Finite Group Databasebeta

← #25106158

Subgroups — #25106158

Order 11008.

1100 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583452C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic
3C4×#13063281C211yesmaximal, characteristic
4#19135570C214yesmaximal, complemented
5#19135537C214yesmaximal, complemented
6#19134695C211yesmaximal, characteristic
7#19134694C211yesmaximal, characteristic
8#19134692C211yesmaximal, characteristic
9C43×#1826C211yesmaximal, characteristic
10#14583452—21no—
11#14583452—21no—
12#14583452—21no—
13#14583452—21no—
14#14583452C412yescomplemented
15#14583452C412yescomplemented
16#14583452C2212yes—
17#14583452C2212yes—
18C2×#13063324C411yescharacteristic, complemented
19C2×#13063324C411yescharacteristic, complemented
20C2×#13063316C411yescharacteristic, complemented
21C2×#13063316C411yescharacteristic, complemented
22C2×#13063302—21no—
23C2×#13063302—21no—
24C2×C4×Dic86—21no—
25C2×C4×Dic86—21no—
26C2×#13063284C2211yescharacteristic
27C2×#13063281—21no—
28C22×C4×Dic43C2211yescharacteristic
29#14582953—21no—
30#14582953—21no—
31#14582949—21no—
32#14582949—21no—
33#14582922C2212yes—
34#14582863C2211yescharacteristic
35M16×Dic43C2212yes—
36C4×Dic43⋊C4C2212yes—
37#14582750—21no—
38C22⋊C4×Dic43—21no—
39C4×C22⋊Dic43C2211yescharacteristic
40#14582744—21no—
41C42×Dic43C2212yes—
42#14582660C2214yes—
43#14582659C2214yes—
44#14582658C2214yes—
45C2×#117×C43C2211yescharacteristic
46C43×#407C2211yescharacteristic
47C4×C22⋊C4×C43C2211yescharacteristic
48C43×#339C2214yes—
49C22×Dic86—21no—
50C22×Dic86—21no—
51C23×Dic43D411yescharacteristic
52C23×Dic43D411yescharacteristic
53C2×#10621877C2312yes—
54#13063324—21no—
55#13063324—21no—
56#13063324—21no—
57#13063324—21no—
58#13063324C2×C412yes—
59#13063324C2×C412yes—
60#13063324C2×C412yes—
61#13063324C2×C412yes—
62#13063316—21no—
63#13063316—21no—
64#13063316—21no—
65#13063316—21no—
66#13063316C2×C412yes—
67#13063316C2×C412yes—
68#13063316C2×C412yes—
69#13063316C2×C412yes—
70#13063302—22no—
71#13063302—22no—
72#13063302—22no—
73#13063302—22no—
74#13063302—22no—
75#13063302—22no—
76#13063302—22no—
77#13063302—22no—
78C4×Dic86—22no—
79C4×Dic86—22no—
80C4×Dic86—22no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84C4×Dic86—22no—
85C4×Dic86—22no—
86#13063284—21no—
87#13063284—21no—
88#13063284C2×C412yes—
89#13063284C2312yes—
90#13063281—28no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—22no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—22no—
104C2×C4×Dic43—22no—
105C2×C4×Dic43C2×C411yescharacteristic
106C2×C4×Dic43C2×C411yescharacteristic
107C2×C4×Dic43C2×C411yescharacteristic
108C2×C4×Dic43C2×C411yescharacteristic
109C2×C4×Dic43D411yescharacteristic
110C2×C4×Dic43D411yescharacteristic
111C2×C4×Dic43D411yescharacteristic
112C2×C4×Dic43D411yescharacteristic
113C2×C4×Dic43D411yescharacteristic
114C2×C4×Dic43D411yescharacteristic
115C2×C4×Dic43C2312yes—
116C2×C4×Dic43C2311yescharacteristic
117C2×C4×Dic43C2311yescharacteristic
118Dic43⋊C8—22no—
119Dic43⋊C8—22no—
120C22⋊(C43⋊C8)—21no—
121C22⋊(C43⋊C8)—21no—
122#13063235—22no—
123C8×Dic43—22no—
124C43⋊#95—21no—
125C43⋊#95—22no—
126C23×C4×C43C2311yescharacteristic
127C2×M16×C43C2312yes—
128#117×C43—21no—
129#117×C43—21no—
130#117×C43C2×C412yes—
131#117×C43C2312yes—
132C2×C4⋊C4×C43C2×C411yescharacteristic
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C42×C43—21no—
137C2×C42×C43C2312yes—
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140#95×C43—21no—
141C24×C43C2×D411yescharacteristic
142C22×C4×C43—24no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—22no—
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—24no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—22no—
156C22×Dic43—42no—
157C22×Dic43C22⋊C411yescharacteristic
158C22×Dic43C22⋊C411yescharacteristic
159C22×Dic43C22⋊C411yescharacteristic
160C22×Dic43C22⋊C411yescharacteristic
161C22×Dic43C22⋊C411yescharacteristic
162C22×Dic43C22⋊C411yescharacteristic
163C22×Dic43C22⋊C411yescharacteristic
164C22×Dic43C22⋊C411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C2×Dic86—22no—
170C2×Dic86—22no—
171C2×Dic86—22no—
172C2×Dic86—22no—
173C2×Dic86—44no—
174C2×Dic86—44no—
175M16×C43—24no—
176C2×C8×C43—22no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C22×C412yes—
180C4⋊C4×C43C22×C412yes—
181C22⋊C4×C43—24no—
182C22⋊C4×C43—22no—
183C22⋊C4×C43—22no—
184C42×C43—22no—
185C42×C43—22no—
186C42×C43—24no—
187C22⋊Dic43—24no—
188C22⋊Dic43—22no—
189C22⋊Dic43—22no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—22no—
193C4⋊Dic43—22no—
194C4⋊Dic43—22no—
195C4⋊Dic43—22no—
196C4⋊Dic43C22×C412yes—
197C4⋊Dic43C22×C412yes—
198Dic43⋊C4—28no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207C4×Dic43—28no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43—24no—
211C4×Dic43—44no—
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22×C411yescharacteristic
221C4×Dic43C22×C411yescharacteristic
222C4×Dic43C22×C411yescharacteristic
223C4×Dic43C22×C411yescharacteristic
224C4×Dic43C2×D411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226C4×Dic43C2×D411yescharacteristic
227C4×Dic43C2×D411yescharacteristic
228#10621877—24no—
229C2×C43⋊C8—22no—
230C23×C43—22no—
231C23×C43—22no—
232C23×C43—41no—
233C23×C43C2×C22⋊C411yescharacteristic
234C23×C43C2×C22⋊C411yescharacteristic
235C23×C43C22×D411yescharacteristic
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—24no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C23×C411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C432−1+414yes—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—24no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43#10414yes—
272C2×Dic43C2×C22⋊C411yescharacteristic
273C2×Dic43C2×C22⋊C411yescharacteristic
274C2×Dic43C2×C22⋊C411yescharacteristic
275C2×Dic43C2×C22⋊C411yescharacteristic
276C2×Dic43C2×C22⋊C411yescharacteristic
277C2×Dic43C2×C22⋊C411yescharacteristic
278C2×Dic43C2×C22⋊C411yescharacteristic
279C2×Dic43C2×C22⋊C411yescharacteristic
280Dic86—44no—
281Dic86—44no—
282Dic86—44no—
283Dic86—44no—
284C8×C43—42no—
285C43⋊C8—42no—
286#21844—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—21no—
291C22×C43—21no—
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—44no—
295C22×C43C2×#10412yes—
296C22×C43C22×C22⋊C411yescharacteristic
297C22×C43#53612yes—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—44no—
301C4×C43—42no—
302C4×C43—42no—
303C4×C43#51912yes—
304C4×C43#53612yes—
305Dic43—21no—
306Dic43—21no—
307Dic43—21no—
308Dic43—21no—
309Dic43—21no—
310Dic43—44no—
311Dic43—42no—
312Dic43—42no—
313Dic43C2×#10412yes—
314Dic43C2×#10412yes—
315Dic43#42112yes—
316C2×#533—431no—
317#2920—431no—
318C4×#117—431no—
319#1994—434no—
320#1986—434no—
321#1826—431no—
322#1826—431no—
323#1826—431no—
324#1826D4311yescharacteristic
325C2×C43—22no—
326C2×C43—22no—
327C2×C43—41no—
328C2×C43#231011yescharacteristic
329C2×C43C22×#10411yescharacteristic
330C2×C43C2×#42111yescharacteristic
331#533—432no—
332#533—432no—
333#533—432no—
334#533—432no—
335#533—861no—
336#533—861no—
337#533—861no—
338#533—861no—
339C2×C4⋊Q8—431no—
340C2×C4⋊Q8—431no—
341C2×#125—431no—
342C2×#125—431no—
343C2×C22⋊Q8—861no—
344C2×C22⋊Q8—861no—
345C2×C4×Q8—861no—
346C2×C4×Q8—861no—
347C2×#117—431no—
348C2×#117—861no—
349C2×#117C2×D4311yescharacteristic
350C22×C42—431no—
351#432—861no—
352#432—861no—
353#431—861no—
354#431—861no—
355#423—432no—
356#407—431no—
357#407C2×D4311yescharacteristic
358C4×M16—432no—
359C4×C4⋊C4—432no—
360C4×C4⋊C4—861no—
361C4×C22⋊C4—431no—
362C4×C22⋊C4—861no—
363C4×C22⋊C4C2×D4311yescharacteristic
364#376—861no—
365C43—432no—
366#339—434no—
367#339—434no—
368#339—434no—
369#339C2×D4314yes—
370C43#2184411yescharacteristic, complemented, Sylow
371C22×Q8—861no—
372C22×Q8—861no—
373C23×C4—431no—
374C23×C4—431no—
375C23×C4C22×D4311yescharacteristic
376C2×M16—432no—
377C2×M16C22×D4312yes—
378C4⋊Q8—432no—
379C4⋊Q8—432no—
380C4⋊Q8—432no—
381C4⋊Q8—432no—
382C4⋊Q8—861no—
383C4⋊Q8—861no—
384C4⋊Q8—861no—
385C4⋊Q8—861no—
386#125—432no—
387#125—432no—
388#125—432no—
389#125—432no—
390#125—861no—
391#125—861no—
392#125—861no—
393#125—861no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396C22⋊Q8—862no—
397C22⋊Q8—862no—
398C22⋊Q8—862no—
399C22⋊Q8—862no—
400C22⋊Q8—862no—
401C22⋊Q8—862no—
402C4×Q8—862no—
403C4×Q8—862no—
404C4×Q8—862no—
405C4×Q8—862no—
406C4×Q8—862no—
407C4×Q8—862no—
408C4×Q8—862no—
409C4×Q8—862no—
410#117—21no—
411#117—21no—
412#117—432no—
413#117—432no—
414#117—868no—
415#117—861no—
416#117—861no—
417#117C4×D4312yes—
418#117C22×D4312yes—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—862no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4C4×D4311yescharacteristic
429C2×C4⋊C4C4×D4311yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C42—21no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—432no—
448C2×C42—862no—
449C2×C42—861no—
450C2×C42—862no—
451C2×C42C22×D4312yes—
452C4⋊C8—862no—
453C4⋊C8—862no—
454C22⋊C8—21no—
455C22⋊C8—21no—
456C22⋊C8—861no—
457C22⋊C8—861no—
458#97—862no—
459C4×C8—862no—
460#95—21no—
461#95—862no—
462#95—861no—
463C24D4×D4311yescharacteristic
464C2×Q8—862no—
465C2×Q8—862no—
466C2×Q8—862no—
467C2×Q8—862no—
468C2×Q8—1724no—
469C2×Q8—1724no—
470C22×C4—24no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—864no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—862no—
490C22×C4—1722no—
491C22×C4C2×C4×D4311yescharacteristic
492C22×C4C2×C4×D4311yescharacteristic
493C22×C4D4×D4311yescharacteristic
494C22×C4D4×D4311yescharacteristic
495C22×C4D4×D4311yescharacteristic
496C22×C4C23×D4311yescharacteristic
497M16—24no—
498M16—864no—
499C2×C8—22no—
500C2×C8—862no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—432no—
504C4⋊C4—432no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—868no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4C2×C4×D4312yes—
521C4⋊C4C2×C4×D4312yes—
522C22⋊C4—24no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—864no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C42—22no—
529C42—22no—
530C42—24no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—868no—
548C42—862no—
549C42—862no—
550C42—864no—
551C42—1724no—
552C23—22no—
553C23—22no—
554C23—41no—
555C23C22⋊C4×D4311yescharacteristic
556C23C22⋊C4×D4311yescharacteristic
557C23C2×D4×D4311yescharacteristic
558Q8—1724no—
559Q8—1724no—
560Q8—1724no—
561Q8—1724no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—431no—
577C2×C4—434no—
578C2×C4—431no—
579C2×C4—431no—
580C2×C4—431no—
581C2×C4—431no—
582C2×C4—431no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—864no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4C22⋊C4×D4311yescharacteristic
602C2×C4C22⋊C4×D4311yescharacteristic
603C2×C4C22×C4×D4311yescharacteristic
604C2×C4C2×D4×D4311yescharacteristic
605C2×C4#1306337214yes—
606C8—42no—
607C8—1722no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—44no—
616C22#104×D4312yes—
617C22C2×C22⋊C4×D4311yescharacteristic
618C22#1458347112yes—
619C4—21no—
620C4—21no—
621C4—44no—
622C4—42no—
623C4—42no—
624C4—432no—
625C4—432no—
626C4—432no—
627C4—861no—
628C4—861no—
629C4—861no—
630C4—861no—
631C4—861no—
632C4—1724no—
633C4—1722no—
634C4—1722no—
635C4#1458337612yes—
636C4#1458347112yes—
637C2—22no—
638C2—22no—
639C2—41no—
640C2#1913718011yescharacteristic
641C2C2×#104×D4311yescharacteristic
642C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1826C2
socleC22×C43C22×C22⋊C4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1826D43
hypocenterC43#21844
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
4. #19135570C2semidirect
5. #19135537C2semidirect
14. #14583452C4semidirect
15. #14583452C4semidirect
18. C2×#13063324C4semidirect
19. C2×#13063324C4semidirect
20. C2×#13063316C4semidirect
21. C2×#13063316C4semidirect
370. C43#21844semidirect

Maximal subgroups

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

subgroupindex
C2×#145834522
#191432242
C4×#130632812
#191355702
#191355372
#191346952
#191346942
#191346922
C43×#18262
#2184443