Finite Group Databasebeta

← #25146341

Subgroups — #25146341

Order 11008.

858 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583097C211yesmaximal, characteristic
2C2×#14583027C211yesmaximal, characteristic, complemented
3#19139959C211yesmaximal, characteristic, complemented
4#19139596C211yesmaximal, characteristic
5#19135978C211yesmaximal, characteristic, complemented
6#19135969C211yesmaximal, characteristic, complemented
7#19135910C211yesmaximal, characteristic, complemented
8#19135908C211yesmaximal, characteristic, complemented
9#19135446C211yesmaximal, characteristic, complemented
10#19135417C211yesmaximal, characteristic
11#19135360C211yesmaximal, characteristic, complemented
12#19135292C211yesmaximal, characteristic, complemented
13#19135280C211yesmaximal, characteristic, complemented
14#19134427C211yesmaximal, characteristic, complemented
15C43×#1973C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063321C2211yescharacteristic
18C2×#13063311—21no—
19C2×Q8×Dic43C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21#14583097—24no—
22#14583027—24no—
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063235C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35#14582841—21no—
36#14582820—21no—
37#14582815—21no—
38#14582814—21no—
39#14582806C2211yescharacteristic
40#14582802C2211yescharacteristic
41#14582801C2211yescharacteristic
42#14582800C2211yescharacteristic
43#14582799—21no—
44#14582798C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582786—21no—
47#14582782—21no—
48#14582764C2211yescharacteristic
49C4⋊C4×Dic43C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic
59C43×#391C2211yescharacteristic
60C43×#390C2211yescharacteristic
61C22×Dic86D411yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C22×C22⋊D43—21no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063321—22no—
71#13063321—22no—
72#13063311—44no—
73Q8×Dic43—22no—
74Q8×Dic43—22no—
75C4×Dic86—22no—
76C4×Dic86—22no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43D411yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4D411yescharacteristic
85C2×Dic43⋊C4D411yescharacteristic
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96#13063256—41no—
97C4⋊(C43⋊C8)—22no—
98Dic43⋊C8—22no—
99Dic43⋊C8D414yes—
100#13063249—22no—
101#13063247—22no—
102#13063247—22no—
103#13063246—22no—
104#13063246—41no—
105#13063245—41no—
106#13063235—22no—
107C8×Dic43—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C22×Q8×C43C2311yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C2×SD16×C43—22no—
118C2×SD16×C43—22no—
119C2×SD16×C43—41no—
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C42×C43C2311yescharacteristic
127#107×C43—41no—
128#103×C43—22no—
129#102×C43—22no—
130#97×C43—22no—
131#95×C43—21no—
132#95×C43—21no—
133C24×C43—21no—
134C23×D43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43#4112yes—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C2×C22⋊D43—42no—
154C2×C22⋊D43—42no—
155C2×C22⋊D43—42no—
156C2×C22⋊D43—42no—
157C2×C22⋊D43—81no—
158C2×C22⋊D43—81no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×Dic86—22no—
173C2×Dic86—22no—
174C2×Dic86—41no—
175SD16×C43—44no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43C2×D412yes—
181C2×C8×C43#4112yes—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C22⋊C4×C43—42no—
187C22⋊C4×C43—81no—
188C42×C43—21no—
189C42×C43—21no—
190C22⋊Dic43—42no—
191C22⋊Dic43—81no—
192#10621884—44no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—81no—
196(C2×D43)⋊C4—81no—
197C4⋊Dic43—22no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—42no—
205C4⋊Dic43—42no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—42no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—42no—
212C4×Dic43—42no—
213C4×Dic43C2×D412yes—
214C4×Dic43#4112yes—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8C2×D412yes—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43C22×D411yescharacteristic
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236Q8×C43—22no—
237Q8×C43—22no—
238Q8×C43—41no—
239Q8×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—22no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43H(5,𝔽2)11yescharacteristic
264C2×C4×C432−1+411yescharacteristic
265C22⋊D43—84no—
266C22⋊D43—84no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43#12112yes—
286C2×Dic43#12112yes—
287C2×Dic43AGL(1,ℤ/8)12yes—
288D172—41no—
289D172—41no—
290D172—41no—
291D172—41no—
292Dic86—44no—
293C8×C43—22no—
294C8×C43—22no—
295C43⋊C8—22no—
296C43⋊C8—41no—
297#25310—431nomaximal, Sylow
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43C2×#12111yescharacteristic
306C22×C43#54811yescharacteristic
307C22×C43#55011yescharacteristic
308C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
309C22×C43#57511yescharacteristic
310C22×C43#57711yescharacteristic
311C22×C43#57711yescharacteristic
312C2×D43—81no—
313C2×D43—81no—
314C2×D43—81no—
315C2×D43—81no—
316C2×D43—81no—
317C2×D43—81no—
318C2×D43—81no—
319C4×C43—42no—
320C4×C43—41no—
321C4×C43—41no—
322C4×C43—81no—
323C4×C43—81no—
324C4×C43#52911yescharacteristic
325C4×C43#54211yescharacteristic
326C4×C43#54611yescharacteristic
327C4×C43#54811yescharacteristic
328Dic43—22no—
329Dic43—22no—
330Dic43—22no—
331Dic43—41no—
332Dic43—81no—
333Dic43—81no—
334Dic43—81no—
335C2×#460—431no—
336C2×#446—431no—
337#2581—431no—
338#2548—431no—
339#2067—431no—
340#2065—431no—
341#2055—431no—
342#2055—431no—
343#1973D4311yescharacteristic, complemented
344#1968—431no—
345#1961—431no—
346#1949—431no—
347#1936—431no—
348#1934—431no—
349#1763—431no—
350C2×C43—161no—
351C2×C43#242611yescharacteristic
352C2×C43#305511yescharacteristic
353C2×C43#305711yescharacteristic
354C2×C43#336811yescharacteristic
355C2×C43#337111yescharacteristic
356C2×C43#339711yescharacteristic
357C2×C43#340111yescharacteristic
358D43—161no—
359C22×SD16—431no—
360C22×SD16C2×D4311yescharacteristic
361C2×#127—431no—
362C2×#124—861no—
363C2×C4×Q8—431no—
364C2×C4×Q8—431no—
365#460—864no—
366#446—864no—
367C2×#107C2×D4311yescharacteristic
368C2×#106—431no—
369C2×C4⋊C8—431no—
370C2×C4⋊C8—431no—
371C2×C4⋊C8—431no—
372C2×#103—431no—
373C2×#103C2×D4311yescharacteristic
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×#102—431no—
379C2×#102C2×D4311yescharacteristic
380C2×#97—431no—
381C2×#97C2×D4311yescharacteristic
382C2×C4×C8—431no—
383#400—861no—
384#395—861no—
385#394—861no—
386#394—861no—
387#391—431no—
388#391C2×D4311yescharacteristic
389#390—431no—
390#390—431no—
391#390—431no—
392#390—861no—
393#390C2×D4311yescharacteristic
394#389—431no—
395#389—431no—
396#387—861no—
397#387—861no—
398#382—431no—
399C4×C4⋊C4—431no—
400#340—431no—
401#340—431no—
402#340—431no—
403#340—431no—
404C43#2531011yescharacteristic, complemented, Sylow
405C22×Q8—431no—
406C22×Q8C22×D4311yescharacteristic
407C22×D4—431no—
408C22×D4—861no—
409C22×D4—861no—
410C22×D4C22×D4311yescharacteristic
411C2×SD16—22no—
412C2×SD16—22no—
413C2×SD16—41no—
414C2×SD16—862no—
415C2×SD16—862no—
416C2×SD16—1721no—
417C22×C8—431no—
418C22×C8—431no—
419C22×C8C22×D4311yescharacteristic
420C22×C8C22×D4311yescharacteristic
421#127—862no—
422#127—862no—
423#124—1724no—
424C4×Q8—862no—
425C4×Q8—862no—
426C4×Q8—862no—
427C4×Q8—862no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C42—431no—
448C2×C42—431no—
449C2×C42—861no—
450C2×C42—861no—
451C2×C42C22×D4311yescharacteristic
452#107—41no—
453#106—1721no—
454C4⋊C8—434no—
455C4⋊C8—862no—
456C4⋊C8—862no—
457#103—22no—
458#103—862no—
459#102—22no—
460#102—862no—
461#102—862no—
462#102—862no—
463#102—1721no—
464#102—1721no—
465#97—22no—
466#97—862no—
467C4×C8—862no—
468#95—21no—
469#95—21no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477C24—21no—
478C24—861no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—862no—
485C2×Q8—862no—
486C2×Q8—1721no—
487C2×Q8#1062189812yes—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—861no—
495C2×D4—861no—
496C2×D4—861no—
497C2×D4—861no—
498C2×D4—861no—
499C2×D4—861no—
500C2×D4—3441no—
501C2×D4—3441no—
502C2×D4—1722no—
503C2×D4—1722no—
504C2×D4—1722no—
505C2×D4—1722no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4D4×D4311yescharacteristic
517C22×C4D4×D4311yescharacteristic
518C22×C4C23×D4311yescharacteristic
519SD16—44no—
520SD16—1724no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—432no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8D4×D4312yes—
532C2×C8#1062190012yes—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—862no—
538C4⋊C4—862no—
539C4⋊C4—862no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—1722no—
547C4⋊C4—1722no—
548C4⋊C4—1722no—
549C22⋊C4—42no—
550C22⋊C4—81no—
551C22⋊C4—3441no—
552C22⋊C4—3441no—
553C22⋊C4—3441no—
554C22⋊C4—1722no—
555C22⋊C4—1722no—
556C22⋊C4—1722no—
557C42—21no—
558C42—21no—
559C42—432no—
560C42—432no—
561C42—861no—
562C42—861no—
563C42—1722no—
564C42—1722no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—1721no—
573C23—1721no—
574C23—1721no—
575C23—1721no—
576C23—1721no—
577C23—1721no—
578C23—1721no—
579C23C2×D4×D4311yescharacteristic
580Q8—22no—
581Q8—22no—
582Q8—41no—
583Q8—41no—
584Q8—1724no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—41no—
589D4—3444no—
590D4—3444no—
591D4—1721no—
592D4—1721no—
593D4—1721no—
594D4—1721no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—432no—
611C2×C4—432no—
612C2×C4—432no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4C2×D4×D4311yescharacteristic
632C2×C4#41×D4311yescharacteristic
633C2×C4C2×#1062190011yescharacteristic
634C2×C4C2×#1062189811yescharacteristic
635C2×C4#1306337011yescharacteristic
636C2×C4#1306337211yescharacteristic
637C8—22no—
638C8—22no—
639C8—862no—
640C8—1721no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—3441no—
649C22—3441no—
650C22—3441no—
651C22—3441no—
652C22—3441no—
653C22—3441no—
654C22—3441no—
655C22#121×D4311yescharacteristic
656C22#1458355811yescharacteristic
657C22#1458356911yescharacteristic
658C22AGL(1,ℤ/8)×D4311yescharacteristic
659C22#1458369811yescharacteristic
660C22#1458370811yescharacteristic
661C22#1458370911yescharacteristic
662C4—41no—
663C4—41no—
664C4—42no—
665C4—81no—
666C4—81no—
667C4—862no—
668C4—862no—
669C4—862no—
670C4—3441no—
671C4—3441no—
672C4—3441no—
673C4—1721no—
674C4#1458342911yescharacteristic
675C4#1458351311yescharacteristic
676C4#1458353911yescharacteristic
677C4#1458355511yescharacteristic
678C2—161no—
679C2—6881no—
680C2#1913815811yescharacteristic
681C2#1914420911yescharacteristic
682C2#1914423211yescharacteristic
683C2#1914732511yescharacteristic
684C2#1914736811yescharacteristic
685C2#1914761211yescharacteristic
686C2#1914766011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1973C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
hypercenter#1973D43
hypocenterC43#25310
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1973

Complements

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

NH ≅ G/Ntype
2. C2×#14583027C2semidirect
3. #19139959C2semidirect
5. #19135978C2semidirect
6. #19135969C2semidirect
7. #19135910C2semidirect
8. #19135908C2semidirect
9. #19135446C2semidirect
11. #19135360C2semidirect
12. #19135292C2semidirect
13. #19135280C2semidirect
14. #19134427C2semidirect
15. C43×#1973C2semidirect
343. #1973D43semidirect
404. C43#25310semidirect

Maximal subgroups

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

subgroupindex
C2×#145830972
C2×#145830272
#191399592
#191395962
#191359782
#191359692
#191359102
#191359082
#191354462
#191354172
#191353602
#191352922
#191352802
#191344272
C43×#19732
#2531043