Finite Group Databasebeta

← #25063802

Subgroups — #25063802

Order 11008.

1102 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148644C211yesmaximal, characteristic
2#19143630C211yesmaximal, characteristic, complemented
3#19133118C211yesmaximal, characteristic, complemented
4#19133114C212yesmaximal, complemented
5#19133106C211yesmaximal, characteristic, complemented
6#19133097C212yesmaximal, complemented
7#19133093C211yesmaximal, characteristic, complemented
8#19133084C212yesmaximal, complemented
9#19133079C211yesmaximal, characteristic, complemented
10C2×#14582635C212yesmaximal, complemented
11C43×#2275C211yesmaximal, characteristic, complemented
12#14583619C411yescharacteristic, complemented
13#14583604—21no—
14#14583589C412yescomplemented
15#14583575—22no—
16D4×Dic86C411yescharacteristic, complemented
17#14583558C412yescomplemented
18#14583554C411yescharacteristic, complemented
19#14583553C411yescharacteristic, complemented
20#14583543—21no—
21#14583514—21no—
22#14583491—22no—
23#14583456C2211yescharacteristic
24#14583433C2211yescharacteristic
25#14583410C2212yes—
26C2×#13063304C2212yes—
27#14583378—21no—
28#14582977—21no—
29#14582971—22no—
30D4×C43⋊C8—21no—
31#14582956C2211yescharacteristic
32#14582952C2211yescharacteristic
33#14582863C2212yes—
34C2×C22⋊(C43⋊C8)C2212yes—
35#14582635C2211yescharacteristic
36#14582635C2212yes—
37#14582635C2212yes—
38#14582635C2212yes—
39#14582635C2211yescharacteristic
40#14582635C2212yes—
41#14582635C2212yes—
42#14582632C2211yescharacteristic
43#14582632C2211yescharacteristic
44#14582632C2212yes—
45C2×C4×D4×C43—21no—
46C2×C4×D4×C43C2211yescharacteristic
47C4×C4⋊C4×C43—21no—
48C4×C4⋊C4×C43C2211yescharacteristic
49C4×C22⋊C4×C43—22no—
50C4×C22⋊C4×C43C2212yes—
51C43×#376C2211yescharacteristic
52C2×#95×C43C2212yes—
53C2×#10621898C2×C412yescomplemented
54C2×#10621900—21no—
55C22×Dic86C2×C412yescomplemented
56C2×#10621877—22no—
57C22×C43⋊C8—22no—
58#13063325C2×C411yescharacteristic, complemented
59#13063325C2×C411yescharacteristic, complemented
60#13063324—21no—
61#13063319—21no—
62#13063318—22no—
63#13063318—22no—
64#13063317—21no—
65#13063317C2×C411yescharacteristic, complemented
66#13063315—22no—
67#13063313C2×C411yescharacteristic, complemented
68#13063312—21no—
69#13063311—22no—
70#13063309—22no—
71#13063308—21no—
72#13063308—22no—
73#13063307—22no—
74#13063306—22no—
75#13063305—21no—
76#13063304—22no—
77#13063304—21no—
78#13063304—22no—
79#13063304C2×C412yescomplemented
80#13063304C2×C412yescomplemented
81#13063304C2×C412yescomplemented
82#13063304C2311yescharacteristic
83#13063304C2312yes—
84#13063303—22no—
85#13063302—22no—
86#13063299C2×C412yescomplemented
87#13063299C2311yescharacteristic
88#13063297—22no—
89#13063296—21no—
90#13063294—22no—
91C4×Dic86—21no—
92C4×Dic86C2×C412yescomplemented
93C4×Dic86C2×C411yescharacteristic, complemented
94#13063290—21no—
95C4×D172C2×C411yescharacteristic, complemented
96D4×Dic43—21no—
97C4×C22⋊D43—22no—
98C4×C22⋊D43—21no—
99C4×C22⋊D43—22no—
100(C22⋊D43)⋊C4—22no—
101#13063284—21no—
102#13063284C2×C412yescomplemented
103#13063282—21no—
104#13063281—22no—
105C2×C4⋊Dic43C2×C412yescomplemented
106C2×Dic43⋊C4—22no—
107C4⋊C4×D43—21no—
108C2×C22⋊Dic43—22no—
109C4⋊(C43⋊C8)—21no—
110C4⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—22no—
113C22⋊(C43⋊C8)C2311yescharacteristic
114C22⋊(C43⋊C8)C2312yes—
115C22⋊(C43⋊C8)C2311yescharacteristic
116#13063236—21no—
117C4×C43⋊C8—21no—
118C22×D4×C43D411yescharacteristic
119C23×C4×C43—22no—
120C23×C4×C43C2312yes—
121C4×D4×C43—28no—
122C4×D4×C43C2×C411yescharacteristic
123C4×D4×C43C2×C411yescharacteristic
124C4×D4×C43C2×C412yes—
125C4×D4×C43D411yescharacteristic
126C4×D4×C43D412yes—
127C4×D4×C43D411yescharacteristic
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43D411yescharacteristic
130C2×C22⋊C4×C43—22no—
131C2×C22⋊C4×C43D412yes—
132C2×C42×C43—21no—
133C2×C42×C43—21no—
134C2×C42×C43—22no—
135C2×C42×C43C2311yescharacteristic
136#95×C43—22no—
137#95×C43—21no—
138#95×C43C2311yescharacteristic
139#95×C43C2312yes—
140#95×C43C2311yescharacteristic
141C24×C43C2×D412yes—
142C2×D4×C43—24no—
143C2×D4×C43C22⋊C411yescharacteristic
144C2×D4×C43C22⋊C412yes—
145C2×D4×C43C22⋊C411yescharacteristic
146C22×C4×C43—28no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—22no—
150C22×C4×C43—82no—
151C22×C4×C43—82no—
152C22×C4×C43—82no—
153C22×C4×C43C22×C412yes—
154C22×C4×C43C22×C412yes—
155C22×C4×C43C2×D412yes—
156C22×C4×C43C2×D412yes—
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D412yes—
160C22×C4×C43C2411yescharacteristic
161C2×C22⋊D43—22no—
162C2×C22⋊D43—22no—
163C2×C22⋊D43—21no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166#10621900—44no—
167#10621898—82no—
168C2×D172C22×C411yescharacteristic
169C2×C4×D43—21no—
170C2×C4×D43—22no—
171C2×Dic86—21no—
172C2×Dic86—22no—
173C2×Dic86—82no—
174C2×Dic86C22×C411yescharacteristic
175C2×Dic86C22×C412yes—
176C4⋊C4×C43—24no—
177C4⋊C4×C43C22⋊C411yescharacteristic
178C4⋊C4×C43C22⋊C412yes—
179C4⋊C4×C43C22⋊C411yescharacteristic
180C22⋊C4×C43—28no—
181C22⋊C4×C43C22⋊C412yes—
182C22⋊C4×C43C22⋊C412yes—
183C22⋊C4×C43C22⋊C412yes—
184C22⋊C4×C43C22⋊C412yes—
185C42×C43—24no—
186C42×C43—81no—
187C42×C43—82no—
188C42×C43C22×C411yescharacteristic
189C42×C43C22×C411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196C22⋊Dic43—21no—
197C22⋊Dic43—22no—
198(C2×D43)⋊C4—21no—
199(C2×D43)⋊C4—21no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—21no—
202(C2×D43)⋊C4—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—22no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43C22×C411yescharacteristic
208C4⋊Dic43C22×C412yes—
209C4⋊Dic43C22×C411yescharacteristic
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—21no—
213Dic43⋊C4—22no—
214Dic43⋊C4—21no—
215Dic43⋊C4—22no—
216Dic43⋊C4—21no—
217Dic43⋊C4—21no—
218Dic43⋊C4—22no—
219C4×Dic43—22no—
220C4×Dic43—22no—
221C4×Dic43—21no—
222#10621877—82no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—22no—
226C2×C43⋊C8—82no—
227C23×C43—22no—
228C23×C43—22no—
229C23×C43—24no—
230C23×C43—42no—
231C23×C43C2×C22⋊C412yes—
232C23×C43C2×C22⋊C412yes—
233C23×C43C22×D411yescharacteristic
234C22×D43—21no—
235D4×C43—24no—
236D4×C43—22no—
237D4×C43#10414yes—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—24no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—42no—
252C2×C4×C43—41no—
253C2×C4×C43—42no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—88no—
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C2×C22⋊C412yes—
259C2×C4×C43C2×C22⋊C411yescharacteristic
260C2×C4×C43C2×C22⋊C411yescharacteristic
261C2×C4×C43C2×C22⋊C412yes—
262C2×C4×C43C2×C22⋊C411yescharacteristic
263C2×C4×C43C23×C411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C22⋊D43—41no—
266C22⋊D43—41no—
267C22⋊D43—44no—
268C22⋊D43—82no—
269C2×Dic43—21no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—44no—
275C2×Dic43—82no—
276D172—41no—
277C4×D43—42no—
278C4×D43—82no—
279Dic86—42no—
280Dic86—41no—
281Dic86—42no—
282Dic86—82no—
283C43⋊C8—41no—
284C43⋊C8—42no—
285C43⋊C8—41no—
286#17548—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—22no—
289C22×C43—22no—
290C22×C43—21no—
291C22×C43—22no—
292C22×C43—22no—
293C22×C43—22no—
294C22×C43—44no—
295C22×C43—44no—
296C22×C43C2×#10414yes—
297C22×C43C22×C22⋊C411yescharacteristic
298C22×C43#57711yescharacteristic
299C22×C43#57811yescharacteristic
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—41no—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—22no—
306C4×C43—22no—
307C4×C43—21no—
308C4×C43—21no—
309C4×C43—21no—
310C4×C43—42no—
311C4×C43—44no—
312C4×C43—42no—
313C4×C43C2×#10412yes—
314Dic43—41no—
315Dic43—42no—
316Dic43—41no—
317Dic43—42no—
318Dic43—41no—
319#3520—431no—
320#2974—431no—
321#2275D4311yescharacteristic, complemented
322#1509—431no—
323#1508—432no—
324#1506—431no—
325#1504—432no—
326#1503—431no—
327#1501—432no—
328#1500—431no—
329C2×#328—432no—
330C2×C43—21no—
331C2×C43—21no—
332C2×C43—24no—
333C2×C43—42no—
334C2×C43#288311yescharacteristic
335C2×C43#289811yescharacteristic
336C2×C43C22×#10411yescharacteristic
337D43—81no—
338#556—431no—
339#554—861no—
340#552—432no—
341#551—862no—
342D4×Q8—431no—
343#548—432no—
344#547—431no—
345#547—431no—
346#546—861no—
347#542—861no—
348#539—862no—
349#533—431no—
350#529—431no—
351#525—432no—
352C2×C22⋊Q8—432no—
353#520—861no—
354C2×C4×D4—21no—
355C2×C4×D4C2×D4311yescharacteristic
356#436—861no—
357#435—862no—
358C8×D4—861no—
359#432—431no—
360#431—431no—
361#407—432no—
362C2×C22⋊C8—432no—
363C4×C4⋊C4—21no—
364C4×C4⋊C4C2×D4311yescharacteristic
365C4×C22⋊C4—22no—
366C4×C22⋊C4C2×D4312yes—
367#376C2×D4311yescharacteristic
368C2×#95C2×D4312yes—
369#328—431no—
370#328—432no—
371#328—432no—
372#328—432no—
373#328—431no—
374#328—432no—
375#328—432no—
376#327—431no—
377#327—431no—
378#327—432no—
379C43#1754811yescharacteristic, complemented, Sylow
380C2×#41—432no—
381C2×#41—861no—
382C22×Q8—432no—
383C22×D4C22⋊D4311yescharacteristic
384C23×C4—22no—
385C23×C4C22×D4312yes—
386C2×M16—862no—
387C22×C8—862no—
388C4⋊Q8—431no—
389C4⋊Q8—431no—
390C4⋊Q8—861no—
391#126—862no—
392#126—862no—
393#126—861no—
394#125—431no—
395#125—862no—
396#125—861no—
397#124—431no—
398#124—861no—
399#124—862no—
400#123—862no—
401#123—862no—
402#123—861no—
403#123—862no—
404#123—862no—
405C22⋊Q8—432no—
406C22⋊Q8—432no—
407C22⋊Q8—432no—
408C22⋊Q8—431no—
409C22⋊Q8—432no—
410C22⋊Q8—862no—
411C22⋊Q8—862no—
412C22⋊Q8—861no—
413C22⋊Q8—862no—
414C22⋊Q8—861no—
415C22⋊Q8—862no—
416#121—432no—
417#121—431no—
418#121—862no—
419#121—861no—
420#120—862no—
421C4×Q8—431no—
422C4×Q8—432no—
423C4×Q8—861no—
424C4×Q8—861no—
425C4×D4—28no—
426C4×D4—431no—
427C4×D4—861no—
428C4×D4—862no—
429C4×D4—862no—
430C4×D4—861no—
431C4×D4—862no—
432C4×D4C4×D4311yescharacteristic
433C4×D4C4×D4311yescharacteristic
434C4×D4C4×D4312yes—
435C4×D4D17211yescharacteristic
436C4×D4D17212yes—
437C4×D4D17211yescharacteristic
438#117—432no—
439#117—861no—
440#117—862no—
441#117—861no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—432no—
444C2×C4⋊C4—862no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4C22⋊D4311yescharacteristic
447C2×C22⋊C4—22no—
448C2×C22⋊C4—862no—
449C2×C22⋊C4C22⋊D4312yes—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—22no—
453C2×C42C22×D4311yescharacteristic
454C4⋊C8—861no—
455C4⋊C8—861no—
456C22⋊C8—431no—
457C22⋊C8—432no—
458C22⋊C8—431no—
459C22⋊C8—862no—
460C22⋊C8—862no—
461#97—861no—
462C4×C8—861no—
463#95—22no—
464#95—21no—
465#95C22×D4311yescharacteristic
466#95C22×D4312yes—
467#95C22×D4311yescharacteristic
468C24C2×C22⋊D4312yes—
469#41—3442no—
470#41—1724no—
471C2×Q8—431no—
472C2×Q8—432no—
473C2×Q8—862no—
474C2×Q8—861no—
475C2×Q8—3442no—
476C2×D4—24no—
477C2×D4—431no—
478C2×D4—862no—
479C2×D4—862no—
480C2×D4—861no—
481C2×D4(C2×D43)⋊C412yes—
482C2×D4(C2×D43)⋊C411yescharacteristic
483C2×D4(C2×D43)⋊C411yescharacteristic
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—28no—
488C22×C4—82no—
489C22×C4—82no—
490C22×C4—82no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—861no—
495C22×C4C2×C4×D4312yes—
496C22×C4C2×C4×D4312yes—
497C22×C4C2×D17212yes—
498C22×C4C2×D17212yes—
499C22×C4C2×C22⋊D4311yescharacteristic
500C22×C4C2×C22⋊D4311yescharacteristic
501C22×C4C2×C22⋊D4312yes—
502C22×C4C23×D4311yescharacteristic
503M16—3442no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—862no—
507C2×C8—3442no—
508C4⋊C4—24no—
509C4⋊C4—431no—
510C4⋊C4—432no—
511C4⋊C4—431no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—861no—
515C4⋊C4—862no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—862no—
520C4⋊C4—861no—
521C4⋊C4—862no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—862no—
525C4⋊C4(C2×D43)⋊C411yescharacteristic
526C4⋊C4(C2×D43)⋊C412yes—
527C4⋊C4(C2×D43)⋊C411yescharacteristic
528C22⋊C4—28no—
529C22⋊C4—862no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—861no—
534C22⋊C4—862no—
535C22⋊C4—861no—
536C22⋊C4—861no—
537C22⋊C4—862no—
538C22⋊C4—861no—
539C22⋊C4—861no—
540C22⋊C4(C2×D43)⋊C412yes—
541C22⋊C4(C2×D43)⋊C412yes—
542C22⋊C4(C2×D43)⋊C412yes—
543C22⋊C4(C2×D43)⋊C412yes—
544C42—24no—
545C42—81no—
546C42—82no—
547C42—862no—
548C42—862no—
549C42—861no—
550C42C2×C4×D4311yescharacteristic
551C42C2×C4×D4311yescharacteristic
552C42C2×D17211yescharacteristic
553C42C2×D17211yescharacteristic
554C23—24no—
555C23—22no—
556C23—22no—
557C23—42no—
558C23—861no—
559C23C2×(C2×D43)⋊C412yes—
560C23C2×(C2×D43)⋊C412yes—
561C23C22×C22⋊D4311yescharacteristic
562Q8—3442no—
563Q8—1721no—
564Q8—1722no—
565Q8—1722no—
566D4—24no—
567D4—22no—
568D4—3442no—
569D4—1721no—
570D4—1724no—
571D4—1721no—
572D4—1721no—
573D4#1306325314yes—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—88no—
593C2×C4—861no—
594C2×C4—862no—
595C2×C4—861no—
596C2×C4—862no—
597C2×C4—861no—
598C2×C4—3442no—
599C2×C4—3442no—
600C2×C4—1724no—
601C2×C4—1722no—
602C2×C4C2×(C2×D43)⋊C411yescharacteristic
603C2×C4C2×(C2×D43)⋊C412yes—
604C2×C4C2×(C2×D43)⋊C411yescharacteristic
605C2×C4C2×(C2×D43)⋊C411yescharacteristic
606C2×C4C2×(C2×D43)⋊C412yes—
607C2×C4C2×(C2×D43)⋊C411yescharacteristic
608C2×C4C22×C4×D4311yescharacteristic
609C2×C4C22×D17211yescharacteristic
610C8—1721no—
611C8—1722no—
612C8—1721no—
613C22—21no—
614C22—22no—
615C22—22no—
616C22—21no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—44no—
621C22—44no—
622C22—1721no—
623C22—1721no—
624C22—1721no—
625C22C2×#1306325314yes—
626C22C22×(C2×D43)⋊C411yescharacteristic
627C22#1458371011yescharacteristic
628C22#1458371411yescharacteristic
629C4—21no—
630C4—21no—
631C4—22no—
632C4—22no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—42no—
637C4—44no—
638C4—42no—
639C4—1722no—
640C4—1721no—
641C4—1721no—
642C4—1721no—
643C4—1722no—
644C4C2×#1306325312yes—
645C2—21no—
646C2—21no—
647C2—24no—
648C2—42no—
649C2—3441no—
650C2#1914305511yescharacteristic
651C2#1914312511yescharacteristic
652C2C22×#1306325311yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2275C2
socleC22×C43C22×C22⋊C4
prime radical#19148644C2
cosocleC22×C4×C43C24
hypercenter#2275D43
hypocenterC43#17548
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2275

Complements

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

NH ≅ G/Ntype
2. #19143630C2semidirect
3. #19133118C2semidirect
4. #19133114C2semidirect
5. #19133106C2semidirect
6. #19133097C2semidirect
7. #19133093C2semidirect
8. #19133084C2semidirect
9. #19133079C2semidirect
10. C2×#14582635C2semidirect
11. C43×#2275C2semidirect
12. #14583619C4semidirect
14. #14583589C4semidirect
16. D4×Dic86C4semidirect
17. #14583558C4semidirect
18. #14583554C4semidirect
19. #14583553C4semidirect
53. C2×#10621898C2×C4semidirect
55. C22×Dic86C2×C4semidirect
58. #13063325C2×C4semidirect
59. #13063325C2×C4semidirect
65. #13063317C2×C4semidirect
67. #13063313C2×C4semidirect
79. #13063304C2×C4semidirect
80. #13063304C2×C4semidirect
81. #13063304C2×C4semidirect
86. #13063299C2×C4semidirect
92. C4×Dic86C2×C4semidirect
93. C4×Dic86C2×C4semidirect
95. C4×D172C2×C4semidirect
102. #13063284C2×C4semidirect
105. C2×C4⋊Dic43C2×C4semidirect
321. #2275D43semidirect
379. C43#17548semidirect

Maximal subgroups

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

subgroupindex
#191486442
#191436302
#191331182
#191331142
#191331062
#191330972
#191330932
#191330842
#191330792
C2×#145826352
C43×#22752
#1754843