Finite Group Databasebeta

← #25156624

Subgroups — #25156624

Order 11008.

840 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583122C211yesmaximal, characteristic
2C2×C4×#10621873C211yesmaximal, characteristic
3#19138382C211yesmaximal, characteristic
4C4⋊C4×Dic86C211yesmaximal, characteristic, complemented
5#19136137C211yesmaximal, characteristic, complemented
6#19136093C211yesmaximal, characteristic, complemented
7#19136000C211yesmaximal, characteristic
8#19135837C211yesmaximal, characteristic
9#19135271C211yesmaximal, characteristic, complemented
10#19134949C211yesmaximal, characteristic
11#19134935C211yesmaximal, characteristic, complemented
12#19134935C211yesmaximal, characteristic, complemented
13#19134866C211yesmaximal, characteristic, complemented
14#19134859C211yesmaximal, characteristic
15C43×#1916C211yesmaximal, characteristic, complemented
16C22×Dic172C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23#14583122—24no—
24C4×#10621873—24no—
25C2×#13063257C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35#14582828—21no—
36#14582825—21no—
37#14582805C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582796—21no—
44#14582796—21no—
45#14582770—21no—
46#14582769C2211yescharacteristic
47#14582768—21no—
48#14582761—21no—
49C4⋊C4×Dic43—21no—
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C2×Dic172—22no—
66C2×Dic172—22no—
67C2×Dic172—22no—
68C2×#10621873—22no—
69C2×#10621873—22no—
70C2×#10621873D414yes—
71#13063313—22no—
72#13063313—41no—
73C4×Dic86—22no—
74C4×Dic86—22no—
75C4×Dic86—22no—
76C4×Dic86—22no—
77C4×Dic86—41no—
78C4×Dic86—41no—
79C4×D172—22no—
80C4×D172—41no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102#13063257—22no—
103#13063257—41no—
104#13063250—22no—
105#13063250—22no—
106#13063250—22no—
107#13063250—22no—
108#13063250—41no—
109#13063247—22no—
110#13063247—22no—
111#13063247—22no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C2×C4⋊C4×C43D411yescharacteristic
124C2×C4⋊C4×C43D411yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127C2×C42×C43C2311yescharacteristic
128C4⋊C8×C43—22no—
129C4×C8×C43—22no—
130#95×C43D411yescharacteristic
131#95×C43D411yescharacteristic
132C23×D43—21no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172C2×D412yes—
153C2×C4×D43—42no—
154C2×C4×D43—42no—
155C2×C4×D43—81no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
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×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C2×D412yes—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—22no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—81no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—42no—
203C4⋊Dic43—81no—
204C4⋊Dic43#4112yes—
205Dic43⋊C4—24no—
206Dic43⋊C4—42no—
207Dic43⋊C4—42no—
208Dic43⋊C4—81no—
209Dic43⋊C4—81no—
210Dic43⋊C4—81no—
211C4×Dic43—24no—
212C4×Dic43—42no—
213C4×Dic43—42no—
214Dic172—44no—
215#10621873—28no—
216C23×C43C22×D411yescharacteristic
217C22×D43—22no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
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—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43#13512yes—
241C2×C4×C43#13712yes—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269D172—22no—
270D172—22no—
271D172—41no—
272D172—41no—
273C4×D43—84no—
274Dic86—22no—
275Dic86—22no—
276Dic86—22no—
277Dic86—41no—
278Dic86—41no—
279Dic86—41no—
280Dic86—41no—
281Dic86#12314yes—
282C8×C43—22no—
283C8×C43—41no—
284C8×C43—41no—
285C8×C43—41no—
286#26161—431nomaximal, Sylow
287C22×C43#52511yescharacteristic
288C22×C43D4211yescharacteristic
289C22×C43#54811yescharacteristic
290C22×C43C2×#13511yescharacteristic
291C22×C43C2×#13711yescharacteristic
292C22×C43#57711yescharacteristic
293C22×C43#57711yescharacteristic
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C4×C43—22no—
302C4×C43—22no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43C2×#12311yescharacteristic
308C4×C43#53911yescharacteristic
309C4×C43#54711yescharacteristic
310C4×C43#55311yescharacteristic
311Dic43—24no—
312Dic43—42no—
313Dic43—81no—
314Dic43—81no—
315Dic43—81no—
316Dic43—81no—
317Dic43—81no—
318C2×#464—431no—
319C2×C4×SD16—431no—
320#2447—431no—
321Q8×C4⋊C4—431no—
322#2096—431no—
323#2088—431no—
324#2071—431no—
325#2042—431no—
326#1933—431no—
327#1916D4311yescharacteristic, complemented
328#1880—431no—
329#1878—431no—
330#1878—431no—
331#1865—431no—
332#1864—431no—
333C2×C43#244311yescharacteristic
334C2×C43#310811yescharacteristic
335C2×C43#312511yescharacteristic
336C2×C43#326611yescharacteristic
337C2×C43#328411yescharacteristic
338C2×C43#336511yescharacteristic
339C2×C43#336911yescharacteristic
340D43—82no—
341C22×Q16—431no—
342C22×SD16—431no—
343C2×#124—431no—
344C2×C4×Q8—431no—
345C2×C4×Q8—431no—
346C2×C4×Q8—431no—
347C2×C4×D4—431no—
348#464—864no—
349C4×SD16—864no—
350C2×#106—431no—
351C2×#106—431no—
352C2×C4⋊C8C2×D4311yescharacteristic
353C2×#103—431no—
354C2×#103—431no—
355C2×#103—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×C4×C8C2×D4311yescharacteristic
362#397—861no—
363#397—861no—
364#391—431no—
365#391—431no—
366#390—431no—
367#389—431no—
368#389—431no—
369#389—431no—
370#389—861no—
371#389—861no—
372#385—861no—
373#384—431no—
374#384—861no—
375#381—861no—
376C4×C4⋊C4—861no—
377C4×C4⋊C4C2×D4311yescharacteristic
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#336C2×D4311yescharacteristic
383#336C2×D4311yescharacteristic
384#336C2×D4311yescharacteristic
385#336C2×D4311yescharacteristic
386C43#2616111yescharacteristic, complemented, Sylow
387C22×Q8—431no—
388C22×Q8—431no—
389C22×D4—431no—
390C23×C4—861no—
391C2×Q16—862no—
392C2×Q16—862no—
393C2×Q16—862no—
394C2×SD16—434no—
395C2×SD16—862no—
396C2×SD16—862no—
397C22×C8C22×D4311yescharacteristic
398C22×C8C22×D4311yescharacteristic
399C22×C8C22×D4311yescharacteristic
400C22×C8C22×D4311yescharacteristic
401#124—862no—
402#124—1721no—
403C4×Q8—862no—
404C4×Q8—862no—
405C4×Q8—862no—
406C4×Q8—862no—
407C4×Q8—1721no—
408C4×Q8—1721no—
409C4×D4—862no—
410C4×D4—1721no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4D17211yescharacteristic
425C2×C4⋊C4D17211yescharacteristic
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C42—861no—
432C2×C42—861no—
433C2×C42—861no—
434C2×C42C22×D4311yescharacteristic
435C2×C42C22×D4311yescharacteristic
436C2×C42C22×D4311yescharacteristic
437#106—862no—
438#106—1721no—
439C4⋊C8—22no—
440#103—862no—
441#103—862no—
442#103—862no—
443#103—862no—
444#103—1721no—
445#102—862no—
446#102—862no—
447#102—862no—
448C4×C8—22no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95D17211yescharacteristic
457#95D17211yescharacteristic
458C24—861no—
459C2×Q8—432no—
460C2×Q8—432no—
461C2×Q8—432no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×D4—432no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—3441no—
485C22×C4—1722no—
486C22×C4—1722no—
487C22×C4C2×D17211yescharacteristic
488C22×C4C2×D17211yescharacteristic
489C22×C4C2×D17211yescharacteristic
490C22×C4C2×D17211yescharacteristic
491C22×C4C2×D17211yescharacteristic
492C22×C4C2×D17211yescharacteristic
493C22×C4C23×D4311yescharacteristic
494Q16—1724no—
495SD16—868no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8D4×D4312yes—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—432no—
511C4⋊C4—864no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—3441no—
522C4⋊C4—3441no—
523C4⋊C4—3441no—
524C4⋊C4—3441no—
525C4⋊C4—1722no—
526C4⋊C4—1722no—
527C4⋊C4—1722no—
528C22⋊C4—3441no—
529C22⋊C4—1722no—
530C22⋊C4—1722no—
531C22⋊C4—1722no—
532C22⋊C4—1722no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—864no—
540C42—1722no—
541C42—1722no—
542C23—862no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23—1721no—
549C23C22×D17211yescharacteristic
550Q8—434no—
551Q8—862no—
552Q8—862no—
553Q8—862no—
554Q8—1721no—
555Q8—1721no—
556Q8—1721no—
557Q8—1721no—
558D4—862no—
559D4—862no—
560D4—1721no—
561D4—1721no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—3444no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4#1306334712yes—
601C2×C4#1306335812yes—
602C2×C4C2×D4×D4311yescharacteristic
603C2×C4#41×D4311yescharacteristic
604C2×C4#41×D4311yescharacteristic
605C2×C4#41×D4311yescharacteristic
606C2×C4#1306337111yescharacteristic
607C2×C4#1306337311yescharacteristic
608C8—22no—
609C8—41no—
610C8—41no—
611C8—41no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22—3441no—
616C22—1722no—
617C22—1722no—
618C22—1722no—
619C22#1458341111yescharacteristic
620C22D4×D17211yescharacteristic
621C22#1458356111yescharacteristic
622C22C2×#1306334711yescharacteristic
623C22C2×#1306335811yescharacteristic
624C22#1458371111yescharacteristic
625C22#1458371111yescharacteristic
626C4—22no—
627C4—22no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—41no—
632C4—864no—
633C4—3441no—
634C4—3441no—
635C4—3441no—
636C4—3441no—
637C4—3441no—
638C4—1722no—
639C4#123×D4311yescharacteristic
640C4#1458349711yescharacteristic
641C4#1458355111yescharacteristic
642C4#1458360011yescharacteristic
643C2—3442no—
644C2#1913833511yescharacteristic
645C2#1914467711yescharacteristic
646C2#1914487411yescharacteristic
647C2#1914611011yescharacteristic
648C2#1914632711yescharacteristic
649C2#1914729311yescharacteristic
650C2#1914733711yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1916C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1916D43
hypocenterC43#26161
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
4. C4⋊C4×Dic86C2semidirect
5. #19136137C2semidirect
6. #19136093C2semidirect
9. #19135271C2semidirect
11. #19134935C2semidirect
12. #19134935C2semidirect
13. #19134866C2semidirect
15. C43×#1916C2semidirect
327. #1916D43semidirect
386. C43#26161semidirect

Maximal subgroups

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

subgroupindex
C2×#145831222
C2×C4×#106218732
#191383822
C4⋊C4×Dic862
#191361372
#191360932
#191360002
#191358372
#191352712
#191349492
#191349352
#191348662
#191348592
C43×#19162
#2616143