Finite Group Databasebeta

← #25064368

Subgroups — #25064368

Order 11008.

990 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148396C211yesmaximal, characteristic
2#19143623C211yesmaximal, characteristic
3#19137528C211yesmaximal, characteristic
4#19133165C212yesmaximal, complemented
5#19133145C211yesmaximal, characteristic, complemented
6#19133126C212yesmaximal, complemented
7#19133113C212yesmaximal, complemented
8#19133108C211yesmaximal, characteristic, complemented
9#19133107C211yesmaximal, characteristic, complemented
10#328×D43C212yesmaximal, complemented
11C43×#1515C211yesmaximal, characteristic, complemented
12#14583610C412yescomplemented
13#14583609—22no—
14#14583609C412yescomplemented
15#14583605—22no—
16Q8×D172C412yescomplemented
17#14583564C412yescomplemented
18#14583527—21no—
19#14583524—21no—
20#14583524—21no—
21#14583456C2211yescharacteristic
22C22⋊Q8×D43C2212yes—
23C22⋊Q8×D43C2212yes—
24#14583373—21no—
25C2×C4×D172C2211yescharacteristic
26#14582972—22no—
27#14582969—22no—
28#14582956C2211yescharacteristic
29#14582861C2212yes—
30C22⋊C8×D43C2212yes—
31#14582788—21no—
32#14582784—21no—
33#14582777—21no—
34#14582761C2211yescharacteristic
35#14582758C2211yescharacteristic
36#14582746—21no—
37#14582746C2211yescharacteristic
38#14582745C2211yescharacteristic
39#95×D43C2211yescharacteristic
40#14582637C2212yes—
41#14582637C2212yes—
42#14582636C2212yes—
43#14582636C2212yes—
44#14582635C2212yes—
45#14582635C2212yes—
46C43×#533C2211yescharacteristic
47C43×#432C2211yescharacteristic
48C43×#383C2211yescharacteristic
49C43×#328C2212yes—
50C43×#328C2212yes—
51C2×Q8×D43C2×C412yes—
52C2×Q8×D43C2×C412yescomplemented
53C22×D172D411yescharacteristic
54C22×C4×D43—21no—
55C22×C4×D43C2311yescharacteristic
56C22×C4×D43C2311yescharacteristic
57C2×#10621872—22no—
58C2×C8×D43—22no—
59#13063325—22no—
60#13063325C2×C411yescharacteristic, complemented
61#13063325C2×C411yescharacteristic, complemented
62#13063324—22no—
63#13063317—21no—
64#13063317—22no—
65#13063316—22no—
66#13063305—22no—
67#13063305—22no—
68#13063305C2×C412yes—
69#13063305C2×C412yescomplemented
70#13063304—21no—
71#13063304C2312yes—
72#13063303—22no—
73#13063303—22no—
74#13063303—22no—
75#13063303—22no—
76#13063303—22no—
77#13063303—22no—
78#13063302—22no—
79#13063302—22no—
80#13063301—22no—
81#13063301—22no—
82#13063301C2×C412yes—
83#13063301C2×C412yescomplemented
84C4×Dic86—21no—
85C4×Dic86C2×C412yescomplemented
86C4×D172—22no—
87C4×D172—22no—
88C4×D172C2×C412yes—
89C4×D172C2×C412yes—
90C4×D172D412yes—
91C4×D172D412yes—
92#13063287—22no—
93#13063287—22no—
94#13063284—21no—
95C2×C4⋊Dic43D411yescharacteristic
96C2×Dic43⋊C4—21no—
97C4⋊C4×D43—22no—
98C4⋊C4×D43—22no—
99C4⋊C4×D43C2×C412yes—
100C4⋊C4×D43C2×C412yescomplemented
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4D411yescharacteristic
105C2×(C2×D43)⋊C4D411yescharacteristic
106C22⋊C4×D43—22no—
107C22⋊C4×D43—22no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C4⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)C2312yes—
112(C2×D43)⋊C8—22no—
113(C2×D43)⋊C8—22no—
114#13063236—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95C2311yescharacteristic
119C43⋊#95C2311yescharacteristic
120C4⋊Q8×C43C2×C411yescharacteristic, complemented
121C4⋊Q8×C43C2×C411yescharacteristic, complemented
122#125×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43C2312yes—
125C4×Q8×C43—21no—
126C4×Q8×C43C2×C412yescomplemented
127#117×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—21no—
130C22⋊C8×C43C2312yes—
131#97×C43—21no—
132#95×C43—21no—
133#95×C43—21no—
134#95×C43C2311yescharacteristic
135#95×C43C2311yescharacteristic
136C23×D43C2×D411yescharacteristic
137C23×D43C2×D411yescharacteristic
138C2×Q8×C43—21no—
139C2×Q8×C43C22×C412yes—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149Q8×D43—82no—
150Q8×D43—82no—
151C2×D172—22no—
152C2×D172—22no—
153C2×D172C22⋊C412yes—
154C2×D172C22⋊C412yes—
155C2×C4×D43—22no—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×C4×D43—81no—
164C2×C4×D43C22×C412yes—
165C2×C4×D43C22×C412yes—
166C2×C4×D43C2×D412yes—
167C2×C4×D43C2×D412yes—
168C2×Dic86—21no—
169C2×Dic86—22no—
170C2×Dic86—22no—
171C2×Dic86C22×C412yes—
172C2×C8×C43—22no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43C22×C412yes—
179C22⋊C4×C43—22no—
180C42×C43—22no—
181C42×C43C22×C411yescharacteristic
182C42×C43C22×C411yescharacteristic
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C22⋊Dic43—22no—
186(C2×D43)⋊C4—22no—
187(C2×D43)⋊C4—22no—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—81no—
193(C2×D43)⋊C4C22⋊C412yes—
194(C2×D43)⋊C4C22⋊C412yes—
195(C2×D43)⋊C4C22⋊C412yes—
196(C2×D43)⋊C4C22⋊C412yes—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202C4⋊Dic43C22⋊C412yes—
203C4⋊Dic43C22⋊C412yes—
204C4⋊Dic43C22×C412yes—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—81no—
212C4×Dic43—22no—
213C4×Dic43—42no—
214C4×Dic43—81no—
215C2×C43⋊C8—22no—
216#10621872—82no—
217C8×D43—82no—
218C23×C43C22×D411yescharacteristic
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43C2×C22⋊C412yes—
226C22×D43C2×C22⋊C412yes—
227C22×D43#13712yes—
228C22×D43#13712yes—
229Q8×C43—42no—
230Q8×C43—81no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C23×C411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43C2×C22⋊C412yes—
260C2×Dic43C2×C22⋊C412yes—
261D172—24no—
262D172—24no—
263C4×D43—42no—
264C4×D43—42no—
265C4×D43—42no—
266C4×D43—42no—
267C4×D43—82no—
268C4×D43—82no—
269C4×D43—82no—
270C4×D43—82no—
271C4×D43—84no—
272Dic86—42no—
273Dic86—82no—
274Dic86—82no—
275Dic86—81no—
276C8×C43—42no—
277C43⋊C8—42no—
278#17621—431nomaximal, Sylow
279C22×C43—21no—
280C22×C43—21no—
281C22×C43C22×C22⋊C411yescharacteristic
282C22×C43C2×#13711yescharacteristic
283C22×C43C2×#13711yescharacteristic
284C2×D43—22no—
285C2×D43—22no—
286C2×D43—22no—
287C2×D43—22no—
288C2×D43—22no—
289C2×D43—42no—
290C2×D43—42no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43#41914yes—
294C4×C43—21no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—42no—
301C4×C43—42no—
302C4×C43—81no—
303C4×C43—81no—
304Dic43—22no—
305Dic43—22no—
306Dic43—42no—
307Dic43—42no—
308Dic43—42no—
309Dic43—81no—
310#3501—431no—
311#2973—431no—
312#2353—431no—
313#1520—432no—
314#1515—431no—
315#1515D4311yescharacteristic, complemented
316#1511—432no—
317#1508—432no—
318#1506—431no—
319#1506—431no—
320C2×#328—432no—
321C2×C43—21no—
322C2×C43—21no—
323C2×C43#288311yescharacteristic
324C2×C43C2×#41911yescharacteristic
325C2×C43#290111yescharacteristic
326D43—24no—
327D43—42no—
328#554—432no—
329#554—432no—
330#554—862no—
331#554—862no—
332D4×Q8—432no—
333D4×Q8—432no—
334#544—861no—
335#543—861no—
336#543—861no—
337#533—431no—
338#533C2×D4311yescharacteristic
339C2×C22⋊Q8—432no—
340C2×C22⋊Q8—432no—
341#518—861no—
342C2×C4×D4—431no—
343#435—862no—
344#435—862no—
345#432—431no—
346#432C2×D4311yescharacteristic
347#407—432no—
348C2×C22⋊C8—432no—
349#388—861no—
350#387—861no—
351#386—861no—
352#383C2×D4311yescharacteristic
353#381—431no—
354#380—431no—
355C4×C22⋊C4—431no—
356C4×C22⋊C4—861no—
357#376—431no—
358C2×#95—431no—
359#328—432no—
360#328—432no—
361#328—432no—
362#328—432no—
363#328—432no—
364#328—432no—
365#328C2×D4312yes—
366#328C2×D4312yes—
367C43#1762111yescharacteristic, complemented, Sylow
368C22×Q8—432no—
369C22×Q8—432no—
370C22×D4—431no—
371C23×C4—431no—
372C23×C4—431no—
373C23×C4—861no—
374C2×M16—862no—
375C22×C8—862no—
376C4⋊Q8—431no—
377C4⋊Q8—431no—
378C4⋊Q8—862no—
379C4⋊Q8—862no—
380C4⋊Q8C4×D4311yescharacteristic, complemented
381C4⋊Q8C4×D4311yescharacteristic, complemented
382#125—21no—
383#125—862no—
384#125—862no—
385#125—861no—
386C22⋊Q8—21no—
387C22⋊Q8—432no—
388C22⋊Q8—432no—
389C22⋊Q8—432no—
390C22⋊Q8—432no—
391C22⋊Q8—432no—
392C22⋊Q8—862no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396C22⋊Q8—862no—
397C22⋊Q8—862no—
398C22⋊Q8—862no—
399C22⋊Q8—862no—
400C22⋊Q8—862no—
401C22⋊Q8—862no—
402C22⋊Q8—862no—
403C22⋊Q8—862no—
404C22⋊Q8—861no—
405C22⋊Q8C22×D4312yes—
406C4×Q8—21no—
407C4×Q8—432no—
408C4×Q8—861no—
409C4×Q8C4×D4312yescomplemented
410C4×D4—432no—
411C4×D4—432no—
412C4×D4—432no—
413C4×D4—432no—
414C4×D4—862no—
415C4×D4—862no—
416C4×D4—862no—
417C4×D4—862no—
418#117—21no—
419#117—861no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—432no—
422C2×C4⋊C4—432no—
423C2×C4⋊C4—862no—
424C2×C4⋊C4—862no—
425C2×C4⋊C4—861no—
426C2×C22⋊C4—431no—
427C2×C22⋊C4—431no—
428C2×C22⋊C4—862no—
429C2×C22⋊C4—862no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C42—861no—
434C2×C42—861no—
435C2×C42C22×D4311yescharacteristic
436C4⋊C8—21no—
437C4⋊C8—861no—
438C22⋊C8—432no—
439C22⋊C8—862no—
440C22⋊C8—862no—
441C22⋊C8C22×D4312yes—
442#97—21no—
443#97—861no—
444#95—21no—
445#95—21no—
446#95—431no—
447#95—431no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95C22×D4311yescharacteristic
452#95C22×D4311yescharacteristic
453C24—431no—
454C24—431no—
455C2×Q8—21no—
456C2×Q8—432no—
457C2×Q8—862no—
458C2×Q8—862no—
459C2×Q8—861no—
460C2×Q8—3442no—
461C2×Q8—3442no—
462C2×Q8C2×C4×D4312yes—
463C2×D4—432no—
464C2×D4—432no—
465C2×D4—862no—
466C2×D4—862no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—432no—
472C22×C4—432no—
473C22×C4—432no—
474C22×C4—432no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—3441no—
482C22×C4—3441no—
483C22×C4—3441no—
484C22×C4—1722no—
485C22×C4—1722no—
486C22×C4D4×D4311yescharacteristic
487C22×C4D4×D4311yescharacteristic
488C22×C4C23×D4311yescharacteristic
489M16—3442no—
490C2×C8—22no—
491C2×C8—862no—
492C2×C8—3442no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—432no—
499C4⋊C4—432no—
500C4⋊C4—432no—
501C4⋊C4—862no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—862no—
510C4⋊C4—861no—
511C4⋊C4—862no—
512C4⋊C4—3441no—
513C4⋊C4C2×C4×D4312yes—
514C22⋊C4—22no—
515C22⋊C4—432no—
516C22⋊C4—432no—
517C22⋊C4—432no—
518C22⋊C4—432no—
519C22⋊C4—862no—
520C22⋊C4—862no—
521C22⋊C4—862no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—3441no—
525C22⋊C4—1722no—
526C22⋊C4—1722no—
527C42—22no—
528C42—862no—
529C42—3441no—
530C42—1722no—
531C42C2×C4×D4311yescharacteristic
532C42C2×C4×D4311yescharacteristic
533C42D4×D4311yescharacteristic
534C42D4×D4311yescharacteristic
535C23—432no—
536C23—432no—
537C23—432no—
538C23—432no—
539C23—861no—
540C23—861no—
541C23—1721no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23C2×D4×D4311yescharacteristic
546Q8—42no—
547Q8—81no—
548Q8—3441no—
549Q8—3442no—
550Q8—3442no—
551Q8—1722no—
552D4—864no—
553D4—864no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—432no—
567C2×C4—432no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—862no—
571C2×C4—3442no—
572C2×C4—3442no—
573C2×C4—3442no—
574C2×C4—3442no—
575C2×C4—3444no—
576C2×C4—1722no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4C22⋊C4×D4311yescharacteristic
588C2×C4C22⋊C4×D4311yescharacteristic
589C2×C4C22⋊C4×D4311yescharacteristic
590C2×C4C22⋊C4×D4311yescharacteristic
591C2×C4C22×C4×D4311yescharacteristic
592C2×C4C2×D4×D4311yescharacteristic
593C8—42no—
594C8—1722no—
595C22—21no—
596C22—21no—
597C22—434no—
598C22—862no—
599C22—862no—
600C22—862no—
601C22—862no—
602C22—862no—
603C22—3441no—
604C22—3441no—
605C22—1722no—
606C22—1722no—
607C22C2×C22⋊C4×D4311yescharacteristic
608C22#137×D4311yescharacteristic
609C22#137×D4311yescharacteristic
610C4—21no—
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—42no—
617C4—42no—
618C4—81no—
619C4—81no—
620C4—862no—
621C4—862no—
622C4—3441no—
623C4—1722no—
624C4—1722no—
625C4—1722no—
626C2—21no—
627C2—21no—
628C2—864no—
629C2—1722no—
630C2#1914305411yescharacteristic
631C2#419×D4311yescharacteristic
632C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1515C2
socleC22×C43C22×C22⋊C4
prime radicalC22×D172D4
cosocleC22×C4×C43C24
hypercenter#1515D43
hypocenterC43#17621
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1515

Complements

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

NH ≅ G/Ntype
4. #19133165C2semidirect
5. #19133145C2semidirect
6. #19133126C2semidirect
7. #19133113C2semidirect
8. #19133108C2semidirect
9. #19133107C2semidirect
10. #328×D43C2semidirect
11. C43×#1515C2semidirect
12. #14583610C4semidirect
14. #14583609C4semidirect
16. Q8×D172C4semidirect
17. #14583564C4semidirect
52. C2×Q8×D43C2×C4semidirect
60. #13063325C2×C4semidirect
61. #13063325C2×C4semidirect
69. #13063305C2×C4semidirect
83. #13063301C2×C4semidirect
85. C4×Dic86C2×C4semidirect
100. C4⋊C4×D43C2×C4semidirect
120. C4⋊Q8×C43C2×C4semidirect
121. C4⋊Q8×C43C2×C4semidirect
126. C4×Q8×C43C2×C4semidirect
315. #1515D43semidirect
367. C43#17621semidirect
380. C4⋊Q8C4×D43semidirect
381. C4⋊Q8C4×D43semidirect
409. C4×Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191483962
#191436232
#191375282
#191331652
#191331452
#191331262
#191331132
#191331082
#191331072
#328×D432
C43×#15152
#1762143