Finite Group Databasebeta

← #25156670

Subgroups — #25156670

Order 11008.

944 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583116C211yesmaximal, characteristic
2C2×#14582979C211yesmaximal, characteristic
3#19138385C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic43C211yesmaximal, characteristic, complemented
5#19136133C211yesmaximal, characteristic, complemented
6#19136092C211yesmaximal, characteristic, complemented
7#19136000C211yesmaximal, characteristic, complemented
8#19135833C211yesmaximal, characteristic, complemented
9#19135273C211yesmaximal, characteristic, complemented
10#19135151C211yesmaximal, characteristic, complemented
11#19134943C211yesmaximal, characteristic
12#19134931C211yesmaximal, characteristic, complemented
13#19134843C211yesmaximal, characteristic, complemented
14#19134840C211yesmaximal, characteristic, complemented
15C43×#1877C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×#13063314C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C22×C4⋊Dic43—21no—
22#14583116—24no—
23#14582979—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582828—21no—
35#14582826—21no—
36#14582806C2211yescharacteristic
37#14582801C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582795C2211yescharacteristic
41#14582774—21no—
42#14582774—21no—
43#14582773—21no—
44#14582769C2211yescharacteristic
45#14582761—21no—
46#14582759—21no—
47C4×C4⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C23×Dic43—21no—
63C23×Dic43—21no—
64C22×C4×D43—21no—
65C2×#10621882—22no—
66C2×#10621882—22no—
67C2×#10621882D414yes—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063314—22no—
71#13063314—41no—
72D4×Dic43—22no—
73D4×Dic43—22no—
74D4×Dic43—41no—
75D4×Dic43—41no—
76#13063287—22no—
77#13063287—41no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—44no—
83C2×C4⋊Dic43D411yescharacteristic
84C2×C4⋊Dic43D411yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×C4×Dic43C2311yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98#13063258—22no—
99#13063258—41no—
100Dic43⋊C8—22no—
101#13063249—22no—
102#13063249—41no—
103#13063247—22no—
104#13063247—22no—
105#13063246—22no—
106#13063245—22no—
107C8×Dic43—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95D411yescharacteristic
114C43⋊#95D411yescharacteristic
115C22×Q8×C43C2311yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C2×SD16×C43—22no—
119C2×SD16×C43—22no—
120C2×SD16×C43—22no—
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C4×D4×C43—22no—
124C4×D4×C43—22no—
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C22⋊C4×C43—21no—
128C2×C42×C43C2311yescharacteristic
129#103×C43—22no—
130#102×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—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43C2×D412yes—
145C2×D4×C43#4112yes—
146C2×D4×C43#4112yes—
147C22×C4×C43—24no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—42no—
152C22×C4×C43—42no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—42no—
160C22×Dic43—42no—
161C22×Dic43—42no—
162C22×Dic43—42no—
163C22×Dic43—81no—
164C22×Dic43—81no—
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172C2×D412yes—
175C2×C4×D43—42no—
176C2×C4×D43—42no—
177C2×C4×D43—81no—
178SD16×C43—44no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43#4112yes—
189C22⋊C4×C43—24no—
190C42×C43—21no—
191C42×C43—21no—
192C22⋊Dic43—42no—
193C22⋊Dic43—42no—
194#10621882—28no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—42no—
198(C2×D43)⋊C4—42no—
199(C2×D43)⋊C4—81no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—42no—
209C4⋊Dic43—42no—
210C4⋊Dic43—42no—
211C4⋊Dic43—81no—
212Dic43⋊C4—81no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8C2×D412yes—
223C23×C43—22no—
224C23×C43—22no—
225C23×C43—22no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43C22×D411yescharacteristic
231C22×D43—22no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238Q8×C43—41no—
239Q8×C43—41no—
240Q8×C43—41no—
241Q8×C43—41no—
242D4×C43—22no—
243D4×C43—22no—
244D4×C43—22no—
245D4×C43#12314yes—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—22no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—48no—
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×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43#13512yes—
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×C4×C432−1+411yescharacteristic
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—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—84no—
289C2×Dic43—84no—
290C2×Dic43AGL(1,ℤ/8)12yes—
291D172—22no—
292D172—22no—
293D172—41no—
294D172—41no—
295C4×D43—84no—
296C8×C43—41no—
297C8×C43—41no—
298C43⋊C8—22no—
299C43⋊C8—41no—
300#26164—431nomaximal, Sylow
301C22×C43—24no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43—42no—
306C22×C43—42no—
307C22×C43—42no—
308C22×C43#52511yescharacteristic
309C22×C43D4211yescharacteristic
310C22×C43#54811yescharacteristic
311C22×C43C2×#13511yescharacteristic
312C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C43#57611yescharacteristic
314C22×C43#57811yescharacteristic
315C2×D43—42no—
316C2×D43—42no—
317C2×D43—42no—
318C2×D43—81no—
319C2×D43—81no—
320C2×D43—81no—
321C2×D43—81no—
322C4×C43—22no—
323C4×C43—42no—
324C4×C43—41no—
325C4×C43—81no—
326C4×C43—81no—
327C4×C43C2×#12311yescharacteristic
328C4×C43#53911yescharacteristic
329C4×C43#54711yescharacteristic
330C4×C43#55311yescharacteristic
331Dic43—22no—
332Dic43—41no—
333Dic43—41no—
334Dic43—41no—
335Dic43—81no—
336Dic43—81no—
337Dic43—81no—
338C2×#463—431no—
339C2×C4×D8—431no—
340#2447—431no—
341D4×C4⋊C4—431no—
342#2095—431no—
343#2087—431no—
344#2071—431no—
345#2042—431no—
346#1933—431no—
347#1916—431no—
348#1879—431no—
349#1877—431no—
350#1877D4311yescharacteristic, complemented
351#1862—431no—
352#1862—431no—
353C2×C43—44no—
354C2×C43#244311yescharacteristic
355C2×C43#310511yescharacteristic
356C2×C43#312411yescharacteristic
357C2×C43#326411yescharacteristic
358C2×C43#328311yescharacteristic
359C2×C43#336111yescharacteristic
360C2×C43#336711yescharacteristic
361D43—82no—
362C22×SD16C2×D4311yescharacteristic
363C22×D8—431no—
364C2×#124—431no—
365C2×C4×D4—431no—
366C2×C4×D4—431no—
367C2×C4×D4—431no—
368C2×C4×D4C2×D4311yescharacteristic
369C22×C4⋊C4—861no—
370#463—864no—
371C4×D8—864no—
372C2×#107—431no—
373C2×#107—431no—
374C2×C4⋊C8—431no—
375C2×#103—431no—
376C2×#103—431no—
377C2×#103C2×D4311yescharacteristic
378C2×#102—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×#102—431no—
382C2×#102C2×D4311yescharacteristic
383C2×C4×C8—431no—
384#397—861no—
385#397—861no—
386#391—431no—
387#391C2×D4311yescharacteristic
388#390—431no—
389#389—431no—
390#389—431no—
391#389—431no—
392#385—861no—
393#385—861no—
394#385—861no—
395#384—431no—
396#381—861no—
397#380—861no—
398C4×C4⋊C4—431no—
399#340—431no—
400#340—431no—
401#340—431no—
402#340C2×D4311yescharacteristic
403#336—431no—
404#336—431no—
405#336—431no—
406#336C2×D4311yescharacteristic
407C43#2616411yescharacteristic, complemented, Sylow
408C22×Q8C22×D4311yescharacteristic
409C22×D4—431no—
410C22×D4C22×D4311yescharacteristic
411C23×C4—21no—
412C23×C4—861no—
413C23×C4—861no—
414C23×C4—861no—
415C2×SD16—22no—
416C2×SD16—22no—
417C2×SD16—22no—
418C2×D8—434no—
419C2×D8—862no—
420C2×D8—862no—
421C22×C8—431no—
422C22×C8—431no—
423C22×C8C22×D4311yescharacteristic
424C22×C8C22×D4311yescharacteristic
425#124—862no—
426#124—1721no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4—862no—
432C4×D4—1721no—
433C4×D4—1721no—
434C4×D4—1721no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—1724no—
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C42—431no—
457C2×C42—431no—
458C2×C42C22×D4311yescharacteristic
459#107—862no—
460#107—1721no—
461C4⋊C8—862no—
462#103—22no—
463#103—862no—
464#103—1721no—
465#102—22no—
466#102—862no—
467#102—862no—
468#102—862no—
469#102—862no—
470C4×C8—862no—
471#95—21no—
472#95—21no—
473#95—431no—
474#95—431no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479#95—861no—
480C24—21no—
481C24—861no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—432no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C2×D4—861no—
496C2×D4—861no—
497C2×D4#1062189812yes—
498C2×D4D4×D4312yes—
499C2×D4#1062190012yes—
500C22×C4—24no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—3441no—
514C22×C4—3441no—
515C22×C4—3441no—
516C22×C4—1722no—
517C22×C4—1722no—
518C22×C4—1722no—
519C22×C4—1722no—
520C22×C4—1722no—
521C22×C4—1722no—
522C22×C4D4×D4311yescharacteristic
523C22×C4D4×D4311yescharacteristic
524C22×C4C23×D4311yescharacteristic
525SD16—44no—
526D8—868no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—432no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—861no—
537C2×C8—861no—
538C2×C8—861no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—862no—
543C4⋊C4—862no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—3441no—
551C4⋊C4—3441no—
552C4⋊C4—1722no—
553C4⋊C4—1722no—
554C4⋊C4—1722no—
555C4⋊C4#1062190012yes—
556C22⋊C4—24no—
557C22⋊C4—3441no—
558C22⋊C4—1722no—
559C22⋊C4—1722no—
560C22⋊C4—1722no—
561C22⋊C4—1722no—
562C22⋊C4—1722no—
563C22⋊C4—1722no—
564C42—21no—
565C42—21no—
566C42—861no—
567C42—861no—
568C42—861no—
569C42—861no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—862no—
578C23—1721no—
579C23—1721no—
580C23—1721no—
581C23—1721no—
582C23—1721no—
583C23—1721no—
584C23C2×D4×D4311yescharacteristic
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8—41no—
589D4—22no—
590D4—22no—
591D4—22no—
592D4—862no—
593D4—862no—
594D4—1721no—
595D4—1721no—
596D4#1306330714yes—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—48no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
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—861no—
623C2×C4—861no—
624C2×C4—3444no—
625C2×C4—3444no—
626C2×C4—3444no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4#1306334612yes—
637C2×C4C2×D4×D4311yescharacteristic
638C2×C4C2×#1062190011yescharacteristic
639C2×C4C2×#1062190011yescharacteristic
640C2×C4C2×#1062189811yescharacteristic
641C2×C4#1306337111yescharacteristic
642C2×C4#1306337211yescharacteristic
643C8—41no—
644C8—41no—
645C8—862no—
646C8—1721no—
647C22—24no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—3441no—
655C22—3441no—
656C22—3441no—
657C22—3441no—
658C22—1722no—
659C22—1722no—
660C22—1722no—
661C22#1458340511yescharacteristic
662C22#1458353311yescharacteristic
663C22#1458355811yescharacteristic
664C22C2×#1306334611yescharacteristic
665C22AGL(1,ℤ/8)×D4311yescharacteristic
666C22#1458370111yescharacteristic
667C22#1458371511yescharacteristic
668C4—22no—
669C4—41no—
670C4—42no—
671C4—81no—
672C4—81no—
673C4—862no—
674C4—3441no—
675C4—3441no—
676C4—3441no—
677C4—1721no—
678C4—1721no—
679C4—1721no—
680C4C2×#1306330711yescharacteristic
681C4#1458349311yescharacteristic
682C4#1458354911yescharacteristic
683C4#1458359511yescharacteristic
684C2—44no—
685C2—3442no—
686C2#1913833611yescharacteristic
687C2#1914464311yescharacteristic
688C2#1914485811yescharacteristic
689C2#1914608111yescharacteristic
690C2#1914631211yescharacteristic
691C2#1914725311yescharacteristic
692C2#1914731411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1877C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenter#1877D43
hypocenterC43#26164
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
3. #19138385C2semidirect
4. D4×C4⋊Dic43C2semidirect
5. #19136133C2semidirect
6. #19136092C2semidirect
7. #19136000C2semidirect
8. #19135833C2semidirect
9. #19135273C2semidirect
10. #19135151C2semidirect
12. #19134931C2semidirect
13. #19134843C2semidirect
14. #19134840C2semidirect
15. C43×#1877C2semidirect
350. #1877D43semidirect
407. C43#26164semidirect

Maximal subgroups

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

subgroupindex
C2×#145831162
C2×#145829792
#191383852
D4×C4⋊Dic432
#191361332
#191360922
#191360002
#191358332
#191352732
#191351512
#191349432
#191349312
#191348432
#191348402
C43×#18772
#2616443