Finite Group Databasebeta

← #25118903

Subgroups — #25118903

Order 11008.

958 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583120C211yesmaximal, characteristic
2C2×#14582993C211yesmaximal, characteristic, complemented
3C2×C4×#10621883C211yesmaximal, characteristic
4#19137668C211yesmaximal, characteristic
5#19137514C211yesmaximal, characteristic, complemented
6#19135405C211yesmaximal, characteristic
7#19135360C211yesmaximal, characteristic, complemented
8#19135280C211yesmaximal, characteristic
9#19135270C211yesmaximal, characteristic, complemented
10#19134947C211yesmaximal, characteristic
11#19134935C211yesmaximal, characteristic, complemented
12#19134864C211yesmaximal, characteristic, complemented
13#19134456C211yesmaximal, characteristic, complemented
14#19134414C211yesmaximal, characteristic, complemented
15C43×#1862C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063312C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23#14583120C418yescomplemented
24#14582993—24no—
25C4×#10621883—24no—
26C2×#13063256C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×C4×C43⋊C8C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582802C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582796—21no—
41#14582794—21no—
42#14582793—21no—
43#14582787—21no—
44#14582772—21no—
45#14582764C2211yescharacteristic
46#14582763—21no—
47C4⋊C4×Dic43—21no—
48C4⋊C4×Dic43C2211yescharacteristic
49C4×Dic43⋊C4C2211yescharacteristic
50C4×C22⋊Dic43—21no—
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×#107×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×Dic86C2311yescharacteristic
64C2×Dic172—22no—
65C2×Dic172—22no—
66C2×Dic172C2×C414yescomplemented
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883C2×C414yes—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063312—22no—
73#13063312C2×C414yes—
74C4×Dic86—22no—
75C4×Dic86—41no—
76#13063290—22no—
77#13063290—22no—
78#13063290—22no—
79#13063290—41no—
80#13063290—41no—
81#13063290C2×C414yescomplemented
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4D411yescharacteristic
90C2×Dic43⋊C4D411yescharacteristic
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102#13063256—22no—
103Dic43⋊C8C2×C414yescomplemented
104#13063250—22no—
105#13063250—41no—
106#13063248—22no—
107#13063248C2×C414yescomplemented
108#13063248D414yes—
109#13063246—22no—
110C4×C43⋊C8—22no—
111C8×Dic43—22no—
112C8×Dic43—22no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95D411yescharacteristic
120C43⋊#95D411yescharacteristic
121C22×D4×C43C2311yescharacteristic
122C23×C4×C43—21no—
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C4×D4×C43—22no—
126C4×D4×C43—41no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C42×C43C2311yescharacteristic
133#107×C43—22no—
134#102×C43—41no—
135#102×C43C2×C414yes—
136#95×C43—21no—
137C24×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43C22×C412yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—42no—
148C22×C4×C43—42no—
149C22×C4×C43—81no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86C22×C412yes—
170C2×Dic86C22×C412yes—
171C2×Dic86C2×D412yes—
172C2×Dic86#4112yes—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43C22×C412yes—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—42no—
184C4⋊C4×C43C22×C412yes—
185C4⋊C4×C43C2×D412yes—
186C22⋊C4×C43—42no—
187C42×C43—21no—
188C42×C43—21no—
189C22⋊Dic43—24no—
190C22⋊Dic43—24no—
191C22⋊Dic43—42no—
192C22⋊Dic43—81no—
193#10621883—28no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—42no—
199Dic43⋊C4—22no—
200Dic43⋊C4—24no—
201Dic43⋊C4—22no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—24no—
208C4×Dic43—42no—
209C4×Dic43—42no—
210C4×Dic43—42no—
211C4×Dic43—81no—
212C4×Dic43C22×C412yes—
213C4×Dic43#4112yes—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8C22×C412yes—
219C2×C43⋊C8C2×D412yes—
220Dic172—28no—
221C23×C43—22no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43C22×D411yescharacteristic
229D4×C43—22no—
230D4×C43—22no—
231D4×C43—41no—
232D4×C43—41no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—41no—
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—84no—
248C2×C4×C43#13512yes—
249C2×C4×C43C23×C411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C432−1+411yescharacteristic
255C2×Dic43—22no—
256C2×Dic43—21no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—22no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43C4×D412yes—
277C2×Dic43C4×D412yes—
278C2×Dic43#13512yes—
279Dic86—22no—
280Dic86—22no—
281Dic86—22no—
282Dic86—22no—
283Dic86—22no—
284Dic86—41no—
285Dic86—41no—
286Dic86C4×D414yes—
287C8×C43—22no—
288C8×C43—41no—
289C43⋊C8—22no—
290C43⋊C8—22no—
291#23000—431nomaximal, Sylow
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43C2×C4×D411yescharacteristic
300C22×C43D4211yescharacteristic
301C22×C43#54811yescharacteristic
302C22×C43C2×#13511yescharacteristic
303C22×C43C2×#13511yescharacteristic
304C22×C43#57711yescharacteristic
305C22×C43#57811yescharacteristic
306C4×C43—22no—
307C4×C43—42no—
308C4×C43—42no—
309C4×C43—41no—
310C4×C43—81no—
311C4×C43C2×C4×D411yescharacteristic
312C4×C43#52011yescharacteristic
313C4×C43#54711yescharacteristic
314C4×C43#55311yescharacteristic
315Dic43—24no—
316Dic43—22no—
317Dic43—22no—
318Dic43—22no—
319Dic43—42no—
320Dic43—41no—
321Dic43—81no—
322Dic43—81no—
323C2×#464—431no—
324C2×C4×Q16—431no—
325C2×C4×SD16—431no—
326#2367—431no—
327#2351—431no—
328#1958—431no—
329#1949—431no—
330#1934—431no—
331#1933—431no—
332#1880—431no—
333#1878—431no—
334#1865—431no—
335#1862D4311yescharacteristic
336C8×C4⋊C4—431no—
337C4×#103—431no—
338C2×C43—82no—
339C2×C43#236111yescharacteristic
340C2×C43C4×#13511yescharacteristic
341C2×C43#294711yescharacteristic
342C2×C43#328211yescharacteristic
343C2×C43#328511yescharacteristic
344C2×C43#336411yescharacteristic
345C2×C43#336511yescharacteristic
346C22×Q16—431no—
347C22×SD16—431no—
348C2×#124—431no—
349C2×C4×Q8—431no—
350C2×C4×Q8—431no—
351C2×C4×Q8—431no—
352C2×C4×Q8—431no—
353C2×C4×D4C2×D4311yescharacteristic
354#464—438no—
355C4×Q16—864no—
356C4×SD16—864no—
357C2×#107C2×D4311yescharacteristic
358C2×#106—431no—
359C2×C4⋊C8—431no—
360C2×#103—431no—
361C2×#103—431no—
362C2×#103—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#102—431no—
366C2×#102C2×D4311yescharacteristic
367C2×#102C2×D4311yescharacteristic
368C2×C4×C8—431no—
369C2×C4×C8—431no—
370C2×C4×C8—431no—
371#391—431no—
372#390—431no—
373#389—431no—
374#389—861no—
375#389—861no—
376#389C2×D4311yescharacteristic
377#388—861no—
378#388—861no—
379#385—861no—
380#382—431no—
381#382—861no—
382C4×C4⋊C4—431no—
383C4×C4⋊C4—431no—
384C4×C4⋊C4—861no—
385C4×C22⋊C4—861no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340C2×D4311yescharacteristic
390#336—431no—
391#336C2×D4311yescharacteristic
392C43#2300011yescharacteristic, complemented, Sylow
393C22×Q8—431no—
394C22×Q8—431no—
395C22×D4C22×D4311yescharacteristic
396C23×C4—21no—
397C2×Q16—434no—
398C2×Q16—862no—
399C2×Q16—862no—
400C2×SD16—434no—
401C2×SD16—862no—
402C2×SD16—862no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8C22×D4311yescharacteristic
406C22×C8C22×D4311yescharacteristic
407#124—434no—
408#124—862no—
409C4×Q8—434no—
410C4×Q8—862no—
411C4×Q8—862no—
412C4×Q8—862no—
413C4×Q8—862no—
414C4×Q8—1721no—
415C4×Q8—1721no—
416C4×Q8—1721no—
417C4×D4—22no—
418C4×D4—41no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
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×C42—431no—
438C2×C42—431no—
439C2×C42—861no—
440C2×C42—861no—
441C2×C42—861no—
442C2×C42—861no—
443C2×C42—861no—
444C2×C42C22×D4311yescharacteristic
445#107—22no—
446#106—862no—
447C4⋊C8—434no—
448#103—434no—
449#103—434no—
450#103—862no—
451#103—862no—
452#103—1721no—
453#102—41no—
454#102—862no—
455#102C4×D4314yes—
456C4×C8—862no—
457C4×C8—862no—
458C4×C8—862no—
459#95—21no—
460#95—431no—
461#95—431no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468C24—21no—
469C2×Q8—432no—
470C2×Q8—432no—
471C2×Q8—432no—
472C2×Q8—432no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4C2×C4×D4312yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—81no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4D4×D4311yescharacteristic
502C22×C4D4×D4311yescharacteristic
503C22×C4C23×D4311yescharacteristic
504Q16—868no—
505SD16—868no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—432no—
512C2×C8—432no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8C2×C4×D4312yes—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—42no—
523C4⋊C4—862no—
524C4⋊C4—864no—
525C4⋊C4—862no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C4⋊C4—1722no—
534C4⋊C4C2×C4×D4312yes—
535C4⋊C4D4×D4312yes—
536C22⋊C4—42no—
537C22⋊C4—864no—
538C22⋊C4—864no—
539C22⋊C4—3441no—
540C22⋊C4—1722no—
541C42—21no—
542C42—21no—
543C42—432no—
544C42—432no—
545C42—864no—
546C42—861no—
547C42—861no—
548C42—3441no—
549C42—1722no—
550C42—1722no—
551C42—1722no—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23C2×D4×D4311yescharacteristic
560Q8—434no—
561Q8—862no—
562Q8—862no—
563Q8—862no—
564Q8—862no—
565Q8—862no—
566Q8—1721no—
567Q8—1721no—
568D4—22no—
569D4—22no—
570D4—41no—
571D4—41no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—84no—
587C2×C4—432no—
588C2×C4—432no—
589C2×C4—432no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
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#1306334412yes—
612C2×C4C22×C4×D4311yescharacteristic
613C2×C4C2×D4×D4311yescharacteristic
614C2×C4#41×D4311yescharacteristic
615C2×C4#41×D4311yescharacteristic
616C2×C4#1306337011yescharacteristic
617C2×C4#1306337311yescharacteristic
618C8—22no—
619C8—41no—
620C8—862no—
621C8—862no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22C4×D4×D4311yescharacteristic
630C22#1458353111yescharacteristic
631C22#1458355911yescharacteristic
632C22#135×D4311yescharacteristic
633C22C2×#1306334411yescharacteristic
634C22#1458370911yescharacteristic
635C22#1458371511yescharacteristic
636C4—22no—
637C4—42no—
638C4—41no—
639C4—42no—
640C4—81no—
641C4—862no—
642C4—864no—
643C4—862no—
644C4—862no—
645C4—3441no—
646C4—3441no—
647C4—1721no—
648C4—1722no—
649C4C4×D4×D4311yescharacteristic
650C4#1458338011yescharacteristic
651C4#1458355111yescharacteristic
652C4#1458359411yescharacteristic
653C2—82no—
654C2#1913761411yescharacteristic
655C2C4×#1306334411yescharacteristic
656C2#1914343511yescharacteristic
657C2#1914630611yescharacteristic
658C2#1914633411yescharacteristic
659C2#1914727911yescharacteristic
660C2#1914729411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1862C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1862D43
hypocenterC43#23000
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. C2×#14582993C2semidirect
5. #19137514C2semidirect
7. #19135360C2semidirect
9. #19135270C2semidirect
11. #19134935C2semidirect
12. #19134864C2semidirect
13. #19134456C2semidirect
14. #19134414C2semidirect
23. #14583120C4semidirect
66. C2×Dic172C2×C4semidirect
81. #13063290C2×C4semidirect
103. Dic43⋊C8C2×C4semidirect
107. #13063248C2×C4semidirect
392. C43#23000semidirect

Maximal subgroups

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

subgroupindex
C2×#145831202
C2×#145829932
C2×C4×#106218832
#191376682
#191375142
#191354052
#191353602
#191352802
#191352702
#191349472
#191349352
#191348642
#191344562
#191344142
C43×#18622
#2300043