Finite Group Databasebeta

← #25119071

Subgroups — #25119071

Order 11008.

954 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×#14583121C211yesmaximal, characteristic
2C2×#14583003C211yesmaximal, characteristic, complemented
3C2×#14582984C211yesmaximal, characteristic
4#19137666C211yesmaximal, characteristic
5Q8×C4⋊Dic43C211yesmaximal, characteristic, complemented
6#19135411C211yesmaximal, characteristic
7#19135358C211yesmaximal, characteristic, complemented
8#19135293C211yesmaximal, characteristic
9#19135272C211yesmaximal, characteristic, complemented
10#19134948C211yesmaximal, characteristic
11#19134934C211yesmaximal, characteristic, complemented
12#19134864C211yesmaximal, characteristic, complemented
13#19134857C211yesmaximal, characteristic
14#19134467C211yesmaximal, characteristic, complemented
15C43×#1763C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23#14583121C418yescomplemented
24#14583003—24no—
25#14582984—24no—
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063235C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582804C2211yescharacteristic
38#14582800C2211yescharacteristic
39#14582798—21no—
40#14582798—21no—
41#14582798C2211yescharacteristic
42#14582798C2211yescharacteristic
43#14582791—21no—
44#14582790—21no—
45#14582773—21no—
46#14582769—21no—
47#14582769C2211yescharacteristic
48C4×C4⋊Dic43—21no—
49C4×C4⋊Dic43C2211yescharacteristic
50C4×(C2×D43)⋊C4—21no—
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C2×#10621885—22no—
66C2×#10621885—22no—
67C2×#10621885C2×C414yescomplemented
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884C2×C414yes—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063313—22no—
74#13063313C2×C414yes—
75Q8×Dic43—22no—
76Q8×Dic43—22no—
77Q8×Dic43—41no—
78Q8×Dic43—41no—
79#13063290—22no—
80#13063290—41no—
81#13063287—22no—
82#13063287—41no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43D411yescharacteristic
90C2×C4⋊Dic43D411yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43C2311yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104#13063256—22no—
105#13063256—22no—
106C4⋊(C43⋊C8)C2×C414yescomplemented
107#13063250—22no—
108#13063250—41no—
109#13063248C2×C414yescomplemented
110#13063247—22no—
111#13063247—41no—
112#13063245C2×C414yes—
113#13063235—22no—
114C8×Dic43—22no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95D411yescharacteristic
120C43⋊#95D411yescharacteristic
121C22×Q8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C4×Q8×C43—22no—
125C4×Q8×C43C2×C414yescomplemented
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C42×C43—21no—
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133#103×C43—22no—
134#103×C43D414yes—
135#97×C43—22no—
136#95×C43—21no—
137C23×D43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43C22×C412yes—
142C2×Q8×C43C2×D412yes—
143C2×Q8×C43#4112yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172C22×C412yes—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43—81no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86C22×C412yes—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43C2×D412yes—
179C4⋊C4×C43—24no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43C22×C412yes—
185C4⋊C4×C43C2×D412yes—
186C42×C43—24no—
187C42×C43—81no—
188C42×C43C22×C412yes—
189C42×C43#4112yes—
190#10621885—28no—
191#10621884—28no—
192(C2×D43)⋊C4—24no—
193(C2×D43)⋊C4—24no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—81no—
197C4⋊Dic43—22no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—41no—
203C4⋊Dic43—42no—
204C4⋊Dic43—42no—
205C4⋊Dic43—42no—
206C4⋊Dic43—81no—
207C4⋊Dic43—81no—
208C4⋊Dic43—81no—
209Dic43⋊C4—42no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—42no—
215C4×Dic43—42no—
216C4×Dic43—42no—
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×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×C43C4×D414yes—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43C4×D412yes—
252C2×C4×C43C4×D412yes—
253C2×C4×C43C23×C411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×C4×C432−1+411yescharacteristic
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—22no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
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#13712yes—
280D172—22no—
281D172—22no—
282D172—41no—
283D172—41no—
284C4×D43—84no—
285Dic86—22no—
286Dic86—22no—
287Dic86—41no—
288Dic86—41no—
289C8×C43—22no—
290C8×C43—41no—
291C43⋊C8—22no—
292C43⋊C8—22no—
293#23013—431nomaximal, Sylow
294C22×C43C2×C4×D411yescharacteristic
295C22×C43D4211yescharacteristic
296C22×C43#54811yescharacteristic
297C22×C43C2×#13711yescharacteristic
298C22×C43#57511yescharacteristic
299C22×C43#57711yescharacteristic
300C22×C43#57711yescharacteristic
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—81no—
308C4×C43—24no—
309C4×C43—22no—
310C4×C43—22no—
311C4×C43—42no—
312C4×C43—42no—
313C4×C43—81no—
314C4×C43C2×C4×D411yescharacteristic
315C4×C43#52011yescharacteristic
316C4×C43#54711yescharacteristic
317C4×C43#55311yescharacteristic
318Dic43—22no—
319Dic43—42no—
320Dic43—41no—
321Dic43—41no—
322Dic43—41no—
323Dic43—81no—
324Dic43—81no—
325C2×#464—431no—
326C2×#441—431no—
327C2×C4×SD16—431no—
328#2367—431no—
329Q8×C4⋊C4—431no—
330#1959—431no—
331#1948—431no—
332#1936—431no—
333#1933—431no—
334#1880—431no—
335#1878—431no—
336#1865—431no—
337#1864—431no—
338#1771—431no—
339#1763D4311yescharacteristic, complemented
340C2×C43#236111yescharacteristic
341C2×C43C4×#13711yescharacteristic
342C2×C43#295211yescharacteristic
343C2×C43#326611yescharacteristic
344C2×C43#327111yescharacteristic
345C2×C43#336911yescharacteristic
346C2×C43#337111yescharacteristic
347D43—82no—
348C22×Q16—431no—
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—
357#441—864no—
358C4×SD16—864no—
359C2×#106—431no—
360C2×#106—431no—
361C2×C4⋊C8—431no—
362C2×#103—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#103C2×D4311yescharacteristic
366C2×#103C2×D4311yescharacteristic
367C2×#102—431no—
368C2×#102—431no—
369C2×#102—431no—
370C2×#97—431no—
371C2×#97C2×D4311yescharacteristic
372C2×C4×C8—431no—
373#391—431no—
374#390—431no—
375#389—431no—
376#389—431no—
377#389—861no—
378#389—861no—
379#388—861no—
380#388—861no—
381#385—861no—
382#384—431no—
383#384—861no—
384C4×C4⋊C4—431no—
385C4×C4⋊C4—861no—
386C4×C4⋊C4C2×D4311yescharacteristic
387C4×C22⋊C4—861no—
388#340—431no—
389#340—431no—
390#340C2×D4311yescharacteristic
391#340C2×D4311yescharacteristic
392#336—431no—
393#336—431no—
394C43#2301311yescharacteristic, complemented, Sylow
395C22×Q8—431no—
396C22×Q8C22×D4311yescharacteristic
397C22×D4—431no—
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—434no—
410#124—862no—
411C4×Q8—22no—
412C4×Q8—862no—
413C4×Q8—862no—
414C4×Q8—862no—
415C4×Q8—1721no—
416C4×Q8—1721no—
417C4×Q8—1721no—
418C4×Q8C4×D4314yescomplemented
419C4×D4—862no—
420C4×D4—1721no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C4⋊C4C22×D4311yescharacteristic
435C2×C4⋊C4C22×D4311yescharacteristic
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—861no—
446C2×C42—861no—
447C2×C42—861no—
448C2×C42C22×D4311yescharacteristic
449#106—862no—
450#106—862no—
451C4⋊C8—434no—
452#103—22no—
453#103—434no—
454#103—862no—
455#103—1721no—
456#103D17214yes—
457#102—434no—
458#102—862no—
459#102—1721no—
460#97—22no—
461#97—862no—
462C4×C8—862no—
463#95—21no—
464#95—431no—
465#95—431no—
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—432no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8C2×C4×D4312yes—
481C2×Q8C2×D17212yes—
482C2×Q8#1062189812yes—
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—3441no—
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—432no—
514C2×C8—432no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8C2×D17212yes—
520C4⋊C4—24no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—862no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—3441no—
531C4⋊C4—3441no—
532C4⋊C4—3441no—
533C4⋊C4—1721no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4C2×C4×D4312yes—
539C4⋊C4C2×D17212yes—
540C22⋊C4—864no—
541C22⋊C4—864no—
542C22⋊C4—3441no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C42—24no—
546C42—81no—
547C42—861no—
548C42—861no—
549C42—861no—
550C42—861no—
551C42—1722no—
552C42—1722no—
553C42—1722no—
554C42C2×C4×D4312yes—
555C42#1062190012yes—
556C23—862no—
557C23—1721no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23C2×D4×D4311yescharacteristic
564Q8—22no—
565Q8—22no—
566Q8—22no—
567Q8—862no—
568Q8—862no—
569Q8—1721no—
570Q8—1721no—
571Q8C4×D17214yes—
572D4—862no—
573D4—862no—
574D4—1721no—
575D4—1721no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—432no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—862no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
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×C4C22×D17211yescharacteristic
618C2×C4C2×#1062190011yescharacteristic
619C2×C4C2×#1062189811yescharacteristic
620C2×C4#1306337111yescharacteristic
621C2×C4#1306337211yescharacteristic
622C8—22no—
623C8—41no—
624C8—862no—
625C8—862no—
626C22—3441no—
627C22—3441no—
628C22—3441no—
629C22—3441no—
630C22—1722no—
631C22—1722no—
632C22—1722no—
633C22C2×(C22⋊D43)⋊C411yescharacteristic
634C22D4×D17211yescharacteristic
635C22#1458355811yescharacteristic
636C22#137×D4311yescharacteristic
637C22#1458369811yescharacteristic
638C22#1458370811yescharacteristic
639C22#1458370911yescharacteristic
640C4—22no—
641C4—24no—
642C4—22no—
643C4—42no—
644C4—42no—
645C4—81no—
646C4—862no—
647C4—3441no—
648C4—3441no—
649C4—1722no—
650C4—1721no—
651C4—1721no—
652C4—1721no—
653C4C2×C4×D17211yescharacteristic
654C4#1458337911yescharacteristic
655C4#1458355311yescharacteristic
656C4#1458359511yescharacteristic
657C2—3442no—
658C2#1913760911yescharacteristic
659C2#1914341011yescharacteristic
660C2#1914347411yescharacteristic
661C2#1914610711yescharacteristic
662C2#1914618211yescharacteristic
663C2#1914733611yescharacteristic
664C2#1914736811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1763C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1763D43
hypocenterC43#23013
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
2. C2×#14583003C2semidirect
5. Q8×C4⋊Dic43C2semidirect
7. #19135358C2semidirect
9. #19135272C2semidirect
11. #19134934C2semidirect
12. #19134864C2semidirect
14. #19134467C2semidirect
15. C43×#1763C2semidirect
23. #14583121C4semidirect
67. C2×#10621885C2×C4semidirect
106. C4⋊(C43⋊C8)C2×C4semidirect
109. #13063248C2×C4semidirect
125. C4×Q8×C43C2×C4semidirect
339. #1763D43semidirect
394. C43#23013semidirect
418. C4×Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831212
C2×#145830032
C2×#145829842
#191376662
Q8×C4⋊Dic432
#191354112
#191353582
#191352932
#191352722
#191349482
#191349342
#191348642
#191348572
#191344672
C43×#17632
#2301343