Finite Group Databasebeta

← #25146151

Subgroups — #25146151

Order 11008.

800 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583122C211yesmaximal, characteristic
2#19140083C211yesmaximal, characteristic
3#19139961C211yesmaximal, characteristic, complemented
4#19135982C211yesmaximal, characteristic
5#19135975C211yesmaximal, characteristic, complemented
6#19135918C211yesmaximal, characteristic, complemented
7#19135913C211yesmaximal, characteristic
8#19135456C211yesmaximal, characteristic, complemented
9#19135449C211yesmaximal, characteristic
10#19135406C211yesmaximal, characteristic
11#19135365C211yesmaximal, characteristic, complemented
12#19135278C211yesmaximal, characteristic
13#19135271C211yesmaximal, characteristic, complemented
14C4×#13063250C211yesmaximal, characteristic, complemented
15C2×C8×Q8×C43C211yesmaximal, characteristic, complemented
16C22×Dic172C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14583122—24no—
21C2×#13063259C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31#14582837—21no—
32#14582825—21no—
33#14582818—21no—
34#14582810—21no—
35#14582805C2211yescharacteristic
36#14582805C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582789—21no—
44#14582789—21no—
45#14582780—21no—
46#14582780—21no—
47#14582765C2211yescharacteristic
48C4×C4⋊Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C8×Q8×C43—24no—
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C2×C4×C8×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C2×Dic172—22no—
65C2×Dic172—22no—
66C2×Dic172—41no—
67C2×#10621873—22no—
68C2×#10621873—22no—
69C2×#10621873—41no—
70#13063313—22no—
71#13063313—22no—
72C4×Dic86—22no—
73C4×Dic86—22no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90#13063259—41no—
91#13063257—41no—
92#13063250—22no—
93#13063250—22no—
94#13063250—22no—
95#13063250—22no—
96#13063250—41no—
97#13063247—22no—
98#13063247—22no—
99#13063247—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×Q8×C43D411yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C4×Q8×C43—22no—
119C4×Q8×C43—22no—
120C2×C4⋊C4×C43D411yescharacteristic
121C2×C4⋊C4×C43D411yescharacteristic
122C2×C4⋊C4×C43D411yescharacteristic
123C2×C42×C43C2311yescharacteristic
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C4⋊C8×C43—22no—
127C4⋊C8×C43—22no—
128C4⋊C8×C43D414yes—
129C4×C8×C43—22no—
130C4×C8×C43—22no—
131C4×C8×C43—22no—
132C23×D43—21no—
133C2×Q8×C43—22no—
134C2×Q8×C43—22no—
135C2×Q8×C43—22no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2411yescharacteristic
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
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×Dic86—21no—
166C2×Dic86—21no—
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×C43C2×D412yes—
178C2×C8×C43C2×D412yes—
179C2×C8×C43#4112yes—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—22no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43C2×D412yes—
188C42×C43#4112yes—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—81no—
194(C2×D43)⋊C4—81no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205Dic43⋊C4—42no—
206Dic43⋊C4—42no—
207Dic43⋊C4—42no—
208C4×Dic43—42no—
209C4×Dic43—81no—
210Dic172—44no—
211#10621873—44no—
212C23×C43C22×D411yescharacteristic
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220Q8×C43—28no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
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#12112yes—
236C2×C4×C43#12112yes—
237C2×C4×C43#13512yes—
238C2×C4×C43#13512yes—
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C2×C4×C432−1+411yescharacteristic
245C2×Dic43—22no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
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—
266D172—41no—
267D172—41no—
268D172—41no—
269D172—41no—
270Dic86—22no—
271Dic86—22no—
272Dic86—41no—
273Dic86—41no—
274Dic86—41no—
275Dic86—41no—
276Dic86—41no—
277Dic86—41no—
278C8×C43—22no—
279C8×C43—22no—
280C8×C43—22no—
281C8×C43—41no—
282#25297—431nomaximal, Sylow
283C22×C43C2×#12111yescharacteristic
284C22×C43#54811yescharacteristic
285C22×C43#55011yescharacteristic
286C22×C43C2×#13511yescharacteristic
287C22×C43C2×#13511yescharacteristic
288C22×C43#57711yescharacteristic
289C22×C43#57811yescharacteristic
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C4×C43—22no—
298C4×C43—22no—
299C4×C43—22no—
300C4×C43—22no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43#52911yescharacteristic
304C4×C43#54211yescharacteristic
305C4×C43#54611yescharacteristic
306C4×C43#54811yescharacteristic
307Dic43—42no—
308Dic43—81no—
309Dic43—81no—
310Dic43—81no—
311Dic43—81no—
312Dic43—81no—
313Dic43—81no—
314C2×#464—431no—
315C2×C8×Q8D4311yescharacteristic, complemented
316#2592—431no—
317#2581—431no—
318#2067—431no—
319#2066—431no—
320#2056—431no—
321#2055—431no—
322#1969—431no—
323#1968—431no—
324#1958—431no—
325#1949—431no—
326#1934—431no—
327#1933—431no—
328C4×#103—431no—
329C2×C43#242611yescharacteristic
330C2×C43#305011yescharacteristic
331C2×C43#306311yescharacteristic
332C2×C43#336411yescharacteristic
333C2×C43#336511yescharacteristic
334C2×C43#339311yescharacteristic
335C2×C43#339411yescharacteristic
336D43—161no—
337C22×Q16—431no—
338C22×SD16—431no—
339C2×#124—431no—
340C2×C4×Q8—431no—
341C2×C4×Q8C2×D4311yescharacteristic
342#464—864no—
343C8×Q8—24no—
344C2×#107—431no—
345C2×#106—431no—
346C2×C4⋊C8C2×D4311yescharacteristic
347C2×C4⋊C8C2×D4311yescharacteristic
348C2×C4⋊C8C2×D4311yescharacteristic
349C2×#103—431no—
350C2×#103—431no—
351C2×#103—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×C4×C8C2×D4311yescharacteristic
358C2×C4×C8C2×D4311yescharacteristic
359C2×C4×C8C2×D4311yescharacteristic
360#400—861no—
361#397—861no—
362#395—861no—
363#393—861no—
364#391—431no—
365#391—431no—
366#391—431no—
367#391—431no—
368#390—431no—
369#390—431no—
370#389—431no—
371#389—431no—
372#388—861no—
373#388—861no—
374#387—861no—
375#387—861no—
376#382—431no—
377C4×C4⋊C4—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382C43#2529711yescharacteristic, complemented, Sylow
383C22×Q8—431no—
384C22×Q8—431no—
385C22×Q8D17211yescharacteristic
386C22×D4—431no—
387C2×Q16—862no—
388C2×Q16—862no—
389C2×Q16—1721no—
390C2×SD16—862no—
391C2×SD16—862no—
392C2×SD16—1721no—
393C22×C8C22×D4311yescharacteristic
394C22×C8C22×D4311yescharacteristic
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397#124—862no—
398#124—862no—
399C4×Q8—22no—
400C4×Q8—22no—
401C4×Q8—862no—
402C4×Q8—862no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4D17211yescharacteristic
412C2×C4⋊C4D17211yescharacteristic
413C2×C4⋊C4D17211yescharacteristic
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C42—861no—
421C2×C42—861no—
422C2×C42C22×D4311yescharacteristic
423C2×C42C22×D4311yescharacteristic
424C2×C42C22×D4311yescharacteristic
425#107—1721no—
426#106—1721no—
427C4⋊C8—22no—
428C4⋊C8—22no—
429C4⋊C8C22⋊D4314yes—
430#103—862no—
431#103—862no—
432#103—862no—
433#103—862no—
434#103—1721no—
435#102—862no—
436#102—862no—
437#102—1721no—
438C4×C8—22no—
439C4×C8—22no—
440C4×C8—22no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454C24—861no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—432no—
459C2×Q8—861no—
460C2×Q8—861no—
461C2×Q8—861no—
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×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4C2×D17211yescharacteristic
484C22×C4C2×D17211yescharacteristic
485C22×C4C2×D17211yescharacteristic
486C22×C4C2×D17211yescharacteristic
487C22×C4C2×D17211yescharacteristic
488C22×C4C2×D17211yescharacteristic
489C22×C4C23×D4311yescharacteristic
490Q16—1724no—
491SD16—1724no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8#1062190212yes—
502C2×C8C2×C22⋊D4312yes—
503C2×C8C2×C22⋊D4312yes—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—1722no—
518C4⋊C4—1722no—
519C4⋊C4—1722no—
520C22⋊C4—3441no—
521C22⋊C4—3441no—
522C22⋊C4—1722no—
523C22⋊C4—1722no—
524C22⋊C4—1722no—
525C22⋊C4—1722no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—3441no—
531C42—1722no—
532C42#1062189812yes—
533C42C2×C22⋊D4312yes—
534C23—1721no—
535C23—1721no—
536C23—1721no—
537C23—1721no—
538C23—1721no—
539C23—1721no—
540C23—1721no—
541C23C22×D17211yescharacteristic
542Q8—28no—
543Q8—862no—
544Q8—862no—
545Q8—1721no—
546Q8—1721no—
547Q8—1721no—
548Q8—1721no—
549Q8—1721no—
550Q8—1721no—
551D4—1721no—
552D4—1721no—
553D4—1721no—
554D4—1721no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—862no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4#1306329912yes—
591C2×C4#1306329912yes—
592C2×C4#1306334712yes—
593C2×C4#1306334712yes—
594C2×C4C22×C22⋊D4311yescharacteristic
595C2×C4#41×D4311yescharacteristic
596C2×C4C2×#1062189811yescharacteristic
597C2×C4C2×#1062190211yescharacteristic
598C2×C4#1306337111yescharacteristic
599C2×C4#1306337311yescharacteristic
600C8—22no—
601C8—22no—
602C8—22no—
603C8—41no—
604C22—3441no—
605C22—3441no—
606C22—3441no—
607C22—3441no—
608C22—3441no—
609C22—3441no—
610C22—3441no—
611C22C2×#1306329911yescharacteristic
612C22#1458356111yescharacteristic
613C22#1458357111yescharacteristic
614C22C2×#1306334711yescharacteristic
615C22C2×#1306334711yescharacteristic
616C22#1458371111yescharacteristic
617C22#1458371611yescharacteristic
618C4—22no—
619C4—22no—
620C4—22no—
621C4—22no—
622C4—41no—
623C4—41no—
624C4—3441no—
625C4—3441no—
626C4—3441no—
627C4—3441no—
628C4—3441no—
629C4—3441no—
630C4—1722no—
631C4#1458343611yescharacteristic
632C4#1458352111yescharacteristic
633C4#1458353711yescharacteristic
634C4#1458356011yescharacteristic
635C2—6881no—
636C2#1913815511yescharacteristic
637C2#1914417611yescharacteristic
638C2#1914428611yescharacteristic
639C2#1914728211yescharacteristic
640C2#1914729311yescharacteristic
641C2#1914758411yescharacteristic
642C2#1914759311yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C8×Q8×C43C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenterC2×C8×Q8D43
hypocenterC43#25297
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
3. #19139961C2semidirect
5. #19135975C2semidirect
6. #19135918C2semidirect
8. #19135456C2semidirect
11. #19135365C2semidirect
13. #19135271C2semidirect
14. C4×#13063250C2semidirect
15. C2×C8×Q8×C43C2semidirect
315. C2×C8×Q8D43semidirect
382. C43#25297semidirect

Maximal subgroups

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

subgroupindex
C2×#145831222
#191400832
#191399612
#191359822
#191359752
#191359182
#191359132
#191354562
#191354492
#191354062
#191353652
#191352782
#191352712
C4×#130632502
C2×C8×Q8×C432
#2529743