Finite Group Databasebeta

← #25133267

Subgroups — #25133267

Order 11008.

1122 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142929C212yesmaximal, complemented
2C4×#13063306C211yesmaximal, characteristic
3#19135947C212yesmaximal, complemented
4#19135761C212yesmaximal, complemented
5#19135581C212yesmaximal, complemented
6#19135008C212yesmaximal
7#19134876C212yesmaximal
8#19134583C211yesmaximal, characteristic
9C43×#3501C211yesmaximal, characteristic
10C2×#13063306C2211yescharacteristic
11C22×C4×Dic43C2211yescharacteristic
12C2×#13063240C2212yes—
13#14582806—22no—
14#14582795—22no—
15#14582787—21no—
16#14582780—24no—
17#14582780—21no—
18#14582779C2211yescharacteristic
19#14582771C2214yes—
20#14582771C2211yescharacteristic
21#14582760C2214yes—
22#14582760C2211yescharacteristic
23#14582759C2212yes—
24C4×Dic43⋊C4—21no—
25C4×C22⋊Dic43—21no—
26C4×C22⋊Dic43C2211yescharacteristic
27#14582666C2214yes—
28#14582666C2212yes—
29#14582666C2214yes—
30C43×#554—22no—
31C43×#554—24no—
32D4×Q8×C43—22no—
33C43×#544—21no—
34C43×#543—21no—
35C43×#543C2212yes—
36C43×#533—21no—
37C2×C22⋊Q8×C43—21no—
38C2×C22⋊Q8×C43C2212yes—
39C43×#518C2212yes—
40C2×C4×D4×C43C2211yescharacteristic
41C23×Dic43C2311yescharacteristic
42C23×Dic43C2311yescharacteristic
43#13063306—22no—
44#13063306Q814yescomplemented
45C2×C4⋊Dic43—22no—
46C2×Dic43⋊C4—21no—
47C2×Dic43⋊C4—21no—
48C2×Dic43⋊C4—24no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×C22⋊Dic43C2314yes—
52C2×C22⋊Dic43C2311yescharacteristic
53C2×C22⋊Dic43C2311yescharacteristic
54C2×C4×Dic43—21no—
55C2×C4×Dic43—22no—
56C2×C4×Dic43—21no—
57C2×C4×Dic43—22no—
58C2×C4×Dic43—21no—
59#13063240—24no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—24no—
63C43⋊#95—24no—
64C43⋊#95—24no—
65C43⋊#95—21no—
66C43⋊#95—21no—
67C43⋊#95—21no—
68C43⋊#95—22no—
69C22×Q8×C43—21no—
70C22×Q8×C43D412yes—
71C22×D4×C43C2311yescharacteristic
72C23×C4×C43D411yescharacteristic
73C23×C4×C43C2311yescharacteristic
74C4⋊Q8×C43—21no—
75C4⋊Q8×C43—21no—
76C4⋊Q8×C43—24no—
77#125×C43—22no—
78#125×C43—24no—
79C22⋊Q8×C43—22no—
80C22⋊Q8×C43—22no—
81C22⋊Q8×C43—24no—
82C22⋊Q8×C43—24no—
83C22⋊Q8×C43—22no—
84C22⋊Q8×C43—22no—
85C22⋊Q8×C43—22no—
86C22⋊Q8×C43—22no—
87C22⋊Q8×C43—22no—
88C22⋊Q8×C43—22no—
89C22⋊Q8×C43—24no—
90C22⋊Q8×C43—24no—
91C4×Q8×C43—22no—
92C4×Q8×C43—22no—
93C4×D4×C43—22no—
94C4×D4×C43—22no—
95C4×D4×C43—24no—
96C4×D4×C43—24no—
97#117×C43—22no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—22no—
100C2×C4⋊C4×C43D412yes—
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C4⋊C4×C43D414yes—
103C2×C22⋊C4×C43—22no—
104C2×C22⋊C4×C43D411yescharacteristic
105C2×C22⋊C4×C43C2311yescharacteristic
106C2×C22⋊C4×C43C2314yes—
107C2×C42×C43D411yescharacteristic
108C24×C43C2×D411yescharacteristic
109C24×C43C2411yescharacteristic
110C2×Q8×C43—22no—
111C2×Q8×C43—22no—
112C2×Q8×C43—22no—
113C2×Q8×C43—22no—
114C2×Q8×C43—44no—
115C2×Q8×C43—82no—
116C2×D4×C43—22no—
117C2×D4×C43—22no—
118C2×D4×C43C2×Q812yes—
119C2×D4×C43#4112yes—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—42no—
125C22×C4×C43—42no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D414yes—
131C22×C4×C43C2×D414yes—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D412yes—
135C22×Dic43—22no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—22no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—24no—
142C22×Dic43—21no—
143C22×Dic43—22no—
144C22×Dic43—42no—
145C22×Dic43C2×Q812yescomplemented
146C4⋊C4×C43—22no—
147C4⋊C4×C43—24no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—24no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—24no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—24no—
157C22⋊C4×C43—24no—
158C22⋊C4×C43—22no—
159C22⋊C4×C43—24no—
160C22⋊C4×C43—22no—
161C22⋊C4×C43—24no—
162C42×C43—24no—
163C42×C43—21no—
164C42×C43—21no—
165C22⋊Dic43—24no—
166C22⋊Dic43—21no—
167C22⋊Dic43—24no—
168C22⋊Dic43—22no—
169C22⋊Dic43—24no—
170C22⋊Dic43—42no—
171C22⋊Dic43C2×Q812yescomplemented
172C4⋊Dic43—44no—
173Dic43⋊C4—24no—
174Dic43⋊C4—48no—
175Dic43⋊C4—42no—
176C4×Dic43—42no—
177C4×Dic43—41no—
178C4×Dic43—42no—
179C4×Dic43—41no—
180C23×C43—21no—
181C23×C43—21no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—41no—
185C23×C43—41no—
186C23×C43C22⋊Q812yes—
187C23×C43C22×D411yescharacteristic
188C23×C43C22×D412yes—
189C23×C43C22×Q811yescharacteristic
190C23×C43C2×#4111yescharacteristic
191C23×C432−1+412yes—
192Q8×C43—44no—
193Q8×C43—82no—
194Q8×C43—82no—
195Q8×C43—82no—
196D4×C43—24no—
197D4×C43—24no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—22no—
201C2×C4×C43—24no—
202C2×C4×C43—21no—
203C2×C4×C43—24no—
204C2×C4×C43—24no—
205C2×C4×C43—21no—
206C2×C4×C43—42no—
207C2×C4×C43—41no—
208C2×C4×C43—42no—
209C2×C4×C43—44no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—44no—
213C2×C4×C43—81no—
214C2×C4×C43—82no—
215C2×C4×C43—82no—
216C2×C4×C43#12011yescharacteristic
217C2×C4×C43#12012yes—
218C2×C4×C43#12011yescharacteristic
219C2×C4×C43C22⋊Q812yes—
220C2×Dic43—24no—
221C2×Dic43—22no—
222C2×Dic43—22no—
223C2×Dic43—22no—
224C2×Dic43—24no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—42no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—42no—
233C2×Dic43—41no—
234C2×Dic43—44no—
235C2×Dic43—44no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—44no—
239#24351—431nomaximal, Sylow
240C22×C43—21no—
241C22×C43—22no—
242C22×C43—21no—
243C22×C43—22no—
244C22×C43—22no—
245C22×C43—41no—
246C22×C43—41no—
247C22×C43—42no—
248C22×C43—42no—
249C22×C43—41no—
250C22×C43—41no—
251C22×C43—81no—
252C22×C43C2×#12011yescharacteristic
253C22×C43C2×C22⋊Q811yescharacteristic
254C22×C43#53611yescharacteristic
255C22×C43#54812yes—
256C22×C43D4×Q812yes—
257C4×C43—22no—
258C4×C43—21no—
259C4×C43—22no—
260C4×C43—41no—
261C4×C43—44no—
262C4×C43—44no—
263C4×C43—41no—
264C4×C43#45812yes—
265Dic43—42no—
266Dic43—42no—
267Dic43—42no—
268Dic43—84no—
269Dic43—81no—
270#3501D4311yescharacteristic
271#2855—432no—
272C4×#123—431no—
273#2062—432no—
274#2030—432no—
275#1996—432no—
276#1890—432no—
277#1867—432no—
278#1799—431no—
279C2×C43—21no—
280C2×C43—22no—
281C2×C43—21no—
282C2×C43—22no—
283C2×C43—42no—
284C2×C43#240911yescharacteristic
285C2×C43C2×#45811yescharacteristic
286C2×C43#302511yescharacteristic
287#554—24no—
288#554—22no—
289D4×Q8—22no—
290#544—21no—
291#543—21no—
292#543C2×D4312yes—
293#533—21no—
294C2×#123—431no—
295C2×C22⋊Q8—21no—
296C2×C22⋊Q8C2×D4312yes—
297#518C2×D4312yes—
298C2×C4×D4C2×D4311yescharacteristic
299C22×C42—431no—
300C2×#99—432no—
301#391—862no—
302#389—862no—
303#388—861no—
304#387—864no—
305#387—861no—
306#386—431no—
307#385—431no—
308#385—434no—
309#381—434no—
310#381—431no—
311#380—432no—
312C4×C4⋊C4—861no—
313C4×C22⋊C4—431no—
314C4×C22⋊C4—861no—
315#342—432no—
316#342—434no—
317#342—434no—
318C43#2435111yescharacteristic, complemented, Sylow
319C22×Q8—21no—
320C22×Q8C22⋊D4312yes—
321C22×D4C22×D4311yescharacteristic
322C23×C4—431no—
323C23×C4—431no—
324C23×C4C22⋊D4311yescharacteristic
325C23×C4C22×D4311yescharacteristic
326C4⋊Q8—21no—
327C4⋊Q8—21no—
328C4⋊Q8—24no—
329#125—22no—
330#125—24no—
331#123—434no—
332#123—862no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—24no—
336C22⋊Q8—24no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—24no—
344C22⋊Q8—24no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—24no—
350C4×D4—24no—
351#117—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—861no—
356C2×C4⋊C4—864no—
357C2×C4⋊C4—862no—
358C2×C4⋊C4C22⋊D4311yescharacteristic
359C2×C4⋊C4C22⋊D4314yes—
360C2×C4⋊C4C22⋊D4312yes—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—431no—
363C2×C22⋊C4—431no—
364C2×C22⋊C4—434no—
365C2×C22⋊C4—861no—
366C2×C22⋊C4—861no—
367C2×C22⋊C4C22⋊D4311yescharacteristic
368C2×C22⋊C4C22×D4311yescharacteristic
369C2×C22⋊C4C22×D4314yes—
370C2×C42—861no—
371C2×C42—861no—
372C2×C42—862no—
373C2×C42—861no—
374C2×C42—862no—
375C2×C42C22⋊D4311yescharacteristic
376#99—864no—
377#95—861no—
378#95—861no—
379#95—861no—
380#95—861no—
381#95—861no—
382#95—862no—
383#95—864no—
384#95—864no—
385#95—864no—
386C24C2×C22⋊D4311yescharacteristic
387C24C23×D4311yescharacteristic
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—44no—
393C2×Q8—82no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4Q8×D4312yes—
397C2×D4#1062190212yes—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—432no—
405C22×C4—862no—
406C22×C4—861no—
407C22×C4—861no—
408C22×C4—862no—
409C22×C4—861no—
410C22×C4—861no—
411C22×C4—862no—
412C22×C4—861no—
413C22×C4—864no—
414C22×C4—1722no—
415C22×C4C2×C22⋊D4311yescharacteristic
416C22×C4C2×C22⋊D4312yes—
417C22×C4C2×C22⋊D4311yescharacteristic
418C22×C4C2×C22⋊D4314yes—
419C22×C4C2×C22⋊D4311yescharacteristic
420C22×C4C2×C22⋊D4311yescharacteristic
421C22×C4C2×C22⋊D4314yes—
422C22×C4C2×C22⋊D4311yescharacteristic
423C22×C4C2×C22⋊D4312yes—
424C4⋊C4—22no—
425C4⋊C4—24no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—24no—
429C4⋊C4—22no—
430C4⋊C4—24no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—24no—
435C4⋊C4—864no—
436C4⋊C4—1724no—
437C4⋊C4—1722no—
438C4⋊C4—1728no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—22no—
442C22⋊C4—24no—
443C22⋊C4—22no—
444C22⋊C4—432no—
445C22⋊C4—864no—
446C22⋊C4—861no—
447C22⋊C4—864no—
448C22⋊C4—864no—
449C22⋊C4—862no—
450C22⋊C4—1722no—
451C42—24no—
452C42—21no—
453C42—21no—
454C42—1722no—
455C42—1721no—
456C42—1722no—
457C42—1721no—
458C23—21no—
459C23—21no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23#1306330112yes—
465C23C22×C22⋊D4312yes—
466C23C22×C22⋊D4311yescharacteristic
467C23C2×Q8×D4311yescharacteristic
468C23C2×#1062190211yescharacteristic
469C23#1306337312yes—
470Q8—44no—
471Q8—82no—
472Q8—82no—
473Q8—82no—
474D4—24no—
475D4—24no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—21no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—21no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—44no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—44no—
491C2×C4—81no—
492C2×C4—82no—
493C2×C4—82no—
494C2×C4—862no—
495C2×C4—864no—
496C2×C4—864no—
497C2×C4—862no—
498C2×C4—862no—
499C2×C4—1721no—
500C2×C4—1721no—
501C2×C4—1724no—
502C2×C4—1724no—
503C2×C4—1724no—
504C2×C4—1721no—
505C2×C4—1721no—
506C2×C4—1721no—
507C2×C4—1722no—
508C2×C4—1721no—
509C2×C4—1722no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4#1306329411yescharacteristic
514C2×C4#1306329412yes—
515C2×C4#1306329411yescharacteristic
516C2×C4#1306330112yes—
517C22—22no—
518C22—21no—
519C22—22no—
520C22—21no—
521C22—22no—
522C22—41no—
523C22—41no—
524C22—42no—
525C22—42no—
526C22—41no—
527C22—41no—
528C22—81no—
529C22C2×#1306329411yescharacteristic
530C22C2×#1306330111yescharacteristic
531C22#1458347311yescharacteristic
532C22#1458356012yes—
533C22Q8×C22⋊D4312yes—
534C4—21no—
535C4—22no—
536C4—22no—
537C4—41no—
538C4—44no—
539C4—44no—
540C4—41no—
541C4—3444no—
542C4—3441no—
543C4—1722no—
544C4—1722no—
545C4—1722no—
546C4#1458308912yes—
547C2—22no—
548C2—21no—
549C2—21no—
550C2—22no—
551C2—42no—
552C2#1913795411yescharacteristic
553C2C2×#1458308911yescharacteristic
554C2#1914398711yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC24×C43C24
FrattiniC24C23×D43
FittingC43×#3501C2
socleC22×C43C2×#120
prime radicalC22×D4×C43C23
hypercenter#3501D43
hypocenterC43#24351
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #19142929C2semidirect
3. #19135947C2semidirect
4. #19135761C2semidirect
5. #19135581C2semidirect
44. #13063306Q8semidirect
145. C22×Dic43C2×Q8semidirect
171. C22⋊Dic43C2×Q8semidirect
318. C43#24351semidirect

Maximal subgroups

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

subgroupindex
#191429292
C4×#130633062
#191359472
#191357612
#191355812
#191350082
#191348762
#191345832
C43×#35012
#2435143