Finite Group Databasebeta

← #25095115

Subgroups — #25095115

Order 11008.

1130 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583001C211yesmaximal, characteristic
2C2×#14582998C211yesmaximal, characteristic
3C2×#14582986C211yesmaximal, characteristic
4#19136959C211yesmaximal, characteristic, complemented
5#19136955C211yesmaximal, characteristic
6#19134495C211yesmaximal, characteristic, complemented
7#107×Dic43C211yesmaximal, characteristic, complemented
8#19134424C211yesmaximal, characteristic, complemented
9#19134419C211yesmaximal, characteristic
10C4×#13063248C211yesmaximal, characteristic, complemented
11#19134414C211yesmaximal, characteristic, complemented
12C4×#13063245C211yesmaximal, characteristic
13#19134409C211yesmaximal, characteristic
14#19134283C211yesmaximal, characteristic, complemented
15C43×#1776C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23#14583001C418yescomplemented
24#14582998C418yescomplemented
25#14582986C418yescomplemented
26C2×#13063259C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063235C2211yescharacteristic
34C2×#13063235C2211yescharacteristic
35C2×C4×C43⋊C8C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×Dic43⋊C4—21no—
43C4×Dic43⋊C4—21no—
44#14582750—21no—
45C4×(C2×D43)⋊C4—21no—
46C4×(C2×D43)⋊C4—21no—
47#14582746—21no—
48#14582745C2211yescharacteristic
49#14582744—21no—
50#95×D43—21no—
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C2×#10621873C2×C414yes—
68C2×#10621873C2×C414yes—
69C2×#10621873C2×C414yes—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C4×Dic86—22no—
73C4×Dic86C2×C414yescomplemented
74#13063290—22no—
75#13063290—22no—
76#13063290C2×C414yescomplemented
77#13063290C2×C414yescomplemented
78C4×D172—22no—
79C4×D172C2×C414yes—
80#13063287—22no—
81#13063287—22no—
82#13063287C2×C414yes—
83#13063287C2×C414yes—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43C2311yescharacteristic
100C2×C4×Dic43C2311yescharacteristic
101#13063259C2×C414yescomplemented
102#13063250C2×C414yescomplemented
103#13063248C2×C414yescomplemented
104#13063248C2×C414yescomplemented
105#13063247C2×C414yes—
106#13063245C2×C414yes—
107#13063245C2×C414yes—
108#13063235—22no—
109#13063235C2×C414yescomplemented
110C4×C43⋊C8—22no—
111C8×Dic43—22no—
112C8×Dic43C2×C414yescomplemented
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95D411yescharacteristic
118C43⋊#95D411yescharacteristic
119C43⋊#95D411yescharacteristic
120C43⋊#95D411yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C42×C43—21no—
128C2×C42×C43—21no—
129C2×C42×C43C2311yescharacteristic
130#107×C43C2×C414yescomplemented
131#106×C43C2×C414yescomplemented
132#97×C43C2×C414yescomplemented
133#95×C43—21no—
134#95×C43—21no—
135C23×D43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2411yescharacteristic
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172C22×C412yes—
154C2×D172C22×C412yes—
155C2×D172C22×C412yes—
156C2×C4×D43—24no—
157C2×C4×D43—24no—
158C2×C4×D43—24no—
159C2×C4×D43—81no—
160C2×C4×D43—81no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×C4×D43—81no—
164C2×C4×D43—81no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86C22×C412yes—
169C2×Dic86C22×C412yes—
170C2×Dic86C22×C412yes—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43C22×C412yes—
174C2×C8×C43C22×C412yes—
175C2×C8×C43C22×C412yes—
176C2×C8×C43C22×C412yes—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C22×C412yes—
182C4⋊C4×C43C22×C412yes—
183C4⋊C4×C43C22×C412yes—
184C4⋊C4×C43C22×C412yes—
185C42×C43—81no—
186C42×C43—81no—
187C42×C43C22×C412yes—
188C42×C43#4112yes—
189(C2×D43)⋊C4—24no—
190(C2×D43)⋊C4—24no—
191(C2×D43)⋊C4—24no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43C22×C412yes—
195C4⋊Dic43C22×C412yes—
196Dic43⋊C4—24no—
197Dic43⋊C4—24no—
198Dic43⋊C4—24no—
199C4×Dic43—24no—
200C4×Dic43—24no—
201C4×Dic43—24no—
202C4×Dic43—81no—
203C4×Dic43—81no—
204C4×Dic43—81no—
205C4×Dic43—81no—
206C4×Dic43C22×C412yes—
207C4×Dic43C22×C412yes—
208C4×Dic43#4112yes—
209C4×Dic43#4112yes—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8C22×C412yes—
215C2×C43⋊C8C22×C412yes—
216#10621873C42116yescomplemented
217C23×C43C22×D411yescharacteristic
218C22×D43—22no—
219C22×D43—22no—
220C22×D43—22no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43C4×D412yes—
242C2×C4×C43C4×D412yes—
243C2×C4×C43C23×C411yescharacteristic
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C23×C411yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43C4×D412yes—
267C2×Dic43C4×D412yes—
268C2×Dic43C4×D412yes—
269C2×Dic43C4×D412yes—
270D172—22no—
271D172—22no—
272D172—22no—
273D172C2×C4214yes—
274C4×D43—84no—
275C4×D43—84no—
276C4×D43—84no—
277Dic86—22no—
278Dic86—22no—
279Dic86—22no—
280Dic86C2×C4214yes—
281C8×C43—22no—
282C8×C43C2×C4214yes—
283C43⋊C8—22no—
284C43⋊C8—22no—
285#20504—431nomaximal, Sylow
286C22×C43C2×C4×D411yescharacteristic
287C22×C43C2×C4×D411yescharacteristic
288C22×C43C2×C4×D411yescharacteristic
289C22×C43#57611yescharacteristic
290C22×C43#57711yescharacteristic
291C22×C43#57711yescharacteristic
292C22×C43#57811yescharacteristic
293C2×D43—24no—
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C4×C43—22no—
301C4×C43—22no—
302C4×C43—42no—
303C4×C43—42no—
304C4×C43—42no—
305C4×C43—42no—
306C4×C43C22×C4211yescharacteristic
307C4×C43C4×#4111yescharacteristic
308C4×C43C4×#4111yescharacteristic
309C4×C43C4×#4111yescharacteristic
310Dic43—22no—
311Dic43—22no—
312Dic43—22no—
313Dic43—22no—
314Dic43—24no—
315Dic43—42no—
316Dic43—42no—
317C2×#440—431no—
318C2×#440—431no—
319C2×C4×SD16—431no—
320#2276—431no—
321#2275—431no—
322#1776—431no—
323#1776D4311yescharacteristic, complemented
324C4×#107—431no—
325#1763—431no—
326#1762—431no—
327C4×#103—431no—
328C4×#103—431no—
329C4×#102—431no—
330C4×#102—431no—
331#1726—431no—
332C2×C43C42×D411yescharacteristic
333C2×C43#294611yescharacteristic
334C2×C43#294611yescharacteristic
335C2×C43#294711yescharacteristic
336C2×C43#294711yescharacteristic
337C2×C43#294911yescharacteristic
338C2×C43#295111yescharacteristic
339D43—44no—
340C22×SD16—431no—
341C2×C4×Q8—431no—
342C2×C4×Q8—431no—
343C2×C4×Q8—431no—
344C2×C4×D4—431no—
345C2×C4×D4—431no—
346C2×C4×D4—431no—
347#440—438no—
348#440—438no—
349C4×SD16—438no—
350C2×#107—431no—
351C2×#107C2×D4311yescharacteristic
352C2×#106C2×D4311yescharacteristic
353C2×#103—431no—
354C2×#103—431no—
355C2×#103—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#97—431no—
360C2×#97—431no—
361C2×#97C2×D4311yescharacteristic
362C2×C4×C8—431no—
363C2×C4×C8—431no—
364C2×C4×C8—431no—
365C4×C4⋊C4—431no—
366C4×C4⋊C4—431no—
367C4×C4⋊C4—431no—
368C4×C4⋊C4—431no—
369C4×C4⋊C4—861no—
370C4×C4⋊C4—861no—
371C4×C4⋊C4—861no—
372C4×C4⋊C4C2×D4311yescharacteristic
373C4×C4⋊C4C2×D4311yescharacteristic
374C4×C22⋊C4—861no—
375C4×C22⋊C4—861no—
376C4×C22⋊C4—861no—
377#376—431no—
378#376—861no—
379C2×#95—861no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340C2×D4311yescharacteristic
385#340C2×D4311yescharacteristic
386C43#2050411yescharacteristic, complemented, Sylow
387C22×Q8—431no—
388C22×D4—431no—
389C23×C4—861no—
390C23×C4—861no—
391C23×C4—861no—
392C2×SD16—434no—
393C2×SD16—434no—
394C2×SD16—434no—
395C22×C8—431no—
396C22×C8—431no—
397C22×C8C22×D4311yescharacteristic
398C22×C8C22×D4311yescharacteristic
399C4×Q8—434no—
400C4×Q8—434no—
401C4×Q8—434no—
402C4×Q8—862no—
403C4×Q8—862no—
404C4×Q8—862no—
405C4×D4—434no—
406C4×D4—434no—
407C4×D4—434no—
408C4×D4—862no—
409C4×D4—862no—
410C4×D4—862no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—431no—
426C2×C42—431no—
427C2×C42—861no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42—861no—
431C2×C42—861no—
432C2×C42—861no—
433C2×C42—861no—
434C2×C42C22×D4311yescharacteristic
435#107—434no—
436#107C4×D4314yescomplemented
437#106C4×D4314yescomplemented
438#103—434no—
439#103—434no—
440#103—434no—
441#102—434no—
442#102—434no—
443#102—434no—
444#97—434no—
445#97—862no—
446#97C4×D4314yescomplemented
447C4×C8—434no—
448C4×C8—862no—
449C4×C8—862no—
450#95—21no—
451#95—21no—
452#95—431no—
453#95—431no—
454#95—431no—
455#95—431no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460C24—861no—
461C2×Q8—432no—
462C2×Q8—432no—
463C2×Q8—432no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×D4—432no—
468C2×D4—432no—
469C2×D4—432no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—864no—
482C22×C4—864no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—864no—
487C22×C4—3441no—
488C22×C4—3441no—
489C22×C4—3441no—
490C22×C4—3441no—
491C22×C4—3441no—
492C22×C4—3441no—
493C22×C4D4×D4311yescharacteristic
494C22×C4D4×D4311yescharacteristic
495C22×C4C23×D4311yescharacteristic
496SD16—4316no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—432no—
500C2×C8—432no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8C2×C4×D4312yes—
506C2×C8C2×C4×D4312yes—
507C2×C8C2×C4×D4312yes—
508C2×C8C2×C4×D4312yes—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—432no—
514C4⋊C4—432no—
515C4⋊C4—864no—
516C4⋊C4—864no—
517C4⋊C4—864no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4C2×C4×D4312yes—
521C4⋊C4C2×C4×D4312yes—
522C4⋊C4C2×C4×D4312yes—
523C4⋊C4C2×C4×D4312yes—
524C22⋊C4—864no—
525C22⋊C4—864no—
526C22⋊C4—864no—
527C42—81no—
528C42—81no—
529C42—432no—
530C42—432no—
531C42—432no—
532C42—432no—
533C42—864no—
534C42—864no—
535C42—864no—
536C42—3441no—
537C42—3441no—
538C42—3441no—
539C42—3441no—
540C42C2×C4×D4312yes—
541C42#1062190212yes—
542C23—862no—
543C23—862no—
544C23—862no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23—1721no—
549C23C2×D4×D4311yescharacteristic
550Q8—434no—
551Q8—862no—
552Q8—862no—
553Q8—862no—
554D4—434no—
555D4—862no—
556D4—862no—
557D4—862no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—432no—
575C2×C4—432no—
576C2×C4—432no—
577C2×C4—432no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—3444no—
592C2×C4—3444no—
593C2×C4—3444no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4#1306328712yes—
599C2×C4#1306328712yes—
600C2×C4C22×C4×D4311yescharacteristic
601C2×C4C22×C4×D4311yescharacteristic
602C2×C4C22×C4×D4311yescharacteristic
603C2×C4#41×D4311yescharacteristic
604C2×C4#41×D4311yescharacteristic
605C2×C4C2×#1062190211yescharacteristic
606C8—22no—
607C8—862no—
608C8—862no—
609C8C42×D4314yes—
610C22—864no—
611C22—1722no—
612C22—1722no—
613C22—1722no—
614C22—1722no—
615C22—1722no—
616C22—1722no—
617C22C4×D4×D4311yescharacteristic
618C22C4×D4×D4311yescharacteristic
619C22C2×#1306328711yescharacteristic
620C22#1458370311yescharacteristic
621C22#1458370811yescharacteristic
622C22#1458370911yescharacteristic
623C22#1458371511yescharacteristic
624C4—22no—
625C4—22no—
626C4—42no—
627C4—42no—
628C4—42no—
629C4—42no—
630C4—862no—
631C4—862no—
632C4—862no—
633C4—862no—
634C4—864no—
635C4—1722no—
636C4—1722no—
637C4C2×C42×D4311yescharacteristic
638C4#1458336711yescharacteristic
639C4C4×#1062190211yescharacteristic
640C4C4×#1062190211yescharacteristic
641C2—1724no—
642C2C4×#1306328711yescharacteristic
643C2#1914342411yescharacteristic
644C2#1914342511yescharacteristic
645C2#1914343611yescharacteristic
646C2#1914343711yescharacteristic
647C2#1914345111yescharacteristic
648C2#1914346711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC43×#1776C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1776D43
hypocenterC43#20504
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1776

Complements

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

NH ≅ G/Ntype
4. #19136959C2semidirect
6. #19134495C2semidirect
7. #107×Dic43C2semidirect
8. #19134424C2semidirect
10. C4×#13063248C2semidirect
11. #19134414C2semidirect
14. #19134283C2semidirect
15. C43×#1776C2semidirect
23. #14583001C4semidirect
24. #14582998C4semidirect
25. #14582986C4semidirect
73. C4×Dic86C2×C4semidirect
76. #13063290C2×C4semidirect
77. #13063290C2×C4semidirect
101. #13063259C2×C4semidirect
102. #13063250C2×C4semidirect
103. #13063248C2×C4semidirect
104. #13063248C2×C4semidirect
109. #13063235C2×C4semidirect
112. C8×Dic43C2×C4semidirect
130. #107×C43C2×C4semidirect
131. #106×C43C2×C4semidirect
132. #97×C43C2×C4semidirect
216. #10621873C42semidirect
323. #1776D43semidirect
386. C43#20504semidirect
436. #107C4×D43semidirect
437. #106C4×D43semidirect
446. #97C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830012
C2×#145829982
C2×#145829862
#191369592
#191369552
#191344952
#107×Dic432
#191344242
#191344192
C4×#130632482
#191344142
C4×#130632452
#191344092
#191342832
C43×#17762
#2050443