Finite Group Databasebeta

← #25164647

Subgroups — #25164647

Order 11008.

832 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138930C211yesmaximal, characteristic, complemented
2#19137610C211yesmaximal, characteristic
3#19135914C211yesmaximal, characteristic, complemented
4#19135779C211yesmaximal, characteristic
5#19135740C211yesmaximal, characteristic, complemented
6#19135601C211yesmaximal, characteristic
7#19135549C211yesmaximal, characteristic, complemented
8#19135270C211yesmaximal, characteristic, complemented
9#19135235C211yesmaximal, characteristic, complemented
10#19135199C211yesmaximal, characteristic, complemented
11#19134928C211yesmaximal, characteristic, complemented
12#19134901C211yesmaximal, characteristic, complemented
13#19134684C211yesmaximal, characteristic, complemented
14C4×#13063245C211yesmaximal, characteristic, complemented
15C43×#1918C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063305C2211yescharacteristic
19C2×#13063300C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063287—21no—
22C2×C4⋊C4×D43C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33#14582839—21no—
34#14582826—21no—
35#14582805C2211yescharacteristic
36#14582804C2211yescharacteristic
37#14582800C2211yescharacteristic
38#14582790—21no—
39#14582788—21no—
40#14582777—21no—
41#14582770—21no—
42#14582765—21no—
43#14582756C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4×(C2×D43)⋊C4C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172—21no—
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C22×C4×D43C2311yescharacteristic
65C2×#10621873—22no—
66C2×#10621873—41no—
67C2×#10621873—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063316—22no—
71#13063316—41no—
72#13063305—22no—
73#13063305—41no—
74#13063300—22no—
75#13063300—22no—
76C4×D172—22no—
77C4×D172—41no—
78#13063287—44no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C4⋊C4×D43—22no—
86C4⋊C4×D43—41no—
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×(C2×D43)⋊C4D411yescharacteristic
94C2×(C2×D43)⋊C4D411yescharacteristic
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97Dic43⋊C8—41no—
98#13063250—22no—
99#13063248—22no—
100#13063248—41no—
101#13063247—41no—
102#13063245—22no—
103#13063245—22no—
104(C2×D43)⋊C8—41no—
105(C2×D43)⋊C8—41no—
106C4×C43⋊C8—41no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95D411yescharacteristic
114C43⋊#95D411yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C42×C43—21no—
123C2×C42×C43C2311yescharacteristic
124#107×C43—22no—
125#95×C43—21no—
126#95×C43—21no—
127C23×D43—21no—
128C23×D43C2×D411yescharacteristic
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C2×D172—24no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—42no—
149C2×D172—42no—
150C2×D172#4112yes—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—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—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43#4112yes—
183C4⋊C4×C43#4112yes—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—42no—
187(C2×D43)⋊C4—24no—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—81no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—42no—
199C4⋊Dic43—42no—
200C4⋊Dic43#4112yes—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—42no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212#10621873—44no—
213C23×C43C22×D411yescharacteristic
214C22×D43—21no—
215C22×D43—21no—
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—22no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43#13512yes—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43AGL(1,ℤ/8)12yes—
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C2×C4×C43H(5,𝔽2)11yescharacteristic
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—22no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270D172—22no—
271D172—22no—
272D172—48no—
273D172—41no—
274D172—41no—
275C4×D43—41no—
276C4×D43—41no—
277C4×D43—41no—
278C4×D43—41no—
279C4×D43—84no—
280C4×D43—84no—
281Dic86—41no—
282Dic86—41no—
283Dic86—41no—
284Dic86—41no—
285C8×C43—41no—
286C8×C43—41no—
287C43⋊C8—41no—
288C43⋊C8—41no—
289#26721—431nomaximal, Sylow
290C22×C43#52511yescharacteristic
291C22×C43#54611yescharacteristic
292C22×C43#54611yescharacteristic
293C22×C43C2×#13511yescharacteristic
294C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
295C22×C43#57711yescharacteristic
296C22×C43#57811yescharacteristic
297C2×D43—22no—
298C2×D43—22no—
299C2×D43—22no—
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—41no—
303C2×D43—41no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—81no—
311C4×C43—22no—
312C4×C43—42no—
313C4×C43—42no—
314C4×C43—41no—
315C4×C43—81no—
316C4×C43—81no—
317C4×C43#52911yescharacteristic
318C4×C43#53811yescharacteristic
319C4×C43#55511yescharacteristic
320C4×C43#55911yescharacteristic
321Dic43—41no—
322Dic43—41no—
323Dic43—41no—
324Dic43—42no—
325Dic43—81no—
326Dic43—81no—
327#2489—431no—
328#2361—431no—
329#2055—431no—
330#2033—431no—
331#2025—431no—
332#2000—431no—
333#1989—431no—
334#1933—431no—
335#1928—431no—
336#1923—431no—
337#1918D4311yescharacteristic, complemented
338#1877—431no—
339#1872—431no—
340#1824—431no—
341C4×#102—431no—
342C2×C43#245911yescharacteristic
343C2×C43#310511yescharacteristic
344C2×C43#312011yescharacteristic
345C2×C43#330011yescharacteristic
346C2×C43#330111yescharacteristic
347C2×C43#331011yescharacteristic
348C2×C43#333011yescharacteristic
349D43—42no—
350D43—82no—
351C22×SD16—431no—
352C2×#125—431no—
353C2×C22⋊Q8—431no—
354C2×#121—431no—
355C2×C4×D4—431no—
356C2×C4×D4—861no—
357C22×C4⋊C4—431no—
358C2×#107C2×D4311yescharacteristic
359C2×C4⋊C8—431no—
360C2×#103—431no—
361C2×#103—431no—
362C2×#103—431no—
363C2×#102—431no—
364C2×#102—431no—
365C2×#102—431no—
366C2×C22⋊C8—431no—
367C2×C22⋊C8—431no—
368C2×C4×C8—431no—
369#400—861no—
370#397—861no—
371#391—431no—
372#391—431no—
373#390—431no—
374#389C2×D4311yescharacteristic
375#388—861no—
376#388—861no—
377#386—861no—
378#385—861no—
379#382—861no—
380#380—431no—
381C4×C4⋊C4—431no—
382C4×C4⋊C4C2×D4311yescharacteristic
383C4×C22⋊C4—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340C2×D4311yescharacteristic
390#340C2×D4311yescharacteristic
391#340C2×D4311yescharacteristic
392#336—431no—
393#336C2×D4311yescharacteristic
394C43#2672111yescharacteristic, complemented, Sylow
395C22×Q8—431no—
396C22×D4—431no—
397C22×D4—861no—
398C23×C4—431no—
399C23×C4—861no—
400C23×C4—861no—
401C2×SD16—862no—
402C2×SD16—1721no—
403C2×SD16—1721no—
404C22×C8—431no—
405C22×C8—431no—
406C22×C8C22×D4311yescharacteristic
407C22×C8C22×D4311yescharacteristic
408#125—862no—
409#125—1721no—
410C22⋊Q8—862no—
411C22⋊Q8—1721no—
412#121—862no—
413#121—862no—
414C4×D4—862no—
415C4×D4—1721no—
416C4×D4—1724no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—862no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—1721no—
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C22⋊C4—431no—
431C2×C22⋊C4—431no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C42—21no—
439C2×C42—431no—
440C2×C42—861no—
441C2×C42C22×D4311yescharacteristic
442#107—22no—
443C4⋊C8—1721no—
444#103—862no—
445#103—862no—
446#103—1721no—
447#102—862no—
448#102—862no—
449#102—1721no—
450C22⋊C8—1721no—
451C22⋊C8—1721no—
452C4×C8—1721no—
453#95—21no—
454#95—21no—
455#95—431no—
456#95—431no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463C24—431no—
464C24—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×D4—432no—
472C2×D4—864no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—1722no—
479C2×D4—1722no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—3441no—
497C22×C4—3441no—
498C22×C4—1722no—
499C22×C4—1722no—
500C22×C4—1722no—
501C22×C4—1722no—
502C22×C4D4×D4311yescharacteristic
503C22×C4D4×D4311yescharacteristic
504C22×C4C23×D4311yescharacteristic
505SD16—1724no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—42no—
525C4⋊C4—432no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—1722no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C4⋊C4#1062189812yes—
534C4⋊C4#1062190212yes—
535C22⋊C4—862no—
536C22⋊C4—864no—
537C22⋊C4—862no—
538C22⋊C4—3441no—
539C22⋊C4—1722no—
540C22⋊C4—1722no—
541C22⋊C4—1722no—
542C22⋊C4—1722no—
543C42—21no—
544C42—21no—
545C42—42no—
546C42—861no—
547C42—861no—
548C42—1722no—
549C23—432no—
550C23—861no—
551C23—861no—
552C23—861no—
553C23—861no—
554C23—861no—
555C23—861no—
556C23—862no—
557C23—1721no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23C2×D4×D4311yescharacteristic
564Q8—1721no—
565Q8—1721no—
566Q8—1721no—
567Q8—1721no—
568D4—862no—
569D4—862no—
570D4—1728no—
571D4—1721no—
572D4—1721no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—862no—
599C2×C4—861no—
600C2×C4—3444no—
601C2×C4—3444no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4#1306334912yes—
615C2×C4#41×D4311yescharacteristic
616C2×C4#41×D4311yescharacteristic
617C2×C4C2×#1062189811yescharacteristic
618C2×C4C2×#1062190211yescharacteristic
619C2×C4#1306337111yescharacteristic
620C2×C4#1306337111yescharacteristic
621C8—41no—
622C8—41no—
623C8—1721no—
624C8—1721no—
625C22—862no—
626C22—862no—
627C22—862no—
628C22—3441no—
629C22—3441no—
630C22—3441no—
631C22—3441no—
632C22—1722no—
633C22—1722no—
634C22—1722no—
635C22—1721no—
636C22—1721no—
637C22—1721no—
638C22—1721no—
639C22#1458340811yescharacteristic
640C22#1458354011yescharacteristic
641C22#1458354111yescharacteristic
642C22#135×D4311yescharacteristic
643C22C2×#1306334911yescharacteristic
644C22#1458370811yescharacteristic
645C22#1458371511yescharacteristic
646C4—22no—
647C4—42no—
648C4—42no—
649C4—41no—
650C4—81no—
651C4—81no—
652C4—3441no—
653C4—3441no—
654C4—1722no—
655C4—1721no—
656C4—1721no—
657C4—1721no—
658C4#1458343411yescharacteristic
659C4#1458348811yescharacteristic
660C4#1458361211yescharacteristic
661C4#1458363411yescharacteristic
662C2—3442no—
663C2—1722no—
664C2#1913853611yescharacteristic
665C2#1914464011yescharacteristic
666C2#1914480711yescharacteristic
667C2#1914648511yescharacteristic
668C2#1914649411yescharacteristic
669C2#1914661411yescharacteristic
670C2#1914689711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1918C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenter#1918D43
hypocenterC43#26721
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
1. #19138930C2semidirect
3. #19135914C2semidirect
5. #19135740C2semidirect
7. #19135549C2semidirect
8. #19135270C2semidirect
9. #19135235C2semidirect
10. #19135199C2semidirect
11. #19134928C2semidirect
12. #19134901C2semidirect
13. #19134684C2semidirect
14. C4×#13063245C2semidirect
15. C43×#1918C2semidirect
337. #1918D43semidirect
394. C43#26721semidirect

Maximal subgroups

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

subgroupindex
#191389302
#191376102
#191359142
#191357792
#191357402
#191356012
#191355492
#191352702
#191352352
#191351992
#191349282
#191349012
#191346842
C4×#130632452
C43×#19182
#2672143