Finite Group Databasebeta

← #25156682

Subgroups — #25156682

Order 11008.

832 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583124C211yesmaximal, characteristic
2C2×#14582986C211yesmaximal, characteristic
3#19138385C211yesmaximal, characteristic
4#19137512C211yesmaximal, characteristic, complemented
5#19136094C211yesmaximal, characteristic, complemented
6#19136009C211yesmaximal, characteristic
7#19135832C211yesmaximal, characteristic
8#19135268C211yesmaximal, characteristic, complemented
9#19135153C211yesmaximal, characteristic, complemented
10#19134949C211yesmaximal, characteristic
11#19134939C211yesmaximal, characteristic, complemented
12#19134933C211yesmaximal, characteristic, complemented
13#19134846C211yesmaximal, characteristic, complemented
14#19134839C211yesmaximal, characteristic
15C43×#2097C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C2×#13063314C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23#14583124—24no—
24#14582986—24no—
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582828—21no—
34#14582826—21no—
35#14582806C2211yescharacteristic
36#14582801C2211yescharacteristic
37#14582796—21no—
38#14582796—21no—
39#14582795C2211yescharacteristic
40#14582795C2211yescharacteristic
41#14582795C2211yescharacteristic
42#14582773—21no—
43#14582763—21no—
44#14582761—21no—
45C4×C4⋊Dic43C2211yescharacteristic
46#14582750—21no—
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#382C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C2×#10621885—22no—
65C2×#10621885—22no—
66C2×#10621885—22no—
67C2×#10621873—22no—
68C2×#10621873—22no—
69C2×#10621873D414yes—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063314—22no—
73#13063314—41no—
74C4×Dic86—22no—
75C4×Dic86—22no—
76#13063290—22no—
77#13063290—22no—
78#13063290—41no—
79#13063290—41no—
80#13063287—22no—
81#13063287—41no—
82C2×C4⋊Dic43D411yescharacteristic
83C2×C4⋊Dic43D411yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102Dic43⋊C8—22no—
103#13063250—22no—
104#13063249—22no—
105#13063248—22no—
106#13063247—22no—
107#13063245—22no—
108#13063245—22no—
109C8×Dic43—22no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C22×Q8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C42×C43C2311yescharacteristic
124#107×C43—41no—
125#106×C43—22no—
126#103×C43—22no—
127#103×C43—41no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43—21no—
131#95×C43—21no—
132C23×D43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172C2×D412yes—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—81no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86C2×D412yes—
166C2×Dic86#4112yes—
167C2×Dic86#4112yes—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43C2×D412yes—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C42×C43—21no—
181C42×C43—21no—
182#10621885—44no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—42no—
187(C2×D43)⋊C4—81no—
188C4⋊Dic43—21no—
189C4⋊Dic43—22no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—41no—
193C4⋊Dic43#4112yes—
194Dic43⋊C4—24no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—81no—
200C4×Dic43—24no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—42no—
206C4×Dic43—42no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213#10621873—28no—
214C23×C43C22×D411yescharacteristic
215C22×D43—22no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—41no—
225Q8×C43—41no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
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×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C2×Dic43—22no—
251C2×Dic43—21no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43#13512yes—
271D172—22no—
272D172—22no—
273D172—41no—
274D172—41no—
275C4×D43—84no—
276Dic86—22no—
277Dic86—22no—
278Dic86—22no—
279Dic86#12314yes—
280C8×C43—22no—
281C8×C43—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#26165—431nomaximal, Sylow
285C22×C43#52511yescharacteristic
286C22×C43D4211yescharacteristic
287C22×C43#54811yescharacteristic
288C22×C43C2×#13511yescharacteristic
289C22×C43#57511yescharacteristic
290C22×C43#57711yescharacteristic
291C22×C43#57811yescharacteristic
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—42no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C2×D43—81no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43—81no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43—81no—
305C4×C43C2×#12311yescharacteristic
306C4×C43#53911yescharacteristic
307C4×C43#54711yescharacteristic
308C4×C43#55311yescharacteristic
309Dic43—24no—
310Dic43—22no—
311Dic43—42no—
312Dic43—41no—
313Dic43—41no—
314Dic43—41no—
315Dic43—81no—
316C2×#464—431no—
317C2×C4×SD16—431no—
318#2447—431no—
319#2351—431no—
320#2097D4311yescharacteristic, complemented
321#2088—431no—
322#2073—431no—
323#2042—431no—
324#1933—431no—
325#1916—431no—
326#1880—431no—
327#1878—431no—
328#1878—431no—
329#1863—431no—
330#1862—431no—
331C2×C43#244311yescharacteristic
332C2×C43#310211yescharacteristic
333C2×C43#312111yescharacteristic
334C2×C43#326911yescharacteristic
335C2×C43#328211yescharacteristic
336C2×C43#336411yescharacteristic
337C2×C43#337111yescharacteristic
338D43—82no—
339C22×Q16—431no—
340C22×SD16—431no—
341C2×#124—431no—
342C2×C4×Q8—431no—
343C2×C4×Q8—431no—
344C2×C4×Q8—431no—
345C2×C4×D4—431no—
346#464—864no—
347C4×SD16—864no—
348C2×#107C2×D4311yescharacteristic
349C2×#106C2×D4311yescharacteristic
350C2×C4⋊C8—431no—
351C2×#103—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#103C2×D4311yescharacteristic
355C2×#103C2×D4311yescharacteristic
356C2×#102—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×C4×C8—431no—
360#397—861no—
361#397—861no—
362#391—431no—
363#391C2×D4311yescharacteristic
364#390—431no—
365#389—431no—
366#389—431no—
367#389—431no—
368#389—861no—
369#389—861no—
370#385—861no—
371#382—861no—
372#382C2×D4311yescharacteristic
373#381—861no—
374C4×C4⋊C4—431no—
375C4×C4⋊C4—861no—
376#340—431no—
377#340—431no—
378#340—431no—
379#340—431no—
380#336—431no—
381#336—431no—
382#336—431no—
383#336C2×D4311yescharacteristic
384C43#2616511yescharacteristic, complemented, Sylow
385C22×Q8—431no—
386C22×Q8C22×D4311yescharacteristic
387C22×D4—431no—
388C23×C4—861no—
389C2×Q16—862no—
390C2×Q16—862no—
391C2×Q16—862no—
392C2×SD16—434no—
393C2×SD16—862no—
394C2×SD16—862no—
395C22×C8—431no—
396C22×C8—431no—
397C22×C8C22×D4311yescharacteristic
398C22×C8C22×D4311yescharacteristic
399#124—862no—
400#124—1721no—
401C4×Q8—862no—
402C4×Q8—862no—
403C4×Q8—862no—
404C4×Q8—862no—
405C4×Q8—1721no—
406C4×Q8—1721no—
407C4×D4—862no—
408C4×D4—1721no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C42—431no—
428C2×C42—431no—
429C2×C42—861no—
430C2×C42—861no—
431C2×C42—861no—
432C2×C42C22×D4311yescharacteristic
433#107—41no—
434#106—22no—
435C4⋊C8—862no—
436#103—22no—
437#103—41no—
438#103—862no—
439#103—862no—
440#103—862no—
441#102—862no—
442#102—862no—
443#102—862no—
444C4×C8—862no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—431no—
450#95—431no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456C24—861no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—432no—
464C2×Q8—432no—
465C2×Q8—432no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×D4—432no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—3441no—
487C22×C4—1722no—
488C22×C4—1722no—
489C22×C4D4×D4311yescharacteristic
490C22×C4D4×D4311yescharacteristic
491C22×C4C23×D4311yescharacteristic
492Q16—1724no—
493SD16—868no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8D4×D4312yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—432no—
513C4⋊C4—862no—
514C4⋊C4—864no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—3441no—
519C4⋊C4—1721no—
520C4⋊C4—1722no—
521C4⋊C4—1722no—
522C4⋊C4—1722no—
523C4⋊C4—1722no—
524C22⋊C4—3441no—
525C22⋊C4—1722no—
526C22⋊C4—1722no—
527C22⋊C4—1722no—
528C22⋊C4—1722no—
529C42—21no—
530C42—21no—
531C42—864no—
532C42—861no—
533C42—861no—
534C42—861no—
535C42—861no—
536C42—1722no—
537C42—1722no—
538C23—862no—
539C23—1721no—
540C23—1721no—
541C23—1721no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23C2×D4×D4311yescharacteristic
546Q8—41no—
547Q8—41no—
548Q8—41no—
549Q8—41no—
550Q8—434no—
551Q8—862no—
552Q8—862no—
553Q8—862no—
554D4—862no—
555D4—862no—
556D4—1721no—
557D4—1721no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
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—41no—
575C2×C4—41no—
576C2×C4—432no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—3444no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4C2×D4×D4311yescharacteristic
599C2×C4#41×D4311yescharacteristic
600C2×C4#41×D4311yescharacteristic
601C2×C4#41×D4311yescharacteristic
602C2×C4#1306337011yescharacteristic
603C2×C4#1306337311yescharacteristic
604C8—22no—
605C8—41no—
606C8—1721no—
607C8—1721no—
608C22—3441no—
609C22—3441no—
610C22—3441no—
611C22—3441no—
612C22—1722no—
613C22—1722no—
614C22—1722no—
615C22#1458340711yescharacteristic
616C22#1458353411yescharacteristic
617C22#1458355911yescharacteristic
618C22#135×D4311yescharacteristic
619C22#1458369811yescharacteristic
620C22#1458370611yescharacteristic
621C22#1458371511yescharacteristic
622C4—41no—
623C4—41no—
624C4—81no—
625C4—81no—
626C4—81no—
627C4—81no—
628C4—864no—
629C4—862no—
630C4—3441no—
631C4—1721no—
632C4—1721no—
633C4—1721no—
634C4—1722no—
635C4#123×D4311yescharacteristic
636C4#1458349511yescharacteristic
637C4#1458355111yescharacteristic
638C4#1458359411yescharacteristic
639C2—3442no—
640C2#1913833311yescharacteristic
641C2#1914461611yescharacteristic
642C2#1914482711yescharacteristic
643C2#1914614911yescharacteristic
644C2#1914630111yescharacteristic
645C2#1914728311yescharacteristic
646C2#1914736611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2097C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2097D43
hypocenterC43#26165
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2097

Complements

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

NH ≅ G/Ntype
4. #19137512C2semidirect
5. #19136094C2semidirect
8. #19135268C2semidirect
9. #19135153C2semidirect
11. #19134939C2semidirect
12. #19134933C2semidirect
13. #19134846C2semidirect
15. C43×#2097C2semidirect
320. #2097D43semidirect
384. C43#26165semidirect

Maximal subgroups

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

subgroupindex
C2×#145831242
C2×#145829862
#191383852
#191375122
#191360942
#191360092
#191358322
#191352682
#191351532
#191349492
#191349392
#191349332
#191348462
#191348392
C43×#20972
#2616543