Finite Group Databasebeta

← #25063143

Subgroups — #25063143

Order 11008.

988 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic
3#431×D43C211yesmaximal, characteristic
4#19133017C211yesmaximal, characteristic, complemented
5#19133016C211yesmaximal, characteristic, complemented
6#19133015C211yesmaximal, characteristic, complemented
7#19132996C214yesmaximal, complemented
8#19132988C214yesmaximal, complemented
9C43×#1485C211yesmaximal, characteristic, complemented
10#14583456C2211yescharacteristic
11#14583455—21no—
12#14583454C411yescharacteristic
13#14583454C411yescharacteristic
14#14583453—21no—
15#14583453C2212yes—
16#14583452—21no—
17#14583451—21no—
18#14583451C412yes—
19C4⋊Q8×D43C411yescharacteristic
20C4⋊Q8×D43C411yescharacteristic
21#125×D43—21no—
22C22⋊Q8×D43—21no—
23C22⋊Q8×D43C412yes—
24C4×Q8×D43—21no—
25C4×Q8×D43C2212yes—
26#117×D43—21no—
27C2×C42×D43C2211yescharacteristic
28#14582954—21no—
29#14582954—21no—
30#14582952C2211yescharacteristic
31#14582951C2212yes—
32#14582950—21no—
33#14582950C2212yes—
34#14582950C2212yes—
35#14582949—21no—
36#14582922—21no—
37C4⋊C8×D43C2212yes—
38#14582862—21no—
39C22⋊C8×D43—21no—
40C4×#10621877C2211yescharacteristic
41C4×C8×D43—21no—
42#14582631C2214yescomplemented
43Q8⋊(C43⋊C8)C2214yescomplemented
44#14582629C2214yescomplemented
45C43×#533C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C4×M16×C43C2211yescharacteristic
48C43×Q8⋊C8C2214yescomplemented
49C2×Q8×D43—21no—
50C2×Q8×D43C2×C412yes—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C2×#10621877—21no—
55C2×C8×D43—22no—
56#13063325C2×C411yescharacteristic
57#13063325C2×C411yescharacteristic
58#13063324—21no—
59#13063324—21no—
60#13063324—21no—
61#13063324C2×C412yes—
62#13063323—21no—
63#13063323C2×C412yes—
64#13063317—21no—
65#13063316—21no—
66#13063316—21no—
67#13063315—22no—
68#13063315—22no—
69#13063305—21no—
70#13063305C2×C412yes—
71#13063304—21no—
72#13063304C2×C412yes—
73#13063303—22no—
74#13063303—22no—
75#13063302—22no—
76#13063302—22no—
77#13063301—21no—
78#13063301C2×C412yes—
79Q8×Dic43—21no—
80Q8×Dic43C2×C412yes—
81C4×Dic86—21no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84C4×Dic86C2312yes—
85#13063290—21no—
86#13063290—22no—
87#13063290—22no—
88#13063290C2×C412yes—
89#13063284—21no—
90#13063283—21no—
91#13063283—21no—
92#13063282—22no—
93#13063281—22no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—22no—
98C4⋊C4×D43—22no—
99C4⋊C4×D43C2×C412yes—
100C22⋊C4×D43—22no—
101C2×C4×Dic43C2×C411yescharacteristic
102C2×C4×Dic43D411yescharacteristic
103C2×C4×Dic43D411yescharacteristic
104C42×D43—22no—
105C42×D43C2×C411yescharacteristic
106C42×D43C2×C411yescharacteristic
107C42×D43D411yescharacteristic
108C42×D43D411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43C2311yescharacteristic
112C42×D43C2311yescharacteristic
113C4⋊(C43⋊C8)C2312yes—
114Dic43⋊C8—22no—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121#13063236—21no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8C2312yes—
124C8×Dic43—22no—
125C2×M16×C43—21no—
126C4⋊Q8×C43C2×C411yescharacteristic
127C4⋊Q8×C43C2×C411yescharacteristic
128#125×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43C2×C412yes—
131C4×Q8×C43—21no—
132C4×Q8×C43C2312yes—
133#117×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43C2312yes—
136C22⋊C8×C43—21no—
137#97×C43—21no—
138C4×C8×C43—21no—
139C4×C8×C43C2312yes—
140C23×D43C22⋊C411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43C22×C412yes—
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×Dic43C22⋊C411yescharacteristic
147C22×Dic43C22⋊C411yescharacteristic
148C22×Dic43C22⋊C411yescharacteristic
149Q8×D43—28no—
150Q8×D43—44no—
151C2×C4×D43—24no—
152C2×C4×D43—24no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—42no—
156C2×C4×D43C22⋊C411yescharacteristic
157C2×C4×D43C22⋊C411yescharacteristic
158C2×C4×D43C22⋊C411yescharacteristic
159C2×C4×D43C22⋊C411yescharacteristic
160C2×C4×D43C22⋊C411yescharacteristic
161C2×C4×D43C22⋊C411yescharacteristic
162C2×C4×D43C22×C411yescharacteristic
163C2×C4×D43C22×C411yescharacteristic
164C2×C4×D43C2×D411yescharacteristic
165C2×C4×D43C2×D411yescharacteristic
166C2×C4×D43C2×D411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×Dic86—21no—
169C2×Dic86—22no—
170C2×Dic86—22no—
171C2×Dic86C22×C412yes—
172M16×C43—42no—
173C2×C8×C43—22no—
174C2×C8×C43—22no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43C22×C412yes—
181C22⋊C4×C43—22no—
182C42×C43—22no—
183C42×C43C22×C411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43C2411yescharacteristic
187C22⋊Dic43—22no—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—22no—
194C4⋊Dic43—22no—
195C4⋊Dic43C22×C412yes—
196Dic43⋊C4—22no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204C4×Dic43—22no—
205C4×Dic43—22no—
206C4×Dic43—22no—
207C4×Dic43C22⋊C411yescharacteristic
208C4×Dic43C22⋊C411yescharacteristic
209C4×Dic43C22⋊C411yescharacteristic
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22×C411yescharacteristic
214C4×Dic43C22×C411yescharacteristic
215C4×Dic43C2×D411yescharacteristic
216C4×Dic43C2×D411yescharacteristic
217C4×Dic43C2×D411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219#10621877—42no—
220C2×C43⋊C8—22no—
221C2×C43⋊C8—22no—
222C8×D43—44no—
223C23×C43C2×C22⋊C411yescharacteristic
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—41no—
227C22×D43C2×C22⋊C411yescharacteristic
228C22×D43C2×C22⋊C411yescharacteristic
229Q8×C43—24no—
230Q8×C43—42no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43C2×C22⋊C411yescharacteristic
237C2×C4×C43C2×C22⋊C411yescharacteristic
238C2×C4×C43C2×C22⋊C411yescharacteristic
239C2×C4×C43C23×C411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—41no—
247C2×Dic43C2×C22⋊C411yescharacteristic
248C2×Dic43C2×C22⋊C411yescharacteristic
249C2×Dic43C2×C22⋊C411yescharacteristic
250C2×Dic43C2×C22⋊C411yescharacteristic
251C2×Dic43C2×C22⋊C411yescharacteristic
252C2×Dic43C2×C22⋊C411yescharacteristic
253C4×D43—22no—
254C4×D43—22no—
255C4×D43—22no—
256C4×D43—22no—
257C4×D43—22no—
258C4×D43—22no—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—41no—
262C4×D43—41no—
263C4×D43—44no—
264C4×D43—44no—
265C4×D43#13114yes—
266C4×D43#13714yes—
267Dic86—24no—
268Dic86—44no—
269Dic86—42no—
270Dic86—44no—
271C8×C43—42no—
272C8×C43—42no—
273C43⋊C8—42no—
274C43⋊C8—42no—
275#17464—431nomaximal, Sylow
276C22×C43—21no—
277C22×C43—21no—
278C22×C43—21no—
279C22×C43C22×C22⋊C411yescharacteristic
280C2×D43—21no—
281C2×D43—21no—
282C2×D43—21no—
283C2×D43—21no—
284C2×D43—44no—
285C2×D43#40812yes—
286C2×D43#41912yes—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—42no—
291C4×C43—42no—
292C4×C43#42112yes—
293C4×C43C2×#13112yes—
294C4×C43C2×#13712yes—
295Dic43—21no—
296Dic43—21no—
297Dic43—21no—
298Dic43—21no—
299Dic43—42no—
300Dic43—42no—
301Dic43#40812yes—
302Dic43#41912yes—
303C2×#533—431no—
304#2920—431no—
305C2×#431—431no—
306#1485—431no—
307#1485—431no—
308#1485—431no—
309#1485D4311yescharacteristic, complemented
310#1481—434no—
311#1479—434no—
312C2×C43—41no—
313C2×C43C2×#40811yescharacteristic
314C2×C43C2×#41911yescharacteristic
315C2×C43C2×#42111yescharacteristic
316D43—22no—
317D43—22no—
318#533—431no—
319#533—431no—
320#533—432no—
321#533—432no—
322#533—431no—
323#533—861no—
324#533—861no—
325#533—861no—
326#533—861no—
327#533C2×D4311yescharacteristic
328C2×C4⋊Q8—431no—
329C2×C4⋊Q8—431no—
330C2×#125—861no—
331C2×C22⋊Q8—432no—
332C2×C22⋊Q8—861no—
333C2×C4×Q8—432no—
334C2×C4×Q8—861no—
335C2×#117—861no—
336C22×C42—431no—
337#432—861no—
338#432—861no—
339#431—432no—
340#431—432no—
341#431—431no—
342#431—432no—
343#431—861no—
344#431—861no—
345#431C2×D4311yescharacteristic
346#423—861no—
347C2×C4⋊C8—432no—
348#407—861no—
349C2×C22⋊C8—861no—
350C4×M16—431no—
351C4×M16C2×D4311yescharacteristic
352C2×C4×C8—861no—
353Q8⋊C8—434no—
354Q8⋊C8—434no—
355Q8⋊C8—434no—
356Q8⋊C8C2×D4314yescomplemented
357C43#1746411yescharacteristic, complemented, Sylow
358C22×Q8—432no—
359C22×Q8—861no—
360C23×C4—431no—
361C23×C4—431no—
362C23×C4—431no—
363C2×M16—21no—
364C2×M16—861no—
365C22×C8—862no—
366C4⋊Q8—432no—
367C4⋊Q8—432no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8—861no—
371C4⋊Q8—861no—
372C4⋊Q8—861no—
373C4⋊Q8—861no—
374C4⋊Q8C4×D4311yescharacteristic
375C4⋊Q8C4×D4311yescharacteristic
376#125—21no—
377#125—862no—
378#125—862no—
379#125—861no—
380#125—861no—
381#125—861no—
382C22⋊Q8—21no—
383C22⋊Q8—432no—
384C22⋊Q8—432no—
385C22⋊Q8—432no—
386C22⋊Q8—862no—
387C22⋊Q8—862no—
388C22⋊Q8—862no—
389C22⋊Q8—862no—
390C22⋊Q8—861no—
391C22⋊Q8—861no—
392C22⋊Q8—861no—
393C22⋊Q8C4×D4312yes—
394C4×Q8—21no—
395C4×Q8—432no—
396C4×Q8—432no—
397C4×Q8—432no—
398C4×Q8—862no—
399C4×Q8—862no—
400C4×Q8—862no—
401C4×Q8—861no—
402C4×Q8—862no—
403C4×Q8—861no—
404C4×Q8—861no—
405C4×Q8C22×D4312yes—
406#117—21no—
407#117—862no—
408#117—862no—
409#117—861no—
410#117—861no—
411#117—861no—
412C2×C4⋊C4—432no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—862no—
416C2×C4⋊C4—862no—
417C2×C4⋊C4—861no—
418C2×C22⋊C4—862no—
419C2×C42—431no—
420C2×C42—431no—
421C2×C42—431no—
422C2×C42—431no—
423C2×C42—431no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—862no—
431C2×C42C22×D4311yescharacteristic
432C4⋊C8—432no—
433C4⋊C8—862no—
434C4⋊C8—862no—
435C4⋊C8—862no—
436C4⋊C8C22×D4312yes—
437C22⋊C8—21no—
438C22⋊C8—862no—
439C22⋊C8—862no—
440C22⋊C8—862no—
441C22⋊C8—861no—
442#97—21no—
443#97—861no—
444C4×C8—21no—
445C4×C8—432no—
446C4×C8—862no—
447C4×C8—861no—
448C4×C8C22×D4312yes—
449C24—431no—
450C2×Q8—21no—
451C2×Q8—432no—
452C2×Q8—862no—
453C2×Q8—862no—
454C2×Q8—868no—
455C2×Q8—861no—
456C2×Q8—1724no—
457C2×Q8C2×C4×D4312yes—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—864no—
474C22×C4—864no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—1722no—
478C22×C4C2×C4×D4311yescharacteristic
479C22×C4D4×D4311yescharacteristic
480C22×C4D4×D4311yescharacteristic
481M16—42no—
482M16—1722no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—862no—
486C2×C8—862no—
487C2×C8—1724no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—432no—
494C4⋊C4—862no—
495C4⋊C4—862no—
496C4⋊C4—862no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—862no—
505C4⋊C4—861no—
506C4⋊C4—862no—
507C4⋊C4C2×C4×D4312yes—
508C22⋊C4—22no—
509C22⋊C4—862no—
510C22⋊C4—862no—
511C22⋊C4—862no—
512C42—22no—
513C42—431no—
514C42—431no—
515C42—431no—
516C42—431no—
517C42—431no—
518C42—431no—
519C42—431no—
520C42—431no—
521C42—431no—
522C42—431no—
523C42—431no—
524C42—431no—
525C42—862no—
526C42—862no—
527C42—862no—
528C42C2×C4×D4311yescharacteristic
529C42D4×D4311yescharacteristic
530C42D4×D4311yescharacteristic
531C42C23×D4311yescharacteristic
532C23—431no—
533C23—431no—
534C23—862no—
535C23—862no—
536C23—1721no—
537C23C22⋊C4×D4311yescharacteristic
538Q8—24no—
539Q8—42no—
540Q8—864no—
541Q8—1724no—
542Q8—1724no—
543Q8—1722no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—431no—
550C2×C4—431no—
551C2×C4—434no—
552C2×C4—434no—
553C2×C4—431no—
554C2×C4—431no—
555C2×C4—431no—
556C2×C4—431no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1724no—
572C2×C4—1724no—
573C2×C4—1721no—
574C2×C4C22⋊C4×D4311yescharacteristic
575C2×C4C22⋊C4×D4311yescharacteristic
576C2×C4C22⋊C4×D4311yescharacteristic
577C2×C4C22×C4×D4311yescharacteristic
578C2×C4C2×D4×D4311yescharacteristic
579C2×C4C2×D4×D4311yescharacteristic
580C8—42no—
581C8—42no—
582C8—1722no—
583C8—1722no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—432no—
588C22—432no—
589C22—861no—
590C22—861no—
591C22—861no—
592C22—861no—
593C22—1724no—
594C22C2×C22⋊C4×D4311yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—42no—
599C4—42no—
600C4—432no—
601C4—432no—
602C4—861no—
603C4—861no—
604C4—861no—
605C4—861no—
606C4—1722no—
607C4—1722no—
608C4#1458291412yes—
609C4#131×D4312yes—
610C4#137×D4312yes—
611C2—41no—
612C2—862no—
613C2—862no—
614C2#408×D4311yescharacteristic
615C2#419×D4311yescharacteristic
616C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1485C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC42×C43C24
hypercenter#1485D43
hypocenterC43#17464
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
4. #19133017C2semidirect
5. #19133016C2semidirect
6. #19133015C2semidirect
7. #19132996C2semidirect
8. #19132988C2semidirect
9. C43×#1485C2semidirect
42. #14582631C22semidirect
43. Q8⋊(C43⋊C8)C22semidirect
44. #14582629C22semidirect
48. C43×Q8⋊C8C22semidirect
309. #1485D43semidirect
356. Q8⋊C8C2×D43semidirect
357. C43#17464semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#191432262
#431×D432
#191330172
#191330162
#191330152
#191329962
#191329882
C43×#14852
#1746443