Finite Group Databasebeta

← #25146142

Subgroups — #25146142

Order 11008.

848 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583114C211yesmaximal, characteristic
2C2×C8×Dic86C211yesmaximal, characteristic, complemented
3#19140078C211yesmaximal, characteristic, complemented
4#19139949C211yesmaximal, characteristic, complemented
5#19135991C211yesmaximal, characteristic, complemented
6#19135970C211yesmaximal, characteristic, complemented
7#19135911C211yesmaximal, characteristic, complemented
8#19135904C211yesmaximal, characteristic
9#19135458C211yesmaximal, characteristic
10#19135450C211yesmaximal, characteristic, complemented
11#19135406C211yesmaximal, characteristic, complemented
12#19135363C211yesmaximal, characteristic, complemented
13#19135276C211yesmaximal, characteristic, complemented
14#19135269C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14583114—24no—
21C8×Dic86—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35#14582835—21no—
36#14582826—21no—
37#14582812—21no—
38#14582811—21no—
39#14582804C2211yescharacteristic
40#14582804C2211yescharacteristic
41#14582802C2211yescharacteristic
42#14582802C2211yescharacteristic
43#14582800C2211yescharacteristic
44#14582800C2211yescharacteristic
45#14582795C2211yescharacteristic
46#14582795C2211yescharacteristic
47#14582790—21no—
48#14582790—21no—
49#14582772—21no—
50#14582772—21no—
51#14582765C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86D411yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C2×#10621883—22no—
65C2×#10621883—22no—
66C2×#10621883—41no—
67C2×#10621882—22no—
68C2×#10621882—22no—
69C2×#10621882—41no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063313—22no—
73#13063313—22no—
74C4×Dic86—22no—
75C4×Dic86—22no—
76C2×C4⋊Dic43D411yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4D411yescharacteristic
82C2×Dic43⋊C4D411yescharacteristic
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063258—41no—
96#13063256—41no—
97C4⋊(C43⋊C8)D414yes—
98Dic43⋊C8—22no—
99Dic43⋊C8—22no—
100#13063250—22no—
101#13063250—41no—
102#13063248—22no—
103#13063247—22no—
104#13063247—41no—
105#13063245—22no—
106C8×Dic43—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—
115C43⋊#95—21no—
116C22×D4×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C4×D4×C43—22no—
121C4×D4×C43—22no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C42×C43—21no—
127C2×C42×C43C2311yescharacteristic
128#102×C43—22no—
129#102×C43—22no—
130C4×C8×C43—22no—
131#95×C43—21no—
132C24×C43—21no—
133C23×D43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43#4112yes—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—42no—
144C22×C4×C43—81no—
145C22×C4×C43—81no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×Dic86—22no—
163C2×Dic86—22no—
164C2×Dic86—22no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43#4112yes—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C22⋊C4×C43—42no—
184C42×C43—81no—
185C42×C43C2×D412yes—
186C42×C43#4112yes—
187C22⋊Dic43—42no—
188C22⋊Dic43—42no—
189C22⋊Dic43—81no—
190C22⋊Dic43—81no—
191#10621883—44no—
192#10621882—44no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—81no—
198(C2×D43)⋊C4—81no—
199C4⋊Dic43—22no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—81no—
207Dic43⋊C4—81no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8C2×D412yes—
217C2×C43⋊C8C2×D412yes—
218C23×C43—22no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43C22×D411yescharacteristic
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233D4×C43—22no—
234D4×C43—22no—
235D4×C43—41no—
236D4×C43—41no—
237C2×C4×C43—21no—
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—41no—
250C2×C4×C43—84no—
251C2×C4×C43#12112yes—
252C2×C4×C43#12112yes—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×C4×C432−1+411yescharacteristic
259C2×Dic43—21no—
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—21no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43#13512yes—
279C2×Dic43#13512yes—
280D172—41no—
281D172—41no—
282D172—41no—
283D172—41no—
284Dic86—28no—
285Dic86—41no—
286Dic86—41no—
287Dic86—41no—
288Dic86—41no—
289C8×C43—22no—
290C8×C43—41no—
291C43⋊C8—22no—
292C43⋊C8—22no—
293#25296—431nomaximal, Sylow
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—42no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43C2×#12111yescharacteristic
302C22×C43#54811yescharacteristic
303C22×C43#55011yescharacteristic
304C22×C43C2×#13511yescharacteristic
305C22×C43C2×#13511yescharacteristic
306C22×C43#57611yescharacteristic
307C22×C43#57711yescharacteristic
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C2×D43—81no—
315C4×C43—22no—
316C4×C43—22no—
317C4×C43—81no—
318C4×C43—81no—
319C4×C43—81no—
320C4×C43#52911yescharacteristic
321C4×C43#54211yescharacteristic
322C4×C43#54611yescharacteristic
323C4×C43#54811yescharacteristic
324Dic43—22no—
325Dic43—22no—
326Dic43—41no—
327Dic43—41no—
328Dic43—81no—
329Dic43—81no—
330Dic43—81no—
331C2×#463—431no—
332C2×C8×Q8—431no—
333#2592—431no—
334#2580—431no—
335#2068—431no—
336#2065—431no—
337#2055—431no—
338#2054—431no—
339#1970—431no—
340#1968—431no—
341#1958—431no—
342#1949—431no—
343#1934—431no—
344#1933—431no—
345C4×#102D4311yescharacteristic, complemented
346C2×C43—82no—
347C2×C43#242611yescharacteristic
348C2×C43#305011yescharacteristic
349C2×C43#306211yescharacteristic
350C2×C43#336011yescharacteristic
351C2×C43#336111yescharacteristic
352C2×C43#339411yescharacteristic
353C2×C43#339611yescharacteristic
354D43—161no—
355C22×SD16—431no—
356C22×D8—431no—
357C2×#124—431no—
358C2×C4×Q8—431no—
359C2×C4×D4C2×D4311yescharacteristic
360#463—864no—
361C8×Q8—864no—
362C2×#107—431no—
363C2×#106—431no—
364C2×C4⋊C8—431no—
365C2×C4⋊C8—431no—
366C2×C4⋊C8—431no—
367C2×#103—431no—
368C2×#103—431no—
369C2×#103—431no—
370C2×#102—431no—
371C2×#102—431no—
372C2×#102—431no—
373C2×#102C2×D4311yescharacteristic
374C2×#102C2×D4311yescharacteristic
375C2×C4×C8—431no—
376C2×C4×C8—431no—
377C2×C4×C8C2×D4311yescharacteristic
378#399—861no—
379#397—861no—
380#393—861no—
381#393—861no—
382#391—431no—
383#391—431no—
384#390—431no—
385#390—431no—
386#390—431no—
387#390—431no—
388#389—431no—
389#389—431no—
390#388—861no—
391#388—861no—
392#385—861no—
393#385—861no—
394#382—431no—
395C4×C4⋊C4C2×D4311yescharacteristic
396#340—431no—
397#340—431no—
398#340C2×D4311yescharacteristic
399#340C2×D4311yescharacteristic
400C43#2529611yescharacteristic, complemented, Sylow
401C22×Q8—431no—
402C22×Q8—431no—
403C22×D4—431no—
404C22×D4C22×D4311yescharacteristic
405C23×C4—21no—
406C2×SD16—862no—
407C2×SD16—862no—
408C2×SD16—1721no—
409C2×D8—862no—
410C2×D8—862no—
411C2×D8—1721no—
412C22×C8—431no—
413C22×C8—431no—
414C22×C8C22×D4311yescharacteristic
415C22×C8C22×D4311yescharacteristic
416#124—862no—
417#124—862no—
418C4×Q8—862no—
419C4×Q8—862no—
420C4×D4—22no—
421C4×D4—22no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C42—21no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42C22×D4311yescharacteristic
447#107—1721no—
448#106—1721no—
449C4⋊C8—434no—
450C4⋊C8—862no—
451C4⋊C8—862no—
452#103—862no—
453#103—862no—
454#103—1721no—
455#102—22no—
456#102—22no—
457#102—862no—
458#102—862no—
459#102—1721no—
460C4×C8—22no—
461C4×C8—862no—
462C4×C8—862no—
463#95—21no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472C24—21no—
473C24—861no—
474C2×Q8—862no—
475C2×Q8—862no—
476C2×Q8—862no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8—861no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—861no—
489C2×D4—861no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4#1062189812yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—42no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4D4×D4311yescharacteristic
509C22×C4D4×D4311yescharacteristic
510C22×C4C23×D4311yescharacteristic
511SD16—1724no—
512D8—1724no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—432no—
519C2×C8—432no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8#1062189812yes—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—862no—
532C4⋊C4—862no—
533C4⋊C4—862no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—3441no—
539C4⋊C4—3441no—
540C22⋊C4—42no—
541C22⋊C4—3441no—
542C22⋊C4—3441no—
543C22⋊C4—3441no—
544C22⋊C4—3441no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C22⋊C4—1722no—
548C22⋊C4—1722no—
549C22⋊C4—1722no—
550C22⋊C4—1722no—
551C42—81no—
552C42—861no—
553C42—861no—
554C42—861no—
555C42—861no—
556C42#1062189812yes—
557C42D4×D4312yes—
558C23—22no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23—1721no—
571C23—1721no—
572C23C2×D4×D4311yescharacteristic
573Q8—868no—
574Q8—1721no—
575Q8—1721no—
576Q8—1721no—
577Q8—1721no—
578D4—22no—
579D4—22no—
580D4—41no—
581D4—41no—
582D4—1721no—
583D4—1721no—
584D4—1721no—
585D4—1721no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—84no—
600C2×C4—432no—
601C2×C4—432no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4#1306329812yes—
622C2×C4#1306329812yes—
623C2×C4C2×D4×D4311yescharacteristic
624C2×C4C2×#1062189811yescharacteristic
625C2×C4C2×#1062189811yescharacteristic
626C2×C4C2×#1062189811yescharacteristic
627C2×C4#1306337111yescharacteristic
628C2×C4#1306337211yescharacteristic
629C8—22no—
630C8—41no—
631C8—862no—
632C8—862no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—3441no—
641C22—3441no—
642C22—3441no—
643C22—3441no—
644C22—3441no—
645C22—3441no—
646C22—3441no—
647C22C2×#1306329811yescharacteristic
648C22#1458355811yescharacteristic
649C22#1458357011yescharacteristic
650C22#135×D4311yescharacteristic
651C22#135×D4311yescharacteristic
652C22#1458370011yescharacteristic
653C22#1458370511yescharacteristic
654C4—22no—
655C4—22no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4—862no—
660C4—862no—
661C4—3441no—
662C4—3441no—
663C4—3441no—
664C4—1721no—
665C4—1721no—
666C4#1458343311yescharacteristic
667C4#1458352011yescharacteristic
668C4#1458354511yescharacteristic
669C4#1458355811yescharacteristic
670C2—82no—
671C2—6881no—
672C2#1913816111yescharacteristic
673C2#1914417511yescharacteristic
674C2#1914427311yescharacteristic
675C2#1914724511yescharacteristic
676C2#1914725611yescharacteristic
677C2#1914759211yescharacteristic
678C2#1914760711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenterC4×#102D43
hypocenterC43#25296
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic86C2semidirect
3. #19140078C2semidirect
4. #19139949C2semidirect
5. #19135991C2semidirect
6. #19135970C2semidirect
7. #19135911C2semidirect
10. #19135450C2semidirect
11. #19135406C2semidirect
12. #19135363C2semidirect
13. #19135276C2semidirect
14. #19135269C2semidirect
15. C4×#102×C43C2semidirect
345. C4×#102D43semidirect
400. C43#25296semidirect

Maximal subgroups

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

subgroupindex
C2×#145831142
C2×C8×Dic862
#191400782
#191399492
#191359912
#191359702
#191359112
#191359042
#191354582
#191354502
#191354062
#191353632
#191352762
#191352692
C4×#102×C432
#2529643