Finite Group Databasebeta

← #25094010

Subgroups — #25094010

Order 11008.

2158 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063333C211yesmaximal, characteristic
2C2×#14583380C211yesmaximal, characteristic
3C2×#14583379C211yesmaximal, characteristic
4#19134315C211yesmaximal, characteristic, complemented
5#19134313C212yesmaximal, complemented
6#19134313C212yesmaximal, complemented
7#19134311C211yesmaximal, characteristic, complemented
8#19134310C212yesmaximal, complemented
9C2×#14582661C211yesmaximal, characteristic, complemented
10#340×D43C212yesmaximal, complemented
11C43×#1736C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C2×#13063333—24no—
14C2×#13063333—24no—
15C2×#13063333C418yescomplemented
16C22×#10621872C2212yes—
17C23×C43⋊C8C2211yescharacteristic
18C22×C8×D43C2212yes—
19#14583380—24no—
20#14583380C418yescomplemented
21#14583379—24no—
22#14583379C418yescomplemented
23C2×C4×Dic86—21no—
24C2×#13063290—21no—
25C2×C4×D172—21no—
26C2×#13063287—21no—
27C2×C4×C22⋊D43—22no—
28C2×(C22⋊D43)⋊C4—22no—
29C2×#13063284C2211yescharacteristic
30C2×#13063283C2212yes—
31C2×#13063283C2212yes—
32C22×C4⋊Dic43C2211yescharacteristic
33C2×C4⋊C4×D43C2212yes—
34C2×C4⋊C4×D43C2212yes—
35#14582662C2212yes—
36#14582662C2212yes—
37#14582661C2211yescharacteristic
38#14582661C2212yes—
39#14582661C2212yes—
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43C22×M16×C43C2211yescharacteristic
44C2×#117×C43C2211yescharacteristic
45C22×C4⋊C4×C43C2211yescharacteristic
46C43×#340C2212yes—
47C43×#340C2212yes—
48C2×#10621898C2×C414yes—
49C2×#10621898C2×C414yes—
50C2×#10621898C2×C414yes—
51C2×#10621898D414yes—
52C2×#10621898D414yes—
53C2×#10621898Q814yes—
54C22×Dic86D411yescharacteristic
55C22×D172D411yescharacteristic
56C22×C22⋊D43D412yes—
57C23×Dic43—21no—
58C22×C4×D43—22no—
59C22×C4×D43—22no—
60C22×C4×D43C2312yes—
61#13063333—232no—
62C2×#10621872—24no—
63C2×#10621872—24no—
64C2×#10621872C2×C418yescomplemented
65C22×C43⋊C8—22no—
66C22×C43⋊C8—22no—
67C22×C43⋊C8C2×C414yescomplemented
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C2×C8×D43—24no—
71C2×C8×D43—24no—
72C2×C8×D43C2×C418yescomplemented
73C4×Dic86—28no—
74#13063290—28no—
75C4×D172—28no—
76#13063287—28no—
77C4×C22⋊D43—216no—
78(C22⋊D43)⋊C4—216no—
79#13063284—22no—
80#13063284C2×C414yescomplemented
81#13063283—24no—
82#13063283—24no—
83#13063283C2×C418yescomplemented
84#13063283C2×C418yescomplemented
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—22no—
87C2×C4⋊Dic43C2×C414yescomplemented
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2312yes—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4—22no—
93C4⋊C4×D43—24no—
94C4⋊C4×D43—24no—
95C4⋊C4×D43C2×C418yescomplemented
96C4⋊C4×D43C2×C418yescomplemented
97C2×C22⋊Dic43—21no—
98C2×(C2×D43)⋊C4—22no—
99C2×(C2×D43)⋊C4—22no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—22no—
102C2×C4×Dic43—22no—
103C23×C4×C43—21no—
104C23×C4×C43C2311yescharacteristic
105C2×M16×C43—22no—
106C2×M16×C43—22no—
107C2×M16×C43C2×C414yescomplemented
108C22×C8×C43C2312yes—
109#117×C43—22no—
110#117×C43C2×C414yescomplemented
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—22no—
113C2×C4⋊C4×C43C2×C414yescomplemented
114C2×C4⋊C4×C43C2312yes—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43—21no—
118C2×C42×C43—21no—
119C24×C43C2×D411yescharacteristic
120C23×D43C2×D412yes—
121C22×C4×C43—24no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43—81no—
126C22×C4×C43—81no—
127C22×C4×C43C22×C412yes—
128C22×C4×C43C22×C412yes—
129C22×C4×C43C22×C412yes—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×D412yes—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×Q812yes—
134C22×C4×C43C2411yescharacteristic
135C2×C22⋊D43C22⋊C418yes—
136C2×C22⋊D43C22⋊C418yes—
137C2×C22⋊D43C4⋊C418yes—
138C22×Dic43—24no—
139C22×Dic43—21no—
140C22×Dic43—22no—
141C22×Dic43—21no—
142C22×Dic43—81no—
143C22×Dic43—81no—
144C22×Dic43C2×D412yes—
145#10621898C42116yes—
146#10621898C22⋊C4116yes—
147#10621898C4⋊C4116yes—
148#10621898C4⋊C4116yes—
149C2×D172C22⋊C414yes—
150C2×D172C22⋊C414yes—
151C2×D172C4⋊C414yes—
152C2×C4×D43—28no—
153C2×C4×D43—28no—
154C2×C4×D43—82no—
155C2×C4×D43—82no—
156C2×C4×D43—82no—
157C2×C4×D43—82no—
158C2×C4×D43C22×C414yes—
159C2×C4×D43C22×C414yes—
160C2×C4×D43C22×C414yes—
161C2×C4×D43C2×D414yes—
162C2×C4×D43C2×D414yes—
163C2×C4×D43C2×Q814yes—
164C2×Dic86C22⋊C414yes—
165C2×Dic86C22⋊C414yes—
166C2×Dic86C4⋊C414yes—
167M16×C43—28no—
168C2×C8×C43—22no—
169C2×C8×C43—22no—
170C2×C8×C43C22×C414yes—
171C4⋊C4×C43—24no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43C22×C414yes—
176C4⋊C4×C43C22×C412yes—
177C4⋊C4×C43C22×C412yes—
178C22⋊C4×C43—24no—
179C42×C43—24no—
180C22⋊Dic43—24no—
181(C2×D43)⋊C4—28no—
182(C2×D43)⋊C4—28no—
183C4⋊Dic43—24no—
184C4⋊Dic43—21no—
185C4⋊Dic43—22no—
186C4⋊Dic43—21no—
187C4⋊Dic43C22×C412yes—
188C4⋊Dic43C22×C414yes—
189C4⋊Dic43C22×C412yes—
190Dic43⋊C4—28no—
191Dic43⋊C4—28no—
192C4×Dic43—24no—
193C4×Dic43—28no—
194C4×Dic43—28no—
195C2×C43⋊C8—28no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8C22×C412yes—
201C2×C43⋊C8C22×C412yes—
202#10621872—216no—
203C8×D43—216no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43C2×C22⋊C412yes—
209C23×C43C2×C22⋊C412yes—
210C23×C43C2×C4⋊C412yes—
211C23×C43C22×D411yescharacteristic
212C22×D43—22no—
213C22×D43—22no—
214C22×D43—22no—
215C22×D43—22no—
216C22×D43C2×C22⋊C414yes—
217C22×D43C2×C22⋊C414yes—
218C22×D43C2×C4⋊C414yes—
219C2×C4×C43—22no—
220C2×C4×C43—24no—
221C2×C4×C43—22no—
222C2×C4×C43—41no—
223C2×C4×C43—42no—
224C2×C4×C43—41no—
225C2×C4×C43—42no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—84no—
229C2×C4×C43C2×C4214yes—
230C2×C4×C43C2×C22⋊C414yes—
231C2×C4×C43C2×C22⋊C412yes—
232C2×C4×C43C2×C22⋊C412yes—
233C2×C4×C43C2×C4⋊C414yes—
234C2×C4×C43C2×C4⋊C414yes—
235C2×C4×C43C2×C4⋊C412yes—
236C2×C4×C43C23×C411yescharacteristic
237C2×C4×C43C23×C411yescharacteristic
238C2×C4×C43C23×C411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×Q811yescharacteristic
242C22⋊D43#95132yes—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—24no—
246C2×Dic43—41no—
247C2×Dic43—42no—
248C2×Dic43—41no—
249C2×Dic43—42no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—84no—
253C2×Dic43C2×C22⋊C414yes—
254C2×Dic43C2×C22⋊C414yes—
255C2×Dic43C2×C4⋊C414yes—
256D172#95116yes—
257C4×D43—88no—
258C4×D43—88no—
259C4×D43C2×C4218yes—
260C4×D43C2×C22⋊C418yes—
261C4×D43C2×C4⋊C418yes—
262C4×D43C2×C4⋊C418yes—
263Dic86#95116yes—
264C8×C43—24no—
265C43⋊C8—22no—
266C43⋊C8—22no—
267#20348—431nomaximal, Sylow
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—22no—
271C22×C43—22no—
272C22×C43—22no—
273C22×C43—22no—
274C22×C43C2×#9514yes—
275C22×C43C22×C22⋊C411yescharacteristic
276C22×C43C22×C22⋊C411yescharacteristic
277C22×C43C22×C4⋊C411yescharacteristic
278C22×C43#57611yescharacteristic
279C22×C43#57711yescharacteristic
280C22×C43#57711yescharacteristic
281C22×C43#57811yescharacteristic
282C2×D43—24no—
283C2×D43—24no—
284C2×D43—24no—
285C2×D43—24no—
286C2×D43—24no—
287C2×D43—24no—
288C2×D43C2×#9518yes—
289C4×C43—42no—
290C4×C43—44no—
291C4×C43—42no—
292C4×C43C2×#9514yes—
293C4×C43C22×C4211yescharacteristic
294C4×C43C22×C22⋊C411yescharacteristic
295C4×C43C22×C4⋊C411yescharacteristic
296C4×C43C22×C4⋊C411yescharacteristic
297Dic43—42no—
298Dic43—44no—
299Dic43—42no—
300Dic43C2×#9518yes—
301C22×#131—431no—
302C2×#520—431no—
303C2×#520—431no—
304#1736—432no—
305#1736—432no—
306#1736—431no—
307#1736D4311yescharacteristic, complemented
308#1735—432no—
309#1735—431no—
310C2×#340—432no—
311C2×#340—431no—
312C2×C43—24no—
313C2×C43C22×#9511yescharacteristic
314C2×C43#289711yescharacteristic
315C2×C43#289711yescharacteristic
316C2×C43#289811yescharacteristic
317C2×C43#289811yescharacteristic
318C2×C43#291211yescharacteristic
319C2×C43#291311yescharacteristic
320D43—28no—
321C22×#41—431no—
322C2×#131—438no—
323C2×#131—864no—
324C2×#131—864no—
325C22×M16—432no—
326C22×M16C2×D4311yescharacteristic
327C23×C8—431no—
328C23×C8—432no—
329#520—438no—
330#520—438no—
331#520—864no—
332#520—864no—
333C2×C4×Q8—861no—
334C2×C4×Q8—861no—
335C2×C4×D4—861no—
336C2×C4×D4—862no—
337C2×C4×D4—861no—
338C2×C4×D4—862no—
339C2×#117—431no—
340C2×#117—432no—
341C2×#117—432no—
342C2×#117C2×D4311yescharacteristic
343C22×C4⋊C4—431no—
344C22×C4⋊C4—432no—
345C22×C4⋊C4—432no—
346C22×C4⋊C4C2×D4311yescharacteristic
347#340—432no—
348#340—432no—
349#340—431no—
350#340—432no—
351#340—432no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340C2×D4312yes—
356#340C2×D4312yes—
357C43#2034811yescharacteristic, complemented, Sylow
358C2×#41—434no—
359C2×#41—434no—
360C2×#41—434no—
361C2×#41—434no—
362C2×#41—434no—
363C2×#41—434no—
364C22×Q8—431no—
365C22×D4—432no—
366C22×D4—431no—
367C23×C4—21no—
368C23×C4—432no—
369C23×C4—862no—
370C23×C4—862no—
371C23×C4—861no—
372C23×C4C22×D4311yescharacteristic
373#131—8632no—
374C2×M16—22no—
375C2×M16—22no—
376C2×M16—438no—
377C2×M16—864no—
378C2×M16—864no—
379C2×M16C4×D4314yescomplemented
380C22×C8—434no—
381C22×C8—431no—
382C22×C8—431no—
383C22×C8—438no—
384C22×C8—864no—
385C22×C8—864no—
386C22×C8—862no—
387C22×C8—862no—
388C22×C8C22×D4312yes—
389C4×Q8—868no—
390C4×Q8—868no—
391C4×D4—868no—
392C4×D4—8616no—
393C4×D4—868no—
394C4×D4—8616no—
395#117—22no—
396#117—434no—
397#117—438no—
398#117—438no—
399#117—864no—
400#117—864no—
401#117—862no—
402#117C4×D4314yescomplemented
403C2×C4⋊C4—21no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—434no—
406C2×C4⋊C4—432no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—438no—
410C2×C4⋊C4—438no—
411C2×C4⋊C4—864no—
412C2×C4⋊C4—864no—
413C2×C4⋊C4—862no—
414C2×C4⋊C4—862no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—862no—
417C2×C4⋊C4C4×D4314yescomplemented
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C4⋊C4C22×D4312yes—
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—862no—
423C2×C22⋊C4—862no—
424C2×C22⋊C4—861no—
425C2×C42—21no—
426C2×C42—862no—
427C2×C42—862no—
428C2×C42—861no—
429C24—432no—
430C24D4×D4311yescharacteristic
431#41—4316no—
432#41—4316no—
433#41—4316no—
434#41—4316no—
435C2×Q8—434no—
436C2×Q8—434no—
437C2×Q8—434no—
438C2×D4—438no—
439C2×D4—438no—
440C2×D4—438no—
441C2×D4—434no—
442C2×D4—434no—
443C2×D4—434no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—24no—
448C22×C4—81no—
449C22×C4—81no—
450C22×C4—432no—
451C22×C4—434no—
452C22×C4—434no—
453C22×C4—434no—
454C22×C4—434no—
455C22×C4—434no—
456C22×C4—434no—
457C22×C4—868no—
458C22×C4—868no—
459C22×C4—864no—
460C22×C4—861no—
461C22×C4—862no—
462C22×C4—861no—
463C22×C4—3442no—
464C22×C4—3442no—
465C22×C4—3442no—
466C22×C4—3442no—
467C22×C4—3441no—
468C22×C4—3441no—
469C22×C4C2×C4×D4312yes—
470C22×C4C2×C4×D4312yes—
471C22×C4C2×C4×D4312yes—
472C22×C4D4×D4311yescharacteristic
473C22×C4D4×D4312yes—
474C22×C4D4×D4312yes—
475C22×C4Q8×D4312yes—
476C22×C4C23×D4311yescharacteristic
477M16—28no—
478M16—8616no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—432no—
482C2×C8—432no—
483C2×C8—8616no—
484C2×C8—868no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8C2×C4×D4314yes—
490C4⋊C4—24no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—434no—
495C4⋊C4—432no—
496C4⋊C4—432no—
497C4⋊C4—868no—
498C4⋊C4—868no—
499C4⋊C4—864no—
500C4⋊C4—861no—
501C4⋊C4—862no—
502C4⋊C4—861no—
503C4⋊C4C2×C4×D4312yes—
504C4⋊C4C2×C4×D4314yes—
505C4⋊C4C2×C4×D4312yes—
506C22⋊C4—24no—
507C22⋊C4—868no—
508C22⋊C4—868no—
509C22⋊C4—864no—
510C42—24no—
511C42—868no—
512C42—868no—
513C42—864no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—434no—
519C23—434no—
520C23—434no—
521C23—862no—
522C23—862no—
523C23—862no—
524C23—862no—
525C23C22⋊C4×D4312yes—
526C23C22⋊C4×D4312yes—
527C23C4⋊C4×D4312yes—
528C23C2×D4×D4311yescharacteristic
529Q8—4316no—
530D4—4332no—
531D4—4316no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—84no—
542C2×C4—434no—
543C2×C4—434no—
544C2×C4—434no—
545C2×C4—438no—
546C2×C4—438no—
547C2×C4—438no—
548C2×C4—438no—
549C2×C4—862no—
550C2×C4—864no—
551C2×C4—862no—
552C2×C4—3448no—
553C2×C4—3448no—
554C2×C4—3444no—
555C2×C4—1722no—
556C2×C4—1721no—
557C2×C4—1722no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4C42×D4314yes—
562C2×C4C22⋊C4×D4314yes—
563C2×C4C22⋊C4×D4312yes—
564C2×C4C22⋊C4×D4312yes—
565C2×C4C4⋊C4×D4314yes—
566C2×C4C4⋊C4×D4314yes—
567C2×C4C4⋊C4×D4312yes—
568C2×C4C22×C4×D4311yescharacteristic
569C2×C4C22×C4×D4311yescharacteristic
570C2×C4C22×C4×D4311yescharacteristic
571C2×C4C2×D4×D4311yescharacteristic
572C2×C4C2×D4×D4311yescharacteristic
573C2×C4C2×Q8×D4311yescharacteristic
574C8—24no—
575C8—862no—
576C8—862no—
577C22—22no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—438no—
584C22—864no—
585C22—864no—
586C22—864no—
587C22—864no—
588C22—864no—
589C22—864no—
590C22#95×D4314yes—
591C22C2×C22⋊C4×D4311yescharacteristic
592C22C2×C22⋊C4×D4311yescharacteristic
593C22C2×C4⋊C4×D4311yescharacteristic
594C22#1458370311yescharacteristic
595C22#1458370811yescharacteristic
596C22#1458370911yescharacteristic
597C22#1458371511yescharacteristic
598C4—42no—
599C4—44no—
600C4—42no—
601C4—438no—
602C4—1724no—
603C4—1722no—
604C4—1722no—
605C4#95×D4314yes—
606C4C2×C42×D4311yescharacteristic
607C4C2×C22⋊C4×D4311yescharacteristic
608C4C2×C4⋊C4×D4311yescharacteristic
609C4C2×C4⋊C4×D4311yescharacteristic
610C2—24no—
611C2—868no—
612C2C2×#95×D4311yescharacteristic
613C2#1914311911yescharacteristic
614C2#1914312011yescharacteristic
615C2#1914312611yescharacteristic
616C2#1914312711yescharacteristic
617C2#1914318911yescharacteristic
618C2#1914319411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC43×#1736C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1736D43
hypocenterC43#20348
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. #19134315C2semidirect
5. #19134313C2semidirect
6. #19134313C2semidirect
7. #19134311C2semidirect
8. #19134310C2semidirect
9. C2×#14582661C2semidirect
10. #340×D43C2semidirect
11. C43×#1736C2semidirect
15. C2×#13063333C4semidirect
20. #14583380C4semidirect
22. #14583379C4semidirect
64. C2×#10621872C2×C4semidirect
67. C22×C43⋊C8C2×C4semidirect
72. C2×C8×D43C2×C4semidirect
80. #13063284C2×C4semidirect
83. #13063283C2×C4semidirect
84. #13063283C2×C4semidirect
87. C2×C4⋊Dic43C2×C4semidirect
95. C4⋊C4×D43C2×C4semidirect
96. C4⋊C4×D43C2×C4semidirect
107. C2×M16×C43C2×C4semidirect
110. #117×C43C2×C4semidirect
113. C2×C4⋊C4×C43C2×C4semidirect
307. #1736D43semidirect
357. C43#20348semidirect
379. C2×M16C4×D43semidirect
402. #117C4×D43semidirect
417. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633332
C2×#145833802
C2×#145833792
#191343152
#191343132
#191343112
#191343102
C2×#145826612
#340×D432
C43×#17362
#2034843