Finite Group Databasebeta

← #25125352

Subgroups — #25125352

Order 11008.

1038 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582894C212yesmaximal
2#19137084C211yesmaximal, characteristic
3#19137000C211yesmaximal, characteristic, complemented
4#19136016C212yesmaximal, complemented
5#19136012C212yesmaximal, complemented
6#19136003C211yesmaximal, characteristic, complemented
7#19136000C211yesmaximal, characteristic, complemented
8#19135999C211yesmaximal, characteristic, complemented
9#19134310C212yesmaximal, complemented
10#336×D43C211yesmaximal, characteristic, complemented
11C43×#2072C211yesmaximal, characteristic, complemented
12C22×#10621902C2211yescharacteristic
13C22×C8×D43C2212yes—
14C2×#13063283C2211yescharacteristic
15C2×#13063283C2212yes—
16C2×C42×D43C2211yescharacteristic
17#14582894—28no—
18C2×#13063249C2212yes—
19C2×#13063247C2212yes—
20C2×#13063245C2212yes—
21#14582806C2211yescharacteristic
22#14582801C2211yescharacteristic
23#14582800C2211yescharacteristic
24#14582777—21no—
25#14582777—21no—
26#14582769C2211yescharacteristic
27#14582764C2212yes—
28#14582756—21no—
29#14582756—21no—
30C4⋊C4×Dic43—21no—
31C4⋊C4×Dic43—21no—
32#14582746—21no—
33#14582746—21no—
34#14582662C2212yes—
35#14582661C2212yes—
36#14582661C2212yes—
37#14582654C2211yescharacteristic
38#14582653C2212yes—
39C2×#103×C43C2212yes—
40C43×#391C2211yescharacteristic
41C43×#384C2211yescharacteristic
42C43×#340C2212yes—
43C43×#336C2211yescharacteristic
44C2×#10621902—22no—
45C2×#10621902—24no—
46C2×#10621902—24no—
47C2×#10621902D414yes—
48C22×D172—21no—
49C22×D172C2311yescharacteristic
50C22×C4×D43—21no—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C22×C43⋊C8C2312yes—
55C2×C8×D43—24no—
56C2×C8×D43—24no—
57C2×C8×D43—24no—
58#13063283—24no—
59#13063283—24no—
60#13063283—24no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43C2311yescharacteristic
64C2×C4⋊Dic43C2312yes—
65C2×(C2×D43)⋊C4—22no—
66C2×(C2×D43)⋊C4—21no—
67C2×(C2×D43)⋊C4—21no—
68C2×(C2×D43)⋊C4—21no—
69C2×(C2×D43)⋊C4—21no—
70C2×(C2×D43)⋊C4—21no—
71C2×C4×Dic43—21no—
72C2×C4×Dic43—22no—
73C2×C4×Dic43D411yescharacteristic
74C2×C4×Dic43D411yescharacteristic
75C2×C4×Dic43C2311yescharacteristic
76C42×D43—24no—
77#13063249—24no—
78#13063247—24no—
79#13063245—24no—
80C43⋊#95—21no—
81C43⋊#95—21no—
82C43⋊#95—22no—
83C43⋊#95—22no—
84C22×Q8×C43C2311yescharacteristic
85C22×C8×C43C2312yes—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2312yes—
90C2×C42×C43C2311yescharacteristic
91#103×C43—24no—
92#95×C43—21no—
93#95×C43—21no—
94C23×D43—21no—
95C23×D43C2×D411yescharacteristic
96C2×Q8×C43—21no—
97C2×Q8×C43—22no—
98C2×Q8×C43—22no—
99C2×Q8×C43C2×D412yes—
100C22×C4×C43—21no—
101C22×C4×C43—21no—
102C22×C4×C43—22no—
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2411yescharacteristic
106C22×Dic43—21no—
107C22×Dic43—22no—
108C22×Dic43C2×D411yescharacteristic
109C22×Dic43C2×D411yescharacteristic
110C22×Dic43C2×D411yescharacteristic
111#10621902—216no—
112#10621902—48no—
113C2×D172—21no—
114C2×D172—24no—
115C2×D172—22no—
116C2×D172—22no—
117C2×D172—42no—
118C2×D172—42no—
119C2×D172C2×D412yes—
120C2×C4×D43—22no—
121C2×C4×D43—22no—
122C2×C4×D43—24no—
123C2×C4×D43—22no—
124C2×C4×D43—22no—
125C2×C4×D43—41no—
126C2×C4×D43—41no—
127C2×C4×D43—42no—
128C2×C4×D43—42no—
129C2×C4×D43C2×D412yes—
130C2×C4×D43#4112yes—
131C2×C4×D43#4114yes—
132C2×C4×D43#4114yes—
133C2×C8×C43—22no—
134C2×C8×C43—22no—
135C2×C8×C43—22no—
136C4⋊C4×C43—22no—
137C4⋊C4×C43—22no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—42no—
140C4⋊C4×C43—42no—
141C42×C43—22no—
142(C2×D43)⋊C4—42no—
143(C2×D43)⋊C4—42no—
144(C2×D43)⋊C4—42no—
145(C2×D43)⋊C4—42no—
146(C2×D43)⋊C4—44no—
147(C2×D43)⋊C4—42no—
148C4⋊Dic43—22no—
149C4⋊Dic43—22no—
150C4⋊Dic43—22no—
151C4⋊Dic43—42no—
152C4⋊Dic43—42no—
153C4×Dic43—22no—
154C4×Dic43—22no—
155C4×Dic43—22no—
156C4×Dic43—44no—
157C4×Dic43—42no—
158C2×C43⋊C8—22no—
159C2×C43⋊C8—22no—
160C2×C43⋊C8—22no—
161C8×D43—48no—
162C23×C43C22×D411yescharacteristic
163C22×D43—21no—
164C22×D43—21no—
165C22×D43—21no—
166C22×D43—21no—
167C22×D43—22no—
168C22×D43—41no—
169C22×D43—41no—
170C22×D43—41no—
171C22×D43—41no—
172C22×D43—41no—
173C22×D43—41no—
174C22×D43#12112yes—
175C22×D43#12312yes—
176C22×D43#12412yes—
177Q8×C43—24no—
178Q8×C43—42no—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—22no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—42no—
187C2×C4×C43—41no—
188C2×C4×C43—42no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—42no—
192C2×C4×C43#13512yes—
193C2×C4×C43#13512yes—
194C2×C4×C43C22×D411yescharacteristic
195C2×C4×C43C2×#4112yes—
196C2×C4×C43C2×#4112yes—
197C2×C4×C43C2×#4111yescharacteristic
198C2×Dic43—21no—
199C2×Dic43—21no—
200C2×Dic43—21no—
201C2×Dic43—21no—
202C2×Dic43—21no—
203C2×Dic43—21no—
204C2×Dic43—42no—
205C2×Dic43—41no—
206C2×Dic43—42no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—42no—
210C2×Dic43#12112yes—
211C2×Dic43#12312yes—
212C2×Dic43#12412yes—
213D172—24no—
214D172—48no—
215D172—42no—
216C4×D43—44no—
217C4×D43—44no—
218C4×D43—48no—
219C4×D43#12318yes—
220C4×D43#12618yes—
221C8×C43—42no—
222C43⋊C8—42no—
223#23627—431nomaximal, Sylow
224C22×C43C2×#12111yescharacteristic
225C22×C43C2×#12311yescharacteristic
226C22×C43C2×#12411yescharacteristic
227C22×C43C2×#13511yescharacteristic
228C22×C43C2×#13511yescharacteristic
229C22×C43#57511yescharacteristic
230C22×C43#57511yescharacteristic
231C2×D43—22no—
232C2×D43—22no—
233C2×D43—22no—
234C2×D43—22no—
235C2×D43—22no—
236C2×D43—22no—
237C2×D43—42no—
238C2×D43—42no—
239C2×D43—42no—
240C2×D43—81no—
241C2×D43—81no—
242C2×D43—81no—
243C2×D43—81no—
244C2×D43#39714yes—
245C4×C43—22no—
246C4×C43—22no—
247C4×C43—42no—
248C4×C43—81no—
249C4×C43—82no—
250C4×C43C2×#12312yes—
251C4×C43C2×#12612yes—
252Dic43—41no—
253Dic43—41no—
254Dic43—81no—
255Dic43—82no—
256Dic43#39714yes—
257C2×#416—432no—
258#2297—431no—
259#2285—431no—
260#2074—432no—
261#2073—432no—
262#2072—431no—
263#2072D4311yescharacteristic, complemented
264#2071—431no—
265#2071—431no—
266#1735—432no—
267C2×#336—431no—
268C2×C43C2×#39711yescharacteristic
269C2×C43#303511yescharacteristic
270C2×C43#303511yescharacteristic
271C2×C43#309111yescharacteristic
272C2×C43#309111yescharacteristic
273C2×C43#313111yescharacteristic
274C2×C43#313511yescharacteristic
275D43—24no—
276D43—82no—
277C22×#41—431no—
278C23×C8—432no—
279C2×#117—432no—
280C2×#117—431no—
281C22×C42—431no—
282#416—868no—
283C2×#103—432no—
284C2×#103C2×D4312yes—
285C2×#102—432no—
286C2×#102—432no—
287#391—431no—
288#391C2×D4311yescharacteristic
289#390—431no—
290#390—431no—
291#386—861no—
292#386—861no—
293#384—431no—
294#384C2×D4311yescharacteristic
295#382—432no—
296#380—861no—
297#380—861no—
298C4×C4⋊C4—861no—
299C4×C4⋊C4—861no—
300C4×C22⋊C4—861no—
301C4×C22⋊C4—861no—
302#340—432no—
303#340—432no—
304#340—432no—
305#340C2×D4312yes—
306#336—432no—
307#336—431no—
308#336C2×D4311yescharacteristic
309C43#2362711yescharacteristic, complemented, Sylow
310C2×#41—434no—
311C2×#41—862no—
312C2×#41—864no—
313C2×#41—864no—
314C22×Q8C22×D4311yescharacteristic
315C22×D4—431no—
316C22×D4—861no—
317C23×C4—431no—
318C23×C4—431no—
319C23×C4—431no—
320C23×C4—861no—
321C22×C8—432no—
322C22×C8—864no—
323C22×C8—864no—
324C22×C8—864no—
325C22×C8C22×D4312yes—
326#117—864no—
327#117—864no—
328#117—864no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—431no—
332C2×C4⋊C4—432no—
333C2×C4⋊C4—861no—
334C2×C4⋊C4—861no—
335C2×C4⋊C4C22×D4311yescharacteristic
336C2×C4⋊C4C22×D4312yes—
337C2×C22⋊C4—861no—
338C2×C22⋊C4—861no—
339C2×C22⋊C4—862no—
340C2×C22⋊C4—861no—
341C2×C22⋊C4—861no—
342C2×C22⋊C4—861no—
343C2×C42—431no—
344C2×C42—431no—
345C2×C42—431no—
346C2×C42—864no—
347C2×C42—861no—
348C2×C42—862no—
349C2×C42C22×D4311yescharacteristic
350#103—24no—
351#103—864no—
352#102—864no—
353#102—864no—
354#95—21no—
355#95—21no—
356#95—861no—
357#95—861no—
358#95—862no—
359#95—862no—
360C24—431no—
361C24—861no—
362#41—8616no—
363#41—1728no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8D4×D4312yes—
368C2×D4—432no—
369C2×D4—864no—
370C2×D4—862no—
371C2×D4—862no—
372C2×D4—861no—
373C2×D4—1722no—
374C2×D4—1722no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—431no—
379C22×C4—432no—
380C22×C4—434no—
381C22×C4—432no—
382C22×C4—434no—
383C22×C4—431no—
384C22×C4—431no—
385C22×C4—864no—
386C22×C4—862no—
387C22×C4—862no—
388C22×C4—862no—
389C22×C4—862no—
390C22×C4—861no—
391C22×C4—862no—
392C22×C4—1721no—
393C22×C4—1721no—
394C22×C4—1722no—
395C22×C4—1722no—
396C22×C4D4×D4311yescharacteristic
397C22×C4D4×D4311yescharacteristic
398C22×C4C23×D4311yescharacteristic
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—862no—
403C2×C8—862no—
404C2×C8—862no—
405C2×C8—1728no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C4⋊C4—862no—
412C4⋊C4—862no—
413C4⋊C4—862no—
414C4⋊C4—1722no—
415C4⋊C4—1722no—
416C22⋊C4—1722no—
417C22⋊C4—1722no—
418C22⋊C4—1724no—
419C22⋊C4—1722no—
420C22⋊C4—1722no—
421C22⋊C4—1722no—
422C42—22no—
423C42—862no—
424C42—862no—
425C42—862no—
426C42—1724no—
427C42—1722no—
428C23—432no—
429C23—432no—
430C23—432no—
431C23—861no—
432C23—861no—
433C23—861no—
434C23—861no—
435C23—862no—
436C23—1721no—
437C23—1721no—
438C23—1721no—
439C23—1721no—
440C23—1721no—
441C23—1721no—
442C23C2×D4×D4311yescharacteristic
443Q8—24no—
444Q8—42no—
445D4—864no—
446D4—1728no—
447D4—1722no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—432no—
462C2×C4—432no—
463C2×C4—432no—
464C2×C4—438no—
465C2×C4—438no—
466C2×C4—861no—
467C2×C4—861no—
468C2×C4—861no—
469C2×C4—861no—
470C2×C4—861no—
471C2×C4—861no—
472C2×C4—1724no—
473C2×C4—1724no—
474C2×C4—1728no—
475C2×C4—1722no—
476C2×C4—1721no—
477C2×C4—1721no—
478C2×C4—1721no—
479C2×C4—1722no—
480C2×C4—1722no—
481C2×C4#1306334612yes—
482C2×C4#1306334812yes—
483C2×C4C2×D4×D4311yescharacteristic
484C2×C4#41×D4312yes—
485C2×C4#41×D4312yes—
486C2×C4#41×D4311yescharacteristic
487C8—42no—
488C8—1722no—
489C22—434no—
490C22—862no—
491C22—862no—
492C22—862no—
493C22—862no—
494C22—862no—
495C22—862no—
496C22—3441no—
497C22—3441no—
498C22—3441no—
499C22—3441no—
500C22—1722no—
501C22—1722no—
502C22—1722no—
503C22#121×D4311yescharacteristic
504C22#123×D4311yescharacteristic
505C22#124×D4311yescharacteristic
506C22C2×#1306334611yescharacteristic
507C22C2×#1306334811yescharacteristic
508C22#1458369511yescharacteristic
509C22#1458369811yescharacteristic
510C4—22no—
511C4—22no—
512C4—42no—
513C4—82no—
514C4—81no—
515C4—434no—
516C4—3442no—
517C4—3441no—
518C4—1721no—
519C4—1721no—
520C4#123×D4312yes—
521C4#126×D4312yes—
522C2—864no—
523C2—3442no—
524C2#397×D4311yescharacteristic
525C2#1914404511yescharacteristic
526C2#1914405311yescharacteristic
527C2#1914450911yescharacteristic
528C2#1914451111yescharacteristic
529C2#1914491911yescharacteristic
530C2#1914493711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2072C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
hypercenter#2072D43
hypocenterC43#23627
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2072

Complements

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

NH ≅ G/Ntype
3. #19137000C2semidirect
4. #19136016C2semidirect
5. #19136012C2semidirect
6. #19136003C2semidirect
7. #19136000C2semidirect
8. #19135999C2semidirect
9. #19134310C2semidirect
10. #336×D43C2semidirect
11. C43×#2072C2semidirect
263. #2072D43semidirect
309. C43#23627semidirect

Maximal subgroups

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

subgroupindex
C2×#145828942
#191370842
#191370002
#191360162
#191360122
#191360032
#191360002
#191359992
#191343102
#336×D432
C43×#20722
#2362743