Finite Group Databasebeta

← #25062464

Subgroups — #25062464

Order 11008.

1246 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583367C211yesmaximal, characteristic
2#19143223C212yesmaximal, complemented
3#19132937C212yesmaximal, complemented
4#19132934C212yesmaximal, complemented
5#19132932C212yesmaximal, complemented
6#19132930C212yesmaximal, complemented
7#19132909C211yesmaximal, characteristic, complemented
8#19132907C212yesmaximal, complemented
9C43×#1458C211yesmaximal, characteristic, complemented
10C22×#10621898C411yescharacteristic
11#14583367—22no—
12#14583367—22no—
13#14583367—22no—
14#14583367—22no—
15C2×#13063290C411yescharacteristic
16C2×#13063290C2211yescharacteristic
17C2×#13063287C411yescharacteristic
18C2×#13063287C2211yescharacteristic
19C2×(C22⋊D43)⋊C4C411yescharacteristic
20C2×(C22⋊D43)⋊C4C411yescharacteristic
21C2×(C22⋊D43)⋊C4C2211yescharacteristic
22C2×(C22⋊D43)⋊C4C2211yescharacteristic
23C2×#13063282C411yescharacteristic
24C2×#13063282C2211yescharacteristic
25C22×C4×Dic43C411yescharacteristic
26C2×C42×D43C411yescharacteristic
27C2×C42×D43C2211yescharacteristic
28#14582955—22no—
29#14582953C2214yes—
30#14582952C2212yes—
31#14582950—22no—
32#14582921—22no—
33#14582861C2214yes—
34C4×#10621872—22no—
35#14582625C2212yes—
36#14582624C2214yes—
37#14582623C2212yes—
38#14582622C2214yes—
39C2×#117×C43C2211yescharacteristic
40C43×#431C2212yes—
41C43×#324C2212yes—
42C43×#323C2212yes—
43C2×#10621898—24no—
44C2×#10621898—22no—
45C2×#10621898—22no—
46C2×#10621898—24no—
47C22×Dic86C2×C411yescharacteristic
48C22×D172C2×C411yescharacteristic
49C22×C22⋊D43C2×C411yescharacteristic
50C22×C22⋊D43C2×C411yescharacteristic
51C23×Dic43C2×C411yescharacteristic
52C23×Dic43C2×C411yescharacteristic
53C22×C4×D43C2×C411yescharacteristic
54C22×C4×D43C2×C411yescharacteristic
55C22×C4×D43C2×C411yescharacteristic
56C22×C4×D43C2×C411yescharacteristic
57C22×C4×D43C2×C411yescharacteristic
58C22×C4×D43C2311yescharacteristic
59C2×#10621872—24no—
60#13063290—22no—
61#13063290—22no—
62#13063290—22no—
63#13063290—22no—
64#13063287—22no—
65#13063287—22no—
66#13063287—22no—
67#13063287—22no—
68(C22⋊D43)⋊C4—22no—
69(C22⋊D43)⋊C4—22no—
70(C22⋊D43)⋊C4—22no—
71(C22⋊D43)⋊C4—22no—
72(C22⋊D43)⋊C4—22no—
73(C22⋊D43)⋊C4—22no—
74(C22⋊D43)⋊C4—22no—
75(C22⋊D43)⋊C4—22no—
76#13063282—22no—
77#13063282—22no—
78#13063282—22no—
79#13063282—22no—
80C2×Dic43⋊C4C2×C411yescharacteristic
81C2×Dic43⋊C4C2×C411yescharacteristic
82C2×Dic43⋊C4C2×C411yescharacteristic
83C2×Dic43⋊C4C2311yescharacteristic
84C2×(C2×D43)⋊C4C2×C411yescharacteristic
85C2×(C2×D43)⋊C4C2×C411yescharacteristic
86C2×(C2×D43)⋊C4C2×C411yescharacteristic
87C2×(C2×D43)⋊C4C2311yescharacteristic
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2×C411yescharacteristic
93C2×C4×Dic43C2×C411yescharacteristic
94C2×C4×Dic43C2×C411yescharacteristic
95C2×C4×Dic43C2×C411yescharacteristic
96C2×C4×Dic43C2×C411yescharacteristic
97C2×C4×Dic43C2×C411yescharacteristic
98C2×C4×Dic43C2×C411yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100C42×D43—21no—
101C42×D43—21no—
102C42×D43—21no—
103C42×D43—21no—
104C42×D43D412yes—
105C42×D43D412yes—
106C42×D43D412yes—
107C42×D43D412yes—
108C4⋊(C43⋊C8)—22no—
109Dic43⋊C8—24no—
110C22⋊(C43⋊C8)C2314yes—
111(C2×D43)⋊C8—24no—
112#13063235—24no—
113C4×C43⋊C8—22no—
114C23×C4×C43C2×C411yescharacteristic
115#117×C43—22no—
116#117×C43—22no—
117C2×C4⋊C4×C43C2×C411yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43C2×C411yescharacteristic
120C2×C22⋊C4×C43C2311yescharacteristic
121C2×C42×C43C2×C411yescharacteristic
122C2×C42×C43C2311yescharacteristic
123C4⋊C8×C43—22no—
124C22⋊C8×C43C2314yes—
125C4×C8×C43—22no—
126C24×C43C22×C411yescharacteristic
127C23×D43C22×C411yescharacteristic
128C23×D43C22×C411yescharacteristic
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—22no—
132C22×C4×C43M1614yescomplemented
133C22×C4×C43C22×C411yescharacteristic
134C22×C4×C43C22×C411yescharacteristic
135C22×C4×C43C22×C411yescharacteristic
136C22×C4×C43C22×C411yescharacteristic
137C22×C4×C43C22×C411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C2×C22⋊D43—22no—
140C2×C22⋊D43—22no—
141C2×C22⋊D43—22no—
142C2×C22⋊D43—22no—
143C2×C22⋊D43—22no—
144C2×C22⋊D43—22no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43C22×C411yescharacteristic
152C22×Dic43C22×C411yescharacteristic
153C22×Dic43C22×C411yescharacteristic
154C22×Dic43C22×C411yescharacteristic
155C22×Dic43C22×C411yescharacteristic
156C22×Dic43C22×C411yescharacteristic
157#10621898—216no—
158#10621898—216no—
159C2×D172—22no—
160C2×D172—22no—
161C2×D172—22no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×C4×D43—42no—
174C2×C4×D43—42no—
175C2×C4×D43C22⋊C412yes—
176C2×C4×D43C22⋊C412yes—
177C2×C4×D43C22⋊C412yes—
178C2×C4×D43C22⋊C412yes—
179C2×C4×D43M1614yescomplemented
180C2×C4×D43C2×D412yes—
181C2×C4×D43C2×D412yes—
182C2×Dic86—22no—
183C2×Dic86—22no—
184C2×Dic86—22no—
185C2×C8×C43—24no—
186C4⋊C4×C43—22no—
187C4⋊C4×C43—22no—
188C22⋊C4×C43—22no—
189C22⋊C4×C43—22no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43C2×D412yes—
193C42×C43C2×D412yes—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C412yes—
217C4×Dic43C22⋊C412yes—
218C4×Dic43C2×D412yes—
219C4×Dic43C2×D412yes—
220C2×C43⋊C8—24no—
221#10621872—48no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43C2×M1612yes—
227C23×C43C23×C411yescharacteristic
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43C2×C22⋊C412yes—
237C22×D43C2×M1612yes—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—24no—
241C2×C4×C43—24no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43C2×C22⋊C412yes—
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×M1612yes—
252C2×C4×C43C2×M1612yes—
253C2×C4×C43C2×M1612yes—
254C2×C4×C43C22×D412yes—
255C22⋊D43—28no—
256C22⋊D43—28no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43C2×C22⋊C411yescharacteristic
272C2×Dic43C2×C22⋊C411yescharacteristic
273C2×Dic43C2×C22⋊C412yes—
274C2×Dic43C2×C22⋊C411yescharacteristic
275C2×Dic43C2×C22⋊C411yescharacteristic
276C2×Dic43C2×M1612yes—
277D172—28no—
278C4×D43—24no—
279C4×D43—24no—
280C4×D43—24no—
281C4×D43—24no—
282C4×D43—24no—
283C4×D43—24no—
284C4×D43—42no—
285C4×D43—42no—
286C4×D43—42no—
287C4×D43—42no—
288C4×D43—42no—
289C4×D43—42no—
290Dic86—28no—
291C8×C43—44no—
292C43⋊C8—44no—
293#17361—431nomaximal, Sylow
294C22×C43—21no—
295C22×C43—21no—
296C22×C43—22no—
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43C22×C22⋊C411yescharacteristic
302C22×C43C22×M1611yescharacteristic
303C22×C43C22×M1611yescharacteristic
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—22no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—42no—
311C2×D43—41no—
312C2×D43—41no—
313C2×D43—42no—
314C4×C43—22no—
315C4×C43—22no—
316C4×C43—22no—
317C4×C43—41no—
318C4×C43—41no—
319C4×C43#40712yes—
320C4×C43#40712yes—
321Dic43—22no—
322Dic43—22no—
323Dic43—21no—
324Dic43—21no—
325Dic43—41no—
326Dic43—41no—
327Dic43#41012yes—
328Dic43#41312yes—
329C2×C4×#41—431no—
330#2920—432no—
331#1467—432no—
332#1466—432no—
333#1465—432no—
334#1465—432no—
335#1458—432no—
336#1458—431no—
337#1458D4311yescharacteristic, complemented
338C2×C43—21no—
339C2×C43—21no—
340C2×C43—42no—
341C2×C43C2×#40711yescharacteristic
342C2×C43C2×#41011yescharacteristic
343C2×C43C2×#41311yescharacteristic
344D43—42no—
345D43—42no—
346C22×#41—431no—
347C4×#41—862no—
348C4×#41—862no—
349C4×#41—862no—
350C4×#41—862no—
351C2×C4×Q8—431no—
352C2×C4×Q8—431no—
353C2×C4×D4—431no—
354C2×C4×D4—431no—
355C2×C4×D4—431no—
356C2×C4×D4—431no—
357C2×C4×D4—431no—
358C2×C4×D4—431no—
359C2×#117—431no—
360C2×#117—431no—
361C2×#117C2×D4311yescharacteristic
362C22×C42—431no—
363C22×C42—431no—
364C22×C42—431no—
365#432—434no—
366#432—862no—
367#431—432no—
368#431—862no—
369#431C2×D4312yes—
370#423—862no—
371#407—434no—
372C4×M16—862no—
373#324—432no—
374#324—434no—
375#324C2×D4312yes—
376#323—432no—
377#323—434no—
378#323C2×D4312yes—
379C43#1736111yescharacteristic, complemented, Sylow
380C2×#41—862no—
381C2×#41—862no—
382C2×#41—864no—
383C2×#41—864no—
384C22×Q8—431no—
385C22×D4—431no—
386C22×D4—431no—
387C22×D4—431no—
388C23×C4—431no—
389C23×C4—431no—
390C23×C4—431no—
391C23×C4—431no—
392C23×C4—431no—
393C23×C4—431no—
394C23×C4—431no—
395C23×C4—431no—
396C23×C4C4×D4311yescharacteristic
397C2×M16—864no—
398C4×Q8—862no—
399C4×Q8—862no—
400C4×Q8—862no—
401C4×Q8—862no—
402C4×D4—862no—
403C4×D4—862no—
404C4×D4—862no—
405C4×D4—862no—
406C4×D4—862no—
407C4×D4—862no—
408C4×D4—862no—
409C4×D4—862no—
410C4×D4—862no—
411C4×D4—862no—
412C4×D4—862no—
413C4×D4—862no—
414#117—22no—
415#117—22no—
416#117—862no—
417#117—862no—
418#117—862no—
419#117—862no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4C4×D4311yescharacteristic
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C22⋊C4—431no—
427C2×C22⋊C4—431no—
428C2×C22⋊C4—431no—
429C2×C22⋊C4—431no—
430C2×C22⋊C4C4×D4311yescharacteristic
431C2×C22⋊C4C22×D4311yescharacteristic
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—432no—
436C2×C42—432no—
437C2×C42—432no—
438C2×C42—432no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—861no—
445C2×C42—861no—
446C2×C42—861no—
447C2×C42—861no—
448C2×C42—861no—
449C2×C42—861no—
450C2×C42—861no—
451C2×C42—861no—
452C2×C42C4×D4311yescharacteristic
453C2×C42C22×D4311yescharacteristic
454C4⋊C8—22no—
455C4⋊C8—864no—
456C4⋊C8—862no—
457C22⋊C8—434no—
458C22⋊C8—864no—
459C22⋊C8C22×D4314yes—
460#97—864no—
461C4×C8—22no—
462C4×C8—862no—
463C24—431no—
464C24—431no—
465C24C2×C4×D4311yescharacteristic
466#41—8616no—
467#41—8616no—
468C2×Q8—862no—
469C2×Q8—862no—
470C2×Q8—862no—
471C2×D4—862no—
472C2×D4—862no—
473C2×D4—862no—
474C2×D4—862no—
475C2×D4—862no—
476C2×D4—862no—
477C2×D4—862no—
478C2×D4—862no—
479C2×D4—862no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—432no—
488C22×C4—432no—
489C22×C4—432no—
490C22×C4—434no—
491C22×C4—432no—
492C22×C4—432no—
493C22×C4—432no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—862no—
507C22×C4—862no—
508C22×C4—862no—
509C22×C4—1722no—
510C22×C4—1722no—
511C22×C4—1722no—
512C22×C4—1722no—
513C22×C4—1722no—
514C22×C4—1722no—
515C22×C4#1062187214yescomplemented
516C22×C4C2×C4×D4311yescharacteristic
517C22×C4C2×C4×D4311yescharacteristic
518C22×C4C2×C4×D4311yescharacteristic
519C22×C4C2×C4×D4311yescharacteristic
520C22×C4C2×C4×D4311yescharacteristic
521C22×C4C23×D4311yescharacteristic
522M16—1728no—
523C2×C8—24no—
524C2×C8—864no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—862no—
528C4⋊C4—862no—
529C4⋊C4—862no—
530C4⋊C4—862no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C42—21no—
538C42—21no—
539C42—431no—
540C42—431no—
541C42—432no—
542C42—432no—
543C42—431no—
544C42—431no—
545C42—432no—
546C42—432no—
547C42—861no—
548C42—861no—
549C42—861no—
550C42—861no—
551C42—861no—
552C42—861no—
553C42—861no—
554C42—861no—
555C42—861no—
556C42—861no—
557C42D4×D4312yes—
558C42D4×D4312yes—
559C23—21no—
560C23—21no—
561C23—41no—
562C23—41no—
563C23—432no—
564C23—432no—
565C23—861no—
566C23—861no—
567C23—861no—
568C23—861no—
569C23—1721no—
570C23—1721no—
571C23—1721no—
572C23—1721no—
573C23C2×#1062187212yes—
574C23C22×C4×D4311yescharacteristic
575Q8—868no—
576D4—868no—
577D4—868no—
578D4—868no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—431no—
590C2×C4—431no—
591C2×C4—431no—
592C2×C4—431no—
593C2×C4—432no—
594C2×C4—432no—
595C2×C4—864no—
596C2×C4—864no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—864no—
604C2×C4—864no—
605C2×C4—864no—
606C2×C4—864no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4—1722no—
612C2×C4—1722no—
613C2×C4—1722no—
614C2×C4—1722no—
615C2×C4—1722no—
616C2×C4—1722no—
617C2×C4—1722no—
618C2×C4—1722no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4C22⋊C4×D4312yes—
622C2×C4C22⋊C4×D4311yescharacteristic
623C2×C4C22⋊C4×D4311yescharacteristic
624C2×C4M16×D4312yes—
625C2×C4C2×#1062187212yes—
626C2×C4C2×#1062187212yes—
627C2×C4C2×D4×D4312yes—
628C8—44no—
629C8—1724no—
630C22—21no—
631C22—21no—
632C22—22no—
633C22—42no—
634C22—42no—
635C22—41no—
636C22—41no—
637C22—862no—
638C22—862no—
639C22—862no—
640C22—862no—
641C22—1722no—
642C22—1722no—
643C22—1722no—
644C22—1722no—
645C22—1721no—
646C22—1721no—
647C22C2×C22⋊C4×D4311yescharacteristic
648C22C2×M16×D4311yescharacteristic
649C22C22×#1062187211yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—41no—
654C4—41no—
655C4—432no—
656C4—432no—
657C4—862no—
658C4—862no—
659C4—861no—
660C4—861no—
661C4—1721no—
662C4—1721no—
663C4#1458286112yes—
664C4#1458286112yes—
665C2—21no—
666C2—21no—
667C2—42no—
668C2—1722no—
669C2—1722no—
670C2C2×#1458286111yescharacteristic
671C2#410×D4311yescharacteristic
672C2#413×D4311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1458C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#10621898C4
cosocleC22×C4×C43C24
hypercenter#1458D43
hypocenterC43#17361
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #19143223C2semidirect
3. #19132937C2semidirect
4. #19132934C2semidirect
5. #19132932C2semidirect
6. #19132930C2semidirect
7. #19132909C2semidirect
8. #19132907C2semidirect
9. C43×#1458C2semidirect
132. C22×C4×C43M16semidirect
179. C2×C4×D43M16semidirect
337. #1458D43semidirect
379. C43#17361semidirect
515. C22×C4#10621872semidirect

Maximal subgroups

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

subgroupindex
C2×#145833672
#191432232
#191329372
#191329342
#191329322
#191329302
#191329092
#191329072
C43×#14582
#1736143