Finite Group Databasebeta

← #25112695

Subgroups — #25112695

Order 11008.

1412 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621898C211yesmaximal, characteristic
2C2×#14582974C212yesmaximal, complemented
3#19135529C212yesmaximal, complemented
4#19134891C212yesmaximal, complemented
5#19134890C212yesmaximal, complemented
6#19134662C211yesmaximal, characteristic, complemented
7#19134574C211yesmaximal, characteristic, complemented
8#19134352C211yesmaximal, characteristic, complemented
9#19134289C211yesmaximal, characteristic, complemented
10#19134287C211yesmaximal, characteristic, complemented
11C43×#1817C211yesmaximal, characteristic, complemented
12C22×#10621898C411yescharacteristic
13C22×#10621877C2212yes—
14C22×#10621872C2212yes—
15C4×#10621898—28no—
16C2×C4×Dic86C411yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×C4×D172C411yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×C22⋊D43C411yescharacteristic
21C2×C4×C22⋊D43C411yescharacteristic
22C2×C4×C22⋊D43C2211yescharacteristic
23C2×C4×C22⋊D43C2211yescharacteristic
24C2×#13063284C411yescharacteristic
25C2×#13063282C411yescharacteristic
26C2×#13063282C411yescharacteristic
27C2×C42×D43C2211yescharacteristic
28C2×C42×D43C2211yescharacteristic
29#14582974—28no—
30C2×Dic43⋊C8C2212yes—
31C2×(C2×D43)⋊C8C2212yes—
32C2×(C2×D43)⋊C8C2212yes—
33C2×(C2×D43)⋊C8C2212yes—
34C2×C8×Dic43C2212yes—
35#14582654C2212yes—
36#14582654C2211yescharacteristic
37#14582654C2211yescharacteristic
38#14582653C2212yes—
39#14582653C2212yes—
40C22×C42×C43C2211yescharacteristic
41C2×C22⋊C8×C43C2212yes—
42C43×#336C2212yes—
43C43×#336C2211yescharacteristic
44C43×#336C2211yescharacteristic
45C2×#10621898—24no—
46C2×#10621898—24no—
47C2×#10621898—24no—
48C22×Dic86C2×C411yescharacteristic
49C22×D172C2×C411yescharacteristic
50C22×C22⋊D43C2×C411yescharacteristic
51C22×C22⋊D43C2×C411yescharacteristic
52C22×C4×D43C2×C411yescharacteristic
53C22×C4×D43C2×C411yescharacteristic
54C22×C4×D43C2×C411yescharacteristic
55C22×C4×D43C2×C411yescharacteristic
56C22×C4×D43C2311yescharacteristic
57C22×C4×D43C2311yescharacteristic
58C2×#10621877—24no—
59C2×#10621877—24no—
60C2×#10621877—42no—
61C2×#10621872—24no—
62C2×#10621872—24no—
63C2×#10621872—42no—
64C22×C43⋊C8C2312yes—
65C22×C43⋊C8C2312yes—
66C4×Dic86—24no—
67C4×Dic86—24no—
68C4×D172—24no—
69C4×D172—24no—
70C4×C22⋊D43—24no—
71C4×C22⋊D43—24no—
72C4×C22⋊D43—24no—
73C4×C22⋊D43D418yes—
74#13063284—24no—
75#13063282—24no—
76#13063282—24no—
77C2×C4⋊Dic43C2×C411yescharacteristic
78C2×C4⋊Dic43C2×C411yescharacteristic
79C2×Dic43⋊C4C2×C411yescharacteristic
80C2×Dic43⋊C4C2×C411yescharacteristic
81C2×Dic43⋊C4C2×C411yescharacteristic
82C2×Dic43⋊C4C2×C411yescharacteristic
83C2×C22⋊Dic43C2×C411yescharacteristic
84C2×C22⋊Dic43C2×C411yescharacteristic
85C2×(C2×D43)⋊C4C2×C411yescharacteristic
86C2×(C2×D43)⋊C4C2×C411yescharacteristic
87C2×(C2×D43)⋊C4C2×C411yescharacteristic
88C2×(C2×D43)⋊C4C2×C411yescharacteristic
89C2×C4×Dic43C2×C411yescharacteristic
90C2×C4×Dic43C2×C411yescharacteristic
91C2×C4×Dic43C2×C411yescharacteristic
92C2×C4×Dic43C2×C411yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95C42×D43—24no—
96C42×D43—24no—
97Dic43⋊C8—24no—
98(C2×D43)⋊C8—24no—
99(C2×D43)⋊C8—24no—
100(C2×D43)⋊C8—42no—
101C8×Dic43—24no—
102C23×C4×C43C2×C411yescharacteristic
103C23×C4×C43C2×C411yescharacteristic
104C23×C4×C43C2311yescharacteristic
105C22×C8×C43C2312yes—
106C22×C8×C43C2312yes—
107C2×C42×C43—24no—
108C2×C42×C43C2×C411yescharacteristic
109C2×C42×C43C2×C411yescharacteristic
110C2×C42×C43C2311yescharacteristic
111C2×C42×C43C2311yescharacteristic
112C22⋊C8×C43—24no—
113C24×C43C22×C411yescharacteristic
114C23×D43C22×C411yescharacteristic
115C23×D43C22×C411yescharacteristic
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—41no—
125C22×C4×C43C22×C411yescharacteristic
126C22×C4×C43C22×C411yescharacteristic
127C22×C4×C43C22×C411yescharacteristic
128C22×C4×C43C22×C411yescharacteristic
129C22×C4×C43C22×C411yescharacteristic
130C22×C4×C43C2×D414yes—
131C22×C4×C43C2411yescharacteristic
132C2×C22⋊D43—22no—
133C2×C22⋊D43—22no—
134C2×C22⋊D43—22no—
135C2×C22⋊D43—22no—
136C2×C22⋊D43—22no—
137C2×C22⋊D43C22⋊C414yes—
138C22×Dic43C22×C411yescharacteristic
139C22×Dic43C22×C411yescharacteristic
140C22×Dic43C22×C411yescharacteristic
141C22×Dic43C22×C411yescharacteristic
142C22×Dic43C22×C411yescharacteristic
143C22×Dic43C22×C411yescharacteristic
144#10621898—232no—
145C2×D172—22no—
146C2×D172—22no—
147C2×D172—22no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—22no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—22no—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—41no—
165C2×C4×D43—41no—
166C2×C4×D43M1614yescomplemented
167C2×C4×D43C2×D414yes—
168C2×Dic86—22no—
169C2×Dic86—22no—
170C2×Dic86M1614yescomplemented
171C2×C8×C43—22no—
172C2×C8×C43—22no—
173C2×C8×C43—22no—
174C2×C8×C43—22no—
175C2×C8×C43—22no—
176C2×C8×C43—22no—
177C42×C43—22no—
178C42×C43—22no—
179C42×C43—22no—
180C42×C43—22no—
181C22⋊Dic43—22no—
182C22⋊Dic43C22⋊C414yes—
183(C2×D43)⋊C4—22no—
184(C2×D43)⋊C4—22no—
185(C2×D43)⋊C4—22no—
186(C2×D43)⋊C4C22⋊C414yes—
187C4⋊Dic43—22no—
188C4⋊Dic43—22no—
189Dic43⋊C4—22no—
190Dic43⋊C4—22no—
191Dic43⋊C4—22no—
192Dic43⋊C4C22⋊C414yes—
193C4×Dic43—22no—
194C4×Dic43—22no—
195C4×Dic43—22no—
196C4×Dic43—22no—
197C4×Dic43—22no—
198C4×Dic43C2×D414yes—
199#10621877—48no—
200C2×C43⋊C8—22no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—22no—
205C2×C43⋊C8#4114yescomplemented
206#10621872—48no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43C2×C22⋊C412yes—
214C23×C43C23×C411yescharacteristic
215C22×D43—21no—
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—21no—
227C22×D43C2×C22⋊C412yes—
228C22×D43C2×M1612yes—
229C2×C4×C43—28no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—24no—
239C2×C4×C43—24no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—44no—
244C2×C4×C43C2×C22⋊C412yes—
245C2×C4×C43C2×M1612yes—
246C2×C4×C43C2×M1612yes—
247C2×C4×C43#13112yes—
248C2×C4×C43C22×D412yes—
249C2×C4×C43C2×#4112yes—
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C2×C4×C432−1+411yescharacteristic
252C22⋊D43—28no—
253C22⋊D43—28no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43C2×C22⋊C412yes—
267C2×Dic43C2×C22⋊C412yes—
268C2×Dic43C2×C22⋊C412yes—
269C2×Dic43C2×M1612yes—
270C2×Dic43C2×M1612yes—
271C2×Dic43C2×M1612yes—
272D172—28no—
273C4×D43—28no—
274C4×D43—24no—
275C4×D43—24no—
276C4×D43—28no—
277C4×D43—44no—
278C4×D43—44no—
279C4×D43—42no—
280C4×D43—42no—
281Dic86—28no—
282C8×C43—42no—
283C8×C43—42no—
284C43⋊C8—24no—
285C43⋊C8—42no—
286#22473—431nomaximal, Sylow
287C22×C43—22no—
288C22×C43—22no—
289C22×C43—22no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43C22×C22⋊C411yescharacteristic
295C22×C43C4×#4111yescharacteristic
296C22×C43#52011yescharacteristic
297C22×C43C22×M1611yescharacteristic
298C22×C43C22×M1611yescharacteristic
299C22×C43C2×#13111yescharacteristic
300C22×C43#56811yescharacteristic
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—22no—
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—41no—
308C2×D43—41no—
309C2×D43—41no—
310C2×D43—41no—
311C2×D43—41no—
312C2×D43—41no—
313C2×D43—41no—
314C2×D43—41no—
315C4×C43—22no—
316C4×C43—22no—
317C4×C43—22no—
318C4×C43—22no—
319C4×C43—41no—
320C4×C43#54612yes—
321C4×C43#54712yes—
322Dic43—22no—
323Dic43—22no—
324Dic43—22no—
325Dic43—41no—
326Dic43—41no—
327Dic43#40714yes—
328C2×C4×#41—431no—
329C2×#436—432no—
330#1984—432no—
331#1870—432no—
332#1870—432no—
333#1817—431no—
334#1817D4311yescharacteristic, complemented
335#1797—431no—
336C4×C22⋊C8—431no—
337#1728—431no—
338#1728—431no—
339C2×C43—42no—
340C2×C43#233911yescharacteristic
341C2×C43C2×#40711yescharacteristic
342C2×C43#288011yescharacteristic
343C2×C43#296511yescharacteristic
344C2×C43#297111yescharacteristic
345C2×C43#298911yescharacteristic
346C2×C43#299111yescharacteristic
347D43—42no—
348D43—42no—
349C22×#41—431no—
350C22×M16—432no—
351C22×M16—432no—
352C4×#41—868no—
353C2×C4×Q8—431no—
354C2×C4×Q8—431no—
355C2×C4×D4—431no—
356C2×C4×D4—431no—
357C2×C4×D4—431no—
358C2×C4×D4—431no—
359C2×C4×D4—431no—
360C2×C4×D4—431no—
361C2×#117—431no—
362C2×#117—431no—
363C2×#117—431no—
364C22×C42—431no—
365C22×C42—431no—
366C22×C42C2×D4311yescharacteristic
367#436—868no—
368C2×C4⋊C8—432no—
369C2×C22⋊C8—432no—
370C2×C22⋊C8—432no—
371C2×C22⋊C8—432no—
372C2×C22⋊C8C2×D4312yes—
373C2×C4×C8—432no—
374#336—432no—
375#336—432no—
376#336—431no—
377#336—432no—
378#336—431no—
379#336C2×D4311yescharacteristic
380#336C2×D4311yescharacteristic
381#336C2×D4312yes—
382C43#2247311yescharacteristic, complemented, Sylow
383C2×#41—864no—
384C2×#41—864no—
385C2×#41—864no—
386C22×Q8—431no—
387C22×D4—431no—
388C22×D4—431no—
389C22×D4—431no—
390C23×C4—431no—
391C23×C4—431no—
392C23×C4—431no—
393C23×C4—431no—
394C23×C4—431no—
395C23×C4—431no—
396C23×C4C4×D4311yescharacteristic
397C23×C4C4×D4311yescharacteristic
398C23×C4C22×D4311yescharacteristic
399C2×M16—864no—
400C2×M16—864no—
401C2×M16—864no—
402C2×M16—864no—
403C2×M16—1722no—
404C2×M16—1722no—
405C22×C8—432no—
406C22×C8—432no—
407C22×C8C22×D4312yes—
408C22×C8C22×D4312yes—
409C4×Q8—864no—
410C4×Q8—864no—
411C4×D4—438no—
412C4×D4—864no—
413C4×D4—864no—
414C4×D4—864no—
415C4×D4—864no—
416C4×D4—864no—
417#117—864no—
418#117—864no—
419#117—864no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C22⋊C4—431no—
427C2×C22⋊C4—431no—
428C2×C22⋊C4—431no—
429C2×C22⋊C4—431no—
430C2×C22⋊C4—431no—
431C2×C22⋊C4—431no—
432C2×C42—24no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—864no—
440C2×C42—864no—
441C2×C42C4×D4311yescharacteristic
442C2×C42C4×D4311yescharacteristic
443C2×C42C22×D4311yescharacteristic
444C2×C42C22×D4311yescharacteristic
445C4⋊C8—864no—
446C22⋊C8—24no—
447C22⋊C8—864no—
448C22⋊C8—864no—
449C22⋊C8—1722no—
450C4×C8—864no—
451C24—431no—
452C24—431no—
453C24C2×C4×D4311yescharacteristic
454#41—8632no—
455C2×Q8—434no—
456C2×Q8—862no—
457C2×Q8—862no—
458C2×D4—434no—
459C2×D4—862no—
460C2×D4—862no—
461C2×D4—862no—
462C2×D4—862no—
463C2×D4—862no—
464C2×D4—862no—
465C2×D4—862no—
466C2×D4—862no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—41no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—434no—
481C22×C4—434no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—1721no—
501C22×C4—1721no—
502C22×C4C2×C4×D4311yescharacteristic
503C22×C4C2×C4×D4311yescharacteristic
504C22×C4C2×C4×D4311yescharacteristic
505C22×C4C2×C4×D4311yescharacteristic
506C22×C4C2×C4×D4311yescharacteristic
507C22×C4D4×D4314yes—
508C22×C4C23×D4311yescharacteristic
509M16—1728no—
510M16—1728no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—434no—
518C2×C8—862no—
519C2×C8—862no—
520C2×C8—862no—
521C2×C8—862no—
522C2×C8—862no—
523C4⋊C4—434no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C4⋊C4—862no—
527C4⋊C4—862no—
528C4⋊C4—862no—
529C22⋊C4—434no—
530C22⋊C4—434no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C42—22no—
536C42—22no—
537C42—22no—
538C42—22no—
539C42—434no—
540C42—862no—
541C42—862no—
542C42—862no—
543C42—862no—
544C42—862no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—432no—
552C23—432no—
553C23—861no—
554C23—861no—
555C23—861no—
556C23—861no—
557C23—861no—
558C23—861no—
559C23—861no—
560C23—861no—
561C23—861no—
562C23—861no—
563C23—861no—
564C23—861no—
565C23C22⋊C4×D4312yes—
566C23C22×C4×D4311yescharacteristic
567Q8—868no—
568D4—868no—
569D4—868no—
570D4—868no—
571C2×C4—28no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—44no—
586C2×C4—432no—
587C2×C4—432no—
588C2×C4—432no—
589C2×C4—432no—
590C2×C4—432no—
591C2×C4—432no—
592C2×C4—868no—
593C2×C4—868no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—864no—
601C2×C4—864no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—1724no—
609C2×C4—1724no—
610C2×C4—1722no—
611C2×C4—1722no—
612C2×C4C22⋊C4×D4312yes—
613C2×C4M16×D4312yes—
614C2×C4M16×D4312yes—
615C2×C4#1306333112yes—
616C2×C4C2×D4×D4312yes—
617C2×C4#41×D4312yes—
618C2×C4#1306337111yescharacteristic
619C2×C4#1306337211yescharacteristic
620C8—42no—
621C8—42no—
622C8—864no—
623C8—1722no—
624C22—22no—
625C22—22no—
626C22—22no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—862no—
632C22—862no—
633C22—862no—
634C22—862no—
635C22—862no—
636C22—862no—
637C22—1721no—
638C22—1721no—
639C22—1721no—
640C22—1721no—
641C22—1721no—
642C22—1721no—
643C22—1721no—
644C22—1721no—
645C22C2×C22⋊C4×D4311yescharacteristic
646C22#1458336711yescharacteristic
647C22#1458337911yescharacteristic
648C22C2×M16×D4311yescharacteristic
649C22C2×M16×D4311yescharacteristic
650C22C2×#1306333111yescharacteristic
651C22#1458366511yescharacteristic
652C4—22no—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—41no—
657C4—434no—
658C4—862no—
659C4—862no—
660C4—862no—
661C4—1721no—
662C4—1721no—
663C4#1458354112yes—
664C4#1458354712yes—
665C2—42no—
666C2—1722no—
667C2—1722no—
668C2#1913741911yescharacteristic
669C2#407×D4311yescharacteristic
670C2#1914304111yescharacteristic
671C2#1914355911yescharacteristic
672C2#1914361211yescharacteristic
673C2#1914371411yescharacteristic
674C2#1914372411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1817C2
prime radicalC22×#10621898C4
cosocleC22×C4×C43C24
hypercenter#1817D43
hypocenterC43#22473
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. C2×#14582974C2semidirect
3. #19135529C2semidirect
4. #19134891C2semidirect
5. #19134890C2semidirect
6. #19134662C2semidirect
7. #19134574C2semidirect
8. #19134352C2semidirect
9. #19134289C2semidirect
10. #19134287C2semidirect
11. C43×#1817C2semidirect
166. C2×C4×D43M16semidirect
170. C2×Dic86M16semidirect
205. C2×C43⋊C8#41semidirect
334. #1817D43semidirect
382. C43#22473semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106218982
C2×#145829742
#191355292
#191348912
#191348902
#191346622
#191345742
#191343522
#191342892
#191342872
C43×#18172
#2247343