Finite Group Databasebeta

← #25065142

Subgroups — #25065142

Order 11008.

952 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic
3C2×#14582955C211yesmaximal, characteristic
4#19133324C212yesmaximal, complemented
5#19133322C212yesmaximal, complemented
6#19133319C212yesmaximal, complemented
7#19133310C212yesmaximal, complemented
8#19133253C211yesmaximal, characteristic, complemented
9#19133252C211yesmaximal, characteristic, complemented
10#19133250C211yesmaximal, characteristic, complemented
11C43×#1542C211yesmaximal, characteristic, complemented
12#14583456C2211yescharacteristic
13#14583455—21no—
14#14583454C2211yescharacteristic
15#14583454C2211yescharacteristic
16#14583453—21no—
17#14583453C412yes—
18#14583452—21no—
19#14583451—21no—
20#14583451C412yes—
21C4⋊Q8×D43C2211yescharacteristic
22C4⋊Q8×D43C2211yescharacteristic
23#125×D43—21no—
24C22⋊Q8×D43—21no—
25C22⋊Q8×D43C412yes—
26C4×Q8×D43—21no—
27C4×Q8×D43C412yes—
28#117×D43—21no—
29C2×C42×D43C2211yescharacteristic
30#14582955—21no—
31#14582955—21no—
32#14582955C2212yes—
33#14582955C2212yes—
34#14582955C2212yes—
35#14582953—21no—
36#14582952C2211yescharacteristic
37#14582950—21no—
38#14582921C2212yes—
39C2×C4⋊(C43⋊C8)C2211yescharacteristic
40#14582861—21no—
41C2×(C2×D43)⋊C8—21no—
42C4×#10621872—21no—
43C2×#13063235—21no—
44#14582648C2212yescomplemented
45#14582647C2212yescomplemented
46#14582647C2212yescomplemented
47#14582646C2212yescomplemented
48#14582645C2212yescomplemented
49#14582644C2212yescomplemented
50C43×#533C2211yescharacteristic
51C43×#431C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C43×#333C2212yescomplemented
54C43×#332C2212yescomplemented
55C2×Q8×D43—21no—
56C2×Q8×D43C2×C412yes—
57C22×C4×D43C2×C411yescharacteristic
58C22×C4×D43D411yescharacteristic
59C22×C4×D43D411yescharacteristic
60C2×#10621872—22no—
61C22×C43⋊C8—21no—
62#13063325C2311yescharacteristic
63#13063325C2311yescharacteristic
64#13063324—21no—
65#13063324—21no—
66#13063324—21no—
67#13063324C2×C412yes—
68#13063323—21no—
69#13063323C2×C412yes—
70#13063317—21no—
71#13063316—21no—
72#13063316—21no—
73#13063315—22no—
74#13063315—22no—
75#13063305—21no—
76#13063305C2×C412yes—
77#13063304—21no—
78#13063304C2×C412yes—
79#13063303—22no—
80#13063303—22no—
81#13063302—22no—
82#13063302—22no—
83#13063301—21no—
84#13063301C2×C412yes—
85Q8×Dic43—21no—
86Q8×Dic43C2×C412yes—
87C4×Dic86—21no—
88C4×Dic86—22no—
89C4×Dic86—22no—
90C4×Dic86C2×C412yes—
91#13063290—22no—
92#13063290—22no—
93#13063290—21no—
94#13063290C2×C412yes—
95#13063284—21no—
96#13063283—21no—
97#13063283—21no—
98#13063282—22no—
99#13063281—22no—
100C4⋊C4×D43—22no—
101C4⋊C4×D43—22no—
102C4⋊C4×D43—21no—
103C4⋊C4×D43—21no—
104C4⋊C4×D43—21no—
105C4⋊C4×D43C2×C412yes—
106C22⋊C4×D43—22no—
107C2×C4×Dic43C2×C411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43D411yescharacteristic
110C42×D43—22no—
111C42×D43C2×C411yescharacteristic
112C42×D43C2×C411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43D411yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43C2311yescharacteristic
118C42×D43C2311yescharacteristic
119C4⋊(C43⋊C8)—21no—
120C4⋊(C43⋊C8)C2312yes—
121C4⋊(C43⋊C8)C2312yes—
122Dic43⋊C8—22no—
123C22⋊(C43⋊C8)—21no—
124(C2×D43)⋊C8—22no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8—22no—
127#13063235—22no—
128#13063235—22no—
129#13063235—22no—
130C4×C43⋊C8—21no—
131C22×C8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133C4⋊Q8×C43C2311yescharacteristic
134#125×C43—21no—
135C22⋊Q8×C43—21no—
136C22⋊Q8×C43C2×C412yes—
137C4×Q8×C43—21no—
138C4×Q8×C43C2×C412yes—
139#117×C43—21no—
140C2×C42×C43C2311yescharacteristic
141C4⋊C8×C43—21no—
142C4⋊C8×C43C2312yes—
143C4⋊C8×C43C2312yes—
144C22⋊C8×C43—21no—
145C4×C8×C43—21no—
146C23×D43C22⋊C411yescharacteristic
147C2×Q8×C43—21no—
148C2×Q8×C43C22×C412yes—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×Dic43C22⋊C411yescharacteristic
153C22×Dic43C22⋊C411yescharacteristic
154C22×Dic43C22⋊C411yescharacteristic
155Q8×D43—44no—
156Q8×D43—44no—
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43—22no—
160C2×C4×D43—22no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43C22⋊C411yescharacteristic
164C2×C4×D43C22⋊C411yescharacteristic
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22⋊C411yescharacteristic
169C2×C4×D43C22×C411yescharacteristic
170C2×C4×D43C22×C411yescharacteristic
171C2×C4×D43C2×D411yescharacteristic
172C2×C4×D43C2×D411yescharacteristic
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×Dic86—21no—
176C2×Dic86—22no—
177C2×Dic86—22no—
178C2×Dic86C22×C412yes—
179C2×C8×C43—22no—
180C2×C8×C43—22no—
181C2×C8×C43—42no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43C22×C412yes—
188C22⋊C4×C43—22no—
189C42×C43—22no—
190C42×C43C22×C411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43C2411yescharacteristic
194C22⋊Dic43—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202C4⋊Dic43C22×C412yes—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211C4×Dic43—22no—
212C4×Dic43—22no—
213C4×Dic43—22no—
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22×C411yescharacteristic
221C4×Dic43C22×C411yescharacteristic
222C4×Dic43C2×D411yescharacteristic
223C4×Dic43C2×D411yescharacteristic
224C4×Dic43C2×D411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226C2×C43⋊C8—22no—
227C2×C43⋊C8—22no—
228C2×C43⋊C8—42no—
229#10621872—44no—
230C23×C43C2×C22⋊C411yescharacteristic
231C22×D43—22no—
232C22×D43—22no—
233C22×D43—41no—
234C22×D43C2×C22⋊C411yescharacteristic
235C22×D43C2×C22⋊C411yescharacteristic
236Q8×C43—42no—
237Q8×C43—42no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—41no—
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43#13712yes—
246C2×C4×C43#13712yes—
247C2×C4×C43C23×C411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43C2×C22⋊C411yescharacteristic
256C2×Dic43C2×C22⋊C411yescharacteristic
257C2×Dic43C2×C22⋊C411yescharacteristic
258C2×Dic43C2×C22⋊C411yescharacteristic
259C2×Dic43C2×C22⋊C411yescharacteristic
260C2×Dic43C2×C22⋊C411yescharacteristic
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—21no—
264C4×D43—21no—
265C4×D43—21no—
266C4×D43—21no—
267C4×D43—22no—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—41no—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—41no—
275C4×D43—44no—
276C4×D43—44no—
277Dic86—44no—
278Dic86—44no—
279Dic86—42no—
280Dic86—42no—
281C8×C43—42no—
282C8×C43—42no—
283C43⋊C8—42no—
284C43⋊C8—42no—
285#17734—431nomaximal, Sylow
286C22×C43—21no—
287C22×C43—21no—
288C22×C43#41912yes—
289C22×C43C22×C22⋊C411yescharacteristic
290C2×D43—21no—
291C2×D43—21no—
292C2×D43—21no—
293C2×D43—21no—
294C2×D43—21no—
295C2×D43—44no—
296C2×D43#41312yes—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—42no—
301C4×C43—42no—
302C4×C43#41912yes—
303C4×C43C2×#13711yescharacteristic
304C4×C43C2×#13711yescharacteristic
305C4×C43#57512yes—
306Dic43—21no—
307Dic43—21no—
308Dic43—21no—
309Dic43—21no—
310Dic43—21no—
311Dic43—21no—
312Dic43—42no—
313Dic43—42no—
314C2×#533—431no—
315#2920—431no—
316C2×#432—431no—
317#1559—432no—
318#1559—432no—
319#1558—432no—
320#1556—432no—
321#1542—431no—
322#1542—431no—
323#1542—431no—
324#1542D4311yescharacteristic, complemented
325C2×C43—22no—
326C2×C43C2×#41311yescharacteristic
327C2×C43C2×#41911yescharacteristic
328C2×C43#289611yescharacteristic
329D43—22no—
330D43—41no—
331#533—431no—
332#533—431no—
333#533—432no—
334#533—432no—
335#533—431no—
336#533—861no—
337#533—861no—
338#533—861no—
339#533—861no—
340#533C2×D4311yescharacteristic
341C2×C4⋊Q8—431no—
342C2×C4⋊Q8—431no—
343C2×#125—861no—
344C2×C22⋊Q8—432no—
345C2×C22⋊Q8—861no—
346C2×C4×Q8—432no—
347C2×C4×Q8—861no—
348C2×#117—861no—
349C22×C42—431no—
350#432—432no—
351#432—432no—
352#432—432no—
353#432—861no—
354#432—861no—
355#432—861no—
356#431—431no—
357#431—861no—
358#431C2×D4311yescharacteristic
359#423—432no—
360C2×C4⋊C8—431no—
361C2×C4⋊C8C2×D4311yescharacteristic
362#407—861no—
363C2×C22⋊C8—861no—
364C4×M16—861no—
365C2×#97—861no—
366#333—432no—
367#333—432no—
368#333—432no—
369#333C2×D4312yescomplemented
370#332—432no—
371#332—432no—
372#332—432no—
373#332C2×D4312yescomplemented
374C43#1773411yescharacteristic, complemented, Sylow
375C22×Q8—432no—
376C22×Q8—861no—
377C23×C4—431no—
378C23×C4—431no—
379C23×C4—431no—
380C2×M16—862no—
381C22×C8—21no—
382C22×C8—861no—
383C4⋊Q8—432no—
384C4⋊Q8—432no—
385C4⋊Q8—431no—
386C4⋊Q8—431no—
387C4⋊Q8—861no—
388C4⋊Q8—861no—
389C4⋊Q8—861no—
390C4⋊Q8—861no—
391C4⋊Q8C22×D4311yescharacteristic
392C4⋊Q8C22×D4311yescharacteristic
393#125—21no—
394#125—862no—
395#125—862no—
396#125—861no—
397#125—861no—
398#125—861no—
399C22⋊Q8—21no—
400C22⋊Q8—432no—
401C22⋊Q8—432no—
402C22⋊Q8—432no—
403C22⋊Q8—862no—
404C22⋊Q8—862no—
405C22⋊Q8—862no—
406C22⋊Q8—862no—
407C22⋊Q8—861no—
408C22⋊Q8—861no—
409C22⋊Q8—861no—
410C22⋊Q8C4×D4312yes—
411C4×Q8—21no—
412C4×Q8—432no—
413C4×Q8—432no—
414C4×Q8—432no—
415C4×Q8—862no—
416C4×Q8—862no—
417C4×Q8—862no—
418C4×Q8—862no—
419C4×Q8—861no—
420C4×Q8—861no—
421C4×Q8—861no—
422C4×Q8C4×D4312yes—
423#117—21no—
424#117—862no—
425#117—862no—
426#117—861no—
427#117—861no—
428#117—861no—
429C2×C4⋊C4—432no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—862no—
433C2×C4⋊C4—862no—
434C2×C4⋊C4—861no—
435C2×C22⋊C4—862no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—862no—
448C2×C42C22×D4311yescharacteristic
449C4⋊C8—21no—
450C4⋊C8—432no—
451C4⋊C8—432no—
452C4⋊C8—862no—
453C4⋊C8—861no—
454C4⋊C8C22×D4312yes—
455C4⋊C8C22×D4312yes—
456C22⋊C8—21no—
457C22⋊C8—862no—
458C22⋊C8—862no—
459C22⋊C8—862no—
460C22⋊C8—861no—
461#97—862no—
462#97—862no—
463#97—862no—
464C4×C8—21no—
465C4×C8—861no—
466C24—431no—
467C2×Q8—21no—
468C2×Q8—432no—
469C2×Q8—862no—
470C2×Q8—862no—
471C2×Q8—861no—
472C2×Q8—1724no—
473C2×Q8—1724no—
474C2×Q8C2×C4×D4312yes—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4C2×C4×D4311yescharacteristic
497C22×C4D4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499M16—1724no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—42no—
503C2×C8—862no—
504C2×C8—862no—
505C2×C8—1722no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—432no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4C2×C4×D4312yes—
526C22⋊C4—22no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C22⋊C4—862no—
530C42—22no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—862no—
544C42—862no—
545C42—862no—
546C42C2×C4×D4311yescharacteristic
547C42D4×D4311yescharacteristic
548C42D4×D4311yescharacteristic
549C42C23×D4311yescharacteristic
550C23—431no—
551C23—431no—
552C23—862no—
553C23—862no—
554C23—1721no—
555C23C22⋊C4×D4311yescharacteristic
556Q8—42no—
557Q8—42no—
558Q8—1722no—
559Q8—1724no—
560Q8—1724no—
561Q8—1722no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—431no—
567C2×C4—431no—
568C2×C4—431no—
569C2×C4—431no—
570C2×C4—431no—
571C2×C4—431no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1724no—
590C2×C4—1724no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4C22⋊C4×D4311yescharacteristic
594C2×C4C22⋊C4×D4311yescharacteristic
595C2×C4C22⋊C4×D4311yescharacteristic
596C2×C4#1306335412yes—
597C2×C4#1306335712yes—
598C2×C4C22×C4×D4311yescharacteristic
599C2×C4C2×D4×D4311yescharacteristic
600C2×C4C2×D4×D4311yescharacteristic
601C8—42no—
602C8—42no—
603C8—1722no—
604C8—1722no—
605C22—21no—
606C22—21no—
607C22—432no—
608C22—861no—
609C22—861no—
610C22—861no—
611C22—861no—
612C22—861no—
613C22—1724no—
614C22#1458290612yes—
615C22C2×C22⋊C4×D4311yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—42no—
620C4—42no—
621C4—861no—
622C4—861no—
623C4—861no—
624C4—861no—
625C4—861no—
626C4—861no—
627C4—1722no—
628C4—1722no—
629C4#1458290612yes—
630C4C2×#1306335411yescharacteristic
631C4C2×#1306335711yescharacteristic
632C4#1458369612yes—
633C2—22no—
634C2—862no—
635C2—1721no—
636C2#413×D4311yescharacteristic
637C2C2×#1458290611yescharacteristic
638C2#1914311011yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1542C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC42×C43C24
hypercenter#1542D43
hypocenterC43#17734
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
4. #19133324C2semidirect
5. #19133322C2semidirect
6. #19133319C2semidirect
7. #19133310C2semidirect
8. #19133253C2semidirect
9. #19133252C2semidirect
10. #19133250C2semidirect
11. C43×#1542C2semidirect
44. #14582648C22semidirect
45. #14582647C22semidirect
46. #14582647C22semidirect
47. #14582646C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
53. C43×#333C22semidirect
54. C43×#332C22semidirect
324. #1542D43semidirect
369. #333C2×D43semidirect
373. #332C2×D43semidirect
374. C43#17734semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#191432232
C2×#145829552
#191333242
#191333222
#191333192
#191333102
#191332532
#191332522
#191332502
C43×#15422
#1773443