Finite Group Databasebeta

← #25101970

Subgroups — #25101970

Order 11008.

1100 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583451C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic
3C2×M16×Dic43C211yesmaximal, characteristic
4#19135582C212yesmaximal, complemented
5#19135437C212yesmaximal, complemented
6#19135064C211yesmaximal, characteristic
7#19135063C211yesmaximal, characteristic
8#19135061C211yesmaximal, characteristic
9#101×Dic43C212yesmaximal, complemented
10#19134390C212yesmaximal, complemented
11C43×#1901C211yesmaximal, characteristic
12C22×#10621877C2211yescharacteristic
13#14583451—21no—
14#14583451—21no—
15#14583451—21no—
16#14583451—21no—
17#14583451—21no—
18#14583451—21no—
19#14583451—21no—
20#14583451—21no—
21C2×#13063324C2211yescharacteristic
22C2×#13063323C2211yescharacteristic
23C2×#13063315C412yes—
24C2×#13063304C2211yescharacteristic
25C2×#13063302C412yes—
26C2×Q8×Dic43C2211yescharacteristic
27C2×#13063290C412yes—
28C2×#13063290C2211yescharacteristic
29C2×#13063281C412yes—
30C22×C4×Dic43C2211yescharacteristic
31#14582953—21no—
32#14582953—21no—
33#14582949—21no—
34#14582949—21no—
35#14582922C2212yes—
36C2×#13063244C2212yes—
37C2×#13063243C2212yes—
38C2×#13063243C2212yes—
39#14582863C2211yescharacteristic
40M16×Dic43—21no—
41M16×Dic43—21no—
42M16×Dic43C2212yes—
43M16×Dic43C2212yes—
44M16×Dic43C2212yes—
45C2×#13063235—21no—
46C2×C8×Dic43—21no—
47#14582668C2212yes—
48#14582667C2212yes—
49#14582667C2212yes—
50C22×M16×C43C2211yescharacteristic
51C2×C22⋊Q8×C43C2211yescharacteristic
52C2×#101×C43C2212yes—
53C43×#407C2211yescharacteristic
54C43×#343C2212yes—
55C22×Dic86C2×C412yes—
56C22×Dic86C2311yescharacteristic
57C23×Dic43C2×C411yescharacteristic
58C23×Dic43C2×C411yescharacteristic
59C2×#10621877—21no—
60C2×#10621877—24no—
61C2×#10621877C2312yes—
62C2×#10621877C2312yes—
63C22×C43⋊C8—21no—
64#13063324—21no—
65#13063324—21no—
66#13063324—21no—
67#13063324—21no—
68#13063323—21no—
69#13063323—21no—
70#13063323—21no—
71#13063323—21no—
72#13063315—22no—
73#13063315—22no—
74#13063315—22no—
75#13063315—22no—
76#13063304—21no—
77#13063304—21no—
78#13063304—21no—
79#13063304—21no—
80#13063302—22no—
81#13063302—22no—
82#13063302—22no—
83#13063302—22no—
84Q8×Dic43—21no—
85Q8×Dic43—21no—
86Q8×Dic43—21no—
87Q8×Dic43—21no—
88#13063290—22no—
89#13063290—22no—
90#13063290—22no—
91#13063290—22no—
92#13063290—21no—
93#13063290—21no—
94#13063290—21no—
95#13063290—21no—
96#13063281—22no—
97#13063281—22no—
98#13063281—22no—
99#13063281—22no—
100C2×C4⋊Dic43C2×C412yes—
101C2×C4⋊Dic43C2311yescharacteristic
102C2×Dic43⋊C4C2×C412yes—
103C2×Dic43⋊C4C2×C412yes—
104C2×Dic43⋊C4C2×C412yes—
105C2×Dic43⋊C4C2×C412yes—
106C2×Dic43⋊C4C2×C412yes—
107C2×C22⋊Dic43C2×C412yes—
108C2×C4×Dic43C2×C412yes—
109C2×C4×Dic43C2×C412yes—
110C2×C4×Dic43C2×C411yescharacteristic
111C2×C4×Dic43C2×C411yescharacteristic
112C2×C4×Dic43D411yescharacteristic
113C2×C4×Dic43D411yescharacteristic
114C2×C4×Dic43D411yescharacteristic
115C2×C4×Dic43D411yescharacteristic
116C2×C4×Dic43D411yescharacteristic
117C2×C4×Dic43D411yescharacteristic
118C2×C4×Dic43D411yescharacteristic
119C2×C4×Dic43D411yescharacteristic
120C2×C4×Dic43C2311yescharacteristic
121C2×C4×Dic43C2311yescharacteristic
122Dic43⋊C8—22no—
123Dic43⋊C8—22no—
124#13063244—24no—
125#13063243—24no—
126#13063243—24no—
127C22⋊(C43⋊C8)—21no—
128C22⋊(C43⋊C8)—21no—
129#13063235—22no—
130#13063235—22no—
131#13063235—22no—
132C8×Dic43—22no—
133C8×Dic43—22no—
134C8×Dic43—22no—
135C22×Q8×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C2×M16×C43—21no—
138C2×M16×C43—24no—
139C2×M16×C43C2312yes—
140C2×M16×C43C2312yes—
141C22×C8×C43—21no—
142C22⋊Q8×C43—21no—
143C22⋊Q8×C43—21no—
144C22⋊Q8×C43—21no—
145C22⋊Q8×C43—21no—
146C2×C4⋊C4×C43C2×C412yes—
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43C2×C412yes—
149#101×C43—24no—
150C22⋊C8×C43—21no—
151C22⋊C8×C43—21no—
152C24×C43C22×C411yescharacteristic
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—22no—
156C2×Q8×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43C22×C412yes—
160C22×C4×C43C22×C411yescharacteristic
161C22×C4×C43C22×C412yes—
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2411yescharacteristic
167C22×Dic43—24no—
168C22×Dic43—42no—
169C22×Dic43C22⋊C411yescharacteristic
170C22×Dic43C22⋊C411yescharacteristic
171C22×Dic43C22⋊C411yescharacteristic
172C22×Dic43C22⋊C411yescharacteristic
173C22×Dic43C22⋊C411yescharacteristic
174C22×Dic43C22⋊C411yescharacteristic
175C22×Dic43C22⋊C411yescharacteristic
176C22×Dic43C22⋊C411yescharacteristic
177C22×Dic43C22×C412yes—
178C22×Dic43C22×C411yescharacteristic
179C22×Dic43C22×C411yescharacteristic
180C22×Dic43C22×C411yescharacteristic
181C22×Dic43C22×C412yes—
182C22×Dic43C22×C411yescharacteristic
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—22no—
186C2×Dic86—22no—
187C2×Dic86—22no—
188C2×Dic86—22no—
189C2×Dic86—44no—
190M16×C43—24no—
191M16×C43—22no—
192M16×C43—22no—
193M16×C43—22no—
194M16×C43#4114yes—
195C2×C8×C43—24no—
196C2×C8×C43—22no—
197C2×C8×C43—22no—
198C4⋊C4×C43—22no—
199C4⋊C4×C43—22no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C22⋊C4×C43—22no—
203C22⋊C4×C43—22no—
204C22⋊Dic43—22no—
205C22⋊Dic43—22no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—22no—
209C4⋊Dic43—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218Dic43⋊C4—22no—
219Dic43⋊C4—22no—
220C4×Dic43—22no—
221C4×Dic43—22no—
222C4×Dic43—22no—
223C4×Dic43—22no—
224C4×Dic43C22⋊C411yescharacteristic
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22⋊C411yescharacteristic
229C4×Dic43C22⋊C411yescharacteristic
230C4×Dic43C22⋊C411yescharacteristic
231C4×Dic43C22⋊C411yescharacteristic
232C4×Dic43C2×D411yescharacteristic
233C4×Dic43C2×D411yescharacteristic
234C4×Dic43C2×D411yescharacteristic
235C4×Dic43C2×D411yescharacteristic
236C4×Dic43C2×D411yescharacteristic
237C4×Dic43C2×D411yescharacteristic
238C4×Dic43C2×D411yescharacteristic
239C4×Dic43C2×D411yescharacteristic
240#10621877—24no—
241#10621877—22no—
242#10621877—22no—
243#10621877—22no—
244#10621877#4114yes—
245C2×C43⋊C8—24no—
246C2×C43⋊C8—22no—
247C2×C43⋊C8—22no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—41no—
251C23×C43C2×C22⋊C411yescharacteristic
252C23×C43C2×C22⋊C411yescharacteristic
253C23×C43C23×C411yescharacteristic
254Q8×C43—41no—
255Q8×C43—41no—
256Q8×C43—42no—
257C2×C4×C43—22no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—24no—
267C2×C4×C43—42no—
268C2×C4×C43C2×C22⋊C411yescharacteristic
269C2×C4×C43C2×C22⋊C411yescharacteristic
270C2×C4×C43C22×D411yescharacteristic
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C2×#4112yes—
273C2×C4×C43C2×#4112yes—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—22no—
277C2×Dic43—22no—
278C2×Dic43—22no—
279C2×Dic43—22no—
280C2×Dic43—22no—
281C2×Dic43—22no—
282C2×Dic43—22no—
283C2×Dic43—22no—
284C2×Dic43—24no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—42no—
289C2×Dic43#10114yescomplemented
290C2×Dic43C2×C22⋊C411yescharacteristic
291C2×Dic43C2×C22⋊C411yescharacteristic
292C2×Dic43C2×C22⋊C411yescharacteristic
293C2×Dic43C2×C22⋊C411yescharacteristic
294C2×Dic43C2×C22⋊C411yescharacteristic
295C2×Dic43C2×C22⋊C411yescharacteristic
296C2×Dic43C2×C22⋊C411yescharacteristic
297C2×Dic43C2×C22⋊C411yescharacteristic
298Dic86—44no—
299Dic86—41no—
300Dic86—41no—
301Dic86—42no—
302Dic86—44no—
303C8×C43—24no—
304C8×C43—42no—
305C43⋊C8—24no—
306C43⋊C8—42no—
307#21425—431nomaximal, Sylow
308C22×C43—21no—
309C22×C43—21no—
310C22×C43—21no—
311C22×C43—21no—
312C22×C43—21no—
313C22×C43—21no—
314C22×C43—21no—
315C22×C43—44no—
316C22×C43C2×#10112yes—
317C22×C43C22×C22⋊C411yescharacteristic
318C22×C43C4×#4112yes—
319C4×C43—21no—
320C4×C43—21no—
321C4×C43—42no—
322C4×C43—42no—
323C4×C43#52511yescharacteristic
324C4×C43#52511yescharacteristic
325C4×C43#53212yes—
326Dic43—21no—
327Dic43—21no—
328Dic43—21no—
329Dic43—21no—
330Dic43—21no—
331Dic43—42no—
332Dic43—42no—
333Dic43C2×#10112yes—
334Dic43C2×#10112yes—
335Dic43#41312yes—
336C2×#533—431no—
337#2920—431no—
338C2×C4×M16—431no—
339#1997—432no—
340#1966—432no—
341#1901—431no—
342#1901—431no—
343#1901—431no—
344#1901D4311yescharacteristic
345C4×#101—432no—
346C4×#101—432no—
347C2×C43—22no—
348C2×C43—22no—
349C2×C43—41no—
350C2×C43#229711yescharacteristic
351C2×C43C22×#10111yescharacteristic
352C2×C43C2×#41311yescharacteristic
353C22×M16—431no—
354C22×M16C2×D4311yescharacteristic
355#533—861no—
356#533—861no—
357#533—861no—
358#533—861no—
359#533—861no—
360#533—861no—
361#533—861no—
362#533—861no—
363C2×C4⋊Q8—431no—
364C2×C4⋊Q8—431no—
365C2×#125—432no—
366C2×C22⋊Q8—431no—
367C2×C22⋊Q8—432no—
368C2×C22⋊Q8C2×D4311yescharacteristic
369C2×C4×Q8—431no—
370C2×C4×Q8—431no—
371C2×C4×Q8—432no—
372C2×#117—432no—
373C22×C42—431no—
374#432—861no—
375#432—861no—
376#431—861no—
377#431—861no—
378#423—432no—
379C2×#101—432no—
380C2×#101—432no—
381C2×#101—432no—
382C2×#101C2×D4312yes—
383#407—431no—
384#407C2×D4311yescharacteristic
385C4×M16—432no—
386C4×M16—432no—
387C4×M16—432no—
388C4×M16—861no—
389C4×M16—861no—
390C2×#97—861no—
391C2×C4×C8—861no—
392#343—432no—
393#343—432no—
394#343—432no—
395#343C2×D4312yes—
396C43#2142511yescharacteristic, complemented, Sylow
397C22×Q8—432no—
398C22×Q8—431no—
399C22×Q8C22×D4311yescharacteristic
400C23×C4—431no—
401C23×C4—431no—
402C23×C4C22×D4311yescharacteristic
403C2×M16—21no—
404C2×M16—24no—
405C2×M16—432no—
406C2×M16—432no—
407C2×M16—864no—
408C2×M16—861no—
409C2×M16C22×D4312yes—
410C2×M16C22×D4312yes—
411C22×C8—21no—
412C22×C8—861no—
413C4⋊Q8—861no—
414C4⋊Q8—861no—
415C4⋊Q8—861no—
416C4⋊Q8—861no—
417C4⋊Q8—861no—
418C4⋊Q8—861no—
419C4⋊Q8—861no—
420C4⋊Q8—861no—
421#125—862no—
422#125—862no—
423#125—862no—
424#125—862no—
425C22⋊Q8—21no—
426C22⋊Q8—21no—
427C22⋊Q8—21no—
428C22⋊Q8—21no—
429C22⋊Q8—862no—
430C22⋊Q8—862no—
431C22⋊Q8—862no—
432C22⋊Q8—862no—
433C22⋊Q8—861no—
434C22⋊Q8—861no—
435C22⋊Q8—861no—
436C22⋊Q8—861no—
437C4×Q8—862no—
438C4×Q8—862no—
439C4×Q8—862no—
440C4×Q8—862no—
441C4×Q8—861no—
442C4×Q8—861no—
443C4×Q8—861no—
444C4×Q8—861no—
445C4×Q8—861no—
446C4×Q8—861no—
447C4×Q8—861no—
448C4×Q8—861no—
449#117—862no—
450#117—862no—
451#117—862no—
452#117—862no—
453C2×C4⋊C4—432no—
454C2×C4⋊C4—432no—
455C2×C4⋊C4—432no—
456C2×C4⋊C4—432no—
457C2×C4⋊C4—432no—
458C2×C4⋊C4—432no—
459C2×C4⋊C4—431no—
460C2×C4⋊C4C4×D4312yes—
461C2×C4⋊C4C22×D4311yescharacteristic
462C2×C22⋊C4—432no—
463C2×C22⋊C4C4×D4312yes—
464C2×C42—431no—
465C2×C42—431no—
466C2×C42—431no—
467C2×C42—431no—
468C2×C42—431no—
469C2×C42—431no—
470C2×C42—431no—
471C2×C42—431no—
472C2×C42—431no—
473C2×C42—431no—
474C2×C42—431no—
475C2×C42—431no—
476C2×C42—432no—
477C2×C42—432no—
478C4⋊C8—862no—
479C4⋊C8—862no—
480#101—24no—
481#101—864no—
482#101—864no—
483#101—864no—
484C22⋊C8—21no—
485C22⋊C8—21no—
486C22⋊C8—861no—
487C22⋊C8—861no—
488#97—862no—
489#97—862no—
490#97—862no—
491C4×C8—862no—
492C4×C8—862no—
493C4×C8—862no—
494C24C2×C4×D4311yescharacteristic
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—862no—
500C2×Q8—862no—
501C2×Q8—861no—
502C2×Q8—861no—
503C2×Q8—862no—
504C2×Q8—862no—
505C2×Q8—1724no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—431no—
519C22×C4—431no—
520C22×C4—432no—
521C22×C4—432no—
522C22×C4—864no—
523C22×C4—1722no—
524C22×C4C2×C4×D4312yes—
525C22×C4C2×C4×D4311yescharacteristic
526C22×C4C2×C4×D4312yes—
527C22×C4D4×D4311yescharacteristic
528C22×C4D4×D4311yescharacteristic
529C22×C4D4×D4311yescharacteristic
530C22×C4D4×D4311yescharacteristic
531C22×C4C23×D4311yescharacteristic
532M16—24no—
533M16—22no—
534M16—22no—
535M16—22no—
536M16—434no—
537M16—864no—
538M16—862no—
539M16—862no—
540M16—862no—
541M16#1062190014yes—
542C2×C8—24no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—864no—
546C2×C8—862no—
547C2×C8—862no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—862no—
553C4⋊C4—862no—
554C4⋊C4—862no—
555C4⋊C4—862no—
556C4⋊C4—862no—
557C4⋊C4—862no—
558C4⋊C4—862no—
559C4⋊C4—862no—
560C4⋊C4—862no—
561C4⋊C4—862no—
562C4⋊C4—862no—
563C4⋊C4—862no—
564C4⋊C4—861no—
565C4⋊C4—861no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—862no—
569C22⋊C4—862no—
570C42—431no—
571C42—431no—
572C42—431no—
573C42—431no—
574C42—431no—
575C42—431no—
576C42—431no—
577C42—431no—
578C42—431no—
579C42—431no—
580C42—431no—
581C42—431no—
582C42—431no—
583C42—431no—
584C42—431no—
585C42—431no—
586C42—862no—
587C42—862no—
588C42—862no—
589C42—862no—
590C23—22no—
591C23—22no—
592C23—41no—
593C23C22⋊C4×D4311yescharacteristic
594C23C22⋊C4×D4311yescharacteristic
595C23C22×C4×D4311yescharacteristic
596Q8—41no—
597Q8—41no—
598Q8—42no—
599Q8—1724no—
600Q8—1724no—
601Q8—1721no—
602Q8—1721no—
603Q8—1722no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—42no—
615C2×C4—431no—
616C2×C4—431no—
617C2×C4—431no—
618C2×C4—434no—
619C2×C4—431no—
620C2×C4—431no—
621C2×C4—431no—
622C2×C4—431no—
623C2×C4—431no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—862no—
627C2×C4—862no—
628C2×C4—862no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—862no—
632C2×C4—862no—
633C2×C4—862no—
634C2×C4—864no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1722no—
639C2×C4C22⋊C4×D4311yescharacteristic
640C2×C4C22⋊C4×D4311yescharacteristic
641C2×C4C2×D4×D4311yescharacteristic
642C2×C4C2×D4×D4311yescharacteristic
643C2×C4#41×D4312yes—
644C2×C4C2×#1062190012yes—
645C8—24no—
646C8—42no—
647C8—864no—
648C8—1722no—
649C22—21no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—44no—
657C22#101×D4312yes—
658C22C2×C22⋊C4×D4311yescharacteristic
659C22C4×#1062190012yes—
660C4—21no—
661C4—21no—
662C4—42no—
663C4—42no—
664C4—432no—
665C4—432no—
666C4—432no—
667C4—861no—
668C4—861no—
669C4—861no—
670C4—861no—
671C4—861no—
672C4—1722no—
673C4—1722no—
674C4#1458340511yescharacteristic
675C4#1458340711yescharacteristic
676C4#1458344412yes—
677C2—22no—
678C2—22no—
679C2—41no—
680C2#1913708011yescharacteristic
681C2C2×#101×D4311yescharacteristic
682C2#413×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1901C2
socleC22×C43C22×C22⋊C4
prime radicalC24×C43C22×C4
cosocleC22×C4×C43C24
hypercenter#1901D43
hypocenterC43#21425
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1901

Complements

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

NH ≅ G/Ntype
4. #19135582C2semidirect
5. #19135437C2semidirect
9. #101×Dic43C2semidirect
10. #19134390C2semidirect
289. C2×Dic43#101semidirect
396. C43#21425semidirect

Maximal subgroups

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

subgroupindex
C2×#145834512
#191432242
C2×M16×Dic432
#191355822
#191354372
#191350642
#191350632
#191350612
#101×Dic432
#191343902
C43×#19012
#2142543