Finite Group Databasebeta

← #24988559

Subgroups — #24988559

Order 11008.

700 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148479C211yesmaximal, characteristic
2#19134616C211yesmaximal, characteristic
3#19133283C211yesmaximal, characteristic, complemented
4#19133267C211yesmaximal, characteristic, complemented
5#19133093C211yesmaximal, characteristic, complemented
6#19132980C211yesmaximal, characteristic
7C43×#1988C211yesmaximal, characteristic, complemented
8#14583624—21no—
9#14583624C412yescomplemented
10#14583623—21no—
11#14583623C412yescomplemented
12#14583584—22no—
13#14583584—22no—
14#14583510—22no—
15#14583473—21no—
16#14583456C2211yescharacteristic
17#14583454—21no—
18#14583454—21no—
19#14583377—21no—
20C4×#10621898C2211yescharacteristic
21#14582952C2211yescharacteristic
22#14582923C2211yescharacteristic
23C2×#13063253—21no—
24#14582659—21no—
25#14582647—21no—
26#14582646—21no—
27#14582645—22no—
28#14582635—22no—
29#14582629—21no—
30#14582626—21no—
31C2×C4⋊Q8×C43C2211yescharacteristic
32C2×C4⋊C8×C43C2211yescharacteristic
33C4×C4⋊C4×C43C2211yescharacteristic
34C43×#340—22no—
35C2×#10621898D411yescharacteristic
36C2×#10621877—21no—
37#13063325D411yescharacteristic
38#13063325D411yescharacteristic
39#13063323—22no—
40#13063320—24no—
41#13063320—24no—
42#13063317—21no—
43#13063316—22no—
44#13063316—22no—
45#13063315—24no—
46#13063315—24no—
47#13063314—22no—
48#13063308—24no—
49#13063305—22no—
50#13063305—22no—
51#13063304—21no—
52#13063304D412yes—
53#13063301—22no—
54#13063301—22no—
55Q8×Dic43—22no—
56Q8×Dic43—22no—
57Q8×Dic43—22no—
58Q8×Dic43—22no—
59C4×Dic86—21no—
60C4×Dic86C2×C412yes—
61C4×Dic86C2×C411yescharacteristic
62C4×Dic86D411yescharacteristic
63#13063290—22no—
64#13063290—22no—
65C4×D172C2×C411yescharacteristic
66C4×D172D411yescharacteristic
67C4×C22⋊D43—21no—
68C4×C22⋊D43—21no—
69#13063284—24no—
70#13063284—21no—
71#13063284D411yescharacteristic
72#13063283—22no—
73#13063283—22no—
74#13063282—21no—
75C42×D43—21no—
76C4⋊(C43⋊C8)—21no—
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)—21no—
79#13063253—42no—
80C22⋊(C43⋊C8)—21no—
81C4×C43⋊C8—21no—
82C22×Q8×C43—21no—
83C22×C8×C43—21no—
84C4⋊Q8×C43—21no—
85C4⋊Q8×C43—21no—
86C4⋊Q8×C43C2×C412yes—
87C4⋊Q8×C43D412yes—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43D412yes—
91C2×C42×C43—21no—
92C2×C42×C43C2311yescharacteristic
93C4⋊C8×C43—21no—
94C4⋊C8×C43—21no—
95#95×C43—21no—
96C2×Q8×C43—22no—
97C2×Q8×C43—22no—
98C2×Q8×C43—41no—
99C2×Q8×C43—41no—
100C2×Q8×C43—41no—
101C2×Q8×C43—41no—
102C22×C4×C43—22no—
103C22×C4×C43—41no—
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C2×C22⋊D43—21no—
108#10621898—21no—
109#10621898—21no—
110#10621898—21no—
111#10621898—21no—
112C2×D172C22⋊C411yescharacteristic
113C2×C4×D43—21no—
114C2×C4×D43—21no—
115C2×C4×D43—21no—
116C2×Dic86—21no—
117C2×Dic86C22⋊C411yescharacteristic
118C2×Dic86C22⋊C412yes—
119C2×C8×C43—42no—
120C2×C8×C43—41no—
121C4⋊C4×C43—22no—
122C4⋊C4×C43—22no—
123C4⋊C4×C43—22no—
124C4⋊C4×C43—22no—
125C4⋊C4×C43—41no—
126C4⋊C4×C43C22⋊C414yes—
127C42×C43—41no—
128C42×C43—41no—
129C42×C43C22×C411yescharacteristic
130C42×C43C2×D411yescharacteristic
131C42×C43C2×D411yescharacteristic
132C42×C43C2×D411yescharacteristic
133C22⋊Dic43—21no—
134C22⋊Dic43—22no—
135(C2×D43)⋊C4—24no—
136(C2×D43)⋊C4—24no—
137(C2×D43)⋊C4—21no—
138(C2×D43)⋊C4—21no—
139C4⋊Dic43—24no—
140C4⋊Dic43—24no—
141C4⋊Dic43—21no—
142C4⋊Dic43—21no—
143C4⋊Dic43—21no—
144C4⋊Dic43C22⋊C412yes—
145C4⋊Dic43C22⋊C411yescharacteristic
146C4⋊Dic43C22⋊C411yescharacteristic
147Dic43⋊C4—24no—
148Dic43⋊C4—24no—
149Dic43⋊C4—21no—
150Dic43⋊C4—22no—
151Dic43⋊C4—21no—
152Dic43⋊C4—22no—
153C4×Dic43—24no—
154C4×Dic43—24no—
155C4×Dic43—21no—
156C4×Dic43—22no—
157C4×Dic43—21no—
158C4×Dic43—21no—
159#10621877—41no—
160#10621877—41no—
161C2×C43⋊C8—41no—
162C2×C43⋊C8—41no—
163C23×C43#12011yescharacteristic
164C22×D43—21no—
165Q8×C43—42no—
166Q8×C43—42no—
167Q8×C43—42no—
168Q8×C43—42no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—24no—
172C2×C4×C43—41no—
173C2×C4×C43—42no—
174C2×C4×C43—42no—
175C2×C4×C43—42no—
176C2×C4×C43—81no—
177C2×C4×C43—81no—
178C2×C4×C43C2×C22⋊C411yescharacteristic
179C2×C4×C43C2×C22⋊C411yescharacteristic
180C2×C4×C43C2×C22⋊C411yescharacteristic
181C2×C4×C43#12011yescharacteristic
182C2×C4×C43#12011yescharacteristic
183C2×C4×C43#12011yescharacteristic
184C2×C4×C43#13511yescharacteristic
185C2×C4×C43#13511yescharacteristic
186C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C43#13711yescharacteristic
188C22⋊D43—41no—
189C22⋊D43—41no—
190C2×Dic43—21no—
191C2×Dic43—21no—
192C2×Dic43—22no—
193C2×Dic43—22no—
194C2×Dic43—21no—
195D172—21no—
196D172—21no—
197C4×D43—42no—
198C4×D43—41no—
199C4×D43—41no—
200C4×D43—41no—
201C4×D43—41no—
202Dic86—21no—
203Dic86—21no—
204Dic86—41no—
205Dic86—41no—
206Dic86—42no—
207C8×C43—81no—
208C43⋊C8—81no—
209C43⋊C8—81no—
210#8427—431nomaximal, Sylow
211C22×C43—21no—
212C22×C43—21no—
213C22×C43#37911yescharacteristic
214C22×C43#44911yescharacteristic
215C22×C43#45211yescharacteristic
216C2×D43—41no—
217C2×D43—41no—
218C2×D43—41no—
219C4×C43—21no—
220C4×C43—21no—
221C4×C43—21no—
222C4×C43—44no—
223C4×C43—82no—
224C4×C43#41611yescharacteristic
225C4×C43#41711yescharacteristic
226C4×C43#44911yescharacteristic
227C4×C43#45211yescharacteristic
228C4×C43#45411yescharacteristic
229C4×C43#45611yescharacteristic
230Dic43—42no—
231Dic43—41no—
232Dic43—42no—
233Dic43—41no—
234Dic43—41no—
235#3509—431no—
236#1988D4311yescharacteristic, complemented
237#1806—431no—
238#1550—431no—
239#1546—431no—
240#1503—431no—
241#1477—431no—
242C2×C43—21no—
243C2×C43—21no—
244C2×C43#178811yescharacteristic
245C2×C43#179311yescharacteristic
246C2×C43#179611yescharacteristic
247D43—81no—
248#557—432no—
249#557—861no—
250#556—432no—
251#556—861no—
252#552—862no—
253#552—862no—
254#541—862no—
255#536—861no—
256#533—431no—
257#533—861no—
258#533—861no—
259C2×C4⋊Q8C2×D4311yescharacteristic
260#519—861no—
261C4×#41—431no—
262#431—431no—
263#423—431no—
264C2×C4⋊C8C2×D4311yescharacteristic
265C2×#104—861no—
266C4×C4⋊C4C2×D4311yescharacteristic
267#340—22no—
268#339—861no—
269#333—861no—
270#332—861no—
271#332—862no—
272#328—862no—
273Q8⋊C8—861no—
274D4⋊C8—861no—
275C43#842711yescharacteristic, complemented, Sylow
276C2×#41—431no—
277C22×Q8—21no—
278C2×M16—861no—
279C22×C8—21no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—431no—
283C4⋊Q8—431no—
284C4⋊Q8—862no—
285C4⋊Q8C4×D4312yes—
286C4⋊Q8D17212yes—
287#126—864no—
288#126—864no—
289#125—862no—
290#125—862no—
291#125—864no—
292#125—864no—
293#125—861no—
294#124—862no—
295#123—864no—
296C22⋊Q8—432no—
297C22⋊Q8—862no—
298C22⋊Q8—862no—
299C22⋊Q8—862no—
300C22⋊Q8—862no—
301C22⋊Q8—861no—
302C4×Q8—431no—
303C4×Q8—432no—
304C4×Q8—431no—
305C4×Q8—862no—
306C4×Q8—862no—
307C4×Q8—862no—
308C4×Q8—862no—
309C4×Q8—862no—
310C4×Q8—862no—
311C4×Q8—861no—
312C4×D4—431no—
313C4×D4—431no—
314C4×D4—861no—
315C4×D4—861no—
316#117—431no—
317#117—862no—
318#117—862no—
319#117—864no—
320#117—861no—
321#117—861no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4C22⋊D4312yes—
325C2×C42—21no—
326C2×C42—861no—
327C2×C42C22×D4311yescharacteristic
328C4⋊C8—21no—
329C4⋊C8—21no—
330C4⋊C8—861no—
331C4⋊C8—861no—
332C4⋊C8—861no—
333#104—1722no—
334C22⋊C8—861no—
335C4×C8—861no—
336#95—21no—
337#41—861no—
338#41—861no—
339#41—861no—
340#41—861no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—41no—
344C2×Q8—41no—
345C2×Q8—41no—
346C2×Q8—41no—
347C2×Q8—431no—
348C2×Q8—432no—
349C2×Q8—861no—
350C2×D4—431no—
351C2×D4—861no—
352C22×C4—22no—
353C22×C4—41no—
354C22×C4—861no—
355C22×C4—861no—
356C22×C4—861no—
357C22×C4D4×D4311yescharacteristic
358C22×C4D4×D4311yescharacteristic
359C22×C4C2×C22⋊D4311yescharacteristic
360M16—1721no—
361M16—1721no—
362C2×C8—42no—
363C2×C8—41no—
364C2×C8—1721no—
365C2×C8—1721no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—41no—
371C4⋊C4—431no—
372C4⋊C4—431no—
373C4⋊C4—432no—
374C4⋊C4—864no—
375C4⋊C4—864no—
376C4⋊C4—864no—
377C4⋊C4—864no—
378C4⋊C4—861no—
379C4⋊C4—862no—
380C4⋊C4—861no—
381C4⋊C4—861no—
382C4⋊C4—861no—
383C4⋊C4—861no—
384C4⋊C4—862no—
385C4⋊C4(C2×D43)⋊C414yes—
386C22⋊C4—864no—
387C22⋊C4—864no—
388C22⋊C4—861no—
389C22⋊C4—862no—
390C22⋊C4—861no—
391C22⋊C4—861no—
392C42—41no—
393C42—41no—
394C42—864no—
395C42—864no—
396C42—861no—
397C42—862no—
398C42—861no—
399C42—861no—
400C42C2×C4×D4311yescharacteristic
401C42C2×D17211yescharacteristic
402C42D4×D4311yescharacteristic
403C42D4×D4311yescharacteristic
404C23—861no—
405C23#1306329311yescharacteristic
406Q8—42no—
407Q8—42no—
408Q8—42no—
409Q8—42no—
410Q8—861no—
411Q8—861no—
412Q8—1722no—
413Q8—1721no—
414Q8—1721no—
415D4—861no—
416D4—861no—
417D4—1721no—
418D4—1721no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—24no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—861no—
429C2×C4—861no—
430C2×C4—862no—
431C2×C4—862no—
432C2×C4—861no—
433C2×C4—1722no—
434C2×C4—1721no—
435C2×C4—1721no—
436C2×C4—1721no—
437C2×C4—1721no—
438C2×C4C22⋊C4×D4311yescharacteristic
439C2×C4C22⋊C4×D4311yescharacteristic
440C2×C4C2×(C2×D43)⋊C411yescharacteristic
441C2×C4#1306329311yescharacteristic
442C2×C4#1306329511yescharacteristic
443C2×C4#1306329511yescharacteristic
444C2×C4#1306334411yescharacteristic
445C2×C4#1306334611yescharacteristic
446C2×C4#1306334911yescharacteristic
447C2×C4#1306335411yescharacteristic
448C8—81no—
449C8—3441no—
450C8—3441no—
451C22—21no—
452C22—21no—
453C22—1721no—
454C22—1721no—
455C22—1721no—
456C22#1458275411yescharacteristic
457C22#1458304111yescharacteristic
458C22#1458305811yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—44no—
463C4—82no—
464C4—1721no—
465C4—1721no—
466C4—1722no—
467C4—1721no—
468C4—1722no—
469C4#1458289211yescharacteristic
470C4#1458289711yescharacteristic
471C4#1458304511yescharacteristic
472C4#1458306211yescharacteristic
473C4#1458307111yescharacteristic
474C4#1458308111yescharacteristic
475C2—21no—
476C2—21no—
477C2—3441no—
478C2#1913453211yescharacteristic
479C2#1913455311yescharacteristic
480C2#1913456711yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1988C2
socleC22×C43#379
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1988D43
hypocenterC43#8427
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
3. #19133283C2semidirect
4. #19133267C2semidirect
5. #19133093C2semidirect
7. C43×#1988C2semidirect
9. #14583624C4semidirect
11. #14583623C4semidirect
236. #1988D43semidirect
275. C43#8427semidirect

Maximal subgroups

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

subgroupindex
#191484792
#191346162
#191332832
#191332672
#191330932
#191329802
C43×#19882
#842743