2#1914461011yescharacteristic
664C2#1914467411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1983C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1983D43
hypocenterC43C4×#464
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×#14582991C2semidirect
5. C4×#13063290C2semidirect
6. #19135363C2semidirect
7. #19135232C2semidirect
10. #19134933C2semidirect
11. #19134611C2semidirect
12. C4⋊C8×Dic43C2semidirect
13. #103×Dic43C2semidirect
23. #14583118C4semidirect
66. C2×#10621885C2×C4semidirect
75. C4×Dic86C2×C4semidirect
106. C4⋊(C43⋊C8)C2×C4semidirect
109. #13063249C2×C4semidirect
324. Dic43#464semidirect
394. C43C4×#464semidirect

Maximal subgroups

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

subgroupindex
C2×#145831182
C2×#145829912
C2×#145829902
#124×Dic432
C4×#130632902
#191353632
#191352322
#191352182
#191349472
#191349332
#191346112
C4⋊C8×Dic432
#103×Dic432
#102×Dic432
C43×#19832
C4×#46443