Finite Group Databasebeta

← #25098406

Subgroups — #25098406

Order 11008.

1718 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
1C2×#14583471C211yesmaximal, characteristic
2C2×#14583376C211yesmaximal, characteristic, complemented
3C2×#14582871C212yesmaximal
4#19137180C211yesmaximal, characteristic, complemented
5#19135054C211yesmaximal, characteristic, complemented
6#19135053C211yesmaximal, characteristic, complemented
7#19135052C212yesmaximal, complemented
8#19135051C211yesmaximal, characteristic, complemented
9#19135050C212yesmaximal, complemented
10#19134326C212yesmaximal, complemented
11C43×#1899C211yesmaximal, characteristic, complemented
12C22×#10621900C2211yescharacteristic
13C23×Dic86C2211yescharacteristic
14#14583471—24no—
15#14583471—22no—
16#14583471—22no—
17C2×#13063324C412yescomplemented
18C2×#13063311C412yescomplemented
19C2×#13063309C2211yescharacteristic
20C2×#13063308C2211yescharacteristic
21C2×#13063306C2211yescharacteristic
22C2×#13063303C412yescomplemented
23C2×#13063302C412yescomplemented
24#14583376—28no—
25C2×C4×Dic86—22no—
26C2×#13063290—22no—
27C2×#13063284C2211yescharacteristic
28C2×#13063281C2212yes—
29C2×#13063281C2212yes—
30C2×#13063281C2212yes—
31C2×#13063281C2211yescharacteristic
32#14582871—28no—
33C2×#13063240C2212yes—
34C2×#13063239C2212yes—
35C2×#13063239C2212yes—
36#14582803—24no—
37#14582762C2211yescharacteristic
38#14582760C2212yes—
39#14582666C2212yes—
40#14582665C2212yes—
41#14582665C2212yes—
42C2×#123×C43C2211yescharacteristic
43C2×#117×C43C2211yescharacteristic
44C2×#99×C43C2212yes—
45C43×#381C2211yescharacteristic
46C43×#342C2212yes—
47C2×#10621900—24no—
48C2×#10621900—22no—
49C2×#10621900—22no—
50C2×#10621900—24no—
51C22×Dic86—24no—
52C22×Dic86—24no—
53C22×Dic86C2×C411yescharacteristic
54C22×Dic86C2×C412yes—
55C22×Dic86C2×C412yes—
56C22×Dic86D414yes—
57C22×Dic86D412yes—
58C22×Dic86D412yes—
59C22×C22⋊D43C2×C411yescharacteristic
60C22×C22⋊D43C2311yescharacteristic
61C23×Dic43C2×C411yescharacteristic
62C23×Dic43C2311yescharacteristic
63C23×Dic43C2311yescharacteristic
64C22×C4×D43C2×C411yescharacteristic
65#13063324—24no—
66#13063324—24no—
67#13063311—24no—
68#13063311—24no—
69#13063309—22no—
70#13063309—22no—
71#13063308—22no—
72#13063308—21no—
73#13063308—21no—
74#13063306—22no—
75#13063306—22no—
76#13063303—24no—
77#13063303—24no—
78#13063302—24no—
79#13063302—24no—
80C4×Dic86—216no—
81#13063290—216no—
82#13063284—24no—
83#13063281—24no—
84#13063281—22no—
85#13063281—22no—
86#13063281—24no—
87#13063281—24no—
88#13063281—24no—
89#13063281—24no—
90#13063281D418yes—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2×C412yes—
93C2×Dic43⋊C4—22no—
94C2×Dic43⋊C4—22no—
95C2×Dic43⋊C4—22no—
96C2×Dic43⋊C4C2×C412yes—
97C2×Dic43⋊C4C2×C412yes—
98C2×Dic43⋊C4C2×C412yes—
99C2×C22⋊Dic43C2×C412yes—
100C2×C22⋊Dic43C2312yes—
101C2×C22⋊Dic43C2311yescharacteristic
102C2×C22⋊Dic43C2312yes—
103C2×(C2×D43)⋊C4C2×C412yes—
104C2×(C2×D43)⋊C4C2×C412yes—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—22no—
107C2×C4×Dic43—22no—
108C2×C4×Dic43—22no—
109C2×C4×Dic43C2×C412yes—
110#13063240—24no—
111#13063239—24no—
112#13063239—24no—
113C43⋊#95—22no—
114C43⋊#95—24no—
115C22×D4×C43C2311yescharacteristic
116C23×C4×C43C2311yescharacteristic
117#123×C43—22no—
118#123×C43—21no—
119#123×C43—21no—
120#117×C43—24no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43C2×C412yes—
123C2×C22⋊C4×C43C2×C412yes—
124C2×C22⋊C4×C43C2312yes—
125C2×C22⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43C2312yes—
127C2×C42×C43—21no—
128#99×C43—24no—
129#95×C43—22no—
130C24×C43C22×C411yescharacteristic
131C24×C43C2411yescharacteristic
132C23×D43C22×C411yescharacteristic
133C2×D4×C43—22no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43C22×C411yescharacteristic
142C22×C4×C43C22×C412yes—
143C22×C4×C43C22×C412yes—
144C22×C4×C43C2×D412yes—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C2×C22⋊D43—22no—
148C2×C22⋊D43—24no—
149C2×C22⋊D43—22no—
150C2×C22⋊D43—21no—
151C2×C22⋊D43—21no—
152C2×C22⋊D43—22no—
153C22×Dic43—22no—
154C22×Dic43—24no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43C22×C411yescharacteristic
160C22×Dic43C22×C412yes—
161C22×Dic43C22×C412yes—
162C22×Dic43C22×C411yescharacteristic
163C22×Dic43C22×C411yescharacteristic
164C22×Dic43C2×D412yes—
165C22×Dic43C2×D412yes—
166C22×Dic43C2×D412yes—
167C22×Dic43C2×D412yes—
168C22×Dic43C2×D414yes—
169C22×Dic43#4114yes—
170#10621900—44no—
171#10621900—44no—
172#10621900—44no—
173#10621900—44no—
174C2×C4×D43—22no—
175C2×C4×D43—24no—
176C2×Dic86—28no—
177C2×Dic86—28no—
178C2×Dic86—24no—
179C2×Dic86—24no—
180C2×Dic86—28no—
181C2×Dic86—28no—
182C2×Dic86—24no—
183C2×Dic86—24no—
184C2×Dic86—22no—
185C2×Dic86—24no—
186C2×Dic86C22⋊C414yes—
187C2×Dic86C22⋊C414yes—
188C2×Dic86C22⋊C414yes—
189C2×Dic86C22⋊C414yes—
190C4⋊C4×C43—24no—
191C4⋊C4×C43—22no—
192C4⋊C4×C43—22no—
193C22⋊C4×C43—22no—
194C22⋊C4×C43—22no—
195C22⋊C4×C43—22no—
196C22⋊C4×C43—21no—
197C22⋊C4×C43—21no—
198C22⋊C4×C43—22no—
199C22⋊C4×C43—22no—
200C22⋊C4×C43C2×D414yes—
201C42×C43—24no—
202C22⋊Dic43—24no—
203C22⋊Dic43—22no—
204C22⋊Dic43—21no—
205C22⋊Dic43—21no—
206C22⋊Dic43—22no—
207C22⋊Dic43—22no—
208C22⋊Dic43C2×D414yes—
209(C2×D43)⋊C4—22no—
210(C2×D43)⋊C4—22no—
211(C2×D43)⋊C4—24no—
212C4⋊Dic43—24no—
213C4⋊Dic43—24no—
214Dic43⋊C4—28no—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217Dic43⋊C4—24no—
218Dic43⋊C4—24no—
219Dic43⋊C4—28no—
220Dic43⋊C4—44no—
221C4×Dic43—28no—
222C4×Dic43—24no—
223C4×Dic43—24no—
224C4×Dic43—28no—
225C4×Dic43—44no—
226C23×C43—21no—
227C23×C43—22no—
228C23×C43—42no—
229C23×C43—42no—
230C23×C43C23×C411yescharacteristic
231C23×C43C22×D411yescharacteristic
232C23×C43C22×D411yescharacteristic
233C23×C43C22×D412yes—
234C23×C43C2×#4112yes—
235C22×D43—21no—
236C22×D43—22no—
237C22×D43—42no—
238D4×C43—41no—
239D4×C43—42no—
240D4×C43—41no—
241C2×C4×C43—24no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—24no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—22no—
248C2×C4×C43—21no—
249C2×C4×C43—22no—
250C2×C4×C43—24no—
251C2×C4×C43—44no—
252C2×C4×C43—42no—
253C2×C4×C43—44no—
254C2×C4×C43—42no—
255C2×C4×C43C2×C22⋊C412yes—
256C2×C4×C43C2×C22⋊C412yes—
257C22⋊D43—41no—
258C22⋊D43—42no—
259C22⋊D43—41no—
260C22⋊D43—44no—
261C2×Dic43—24no—
262C2×Dic43—22no—
263C2×Dic43—24no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—24no—
269C2×Dic43—44no—
270C2×Dic43—44no—
271C2×Dic43—42no—
272C2×Dic43—44no—
273C2×Dic43—42no—
274C2×Dic43C2×C22⋊C414yes—
275C2×Dic43C2×C22⋊C412yes—
276C2×Dic43C2×C22⋊C412yes—
277C2×Dic43C4×D414yes—
278C2×Dic43C4×D414yes—
279C2×Dic43#12014yes—
280C2×Dic43#12114yes—
281C2×Dic43#12114yes—
282C2×Dic43#12314yes—
283C4×D43—44no—
284Dic86—28no—
285Dic86—28no—
286Dic86—28no—
287Dic86—28no—
288Dic86—44no—
289#20986—431nomaximal, Sylow
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—22no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—41no—
297C22×C43—82no—
298C22×C43C22×C22⋊C411yescharacteristic
299C22×C43C2×C4×D412yes—
300C22×C43C2×#12011yescharacteristic
301C22×C43C2×#12112yes—
302C22×C43C2×#12311yescharacteristic
303C2×D43—42no—
304C2×D43—41no—
305C2×D43—82no—
306C4×C43—22no—
307C4×C43—22no—
308C4×C43—44no—
309C4×C43—42no—
310C4×C43—41no—
311C4×C43—82no—
312Dic43—24no—
313Dic43—44no—
314Dic43—42no—
315Dic43—41no—
316Dic43—82no—
317Dic43#38614yes—
318Dic43#38614yes—
319C2×#536—431no—
320C2×#519—431no—
321C2×#410—432no—
322#2310—431no—
323#1899—432no—
324#1899—431no—
325#1899—432no—
326#1899—431no—
327#1899—431no—
328#1899D4311yescharacteristic, complemented
329#1740—432no—
330C2×C43—21no—
331C2×C43—22no—
332C2×C43—22no—
333C2×C43—21no—
334C2×C43—81no—
335C2×C43C2×#38611yescharacteristic
336C2×C43#288412yes—
337D43—81no—
338C22×#41—431no—
339C23×Q8—431no—
340#536—862no—
341#536—862no—
342#536—864no—
343C2×C4⋊Q8—432no—
344C2×#124—432no—
345C2×#123—431no—
346C2×#123—431no—
347C2×#123—431no—
348C2×#123C2×D4311yescharacteristic
349C2×C22⋊Q8—432no—
350C2×C22⋊Q8—432no—
351#519—868no—
352C2×C4×Q8—862no—
353C2×C4×Q8—862no—
354C2×#117—431no—
355C2×#117—431no—
356C2×#117—432no—
357C2×#117—432no—
358C2×#117—432no—
359C2×#117C2×D4311yescharacteristic
360#410—868no—
361C2×#99—432no—
362C2×#99—432no—
363C2×#99—432no—
364C2×#99C2×D4312yes—
365#391—864no—
366#381—431no—
367#381—432no—
368#381C2×D4311yescharacteristic
369#342—432no—
370#342—432no—
371#342—432no—
372#342C2×D4312yes—
373C43#2098611yescharacteristic, complemented, Sylow
374C2×#41—862no—
375C2×#41—862no—
376C2×#41—864no—
377C2×#41—864no—
378C22×Q8—432no—
379C22×Q8—432no—
380C22×Q8—431no—
381C22×Q8—432no—
382C22×Q8—432no—
383C22×Q8—434no—
384C22×Q8—864no—
385C22×Q8—864no—
386C22×D4—431no—
387C22×D4—431no—
388C22×D4C22×D4311yescharacteristic
389C23×C4—431no—
390C23×C4—431no—
391C23×C4—431no—
392C23×C4—431no—
393C23×C4C22×D4311yescharacteristic
394C4⋊Q8—864no—
395C4⋊Q8—864no—
396#124—864no—
397#124—864no—
398#123—22no—
399#123—21no—
400#123—21no—
401#123—862no—
402#123—862no—
403#123—862no—
404#123—862no—
405#123—862no—
406#123—861no—
407#123—861no—
408C22⋊Q8—864no—
409C22⋊Q8—864no—
410C22⋊Q8—864no—
411C22⋊Q8—864no—
412C4×Q8—8616no—
413C4×Q8—8616no—
414#117—24no—
415#117—438no—
416#117—864no—
417#117—864no—
418#117—862no—
419#117—862no—
420#117—864no—
421#117—864no—
422#117—864no—
423#117—864no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—432no—
426C2×C4⋊C4—432no—
427C2×C4⋊C4—432no—
428C2×C4⋊C4—432no—
429C2×C4⋊C4—862no—
430C2×C4⋊C4—862no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—862no—
433C2×C4⋊C4C4×D4312yes—
434C2×C22⋊C4—432no—
435C2×C22⋊C4—432no—
436C2×C22⋊C4—431no—
437C2×C22⋊C4—432no—
438C2×C22⋊C4—432no—
439C2×C22⋊C4—432no—
440C2×C22⋊C4C4×D4312yes—
441C2×C22⋊C4C22×D4312yes—
442C2×C22⋊C4C22×D4311yescharacteristic
443C2×C22⋊C4C22×D4312yes—
444C2×C42—21no—
445C2×C42—432no—
446C2×C42—862no—
447C2×C42—862no—
448C2×C42—861no—
449C2×C42—862no—
450#99—24no—
451#99—864no—
452#99—864no—
453#99—864no—
454#95—22no—
455#95—864no—
456#95—862no—
457C24—431no—
458C24C2×C4×D4311yescharacteristic
459C24C23×D4311yescharacteristic
460#41—1724no—
461#41—1724no—
462#41—1724no—
463#41—1724no—
464C2×Q8—434no—
465C2×Q8—434no—
466C2×Q8—434no—
467C2×Q8—434no—
468C2×Q8—864no—
469C2×Q8—864no—
470C2×Q8—868no—
471C2×Q8—868no—
472C2×Q8—868no—
473C2×Q8—868no—
474C2×Q8—864no—
475C2×Q8—864no—
476C2×Q8—862no—
477C2×Q8—864no—
478C2×D4—22no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—22no—
482C2×D4—862no—
483C2×D4—864no—
484C2×D4—862no—
485C2×D4—861no—
486C2×D4—861no—
487C2×D4—862no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—432no—
495C22×C4—432no—
496C22×C4—434no—
497C22×C4—434no—
498C22×C4—432no—
499C22×C4—432no—
500C22×C4—432no—
501C22×C4—431no—
502C22×C4—432no—
503C22×C4—862no—
504C22×C4—864no—
505C22×C4—862no—
506C22×C4—864no—
507C22×C4—862no—
508C22×C4—862no—
509C22×C4—862no—
510C22×C4—862no—
511C22×C4C2×C4×D4311yescharacteristic
512C22×C4C2×C4×D4312yes—
513C22×C4C2×C4×D4312yes—
514C22×C4D4×D4312yes—
515C22×C4D4×D4311yescharacteristic
516C22×C4D4×D4311yescharacteristic
517C4⋊C4—24no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—864no—
521C4⋊C4—864no—
522C4⋊C4—864no—
523C4⋊C4—868no—
524C4⋊C4—868no—
525C4⋊C4—864no—
526C4⋊C4—862no—
527C4⋊C4—862no—
528C4⋊C4—1724no—
529C22⋊C4—22no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—434no—
537C22⋊C4—864no—
538C22⋊C4—864no—
539C22⋊C4—862no—
540C22⋊C4—861no—
541C22⋊C4—861no—
542C22⋊C4—862no—
543C22⋊C4—862no—
544C22⋊C4—862no—
545C22⋊C4—862no—
546C22⋊C4D4×D4314yes—
547C42—24no—
548C42—864no—
549C42—868no—
550C42—864no—
551C42—868no—
552C42—1724no—
553C23—21no—
554C23—22no—
555C23—42no—
556C23—42no—
557C23—862no—
558C23—861no—
559C23—1722no—
560C23C22×C4×D4311yescharacteristic
561C23C2×D4×D4311yescharacteristic
562C23C2×D4×D4311yescharacteristic
563C23C2×D4×D4312yes—
564C23#41×D4312yes—
565Q8—868no—
566Q8—868no—
567Q8—868no—
568Q8—868no—
569Q8—1724no—
570D4—41no—
571D4—42no—
572D4—41no—
573D4—1724no—
574D4—1721no—
575D4—1722no—
576D4—1721no—
577C2×C4—24no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—24no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—44no—
588C2×C4—42no—
589C2×C4—44no—
590C2×C4—42no—
591C2×C4—432no—
592C2×C4—432no—
593C2×C4—434no—
594C2×C4—434no—
595C2×C4—434no—
596C2×C4—434no—
597C2×C4—434no—
598C2×C4—434no—
599C2×C4—434no—
600C2×C4—864no—
601C2×C4—862no—
602C2×C4—864no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—861no—
606C2×C4—862no—
607C2×C4—864no—
608C2×C4—1724no—
609C2×C4—1724no—
610C2×C4—1724no—
611C2×C4—1722no—
612C2×C4—1724no—
613C2×C4—1722no—
614C2×C4C22⋊C4×D4312yes—
615C2×C4C22⋊C4×D4312yes—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—41no—
623C22—82no—
624C22—3442no—
625C22—1722no—
626C22—1721no—
627C22C2×C22⋊C4×D4311yescharacteristic
628C22C4×D4×D4312yes—
629C22#120×D4311yescharacteristic
630C22#121×D4312yes—
631C22#123×D4311yescharacteristic
632C4—22no—
633C4—22no—
634C4—44no—
635C4—42no—
636C4—41no—
637C4—82no—
638C4—434no—
639C4—434no—
640C4—864no—
641C4—3442no—
642C4—1724no—
643C4—1722no—
644C4—1721no—
645C2—21no—
646C2—22no—
647C2—22no—
648C2—21no—
649C2—81no—
650C2—3441no—
651C2#386×D4311yescharacteristic
652C2#1914305712yes—
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1899C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#10621900C22
cosocleC24×C43C24
hypercenter#1899D43
hypocenterC43#20986
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1899

Complements

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

NH ≅ G/Ntype
2. C2×#14583376C2semidirect
4. #19137180C2semidirect
5. #19135054C2semidirect
6. #19135053C2semidirect
7. #19135052C2semidirect
8. #19135051C2semidirect
9. #19135050C2semidirect
10. #19134326C2semidirect
11. C43×#1899C2semidirect
17. C2×#13063324C4semidirect
18. C2×#13063311C4semidirect
22. C2×#13063303C4semidirect
23. C2×#13063302C4semidirect
328. #1899D43semidirect
373. C43#20986semidirect

Maximal subgroups

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

subgroupindex
C2×#145834712
C2×#145833762
C2×#145828712
#191371802
#191350542
#191350532
#191350522
#191350512
#191350502
#191343262
C43×#18992
#2098643