Finite Group Databasebeta

← #25155451

Subgroups — #25155451

Order 11008.

818 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
1C2×#14583305C211yesmaximal, characteristic, complemented
2C2×#14582939C211yesmaximal, characteristic
3#19138308C211yesmaximal, characteristic
4#19136071C211yesmaximal, characteristic, complemented
5#19136067C211yesmaximal, characteristic, complemented
6#19135933C211yesmaximal, characteristic, complemented
7#19135925C211yesmaximal, characteristic, complemented
8#19135330C211yesmaximal, characteristic, complemented
9#19135325C211yesmaximal, characteristic, complemented
10#19134792C211yesmaximal, characteristic
11#19134788C211yesmaximal, characteristic
12#19134751C211yesmaximal, characteristic, complemented
13#19134626C211yesmaximal, characteristic
14#19134379C211yesmaximal, characteristic
15C43×#2440C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19#14583305—24no—
20#14582939—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063236C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582835—21no—
35#14582822—21no—
36#14582797C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582796—21no—
39#14582782—21no—
40#14582769C2211yescharacteristic
41#14582759C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×C4⋊Q8×C43C2211yescharacteristic
51C2×C22⋊Q8×C43—21no—
52C22×C4⋊C4×C43C2211yescharacteristic
53C43×#398—21no—
54C43×#395—21no—
55C43×#389C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#385—21no—
58C43×#384C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C4×C22⋊C4×C43C2211yescharacteristic
61C2×#10621877—22no—
62C2×#10621877—22no—
63C2×#10621877Q814yescomplemented
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063317—22no—
69#13063317—41no—
70#13063284—22no—
71#13063284—41no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C4×Dic43—21no—
85#13063258—22no—
86#13063258—22no—
87#13063258—22no—
88#13063258D414yes—
89#13063256—22no—
90#13063256—22no—
91#13063256—22no—
92#13063256—22no—
93#13063256—41no—
94#13063256—41no—
95C22⋊(C43⋊C8)Q814yescomplemented
96#13063236—22no—
97C4×C43⋊C8—22no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C22×Q8×C43—21no—
102C23×C4×C43—21no—
103C23×C4×C43C2311yescharacteristic
104C4⋊Q8×C43—22no—
105C4⋊Q8×C43—41no—
106C22⋊Q8×C43—44no—
107C2×C4⋊C4×C43—22no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—41no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43D411yescharacteristic
121C2×C22⋊C4×C43D411yescharacteristic
122C2×C42×C43C2311yescharacteristic
123C2×C42×C43C2311yescharacteristic
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127#95×C43D411yescharacteristic
128#95×C43D411yescharacteristic
129C24×C43C2×D411yescharacteristic
130C2×Q8×C43—42no—
131C2×Q8×C43—42no—
132C2×Q8×C43—81no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—42no—
142C22×C4×C43—42no—
143C22×C4×C43—81no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×Q812yes—
150C22×C4×C43C2×Q812yes—
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—42no—
164C4⋊C4×C43—42no—
165C4⋊C4×C43—42no—
166C4⋊C4×C43—42no—
167C4⋊C4×C43—42no—
168C4⋊C4×C43—81no—
169C4⋊C4×C43C2×D412yes—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—42no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—21no—
177C22⋊Dic43—42no—
178C22⋊Dic43—81no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—42no—
187C4⋊Dic43—81no—
188C4⋊Dic43C2×D412yes—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—81no—
193C4×Dic43—42no—
194#10621877—28no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8C2×D412yes—
202C2×C43⋊C8C2×Q812yes—
203C2×C43⋊C8C2×Q812yes—
204C2×C43⋊C8C2×Q812yes—
205C2×C43⋊C8C2×Q812yes—
206C2×C43⋊C8#4112yes—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43C4⋊Q812yes—
214C23×C43C22×D411yescharacteristic
215Q8×C43—84no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—84no—
245C2×C4×C43C4⋊Q812yes—
246C2×C4×C43AGL(1,ℤ/8)12yes—
247C2×C4×C43#13712yes—
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×Q811yescharacteristic
250C2×C4×C43C22×Q811yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C2×C4×C432−1+411yescharacteristic
254C2×Dic43—22no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C43⋊C8—22no—
267C43⋊C8—22no—
268C43⋊C8—22no—
269C43⋊C8C22⋊Q814yescomplemented
270#26078—431nomaximal, Sylow
271C22×C43—22no—
272C22×C43—22no—
273C22×C43—22no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43C2×C4⋊Q811yescharacteristic
279C22×C43D4211yescharacteristic
280C22×C43#54711yescharacteristic
281C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C43C2×#13711yescharacteristic
283C22×C43#57711yescharacteristic
284C22×C43#57711yescharacteristic
285C4×C43—22no—
286C4×C43—22no—
287C4×C43—22no—
288C4×C43—41no—
289C4×C43—42no—
290C4×C43—41no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43C2×C22⋊Q811yescharacteristic
295C4×C43#54411yescharacteristic
296C4×C43D4×Q811yescharacteristic
297C4×C43#55411yescharacteristic
298Dic43—42no—
299Dic43—81no—
300Dic43—81no—
301Dic43—81no—
302C2×#501—431no—
303C2×#428—431no—
304#2441—431no—
305#2440D4311yescharacteristic
306#2084—431no—
307#2083—431no—
308#2059—431no—
309#2058—431no—
310#1943—431no—
311#1942—431no—
312#1854—431no—
313#1853—431no—
314#1844—431no—
315#1809—431no—
316#1753—431no—
317C2×C43—42no—
318C2×C43#244011yescharacteristic
319C2×C43#316311yescharacteristic
320C2×C43#316511yescharacteristic
321C2×C43#327211yescharacteristic
322C2×C43#327811yescharacteristic
323C2×C43#334411yescharacteristic
324C2×C43#334511yescharacteristic
325C22×M16—431no—
326C2×C4⋊Q8C2×D4311yescharacteristic
327C2×#125—431no—
328C2×C22⋊Q8—21no—
329C2×#117—431no—
330C22×C4⋊C4C2×D4311yescharacteristic
331#501—864no—
332#428—864no—
333C2×#107—431no—
334C2×#107—431no—
335C2×#107—431no—
336C2×#107—431no—
337C2×#106—431no—
338C2×#106—431no—
339C2×#106—431no—
340C2×#106—431no—
341C2×#106—431no—
342C2×#106—431no—
343C2×C22⋊C8—431no—
344C2×#97—431no—
345C2×C4×C8—431no—
346#399—861no—
347#398—21no—
348#396—861no—
349#395—21no—
350#389—431no—
351#389—431no—
352#389—861no—
353#389C2×D4311yescharacteristic
354#389C2×D4311yescharacteristic
355#387—861no—
356#385—21no—
357#384—431no—
358#384C2×D4311yescharacteristic
359#380—431no—
360#380C2×D4311yescharacteristic
361C4×C22⋊C4C2×D4311yescharacteristic
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#336—431no—
369#336—431no—
370C43#2607811yescharacteristic, complemented, Sylow
371C22×Q8—21no—
372C23×C4—21no—
373C23×C4C22×D4311yescharacteristic
374C2×M16—434no—
375C2×M16—862no—
376C2×M16—862no—
377C22×C8—431no—
378C22×C8—431no—
379C22×C8—431no—
380C22×C8—431no—
381C4⋊Q8—22no—
382C4⋊Q8—41no—
383#125—862no—
384#125—1721no—
385C22⋊Q8—44no—
386#117—862no—
387#117—1721no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—41no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4C22⋊D4311yescharacteristic
414C2×C22⋊C4C22⋊D4311yescharacteristic
415C2×C42—861no—
416C2×C42C22×D4311yescharacteristic
417C2×C42C22×D4311yescharacteristic
418#107—434no—
419#107—862no—
420#107—862no—
421#107—862no—
422#106—862no—
423#106—862no—
424#106—862no—
425#106—862no—
426#106—1721no—
427#106—1721no—
428C22⋊C8—434no—
429#97—862no—
430C4×C8—862no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95C22⋊D4311yescharacteristic
438#95C22⋊D4311yescharacteristic
439C24C2×C22⋊D4311yescharacteristic
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8—81no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—81no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4Q8×D4312yes—
459C22×C4Q8×D4312yes—
460C22×C4C2×C22⋊D4311yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
462C22×C4C2×C22⋊D4311yescharacteristic
463C22×C4C2×C22⋊D4311yescharacteristic
464C22×C4C2×C22⋊D4311yescharacteristic
465C22×C4C23×D4311yescharacteristic
466M16—868no—
467C2×C8—432no—
468C2×C8—432no—
469C2×C8—432no—
470C2×C8—432no—
471C2×C8—432no—
472C2×C8—432no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—81no—
492C4⋊C4—432no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—3441no—
501C4⋊C4—3441no—
502C4⋊C4—1722no—
503C4⋊C4—1722no—
504C4⋊C4—1722no—
505C4⋊C4—1722no—
506C4⋊C4D4×D4312yes—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—42no—
510C22⋊C4—3441no—
511C22⋊C4—1722no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—1722no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23#1306332312yes—
524C23C22×C22⋊D4311yescharacteristic
525Q8—84no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—84no—
555C2×C4—862no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4#1306332312yes—
568C2×C4#1306335112yes—
569C2×C4#1306335612yes—
570C2×C4C2×D4×D4311yescharacteristic
571C2×C4C2×Q8×D4311yescharacteristic
572C2×C4C2×Q8×D4311yescharacteristic
573C2×C4#41×D4311yescharacteristic
574C2×C4#1306337011yescharacteristic
575C2×C4#1306337211yescharacteristic
576C8—434no—
577C8—862no—
578C8—862no—
579C8—862no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C2×#1306332311yescharacteristic
588C22D4×C22⋊D4311yescharacteristic
589C22#1458354811yescharacteristic
590C22C2×#1306335111yescharacteristic
591C22C2×#1306335611yescharacteristic
592C22#1458370711yescharacteristic
593C22#1458371011yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—41no—
598C4—41no—
599C4—42no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4—3441no—
604C4—3441no—
605C4—3441no—
606C4—1722no—
607C4C22⋊Q8×D4311yescharacteristic
608C4#1458352811yescharacteristic
609C4#1458356211yescharacteristic
610C4#1458360311yescharacteristic
611C2—42no—
612C2#1913829411yescharacteristic
613C2#1914512111yescharacteristic
614C2#1914513711yescharacteristic
615C2#1914619111yescharacteristic
616C2#1914625711yescharacteristic
617C2#1914704411yescharacteristic
618C2#1914706511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2440C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2440D43
hypocenterC43#26078
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
1. C2×#14583305C2semidirect
4. #19136071C2semidirect
5. #19136067C2semidirect
6. #19135933C2semidirect
7. #19135925C2semidirect
8. #19135330C2semidirect
9. #19135325C2semidirect
12. #19134751C2semidirect
63. C2×#10621877Q8semidirect
95. C22⋊(C43⋊C8)Q8semidirect
269. C43⋊C8C22⋊Q8semidirect
370. C43#26078semidirect

Maximal subgroups

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

subgroupindex
C2×#145833052
C2×#145829392
#191383082
#191360712
#191360672
#191359332
#191359252
#191353302
#191353252
#191347922
#191347882
#191347512
#191346262
#191343792
C43×#24402
#2607843