Finite Group Databasebeta

← #25156733

Subgroups — #25156733

Order 11008.

826 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×#14583123C211yesmaximal, characteristic
2#19138387C211yesmaximal, characteristic
3Q8×Dic43⋊C4C211yesmaximal, characteristic, complemented
4#19136120C211yesmaximal, characteristic
5#19136084C211yesmaximal, characteristic, complemented
6#19136006C211yesmaximal, characteristic, complemented
7#19135832C211yesmaximal, characteristic
8#19135278C211yesmaximal, characteristic
9#19135152C211yesmaximal, characteristic, complemented
10#19134950C211yesmaximal, characteristic
11#19134948C211yesmaximal, characteristic
12#19134938C211yesmaximal, characteristic, complemented
13#19134849C211yesmaximal, characteristic, complemented
14#19134847C211yesmaximal, characteristic, complemented
15C2×C4×Q16×C43C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063314C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20#14583123—24no—
21C2×#13063258C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29#14582834—21no—
30#14582825—21no—
31#14582806C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582800C2211yescharacteristic
34#14582797—21no—
35#14582797C2211yescharacteristic
36#14582795—21no—
37#14582795C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582790—21no—
40#14582790—21no—
41#14582768—21no—
42#14582768C2211yescharacteristic
43C4×Dic43⋊C4—21no—
44C4×Dic43⋊C4C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×Q16×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C4×Q16×C43—24no—
57C2×#107×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C2×#10621884—22no—
63C2×#10621884—22no—
64C2×#10621884—22no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063314—22no—
68#13063314—41no—
69Q8×Dic43—22no—
70Q8×Dic43—22no—
71Q8×Dic43—22no—
72Q8×Dic43—41no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4D411yescharacteristic
84C2×Dic43⋊C4D411yescharacteristic
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063258—41no—
96Dic43⋊C8—22no—
97#13063249—22no—
98#13063249—22no—
99#13063249—22no—
100#13063247—22no—
101#13063247—22no—
102#13063245—41no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95D411yescharacteristic
109C43⋊#95D411yescharacteristic
110C22×Q8×C43C2311yescharacteristic
111C22×Q8×C43C2311yescharacteristic
112C2×Q16×C43—22no—
113C2×Q16×C43—22no—
114C2×Q16×C43D414yes—
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C4×Q8×C43—22no—
118C4×Q8×C43—22no—
119C4×Q8×C43—41no—
120C4×Q8×C43—41no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C42×C43—21no—
126C2×C42×C43—21no—
127C2×C42×C43C2311yescharacteristic
128#107×C43—22no—
129#103×C43—22no—
130#103×C43—22no—
131C4×C8×C43—22no—
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—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43C2×D412yes—
142C2×Q8×C43C2×D412yes—
143C2×Q8×C43#4112yes—
144C2×Q8×C43#4112yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165Q16×C43—28no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C2×D412yes—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43—42no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—42no—
181C42×C43—42no—
182#10621884—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—
188(C2×D43)⋊C4—81no—
189C4⋊Dic43—24no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—42no—
196C4⋊Dic43#4112yes—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—42no—
200Dic43⋊C4—81no—
201Dic43⋊C4—81no—
202Dic43⋊C4—81no—
203Dic43⋊C4—81no—
204C4×Dic43—24no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—42no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C23×C43C22×D411yescharacteristic
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224Q8×C43—22no—
225Q8×C43—22no—
226Q8×C43—22no—
227Q8×C43—22no—
228Q8×C43—22no—
229Q8×C43—41no—
230Q8×C43—41no—
231Q8×C43#12314yes—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—22no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43#13712yes—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C432−1+411yescharacteristic
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—22no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43#13512yes—
277D172—41no—
278D172—41no—
279D172—41no—
280D172—41no—
281C8×C43—22no—
282C8×C43—41no—
283C43⋊C8—41no—
284C43⋊C8—41no—
285#26169—431nomaximal, Sylow
286C22×C43#52511yescharacteristic
287C22×C43D4211yescharacteristic
288C22×C43#54811yescharacteristic
289C22×C43C2×#13511yescharacteristic
290C22×C43C2×#13711yescharacteristic
291C22×C43#57611yescharacteristic
292C22×C43#57811yescharacteristic
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C4×C43—24no—
301C4×C43—22no—
302C4×C43—42no—
303C4×C43—41no—
304C4×C43—81no—
305C4×C43—81no—
306C4×C43C2×#12311yescharacteristic
307C4×C43#53911yescharacteristic
308C4×C43#54711yescharacteristic
309C4×C43#55311yescharacteristic
310Dic43—22no—
311Dic43—41no—
312Dic43—42no—
313Dic43—41no—
314Dic43—41no—
315Dic43—81no—
316Dic43—81no—
317C2×#464—431no—
318C2×C4×Q16D4311yescharacteristic, complemented
319#2448—431no—
320Q8×C4⋊C4—431no—
321#2093—431no—
322#2086—431no—
323#2072—431no—
324#2042—431no—
325#1934—431no—
326#1916—431no—
327#1880—431no—
328#1880—431no—
329#1878—431no—
330#1863—431no—
331#1863—431no—
332C2×C43#244311yescharacteristic
333C2×C43#310811yescharacteristic
334C2×C43#312411yescharacteristic
335C2×C43#327011yescharacteristic
336C2×C43#328711yescharacteristic
337C2×C43#336411yescharacteristic
338C2×C43#337511yescharacteristic
339D43—161no—
340C22×Q16C2×D4311yescharacteristic
341C22×SD16—431no—
342C2×#124—431no—
343C2×C4×Q8—431no—
344C2×C4×Q8—431no—
345C2×C4×Q8C2×D4311yescharacteristic
346C2×C4×Q8C2×D4311yescharacteristic
347#464—864no—
348C4×Q16—24no—
349C2×#107—431no—
350C2×#107C2×D4311yescharacteristic
351C2×C4⋊C8—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#103C2×D4311yescharacteristic
356C2×#103C2×D4311yescharacteristic
357C2×#102—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×C4×C8C2×D4311yescharacteristic
361#399—861no—
362#397—861no—
363#391—431no—
364#390—431no—
365#390—431no—
366#389—431no—
367#389—431no—
368#389—431no—
369#389—861no—
370#389—861no—
371#388—861no—
372#388—861no—
373#384—431no—
374#384—861no—
375C4×C4⋊C4—431no—
376C4×C4⋊C4—861no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#336—431no—
382#336—431no—
383#336—431no—
384#336—431no—
385C43#2616911yescharacteristic, complemented, Sylow
386C22×Q8C22×D4311yescharacteristic
387C22×Q8C22×D4311yescharacteristic
388C22×D4—431no—
389C2×Q16—22no—
390C2×Q16—22no—
391C2×Q16C22⋊D4314yes—
392C2×SD16—862no—
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—22no—
402C4×Q8—22no—
403C4×Q8—41no—
404C4×Q8—41no—
405C4×Q8—862no—
406C4×Q8—862no—
407C4×Q8—862no—
408C4×Q8—1721no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
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⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—861no—
436C2×C42—861no—
437C2×C42C22×D4311yescharacteristic
438#107—22no—
439#107—1721no—
440C4⋊C8—862no—
441#103—22no—
442#103—22no—
443#103—862no—
444#103—862no—
445#103—862no—
446#102—862no—
447#102—862no—
448#102—1721no—
449C4×C8—22no—
450#95—431no—
451#95—431no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457C24—861no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8#1062189812yes—
467C2×Q8#1062189812yes—
468C2×Q8C2×C22⋊D4312yes—
469C2×Q8C2×C22⋊D4312yes—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4D4×D4311yescharacteristic
488C22×C4D4×D4311yescharacteristic
489C22×C4C23×D4311yescharacteristic
490Q16—28no—
491SD16—1724no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8C2×C22⋊D4312yes—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—432no—
511C4⋊C4—862no—
512C4⋊C4—864no—
513C4⋊C4—862no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—3441no—
520C4⋊C4—3441no—
521C4⋊C4—3441no—
522C4⋊C4—3441no—
523C4⋊C4—1722no—
524C4⋊C4—1722no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—1722no—
528C22⋊C4—1722no—
529C22⋊C4—1722no—
530C22⋊C4—1722no—
531C42—21no—
532C42—21no—
533C42—42no—
534C42—42no—
535C42—864no—
536C42—861no—
537C42—861no—
538C42—861no—
539C42—861no—
540C42—1722no—
541C23—1721no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23C2×D4×D4311yescharacteristic
549Q8—22no—
550Q8—22no—
551Q8—22no—
552Q8—22no—
553Q8—22no—
554Q8—41no—
555Q8—41no—
556Q8#1306330814yes—
557D4—1721no—
558D4—1721no—
559D4—1721no—
560D4—1721no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—432no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—862no—
582C2×C4—861no—
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—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4#1306335712yes—
600C2×C4C22×C22⋊D4311yescharacteristic
601C2×C4#41×D4311yescharacteristic
602C2×C4C2×#1062189811yescharacteristic
603C2×C4C2×#1062189811yescharacteristic
604C2×C4#1306337011yescharacteristic
605C2×C4#1306337211yescharacteristic
606C8—22no—
607C8—41no—
608C8—1721no—
609C8—1721no—
610C22—3441no—
611C22—3441no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22—3441no—
616C22—3441no—
617C22#1458340811yescharacteristic
618C22D4×C22⋊D4311yescharacteristic
619C22#1458355811yescharacteristic
620C22#135×D4311yescharacteristic
621C22C2×#1306335711yescharacteristic
622C22#1458370111yescharacteristic
623C22#1458371211yescharacteristic
624C4—24no—
625C4—22no—
626C4—42no—
627C4—41no—
628C4—81no—
629C4—81no—
630C4—862no—
631C4—3441no—
632C4—3441no—
633C4—1721no—
634C4—1721no—
635C4—1722no—
636C4—1721no—
637C4C2×#1306330811yescharacteristic
638C4#1458349111yescharacteristic
639C4#1458354811yescharacteristic
640C4#1458359811yescharacteristic
641C2—6881no—
642C2#1913832411yescharacteristic
643C2#1914467911yescharacteristic
644C2#1914486311yescharacteristic
645C2#1914616511yescharacteristic
646C2#1914634911yescharacteristic
647C2#1914728111yescharacteristic
648C2#1914740711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C4×Q16×C43C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenterC2×C4×Q16D43
hypocenterC43#26169
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. Q8×Dic43⋊C4C2semidirect
5. #19136084C2semidirect
6. #19136006C2semidirect
9. #19135152C2semidirect
12. #19134938C2semidirect
13. #19134849C2semidirect
14. #19134847C2semidirect
15. C2×C4×Q16×C43C2semidirect
318. C2×C4×Q16D43semidirect
385. C43#26169semidirect

Maximal subgroups

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

subgroupindex
C2×#145831232
#191383872
Q8×Dic43⋊C42
#191361202
#191360842
#191360062
#191358322
#191352782
#191351522
#191349502
#191349482
#191349382
#191348492
#191348472
C2×C4×Q16×C432
#2616943