Finite Group Databasebeta

← #25146345

Subgroups — #25146345

Order 11008.

788 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×#14583122C211yesmaximal, characteristic
2#19140083C211yesmaximal, characteristic
3#19139965C211yesmaximal, characteristic, complemented
4#19135975C211yesmaximal, characteristic, complemented
5#19135968C211yesmaximal, characteristic
6#19135918C211yesmaximal, characteristic, complemented
7#19135913C211yesmaximal, characteristic
8#19135466C211yesmaximal, characteristic, complemented
9#19135449C211yesmaximal, characteristic
10#19135411C211yesmaximal, characteristic
11#19135359C211yesmaximal, characteristic, complemented
12#19135292C211yesmaximal, characteristic
13#19135271C211yesmaximal, characteristic, complemented
14#19134426C211yesmaximal, characteristic, complemented
15C2×C43×#446C211yesmaximal, characteristic, complemented
16C22×Dic172C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14583122—24no—
21C2×#13063257C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31#14582832—21no—
32#14582832—21no—
33#14582825—21no—
34#14582810—21no—
35#14582806—21no—
36#14582805C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582805C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582801C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582797C2211yescharacteristic
44#14582795—21no—
45#14582789—21no—
46#14582789—21no—
47#14582769C2211yescharacteristic
48C4×C4⋊Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C43×#446—24no—
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic
59C2×#97×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⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
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×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92#13063257—41no—
93#13063257—41no—
94#13063250—22no—
95#13063250—22no—
96#13063250—22no—
97#13063250—22no—
98#13063250—41no—
99#13063247—22no—
100#13063247—22no—
101#13063247—41no—
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—
129#97×C43—22no—
130#97×C43—22no—
131C4×C8×C43—22no—
132C23×D43—21no—
133C2×Q8×C43—22no—
134C2×Q8×C43—22no—
135C2×Q8×C43—41no—
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—
205C4⋊Dic43—42no—
206C4⋊Dic43—81no—
207Dic43⋊C4—42no—
208Dic43⋊C4—81no—
209Dic43⋊C4—81no—
210C4×Dic43—42no—
211C4×Dic43—81no—
212Dic172—44no—
213#10621873—44no—
214C23×C43C22×D411yescharacteristic
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222Q8×C43—44no—
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—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43#12112yes—
239C2×C4×C43#12112yes—
240C2×C4×C43#13712yes—
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C2×Dic43—22no—
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—
266C2×Dic43—41no—
267C2×Dic43—41no—
268D172—41no—
269D172—41no—
270D172—41no—
271D172—41no—
272Dic86—22no—
273Dic86—22no—
274Dic86—41no—
275Dic86—41no—
276Dic86—41no—
277Dic86—41no—
278Dic86—41no—
279Dic86—41no—
280C8×C43—22no—
281C8×C43—22no—
282C8×C43—22no—
283C8×C43—41no—
284#25311—431nomaximal, Sylow
285C22×C43C2×#12111yescharacteristic
286C22×C43#54811yescharacteristic
287C22×C43#55011yescharacteristic
288C22×C43C2×#13711yescharacteristic
289C22×C43#57511yescharacteristic
290C22×C43#57711yescharacteristic
291C22×C43#57711yescharacteristic
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C2×D43—81no—
299C4×C43—22no—
300C4×C43—22no—
301C4×C43—22no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43#52911yescharacteristic
306C4×C43#54211yescharacteristic
307C4×C43#54611yescharacteristic
308C4×C43#54811yescharacteristic
309Dic43—42no—
310Dic43—81no—
311Dic43—81no—
312Dic43—81no—
313Dic43—81no—
314Dic43—81no—
315Dic43—81no—
316C2×#464—431no—
317C2×#446D4311yescharacteristic, complemented
318#2592—431no—
319#2582—431no—
320#2066—431no—
321#2065—431no—
322#2056—431no—
323#2055—431no—
324#1971—431no—
325#1968—431no—
326#1959—431no—
327#1948—431no—
328#1936—431no—
329#1933—431no—
330#1763—431no—
331C2×C43#242611yescharacteristic
332C2×C43#305611yescharacteristic
333C2×C43#306011yescharacteristic
334C2×C43#336911yescharacteristic
335C2×C43#337111yescharacteristic
336C2×C43#340011yescharacteristic
337C2×C43#340111yescharacteristic
338D43—161no—
339C22×Q16—431no—
340C22×SD16—431no—
341C2×#124—431no—
342C2×C4×Q8—431no—
343C2×C4×Q8C2×D4311yescharacteristic
344#464—864no—
345#446—24no—
346C2×#106—431no—
347C2×#106—431no—
348C2×C4⋊C8C2×D4311yescharacteristic
349C2×C4⋊C8C2×D4311yescharacteristic
350C2×C4⋊C8C2×D4311yescharacteristic
351C2×#103—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#103—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#97C2×D4311yescharacteristic
360C2×#97C2×D4311yescharacteristic
361C2×C4×C8C2×D4311yescharacteristic
362#398—861no—
363#398—861no—
364#397—861no—
365#393—861no—
366#391—431no—
367#391—431no—
368#391—431no—
369#391—431no—
370#391—861no—
371#390—431no—
372#390—431no—
373#389—431no—
374#389—431no—
375#389—861no—
376#388—861no—
377#388—861no—
378#384—431no—
379C4×C4⋊C4—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384C43#2531111yescharacteristic, complemented, Sylow
385C22×Q8—431no—
386C22×Q8—431no—
387C22×Q8D17211yescharacteristic
388C22×D4—431no—
389C2×Q16—862no—
390C2×Q16—862no—
391C2×Q16—1721no—
392C2×SD16—862no—
393C2×SD16—862no—
394C2×SD16—1721no—
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397C22×C8C22×D4311yescharacteristic
398C22×C8C22×D4311yescharacteristic
399#124—862no—
400#124—862no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—862no—
404C4×Q8—862no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4D17211yescharacteristic
416C2×C4⋊C4D17211yescharacteristic
417C2×C4⋊C4D17211yescharacteristic
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C42—861no—
425C2×C42—861no—
426C2×C42C22×D4311yescharacteristic
427C2×C42C22×D4311yescharacteristic
428C2×C42C22×D4311yescharacteristic
429#106—1721no—
430#106—1721no—
431C4⋊C8—22no—
432C4⋊C8—22no—
433C4⋊C8C22⋊D4314yes—
434#103—862no—
435#103—862no—
436#103—862no—
437#103—862no—
438#103—1721no—
439#102—862no—
440#102—862no—
441#102—1721no—
442#97—22no—
443#97—22no—
444C4×C8—22no—
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—
454#95—861no—
455#95—861no—
456C24—861no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—41no—
460C2×Q8—432no—
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×Q8—861no—
471C2×Q8—861no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4C2×D17211yescharacteristic
486C22×C4C2×D17211yescharacteristic
487C22×C4C2×D17211yescharacteristic
488C22×C4C2×D17211yescharacteristic
489C22×C4C2×D17211yescharacteristic
490C22×C4C2×D17211yescharacteristic
491C22×C4C23×D4311yescharacteristic
492Q16—1724no—
493SD16—1724no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8#1062190212yes—
504C2×C8C2×C22⋊D4312yes—
505C2×C8C2×C22⋊D4312yes—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
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—861no—
518C4⋊C4—861no—
519C4⋊C4—3441no—
520C4⋊C4—3441no—
521C4⋊C4—3441no—
522C4⋊C4—1722no—
523C4⋊C4—1722no—
524C22⋊C4—3441no—
525C22⋊C4—3441no—
526C22⋊C4—1722no—
527C22⋊C4—1722no—
528C22⋊C4—1722no—
529C22⋊C4—1722no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—3441no—
535C42—1722no—
536C42#1062189812yes—
537C42C2×C22⋊D4312yes—
538C23—1721no—
539C23—1721no—
540C23—1721no—
541C23—1721no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23C22×D17211yescharacteristic
546Q8—44no—
547Q8—862no—
548Q8—862no—
549Q8—1721no—
550Q8—1721no—
551Q8—1721no—
552Q8—1721no—
553Q8—1721no—
554Q8—1721no—
555D4—1721no—
556D4—1721no—
557D4—1721no—
558D4—1721no—
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—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—862no—
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—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4#1306329912yes—
596C2×C4#1306329912yes—
597C2×C4#1306335812yes—
598C2×C4C22×C22⋊D4311yescharacteristic
599C2×C4#41×D4311yescharacteristic
600C2×C4C2×#1062189811yescharacteristic
601C2×C4C2×#1062190211yescharacteristic
602C2×C4#1306337111yescharacteristic
603C2×C4#1306337311yescharacteristic
604C8—22no—
605C8—22no—
606C8—22no—
607C8—41no—
608C22—3441no—
609C22—3441no—
610C22—3441no—
611C22—3441no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22C2×#1306329911yescharacteristic
616C22#1458356111yescharacteristic
617C22#1458357111yescharacteristic
618C22C2×#1306335811yescharacteristic
619C22#1458369911yescharacteristic
620C22#1458371111yescharacteristic
621C22#1458371111yescharacteristic
622C4—22no—
623C4—22no—
624C4—22no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—3441no—
629C4—3441no—
630C4—3441no—
631C4—3441no—
632C4—3441no—
633C4—3441no—
634C4—1722no—
635C4#1458343611yescharacteristic
636C4#1458352111yescharacteristic
637C4#1458353711yescharacteristic
638C4#1458356011yescharacteristic
639C2—6881no—
640C2#1913815511yescharacteristic
641C2#1914422511yescharacteristic
642C2#1914425711yescharacteristic
643C2#1914733711yescharacteristic
644C2#1914736511yescharacteristic
645C2#1914765011yescharacteristic
646C2#1914766311yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#446C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenterC2×#446D43
hypocenterC43#25311
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
3. #19139965C2semidirect
4. #19135975C2semidirect
6. #19135918C2semidirect
8. #19135466C2semidirect
11. #19135359C2semidirect
13. #19135271C2semidirect
14. #19134426C2semidirect
15. C2×C43×#446C2semidirect
317. C2×#446D43semidirect
384. C43#25311semidirect

Maximal subgroups

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

subgroupindex
C2×#145831222
#191400832
#191399652
#191359752
#191359682
#191359182
#191359132
#191354662
#191354492
#191354112
#191353592
#191352922
#191352712
#191344262
C2×C43×#4462
#2531143