Finite Group Databasebeta

← #25094003

Subgroups — #25094003

Order 11008.

2270 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D43C211yesmaximal, characteristic
2C22×#13063283C211yesmaximal, characteristic
3C2×#117×D43C211yesmaximal, characteristic
4#19134316C211yesmaximal, characteristic, complemented
5#19134315C211yesmaximal, characteristic, complemented
6#19134314C211yesmaximal, characteristic, complemented
7#19134313C214yesmaximal, complemented
8#19134310C214yesmaximal, complemented
9C43×#1736C211yesmaximal, characteristic, complemented
10C23×C4×D43C2211yescharacteristic
11C22×#10621877C2211yescharacteristic
12C22×#10621872C2212yes—
13C2×M16×D43—24no—
14C2×M16×D43—24no—
15C2×M16×D43C418yescomplemented
16C22×C8×D43C2212yes—
17C2×#13063284C2211yescharacteristic
18C2×#13063283—24no—
19C2×#13063283—21no—
20C2×#13063283—21no—
21C2×#13063283C418yescomplemented
22C2×#13063283C2212yes—
23C2×#13063283C2212yes—
24C2×#13063283C2212yes—
25C2×#13063282—21no—
26C2×#13063281—21no—
27#117×D43—24no—
28#117×D43C418yescomplemented
29C22×C4⋊Dic43C2211yescharacteristic
30C2×C4⋊C4×D43C2212yes—
31C22×(C2×D43)⋊C4—21no—
32C2×C22⋊C4×D43—21no—
33C22×C4×Dic43—21no—
34C2×C42×D43—21no—
35#14582662C2214yescomplemented
36#14582661C2214yescomplemented
37#14582661C2214yescomplemented
38C22×M16×C43C2211yescharacteristic
39C2×#117×C43C2211yescharacteristic
40C22×C4⋊C4×C43C2211yescharacteristic
41C43×#340C2214yescomplemented
42C24×D43D411yescharacteristic
43C23×Dic43—21no—
44C23×Dic43D411yescharacteristic
45C22×C4×D43—22no—
46C22×C4×D43C2×C414yes—
47C22×C4×D43C2×C414yes—
48C22×C4×D43C2×C414yes—
49C22×C4×D43D411yescharacteristic
50C22×C4×D43D411yescharacteristic
51C22×C4×D43D414yes—
52C22×C4×D43D414yes—
53C22×C4×D43Q814yes—
54C22×C4×D43C2311yescharacteristic
55C22×C4×D43C2311yescharacteristic
56C2×#10621877—22no—
57C2×#10621877—22no—
58C2×#10621877C2×C414yescomplemented
59C2×#10621872—24no—
60C2×#10621872—24no—
61C2×#10621872C2×C418yescomplemented
62M16×D43—232no—
63C22×C43⋊C8C2312yes—
64C2×C8×D43—24no—
65C2×C8×D43—24no—
66C2×C8×D43C2×C418yescomplemented
67#13063284—22no—
68#13063284C2×C414yes—
69#13063283—28no—
70#13063283—28no—
71#13063283—24no—
72#13063283—24no—
73#13063283—24no—
74#13063283C2×C418yes—
75#13063283C2×C418yescomplemented
76#13063283C2×C418yescomplemented
77#13063282—28no—
78#13063281—28no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—22no—
81C2×C4⋊Dic43C2×C414yescomplemented
82C2×C4⋊Dic43C2312yes—
83C2×C4⋊Dic43C2312yes—
84C2×Dic43⋊C4—22no—
85C4⋊C4×D43—24no—
86C4⋊C4×D43C2×C418yescomplemented
87C2×C22⋊Dic43—21no—
88C2×(C2×D43)⋊C4—28no—
89C2×(C2×D43)⋊C4—22no—
90C2×(C2×D43)⋊C4—22no—
91C2×(C2×D43)⋊C4—22no—
92C22⋊C4×D43—28no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—28no—
95C2×C4×Dic43—22no—
96C2×C4×Dic43—22no—
97C2×C4×Dic43—22no—
98C42×D43—28no—
99C23×C4×C43—21no—
100C23×C4×C43C2311yescharacteristic
101C2×M16×C43—22no—
102C2×M16×C43—22no—
103C2×M16×C43C2×C414yescomplemented
104C22×C8×C43C2312yes—
105#117×C43—22no—
106#117×C43C2×C414yes—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—22no—
109C2×C4⋊C4×C43C2×C414yescomplemented
110C2×C4⋊C4×C43C2312yes—
111C2×C4⋊C4×C43C2312yes—
112C2×C22⋊C4×C43—21no—
113C2×C42×C43—21no—
114C24×C43C2×D411yescharacteristic
115C23×D43—42no—
116C23×D43—42no—
117C23×D43C22⋊C414yes—
118C23×D43C22⋊C414yes—
119C23×D43C4⋊C414yes—
120C23×D43C2×D411yescharacteristic
121C23×D43C2×D411yescharacteristic
122C22×C4×C43—24no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—44no—
126C22×C4×C43C22×C412yes—
127C22×C4×C43C22×C412yes—
128C22×C4×C43C22×C412yes—
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×Q812yes—
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—24no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—44no—
138C22×Dic43C22⋊C414yes—
139C22×Dic43C22⋊C414yes—
140C22×Dic43C4⋊C414yes—
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C2×C4×D43—28no—
144C2×C4×D43—44no—
145C2×C4×D43—44no—
146C2×C4×D43C42116yes—
147C2×C4×D43C22⋊C4116yes—
148C2×C4×D43C22⋊C414yes—
149C2×C4×D43C22⋊C414yes—
150C2×C4×D43C22⋊C414yes—
151C2×C4×D43C22⋊C414yes—
152C2×C4×D43C4⋊C4116yes—
153C2×C4×D43C4⋊C4116yes—
154C2×C4×D43C4⋊C414yes—
155C2×C4×D43C4⋊C414yes—
156C2×C4×D43C22×C412yes—
157C2×C4×D43C22×C412yes—
158C2×C4×D43C22×C412yes—
159C2×C4×D43C22×C412yes—
160C2×C4×D43C22×C412yes—
161C2×C4×D43C22×C412yes—
162C2×C4×D43C2×D412yes—
163C2×C4×D43C2×D412yes—
164C2×C4×D43C2×D412yes—
165C2×C4×D43C2×D412yes—
166C2×C4×D43C2×Q812yes—
167C2×C4×D43C2×Q812yes—
168M16×C43—28no—
169C2×C8×C43—22no—
170C2×C8×C43—22no—
171C2×C8×C43C22×C414yes—
172C4⋊C4×C43—24no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43C22×C414yes—
176C4⋊C4×C43C22×C414yes—
177C22⋊C4×C43—24no—
178C42×C43—24no—
179C22⋊Dic43—24no—
180(C2×D43)⋊C4—28no—
181(C2×D43)⋊C4—28no—
182(C2×D43)⋊C4—28no—
183C4⋊Dic43—24no—
184C4⋊Dic43—22no—
185C4⋊Dic43—22no—
186C4⋊Dic43C22×C414yes—
187C4⋊Dic43C22×C414yes—
188Dic43⋊C4—28no—
189C4×Dic43—24no—
190C4×Dic43—28no—
191C4×Dic43—28no—
192C4×Dic43—28no—
193#10621877—28no—
194C2×C43⋊C8—22no—
195C2×C43⋊C8—22no—
196C2×C43⋊C8C22×C414yes—
197#10621872—216no—
198C8×D43—216no—
199C23×C43—22no—
200C23×C43—22no—
201C23×C43C2×C22⋊C412yes—
202C23×C43C2×C22⋊C412yes—
203C23×C43C2×C4⋊C412yes—
204C23×C43C22×D411yescharacteristic
205C22×D43—22no—
206C22×D43—22no—
207C22×D43—22no—
208C22×D43—22no—
209C22×D43—44no—
210C22×D43—44no—
211C22×D43—48no—
212C22×D43—48no—
213C22×D43#95116yes—
214C22×D43C2×C22⋊C412yes—
215C22×D43C2×C22⋊C412yes—
216C22×D43C2×C22⋊C412yes—
217C22×D43C2×C22⋊C412yes—
218C22×D43C2×C4⋊C412yes—
219C22×D43C2×C4⋊C412yes—
220C2×C4×C43—24no—
221C2×C4×C43—24no—
222C2×C4×C43—48no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—44no—
226C2×C4×C43C2×C4214yes—
227C2×C4×C43C2×C22⋊C414yes—
228C2×C4×C43C2×C22⋊C412yes—
229C2×C4×C43C2×C22⋊C412yes—
230C2×C4×C43C2×C4⋊C414yes—
231C2×C4×C43C2×C4⋊C414yes—
232C2×C4×C43C2×C4⋊C412yes—
233C2×C4×C43C23×C411yescharacteristic
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C23×C411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×Q811yescharacteristic
239C2×Dic43—24no—
240C2×Dic43—24no—
241C2×Dic43—48no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—44no—
245C2×Dic43#95116yes—
246C2×Dic43C2×C22⋊C412yes—
247C2×Dic43C2×C22⋊C412yes—
248C2×Dic43C2×C22⋊C412yes—
249C2×Dic43C2×C22⋊C412yes—
250C2×Dic43C2×C4⋊C412yes—
251C2×Dic43C2×C4⋊C412yes—
252C4×D43—416no—
253C4×D43#95116yes—
254C4×D43#95116yes—
255C4×D43C2×C4214yes—
256C4×D43C2×C4214yes—
257C4×D43C2×C22⋊C414yes—
258C4×D43C2×C22⋊C414yes—
259C4×D43C2×C4⋊C414yes—
260C4×D43C2×C4⋊C414yes—
261C4×D43C2×C4⋊C414yes—
262C4×D43C2×C4⋊C414yes—
263C8×C43—24no—
264C43⋊C8—24no—
265#20347—431nomaximal, Sylow
266C22×C43—24no—
267C22×C43—22no—
268C22×C43—22no—
269C22×C43—24no—
270C22×C43C2×#9514yes—
271C22×C43C22×C22⋊C411yescharacteristic
272C22×C43C22×C22⋊C411yescharacteristic
273C22×C43C22×C4⋊C411yescharacteristic
274C22×C43#57512yes—
275C22×C43#57512yes—
276C2×D43—22no—
277C2×D43—22no—
278C2×D43—24no—
279C2×D43—22no—
280C2×D43—22no—
281C2×D43—24no—
282C2×D43—24no—
283C2×D43—24no—
284C2×D43—416no—
285C2×D43C2×#9514yes—
286C2×D43C2×#9514yes—
287C4×C43—44no—
288C4×C43—44no—
289C4×C43C2×#9514yes—
290C4×C43C22×C4211yescharacteristic
291C4×C43C22×C22⋊C411yescharacteristic
292C4×C43C22×C4⋊C411yescharacteristic
293C4×C43C22×C4⋊C411yescharacteristic
294Dic43—44no—
295Dic43—44no—
296Dic43C2×#9514yes—
297Dic43C2×#9514yes—
298C23×M16—431no—
299C22×#117—431no—
300C22×#117—431no—
301#1736—434no—
302#1736—431no—
303#1736—431no—
304#1736—431no—
305#1736D4311yescharacteristic, complemented
306#1735—434no—
307C2×C43—24no—
308C2×C43C22×#9511yescharacteristic
309C2×C43#289611yescharacteristic
310C2×C43#289612yes—
311C2×C43#289611yescharacteristic
312C2×C43#291112yes—
313D43—24no—
314D43—24no—
315C24×C4—431no—
316C22×M16—431no—
317C22×M16—438no—
318C22×M16—432no—
319C22×M16—864no—
320C22×M16—864no—
321C22×M16C2×D4311yescharacteristic
322C23×C8—432no—
323C2×#117—431no—
324C2×#117—438no—
325C2×#117—432no—
326C2×#117—432no—
327C2×#117—432no—
328C2×#117—438no—
329C2×#117—861no—
330C2×#117—861no—
331C2×#117—861no—
332C2×#117—864no—
333C2×#117—861no—
334C2×#117—864no—
335C2×#117C2×D4311yescharacteristic
336C22×C4⋊C4—431no—
337C22×C4⋊C4—432no—
338C22×C4⋊C4C2×D4311yescharacteristic
339C22×C22⋊C4—861no—
340C22×C22⋊C4—861no—
341C22×C42—861no—
342C22×C42—861no—
343#340—434no—
344#340—434no—
345#340—434no—
346#340C2×D4314yescomplemented
347C43#2034711yescharacteristic, complemented, Sylow
348C25—431no—
349C23×C4—21no—
350C23×C4—431no—
351C23×C4—434no—
352C23×C4—434no—
353C23×C4—434no—
354C23×C4—431no—
355C23×C4—434no—
356C23×C4—434no—
357C23×C4—431no—
358C23×C4—434no—
359C23×C4—431no—
360C23×C4—431no—
361C23×C4—862no—
362C23×C4—861no—
363C23×C4C22×D4311yescharacteristic
364C2×M16—22no—
365C2×M16—22no—
366C2×M16—434no—
367C2×M16—438no—
368C2×M16—864no—
369C2×M16—864no—
370C2×M16—8632no—
371C2×M16—862no—
372C2×M16—862no—
373C2×M16C4×D4314yescomplemented
374C22×C8—432no—
375C22×C8—438no—
376C22×C8—864no—
377C22×C8—864no—
378C22×C8C22×D4312yes—
379#117—22no—
380#117—434no—
381#117—438no—
382#117—438no—
383#117—438no—
384#117—868no—
385#117—868no—
386#117—868no—
387#117—868no—
388#117—864no—
389#117—864no—
390#117—864no—
391#117—862no—
392#117C4×D4314yes—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—434no—
396C2×C4⋊C4—432no—
397C2×C4⋊C4—432no—
398C2×C4⋊C4—438no—
399C2×C4⋊C4—864no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—862no—
403C2×C4⋊C4C4×D4314yescomplemented
404C2×C4⋊C4C22×D4312yes—
405C2×C4⋊C4C22×D4312yes—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—868no—
408C2×C22⋊C4—868no—
409C2×C22⋊C4—862no—
410C2×C22⋊C4—862no—
411C2×C22⋊C4—862no—
412C2×C22⋊C4—861no—
413C2×C42—21no—
414C2×C42—868no—
415C2×C42—868no—
416C2×C42—862no—
417C2×C42—862no—
418C2×C42—862no—
419C2×C42—861no—
420C24—431no—
421C24—431no—
422C24—434no—
423C24—434no—
424C24—434no—
425C24—1722no—
426C24—1722no—
427C24D4×D4311yescharacteristic
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—44no—
432C22×C4—434no—
433C22×C4—434no—
434C22×C4—434no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—4316no—
438C22×C4—434no—
439C22×C4—434no—
440C22×C4—434no—
441C22×C4—434no—
442C22×C4—4316no—
443C22×C4—434no—
444C22×C4—434no—
445C22×C4—4316no—
446C22×C4—4316no—
447C22×C4—432no—
448C22×C4—432no—
449C22×C4—432no—
450C22×C4—432no—
451C22×C4—432no—
452C22×C4—432no—
453C22×C4—432no—
454C22×C4—432no—
455C22×C4—432no—
456C22×C4—432no—
457C22×C4—432no—
458C22×C4—432no—
459C22×C4—868no—
460C22×C4—864no—
461C22×C4—862no—
462C22×C4—862no—
463C22×C4—1724no—
464C22×C4—1724no—
465C22×C4—1724no—
466C22×C4C2×C4×D4312yes—
467C22×C4C2×C4×D4312yes—
468C22×C4C2×C4×D4312yes—
469C22×C4D4×D4311yescharacteristic
470C22×C4D4×D4312yes—
471C22×C4D4×D4312yes—
472C22×C4Q8×D4312yes—
473C22×C4C23×D4311yescharacteristic
474M16—28no—
475M16—8616no—
476M16—868no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—434no—
480C2×C8—8616no—
481C2×C8—862no—
482C2×C8—862no—
483C2×C8C2×C4×D4314yes—
484C4⋊C4—24no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—434no—
488C4⋊C4—434no—
489C4⋊C4—868no—
490C4⋊C4—864no—
491C4⋊C4—862no—
492C4⋊C4—862no—
493C4⋊C4C2×C4×D4314yes—
494C4⋊C4C2×C4×D4314yes—
495C22⋊C4—24no—
496C22⋊C4—868no—
497C22⋊C4—868no—
498C22⋊C4—868no—
499C22⋊C4—864no—
500C42—24no—
501C42—868no—
502C42—868no—
503C42—868no—
504C42—864no—
505C23—22no—
506C23—22no—
507C23—432no—
508C23—432no—
509C23—432no—
510C23—432no—
511C23—432no—
512C23—432no—
513C23—4316no—
514C23—862no—
515C23—862no—
516C23—862no—
517C23—862no—
518C23—1728no—
519C23—1724no—
520C23—1728no—
521C23—1724no—
522C23C22⋊C4×D4312yes—
523C23C22⋊C4×D4312yes—
524C23C4⋊C4×D4312yes—
525C23C2×D4×D4311yescharacteristic
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—48no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—432no—
533C2×C4—432no—
534C2×C4—432no—
535C2×C4—432no—
536C2×C4—432no—
537C2×C4—432no—
538C2×C4—4316no—
539C2×C4—434no—
540C2×C4—434no—
541C2×C4—434no—
542C2×C4—434no—
543C2×C4—434no—
544C2×C4—434no—
545C2×C4—434no—
546C2×C4—434no—
547C2×C4—4316no—
548C2×C4—4316no—
549C2×C4—864no—
550C2×C4—864no—
551C2×C4—17216no—
552C2×C4—1728no—
553C2×C4—1722no—
554C2×C4—1722no—
555C2×C4—1724no—
556C2×C4C42×D4314yes—
557C2×C4C22⋊C4×D4314yes—
558C2×C4C22⋊C4×D4312yes—
559C2×C4C22⋊C4×D4312yes—
560C2×C4C4⋊C4×D4314yes—
561C2×C4C4⋊C4×D4314yes—
562C2×C4C4⋊C4×D4312yes—
563C2×C4C22×C4×D4311yescharacteristic
564C2×C4C22×C4×D4311yescharacteristic
565C2×C4C22×C4×D4311yescharacteristic
566C2×C4C2×D4×D4311yescharacteristic
567C2×C4C2×D4×D4311yescharacteristic
568C2×C4C2×Q8×D4311yescharacteristic
569C8—24no—
570C8—864no—
571C22—24no—
572C22—22no—
573C22—24no—
574C22—22no—
575C22—434no—
576C22—434no—
577C22—864no—
578C22—864no—
579C22—862no—
580C22—862no—
581C22—864no—
582C22—864no—
583C22—862no—
584C22—862no—
585C22—17216no—
586C22#95×D4314yes—
587C22C2×C22⋊C4×D4311yescharacteristic
588C22C2×C22⋊C4×D4311yescharacteristic
589C22C2×C4⋊C4×D4311yescharacteristic
590C22#1458369512yes—
591C22#1458369812yes—
592C4—44no—
593C4—44no—
594C4—434no—
595C4—434no—
596C4—1724no—
597C4—1724no—
598C4#95×D4314yes—
599C4C2×C42×D4311yescharacteristic
600C4C2×C22⋊C4×D4311yescharacteristic
601C4C2×C4⋊C4×D4311yescharacteristic
602C4C2×C4⋊C4×D4311yescharacteristic
603C2—24no—
604C2—864no—
605C2—864no—
606C2C2×#95×D4311yescharacteristic
607C2#1914310911yescharacteristic
608C2#1914311112yes—
609C2#1914311311yescharacteristic
610C2#1914318212yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC43×#1736C2
socleC23×C43C22×D4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenter#1736D43
hypocenterC43#20347
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. #19134316C2semidirect
5. #19134315C2semidirect
6. #19134314C2semidirect
7. #19134313C2semidirect
8. #19134310C2semidirect
9. C43×#1736C2semidirect
15. C2×M16×D43C4semidirect
21. C2×#13063283C4semidirect
28. #117×D43C4semidirect
35. #14582662C22semidirect
36. #14582661C22semidirect
37. #14582661C22semidirect
41. C43×#340C22semidirect
58. C2×#10621877C2×C4semidirect
61. C2×#10621872C2×C4semidirect
66. C2×C8×D43C2×C4semidirect
75. #13063283C2×C4semidirect
76. #13063283C2×C4semidirect
81. C2×C4⋊Dic43C2×C4semidirect
86. C4⋊C4×D43C2×C4semidirect
103. C2×M16×C43C2×C4semidirect
109. C2×C4⋊C4×C43C2×C4semidirect
305. #1736D43semidirect
346. #340C2×D43semidirect
347. C43#20347semidirect
373. C2×M16C4×D43semidirect
403. 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×M16×D432
C22×#130632832
C2×#117×D432
#191343162
#191343152
#191343142
#191343132
#191343102
C43×#17362
#2034743